Aerodynamics of Road Vehicles. From Fluid Mechanics to Vehicle Engineering

Aerodynamics of Road Vehicles From Fluid Mechanics to Vehicle Engineering

Edited by Wolf-Heinrich Hucho

Contributors Syed R. Ahmed Hans-Joachim Emmelmann Klaus-Dieter Emmenthal Helmut Flegl Werner Gengenbach Hans Götz Wolf-Heinrich Hucho Dietrich Hummel Görgün A. Necati Raimund Piatek Michael Rauser

Butterworth-Heinemann London Boston Singapore Sydney Toronto Wellington

(^ PART OF REED INTERNATIONAL P.L.C.

All rights reserved. No part of this publication may be reproduced in any material form (including photocopying or storing it in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright owner except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 33-34 Alfred Place, London, England WC1E 7DP. Applications for the copyright owner's written permission to reproduce any part of this publication should be addressed to the Publishers.

Warning: The doing of an unauthorised act in relation to a copyright work may result in both a civil claim for damages and criminal prosecution.

This book is sold subject to the Standard Conditions of Sale of Net Books and may not be re-sold in the UK below the net price given by the Publishers in their current price list.

English edition first published 1987 Reprinted 1990

Originally published under the title Aerodynamik des Automobils by Vogel-Verlag, Würzburg, West Germany. © Vogel-Verlag, Würzburg, 1981 English edition © Butterworth-Heinemann Ltd, 1987

British Library Cataloguing in Publication Data

Aerodynamics of road vehicles : from fluid mechanics to vehicle engineering. 1. Motor vehicles — Aerodynamics I. Hucho, Wolf-Heinrich II. Aerodynamik des Automobils. English 629.04'9 TL245

ISBN 0-408-01422-9

Library of Congress Cataloging-in-Publication Data

Aerodynamik des Automobils. English. Aerodynamics of road vehicles.

Translation of: Aerodynamik des Automobils. Bibliography: p. Includes index. 1. Motor vehicles—Aerodynamics. I. Hucho,

Wolf-Heinrich. TL245.A4713 1986 629.2 86-13693 ISBN 0-408-01422-9

Typeset by Scribe Design, Gillingham, Kent Printed in Great Britain at the University Press, Cambridge

Preface

The performance, handling and comfort of an automobile are significantly affected by its aerodynamic properties. A low drag is a decisive prerequisite for good fuel economy. Increasing fuel prices and stringent legal regulations ensure that this long-established relationship becomes more widely acknowledged. But the other aspects of vehicle aerodynamics are no less important for the quality of an automobile: side wind stability, wind noise, soiling of the body, the lights and the windows, cooling of the engine, the gear box and the brakes, and finally heating and ventilating of the passenger compartment all depend on the flow field around and through the vehicle.

Vehicle aerodynamics is still an empirical science, if not an art. Whereas other technical disciplines such as aeronautics, naval architecture and turbomachinery are governed by well-established theoretical and ex-perimental methods of fluid mechanics, no consistent design procedures are yet available for road vehicles. The complexity of the flow field around a car, which is characterized by separation, must be blamed for this lack, and this means that the vehicle aerodynamicist must refer to a large amount of detail resulting from earlier development work. His success depends on his ability to transfer these results to his own problem and to combine results originating from many different earlier developments to a consistent solution.

It is the intention of the present book to introduce the vehicle engineer to this approach. His interest is focused on three aspects:

• the fundamental of fluid mechanics as related to vehicle aerodynamics; • the essential experimental results, presented as ground rules of fluid

mechanics and brought to general validity wherever possible; • design strategies, showing how many existing single results can be

combined to provide general solutions.

The aerodynamics of passenger cars, commercial vehicles, sports cars and race cars is dealt with in detail. Not only the external flow field is covered; the problems of the several internal flow systems are treated as well. Because the external and the internal flow fields are interrelated, both have to be considered at the same time. The related test techniques are described in detail, emphasizing the correlation between the wind tunnel, which is the main tool of the vehicle aerodynamicist, and the road,

Preface

which is the real world for the car in a customer's hands. A chapter on numerical methods concludes the book. Although theoretical models are still of limited evidential value they are more and more used for guiding and supporting, rather than replacing, wind tunnel tests.

The first German edition of this book was originally based on a course given by the authors at the 'Haus der Technik', Essen, Germany, under the aegis of Dr H. Hahn. This English version is a completely revised second edition. It is intended for vehicle engineers in industry and research, at universities and in administrative departments. But it is also aimed at stylists and designers, students and professional writers in the car world. Detailed knowledge of fluid mechanics is not assumed. The chapter on the fundamentals of fluid mechanics provides the reader with the necessary details.

This present English edition would not have come about were it not for the efforts of two true friends of the editor: Mr Gordon Taylor built the bridge to Butterworths and Dr Gino Sovran involved the publication department of the Society of Automotive Engineers (SAE), thus providing a sufficiently broad basis for the project. The editor is deeply indebted to both his friends. He also wishes to express his sincerest thanks to all who have contributed to this book: first of all, of course, to the authors for their readiness to carry the burden of preparing the manuscripts; thanks as well to the secretaries and draughtsladies for typing the manuscripts and for drawing the figures; thanks to the companies of the authors for having given them permission to contribute to the book. The editor expresses his warmest thanks to his wife, Irmgard, for her untiring assistance during the preparation of the extensive material and to his former secretary, Mrs Hildegard Backes, for typing and editing the final manuscript and for continuing to do so even when the editor was in the course of changing his employer. Finally, thanks are owed to the publishers: to Vogel-Verlag, Würzburg, for granting the licence, to Butterworths for good and patient cooperation and the SAE publications department for sharing the project.

Wolf-Heinrich Hucho Schwalbach am Taunus, Federal Republic of Germany

December 1986

Contributors

Dr.-Ing. Syed R. Ahmed is divisional head in the Institute of Design Aerodynamics, German Aeronautical and Space Research Establishment (DLR), Braunschweig, Federal Republic of Germany. He received a Dipl.-Ing. Degree in 1964, followed in 1970 by a Dr.-Ing. degree in fluid mechanics from the Technical University at Braunschweig. Since 1975 he has been actively engaged in theoretical and experimental study of vehicle aerodynamics.

Dipl.-Ing. Hans-Joachim Emmelman studied mechanical and aircraft engineering at the Technical University, Darmstadt, Federal Republic of Germany. From 1970 to 1978 he was test engineer and assistant department head in the climatic wind tunnel of Volkswagen AG. Since 1979 he has been an assistant staff engineer, aerodynamics, at Adam Opel AG.

Dr.-Ing. Klaus-Dieter Emmenthal studied mechanical engineering at the Technical University, Braunschweig. He then worked for nine years at the German Aerospace Authority as research engineer. Since 1970 he has been with Volkswagen AG and is currently department manager responsible for engine and accessories research. He obtained his doctorate at the Technical University, Aachen, Federal Republic of Germany.

Dipl.-Ing. Helmut Flegl studied mechanical engineering at the Technical University, Munich. In 1966 he began work at the Dr.-Ing.h.c. F. Porsche AG. As test engineer he was responsible for the design of many successful racing cars. He is currently director of research at Porsche's R&D Centre, Weissach, Federal Republic of Germany.

Dr.-Ing. Werner Gengenbach studied mechanical engineering at the Technical University, Karlsruhe, from 1954 to 1959. He obtained his doctorate in 1967 for his thesis on 'Behaviour of car tyres on dry and especially wet pavement'. Since 1971 he has worked for Audi AG, Ingolstadt, Federal Republic of Germany, first as manager for testing heating, air conditioning and cooling systems; and since 1980 as manager of quality analysis.

Dipl.-Ing. Hans Götz is manager of body development at Daimler-Benz in Sindelfingen, Federal Republic of Germany. He studied mechanical

Contributors

engineering at the Technical University, Stuttgart. After a period as a research engineer on air conditioning, he joined Daimler-Benz in 1961. He has been involved in aerodynamics, safety, vibration and acoustic technologies.

Dr.-Ing. Wolf-Heinrich Hucho studied mechanical engineering at the Technical University, Braunschweig. From 1961 to 1968 he was assistant to Professor Schlichting. For 11 years he worked for Volkswagen AG, first as head of the wind tunnel department, later as departmental manager, engine research and fluid dynamics. Since 1979 he has held positions as director of Research & Development and general manager in the German automobile supply industry.

Prof. Dr.-Ing. Dietrich Hummel, Institute for Fluid Mechanics of the Technical University, Braunschweig, Federal Republic of Germany, studied mechanical engineering at the Technical Universities in Stuttgart and Braunschweig. As assistant to Professor Schlichting in 1968 he obtained his doctorate, and in 1972 he qualified as lecturer in fluid mechanics and aircraft aerodynamics. His special interests are separated flows and bird flight.

Dr.-Ing. Görgün A. Necati studied mechanical engineering at the Technical University, Istanbul, Turkey. His postgraduate studies were at the Technical University, Hanover, Federal Republic of Germany. Since 1969 he has worked in the R&D section of Ford-Werke, Cologne, Federal Republic of Germany. Major activity fields: wind tunnel and road testing, dynamics, aerodynamics and acoustics of motor vehicles.

Dipl.-Ing. Raimund Piatek studied mechanical engineering, especially fluid mechanics, at the University of Bochum, Federal Republic of Germany. Since 1978 he has been employed by Volkswagen AG as research engineer in the climatic wind tunnel department.

Dipl.-Ing. Michael Rauser studied aeronautics and astronautics at the University of Stuttgart and is presently supervisor of aerodynamics, vehicle research, at the Dr.-Ing.h.c.F.Porsche AG, R&D Centre, Weissach, Federal Republic of Germany.

Chapter 1

Introduction to automobile aerodynamics Wolf-Heinrich Hucho

1.1 Scope 1.1.1 Basic principles

The flow processes to which a moving vehicle is subjected fall into three categories: • flow of air around the vehicle; • flow of air through the body; • flow processes within the machinery.

The first two flow fields are closely related. For example, the flow of air through the engine compartment is directly dependent upon the flow field around the vehicle. Both fields must be considered together. On the other hand, the flow processes within the engine and transmission are not directly connected with the first two, and are not treated here.

The external flow subjects the vehicle to forces and moments which greatly influence the vehicle's performance and directional stability. Until recently vehicle aerodynamics was concerned almost exclusively with these two effects, and has only lately focused on the need to keep the windows and lights free of dirt and accumulated rain water, to reduce wind noise, to

Figure 1.1 Streamlines in the longitudinal midsection of a VW Golf I (Rabbit), photographed for a full-sized vehicle in the large climatic wind tunnel of the Volkswagen AG. The lines of smoke were introduced in the plane of the longitudinal centreline to show the flow pattern with symmetrical oncoming flow. This flow state exists only when there is no side wind

1

2 Introduction to automobile aerodynamics

prevent windscreen wipers lifting, and to cool the engine oil sump and brakes, etc.

From the flow pattern shown in Fig. 1.1 some significant flow processes can be discerned, for example flow separation at the rear of the vehicle. Although the streamlines follow the contour of the vehicle over long stretches, even in the area of sharp curves, the air flow separates at the rear edge of the roof, forming a large wake which can be observed (Fig. 1.2) by introducing smoke into the bubble behind the vehicle instead of in the adjacent external flow as in Fig. 1.1.

Figure 1.2 Wake of a VW Golf I, photographed as in Fig. 1.1, smoke introduced into the wake

The aerodynamic drag D, as well as the other force components and moments, increases with the square of the vehicle speed V:

D~V2 (1.1) With a medium-size European car, aerodynamic drag accounts for

nearly 80 per cent of the total road resistance at 100 km/h (62mile/h). There is therefore much scope for improving economy by reducing aerodynamic drag. For this reason drag remains the focal point of vehicle aerodynamics, whether the objective is speed or fuel economy.

The complete expression for Eqn 1.1 is:

D = cOA^- V2 (1.2)

where cD is the non-dimensional drag coefficient; A is the projected frontal area of the vehicle (Fig. 1.3); and p is the density of the surrounding air.

The drag D of a vehicle is therefore determined by its frontal area A, and by its shape, the aerodynamic quality of which is described by the drag coefficient cD. Generally the vehicle size, and hence frontal area, is determined by the design requirements, and efforts to reduce drag are concentrated on reducing the drag coefficient.

The distance between the streamlines ahead of the car compared with those above the vehicle provide an indication of the lift (Fig. 1.1). Closely spaced streamlines mean high velocity and consequently low static pressure (see section 2.3.1). The pressure difference between the upper and lower

Scope 3

Projection plane

Frontal area

Parallel light

Figure 1.3 Definition of the frontal area A of a vehicle

sides of the vehicle produces a resultant force, at right angles to the direction of motion, which is called lift. As a rule the lift is in the upward direction, i.e. it tends to lift the vehicle and therefore reduces effective wheel loads. It is coupled with a pitching moment, which differentially affects the wheel loads at the front and rear. Below 100 km/h (62 mile/h) lift and pitching moment have only a small effect upon the vehicle, even in a cross-wind. They do change the attitude of the car in relation to the road and therefore slightly affect the aerodynamic drag. The reduction of the wheel loads, however, is small in relation to the static wheel load and the directional stability is hardly affected by lift.

This does not apply to high-speed sports cars, where spoilers are often added to counteract the effects of lift. With racing cars, wings ensure that

Figure 1.4 Negative lift wings on a Formula 1 racing car


the-wheel loads increase with speed (Fig. 1.4). How such negative lift wings are tuned in specific cases is described in Chapter 7.

With cross-winds the air flow around the vehicle is asymmetric to the longitudinal centre plane. The shape of the car must be such that the additional forces and moments remain so small that the directional stability is not greatly affected (see Chapter 5). First, the need to react to a cross-wind of varying intensity and direction is inconvenient, as the driver must continually apply steering corrections. Secondly, in very rare cases there is the danger of total loss of control; this can only be countered by suitable aerodynamic design. However, it is also important to prevent drivers from being surprised by side-wind gusts, and being unable to react quickly enough. Better design of roads and their surroundings can help to overcome this problem.

Soiling of the rear of the vehicle can be studied from the wake flow as shown in Fig. 1.2; details are discussed in Chapter 6. Dust or dirty water is whirled up by the wheels, and dust particles and water droplets distributed throughout the entire wake region by turbulent mixing, and deposited on the rear of the vehicle. Since the flow pattern at the rear has a significant influence upon the aerodynamic drag, soiling of the rear cannot be considered in isolation.

Figure 1.1 shows how the external flow field relates to flow processes inside the vehicle. The flow into the radiator (see Chapter 9) is determined by the flow pattern in front of the vehicle. It can be seen that the stagnation point is at the level of the bumper, and that the air flow is oblique to the openings above and below the bumper (not visible in Fig. 1.1). The grill should be designed to direct this air to the radiator, which is generally vertical, while keeping the pressure loss as low as possible.

The flow is attached in the region of the concave space formed by the engine hood and the windscreen. Here there is a pressure build-up, which, as described in Chapter 10, can be utilized for driving air through the heating and ventilation system. On most vehicles the fresh air inlet opening is positioned in the middle of this area. However, at this point the pressure is dependent upon the driving speed, which results in an increase of the fresh air flow as speed increases, making maintenance of steady conditions in the passenger compartment quite difficult. If the inlet openings for the fresh air are moved to points on the body which are at ambient pressure, it is possible to separate the external and internal flow fields, at least while the oncoming flow is symmetrical (no side wind). The fresh air fan, which must be correspondingly larger, then provides a flow which is independent of the driving speed (though only when the exit vents in the body are located in areas of ambient pressure as well).

The most important internal flow fields are the air flow through the radiator and engine compartment, and the heater or ventilation flow through the passenger compartment. Some types of vehicles—such as racing cars—have separate flow ducts for the oil cooler, brake cooling, and the combustion air for the engine (see Chapter 7).

The engine cooling system has the task of removing a heat flux Q, which is of approximately the same magnitude as the useful engine power P:

Q~P (1.3)

Scope 5

As vehicle design has developed, the requirements for cooling air have increased considerably. Since a larger cooling air flow is required for water cooling than for air cooling, these requirements must be related to the type of cooling (see Chapter 9 for details):

1. Engine power has increased continuously over the years, making necessary greater volumes of cooling air.

2. Following the demands of styling and aerodynamics, the front end of cars has become flatter over the years. The openings available for entry of the cooling air have become smaller as a result (Fig. 1.5). Moreover, the earlier large coherent inlet area has been broken up into individual sub-areas.

3. As a result of compact design, less space is available in the engine compartment for the radiator and cooling air duct.

4. In the interests of safety the body has continuously been reinforced at the front end ('hard edge'), so that the flow is impeded by wide bumpers and cross-members.

1950 1955 1960 1965 1970 1975

Y e a r — ► Figure 1.5 Cooling air inlet area in relation to installed engine power, shown as a function of time, after K.-D. Emmenthal

The cooling air must be routed in such a manner that the velocity of the air in front of the radiator is as uniform as possible, thus ensuring optimum radiator efficiency. In addition, the aerodynamic drag of the car is considerably increased as a result of the loss of momentum in the cooling air duct. This increase in drag can be kept small with suitable measures (see section 4.3.2.12). If the ram air flow is not sufficient for cooling, a fan must be added; radiator and fan must be matched to produce an economical system so that the smallest possible amount of power is required to drive the fan.

The air flowing through the passenger compartment must perform three groups of tasks (see Chapter 10): 1. Sufficient ventilation must be assured. All contaminants in the form of

gases, vapours and dust must be expelled from the passenger compartment. Simultaneously, this provides for replacement of the oxygen consumed through breathing.

2. A comfortable internal climate must be produced and assured for a wide range of variation in the external conditions. For winter operation


a high-performance heater must be provided. In summer comfort must be ensured by the circulation of fresh air. In extremely hot countries this alone is not sufficient and the air must be cooled with an air conditioner.

3. The internal flow must pass along the windows so that mist evaporates (demisting) and ice, which can form on both sides of the windows, melts (deicing).

Particular requirements are placed on the dynamic characteristic of the flow system in the passenger compartment. For instance, the heater is expected to provide heat quickly after the engine is started. However, during cruise the internal climate should be independent of the vehicle speed, the operating state of the engine and the external climate. The flow should produce as little noise as possible; wind noises must be avoided and the fan noise minimized. The openings in the body, with which the internal flow is coupled with the external flow, must be designed so that water cannot enter even under extreme conditions (e.g. in a car wash).

The objectives of the aerodynamic design work outlined above are influenced by the type of vehicle under consideration. For instance, during the aerodynamic design of a passenger car, the main consideration is drag. On a high-speed minibus or van, reduction of sensitivity to cross-winds may be the primary goal. Various solutions are available depending upon the type of vehicle. On a racing car the objective will be to improve the traction of the tyres, using negative aerodynamic lift regardless of styling; the wings at the front and back have even become characteristic of modern racing cars. On the other hand minimizing the drag of a passenger vehicle must be accomplished with less conspicuous methods which conform to current styles.

1.1.2 Working methods

Parallels exist between the aerodynamics of automobiles and aircraft. The primary objectives are very similar: good driving or flying characteristics (longitudinal dynamics); low aerodynamic drag; balance of forces and moments in both axes perpendicular to the direction of forward motion to ensure good driving or flight stability (transverse stability). Further processing of the measured aerodynamic data in the equations of motion also indicates similarities.

In spite of this, motor vehicle aerodynamics differs in significant respects from aircraft aerodynamics. For example, aircraft aerodynamics are permeated to a great extent by theory.1 The aerodynamic design of an aircraft nowadays derives initially from theoretical, i.e. numerical, considerations, followed by experimental work on small-scale models in wind tunnels and finally in flight tests with a prototype. However, with motor vehicles most of the aerodynamic development work is done experimentally. In principle two different approaches are followed. Until recently, work started with a model (full scale or small scale) designed by the styling department. Aerodynamic development was mainly fine tuning, maintaining the styling as little changed as possible (detail optimization). Nowadays work often starts with a low drag body which is developed into a car in the wind tunnel in conjunction with the stylist (see section 4.4). The

Scope 7

smaller dimensions of the motor vehicle offer the advantage of wind tunnel testing of full-scale models or even ready-to-drive prototypes.

There are primarily two reasons why the procedure differs from that of aircraft design. In contrast to an aircraft, the design of a vehicle is not dictated wholly by aerodynamics. Style, performance, handling, safety, comfort and, of course, production engineering are all important considerations. Increased fuel prices have, however, led to greater emphasis upon aerodynamics.

Repeated attempts have been made to apply the results of aircraft aerodynamics to motor vehicles and significant achievements have been made in the solution to individual problems. However, a comprehensive theory of motor vehicle aerodynamics does not yet exist.

The computation of the air flow around aircraft is simplified by the fact that the flow fields around the individual components such as the wing,

Figure 1.6 Flow around a passenger car (schematic)


fuselage and tail unit can be handled separately. The interaction between the components can also be assessed theoretically. Since the air flow is generally 'attached', the calculation can be accomplished in two steps. First the non-viscous flow field is determined; then the effect of viscosity is calculated from 'boundary layer' theory. The theoretical methods upon which this procedure is based have been developed continuously and have been expanded to include other requirements such as those resulting from higher flying speeds (Mach-number effects).

The flow field around a car cannot be treated in the same way, for two reasons. From Figs 1.1 and 1.2 it is clear that the flow past a car is strongly governed by separation. Figure 1.6 provides further information on the type and location of separation. The effect of viscosity is no longer confined to comparatively small zones close to the surface of the body (boundary layer). Furthermore, with a car it is not possible to distinguish several more or less independent flow fields. The flow field around a car body has to be treated as a whole.

Chapter 13 summarizes the present state of numerical methods in car aerodynamics. These methods may be used to guide the work in the wind tunnel. However, much of the aerodynamic design of a car is to prevent, or to tune, separation. The only way to do this is through experimentation.

1.1.3 Related fields

There are also useful parallels to related fields illustrated in Fig. 1.7, for example in the aerodynamics of buildings:

• flow around bluff bodies • flow fields governed by separation • ground influence and ground boundary layer • interference between buildings • wind tunnel testing techniques.

Figure 1.7 Fields related to automobile aerodynamics

Scope 9

Building aerodynamics addresses a number of similar objectives:

• determination of the effective air forces on the building as a whole • calculation of the air forces upon parts such as roofs, facades and windows • influencing the surrounding flow field for protection of pedestrians • matching of the surrounding flow and the internal flow (climate, chimney draught).

Useful reference material includes Hoerner1 2 (wind forces on build-ings), Ackeret1 3 (significant problems of building aerodynamics, based on clear examples), Sachs 1A (presentation of the current state of knowledge), and construction aerodynamics in condensed form by Houghton and Carruthers.15

The flow field surrounding a train is very similar to that surrounding a road vehicle. The primary difference results from coupling of individual cars into long trains, which produces a very long body in comparison to its height and width. Special relationships result when trains meet one another, due to the small gap between the tracks, as well as when driving into tunnels and driving through very narrow tunnels. The primary development goals for railway aerodynamics are:

• low aerodynamic drag • reduction of the pressure peaks when trains meet one another, and when driving into a tunnel • reduction of the influence of side winds • matching internal and external flow for purposes of cooling and ventilation.

In contrast to the development of road vehicles, for which the trend to higher driving speeds has virtually vanished with the exception of racing cars, speeds are still being increased in the railway sector. For this reason aerodynamics is becoming increasingly significant in this branch of transportation technology. Some early data on the resistance of trains is given by Hoerner.1 4 A comprehensive survey on train aerodynamics including many references has been presented by Peters.16 Further information has been provided by Gawthorpe.1 7 The problems encoun-tered with high-speed trains, particularly in driving through tunnels have been given by Neppert and Sanderson1 δ and by Steinheuer.1 9

The flow field around a ship above the water line is also a focus of increasing attention. The aerodynamic drag of a water-displacing ship is small in comparison to its water resistance, but not so for fast hydroplanes, hydrofoils and hovercraft. The aerodynamics of a surface ship include the lateral force in addition to the resistance, which is of particular concern for ships with high superstructures, such as ferries, when docking. On the other hand, the flow of air around the funnel is a prime concern for passenger ships. The aerodynamics of the sail have many problems in common with wings.

As for trains, naval architects depend upon individual publications, there being no comprehensive work on this subject. Data on the aerodynamic drag are given by Hoerner.12 Of the numerous works on the funnel air flow, those from Thieme1 10 are worthy of mention. Gould1 n


considered questions of the lateral forces resulting from wind on ships. His work also includes information on simulation of the water surface and of the air boundary layer over the water surface in a wind tunnel.

There are also parallels in other disciplines on the flow inside the vehicles. The flow of air through the radiator in a car is comparable to the flow of air through the water or oil cooler in an aircraft. In fact much knowledge has been drawn from Küchemann and Weber112 and is utilized in Chapter 9 to describe automobile cooling. The counterpart of the climatization of the passenger compartment is room climatization in buildings (see Chapter 10).

1.2 Historical development 1.2.1 Survey

The history of automobile aerodynamics occupies four chronologically indistinct phases, as illustrated in Fig. 1.8 (see Hucho, Janssen and Emmelmann1 13).

-ö C

Ά E

— f r

8- s

a. 2.

1900 to

1930

1921 to

1923

1922 to

1939

1934 to

1939

Since 1955

Since 1974

Since 1983

Torpedo Boat tail Air ship

Rumpler 3

Bugatti

Jaray

Ώ Ζ

Kamm

Citroen

VW-Scirocco I

Audi 100IH

Schlor

NSU-R08O

VW-Golf I

Ford Sierra

Figure 1.8 The four primary phases of car aerodynamics (updated version, concentrating on passenger cars, of the one in ref. 1.13 by Hucho, Janssen and Emmelmann)

Historical development 11

Initial development concentrated exclusively on drag, and the problem of cross-wind sensitivity only arose with increasing driving speeds. Lately attempts have been made, by suitable shaping, to eliminate the deposition of dirt and water on the windows and lights.

The following brief history is based upon available literature. Early numerical data, particularly drag coefficients, must be considered very unreliable. Drag coefficient was sometimes measured on test vehicles through coast-down tests, or by measuring the top speed, both of which can lead to errors (see Chapter 12). Most measured data, however, came from wind tunnel tests on models of varying quality and scale. Nor were the techniques for representation of the roadway uniform, so that, as indicated in Chapter 11, the absolute accuracy of the data is low and the comparability of data from different authors is uncertain.

This brief account of the history of automobile aerodynamics has two aims. The first is to show which work contributed to the development of automobile aerodynamics; the second illustrates how this knowledge was applied to autornobile design. Developments up to 1939 are described by Koenig-Fachsenfeld.14 Newer works on the history of automobile aerodynamics, primarily from the American point of view, have been published by Ludvigsen 1 5 and by McDonald.116 The many attempts to apply the growing aerodynamic knowledge to production cars have been illustrated quite recently by Kieselbach,1 19 whose books have appeared in German and English.

1.2.2 Basic shapes

In the first phase, dating from the turn of the century, an attempt was made to apply to the automobile streamlined shapes from other disciplines such as naval architecture and airship engineering. They were little suited to the automobile, for instance the 'airship form', or ineffective, for instance the 'boat tail'. Due to the poor roads and low engine power, speeds were still so low that aerodynamic drag only played a subordinate role. Most cars derived from these basic shapes had one error in common: they neglected the fact that the flow past a body of revolution is no longer axially

Figure 1.9 Record-breaking car from Camille Jenatzy, 1899


Figure 1.10 Alfa-Romeo of Count Ricotti, 1913 (courtesy Alfa Romeo, Milan)

symmetrical when the body is close to the ground, and when wheels and axles are added. In spite of this, shapes represented great progress toward lower drag in comparison to shapes based on the horse-drawn carriage. Certainly the oldest vehicle developed according to aerodynamic principles was the car built by Camille Jenatzy, who was the first to exceed 100 km/h (62mile/h) with this electrically driven vehicle on 29 April 1899 (Fig. 1.9); see Frankenberg and Matteuchi.1 20 With its torpedo shape with a ratio of length to diameter of 4, the body alone was streamlined; the exposed wheels and driver were not 'integrated', which certainly led to a considerable increase in the drag. Jenatzy's record-breaking car was the predecessor of all single-seat race cars, even though the body of the car was still positioned above rather than between, the wheels.

Figure 1.10 shows a vehicle with a body in the shape of an airship, afi

Figure 1.11 Boat-tailed 'Audi-Alpensieger', 1913 (courtesy Deutsches Museum, Munich)


Alfa Romeo from 1913. The length to height ratio for this body is approximately 3. Similar designs existed in which the wheels were partly enclosed by the body (design by O. Bergmann, refs 1.20 and 1.14). The attempt to design a car with an integrated ideal' body was repeated several times, but without production success.

In contrast to the shapes shown in Figs 1.9 and 1.10 the so-called 'boat tail' is completely ineffective in terms of aerodynamics (Fig. 1.11). The flow, separating at the front and from the fenders, will not re-attach because of 'boat tailing' the rear end. The boat tail, which was applied in different variants on mass-production limousines and sports cars, is an example of how aerodynamic arguments are often misused to justify stylistic curiosities.

1.2.3 Streamlined shapes

The analysis of the tractive resistance of road vehicles carried out by Riedler in 1911 gave vehicle aerodynamics a rational basis. The more Prandtl and Eiffel worked out the nature of aerodynamic drag, the more this knowledge was used to explain the aerodynamic drag of cars; see for instance Aston.1'22 However, getting away from Newton's 'Impact Theory' was a very slow process.

Figure 1.12 Rumpler car, 1924, photographed by R. Buchheim in the large wind tunnel of Volkswagen AG, 1979

After the First World War, the design of streamlined bodies started at a number of locations simultaneously. E. Rumpler, who had become well known through his successful aircraft, the 'Rumpler-Taube', developed several vehicles which he designated 'teardrop cars'. The most famous Rumpler limousine is shown in Fig. 1.12. In order to make use of the narrow space in the rear of the vehicle, Rumpler decided on a rear engine configuration. Viewed from the top, his car has the shape of an aerofoil. But the roof is also well streamlined, thus proving that Rumpler was aware of the three-dimensional character of the flow field (Fig. 1.13). Details are to be found in papers by Heller,1 23 Eppinger1 24 and Rumpler himself.1 25


Figure 1.13 (a) Two-dimensional flow around a profile; (b) three-dimensional flow field around a profile section close to ground (schematic)

Measurements performed by Buchheim in the large wind tunnel of Volkswagen AG in 1979, on an original Rumpler car provided by the Deutsches Museum in Munich, gave the following results:

Frontal area A = 2.57 m2; drag coefficient cD = 0.28

On the Rumpler car the wheels are uncovered, resulting in an increase in drag, which becomes more significant as the aerodynamic quality of the vehicle body improves; see section 4.3. On the Rumpler car this increase in drag must have been at least 50 per cent, as measurements performed by Klemperer 1 2 6 as early as 1922 show.

The car entered in the Strassburg Grand Prix by Bugatti in 1923 was developed primarily according to two-dimensional theory (Fig. 1.14).

Figure 1.14 Two litre Grand Prix race car from Bugatti, 1923

However, the horizontal profile forming the body pays more attention to the path of the flow in the vicinity of the ground. As on modern championship race cars, the air flow below the car is controlled as much as possible by extending the body downward. The arched shape also facilitates enclosure of the wheels. However, the flow over the tail must have been disturbed considerably by the driver.

The three-dimensional flow around a bluff body in the vicinity of the ground was originally analysed by P. Jaray. In his pioneer work The Streamlined Car, a New Shape for Automobile Bodies121 the term 'streamlined car' is used for the first time. A detailed report on the work of Jaray has been published by Bröhl.1'28 Many sketches, patent-drawings and photos from this unique work clearly demonstrate Jaray's ideas and their application all over the world. Jaray recognized that the flow around a body of revolution, which has a very low drag coefficient in free air, is no longer axially symmetrical when close to the ground. As a result the drag increases, owing to the flow separation occurring at the rear upper side. At


the limit, where the ground clearance approaches zero, the optimum shape in terms of drag is a half-body, which forms a complete body of revolution together with its mirror image—produced through reflection from the roadway. This half-body, which had a ratio of length to height of 4, was modified by Jaray so that the mid-section formed a rectangular cross-section with rounded upper corners.

Wind tunnel tests performed by Klemperer1 26 at Jaray's request showed that the drag of this half-body increased with increasing ground clearance, due to the air flow around the sharp lower edge; by rounding off these edges it was possible to eliminate this increase (Fig. 1.15). Jaray then attempted to approximate the shape of this half-body by assembling individual aerodynamically shaped bodies. The half-body itself, as will be illustrated later, was used again and again by a number of designers.

j — | B £&-□α^ ra

Φ-Ifes ALF v-/>

[ Large Jaray ca

dä^ Small Jaray c<

1 ^\s

Half-body 1 without wheels

Half-body 1 with wheels

►

rs

ar

A 1 : 1 [m2]

2.99

2.86

1.87

2.99 front with sharp edges front edges rounded

cD I

0.64

0.30

0.29

0.13

0.09

0.15

Figure 1.15 Drag measurements on Jaray cars and half-bodies, carried out by W. Klemperer, 1922, see ref 1.26, on one-tenth scale models; cooling-air duct closed

Figure 1.16 'Combination forms' according to P. Jaray (schematic)

Figure 1.16 shows how Jaray laid out his vehicle shapes, using sections from profiles and bodies of revolution. In both examples the basic body is formed by a profile segment. On the first, a second profile is attached vertically, and in the second example half of a body of revolution serves as the upper part. This body, later called the 'combination form', was based


upon the consideration that low drag can only be achieved when the separation at the rear is eliminated. With a rear end in the shape of a half-body this can be achieved only with a very long, slender tail. In the combination form, the tapering of the rear end is subdivided into two planes to prevent excessive pressure increase, which could result in separation. Unfortunately Jaray1 29 published only a 'schematic' pressure distribution for a combination form. Wool-tuft pictures for Jaray cars114

indicate that separation can be prevented only for extremely slender versions of the combination form.

In 1935 Jaray made up a table of types in which he illustrated the large variety of shaping possibilities according to aerodynamic aspects; see for instance ref. 1.14. The characteristic of all of his designs was the relatively sharp horizontal rear edge. Jaray suggested classifying the individual shape parameters by numbers, similar to the system introduced by the National Advisory Committee for Aeronautics (NACA) in the USA for aircraft wing profiles. This approach did not prove particularly practical for road vehicles.

The most important of Klemperer's measurements on models of the first Jaray cars are summarized in Fig. 1.15. Compared to the box body styles of the time, it was possible to halve the drag with the combination form to cD = 0.30, though it took 60 years to exploit this potential with a production car: the Audi 100 III of 1982, with a drag coefficient of 0.30. On the other hand, Klemperer's early measurements clearly show that the drag coefficient of Jaray's combination form of 0.30 is still twice as high as that of the half-body with wheels, 0.15. Chapter 4 shows how modern automobile aerodynamics uses this potential—first published by Jaray and Klemperer in 1922.

As can be seen from Fig. 1.15 the first Jaray models were as high as the box-type cars of the day; the length/height ratio was only 2.1, while this ratio is approximately 3.0 with today's cars. Many prototypes were built to the patents and ideas of Jaray (see Bröhl1 28 and Kieselbach1 1 7 1 1 8 ) by various car manufacturers in Europe and the United States. The prototypes built for Ley, Audi and Dixi (1922 to 1924), and for Chrysler (1927/28), were not readily accepted by the public. Their shape was too

Figure 1.17 The 1.5 litre Adler-Trumpf, 1934/35, designed by E. Kleyer (courtesy Frhr. v. Koenig-Fachsenfeld)


revolutionary, but also Jaray adhered too closely to his basic principles. The prototypes built for the various makes all looked alike.

From 1934, several more attractive Jaray-shape cars were developed, for example the 1934/35 Adler Trumpf sports car (Fig. 1.17). The slender shape, with llh = 3.3 and sloping rear end, led to low utility of internal space. As more high-speed highways were constructed cars of streamlined shape became very popular until World War Two ended the era of Jaray cars.

One mass produced Jaray-style car was the Tatra 87 of 1937, designed by H. Ledwinka (Fig. 1.18). With llh = 2.9, this car was less slender than the

Figure 1.18 The 3 litre 8 cylinder Tatra Type 87, designed by H. Ledwinka

Adler Trumpf, and by placing the engine at the rear end it was possible to locate the passenger compartment further forward, where more space was available. Wind tunnel tests, performed on a one-fifth scale model of the Tatra 87 by Lange in the DVL wind tunnel at Berlin-Adlershof, gave a suspiciously low cD = 0.244.13° A calculated value of cD = 0.31 was deduced from the top speed and the engine power. The actual value of cD = 0.36 was measured by Buchheim in the Volkswagen wind tunnel in 1979 on an original vehicle supplied by the Deutsches Museum, Munich!

The wind tunnel tests on Jaray shapes, which were initiated by Klemperer in 1921/22,126 were continued in 1938 in the Aerodynamische Versuchs-Anstalt (AVA) in Göttingen under the direction of Ludwig Prandtl. A body shape was developed which consisted of a horizontal basic

Figure 1.19 Lange car; length / to height h, llh = 3.52; CD = 0.14 to 0.16, completely smooth model


profile upon which a second horizontal profile was added from the windscreen. As with all Jaray shapes, this second profile was also rounded at the front from the top view. The resulting shape is known as the 'Lange car'. A drag coefficient of 0.14 was achieved with the model of this Lange car shown in Fig. 1.19 (see Lange1·31). Measurements performed by the author and his co-workers on a one-fifth scale model approximately confirmed this value with 0.16. However, the model lacked details such as running gear, wheel wells or window recesses. Approximately the same low drag coefficient can be achieved with the Lange shape as with half-body shapes (Fig. 1.15), which, however, were more blunt: llh = 3. The Porsche 911 has a shape similar to that of the Lange car.

The relatively large llh necessary for a Jaray-shape prevented the success of Jaray's idea, though numerous pseudo-Jaray shapes, called fastbacks, were built, such as the 1934 Chrysler Airflow and the Volkswagen Beetle. As will be shown in Chapter 4, this shape, with its steep-sloping rear end, produces two distinct longitudinal vortices. Due to the downwash induced by these trailing vortices, the flow along the longitudinal mid-section of the car remains attached over a long path; however, a high vortex-induced drag is produced so that the total drag is higher than for true Jaray shapes. In comparison to the box-shaped bodies with drag coefficients between 0.6 and 0.8, the pseudo-streamlined cars with drags of 0.4 or 0.5 still represented an improvement.

An approach similar to that of Jaray was pursued in France by Mauboussin1 32 in 1939. His car, the Mistral, had the shape of an aerofoil in plan—the rear ending in a vertical knife edge. The rear wheels were covered by a horizontal profile, producing an intersection at the rear similar to the Jaray shape. However, the slender taper of the body greatly limited the internal space.

The measurements by Klemperer1 26 indicated an achievable limit of cD = 0.15 with uncompromising design, which has only recently been bettered (see Chapter 4). However, Jaray's attempt to approach this limit as closely as possible with his combination form led to impractical shapes, and his work provided no indication of the way in which the typical drag of automobiles of the 1920s (around 0.7) could be brought step by step nearer to the goal of 0.15.

However, Lay1 3 3 working at Michigan University in the early 1930s started to close this gap. By systematically modifying the shape of the car at the front and the rear, Lay isolated the individual aerodynamic effects (Fig. 1.20). His investigations revealed the strong interaction between the flow fields of the car's fore-body and rear end. The low drag of a long-tail model was maintained only when the flow around the fore-body was well attached. The drag increased significantly when the flow separated at the steep windscreen. On the other hand, if the drag was already high due to the blunt rear end the drag increase from a steep windscreen was only moderate. Unfortunately Lay's model, which could be built up from segments, had parallel side walls and sharp corners, which resulted in a fairly high drag and limited the significance of his findings.

The most important result of Lay's work was that a blunt rear end resulted in only a relatively small increase in drag in comparison to a long tapered rear end. Similar findings were made by Dornier as early as 1920


Figure 1.20 Influence of main body parameters on the drag of a car and their interactions, after ref. 1.33

with measurements on aerofoil sections with a cut-off trailing edge (see Hoerner1 2) .

From 1934, the blunt rear end shape which first occurred in the work of Lay led to the development of the 'Kamm-back', which combined the advantage of greater headroom in the back seat with that of low drag. The Kamm-back, the Lay blunt back and Klemperer's long-tail design are compared in Fig. 1.21. The low drag is achieved because the flow remains

I ^ ^ / ^ W'E- L a y

X*C. .W. Kamm \S( \ . ^ W Klemperer Figure 1.21 Comparison of three different

\ v < v x r e a r end shapes: W. Klemperer's long tail

] \ and the blunt rear ends of W.E. Lay and I ^Ji } W. Kamm

attached for as long as possible and is then forced to separate by cutting off the rear end at an already much diminished cross-sectional area. This results in a small wake. By tapering the body moderately, the flow is subjected to a pressure increase which ensures that the pressure at the rear of the vehicle, the 'base pressure', is comparatively high, which itself then reduces the overall drag. Kamm proposed this idea in a paper published in 1934,134 but presented no practical design, referring only to the earlier work of Klemperer1 2 6 and Lay.1 From patent records (see Kieselbach1 17), R.v. Koenig-Fachsenfeld must be credited with the invention of the cut-off rear end, and his published measurements on bus models in 19361'35 clearly proved its advantages (see section 1.2.6). Despite this, the cut-off rear end became known as the 'Kamm-back' (sometimes called K-back). Much later (1948) Everling1 36 claimed that he was the first to recognize the advantage of the cut-off rear end in 1934, when he had designed a bus with a cut-off tail.


Whoever originated this idea, W. Kamm was the first to undertake systematic investigation of rear end design in 1935 at the Research Institute for Motor Vehicles and Vehicle Engines (FKFS) at the Technical University of Stuttgart. In 1938 the first passenger vehicle with a Kamm rear end, the Everling car, was built (Fig. 1.22). Kamm went on to build

Figure 1.23 Kamm car of 1938/39 in the wind tunnel of Volkswagen AG, 1979 (courtesy Volkswagen AG)

several K-cars, and with the K5 (Fig. 1.23) the shape was developed to the point where mass production would have been possible, but this was thwarted in 1939 by the outbreak of war. The advantage of the Kamm-back, in comparison with other aerodynamic designs, can be clearly seen in Fig. 1.24.

The drag coefficients published for the Everling and Kamm cars indicate a high degree of scatter (Table 1.1), and appear to be too favourable. Dörr, who did the measurements on the Everling car,1-37 also tested the contemporary Mercedes Benz DB 170 V and devised coast-down test results of cD = 0.48, a figure which seems far too low when it is compared with wind tunnel results published by White1"38 on similar cars, which averaged cD = 0.55 (bottom right, Table 1.1). Buchheim tested the 1938/39

Tatra Type 87 _ ^ .Kamm

^ /J ^ ^ A d l e r Trumpf

Figure 1.24 The Kamm-back in comparison to two versions of the Jaray-back; the Tatra 87 contour is drawn without the rear fin


Table 1.1 Comparison of published data measured on cars from E. Everling and W. Kamm

Type of measurement Everling, 1938 KammK5, 1939 DB 170V

■-Λ' 'O1

A = 2.24 m2

^B& A = 2.17 m2

Model

Expected for full scale car

cD =0.15

cD = 0.24

Coast down cD =0.31

Wind tunnel, full scale

cD = 0.24

cD = 0.37

cD = 0.48

0.52 < c D <0.55

CD~=0.55

Kamm car, now on display at Langenburg Castle, in the Volkswagen wind tunnel in 1979 and obtained a drag coefficient cD = 0.37 and a measured frontal area of 2.10 m2, which shows the caution with which one should view the literature!

Although vehicle aerodynamics initially concentrated on the drag in still air conditions (symmetrical oncoming flow), the problems of side wind as well as cooling and ventilation soon became apparent, as noted by Klemperer,1 26 whose results (Fig. 1.25) showed that drag varied little with

i 1.0

0.8

0.6

0.4

0.2

Ί — T ? = F Standard car N >

V \

Λ. Jaray car H

5° 10° 15° 20° 25° 30° 35° 40° 45° 50°

ß Figure 1.25 Drag variation versus yaw angle, after W. Klemperer1 26

increasing yaw angle for 'sharp edged' cars which already had high aerodynamic drag, but decreased sharply—after a slight increase—with streamlined shapes. He stated: 'The body of the vehicle then acts like the sail of a ship sailing hard to windward'. However, he made no measurements of lateral force and yawing moment, the most significant in cross-wind sensitivity. The drag curve for cross-wind will be examined in detail in Chapters 4 and 8, which also show that Fig. 1.25 is too optimistic regarding the effect of the side wind drag. Large angles of yaw, at which Klemperer's 'sail-effect' becomes effective, occur in practice only at low driving speeds, at which drag is insignificant anyway. On the other hand, at small angles of yaw additional resistances occur, which are considerably higher than might be deduced from Fig. 1.25.


Directional stability in cross-winds became increasingly significant with higher driving speeds, when it was realized that vehicles with low drag often possessed poor cross-wind stability (Kamm1-39). It was eventually discovered that only vehicles with long, tapering rear ends suffered in this respect, while the yawing of vehicles with truncated rear ends (Kamm back) was not uncommonly high (see Chapter 5).

It was even possible to produce aerodynamically stable yawing moment characteristics by adding tail fins, the effectiveness of which was proved in driving tests by Sawatzki.140 However, fins were used only on record-breaking cars and motor-cycles, and were unsuitable for use on mass-production cars. False fins were sometimes used as styling elements, but even the rather large fin on the Tatra 87 (Fig. 1.18) probably contributed little to stability.

The danger from cross-winds results primarily from gusts, which occur naturally but are also caused by the terrain as well as the presence of vegetation and buildings, as originally reported by Huber. However, little thought has been given to reducing cross-winds by proper landscaping, although the barriers and walls constructed to protect the environment from road noise may provide wind protection as well. Special attention has to be paid to gaps in these barriers and walls; see section 5.3.

With the start of systematic work on automobile aerodynamics, the problems of the flow of air through the vehicle were examined. Klemperer1 26 considered the air flow through the cooling system in his model tests and showed that air flow through the radiator increases vehicle drag. Fiedler and Kamm1,42 suggested ways of reducing this drag increase. In Kamm's school the flow processes in the radiator were examined in detail. The interaction between the vehicle, radiator and cooling air fan was investigated by Schmitt143 and Eckert.144 The principles for ventilating the passenger compartment were also elaborated by Kamm and his students, who investigated the relation between the external flow field and the volume of air passing through the passenger compartment. Much later (see Chapter 10), the possibility of improving passenger comfort by properly shaping the pattern of the internal flow field was investigated.

As mentioned earlier, true aerodynamically designed 'streamlined shapes' were used only sporadically for mass produced automobiles. The findings of Jaray, Lay, Everling and Kamm were applied, but their potential was not really exploited. Nevertheless, even at a very early date there were attempts to achieve even lower drag following the ideas of Klemperer and his 'half-body shapes'.

As early as 1922 Persu1,45 built a car in Berlin which was derived from a half-body. The engine was located in the tapering rear end. No test results have been found for this vehicle. From 1930 several American authors worked with half-body cars, but their work was confined to the model stage. The results achieved by Fishleigh,1 46 Heald,1 47 Lay133 and Reid1 48

are summarized in Fig. 1.26. To evaluate the results achieved on the models with varying perfection and different scales, each half-body shape is compared with a contemporary limousine model tested by the same author. With the exception of the extremely long rear end examined by Lay, all half-body models had a drag coefficient approximately one-third of that of the contemporary limousine.


Author Year Scale

Optimized half body shape Car for comparison

W.T. Fishleigh 1931 M 1:4

drag-ratio 1:2.6

R. H. Heald 1933 1:15

cD = 0.20 cD =0.71 cD = 0.55

W.E. Lay 1933 1:8 (0

cD =0.30 0.24 0.20 0.13 cD =0.61

E.G. Reid 1935

cD =0.15^3.20 (©

cD = 0.61

Figure 1.26 Bodies with low aerodynamic drag in comparison to contemporary US passenger cars

The development of a practical car of half-body design superstructure was achieved in 1937 at the Aerodynamische Versuchs-Anstalt (AVA) in Göttingen under Ludwig Prandtl. An analysis of the flow around the Lange car (Fig. 1.19) by Hansen and Schlör1 49 led to the model shown in Fig. 1.27. The longitudinal mid-section is composed of two 'Göttingen aerofoils' each of which had the same drag coefficient of cD = 0.125. The

1275

2100

Figure 1.27 Plan and side elevation of the Schlör car, after ref. 1.49


lateral sections were developed from a rotational half-body so that the flow remains attached around a body with the largest possible internal space. The most important test results for this vehicle and scale models are given in Fig. 1.28. The drag coefficient cD is plotted against the ground clearance e, which is made non-dimensional with the height h of the vehicle. With high ground clearance, the half-body had lower drag than the profile from which it was derived. With decreasing ground clearance, the drag

0.20

0.18

0.16

, Standard underbody

Profile 571 Profile 570

^ ^ ^

quarter-scale model; VW measurement

smooth underbody

full-scale vehicle one-fifth scale model

0.5 1.0 1.5 2.0 2.5 3.0 3.5

e/h ►

Figure 1.28 Drag coefficient of the Senior car; measurements on models one-fifth scale (AVA), quarter-scale (VW) and full-scale car (AVA)

increases. The value of cD = 0.15 measured by the author and his co-workers on a quarter-scale model (smooth bottom) with ground clearance suitable for a motor vehicle corresponds quite well with the data obtained by the AVA on the full-scale model with smooth bottom. On the actual vehicle, cD = 0.186 was measured in the large AVA wind tunnel with elliptical nozzle (7 x 4.5 m). This accords well with coast-down tests performed at the Technical University in Hanover in 1939, resulting in cD = 0.189. The Schlör car suffered from an unusually large frontal area of A = 2.54 m2, resulting primarily from its great width of 2.10 m, needed for

^ ^ Ρ ^ > ID 19

. . / T T N I ^LJJ^

GS

—ml^T l Γ ^ ,

*m-Lfeä CX 2000

/ττ^, <feW-&

|_ BX

Model Year

1956

1970

1974

1982

A[m2]

2.14

1.77

1.96

1.89

Co

0.38

0.37

0.40

0.33 - 0.34

Figure 1.29 Model line-up of Citroen cars from 1956 to 1982


lock-to-lock clearance of the completely covered front wheels. The large frontal area must therefore be considered intrinsic to this design.

The development of half-body designs reached its zenith with the Schlör car, which is impractical for mass produced automobiles.

The development of streamlined automobiles was interrupted by the Second World War. Citroen and Panhard were the only car manufacturers resuming this development after the war, as can be seen from Fig. 1.29. While Jaray's ideas can still be recognized on the ID 19 body (basic body and attached profile) the GS and the CX are more closely related to Kamm's ideas (cut-off rear end). All three models have an extremely low drag coefficient in comparison to their contemporary competitors. The

356 A

Model year

1950

A [m2]

1.61

cD

0.34

1959 1.61 0.39-0.40

356 B

1976 1.77 0.40

911 S

1975 1.79 0.33

924

1981 1.82 0.35

944

1977 1.95 0.38

928 S

Figure 1.30 The Porsche car family from 1950 to the present


latest Citroen, the BX, can hardly be recognized as a streamlined car any more.

In the area of sports cars, Porsche, above all, has paid consistent attention to aerodynamic design, as can be recognized from the model series in Fig. 1.30. While the older models 356 A and B can be called Jaray shapes, the 911 is more closely related to the Lange model; see Fig. 1.19. The newer models from Porsche, the 924, 944 and 928, also have a distant relationship to the Lange shape.

In the course of styling a new model, the aerodynamicist is frequently confronted with a question like, 'What happens with drag if one or other detail of the body is changed?' In order to give helpful answers and to convey the basic facts of practical aerodynamics to the stylists, White1 38

developed a 'Rating Method', based on the many measurements on full-scale cars performed at MIRA up to 1967. He selected nine body parameters crucial to the flow pattern around a car, and thus decisive for its drag; see Fig. 1.31. Each is rated with regard to its aerodynamic quality.

(V) 1 to 6 a 4; 1 to 5+

m (7) 1 to 5+

(2) 1 to 6+

(5) 1 to3

($) 1 to 3

3 1 to 5

(6) 1 to 3

05 (§) 1 to 5

Chassis Figure 1.31 Details of the body, which are important for drag, together with their ratings, after ref. 1.38

Good flow quality is awarded low figures; body details likely to spoil the flow quality, for instance large flanges at the A-pillars, are penalized with additional points. The sum of points corresponds to the drag coefficient:

cD = a Σ Pi i = l

(1.4)

This linear relation is shown in Fig. 1.32 together with the bandwidth of error, which is stated by White to be ±7 per cent, not including the drag

50

40

A 30 91 zi2 0

/=1 10

F - "

6

:.-_-

-t-■

4-| I

-

'

I i 0.1 0.2 0.3 ^0.4 0.5 0.6 Figure 1.32 Correlation between the sum of

co ^ rating and drag, after ref. 1.38


due to the cooling air flow. It might be difficult to estimate the cooling air flow drag better than its average value of AcDC = 0.03; see Fig. 4.95. This adds another ±5 per cent of error to the drag estimate. In fact, the total error in the drag estimate is ±15 per cent, which covers almost completely the bandwidth of drag coefficients of today's cars. Therefore White's rating method is not appropriate to differentiate today's cars with regard to their drag, not least because low-drag cars, which are coming into production more and more, were not around when White established his rating method. The merit of the method, however, was to identify clearly those areas of a car which have a major influence on drag, and to make them known to people in the car business who have no experience in aerodynamics.

1.2.4 Optimization of body details

Despite the success of modern streamlined cars, aerodynamics has only recently become the dominating design criterion. Previously, ways were found of adapting aerodynamics to practical automotive engineering requirements of styling, packaging, safety, comfort and production. The method of optimizing body details developed by Hucho, Janssen and Emmelmann 13 represents one approach. This 'third phase' is character-ized in Fig. 1.8 by the Volkswagen Scirocco I and Golf (Rabbit) I. Since this method is treated in detail in section 4.4.1, only the principles will be presented here.

The starting point for aerodynamic development is the stylistic design; modifications to the shape must be made within the styling concept. Details such as radii, curvature, taper, spoilers etc. (Fig. 1.33) are modified in sequence or where required, in combination, step by step, to prevent separation or to control the separation so that the drag is minimized. Practice has shown that in comparison to the initial shape considerable

u c Angle of attack a = -0 .5° Figure 1.33 Example of development aceording to the Optimization of body details'

28

Opel - GT

ΏΖ Model year: 1969 >4 = 1.51 CD =0.41

VW-Scirocco I

Model year: 1974 4 = 1.73 cD =0.41

Figure 1.34 Comparison of drag coefficients for Opel-GT, styled by streamlining, and Volkswagen Scirocco I, designed by 'detail optimization'

Basic body I Basic shape I Basic model I Styling model Figure 1.35 Development of a low drag car body, starting from an 'ideal1 body, after ref. 1.51


reductions in the drag can be achieved in this manner (Fig. 1.34). Using the technique described, it was possible to reduce the drag coefficient of a VW Scirocco I from 0.50 in the original style model to 0.41. In spite of the emphatic 'hard' styling, it was possible to achieve the same drag coefficient as the Opel GT, which was styled according to the principles of streamlining. However, from many cars developed by detail optimization, it may be concluded that a limit of cD = 0.40 can hardly be bettered.

For car manufacturers who still launch cars with cD > 0.45, this method may serve as a design tool for a good while. To achieve a drag coefficient lower than cD = 0.40 requires more advanced techniques.

One such method is 'interactive shape optimization', which permits significant deviations from the original styling concept; see section 4.4. The other is to start from a body of extremely low drag, and to convert this into a real car with low drag.

1.2.5 Shape development starting from low drag configurations

Unlike the detail optimization method, the aerodynamic development of a car can start from a low-drag body with the same overall dimensions as the final car. This low-drag configuration is converted into a real car step by step, applying the optimization technique for each detail. This method has been elaborated by the author and his co-workers150 and is outlined in Fig. 1.35, after Buchheim et al.1 51 Details are discussed in section 4.4.2. The Audi 100 III—with a drag coefficient of cD = 0.30—is a striking example of the potential of this method (see bottom of Fig. 1.8). Figure 1.36 shows the two different routes to low-drag cars.

0.5 H

0.15H nnunnnnnnnw

Complexity of shape

Figure 1.36 Alternative routes to low drag cars, after ref. 1.64


1.2.6 Trucks and buses

The need for high-speed trucks and buses arose with the construction of high-speed road systems in the 1930s. Prior to the construction of the Autobahn, autostrada, motorway and highway, mass transport of goods and people was accomplished by rail. The first buses and trucks were designed like elongated passenger cars. The same aerodynamic design principles were applied: at first the Jaray lines, later the Kamm-back. Kieselbach1 19 recorded this period with many photographs and design drawings. With the introduction of the 'tram-bus' by Gaubschat in 1936, the shape of buses broke away from cars. With the engine underneath the floor—or later at the rear—more seats could be placed within the same overall length. The front end of the tram-bus was extremely well rounded (Fig. 1.37).

Figure 1.37 The Tram-bus' first built by F. Gaubschat on a Bussing chassis, 1936 (courtesy R J.F. Kieselbach)

By 1930 Pawlowski1 52 had published data on the influence of leading edge radii on the drag of rectangular bodies. As can be seen from Fig. 1.38, comparatively small radii are sufficient to arrive at minimum drag for box-shaped vehicles. Although this result was confirmed by Lay in 1933 with road tests, and although this finding has been repeated several times (see Chapters 8 and 11), it was not applied for a long time.

In 1936 the Kamm-back was introduced to bus design, based on measurements from Koenig-Fachsenfeld.1 35 Because it allowed for one more row of seats in comparison to the Jaray back (Fig. 1.39) it was well accepted in practice.

Another milestone in the aerodynamics of commercial vehicles was the front design of the first Volkswagen van by Möller1 53 in 1951 (Fig. 1.40). The two reasons for the wide recognition given to this work, apart from the drastic drag reduction, were the unique market position long held by this van all over the world, and the reference made by H. Schlichting in his famous book Boundary Layer Theory.154 There the result is used to demonstrate the interaction between a body's shape, the flow pattern and the related drag.

However, for the first Volkswagen van no use was made of the earlier work of Pawlowski. The front end of the first VW van was much more rounded than was necessary to achieve an attached flow and the related low drag.

31

0.40 'I 1 1 1 1

0.05

01 I I I I 0 1 2 3 4

Radius of Edge and Corner Rounding, in.

Figure 1.38 Influence of leading edge radii on drag of a rectangular box, after F.W. Palowski,152 1930

Figure 1.39 Jaray and Kamm backs on a bus


a) Sharp-edged front

^,—·2ς-~7£~ ^ ^ - » ~_^_ -, -a -a

Separated

cD = 0.76

b) Rounded edge front

--G 0.42

Attached

Figure 1.40 Flow around a model of the first Volkswagen van, after E. Möller,153 1951

The first van—to the knowledge of the author—which was designed according to the ideas of Pawlowski was the Volkswagen LT (Light Truck). The basic work was done on a quarter-scale model in 1969. Owing to the long lead time of this vehicle, these data were not published—together with full-scale measurements—until 1976 (see ref. 1.13, Fig. 29, van B); further details followed in 1978.155 Figure 1.41 clearly shows that a non-dimensional leading-edge radius of 0.045 is sufficient to keep the flow behind the corner attached. The smoke trails taken on a full-scale vehicle (Fig. 1.42) show that only a small radius is needed to prevent separation.

Today leading-edge radii of buses and cabs of trucks, sometimes even those of trailers, are optimized in the same way; see Chapter 8.

r·—I ·

Section 600

I.

vv\\\\w vvv\vv\vv ^ ^ 0.02 0.04 0.06 _L 0.10 b

Figure 1.41 Determination of optimum leading edge radius for Volkswagen LT, after ref. 1.55

33

Figure 1.42 Smoke trails, taken from full-scale VW LT. Top: optimum radius, flow attached; bottom: sharp corner, causing separation; after ref. 1.55

Figure 1.43 Cab-spoiler, providing, if correctly matched, attached flow on top of the trailer; from ref. 1.66


A further step to improve specifically truck aerodynamics was the invention of the cab-spoiler by Saunders. The idea of guiding the flow by vanes goes back to the work which Frey157 published as early as 1933. Guide vanes have long been applied to steam locomotives, mainly to keep the smoke away from the driver's cab, but also to reduce drag. Figure 1.43 shows how a guide vane, if properly tuned to cab and trailer, can improve the flow pattern and thus reduce the drag (see Chapter 8). The big advantage of this spoiler, and others, is that it can be attached to trucks already on the road. It also allows for individual matching to various trailer configurations.

1.3 Development trends 1.3.1 Vehicle engineering

The primary dimensions for European passenger cars are established within narrow limits for the individual vehicle classes. The size of the engine and drive train, the space available for the passengers and the volume of the trunk (boot) largely determine the primary dimensions shown in Fig. 1.44.158 Japanese cars come well within the same

Enveloping box

Figure 1.44 Design constraints for a passenger car, according to ref. 1.58

dimensional limits as the European cars. The 'down-sizing' programme of the US auto industry has brought US cars closer to European dimensions. But the free space offered by the 'box dimensions', length /, height h and width w, is ineffectively utilized by the design shape.

Nevertheless, the main proportions of the body shapes vary little (Fig. 1.45). In the smaller class, e.g. Ford Escort, VW Golf I, GM Astra, there are two different shapes: the traditional notchback and the squareback (Fig. 1.45a). On the latter, significant differences in the slant angle of the rear end are present (for more detail see Chapter 4). The middle range, e.g. Audi 80, Ford Sierra, GM Cavalier (Fig. 1.45b), again includes two different types of rear end; in addition to the notchback, the fastback is offered as a sporting alternative. Station wagons are not considered here. The larger passenger cars such as the Mercedes 240 (W 123) or Audi 100 (Fig. 1.45c) are similar in silhouette.159

If passenger cars are listed according to kerb weight and examined for changes in primary dimensions over the years, one finds that the length, width and wheelbase have remained nearly constant during the last 20

Development trends 35

Figure 1.45 Centreline cross-section of European cars, after ref. 1.58: (a) small cars, (b) medium-size cars, (c) 'full-size' cars

years. According to ref. 1.60 (see Fig. 1.46), passenger cars have become continuously lower in height. The vehicles in all weight classes converge to practically the same height dimension; however, the ergonomic limit now seems to have been reached. For very small cars—the minis—the height is


Kerb weight = 1400 kg ,.1200 kg

1300 —

1954 56 58 60 62 64 66 68 70 72 74 76 78

Model year—^

Figure 1.46 Development trend of car height for European cars over the years, after ref. 1.60

increasing again. How height is traded off against length has been demonstrated by Costelli1 61 for the Fiat Uno car.

In automobile aerodynamics the frontal area A, which was defined in Fig. 1.3, is used to designate the size of a car. Figure 1.47, from Hucho,1 58

shows that this is in fact a suitable parameter for this purpose. On

2.4 2

m

* 2 . 2

^ 2 . 0 CO 0) 11.8 CO c O it 1.6

H^-

^M

500 1000

Kerb weight I m

1500 kg 2000

Figure 1.47 Correlation between frontal area A and kerb weight m for European passenger cars, after ref. 1.58

European passenger cars a good correlation exists between the frontal area A and the kerb weight m. In the future the slope of the line A versus m shown in Fig. 1.47 will probably become steeper. While the frontal area A can be assumed to be constant as a comfort dimension for the individual car classes, the kerb weight will be reduced further.

Among the various cars there is little variation in cross-sectional shape. Flegl and Bez1 62 defined a shape factor/(Fig. 1.48) by which the frontal area can be correlated to the rectangle made up from the car's width and height. The average for/, measured for 85 European cars, is 0.81 with very little scatter. Car designers have cut off from the rectangle what was not needed for the passengers' comfort (see hatched area in Fig. 1.48). Among the different car classes, the frontal area of cars from competing manufacturers is almost identical. This again confirms that the frontal area is well suited to characterize the size of a car for aerodynamic purposes.


Car class

Mini

Medium size

Upper medium size

Full size

Frontal area A [m2]

1.8

1.9

2.0

2.1

A ^0 .81 ■ (b-h) Figure 1.48 Frontal area of cars, shape factor/for European cars, after ref. 1.62

The weight-to-power ratio for passenger cars has decreased continuously over the last 20 years. In Fig. 1.49 (from ref. 1.60) the kerb weight in relation to the engine power is plotted against time, again with kerb weight as a parameter. The trend to more powerful engines is now beginning to fade, whereas the trend to lighter vehicles, triggered by the energy crisis in the winter of 1973/74, is likely to continue; a further but moderate decrease in the weight-to-power ratio can therefore be expected in the foreseeable future.

60 kg/kW , 50

40

30

20

10

CD

o a

^ 0 0

JS00

^ - 1 0 0 t f

I20CFP*=

Kerb weight = 1400

l _ 1 1

k g " ^ ^

J ., .1.. 1 J . 1

: = : =

1. ,

I 1954 56 58 60 62 64 66 68 70 72 74 76 78

Model year ►·

Figure 1.49 Weight to power ratio for European cars, parameter kerb weight, after ref. 1.60

Lower weight-to-power ratios have led to increases in top speeds; see Fig. 1.50 (from ref. 1.60). Despite the fact that there are speed limits in most industrial countries (with the exception of unlimited top speed on the German Autobahn) top speeds are still increasing. The speeds technically obtainable have progressed far beyond the top and average speeds driven in road traffic and even in racing. Figure 1.51 shows the world speed records over the years.1 20 The dream of driving faster than the speed of sound was achieved in December 1979 in an unofficial record run. However, a relationship between speed records and the practical requirements of automotive engineering is no longer valid (see also section 7.5.2).


200 , km/h

180

'S 160 α CO α o

140 Κ^

I I I I I Kerb weight = 1400 kg^

I , I

^ ^ ι ο π π

5" 1

_ _J

MX)

.800

600

1 1 , _ _ l L

_

. . J

120h

100

80 1954 56 58 60 62 64 66 68 70 72 74 76 78

Model year ►

Figure 1.50 Top speed of European cars, parameter kerb weight, after ref. 1.60

10"

· · · World record °° Passenger car'1400 kg

10

km/h

6 5

t :

1 1900 10 20 30 40 50 60 70 80

Model year ►

Figure 1.51 Official land speed records compared with top speeds of passenger cars

Γ—-4-1

) ,

1

1 [ ' ! .

*-■*+

f Φ

*

—\

-

•

• r

^ · t-

! · ·

t 1 T — \

J

■•i 1

! ' " ;" ~^ - - t r ■■ ■

-f t -Λ - \ \ j ■ ; r «- - ■ - t- t- - ! ■ j · _ \ + + l __

,. o o

1 -i r. \ .ό^0°°.°..

1 ;

,

1

1.3.2 Automobile aerodynamics

The trend in the aerodynamic development of cars is summarized in the next two diagrams. Figure 1.52113 shows how drag decreased between 1920 and the mid-1970s. Owing to the lack of statistical data only a general tendency can be outlined.

The reduction of the drag coefficient from cD ~ 0.8 for cars in the 1920s to an average value of 0.45 for the cars of the 1960s and 1970s occurred in two stages. In the first, the period between the two World Wars, the cars were stretched and body details were rounded while maintaining significant characteristics such as projecting fenders and headlights. In addition to a lower drag coefficient of approximately 0.55, frontal areas were decreased, resulting in a considerable reduction of the total aerodynamic drag.

The second stage in the reduction of drag was reached with the introduction of the pontoon body with its variants, the notchback, fastback and squareback. By incorporating the fenders and headlights in a closed body shape, it was possible to improve significantly the flow of air around


_ _l I I i I I I

1920 1930 1940 1950 1960 1970 1980

Year of design ^

Figure 1.52 Trend in aerodynamic drag coefficient cD against time, from 1920 to the mid-seventies, after ref. 1.13

the vehicle. Using this design, drag coefficients of 0.4 to 0.5 were achieved, depending upon the detail design. This scatter range has remained unchanged since about 1960. However, it is difficult to determine whether the reduction in drag resulted from the influence of aerodynamics, from styling or from more advanced manufacturing techniques.

The recent past is illustrated in Fig. 1.53. The histograms, from ref. 1.63, comprise the population of current European cars, classified by drag coefficient. The class-width is chosen as AcO = 0.01. From these data, the average drag coefficient has been calculated and plotted against time. These data are comparable in that they are all derived from measurements carried out in the Volkswagen wind tunnel. The average drag coefficient began to drop in 1978. The range of data—the scatter—is still enormous. Even some contemporary cars have drag coefficients worse than 0.50, while the best, the Opel Omega, has cD = 0.28!

With concept cars (see section 4.63) there is still room for further drag reductions. Drag figures of 0.14 (GM Aero 2002) and 0.15 (Ford Probe IV) have been claimed for operational cars. Klemperer's value of 0.15, established in 1922, at last seems attainable. Today a drag coefficient of 0.30 is possible without major and expensive technical compromise. In the long run 0.20 might be achieved with production cars.

Increasing fuel prices will also encourage aerodynamic development of commercial vehicles. Drag coefficients for box vans cover the range of 0.4 to 0.5. A value of 0.40 can be realized without loss of transport space. Today the drag coefficients for heavy trucks lie between 0.6 and 1.0, the wide range being the result of the great variations in shape. Considerable drag reduction can be achieved through the design of the cab and the use of air deflectors. A value of 0.40 is a realistic goal for trucks and buses.

1.3.3 Vehicle aerodynamics and design

The relationship between aerodynamicist and stylist has been delicate in the past but is steadily improving. In early times, most of the aerodynamic

0.50

CD

0.45

0.40

• I

I·

(1)

74

75

76

ε I 2l

·

N

= 71

"c

B=

0.46

irTtr

Hs

ΠΙΙΜ

ΜΜ

ΙΠ

■ill

llllll

llllll

0.

40

0.4

5

Co

(2) 16,

I 8|

I 6|

_N

=

86

CQ

-= 0

.46

'

Sf

ΙΠΙΙ

ΠΙ

4r ■l-illllllll s

0.

38

0.40

0.

42

0.44

0.

46

0.48

0.

50

0.52

Fig

ure

1.53

Rec

ent t

rend

in d

rag

coef

ficie

nt o

f Eu

rope

an c

ars:

(1) a

fter

ref.

1.68

; (2

) afte

r re

f. 1.

58;

(3) a

fter

ref.

1.69

; (4

) afte

r re

f. 1.

67;

(5) a

fter

ref.

1.65

. All

data

fro

m V

W

mea

sure

men

ts

80

81

Yea

r

0.38

0.

40

0.42

0.

44

0.46

0.

48

0.50

0.

52 0

.54


work was done by experts from outside the car industry, with experience in fluid mechanics on aircraft aerodynamics but with little understanding of the automobile. Most of their suggestions were too advanced for their time and were therefore not considered. The work of Rumpler and of Schlör is typical. And even Jaray, whose ideas were much closer to the automobile, had little success because of his unwillingness to interact with the stylists. All his cars looked alike, which is just what the stylist does not want. On the other hand, stylists used, and sometimes misused, aerodynamic 'devices' as marketing gimmicks. The boat tail, fastback and tailfins are examples.

This situation started to change when the car makers began to carry out aerodynamic development in their own purpose-built wind tunnels. The aerodynamicist, now an employee, became an automobile engineer and had to interact with design. He became aware that the demands of aerodynamics did not ease the task of the stylist, who already had many technical restraints and legal requirements to observe. The stylist, however, discovered that aerodynamics could set trends more logically and reasonably than did fashion, and began to accept this trend as valid for design criteria. The trend of drag coefficient against time shown in Figs 1.52 and 1.53 is a direct record of the cooperation between the two departments.

Figure 1.54 Top: Citroen GS, 1970, cD = 0.38 (courtesy Citroen). Bottom: NSU Ro 80, 1976, cD = 0.38. Model launched 1967, cD = 0.36 (courtesy Volkswagen AG)

42

(a)

Β^?Ξ>

es»

(b)


(c)

Figure 1.55 (a) Audi 100 III, 1982, cD = 0.30 (courtesy Audi AG). (b) Ford Sierra, 1982, cD = 0.34 (courtesy Ford Werke AG), (c) Mercedes Benz 190 ('Baby Benz'), 1982, cD = 0.33 (courtesy Daimler Benz AG), (d) Renault 25,1984, cD = 0.31 (courtesy Renault)

Now aware of this improved cooperation, the buying public and motoring journalists became increasingly concerned that aerodynamics might lead to uniformity, and make all cars look alike. The following examples prove that this has not been true in the past, is far from being true at present, and need not necessarily be so in the future.

Examples from the past are shown in Fig. 1.54. The Citroen GS of 1970 accompanied the unique Citroen ID 19 and was a contemporary of the NSU Ro80, which was launched in 1967. Of course the good aerodynamics of both cars is apparent.

Four examples from the present are displayed in Fig. 1.55. All four cars, the Audi 100 III, the Ford Sierra, the Mercedes Benz 190 ('Baby-Benz')

44

Figure 1.56 Possible future low drag car shape: Citroen XENIA, 1981

15 16 Figure 1.57 Contour comparison of today's 'standard' car, cD = 0.43 and a low drae car c^ -0.30, after ref. 1.64 & ' D

1 round front end 9 covered wheels 2 cooling air duct optimized 10 smooth underside 3 bonnet slope 11 round wheel-well moulding 4 windscreen slope 12 wheel fairing 5 roof camber 13 top view tapered 6 rear window slope 14 A-pillar round 7 trunk height 15 windscreen curved 8 rear diffuser 16 C-pillar inswept

17 rear end boat tailed


and the Renault 25, were designed under ambitious aerodynamic guidelines, but they still maintained their marque identities.

What might be expected from the future can be seen in Fig. 1.56. More examples are given in section 4.6.3. Although the drag coefficient will be reduced still further, there is ample room for individuality even for cars with cD = 0.15, which is close to the limit for an 'ideal body' with wheels.

Today's cars are very similar not only in cross-section, as has been demonstrated in Fig. 1.45, but also in many other details such as rectangular head- and tail-lamps. Aerodynamics cannot therefore be blamed. However, future cars will have several common characteristics because of aerodynamics. These are identified in Fig. 1.57, after Hucho.1,63'1'64 This similarity will be no more pronounced than it is coday, for reasons other than aerodynamics. Neither is it expected that only one set of the many ruling parameters will lead to a target drag figure, or that there will be no room for product identity.

1.3.4 Development expenditure

Aerodynamic development of motor vehicles is expensive. Much capital must be invested in testing facilities such as wind tunnels and climatic tunnels. Secondly, considerable costs result from the work itself. Finally, the development time may be lengthened by aerodynamic work. The efforts to improve the aerodynamics of vehicles is witnessed by the large number of wind tunnels constructed specifically for this purpose. Nearly all major manufacturers now have such facilities at their disposal or are currently building them. These wind tunnels are described in greater detail in Chapter 11. Generally, the demands upon the quality of a wind tunnel increase with the expectations placed upon the quality and reliability of the results. Similarly, the development costs increase steeply with the quality of the intended results.

If a drag coefficient of 0.50 is to be achieved, hardly any costs result for the aerodynamic development. If the individual results published in the literature are properly applied, wind tunnel tests can be eliminated completely for such a conservative development goal. If a value of 0.45 is sought, development costs still remain moderate. Several days of testing in a model wind tunnel on a model with a scale of 1:4 or 1:5 will assure that the objective is reached. The development time for the new model is not lengthened. On the other hand, a value of 0.40 is achieved only at high cost. Measurements requiring a number of weeks on painstakingly prepared, full-size models in a large wind tunnel are indispensable. The suggestions for modification of the shape must be clarified in consultation with the stylists, the designers and the production engineers; the development process is affected considerably by this. If a value of 0.30 is set as target, development of the shape must precede the actual development of the vehicle. With the present state of knowledge in automobile aerodynamics, several months must be scheduled for this. This procedure also requires full-size models and a large wind tunnel. The absolute magnitude of the development costs is dependent upon the specific company and cannot be given in generally valid figures. Buchheim et al.1-65 said that 1000 hours in the wind tunnel were necessary to develop


the Audi 100 III. However, this figure includes the work for engine cooling and compartment ventilation as well. Assuming a cost of $1500 per hour, this alone results in $1.5 million wind tunnel cost, not taking into account the cost of the models and of numerical calculations.

The increase in development costs resulting from higher development goals must be counteracted by the availability of greater in-depth knowledge and the application of theoretically sound development procedures. Already today there are methods on hand to predict fairly accurately the characteristics of an engine cooling system or a passenger compartment heating system (see Chapters 9 and 10). Numerical methods, which allow the calculation of the external flow field or parts thereof, are under development. What they can accomplish today and what they are unable to predict is outlined in Chapter 13. In the future, improved predictions can be expected from new calculation procedures. Even so, they will not replace testing, and at most will facilitate test preparation and evaluation, and thus will allow the test expenditure—in terms of costs as well as time—to be kept in check.

1.4 Notation

A Ac

D P Q T

vx V a cD cT e h I m w A a

ß P

frontal area; Fig. 1.3 cooling air inlet area; Fig. 1.5 aerodynamic drag engine power heat flux; Eqn 1.3 tangential force; Fig. 1.25 oncoming flow velocity; Fig. 1.25 driving speed wheelbase; Fig. 1.44 drag coefficient; Eqn 1.2 tangential force coefficient; Fig. 1.25 ground clearance height of vehicle length of vehicle vehicle mass width of vehicle aspect ratio angle of attack angle of yaw; Fig. 1.25 air density

Chapter 2

Some fundamentals of fluid mechanics Dietrich Hummel

2.1 Properties of incompressible fluids 2.1.1 Density

The density of any material is defined as its mass per unit volume. In fluids this property depends on the pressure p and on the temperature T. The highest speeds achieved by land-vehicles during record attempts (Fig. 1.51) are in the order of the speed of sound, which is for air a = 340 m/s = 1225 km/h = 765.6 mile/h. In the flow field of a body exposed to such a free stream the compressibility of the air, i.e. the variation of density due to changes of pressure and temperature, is very important. On the other hand, most vehicles including racing cars are operated at speeds V which are lower than one-third of the speed of sound. For this speed range the variations of pressure and temperature in the flow field vary little from those of the free stream values, and therefore the corresponding density changes can be neglected. Thus the fluid can be regarded as incompress-ible. In the case of air the density is a constant property, the numerical value of which is, according to US standard atmosphere sea-level conditions (p = latm, T = 288 K)

p = 1.2250 kg/m3 (= Ns2/m4)

2.1.2 Viscosity

Viscosity is caused by the molecular friction between the fluid particles; it relates momentum flux to velocity gradient, or applied stress to resulting

Y * \

<Mv)

rf/;////,-Figure 2.1 Distribution of velocity and temperature in the vicinity of a wall (schematic)

47

48 Some fundamentals of fluid mechanics

strain rate. According to Newton's law for the flow parallel to a wall (Fig. 2.1)

τ = μ — (2.1)

the shear stress τ is proportional to the velocity gradient du/dy. The constant factor μ is a property of the fluid and is called dynamic viscosity. In general its value depends on the temperature; see Schlichting.2-1 Often the quotient

v = B ( 2 . 2 )

is used, which is called kinematic viscosity and which depends on pressure and temperature. For incompressible fluids only, a temperature depend-ence exists for μ and v. For air the US standard atmosphere sea-level values are

μ = 1.7894 x ΗΓ5 Ns/m2

v = 1.4607 x 10~5 m2/s

The viscosity of a real fluid is the physical reason for the occurrence of a friction drag in the presence of a velocity gradient at a wall.

2.1.3 Thermal conductivity

This property of a fluid is connected with its ability to transport heat by conduction. Thermal conductivity relates heat flux to temperature gradient. According to Fourier's law

the heat flux q per unit area and time is proportional to the temperature gradient (Fig 2.1). The negative sign indicates that the heat flux is reckoned as positive in the direction of a negative temperature gradient. The constant k is a property of the fluid which is called thermal conductivity. In general its value depends on the temperature. For air, the US standard atmosphere value is

k = 0.0253 J/m s K = N/s K

The thermal conductivity of a fluid is the physical reason for the heat transfer in the presence of a temperature gradient at a wall.

2.2 Flow phenomena related to vehicles

The various flow phenomena related to vehicles can be divided into two groups. These are (a) the external flow around the vehicle, including all details of its surface, and (b) the internal flow through different systems such as carburettor, engine, exhaust system and cooling system as well as the flow through the passenger cabin itself; see section 1.1.1.

Flow phenomena related to vehicles 49

2.2.1 External flow

The external flow around a vehicle is shown in Fig. 2.2. In still air, the undisturbed velocity V«, is the speed of the car. Provided no flow separation takes place, the viscous effects in the fluid are restricted to a thin layer of a few millimetres thickness, called the boundary layer. Beyond this layer the flow is inviscid and its pressure is imposed on the boundary layer. Within the boundary layer, the velocity decreases from the value of the inviscid external flow at the outer edge of the boundary layer to zero at the wall, where the fluid fulfils a no-slip condition. When the flow separates at the rear part of the vehicle (Fig. 2.2) the boundary layer is

Figure 2.2 Flow around a vehicle (schematic)

'dispersed', and the flow is entirely governed by viscous effects. Such regions are quite significant compared with the characteristic length of the vehicle. At some distance from the vehicle, there exists no velocity difference between the free stream and the ground. Therefore, in vehicle-fixed coordinates, the ground plane is a stream surface with constant velocity Vx and at this surface no boundary layer is present. This fact is very important for the simulation of flows around vehicles in wind tunnels.

The boundary layer concept is only valid for large values of the order

Re, = ψ> 104 (2.4)

This dimensionless parameter is called the Reynolds number. It is a function of the speed of the vehicle VOo, the kinematic viscosity v of the fluid and a characteristic length of the vehicle, e.g. its total length / as in Fig. 2.2. The character of viscous flow around a body depends only on the body shape and the Reynolds number. For different Reynolds numbers entirely different flows may occur for the same body geometry. Thus the Reynolds number is the dimensionless parameter that characterizes a viscous flow.

Flows around geometrically similar bodies are called 'mechanically similar' if the Reynolds number according to Eqn 2.4 has the same value for different body lengths /, airspeeds VOo and fluid properties v. Mechanical similarity is the basis for model tests. The results of tests on scale models in terms of dimensionless aerodynamic coefficients are the same as for the original vehicle if Reynolds numbers are the same; see section 11.4.2. Sometimes it is difficult to fulfil this similarity requirement. For models smaller than the original vehicle it is necessary to increase the free stream velocity V«,, but the value must remain in the low subsonic regime. This means that it is not possible to perform tests on very small


models in supersonic flow since the similarity law of compressible flow, which demands equal Mach numbers Ma^ = VJa^ = constant for both cases, would then be violated.

Sometimes we need to investigate the flow around details such as a mirror, separate from the car. In such a case, correct results will be obtained if the tests are performed at the same Reynolds number as a characteristic dimension of this detail, for example the mirror's diameter, and on the local velocity in the vicinity of this detail at the vehicle, which is usually different from the free stream velocity; see Chapter 4.

2.2.2 Internal flow

Internal flow is that which is surrounded by walls. In the simple case of Fig. 2.3 all streamlines are parallel to the pipe axis. In general, internal flows cannot be divided into an inviscid flow far away from the walls and a

0 = 2/? I

L Figure 2.3 Velocity distribution of the flow through a pipe

viscous boundary-layer flow close to the walls. The effects of viscosity are found everywhere in the flow field. The development of an internal viscous flow is again characterized by the Reynolds number

V D Reu = ^ψ- (2-5)

based on a velocity typical for the problem, e.g. the mean velocity Vm as in Fig. 2.3, and the pipe diameter D as a typical length. For different values of ReO, different types of flow may occur.

2.3 External flow problems 2.3.1 Basic equations for inviscid incompressible flow

The development of the inviscid flow at the outer edge of the boundary layer determines the pressure distribution on the body surface. Therefore the fundamentals of such a flow are discussed first.

To begin with, the law of mass conservation has to be formulated. The most simple form of this law is for incompressible flow (p = constant):

ws = constant (2.6) where s denotes the local cross-section of a small stream-tube as in Fig. 2.2 and w is the local velocity, which is assumed to be constant across s. Eqn 2.6 indicates narrow distances between the streamlines in regions of high velocity and vice versa, see Fig. 1.1.

Furthermore the flow obeys Newton's well-known law of momentum conservation: mass times acceleration is equal to the sum of the acting

External flow problems 51

forces. If this law is applied to an inviscid flow, it turns out that inertia forces and pressure forces are balanced. The integration of the momentum equation along a streamline for incompressible flow leads to

g = p + ^ w2 = constant (2.7)

Eqn 2.7 is Bernoulli's equation, which relates the pressure p and the velocity w along a streamline (p is static pressure, pw2/2 is dynamic pressure, and g is total pressure).

In inviscid flow, the sum of static pressure and dynamic pressure is constant along a streamline. Eqn 2.7 indicates low pressure in regions of high local velocities and vice versa. If the flow comes to rest, w = 0, a so-called 'stagnation point', as on the nose of a vehicle (Fig. 2.2), the static pressure there will be equal to the total pressure, and this is the highest possible pressure in the flow field. For the external flow around a vehicle, as in Fig. 2.2, all streamlines start from the same free stream with static pressure poo and free stream velocity V«,. Therefore the total pressure g is constant for all streamlines

g = Poo + 2 Vi = constant (2.8)

Such a flow field is called 'isoenergetic', and g is Bernoulli's constant of it.

2.3.2 Applications

The fundamental equations for inviscid flow may be applied to simple examples related to vehicle aerodynamics and experimental techniques.

The two-dimensional flow around a vehicle-shaped body is shown in Fig. 2.4. This flow is a considerable simplification of a three-dimensional flow around a vehicle, and may be regarded as a qualitative picture of the flow at the centre section of a car. The upper figure indicates the streamlines. Three stagnation points occur - in the nose region, in the corner between

side Figure 2.4 Flow field and pressure distribution for vehicle-shaped body in two-dimensional inviscid flow (schematic)


bonnet and windscreen, and at the trailing edge. The pressure distribution on the contour is drawn schematically as cp (x/l) in the lower figure, where

(2.9) JL v2

2 ™

is the dimensionless pressure coefficient. The application of Eqns 2.7 and 2.8

P + -hrw2 = PoD +4- Vl

leads to

w (2.10)

In the stagnation points of the flow field, w = 0, Eqn 2.10 yields cp = 1. At the lower surface of the vehicle, the pressure is higher than the free stream pressure, cp > 0, but for very small ground distances even suction, cp < 0, may be present. At the upper surface, high pressures, cp > 0, are observed in the region of the bonnet and the windscreen, whereas high suction, cp < 0, is found at the cabin roof. On the rear part of the vehicle's upper surface a steep pressure rise occurs, and it is in this region where considerable differences exist between the real flow of a viscous fluid and the inviscid flow shown here. The pressure distribution in Fig. 2.4 indicates that the pressure level on the upper side of the vehicle is much lower than on the lower side. This means that a net upwards lift force acts on the vehicle. If all x-components of the pressure distribution on the vehicle surface are integrated, the result for the drag will be D = 0. This is the well-known d'Alembert's paradox, which means that in incompressible, inviscid, two-dimensional flow no drag is present. In the real, viscous flow there exists a drag force, but it cannot be explained by considering an ideal, inviscid fluid.

From the pressure distribution shown in Fig. 2.4, suitable positions for the air intake and outlet for the cooling and ventilation system can be chosen. The intake may be placed in regions of high pressure, e.g. in the nose region or in front of the windscreen, whereas the outlet may be arranged in a region of suction. In this case the pressure difference can be

m

w g

€

ϊ ϊ 9 P

Figure 2.5 Pitöt-static probe for velocity measurements in fluids


used to assist the cooling and the ventilation systems, and fans can be kept small. Practical examples for this are discussed in Chapter 6.

As another example for the application of the basic equations of inviscid flows, the measurement of velocities may be considered. Figure 2.5 shows a Pitot-static probe. At the tip of the probe a stagnation point occurs in the flow and from this point the total pressure g is taken through a small tube. A few diameters downstream of the tip of the probe, the static pressure p corresponding to the velocity w acts on the probe surface. This static pressure is taken through some holes around the circumference of the probe body. The application of Eqn 2.7 leads to

w - V 2(g - P) (2.11)

If the pressure difference g — p is measured by manometer, the corresponding velocity can be calculated from Eqn 2.11. The Pitöt-static probe is widely used for velocity measurements in fluids, as well as for measurements of total pressure g (Pitöt probe) and static pressure p (static probe). In these cases the pressures g and p are measured separately against some reference pressure. To ensure accurate results the probe axis should be carefully aligned with the local flow direction; see section 12.1.2.

2.3.3 Effects of viscosity

Despite the thinness of the boundary layer at the wall, the viscous flow within it has a strong influence on the development of the whole flow field. The occurrence of drag in two-dimensional incompressible flow can only be explained by these viscous effects.

2.3.3.1 Laminar and turbulent boundary-layer development

The flow in a boundary layer along a thin flat plate is shown in Fig. 2.6. The corresponding external flow has parallel streamlines and constant velocity V«, and pressure p«,. The viscous flow within the boundary layer fulfils the 'no-slip' condition along the wall. In the front part of the plate the boundary layer flow is steady and (almost) parallel to the wall. This

p.. =const.

v h

-laminar ■*(-· turbulent -

transition Vm

Kc / / / / / / 7 / / / ? > / / > / >

δ(χ)

i / / V / /—7

i / ( y )

Xtr

Figure 2.6 Boundary layer along a thin flat plate (dimensions in ^-direction very much enlarged)


state of the flow is called laminar. The thickness of the boundary layer increases downstream according to

V (£-) · " (2.12)

With increasing distance x and kinematic viscosity v and with decreasing free stream velocity V«>, the boundary layer thickness increases.

The laminar state of the boundary layer flow is stable against disturbances for certain conditions only. At a distance x = xtr from the leading edge of the plate a transition to the so-called turbulent state of the boundary layer takes place. The transition between the two states of the boundary layer flow is largely governed by the value of the Reynolds number. For the flat plate, transition occurs around

Rex = V~x« = 5 x l 0 5 (2.13)

but this value applies only for a negligible pressure gradient in the external flow. In cases with a pressure gradient, a pressure decrease in the flow direction leads to a stabilization of the laminar boundary layer, whereas an adverse pressure gradient causes an earlier transition to the turbulent state. Furthermore, disturbances of the laminar flow, e.g. by surface roughness, may lead to transition; see Schlichting.2Λ In general, for medium Reynolds numbers transition from laminar to turbulent occurs in the region of minimum pressure, and with increasing Reynolds number the transition point moves upstream.

In the region of the turbulent boundary layer the flow is basically unsteady. The time-averaged flow is still attached and (almost) parallel to the wall, but in addition to the mean velocity u (y), fluctuations u'', ν', w' are superimposed in all three coordinate-directions. The velocity component parallel to the wall in Fig. 2.6 is thus

u(y,t) = u(y) + u'(y,t) (2.14)

and u (y) is defined as

At

(2.15)

W0 + Δ/

ü(y) = -^ Ju(y,t)dt

where At is chosen so large that ü (y) does not depend on At. Owing to the velocity fluctuations, intensive mixing takes place. Therefore, in addition to the shear stress caused by molecular friction according to Eqn 2.1, a shear stress due to turbulent mixing

Xturb = - p w V (2.16)

is present. In this expression u' and v' denote the velocity fluctuations in x-and ^-directions and u'v' is the time-average derived from Eqn 2.15. Since u' and v' always have the opposite sign, the expression for xturb is always positive. The turbulent velocity fluctuations manifest themselves in an apparent increase in the viscosity of the fluid. Therefore the boundary


layer thickness along the flat plate in Fig. 2.6 increases more rapidly downstream of the transition point as

„4/5 (2.17)

Due to the mixing process in turbulent boundary layer flow, the velocity profiles show higher velocities close to the wall than in laminar flow.

2.3.3.2 Separation

Laminar and turbulent boundary layer flows depend strongly on the pressure distribution which is imposed by the external flow. For a pressure increase in flow direction the boundary layer flow is retarded, especially near the wall, and even reversed flow may occur. This behaviour is shown schematically in Fig. 2.7. It can be seen that, between forward and reverse

= 0 (2.18)

Figure 2.7 Separation of the boundary layer flow at a wall (schematic)

flow, a dividing streamline leaves the wall. This phenomenon is called separation. For the separation point A, the condition

du

holds. Turbulent boundary layers can withstand much steeper pressure gradients without separation than can laminar boundary layers. This is because the turbulent mixing process leads to an intensive momentum transport from the outer flow towards the wall. For a pressure decrease in the flow direction there exists no tendency to flow separation.

2.3.3.3 Friction drag

If a velocity gradient duldy is present in a viscous fluid at the wall, due to molecular friction a shear stress xw acts everywhere on the surface of a

Figure 2.8 Determination of the drag of a body (example of two-dimensional flow)

body as indicated in Fig. 2.8. The integration of the corresponding force components in the free-stream direction according to

Dt = j>Tw cos φ dS (2.19)


leads to the so-called friction drag D{. In the absence of flow separation, this is the main contribution to the total drag of a body in two-dimensional viscous flow. Two examples may illustrate this.

0.012

0.1 0.2 0.3 0.4 0.6 0.8 1 2 lO"6 ReL —

3 4 6 8 10

Figure 2.9 Drag coefficient for flat plates and aerofoils as a function of Reynolds number, from Schlichting2Λ

Figure 2.9 shows results for the flow along a thin flat plate of Fig. 2.6. In order to get results which do not depend on the actual dimensions (length /, width b) of the plate and on the free stream conditions (dynamic pressure #oc = pôo2/2), a dimensionless drag coefficient

D CO =

P. 1/2 (2.20)

bl

is defined. In the case of a flat plate, only friction drag D = Df occurs on both sides of the plate. The planform area b x / is used as the reference area. In Fig. 2.9 the drag coefficient is plotted against Reynolds number Ret = Voo IN based on the total length / of the plate or of the chord length / in the case of an aerofoil.

Results for flat plates are discussed first. For laminar boundary layers, the resistance law is

CO 2.656 V(/^7) ( f o r t e / < 5 x 105) (2.21)

and for turbulent boundary layers over the whole length / of the plate and medium Reynolds numbers, the corresponding law is

cO = 0.148

V(^) (for 5 x 105 < Re{ < 107) (2.22)


For even larger Reynolds numbers, an asymptotic law holds:

0 91 CD = ( i ^ i ^ ( f o r Ä e ' > 1 0 7 ) ( 2 ·2 3 )

Assuming that the front part of the plate has a laminar boundary layer and the rear part a turbulent boundary layer, a transitional curve is derived, as shown in Fig. 2.9. For low Reynolds numbers this curve ends at the law for fully laminar flow, since no turbulent flow then occurs, and for high Reynolds numbers the transitional curve approaches asymptotically the law for fully turbulent flow, since the relative length of the laminar part decreases with increasing Reynolds number. In turbulent boundary layer flow, the friction drag is much higher than in the laminar case. This is because the turbulent mixing process leads to velocity profiles with a much steeper velocity gradient at the wall than in the laminar case. Furthermore, Fig. 2.9 indicates that in turbulent boundary layer flow the friction drag is increased by surface roughness. With increasing relative roughness kjl the drag coefficient increases and the depedence on the Reynolds number declines. A very rough plate behaves like the sum of a large number of blunt bodies. Details may be taken from appropriate textbooks (refs 2.1 to 2.7) and data works (refs 2.8 and 2.9).

The drag of bodies with finite thickness mainly consists of friction drag, which is small in all cases in which no flow separation occurs. This can be achieved by slender shapes on the rear part of the body which produce only a weak pressure rise in the flow direction. Shapes of this kind are aerofoils and 'streamlined' bodies. Some drag coefficients of aerofoils are drawn in Fig. 2.9. On the aerofoils NACA 0012, 4412 and 23012 the boundary layers are mainly turbulent and therefore the drag coefficients of these aerofoils are of the same order of magnitude as for the flat plate with fully turbulent boundary layer. Over large portions of the surface of the NACA-6 aerofoils the boundary layer is laminar and therefore the drag coefficients are considerably reduced.

Finally, Fig. 2.9 clearly indicates that the friction drag Df in general depends strongly on the Reynolds number.

2.3.3.4 Pressure drag

Blunt bodies, such as a circular cylinder, a sphere or a flat plate normal to the flow, show quite different drag characteristics. On the rear part of such bodies in the inviscid external flow, extremely steep pressure gradients occur which lead to flow separation (Fig. 1.2). The pressure distribution is thereby considerably altered when compared with the theoretical case of inviscid flow. As an example, Fig. 2.10 shows the pressure distribution for a circular cylinder. In the front part the pressure distribution is similar to that in inviscid flow, whereas on the rear part the flow separation leads to considerable suction. The pressure distribution is therefore asymmetrical with respect to the >>-axis. Integrating the force components in the free stream direction, resulting from the pressure distribution,

Dp = <j>p sin ydS (2.24)


360°

Figure 2.10 Pressure distribution and streamline pattern for a circular cylinder at different Reynolds numbers ReO = V^DN: (a) inviscid flow; (b) sub-critical flow, boundary layer laminar; (c) supercritical flow, boundary layer turbulent.

gives the so-called 'pressure drag' Dp, see Fig. 2.8. Friction drag also results from the wall shear stresses, but for blunt bodies the pressure drag is predominant. In general, the drag of a body may be written as

D = Df + Dp (2.25)

For blunt bodies, the drag coefficient

D C D , A — (2.26)

VIA

is based on the free stream dynamic pressure pVL/2 and on the largest cross-section of the body, A. This is the projection of the body in a plane perpendicular to the free stream (frontal area).

Figure 2.11 shows this drag coefficient plotted against the Reynolds number ReO = VooD/v for a circular cylinder and a flat plate. If very small

4.0

2.0

, 0

I 0.6 cD 0.4

0.2

0.1

YM.

Lh=

"R.I ΤΓΤ ffi

— ' @ 3 D

1 1

rN

11

«—U-m b)

^trr \

ftLk c)

4 6 8 103 104

4 6 8

ReD =

4 6 8 Vm D Ί06

Figure 2.11 Drag coefficients of blunt bodies as a function of Reynolds number. Points (b) and (c) as in Fig. 2.10, two-dimensional flow


Reynolds numbers are excluded, for bodies with sharp edges flow separation will occur in the same way for all Reynolds numbers, and therefore the drag coefficients do not depend on the Reynolds number. However, for slightly rounded bodies, separation is not fixed and the position of the separation point depends on the state of the boundary layer. At low Reynolds numbers the boundary layer is laminar; see case (b) in Figs 2.10 and 2.11. The separation point is located close to the point of maximum thickness. The resulting 'wake' region behind the body is broad and the corresponding drag coefficient is high. At a critical Reynolds number of about ReOcnt = 5 x 105, a sudden transition to a turbulent boundary layer occurs in the front part of the body. The turbulent boundary layer remains attached longer; see case (c) in Figs 2.10 and 2.11. The corresponding wake region is narrow and the drag coefficient is much lower than for sub-critical Reynolds numbers.

Generally, a sudden change of the drag coefficient of a vehicle as a function of its Reynolds number should be avoided. For this purpose, flow separation is fixed at certain points, for instance at the upper edge of the sloping rear window, Up to this point the shape of the body should be designed so that the flow remains attached and that the pressure rise is as large as possible for various free stream conditions. The resulting wake should be as small as possible to obtain low drag. The drag coefficients achieved by present-day European cars (excluding sports cars and racing cars) range from 0.30 to 0.52; see Hucho. ° In general, the dependence of these drag coefficients on Reynolds number is very small and sudden changes do not occur. This demonstrates that the predominant part of the drag of these vehicles is pressure drag. For some unconventional 'streamlined' body shapes, drag coefficients have been measured in the region 0.15 to 0.27. For bodies of this type the portion of pressure drag is relatively small. These drag coefficients thus contain a large proportion of friction drag and therefore they depend noticeably on the Reynolds number; see Hucho.2 10

Figure 2.12 Flow separation on a bluff body (separation line perpendicular to the flow direction)

The flow separations that lead to a pressure drag can be divided into two different types. As shown in Fig. 2.12, the separation line may be located perpendicular to the flow direction. In this case, vortices are generated -the axes of which are also perpendicular to the outer flow. Thus the velocity components parallel to the vortex axes are very small. A symmetrical flow in the separated region as shown in Fig. 2.12 exists only for small Reynolds numbers, e.g. on a circular cylinder, for ReO < 60; see Schlichting.2Λ For larger Reynolds numbers, periodic vortex shedding

'///////

//////////] 5)


occurs and the flow in the separated region is basically unsteady. The kinetic energy of the vortex field is rapidly dissipated by turbulent mixing and irreversibly converted into frictional heat. This leads to a considerable total pressure loss in the region behind the body and the corresponding deficit in kinetic energy is equal to the work which is necessary to overcome the pressure drag. Behind the body a wake is formed in which time-averaged, relatively uniform suction and very low flow velocities are present.

The other type of flow separation is characterized by a separation line inclined with respect to the oncoming flow, see Fig. 2.13. In this case, vortices are shed, the axes of which are roughly parallel to the separation lines. A considerable velocity component, parallel to the separation line

Figure 2.13 Flow separation on a body with oblique blunt base (separation line at an angle to the flow direction)

and therefore in the direction of the vortex axes, is present. Thus, a well-ordered, steady three-dimensional flow separation is found. On the rearward surface of the body this separated flow induces suction which leads to a pressure drag. On the inclined base of the body the flow is attached. In the vicinity of the vortices the pressure distribution is characterized by suction peaks. This kind of flow separation is well known in the aeronautical sciences from investigations on the flow field of delta wings; see the survey given by Hummel.211 Behind the body only relatively small total pressure losses are observed. The flow field of the concentrated vortices, however, contains a lot of kinetic energy which corresponds to the work necessary to overcome the pressure drag.

A relationship exists between both types of flow separation behind blunt bodies, which has already been investigated in the aeronautical sciences; see Thwaites2 12 and Hummel.2 n As the angle of attack of a delta wing is increased a sudden change of the structure of the vortices is observed which is called 'vortex breakdown' or 'vortex bursting'. The phenomenon is not yet fully understood. It leads, however, to a destruction of the well-ordered three-dimensional vortex flow; this process starts in the vortex centre and spreads downstream over large portions of the vortex. The final state is a separated flow in the region of the vortex centre which is


embedded in a well-ordered three-dimensional flow. Systematic ex-perimental investigations on vehicles with different inclinations of the rear surface have been carried out by Janssen and Hucho,2 13 Morel,2'14 and Ahmed.2 2 2 ' 2 2 3 These investigations clearly indicated both types of flow separation. Transition from one type to the other leads to characteristic changes of the pressure drag which are also known from delta wings. This is discussed in detail in section 4.3.2.4.

Table 2.1 Drag coefficients for different bodies (cDjC = DlqooSc, see Eqn 2.6, *subcritical flow), after Hoerner29

Body

Circular plate

Sphere

Half-sphere

60°-cone

Cube

Cube

Circular cylinder l/D > 2

Circular cylinder l/D > 1

Streamlined body l/D = 2,5

Circular half-plate at a ground plane

Streamlined half-body at a ground plane

Flow situation

. * . . --

-e - 3 - <

- Ö - ^

- * J ■—4io U-/- .J

- M° -°m -+~ |

' ' . ■ ■ , V / , V 7 //

-** V^l\ //////////

CD.c

1.17

0.47*

0.42*

0.50

1.05*

0.80*

0.82

1.15

0.04

1.19

0.09

On the drag problem of a body, it might be mentioned finally that the shape of a body in front of the largest cross-section has only minor influence on the total drag. The main contributions to the drag force originate from the rear part of the body. It is not important to find a proper shape to divide the oncoming flow but it is very important to design a rear body surface which brings the divided streamlines smoothly together. Optimum shapes are 'streamlined' bodies having a very slender rear part. Table 2.1 lists some data on drag coefficients for different bodies.


2.3.3.5 Overall forces and moments

In addition to the drag discussed in detail so far, other forces and moments occur on a vehicle which are shown schematically in Fig. 2.14. In symmetrical flow (ß = 0) the drag D is accompanied by a lift force L (see the pressure distribution of Fig. 2.4). Furthermore, a pitching moment M with respect to the lateral axis (y-axis) is present. The three components L, D and M completely determine the vector of the resulting airforce. For a known position of the centre of gravity, which is used as the pitching moment reference point, the additional forces acting at the front and rear axle resulting from the flow around the vehicle can easily be evaluated.

Figure 2.14 Forces and moments acting on a vehicle (e.g. = centre of gravity)

In cross-wind conditions (β Φ 0) an asymmetrical flow field around the vehicle is present. In this case, in addition to the forces and moments mentioned so far, a side force Y is observed. Furthermore, there occur a rolling moment R with respect to the longitudinal axis (x-axis) and a yawing moment N with respect to the vertical axis (z-axis). Thus six components L, D, M and Y, R, N determine the vector of the total force. For a known position of the reference point the additional forces acting at the four wheels of the vehicle can be evaluated.

The forces and moments acting on vehicles may be obtained from wind tunnel measurements on full-scale cars or on smaller models. Three- and six-component measurements are carried out in symmetrical and in asymmetrical flow respectively. In order to get results from model tests that are also valid for the full-scale vehicle, the Reynolds similarity law has to be fulfilled. This means that for both cases the Reynolds number,

V I ' v

from Eqn 2.4, has to be the same. The results will be independent of the actual dimensions of the tests, if dimensionless coefficients are formed by analogy with the drag coefficient as


cD = (drag)

cM= (pitching moment) (2.27) f V.AI

Y cY = (side force)

P 2

P 2

P 2

P 2

VlA

M

VlAl

Y

VlA

R

VlAl

N

cR = (rolling moment)

cN = (yawing moment)

All these coefficients are based on the free stream dynamic pressure pFi /2 and on the largest cross-section, the frontal area Λ, of the body. In addition, a characteristic dimension such as the total length / of the vehicle is used for the three moments.

The dimensionless aerodynamic coefficients can only be dependent on other dimensionless parameters of the flow problem, e.g. on the Reynolds number Rei or on the angle of yaw ß. In this relation, a problem of stability occurs which may be explained for a vehicle in cross-wind, see section 5.2.3. In asymmetrical flow, a yawing moment acts on the body and the corresponding coefficient is cN. This yawing moment has the tendency to rotate the vehicle about its vertical axis (z-axis). The vehicle is aerodynamically stable if the resulting yawing moment has the tendency to reduce the angle of yaw. With the notation of Fig. 2.14, this is valid for

dc —£- > 0 (stable) (2.28) dß

Conversely, the vehicle is aerodynamically unstable for

< 0 (unstable) (2.29) dcN

dß

As will be shown in section 5.2.3, cars and box type vans generally are aerodynamically unstable. Only very long and thus unacceptable rear fins would lead to aerodynamic stability according to Eqn 2.28.

Similarly, as discussed for the drag coefficient, all other forces and moments may be influenced by proper shape of the vehicle. Without going into detail, some possibilities may be discussed. The shape of the car's underside has a large influence on the overall lift. With small ground clearances and a smooth shape of the lower surface, high velocities may be obtained between the vehicle and the ground. This leads to low pressures at the underside of the vehicle which keep the lift force small; see sections


7.3.1 and 7.4.1. Vortex type flow separations as in Fig. 2.13, related to inclined shapes of the base of a vehicle, may cause considerable contributions to the overall lift. Furthermore, the behaviour of vehicles in cross-wind conditions can be influenced quite strongly by proper shaping; see Hucho.2 15 For small angles of cross-wind, larger values of the yawing moment derivative dcN/dß may be allowed since the yawing moment N is still small and the main problem in this case is to reduce drag. For larger angles of yaw, the drag must be allowed to increase since the main problem is now to keep the yawing moment to a tolerable order of magnitude. How this can be achieved will be discussed in detail in section 5.2.3.

2.3.3.6 Thermal boundary layers

Like the velocity field of a viscous flow around a body, the temperature field has a boundary layer character. For instance, the region of increased temperature in the vicinity of a heated body is restricted to a thin layer close to the body. Such a thermal boundary layer is sketched in Fig. 2.15 for the simple flow along a flat plate. The corresponding velocity boundary layer is shown in Fig. 2.6. The wall temperature Tw of the heated plate may be kept constant. Within the thermal boundary layer of thickness δτ, the temperature decreases to the value T^ in the outer flow.

Too = konst.

Poo = const. |

V«, V1

^

"*

I

ί*

— lam mar - ^

Too

^^

A

,-.— k Tlv) V ' "

-V U T - W ^

*■ turbulent -

| Too .

-f « T ( X )

Λ

^ Η - "

νπν) , . , > , Ν ι J ifc

— f.. *

Figure 2.15 Thermal boundary layer along a thin flat plate (dimensions in y-direction very much enlarged)

For laminar flow according to Eqn 2.12 the thickness of the velocity boundary layer increases as δ ~ ^ν; for incompressible flow (p = constant) this also means δ ~ )μ. By analogy, the corresponding result for the thickness of the thermal boundary layer is

δτ~ Jk

The ratio of the two boundary layer thicknesses is thus

(2.30)

In this equation cp denotes the specific heat capacity for constant pressure of a gas; for liquids cp may be replaced by the specific heat of the fluid. The expression \icplk represents a dimensionless quantity


Pr = ^ (2.31)

which is called the Prandtl number. This parameter depends only on fluid properties. Its value is mainly governed by the ratio of dynamic viscosity and heat conductivity, which is actually the ratio of the fluid property for momentum transport to the fluid property for heat transport. The Prandtl number of air is Pr ~ 0.7. This means that in this case the two thicknesses of the velocity and the thermal boundary layer are of the same order of magnitude, and for approximations the Prandtl number can be set as Pr = 1. For other fluids, different values may apply: the Prandtl number for water is Pr = 7 (δ > δτ) and for highly viscous oils Pr = 10000 (δ > > bT).

In incompressible flows, no work is necessary for the compression of the fluid and the frictional heat produced by dissipation of kinetic energy is of minor importance for the temperature distribution in the boundary layer. The essentials are heat transport by thermal conduction according to Eqn 2.3 and heat transport by convection. This means that the temperature field depends on the velocity field, but the converse does not hold. A particularly simple situation is that of the flow along a flat plate as in Figs 2.6 and 2.15 with p = p^ = constant, and for the special case Pr = 1. For laminar flow the velocity profiles u (y) and the temperature profiles T (y) coincide in the dimensionless form

u(y) T(y) - Γ . V T - T " oo -* w ■*- oo

This function is shown in Fig. 2.16

(2.32)

Y*

t 1

' / /

, ' /}

V„

»J . /

. / /? Φ) '////// /*

Figure 2.16 Velocity and temperature distribution in the laminar boundary layer along a flat plate without frictional heat and for Pr = 1(δ = δΓ)

In Eqn 2.32 a relation between the velocity gradient at the wall (dw/dy)w and the temperature gradient at the wall (d77dy)w is demonstrated. This means that the shear stress at the wall according to Eqn 2.1 is related to the heat flux at the wall according to Eqn 2.3. After some calculation Eqn 2.32 yields

Nu(x) = ViCf (x)Rex (2.33)

where c{ (x) is the dimensionless shear stress at the wall


cm = - ^ - (2.34) P-V2

2 " Rex is the Reynolds number Rex = VxxN based on the local distance x from the apex of the plate, and

"*> - «i^b ( 2 3 5 > is the dimensionless heat flux at the wall, which is called the Nusselt number. The result according to Eqn 2.33 is the so-called Reynolds analogy between shear stress and heat flux at the wall. In section 9.5 it will be shown that experimental results on engine radiators can be arranged by application of the Nusselt number defined in Eqn 2.35.

In turbulent flows according to the mixing process an eddy heat flux

<7mrb = pCpVT' (2.36) is observed by analogy to Eqn 2.16. The total shear stress and heat flux in turbulent flow is thus

du du τ = μ j - - ?Wv' = (μ + Ατ) — (2.37)

q = ~ k — + pcp7T = - (* + CpAq)— (2.38)

Irrthese equations u'', v', T are the fluctuations derived in Eqn 2.14, and u'v' and v'T denote time averages calculated for these quantities, as indicated in Eqn 2.15. The apparent increase of dynamic viscosity and heat conductivity is expressed in Eqns 2.37 and 2.38 by means of the exchange coefficients for momentum Λτ and heat Aq.

In addition to the molecular Prandtl number Pr = \kcplk it is convenient to introduce a corresponding, dimensionless, turbulent Prandtl number

Pri=-^- (2.39)

which is important for the transport phenomena in turbulent flows. A good approximation for the turbulent Prandtl number is Prt = 1. This means that in turbulent flows the same mechanism for the eddy viscosity and the eddy conductivity is present. For the special case Pr = 1 and Prt= 1, which is approximately valid for air, the relation between velocity and temperature profiles according to Eqn 2.32 holds again; this means that the Reynolds analogy defined in Eqn 2.33 is also valid for the turbulent boundary layer along a flat plate as shown in Figs 2.6 and 2.15.

From Eqns 2.33, 2.34 and 2.35, the heat flux can be deduced as

k{T^-T^) d(u/V^)w q- = 6 ' d(y/6) ( 2 ' 4 0 )

This equation demonstrates that the heat flux at the wall is propertional to the heat conductivity k of the fluid and is proportional to the imprinted


temperature difference Tw - T^. In the front part, where the boundary layer thickness δ is small, high heat flux occurs. Downstream of the laminar/turbulent transition point the thickness of the turbulent boundary increases quite rapidly, but the corresponding increase of the velocity gradient of the turbulent velocity profiles at the wall is predominant. Therefore, in turbulent boundary layers, a higher heat flux at the wall is observed than in laminar boundary layers.

For many technical problems the situation is not as simple as in the case of the flow along a flat plate. Therefore Eqn 2.40 is often written as

q„ = a ( r w - Γ . ) (2.41)

and the special problem is now found in the new heat transfer coefficient a which may be taken from the literature for different flow conditions.2 16

2.3.4 Special problems

2.3.4.1 Aerodynamic noise

The flow around a vehicle causes aerodynamic noise; see section 6.5. In almost all cases the physical reason is periodic flow separation from certain elements of the surface - gutters, mirrors and the radio antenna, for instance. Such a periodic flow separation is sketched for a circular cylinder in Fig. 2.17. It is present in the Reynolds number range 60 ^ ReD ^ 5000. For smaller Reynolds numbers a non-periodic, symmetrical wake (as in Fig. 2.10) occurs, whereas for larger Reynolds numbers a turbulent mixing process without the existence of discrete vortices can be observed.

-^j> Figure 2.17 Periodic vortex shedding from a circular cylinder (schematic)

In the region of periodic flow separations, vortices are shed from both sides of the body in alternating sequence. These vortices move downstream in the wake and they can be observed over a long distance. In a coordinate system moving downstream with the vortices, a regular pattern of these vortices is found, which is called a von Karman's vortex street. Due to periodic vortex shedding, the whole flow field is basically unsteady. At a certain point of the flow field, all flow quantities change with the frequency n of the vortex separation from the body. The dimensionless frequency is an important parameter

nD St = _ - (2.42)

which is called the Strouhal number. This parameter is a unique function of the Reynolds number which is shown in Fig. 2.18 for a circular cylinder. For Re > 103 the Strouhal number is practically independent of the Reynolds number and its value is St = 0.21. A simple calculation for


St = nD

0.22 i

0.20

0.18

0.16

0.14

0.12

k /Co

I £

V

jg$r

l·8 ol

^J^LLZ^ vy 7 t

D O (

T °c

T * C

EBL.

r?pv\

[cm]

).0235

).0613 ■

).0989

).3180 .

V 0.6350

I I I

ΤΊ2.0

it cD

10 2 4 6 8 1 0 2 2 4 6 810 3 2 4 6 8 104

Re- V~D

Figure 2.18 Strouhal number as a function of Reynolds number for the flow around a circular cylinder, from Schlichting2Λ

D vx V

Re n

= = = = =

4 mm 5 m/s 1.461 x V^D/v = StVJD

10"5m2/s = 1369 = 2621/s

shows that the resulting frequency lies in the audible range, so that pressure fluctuations within the unsteady flow field manifest themselves as noise.

Preventive measures against such noise are (a) to avoid inducing the flow separations and (b) to disturb the periodic wake flow by proper means. A survey of the present knowledge on airframe noise has recently been given by Heller and Dobrzynski.2

2.3.4.2 Aeroelastic effects

These problems arise when aerodynamic forces acting on an elastic body cause elastic deformation of the body which influences the inducing aerodynamic forces.

The static aeroelastic problems will be considered first. The aerodyna-mic loading causes a deformation and the new geometry leads to modified aerodynamic forces. The final deformation is reached for equilibrium between aerodynamic and elastic forces. An example of this kind of problem is the deformation of a radio antenna due to wind loads. The modifications of the aerodynamic forces result from the fact that the deflected flow is no longer perpendicular to the axis of the antenna. If velocity is increased, the static aeroelastic forces will also increase and at a certain speed the antenna will fracture.

Much more difficult to understand are the dynamic aeroelastic problems. Consider a body in a periodic motion of a certain frequency. In the presence of a flow the corresponding aerodynamic forces are also periodic with the same frequency. During the motion of the body the


aerodynamic forces may act in the direction of motion or against it. If the oscillating system, time-averaged over the whole period of the motion, does not absorb energy from the flow, no danger of self-excited oscillations exists. As an example of this kind (Fig. 2.19) the combined beating and twisting oscillations of a flat plate are considered. Without a phase difference between the two motions, i.e. if maximum stroke and maximum twist occur simultaneously, the aerodynamic force partly acts in the direction of motion and partly against it. Therefore, when time-averaged, no work is done by the aerodynamic forces. But there exist other situations for which the aerodynamic forces perform work at the oscillating system.

Positive work y^

7* ♦^

Negative \ work

ΤΓ

Positive work

Negative work

Phase difference 0* Total work zero

1 _ v

Positive work

Positive work

\Oscillating motion

i aerodynamic force

Figure 2.19 Energy balance for a flat plate with combined beating and torsional oscillations (schematic), after Forschung218

In the bottom example of Fig. 2.19 the phase difference between beating and twisting motion is 90° and the maximum twist is present for zero stroke. In this case the aerodynamic force always acts in the direction of motion. Therefore a self-excited oscillation occurs, called flutter. In such a situation the inner damping of the elastic system is no longer sufficient to maintain stability and an abrupt instability of the whole system is observed.

In the example of Fig. 2.19 the aerodynamic forces result from the unsteady attached flow around the flat plate. There also exist flutter effects for which the stimulating aerodynamic forces are due to periodic flow separations on the rear part of the body. Details cannot be discussed here, but may be taken from the survey on these problems given by Försching.2 18


2.3.4.3 Transport of solids

The flow around a vehicle may contain different inhomogeneities such as rain drops, mud particles and insects. The behaviour of these in-homogeneities in the flow field of the vehicle are very important for the practical use of the vehicle; see sections 6.4 and 8.7.

streamlines

f l ight-path of particle

D Drag

/ Inertia force

Figure 2.20 Particle motion in a flow field: (a) velocity vectors; (b) acting forces

The motion of particles in a flow field, the density of which is different from that of the fluid, is sketched in Fig. 2.20. The flight paths of the particles and the streamlines are different. For an arbitrarily located point of the flow field the local flow velocity Vs is tangential to the streamline and the local particle velocity vp is tangential to the flight path. Thus the flow around the particle is governed by the relative velocity

V rel Vr (2.43)

and the drag force D acts on the particle in the direction of this relative velocity. For asymmetrical particle shapes a lift force may also be present, but this is not taken into account for the present considerations. The flight path and the velocity of the particle on it have to adjust in such a way that the inertia force / resulting from this motion compensates for the drag of the particle, as indicated in Fig. 2.20. This inertia force contains the gravitational acceleration as well as all other accelerations resulting from the changes in magnitude and direction of the velocity vector. In the vicinity of a body the gravitational acceleration can often be neglected, i.e. the weight of the particles need not be taken into account.

The problem of the determination of particle flight paths in a flow field has not yet been treated comprehensively in the literature. Some references may be taken from Brun,2 19 who investigated the motion of small droplets in the flow field of a wing in connection with the problem of icing. But this problem is a special case since droplets in fog and clouds have a negligibly small vertical velocity in the atmosphere. Therefore in the free stream there exists no relative velocity between the flow and the droplets. In more general cases, such as for instance for falling rain drops

Internal flow problems 71

or whirled-up mud already in the free stream far away from the vehicle, considerable relative velocities are present.

For the determination of the flight paths of the particles, and for the estimation of the amount of mud on the surface of a vehicle, the three-dimensional flow field must first be known. Up to the present, this problem has not been solved sufficiently and in the necessary detail by aerodynamic theory. Therefore experimental investigations are necessary, which may be performed either on the road or in a wind tunnel for real conditions. If experiments are carried out on models smaller than the original vehicle, the question of the corresponding similarity rules arises. For a mechanically similar flow field the Reynolds number

VJ Re i = = constant (2.44)

v

must be constant. If the weight of the particles can be neglected, the same flight paths are obtained (see Brun2 ) if the parameter

P / Ψ = — — = constant (2.45)

PP dp

is constant. In this equation, p/pp is the ratio of the density of the fluid p to the density of the particles pp and l/dp denotes the ratio of the characteristic length of the vehicle / to the characteristic dimension dp of the particles. If both equations are fulfilled simultaneously, this leads - for the case of the same fluid (vx = v2) for model (2) and original (1) and for a length scale lxll2 - to

Voo2 = ^- Vooi (2.46)

If particles of the same kind are used (ppl = pp2), the size of the particles has to be chosen so that

dp2 = - f dpl (2.47)

This means that for experiments on smaller models, smaller particles have to be used - which is difficult to handle.

For the interpretation of experimental results the basic ideas considered so far are important. Accumulation of mud on the surface of a vehicle occurs due to the fact that the mud particles are not able to follow the streamlines - especially in regions of high streamline curvature. The flight paths of the mud particles show relatively low curvature up to the impact on the vehicle surface. This effect is present for instance in the highly curved flows between the bonnet and the windscreen in the front part as well as in the vortex flow over the rear part of a vehicle.

2.4 Internal flow problems 2.4.1 Basic equations for incompressible flow As already mentioned in section 2.2.2, fully developed internal flows cannot be split up into an inviscid outer flow and a viscous boundary layer


flow close to the wall. In general, the viscous effects extend over the whole cross-section. Therefore, in the equations of motion, the viscous forces have to be taken into account from the beginning.

To start with, the law of mass conservation can be written, for a flow as shown in Fig. 2.3, as

fy p J V dS = constant (5)

(2.48)

This means that the mass flow through the cross-section S(x) is constant along x. If a mean velocity is introduced by

1 V m ~ 5" (S)

VdS (2.49)

the equation of continuity may be written in the form

pVmS = constant (2.50)

by analogy to Eqn 2.6. For constant density p the mean velocity is high in narrow cross-sections and vice versa.

For internal flows Newton's law is also valid but, in addition to the pressure forces, viscous forces have to be considered. Figure 2.21 shows as

m laminar

Figure 2.21 Laminar and turbulent pipe flow

a simple example the fully developed flow through a cylindrical pipe. In this case the velocity distribution V(y) is the same for all cross-sections; x = constant. No acceleration is present in the flow and therefore no inertia forces occur. The pressure is constant over the cross-section and, due to the friction forces, a pressure difference ργ — p2 > 0 between the two sections 1 and 2 must exist to move the fluid against the friction drag through the pipe. This means that the friction effects cause a pressure decrease in flow direction which is called the pressure loss due to friction Ap. If this pressure loss is taken into account, Bernoulli's equation, Eqn 2.7, can be written in extended form as

Pi + -^V2ml=p2 + -?-V2

m2 + Ap (2.51)

In this equation the internal flow is regarded as a one-dimensional problem. The pressure p and the mean velocity Vm are constant over the


cross-section S and all quantities depend only on the coordinate x in the flow direction. Eqns 2.51 and 2.7 are only valid for flows in which no or only negligibly small variations of the geodetic height occur. If such variations are taken into account, terms resulting from hydrostatics have to be added on each side of Eqn 2.51, which yields

Px + — V2ml + pgAi = Pi + — V2

m2 + pgh2 + Ap (2.52) 2 2

In this formula hi and h2 are the geodetic heights of the streamtube at the stations 1 and 2. In viscous flow, the sum of static pressure [p + pgh) and dynamic pressure pVm/2 is not constant. The total pressure decreases downstream by the pressure loss Δρ caused by viscosity.

In general the pressure loss Δρ is related to the dynamic pressure p V^/2 (sometimes also to pVm2/2) which leads to a dimensionless loss coefficient

ζ = Ap (2.53)

2 m l

This loss coefficient is different for various internal flow problems and its value is in general also a function of the Reynolds number. The loss coefficient is a criterion for the quality of cooling ducts and radiators; see sections 9.4.1 and 9.5.1. Some important elements of cooling systems will be discussed subsequently.

2.4.2 Applications

2.4.2.1 Laminar and turbulent pipe flow

At a certain distance downstream of the entrance of a pipe, the velocity distribution over the cross-section ceases to change. This state is called the fully developed pipe flow, which is sketched in Fig. 2.21. The equation of continuity, Eqn 2.50, is thus fulfilled and for a horizontal pipe {hx = h2, Vm\ = Vmi) Eqn 2.52 yields

Pi- p2 = Δρ (2.54) In this case no inertia forces are present. From the equilibrium of pressure forces and viscous forces shown in Fig. 2.21

x(y) = ^ - = - ^ y (2.55)

can be deduced. Thus the distribution of the shear stress across the pipe cross-section is linear. This result is valid for laminar as well as for turbulent pipe flow.

For Reynolds numbers ReO = VmD/v < 2300 laminar flow is found in a pipe. With the notation of Fig. 2.21 Newton's law, Eqn 2.21, can be written as

dV τ = — μ—-— (2.56)

ay


Combining Eqns 2.55 and 2.56, integration can be carried out and the well-known parabolic velocity distribution

νω-*^(*-Λ (2.57)

results, for which the mean velocity according to Eqn 2.49 can be calculated as

V = P l - P 2 D2

32μ/ For the loss coefficient ζρ in a pipe Eqn 2.53 yields

Δρ = 64 μ /

pVmD D

(2.58)

(2.59)

The loss coefficient is proportional to the length/diameter ratio of the pipe. In order to get an expression which is independent of / and D the so-called frictional resistance

is introduced and, with this notation, Eqn 2.59 reads 64

λ = Rer

(2.60)

(2.61)

This function is shown in Fig. 2.22. It is in excellent agreement with experimental data.

12

10

■qpmAftaflA QO Afl

100λ 2.5

2.θ|

1.5

1.2

1.0^

i°£ =507 + # *s = 9 5 9 ■ ;* iî\ Nikuradse !· = Izb V, . jo =60 I ( s a n d

• =30,6 | roughness) = 15 J

(commercially rough)

SL 4 6 8 103 2 4 6 8 104 2 4 6 8 105 2 4 6 8 106 2

ReO ►

Figure 2.22 Frictional resistance in pipes, from Schlichting2 ': (1) laminar, Eqn 2.61; (2) turbulent, Eqn 2.92; (3) turbulent, Eqn 2.63


For ReO > 2300 the pipe flow is turbulent. As we already know from the flow along a flat plate, the velocity profiles in turbulent flow show higher velocities close to the wall than those in laminar flow. The calculation of these velocity distributions is rather complicated since for turbulent flow Eqn 2.56 has to be replaced by another expression, Eqn 2.37 for the shear stress. The frictional resistance of pipes for turbulent flow is, according to Schlichting,2 Λ

λ = ^ 6 4 for 2.3 x 103 < ReO < 105 (2.62)

and

νλ

V/teD

= 2 · log (ReOΛ/λ) - 0.8 for ReO > 105 (2.63)

These functions are also drawn in Fig. 2.22. The flow through a pipe is an internal flow problem without any flow

separation. The resistance is due to pure friction drag. By analogy to the flow along a flat plate, the frictional resistance depends strongly on the Reynolds number. In Fig. 2.22 the frictional resistance is also shown for rough pipes. As in the case of a flat plate (see Fig. 2.9), surface roughness further increases the drag and the frictional resistance becomes independent of the Reynolds number. This is because flow separations occur on the roughness elements. Therefore a rough surface behaves like the sum of a large number of bluff bodies, see Fig. 2.11. Further details may be taken from the literature, refs. 2.1 to 2.9.

The flow through pipes having non-circular cross-sections can be related to an equivalent pipe flow with circular cross-sections. For given dimensions of the non-circular pipe (cross-sectional area 5, circumferential length U) the diameter of the equivalent circular pipe is given by

45 U

Deq = £ (2.64)

2.4.2.2 Curvedpipes

Flow separations may also occur in pipes. As an example, the flow in a curved pipe is shown in Fig. 2.23. The deflection of the flow by the walls is induced by a pressure gradient perpendicular to the streamlines. In a curved pipe, the pressure at the outer radius is higher and at the inner radius is lower than the pressure in the flow upstream and downstream.

Table 2.2 Loss coefficients ^ for curved pipes (from ref. 2.8. See Fig. 2.23 for notation)

δ 0° 15° 22.5° 45° 60° 90°

ζτ

r/D = 1 r/D = 2 r/D = 4 r/D = 6

0 0 0 0

0.03 0.03 0.03 0.03

0.045 0.045 0.045 0.045

0.14 0.09 0.08 0.075

0.19 0.12 0.10 0.09

0.21 0.14 0.11 0.09


Therefore a danger of flow separation, caused by pressure increase in the flow direction, is present at the outer radius close to the entrance and at the inner radius near the exit of the curved pipe, as indicated in Fig. 2.23.

//////////_

separated flow

separated -flow

Figure 2.23 Flow in a curved pipe

These effects increase with decreasing curvature radius r and with increasing angle δ. Due to the flow separations, loss coefficients ζ € according to Eqn 2.53 occur that are almost independent of the Reynolds number. This means that a quadratic resistance law, Ap ~ V^, exists -which is well-known for bluff bodies as in Fig. 2.11. Values for curved pipes taken from ref 2.8 are shown in Table 2.2. They indicate that for δ > 45° low loss coefficients ζ€ can only be achieved by a large curvature radius r compared to the pipe diameter D.

2.4.2.3 Inlets

The flow through an inlet (Fig. 2.24) may also cause total pressure losses Ap. Especially for sharp-edged inlets, flow separations occur and the corresponding values for the loss coefficients ζ! according to Eqn 2.53 are

y rounded Y no flow

W / / / / / /////,

y sharp-edged γ flow separation 1/

Shape

sharp-edged

blunt

well rounded

f/

0.50 1

0.25

0.05

Figure 2.24 Flow field and loss coefficients2·* for inlets


high. The values in the small table in Fig. 2.24 indicate that, to achieve small loss coefficients, inlets have to be well rounded rather than sharp-edged.

2.4.2.4 Local contractions

Local reductions of the cross-sectional area - for instance in sleeve valves, flap valves etc. - are used to control the flow rate in pipes, e.g. in the control of heating and cooling systems, see section 10.4.4. Two examples

a) Sleeve valve

-D-

b) Flap valve

Position h/D

0 0.25 0.50 0.75 0.87

r$

0 0.26 2.1

17.0 98.0

| Position δ[°]

0 10 20 40 60

1 70

f.F 0 0.52 1.54

10,8 110 751

Figure 2.25 Flow field and loss coefficients2 8 in valves: (a) sleeve valve; (b) flap valve

are shown in Fig. 2.25. In the local contractions, high velocities (see the continuity equation, Eqn 2.50) and low pressures (see Eqn 2.51) are present. On the rear part of the element, which produces the contraction, the flow separates. Downstream of the smallest cross-section the pressure increases at the walls and the flow may separate there too. The corresponding loss coefficients are extremely high - especially for nearly closed positions of the valves.

Local contractions of the cross-sectional area can also be used to measure the flow rate through a pipe. A well-known example of this kind is an orifice meter in which the flow field is much as sketched in Fig. 2.25 for a sleeve valve. The loss coefficient ζ 0 of an orifice-meter depends strongly on the area ratio and on the shape of the edges of the orifice, but does not depend on the Reynolds number. For a known value of the loss coefficient ζο, Eqn 2.53 can be used to determine the mean velocity Vm and thus the flow rate from the measured pressure loss Ap. Details may be found in the literature, especially refs. 2.3, 2.6 and 2.8.

2.4.2.5 Cross-section enlargements

In cross-section enlargements, as shown in Fig. 2.26, the mean velocity decreases in flow direction according to the continuity equation

Vm2 = (2.65)


S///?A7

a) Diffuser

///////_////////. b) Abrupt

enlargement

Figure 2.26 Flow through cross-section enlargements: (a) diffuser; (b) abrupt enlargement

This means that a pressure rise in flow direction is present and therefore flow separations may occur. In non-viscous flow the largest possible pressure increase would be, according to Eqn 2.51, for Ap = 0

(2.66) P2 ~ Pi 2 m '-£ Due to the viscous effects in real flow, only a smaller pressure increase P2~P\ is achieved and the corresponding pressure loss is

Ap = p2 - p2 (2.67) For gradual cross-section enlargements in diffusers having small angles

2a < 8°, the flow remains attached. In this case the pressure losses Ap are proportional to the theoretical value for the pressure increaseρ'χ-ρχ, which can be written as

Ap

-2-v? ζο

ml

Pi ~ Pi (2.68)

with ε = 0.05 to 0.3. Using Eqn 2.66 leads to

S2 ζϋ = ε 1 - (2.69)

The loss coefficient ζΌ of a diffuser depends on the area ratio Si/S2 while the factor ε is a function of the relative length of the diffuser lO/Du of the diffuser shape and of the velocity distribution at the diffuser inlet. In the case of attached flow, a particular theory is available, see Truckenbrodt,2 7

and Schlichting and Gersten.2 2() Comprehensive experimental data on flows in diffusers have been published by Sprenger.2

Relationships between external and internal flow on vehicles 79

For larger diffuser angles 2a, the flow separates and the loss coefficients are much greater. The limiting case of an abrupt cross-section enlargement is also shown in Fig. 2.26. For this case, a particular theory is also available; see Truckenbrodt.2 7 In the absence of viscosity the theoretical pressure rise is given by

P2th -Pi = P^m2(Vml - Vm2) (2.70) Compared to the largest possible value according to Eqn 2.66, a pressure

loss Apth can be calculated for inviscid flow from Eqn 2.67 as

Δρ* = \ (Vml - Vm2f (2.71)

and the corresponding theoretical loss coefficient for an abrupt cross-section enlargement ζΑ th is

_P_ y2 \ S2

2 m

In real viscous flow, still higher loss coefficients

ζΑ = βζΑ«Η = β ( l - | ^ - ) (2-73)

occur and the factor ß = 1.1 to 1.2. A comparison of the results according to Eqns 2.69 and 2.73 leads to the

conclusion that small cross-section enlargements may be designed as abrupt ones, since in this case the loss coefficients are not larger than those for a diffuser. For high area ratios a diffuser has to be designed, but in vehicles the length /D necessary for a good diffuser design unfortunately is often not available and in this case higher loss coefficients have to be taken into account; see section 9.4.1.

2.5 Relationships between external and internal flow on vehicles For a vehicle, external and internal flow are closely related; see Fig. 2.4. The system for cooling the engine, for instance, may use the pressure difference in the external flow between the stagnation region in the front part of the vehicle and the low pressure region on its underside; see Chapter 9. Similarly, for the ventilation of the passenger compartment, the pressure difference between the stagnation region in front of the windscreen and the ventilation exits at the rear end of the passenger cabin may be used; see Chapters 6 and 10.

The pressure differences utilized by these systems are proportional to the square of the speed of the vehicle V. They are not present for the vehicle at rest and they are maximum for maximum speed. The mass flow of the internal flow adjusts in such a way that the sum of all pressure losses Δ/7 of the involved elements is equal to the pressure difference which exists between inlet and exit. Therefore the mass flow rate depends strongly on the speed of the vehicle. The link between the external and internal flows is

(2.72)


the fact that, at the inlet and at the outlet of the internal flow system, the pressure is the same for the external and the internal flow.

However, the mass flow through the internal flow system may cause changes in the external flow. At the inlet of the internal flow system, suction of the external flow takes place and, at the outlet of the internal flow system, blowing into the external flow is present. The amount of the interference depends on the mass flow rate of the internal flow and the corresponding effects need not be adverse. For instance, blowing over well-designed exhaust slits may cause favourable effects in the boundary layer of the external flow.

The dependence of the available pressure difference on the speed of the vehicle is rather disadvantageous since for low speeds only very small mass flow rates through the internal flow systems occur. Therefore, in the cooling system of the engine (see Chapter 9) as well as for the ventilation of the passenger cabin (see Chapter 10), additional fans are used, which ensure a certain mass flow rate pQ even for zero velocity of the vehicle. The pressure difference necessary to overcome all pressure losses Δ/? has to be provided by the fan and the corresponding power is

P=QAp (2.74)

where Q is the volume rate in m3/s. In order to keep this additional power as small as possible the internal flow system has to be designed for low loss coefficients in all its parts. The use of powerful fans may lead to increased interference between the internal and the external flow and to noise.

2.6 Notation A cross-sectional (frontal) area Ax, Aq exchange coefficients; Eqns 2.37 and 2.38 D diameter (D = 2R) D drag; Fig. 2.14 D{ friction drag; Eqn 2.19 Dp pressure drag; Eqn 2.24 / inertia force; Fig. 2.20 L lift; Fig. 2.14 M pitching moment, reference point and sign; Fig. 2.14 N yawing moment, reference point and sign; Fig. 2.14 Nu local Nusselt number; Eqn 2.35 P power; Eqn 2.74 Pr Prandtl number; Eqn 2.31 Q volume rate R radius (R = Oil) R rolling moment, reference point and sign; Fig. 2.14 Re Reynolds number ReO Reynolds number, based on a diameter (= VooD/v external flow

problem, VmD/v internal flow problem) Rei Reynolds number, based on a length in flow direction (= V^l/v) Rex Reynolds number, based on the distance x from apex (=VooX/v) S cross-sectional area of ducts St Strouhal number; Eqn 2.42

T temperature Τ temperature fluctuation; Eqn 2.14 U circumferential length of a non-circular cross-section V flow velocity Vm mean velocity; Fig. 2.21 and Eqn 2.49 Y side force; Fig. 2.14 a speed of sound b width of plate; Eqn 2.20 cD drag coefficient df dimensionless shear stress at the wall; Eqn 2.34 cL lift coefficient cM pitching moment coefficient cN yawing moment coefficient cp pressure coefficient; Eqn 2.9 cp specific heat capacity at constant pressure; Eqn 2.30 cR rolling moment coefficient cY side force coefficient d particle size in Eqn 2.45 g total pressure h geodetic height in Eqn 2.52 k thermal conductivity; Eqn 2.3 ks height of roughness elements; Fig. 2.9 / characteristic length; Fig. 2.2 n frequency p static pressure q dynamic pressure q heat transfer per unit area and time; Eqn 2.3 r radial coordinate; Fig. 2.3 s local area of a stream-tube; Fig. 2.2 t time u, v velocity components in x-, y-direction u\ v\ wf velocity fluctuations; Eqn 2.14 w local flow velocity; Fig. 2.2 xy y, z rectangular coordinates a heat transfer coefficient, Eqn 2.41 β angle of yaw, Fig. 2.14 δ boundary layer thickness, Fig. 2.6 ζ loss coefficient. Eqn 2.53 λ coefficient of frictional resistance in a pipe, Eqn 2.60 μ dynamic viscosity, Eqn 2.1 v kinematic viscosity, Eqn 2.2 p density τ shear stress, Eqn 2.1 φ angle, Figs 2.8 and 2.10 Ψ parameter, Eqn 2.45

Subscripts

oo free steam conditions crit critical quantity


m mean value p quantity related to a solid particle rel relative quantity s quantity acting parallel to the streamlines t quantity acting parallel to the flight path of a solid particle th theoretical quantity tr quantity related to laminar/turbulent transition turb quantity related to the turbulent state of the flow w quantity at the wall (y = 0) A abrupt cross-section enlargement C curved pipe D diffuser F flap-valve I inlet O orifice-meter P pipe S sleeve valve T quantity related to the thermal boundary layer —> vector

time-averaged value, Eqn 2.15

Chapter 3

Performance of cars and light vans Hans-Joachim Emmelmann

3.1 Introduction

Top speed and acceleration have long been of prime interest in vehicle performance. However, the drastic increase in fuel cost has now focused attention on fuel consumption, which has become one of the most important aspects to be considered in vehicle development. This chapter introduces the resistance to vehicle motion equation and explains the individual resistances and their effects on the various values which make up vehicle performance. Topics affecting fuel consumption will be dealt with explicitly. The performance examples are restricted to cars and light vans; trucks and buses will be covered in Chapter 8. Naturally, the same equations of resistance to motion apply to both passenger and commercial vehicles, but the significance of the individual resistances in the two groups differs sufficiently to justify separate treatment.

3.2 Resistance to vehicle motion 3.2.1 Equation of resistance to motion

The motion of a vehicle is resisted by the following forces:

Aerodynamic drag WO

Rolling resistance WR

Climbing resistance (gravitational) Wc

Acceleration resistance (inertial) WA

The force on the driven wheels necessary for vehicle motion is therefore

Z = WD + WK + Wc + WA N (3.1)

The engine performance necessary to overcome a vehicle's resistance to motion is

7V x 10"3 kW (3.2) ηοηΑ

where η α and η Α represent the efficiencies of the gearbox and axle respectively, and V is the driving speed.

83

84 Performance of cars and light vans

3.2.2 Analysis of the resistances to motion

3.2.2.1 Aerodynamic drag

The aerodynamic drag results from flow characteristics and the aerodyna-mic data of the vehicle body

WD = γ VlcTA N (3.3)

where the air density p = 1.22 kg/m3, the resultant air speed V«, m/s, the tangential force coefficient cT (ß) (cT(ß=0) = cD) and the frontal area of the vehicle is A m2.

The resultant air speed V«, is the sum of the vectors of the driving speed V and the wind speed Vs. The vector of the resulting airflow and driving direction determine the yaw angle ß (Fig. 3.1).

Tangential force coefficient

riß) cT(ß)-

VIA

Average resistance coefficient

C*D

V2A

db «■Jj/^pFw,]s

c . - I ^ C r ( « [ l + ( Ä ) 2+ 2 ^ c o , 6 db

Figure 3.1 Side wind averaged drag coefficient, after ref. 3.1

In the case of head- or tail-winds the following, based on Eqn 3.3, holds true:

WO = -^ (V ± VsYcuA

Or under still-air conditions

(3.4)

WD = y V2COA (3.5)

This still-air condition seldom occurs, so a typical tangential force curve (Fig. 3.1), causing increased aerodynamic drag compared to the still-air condition, must be reckoned with. It is possible, for a defined vehicle usage and wind spectrum, to determine a mean aerodynamic drag coefficient, as described in Fig. 3.1. See also sections 4.2 and 8.4.3.

Resistance to vehicle motion 85

3.2.2.2 Rolling resistance

The rolling resistance of vehicle tyres is dependent on the load (normal force), tyre size and construction, tyre pressure and the axle geometry, i.e. caster and camber angles.

Assuming that the tyre manufacturer specifies tyre pressure in accordance with vehicle weight, and that for similar weight to tyre-pressure relationships similar rolling resistance results, the rolling resistance of a vehicle can be calculated with the formula

WR = / r G N (3.6)

where GN is the normal force (newtons) due to the weight of the vehicle and/ r is the rolling resistance coefficient, which is dependent upon the type and size of the tyres. Figure 3.2 shows typical rolling resistance diagrams for radial and cross-ply tyres. The influence of caster and camber angles will be ignored.

0.040

0.035

0.030

0.025

0.020

0.015

0.010

*

Cross

—~

ply tyres

*ς

/ X /

Radial tyres

50 100

V 1

150 km 200 h

Figure 3.2 Rolling resistance coefficients for typical radial and crossply tyres

3.2.2.3 Climbing resistance

Climbing resistance may be expressed by

Wc = sincp G9.81 N (3.7)

Climbing resistance is not taken into consideration for fuel consumption calculations, whether for steady speeds or for specified driving cycles. The reason is that representative altitude profiles for the respective driving cycles are unknown.

Investigations such as those by Schubert,3 2 defining the frequency of ascents on specific freeways and cross-country routes (Fig. 3.3), are insufficient for general purposes.


I I BAB I Ulm - Augsburg I I 66 km

Γ Ί BAB II Kassel - Bad Hersfeld I I 66 km

H j Bundesstraße hilly circuit 74.7 km

60

%

50

40

30

20

10

-9% - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1

Descents 1 2 3 4 5 6 7 8 % 9

Ascents ► Figure 3.3 Distribution of ascents and descents on three observed routes (one direction), after ref. 3.2

3.2.2.4 Acceleration resistance

Resistance to acceleration may be expressed by

WA = Vm(l + Ej) 9.81 N (3.8) where the rotating masses in the various gears are taken into consideration b y Ej.

Representative Ej values for cars, according to Bussien, 3 3 are as follows:

1st gear 2nd gear 3rd gear 4th gear

0.25 0.15 0.10 0.075

For exact calculations, the moments of inertia of all rotating parts relative to the vehicle mass must be established.

3.3 Performance 3.3.1 Motive force diagram

From the motive force diagram the speed-dependent propelling force at full engine load, the climbing ability and the necessary engine power in the various gears can be read off, see Fig. 3.4. The respective engine speeds are shown on a supplementary diagram (lower section of Fig. 3.4).

From the intersection of the driving resistance curve, consisting of rolling resistance and aerodynamic drag, and the propelling force at full

Performance 87

960

kp

880 1

800

720

640

^560

>48Ü >

;|400 >

320

240

160

80

U

10 > c 30

f 50

70 I x 10

1 1

l

"_J

1 : i \\\\w} 1

1 i 1 \ ι \ \ ' T U T U T i 1 1 1 \ \ \ \_

\\\\ \ L

f-- -

50%

■ ■—

- - L, J i - -^40%

\Λ v \' \ W ^

\ \ —^Ατ^ΗΤ

" ^ +\p"-

- - f . r- - r -1 - 1 ,

^ ^ 0 ! 40

! 1

i 'step

2 'ge«

'ονί

r

•rail

--

—

L39.5%

L . . 30%

60

1.68

3.

15.

15

77

^2

^

- -

| -

I

j

2.6% 20%

—

—

—

- -i --T

-

—

^ς-13.8% «JfJ

—

z

V

Ξ

Vehicle data

Displacement 1 .1 litre Weight 975 kg Frontal area 1.84 m2

CD 0.42 Tyres 145SR13 Dynamic radius 0.274 m Axle ratio iA - 4.571

- I -

;

^ 8 . 7 %

80 100 120 140 1(

^

1.52

2.C 9.2

)5 17

Speed V -

^ 1.41

1. 6.

35 17

0 4

96 39

—

0%

50

—

—

180

—

—■

200

- -

—

km/h 2'

:

CL

^45 30

lo,b

Figure 3.4 Typical motive force and speed diagram for a car

engine load in top gear, the top speed of the vehicle can be established. The propelling force remaining when the sum of rolling resistance and aerodynamic drag is deducted from available power for a given vehicle speed, can be used to climb hills and/or accelerate the vehicle in accordance with Eqn 3.1.

3.3.2 Acceleration time and elasticity

When one substitutes the above mentioned propelling force difference ΔΖ for the acceleration resistance WA in Eqn 3.8, it is possible to calculate instantaneous values for acceleration and driving speed:


V ΔΖ m(\ + ει) x 9.81 m/s2 (3.9)

t

V = 3.6 I Kdikm/h = 2.24 f V'dimile/h / /

(3.10)

It is customary in Europe for acceleration to be quoted as the time necessary to accelerate from V = 0 to 100km/h (62.5mile/h), through the gears. The time necessary to accelerate from 40 km/h to 100 km/h (25 to 62.5 mile/h) in top gear is often used to express the elasticity of the vehicle, although other figures are also used.

V? \ u

1 1 1 1 1 1 Acceleration through the gears

E fl

lastic i t \ / (ft "»n Π Ρ;

•om 40 km/h

1

■'max

ir)

160 km/h 140

120

100

J 80

V 60

40

20

5 10 15 20 25 30 35 40 sec 50

Figure 3.5 Acceleration and elasticity of a lower medium class vehicle

Figure 3.5 shows the resultant driving speed of the vehicle against time, the performance diagram and data for the vehicle being presented in Fig. 3.4.

Calculated acceleration sometimes fails to correlate with test results. This is partially due to the power output tolerance of production engines, which often vary from their published outputs by ±5 per cent. Additionally, these calculations use engine data which is measured on a static engine installation. During acceleration tests, rapid changes in rev/min occur, particularly in the lower gears.

3.4 The estimation of fuel consumption 3.4.1 Concept of estimation

During the development of a new vehicle, the various items affecting fuel economy must be evaluated in a cost benefit analysis. In order to do this, it is necessary to compute the fuel consumption in relation to all influential parameters, yet retaining the main customer requirements. The computer model can be based on a suitable predetermined driving cycle. It is helpful to use a specific fuel consumption map for an engine over a known range,

The estimation of fuel consumption 89

although this data is generally available for steady speed engine operation only (on a test bed). The engine output while accelerating can be represented by the following supplementary computation.

3.4.2 The specific fuel consumption map

The fuel consumption of a vehicle is largely determined by the specific fuel consumption of its engine. It is dependent on the engine loading (torque, engine revolutions) and is illustrated in Fig. 3.6. The accuracy of fuel consumption computations is therefore only as good as the accuracy of the available specific fuel consumption map; it is therefore essential that a representative diagram for the engine is used for the calculations.

A

Petrol engine

MEP

Diesel engine'

265-y

270-^

300—-325—-,

[380-.= 1 Λ"7Κ

*\

^-~

^

1 1

VH =2.7 litres

~ir ^

>J y] r /

2000 1 min

4000

Figure 3.6 Specific Fuel Consumption (SFC) map calculated from standardized diagrams, after ref. 3.4

Often the specific fuel consumption diagram is not available at the time of calculation, particularly if theoretical variations of engine output are required. In this case hypothetical performance maps can be constructed by normalizing that for an existing engine. In effect, the mean effective pressure (MEP) and the engine revolutions n of this known diagram can be adjusted according to the ratio of the stated outputs of the engines. The hypothetical diagrams are therefore derived as follows:

Specific fuel consumption, bs = bso

Mean effective pressure, MEP = MEP0

* stated p 1 stated o

(3.11)

(3.12)

Engine speed, n = nQ ^stated

(3.13) ^stated o

where the suffix Ό ' refers to the values from the diagram of the existing representative engine.


Some general fuel consumption diagrams for petrol and diesel engines, derived from standard diagrams, are shown in Fig. 3.6.

The fuel consumption on idle and the amount of fuel injected by the accelerator pump are adapted to suit the various engines using the following formulae

Idle consumption: Βλ = Βιο VH

HO

Accelerator pump amount: BA = BAO VH

V HO

(3.14)

(3.15)

where VH is the displacement volume of the engine.

3.4.3 Gear ratio matching

Most European cars have their gearing designed for an engine speed of 100 rpm above the stated peak power speed when the vehicle is travelling at top speed in top gear. Similarly, light vans are set up with engine speed 400 rpm above the stated peak power speed. The gear ratios must be

MEP

200 Figure 3.7 Driving resistance curves on a SFC map for various drag coefficients cD, with and without gear ratio matching, after ref. 3.5


chosen so that acceleration and climbing capabilities meet the require-ments and of course significant overlapping of adjacent gears must be ensured.

When aerodynamic drag is reduced for an existing car the gear ratio should be adjusted to suit the new top speed. Figure 3.7 shows the outcome when this ratio adjustment is not conducted. In order to illustrate the effect clearly, large steps in drag coefficient cD from 0.5 to 0.4 to 0.3 are assumed.

For the same gear ratio of i4 = 3.98 for the initial vehicle exhibiting cD = 0.5 (solid line), the broken line and the dotted lines show cD = 0.4 and 0.3 respectively. The effect of increased specific fuel consumption despite unchanged engine and vehicle speeds for a vehicle with reduced drag coefficient, i.e. less than 0.5, can be seen. This can mean that at lower partial load conditions, in spite of reduced performance requirements, higher fuel consumption can result. The new top speeds also lead to engine speeds which are above the maximum allowable.

When the gear ratios are changed in accordance with the previously mentioned criterion regarding the engine speed at maximum vehicle speed, the load points remain on a curve of constant power, which in the diagram (Fig. 3.7) is a hyperbolic function, back to the curve for cD = 0.5.

This gear ratio modification means that the same specific fuel consumption for all three drag coefficients can be achieved for the full engine load condition. However, because the load points on the original curve, which are achieved by the gear ratio changes, lead to different driving speeds (see lower part of Fig. 3.7), a new spectrum (see Fig. 3.8) is

800 r

- 3 -kWh 700

600

500

400

P = 55 kW G= 1050 kg Radial tyres

50 100 150 km_ 200 „ ^ h

Figure 3.8 Specific fuel consumption at constant vehicle speed for a reduction of drag coefficient, with and without gear ratio matching.

obtained for the complete vehicle speed range. For clarity, only the curves for the original drag coefficient of 0.5 and the newly achieved 0.3 are shown.

As can be seen, with the help of gear ratio matching, the same specific fuel consumption under partial load can be achieved as for the original


condition. In the lower partial load region specific consumption is slightly greater. Therefore, in spite of the reduced power requirement, higher fuel consumption occurs than for cD = 0.5.

When driving cycles are taken into consideration the matching of the various gears is important. The following matching techniques are the most reasonable:

(a) Changing the axle ratio—whereby all gears are equally affected. (b) Stepped matching rate for the various gears (1st gear unchanged, 2nd gear stepped to 33 per cent, 3rd gear to 57 per cent and 4th and 5th gears to 100 per cent, based on matching technique (a). (c) Stepped matching rate for all the gears, with the vehicle weight and engine power also being taken into consideration.

The order in which the above possibilities are presented also indicates the order of practicability. The simplest to realize is possibility (a). It offers the best improvement with respect to fuel consumption, but has a negative effect in terms of acceleration in the lower gears. With an increase of 10 per cent in top speed, which results from approximately a 30 per cent reduction in aerodynamic drag, the acceleration time from 0 to 100 km/h (62.5 mile/h) would be approximately 10 per cent longer. Should this effect be unacceptable, gear matching according to method (b) is necessary.

For fuel-consumption calculations on vehicles which are also undergoing a weight reduction process along with aerodynamic drag reduction, method (c) must be used if acceleration characteristics are to be kept constant.

For first gear, a weight- or performance-based matching process must be effected to achieve acceleration characteristics similar to those of the original vehicle. A stepped matching of the second and third gears is then necessary. No weight- or performance-dependent matching is undertaken for fourth, or overdrive, therefore the overall process can be summarized as in Table 3.1.

Table 3.1 Gear matching methods

Gear

Aerodynamic drag-dependent matching (%)

Weight/performance-dependent matching (%)

1

0

100

2

33

67

3

67

33

4

100

0

5 (Overdrive)

100

0

When matching processes (b) and (c) are applied it must be ensured that sufficient overlap exists between the newly selected adjacent gears.

3.4.4 Driving cycles

When fuel consumption is discussed, one must differentiate between results measured during legally established artificial driving cycles, which


take into account the requirements of various governmental standards (see Fig. 3.9) and the actual fuel consumption of a vehicle under daily use by its owner.

European Urban Cycle (ECE)

20 40 60 80 100 120 140 160 sec 200

EPA Highway Cycle

2 4 6 8 10 min 14

60

mph

2 4 6 8 10 12 14 16 18 min 22 2 4 6 8

Figure 3.9 ECE and EPA driving schedules

y Urban Cycle

J \i...iil..,.y i l A (Λ/1Ι.. Hi H.-J. Emmelmann has published data3 6 on the influence of various

parameters on a driving cycle based on such normal vehicle usage. The cycle designated E75 is based on 1975 traffic statistics for West Germany. However, because such a cycle does not represent general use, one is forced to adopt the obligatory legal driving cycles as a means of establishing the influence of aerodynamic drag and vehicle weight on fuel economy.

The so-called Euromix cycle is the recognized cycle for Europe, consisting of one-third city use consumption, measured in the ECE cycle (see Fig. 3.9), one-third at a constant 90 km/h (56mile/h) and one-third at a constant 120 km/h (75mile/h):

Êuromix ~ ~ (#ECE + #90 + #12θ) (3.16)

In the above formula BECE is obtained from dynamometer test bed tests for the middle value of certain load classes. For these, neither the actual


weight of the car nor its aerodynamic drag is given any consideration, because the test was originally an emission test which used an artifical driving cycle (speed versus elapsed time).

Vehicle weight reduction only leads to a reduction in City Cycle (#ECE) fuel consumption when it results in a change in test class to a lower level.

In the USA, fuel consumption is determined using a combination of test cycles based on the driving habits of that country. The 'Combined Fuel Economy' is established from the results of 55 per cent city traffic and 45 per cent highway traffic:

Bcomb = 0.55 Burh + 0.45£high (3.17)

FEcomb = 0.55/FEUTh + 0.45/F£high ( 3 ' 1 8 )

BUTb can also be established for a corresponding loading class on a brake dynamometer. The various loading classes are shown in Table 3.2.

Table 3.2 Kerb weight classes (kg)

ECE

Up to: 920 1150 1370 1600

Sweden

Up to: 941 1055 1168 1338 1565

USA-EPA

Up to: 943.2 1056.8 1170.5 1340.9 1568.2

3.4.5 Gear change points

The points for changing up to the next gear are specified for the EPA Urban Cycle and the EPA Highway Cycle as follows:

1st to 2nd gear at VO = 24.0 km/h (15 mile/h) 2nd to 3rd gear at VO = 40.0 km/h (25 mile/h) 3rd to 4th gear at VO = 64.0 km/h (40 mile/h)

Changing from 4th to 5th in suitably equipped vehicles can be conducted as follows:

4th to 5th gear at VD = 73.6 km/h (46 mile/h)

The effect of this extra change point is that, for instance, during the City Cycle the percentage of time in 4th gear is reduced from 14.9 per cent of the complete cycle to only 1 per cent, with the remaining 13.9 per cent being driven in 5th gear. The gears remain engaged, during deceleration phases, until idle speed is reached.

The shift points for the ECE Cycle are shown in Table 3.3.

3.5 Fuel consumption and performance 3.5.1 Comparison of drag and rolling resistance

During constant speed driving on level road, the resistance to vehicle movement consists of both aerodynamic drag and rolling resistances, see

Tab

le 3

.3 S

hift

poi

nts

for

the

ECE

cycl

e

No.

1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

Ope

ratio

nal

cond

ition

Idle

A

ccel

erat

ion

Con

stan

t sp

eed

Dec

eler

atio

n D

ecel

erat

ion

with

di

seng

aged

Id

le

Acc

eler

atio

n G

ear

chan

ge

Acc

eler

atio

n C

onst

ant

spee

d D

ecel

erat

ion

Dec

eler

atio

n w

ith

dise

ngag

ed

Idle

A

ccel

erat

ion

Gea

r ch

ange

A

ccel

erat

ion

Gea

r ch

ange

A

ccel

erat

ion

Con

stan

t sp

eed

Dec

eler

atio

n C

onst

ant

spee

d G

ear

chan

ge

Dec

eler

atio

n D

ecel

erat

ion

with

di

seng

aged

Id

le

engi

ne

engi

ne

engi

ne

Test

se

ctio

n

1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

Acc

eler

atio

n (m

/s2 )

1.04

-0.6

9 -0

.92

0.83

0.94

-0.7

5 -0

.92

0.83

0.62

0.52

-0.5

2

-0.8

6 -0

.92

Spee

d (k

m/h

)

0-15

15

15

-10

10-0

0-15

15-3

2 32

32

-10

10-0

0-15

15-3

5

35-5

0 50

50

-35

35

32-1

0 10

-0

Tim

e pe

riod

op

erat

iona

l co

nditi

on (

s)

11 4 8 2 3 21 5 2 5 24 8 3 21 5 2 9 2 8 12 8 13 2 7 3 7

of e

ach:

te

st

sect

ion

(s)

11 4 8 5 21

12

24

11

21

26

12 8 13

12 7

Tota

l tim

e (s

) 11

15

23

25

28

49

54

56

61

85

93

96

117

122

124

133

135

143

155

163

176

178

185

188

195

Tran

slat

ion

ratio

to

be

used

for

mec

hani

cal

gear

boxe

s

6sP

M +

5

SK

/ 1 1 1 K

!

6sP

M +

5

sK/

1 2 2 2 K2

16sP

M +

5s

Ki

1 2 3 3 3 3 2 Ki

7sP

M

1 PM

=

Idle

with

eng

ine

enga

ged

Ki,

K2

= 1s

t or 2

nd g

ear

with

eng

ine

dise

ngag

ed


Eqn 3.1. The proportions of these resistances as part of the total resistance vary with vehicle speed. This is illustrated in Fig. 3.10 from Hucho and Emmelmann.3 7 The relationship between the aerodynamic drag WO and the total resistance to movement, WO + WK, versus the driving speed Vis shown; the parameter of the curves is the drag coefficient cD. Cars, light

Figure 3.10 Proportion of the aerodynamic drag from the total external resistance for a car, van and truck, after ref. 3.4

vans and heavy trucks have been studied. The reduction of rolling resistance is seen to be most worthwhile for low speed (city) usage and for heavy vehicles, where the change from diagonal to radial tyres has provided an important means of reducing this rolling resistance.

3.5.2 Top speed

The top speed of a vehicle as a measure of its performance is only really meaningful in countries which do not have speed limits on their freeways (i.e. West Germany). Car magazines do of course still use this criterion in evaluating and comparing vehicles even though use of the vehicles at these speeds on public roads is only theoretical.

The top speed, despite its almost theoretical nature, and its use being hardly possible in normal traffic conditions, is a good guide to the fuel consumption characteristics of a vehicle. When two vehicles from the same weight class and having similar engine concepts are compared, the vehicle which exhibits the highest top speed will also present the lowest fuel

Fuel consumption and performance 97

consumption. In this respect theoretical top speed is also of interest in countries having speed restrictions, hence the interest by car magazines.

The interdependence between aerodynamic drag, top speed and engine power output is shown by the following equation, in which the vehicle weight is contained in the constant k.

v- = * V ( ^ ) (3-l9) where N is measured in kilowatts.

For a medium-class vehicle, k = 38.15, which gives the result in kilometres per hour. Miles per hour values are obtained by using k = 23.71.

J I I I 100 150 200 250

V [km/h]

Figure 3.11 Influence of aerodynamic drag on top speed

Figure 3.11, which illustrates Eqn 3.19, suggests that aerodynamic drag reduction offers the possibility of reducing the drive train power output without loss of top speed performance. The fact that the resultant power output reduction worsens acceleration characteristics at lower speeds normally prevents its application as a means of fuel consumption reduction (see section 3.5.3).

3.5.3 Background to the fuel consumption discussion

The potential for the reduction of fuel consumption is heavily dependent on vehicle class, as is suggested by Fig. 3.10.

Reference 3.6 discusses the four main European vehicle classes, and what follows expands the discussion to extreme sub-compacts and full-size

I O U

100

Ξ .* Q.

50 h

tv


cars. The relative vehicle data are defined in Table 3.4. Light vans are dealt with in section 3.5.5 and heavy trucks in Chapter 8. The question to be answered is to what extent the various parameters that influence fuel consumption can be reduced.

Table 3.4 Definition of sub-compact and full-size cars

Vehicle G P

Sub-compact 900 kg 40 kW (-2000 lb)

Full-size car 1800 kg 150 kW (-4000 lb)

In section 3.5.2 it is shown that by reducing aerodynamic drag the power required can be reduced without significantly affecting top speed. However, when one compares the aerodynamic drag development of recent years (see Fig. 1.53) with the engine sizes being used, one comes to the conclusion that buyers have continued to purchase the same power units, priority being given to higher top speed. They could have turned to the next smaller engines in the vehicle programmes with a view to obtaining better fuel consumption, which has been shown by Janssen and Emmelmann36—a 10 per cent drive-power reduction could mean approximately 4 per cent lower fuel consumption. But since this drive-power reduction also reduces the acceleration characteristic of vehicles, which is considered of foremost importance at the present time, it appears unrealistic to discuss this possibility any further.

Continual efforts are still being made to reduce vehicle weight, often through the use of more expensive materials. This weight reduction has of course an influence on the fuel consumption, but an 'official' gain is rarely achieved. That is to say, only when testing on the brake dynamometer is brought into a lower vehicle test loading class is a reduced fuel consumption, of 0.3 to 0.4 litres/100 km in Burb, or BBCE in Europe, measurable.

As a result of attempts to reduce vehicle weight many conflicting design goals occur, such as noise level and mechanical strength (crash test). It is generally true to say that weight reduction, independent of this test class change aspect, rarely allows for greater than a 3 per cent consumption reduction, for which a weight reduction of more than 10 per cent is necessary.

In refs. 3.7 and 3.8 Emmelmann shows that the product of the aerodynamic drag coefficient cD and the frontal area A can be reduced to a value of cÂ x 0.6m2 (Fig. 3.12) for all vehicles, independent of vehicle class, when the available aerodynamic 'know how' is applied effectively. The GM-Opel Corsa SR is proof of this, being in autumn 1983 the first production vehicle to exhibit a value slightly lower than the above mentioned C&A = 0.6 m2. This has been achieved in spite of a vehicle length of only 3.60m. It is also expected, within the foreseeable future,


CD.A [m2]

1.00 Y-

0.9ok

0.80 U

0.70 V-

0.60 U

0.50 U

t 1977 1983 1989

MY Figure 3.12 Trend of aerodynamic development, after ref. 3.8

that some particularly aerodynamically designed vehicles will exhibit drag areas cÂ of approximately 0.55 m2.

This discussion shows that by far the biggest potential is offered by aerodynamic drag reduction. Since some current cars still exhibit values of CjyA = 1.0 m2, it seems to be realistic to discuss aerodynamic drag reduction potentials of 40 per cent and more. Conversely, the discussed weight reduction potential of 10 per cent is still hard to achieve.

25 r

20

10

Sub compact car

Change of CD . A

ΤίΤ. ΓΤ .T. Change of G

ACD.A [%]

AG [%] Figure 3.13 Impact of changes in aerodynamic drag and vehicle weight on fuel consumption for a sub-compact car


3.5.4 Impact of aerodynamic drag and weight on fuel consumption

The results presented in this section represent on-road driving for vehicle speeds corresponding to ECE and EPA driving schedules. The correlation between daily on-road use and ECE or EPA dynamometer tests is not addressed.

Figure 3.13 shows the impact of changes in aerodynamic drag and vehicle weight on fuel consumption for a sub-compact car. It is evident that a linear dependence exists for all considered driving schedules. Due to the constant velocity sections of the Euromix Cycle, the influence of the aerodynamic drag under this cycle is greater than for the EPA Composite.

Even so, the influence of a weight reduction is slightly higher for the Euromix Cycle compared to the EPA Composite Cycle because the ECE Urban Cycle includes some very steep velocity gradients (Fig. 3.9).

2 5 r -

20 h-

15

10

5 h

Full-size car

Change of CD . A

Change of G

20 25

ACD. A [%] AG [%]

Figure 3.14 Impact of changes in aerodynamic drag and vehicle weight on fuel consumption for a full-size car

Similar results can be observed for the full-size car; see Fig. 3.14. In this case, the influence of reduction of the aerodynamic drag on the EPA Composite is less than for the sub-compact, while a reduction of weight leads to a larger percentage fuel consumption decrease than for sub-compacts.

Figures 3.13 and 3.14 clearly show that the potential for reducing fuel consumption by reducing aerodynamic drag is far greater than the potential by weight reduction, even though the scope available for reducing the two parameters is vastly different. Reduction of vehicle weight does of course influence acceleration and rolling resistance.

Detailed information concerning the impact of changes in aerodynamic drag and mass (weight) reduction for a percentage change in cÂ has been elaborated by Sovran.3 1() The analysis is based on the tractive energy

101

0.7

0.6

" Π R l · 0.5

0.4

0.3

3 0.2

0.1

0.0

l ^ s = ^ P ^ Γ f -0.00^

h* t;

I

■^r»

I

/£ A / / r / 1 / A A

/ / / #

/ / /£ 1 / / °\°

r l i i 4.0 8.0 10 20 30

% change fuel economy 5.0 6.0 7.0 CDA/G x104 [m2/kg]

Figure 3.15 Impact of changes in aerodynamic drag on fuel consumption for the EPA schedules, after ref. 3.10

40

2.5

^ 2.0

1.5

O 1.0

0.5

0

A -s*0$\

Γ iHJ Γ u \ I

t -0 .002.J

—^τάόίόΐ I

4.0

3.5

3.0

2.5 l·

2.0

1.5

1.0 E-.-

0.5

\ *A Kx J\

[ //^ύ Hy///s^

l·^ I I I I

4.0 5.0 6.0 7.0 8.0 4.0 5.0 6.0 7.0 8.0

CDA/G x 104 [m2/kg] CD/VG χ 104 [m2/kg]

Figure 3.16 Mass and tyre coefficient reduction required for equivalent fuel saving for a 1 per cent change of aerodynamic drag, after ref. 3.10


required by vehicles to negotiate a driving schedule (see also Sovran and Bohn3 1 1).

Figure 3.15 shows the corresponding impact of changes in aerodynamic drag on fuel consumption for the three EPA Schedules, Highway (H), Urban (U) and Composite (C). With the help of the appropriate diagram the impact on fuel economy can be calculated. The control parameter of the curves in the left diagram is the rolling resistance (tyre) coefficient/,.. Figure 3.16 shows on the left the mass reduction and on the right the tyre coefficient reduction required to achieve the equivalent fuel saving of a 1 per cent change in aerodynamic drag. The working charts shown in Figs 3.15 and 3.16 are valid for any vehicle driving the EPA schedules.

3.5.5 Fuel consumption of light vans

The influence of aerodynamic drag on the fuel consumption of light vans has been studied by Hucho and Emmelmann.34 Table 3.5 shows the essential data of the vehicles investigated. For comparison purposes both

Table 3.5 Data for fuel consumption calculations (after ref. 3.4)

Item

Frontal area Kerb weight Gross vehicle weight Tyres Gearbox efficiency Power output

at rpm Displacement volume Original drive ratios «1

h h i4

Rolling resistance coefficient

Petrol engine

4300 min - 1

2000 cm3

24.39 12.31 7.61 4.87

4 m2

1600 kg 3000 kg 195R14C 0.9 50 kW

Diesel engine

3600 min"1

2700 cm3

18.32 9.24 5.39 3.67

0.0130 to 0.0145 according to speed

petrol and diesel engined vehicles were studied. The fuel consumption of these vehicles with unchanged drive ratios over the speed range is shown in Fig. 3.17. The control parameter of the curves is the aerodynamic drag coefficient cD, which is established in each case for the vehicles with half payload, this being the load condition used when measuring fuel consumption in accordance with DIN and the more recently adopted ECE standards.

These computed data correlate well with measured results, as was demonstrated by Hucho, Janssen and Schwarz3 12 on passenger cars. The advantage of the diesel engine in offering low fuel consumption, especially under low engine loading, is clearly demonstrated.

The influence of aerodynamic drag on fuel consumption is considerable. For the petrol engine under constant speed conditions its effect is more evident than for the diesel. Adjusting the ratios of the gearbox would offer even better fuel economy potential along with drag reduction.

In order to evaluate the fuel consumption characteristics of light vans the


Petrol engine Diesel engine

80 km. 100 h

40 60 80 km 100 h

Figure 3.17 Impact of changes in aerodynamic drag on fuel consumption of a van, after ref. 3.4

EPA Combined Cycle, consisting of 45 per cent highway driving and 55 per cent city driving, was used. The reason for this choice is that light vans are driven as cars in similar traffic conditions, their use being centred around both town and local traffic environments. No freeway input was made as no information concerning this type of usage was available. For the same reason hill climbing was also not taken into consideration.

Petrol engine Diesel engine

0.3 0.4 0.5 0.6 0.3 0.4 0.5 0.6

CQ ^ ^ CQ *^

Figure 3.18 Fuel consumption of vans for the EPA Composite Cycle, after ref. 3.4


The fuel consumption for this cycle is shown in Fig. 3.18 as a function of the drag coefficient. Starting point for the study is the average drag coefficient of vans, 0.46, which was established by the measurement of 17 vans.3 4 In this case the gearing is matched in order that the stated engine speed for maximum power output plus 400 rev/min is achieved when the vehicle is driven at top speed with half payload. If aerodynamic drag is reduced and the gear ratios are adjusted suitably, the continuous line shows the achievable fuel consumption.

The fuel saving is then approximately 50 per cent greater than that obtained with no matching (dotted line). Because light vans are essentially lower in performance than cars, when frontal area and weight are considered, their engines operate closer to the full load curve on the specific fuel consumption map during the driving cycle. As a result of this, more favourable specific fuel consumption is achieved, resulting in relatively low absolute consumption values. Because the increase in specific fuel consumption as a result of reduced load in this part of the diagram is less apparent than under partial load conditions, the effect of the increased specific consumption resulting from drag reduction is not so detrimental to the achieved absolute fuel consumption improvement. This leads to greater effectiveness of drag reduction in lowering fuel consumption on this type of vehicle than on passenger cars.

The effectiveness of the drag reduction on the fuel consumption B, for half payload, in the case where the gear ratios are matched is

AB AcD Petrol engine - — = 0.40 — - (3.20)

AB AcO

Diesel engine — - = 0.50 — - (3.21) # o cDo

where Ba and cDo are values for the fuel consumption and drag coefficients before the drag improvement AcO. The effectiveness of the drag reduction is therefore greater for a van with a diesel engine than for one with a petrol engine. The reason is that the given driving cycle includes a considerable amount of engine operation in a specific consumption area (in the specific fuel consumption map) where the difference in consumption between petrol and diesel engines is considerable.

If, in the given example, the drag coefficient cD was reduced from 0.46 to 0.30, a fuel consumption reduction for a petrol-engined vehicle of 14 per cent would be returned. For a diesel-engined variant, a reduction of 17 per cent would result.

3.6 Outlook

The continual depletion of crude oil supplies will certainly ensure gradual fuel price increases. Alternative fuels based on coal and alcohol will have little effect on the situation, but they may help to reduce the effect. Low fuel consumption will therefore be an important selling point.

Vehicles with favourable fuel consumption will be more expensive to manufacture than current vehicles. Further development of lighter vehicles

Notation 105

will almost certainly lead to the use of more expensive materials. Aerodynamic requirements such as more rounded glass or flush window areas also add to product costs.

In order to decide which product price increases can be tolerated in the market place to obtain reduced fuel consumption, it is advisable to use a customer-oriented cost-benefit calculation. This ensures that only con-structive measures that are economically viable in the eye of the customer are adopted.

3.7

A B BA BI GN P V V v„ Vs

v„ WA

Wc

wO wR z K cD cT

Λ / m n

ß ηΑ ηο P Φ

Notation

frontal area fuel consumption (1/100 km) accelerator pump amount idle consumption normal force (weight) engine power vehicle speed acceleration displacement volume side-wind speed air speed accleration resistance climbing resistance aerodynamic drag rolling resistance tractive force specific fuel consumption drag coefficient tangential force coefficient rolling resistance coefficient gear ratio mass engine speed yaw angle axle efficiency gearbox efficiency air density ascent angle

Chapter 4

Aerodynamic drag of passenger cars Wolf-Heinrich Hucho

4.1 The passenger car as a bluff body

The subject of air resistance of road vehicles is still essentially speculative. Accurate theoretical prediction is not yet possible, nor are we able to make a quantitative assessment of drag from existing experimental data. Despite this, some quantitative prediction is essential if drag reduction is to become a part of normal vehicle development.

It is easy to see why prediction of drag is so difficult when the complex shape of the car is compared with standard bluff bodies (Fig. 4.1).

- I ..

A frontal area p air density

W7< - 1 -

0.9

VL-^r^l-Λ \h 0.45

d U-/—J cD = 0.05

/

Figure 4.1 Comparison of the drag of passenger car and other bluff bodies

The drag of a body of revolution, cD = 0.05, consists mainly of frictional drag. The extreme case of pure frictional drag would, of course, be a flat plate in a parallel air flow (see section 2.3.3). The viscosity of the air is significant only within the narrow zone adjacent to the wall, called the boundary layer. The thickness of this layer, the shear stress at the wall, and the point of separation can be calculated from experimentally determined wall stress laws, having first calculated the friction-free (non-viscous) external flow. In this way it is possible to optimize the body of revolution.4Λ The shape for minimum drag can be calculated for a body of given fineness ratio and volume, and the theory can be used to translate results from scale models to full-size bodies. However, the accuracy of this prediction decreases as the fineness of the body decreases, mainly because

106

Flow field around a passenger car 107

of uncertainty in predicting the point of separation and pressure within the wake.

The drag of a rectangular box with air flowing along its longitudinal axis, cD = 0.9, is almost entirely pressure drag (section 2.3.3), the purest form of which occurs with the flat plate perpendicular to the oncoming flow. Even in this simple case (simple because the point of separation is determined by the sharp edges) the pressure drag cannot be calculated for the turbulent wake. The interaction of the flow field (in which viscous effects predominate) and the non-viscous exterior flow is much stronger than in the case of the boundary layer. A reliable model for the turbulent wake still eludes us despite the efforts of Tanner42 and others. Iterative calculation of the non-viscous outer flow and the flow in regions where viscosity predominates is therefore still not possible. Accurate calculation is possible using the Navier-Stokes equations where flow is laminar, but no such laws of general validity are available for turbulent flow (see Hirt and Ramshaw4 3 and Chapter 13).

In spite of its comparatively low drag, the passenger car is closer to a rectangular box in terms of fluid mechanics than it is to a body of revolution, though with refinements in aerodynamics progress is towards the body of revolution. The flow round a car body is characterized by separation (Figs 1.1 and 1.2) and its drag is primarily pressure drag.

Attempts to relate drag to primary shape characteristics (see section 1.2.3) have been unsuccessful. The number of parameters describing the geometry of a car is too large and the interaction of the individual flow fields too complex. This chapter therefore deals mainly with qualitative data. Results for individual models are listed, but these should be treated with caution and not used for the assessment of drag of superficially similar vehicles. A prediction of possible low drag shapes for passenger cars of the future completes the chapter.

4.2 Flow field around a passenger car

As a rule, the flow around a moving vehicle is asymmetric. The flow velocity VOo results from the vehicle speed V and the velocity Vs of the natural wind giving rise to an angle of yaw ß relative to the direction of vehicle motion; see Fig. 4.2. For the sake of simplicity, symmetrical flow is considered first; the influence of side wind upon drag is then discussed in section 4.5.2. The asymmetrical flow field is described in detail in the context of directional stability in Chapter 5.

The flow field around a vehicle is not yet fully understood, so a picture must be built up from pressure distribution measurements, velocity field measurements and flow observations on the vehicle surface. This is treated in greater detail in Chapter 6.

~W-Figure 4.2 Vector diagram of driving speed V and speed Vs of natural wind

108

Figure 4.3 Flow around a car, front end and details, schematic

Figure 4.4 Flow pattern for different rear end configurations, schematic


The flow field for a passenger car—derived from such information—is illustrated in Figs 4.3 and 4.4, and is characterized by numerous separations (see Figs 2.12 and 2.13, section 2.3.4 for the two types of separation).

Where the streamlines are illustrated with dots in Figs 4.3 and 4.4, or where the areas of separation are dotted, the separation has a quasi-two-dimensional character. In this case the line of separation tends to run perpendicular to the local flow direction. If reattachment occurs, so-called separation bubbles are formed. Of course the flow inside the bubble, which is shed from a three-dimensional body, is three-dimensional in nature. However, since the separation itself is mainly two-dimensional with separation line normal to the flow and vortex axes parallel to separation line, it is designated 'quasi-two-dimensional'. This type of flow can occur at the leading edge of the front hood, at the sides on the fenders, on the cowl and on the front spoiler, and possibly in the notch of a notchback. Wakes also form on the blunt rear of a squareback. Depending on the outer flow field, long wakes are formed, which extend far downstream, or the wakes are short and closed (see Fig. 4.5, after ref. 4.4).

Figure 4.5 Large, long, open wake of a squareback and small, short, closed wake of a fastback, after ref. 4.4

Although the flow in these separation bubbles is unsteady, its time average identifies a macrostructure in which the separation bubbles contain circulation, and the axes of the vortices run primarily perpendicular to the undisturbed flow and parallel to the line of separation. Little is known of how these vortices 'double back' in the shape of a horseshoe in the main flow direction at the side boundaries of the separation bubbles and how they interfere with the exterior flow. These vortices, which rotate transverse to the oncoming flow, have been made visible within the wake at the rear end by Ahmed and Baumert,4 5 and their course as a vortex pair has been followed downstream (see also Ahmed4 6) .

Figure 4.6 shows the counter-rotating vortex pair for a notchback, a fastback and a squareback. The lower vortex rotates counterclockwise and is responsible for carrying the contamination to the rear of the vehicle (see section 6.4). The upper vortex rotates in the opposite direction. After the separation bubble closes, a pair of counter-rotating longitudinal vortices forms in the trailing wake. This produces an upwash in the case of a squareback, and induces a downwash in the trailing wake flow on a notchback or fastback. The vector diagrams in Fig. 4.7 clearly show these

110

notchback fastback

squareback

Figure 4.6 Counter-rotating transverse vortices in the wake of cars with the three typical rear end configurations, after refs 4.5 and 4.6

i-2i mttf ilMiil 0.8|

0.6

0.4

0.2

0 1.2r

1.0f

Notchback

Plane

1 2 3 4

X

7 0.04 0.24 0.48 0.96

0 0.2 0.6 1.0 1.4 0 0.2 0.6 1.0 1.4 0 0.2 0.6 1.0 1.4

y fib/2)· y/ib/2)-

Figure 4.7 (continued opposite)

Fastback

Plane

1 2 3 4

X

1 0.04 0.24 0.48 0.96

0 0.2 0.6 1.0

y/{b/2)—* 0.6 1.0

y/(b/2)—■ 0.6 1.0

y/[b/2)—*

Squareback

Plane

1 2 3

I 4

/ 0.04 0.24 0.48 0.961

0 0.2 0.6 1.0 1.4 0 0.2 0.6 1.0 1.4 0 0.2 0.6 1.0 1.4 y/(b/2)—+~ y/(b/2)—+» y/{b/2)—+»

Figure 4.7 Transverse velocity vector diagrams for notchback, fastback and squareback after refs 4.5 and 4.6

112 Aerodynamic drag of passenger cars

vortices, and confirm earlier information given by Howell,47 who measured the downwash field for a notchback. On a squareback, the vortex pair rises in the flow direction and wanders toward the plane of symmetry. On fastbacks and notchbacks the vortices approach the road downstream and move to the outside. It can be postulated that these longitudinal vortices are the continuation of the lateral vortices described above. Note the velocity decrease toward the centre of the vortex (Fig. 4.7). The longitudinal vortices are slowly exhausted downstream by dissipation (Fig. 4.8, after Ahmed and Baumert4 5 and Ahmed4 6) .

0.3

0.2 l·

r

0.1 l·

r »«_ /Fastback

i 1 1 1 1 1

.Squareback A

I | I

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

x/l ► Figure 4.8 Decay of circulation in the trailing vortices, after refs 4.5 and 4.6

The second type of separation is three-dimensional in nature. It is shown in Figs 4.3 and 4.4 with dashed lines and hatched shading. Vortex trains are formed at sharp edges where the flow is oblique, as with a delta wing. Such a vortex pair forms on the two A-pillars (section 6.5) and is bent back toward the roof at the upper end of the A-pillars. Its effect on the rear end flow is still unknown. A strong vortex pair forms at the rear of the vehicle, depending on the inclination of the rear end (Fig. 4.4). These rear vortices interact with the external flow field and with the quasi-two-dimensional wake and are similar to the tip vortices of a wine of low aspect ratio. These vortices were measured in detail by Hummel for slender delta wings. They induce a downwash field in the space between their axes, which determines the position of the separation line for the wake. This mechanism is shown in Fig. 4.5. A strong vortex pair is present in the right-hand portion of the figure. Its formation is artificially prevented in the left-hand portion. In the first instance the downwash induced by the vortex pair has the effect that the separation line is quite low and a short wake is formed. In the second instance the flow separates at the upper edge of the roof; the wake is long.

The interaction of the C-pillar vortex pair ('tip vortices') and the vortex system of the quasi-two-dimensional separation bubble has been examined by Ahmed.4 9 Figure 4.9 shows the flow at the rear of a vehicle for three angles of inclination φ of the rear end. In case (a) φ = 5°. This is a


Figure 4.9 Flow pattern on rear end, after ref. 4.9. — Stagnation or separation line

squareback and the flow corresponds to that shown in Fig. 4.7. The stronger lower vortex, which rotates counterclockwise in the vicinity of the vehicle, generates an upwash with its developing horseshoe vortex. This can also be seen clearly in the vector diagram in Fig. 4.10. At the higher angle of inclination of the rear end, φ = 15° (Fig. 4.9b and 4.10c), the C-pillar vortex pair has developed. It induces a downwash, which forces the external flow downward in the area of the rear end and keeps it attached. At φ = 30° (Fig. 4.9c) the C-pillar vortices are highly pronounced; however, the flow separates in front of the rear edge. At angles of φ > 30° the flow separates at the upper edge of the roof, C-pillar vortices are not formed and a squareback flow regime is again present.

Between 10° < φ < 15° the effect of the downwash-inducing C-pillar


y/lb/2) y/(b/2) f Figure 4.10 Transverse velocity vector diagrams and drag coefficients for a fastback car with different rear end slope angles φ, after ref. 4.9

vortex pair and the upwash-inducing vortex from the separation bubble counteract one another. As Fig. 4.10e shows, the drag is at a minimum at this angle. For φ = 30° the drag is at maximum. The C-pillar vortices are so strong that flow remains attached over almost all of the sloping back, despite the large angle of inclination φ.

According to Ahmed,4 9 the flow field was rather unstable for φ = 30°. The separation line changed its position from the upper edge of the slant to the lower end at random, moving up and down several times during the time it took to traverse the vz-plane.

As Fig. 4.8 shows, the vortex strength Γ is significantly higher on a fastback than a notchback, and the decay of the vortex strength behind the vehicle is less pronounced.

From the details elaborated above, the vortex pattern sketched in Fig. 4.11 can be deduced. In principle there are three different vortex systems. Vortex C, emanating at the C-pillars, has a 'potential flow' character. With the exception of a comparatively small viscous core area, its circumferen-tial speed increases with decreasing radius (measured from the vortex centre). The strength Γ of this C-pillar vortex increases with slant angle cp; see Fig. 4.11, bottom sketch. If the slant angle φ exceeds 30° this vortex bursts (see Hummel4 8) and the flow pattern changes to the squareback flow regime. Vortex A and vortex B are generated in the quasi-two-dimensional manner at the edges A and B respectively. They are of the viscous type and their vorticity is low. They are inclined rearwards as shown. They are either dissipated (Fig. 4.8, lower curve) or somehow


merge into C-pillar vortices. A picture of this vortex system has been derived by Ahmed et al.410 (Fig. 4.12). In the high drag flow regime at φ = 30° (Fig. 4.12b) a fourth vortex E is generated at the slant. For further details see section 4.3.2.5.

Figure 4.11 Vortex system for a sloping rear end, schematic

The flow along the underside of the vehicle is particularly unclear and suggests comparison with that of a very rough plate or with the flow in a narrow channel with one very rough wall. The shape of the flow field in the wheel wells and around the rotating wheels is also vague (see section 4.3.2.8). On the other hand, as deduced in Chapter 9, the relatively complex flow through the cooling air duct, consisting of grill, radiator, fan and engine compartment, can be described quite well using the methods of pipe hydraulics, which are outlined in section 2.4. However, detail problems, such as the distribution of the air velocity across the radiator matrix, cannot be solved in this manner.

116

(a)

(b)

Figure 4.12 Vortex system for a sloping rear end, after ref. 4.10: (a) low drag flow regime; (b) high drag flow regime, φ = 30°

Analysis of aerodynamic drag 117

4.3 Analysis of aerodynamic drag 4.3.1 Global considerations

The object of analysing aerodynamic drag is to determine the relationship between cause and effect. If each detail's contribution to drag could be defined and then minimized, a vehicle with the minimum aerodynamic drag would be obtained, but the high degree of interaction between parts limits the success of this procedure (section 4.4.4.1). Cars with very low aerodynamic drag cannot be designed piecemeal, but require total consideration of the drag phenomenon.

Different explanations of drag have been based on

• the physical causes • the local origin • the effect upon the surrounding field. Consistent application of each of these methods leads to the correct result, but errors often appear when partial arguments from the three categories are mixed with one another. One example of this is the induced drag, as is shown in this section.

The physical causes of aerodynamic drag can be investigated by comparing the actual, frictional (viscous) flow with the ideal, friction-free (non-viscous) flow and breaking down the drag into its pressure and frictional components. The occurrence of both components is explained in Fig. 4.13. The surrounding flow field generates a pressure and shear stress distribution around the vehicle. At points where the flow is opposed by a high pressure increase, it tends to separate from the contour. This phenomenon is explained in section 2.3.3, Fig. 2.7. In the example in Fig. 4.13 it is assumed, for the sake of simplicity, that separation occurs only at the rear end of the vehicle. As a consequence the pressure distribution there deviates from that in non-viscous flow. If the pressure is plotted against the width of the vehicle, as shown upper right in Fig. 4.13, it becomes evident that this change in the pressure distribution is highly significant for the origin of drag.

The shear stresses at the wall decrease with increasing boundary layer thickness, and fall to zero at the separation point. If the pressure and shear stresses are integrated over the entire surface, as described in the two

pressure p shear stress r0 y/b rear, /viscous flow

*-Y-2

front, viscous and ideal flow rear, ideal flow

viscous flow

ideal flow £ o = 0 separation

Op = fp smydA Dp = / r 0 cos φ dA bluff bodies DF< Dp

Figure 4.13 Definition of pressure drag DP and skin friction drag DF; distribution of pressure and shear stress on a car (schematic), after ref. 4.4


integrals in Fig. 4.13, the pressure and frictional drag are obtained and, by addition, the total drag. This also includes drag induced by any vortices present, often called 'induced drag' from aircraft wing aerodynamics. This drag component is treated separately later.

The frictional drag of a passenger car can be estimated simply if the surface of the vehicle is treated as a flat plate in parallel flow. (The data upon which the estimation is based are summarized in Table 4.1.) If a mean effective surface velocity of approximately 10 per cent higher than the vehicle speed is assumed, as did Carr,4 n and the underside treated as a smooth flat wall, this results in a frictional drag coefficient of cDF = 0.04.

Since it was assumed that the entire surface was smooth, this value can be considered to be a limit that cannot be improved significantly by further refinement of vehicle aerodynamics. Carr4 assumed an additional drag coefficient of AcDF = 0.07 for a rough underside. As will be illustrated in Table 4.1 Estimation of friction drag coefficient cDF

typical dimensions [mm]

I = 4700 t = 725 b = 1780 e = 190 h = 1440 Γ = 2300

frontal area: A = 0.83-b-h = 2.1 m2 (see Fig 1.48)

tangential surface S = 26.1 m2

fr iction drag coefficient

CDF"Cf Ä KvZ) c, =0.003 (see Fig. 2.9, Re = 1.107)

cDF =0.003 ^ - 1 .2^0 .04 2.1


section 4.3.2.9 this additional drag can be greatly reduced with front spoilers.

From this estimate it follows that the pressure drag is the largest component in the aerodynamic drag. Its minimization is the true objective of motor vehicle aerodynamics.

Table 4.2 Breakdown of the aerodynamic drag of cars

Total air drag

External drag

Body drag

Protuberance drag

I Engine cooling drag

Internal drag

Heating and ventilation drag

Component cooling drag

Drag can be broken down as shown in Table 4.2, based on Carr.411

Quantitative results for the body drag have been presented by Ahmed et aj 4.io ^pjg 4 i4) p o r the v e ry simple configuration investigated, the forebody drag c£ turned out to be small and almost unaffected by changes of the rear end. Friction drag cR is also fairly constant in absolute figures, when the rear slant angle φ is increased. The drag of the slant is increased

^c - s ^

V

Drag Coefficient

Figure 4.14 Variation of total drag and drag shares of body parts with rear end slope angle cp, after ref. 4.10


drastically with increasing φ, partly because of the slant's increasing contribution to the total frontal area, partly because of the vortex-induced pressure decreasing with cp. For slant angles above φ = 30° drag is reduced drastically. Owing to vortex burst the base pressure is increased; thus pressure drag cl at the slant is small.

The effect of aerodynamic drag upon the surrounding field is shown in a highly simplified form in Fig. 4.15a. By applying the theorem of momentum to the reference volume C, the drag of the vehicle can be calculated. By measuring the velocity field in the plane S, the structures of the wake and the vortex field can be made visible, as shown in Figs 4.7, 4.10 and 4.15b. The proportion of drag caused by the vortex system, the 'induced' drag, can be isolated in this manner. However, it must be reiterated that this portion is taken care of during the integration of the pressure and frictional drag according to Fig. 4.13.

As in aircraft aerodynamics the term 'induced drag' is often used and the total drag is broken down as in wing theory, but the formula derived for wings cannot be applied to cars, as will be shown below.

The drag coefficient cD of a wing is composed of the profile drag cDo and the induced drag cDi.

CD = CDo + CD i (4 .1 )

Figure 4.15 (a) Effect of a car upon the surrounding flow field. Derivation of drag and its components with the aid of momentum theorem, see refs 4.97, 4.98

121

Figure 4.15 (b) Wake survey of Opel Kadett model year 1980, top, and Opel Kadett model year 1985, bottom; see refs 4.99, 4.100


The profile drag consists of a pressure and a friction component. It is measured or calculated under two-dimensional conditions and comprises all effects of the viscosity of the medium flowing around the body (section 2.3.3). The induced drag cDi, on the other hand, is calculated using potential flow theory, i.e. in frictionless flow (see Schlichting and Truckenbrodt4 12). The induced drag results from the system of free vortices generated by the wing's lift. This is taken into consideration by relationships in the form of

Λ

A

Induced drag cDi ~ —— (4.2)

Aspect ratio Λ = —— (4.3)

Wing area A = bl

where b = wingspan and / = chord length. However, breakdown of the total drag cD according to Eqn 4.1 is only practical when the two flow fields responsible for the fractional drags cDo (profile drag, two-dimensional flow) and cDi (induced drag, three-dimensional vortex field) do not interfere with one another, which only occurs with wings of high aspect ratio. However, because the aspect ratio according to Eqn 4.3 is very small for vehicles (Λ = 0.3) a breakdown of the flow field into two- and three-dimensional components is not possible. The effect of the vortex field can therefore not be separated from that of the other flow field, as is possible for aircraft wings with a high aspect ratio.

A relationship between induced drag and lift similar to Eqn 4.2 has been derived for wings close to the ground, and in motor vehicle aerodynamics a corresponding relationship derived by Wieselsberger4 13 was used (see Morelli414~ ). Potthoff4 18 determined the proportionality factor in Eqn 4.2 to be 0.5/π from downwash measurements on blunt bodies near the ground. Measurements on vehicles, for which a model line-up exists with notchback, fastback and squareback, can be classified quite well according to Eqns 4.1 and 4.2 (see Fig. 4.16). But to assume from this that the 'profile

0.6

10.4

0.2

i / /

- C D O — t - * * ~

I

h'-fa

1

|

1

1 I

4 -· ^ \ l

•

0.6

A0.4

0.2

/

/

in l \

|

CD

cD cD o

CDi

0.2 0.4 cD ►

= cDo + cDl

= Total drag = Profile drag

= Induced drag

0.6 0.2 0.4 0.6 cD ►

— o — Type 3 Model 1:4(DFL)

— · — Type 3

— ■ — Type 4

— Δ — Opel Olympia/Kadett

Figure 4.16 Lift versus drag for several car families, notchback, fastback and squareback


drag' of the three different rear end shapes is equal is hardly plausible because, as shown in Fig. 4.9 for example, the position of the separation line changes when the flow pattern is changed from the fastback type into a squareback type and vice versa, i.e. the characteristic properties of the flow field around the 'profile' are significantly different. Therefore the profile drag will also change. Muto4 1 9 has plotted numerous measurements made by Motor Industry Research Association (MIRA) and Japan Automobile Research Institute (JARI) in diagrams of the shape cL (cD). Through curve fitting he deduced a relationship of the shape cD = cDo + Kci2. However, more than a tendency for vehicles with high lift frequently to have a high drag, cannot be obtained from this. The derived formula is of low significance.

Similar trends have been observed with racing cars; see section 7.4.1. Most of the devices producing high negative lift have the disadvantage of causing a high drag increase.

Measurements have also been made in which an increase in lift was accompanied by a reduction of drag. One example of this is Fig. 4.17, from Hucho.4 4 Various flow conditions were generated with different spoilers

A ^ Γ Τ = ^

Basic configuration

Rear spoiler

c 4*HT%

Fender spoiler

^ f H " g p Front spoiler

CD ! cL |

1 0.34 1 0.38

1 0.33 | 0.18

I

0.38 j 0.48

0.38 j 0.29 Figure 4.17 Pairs of drag and lift coefficients produced by different add-on parts to a basic car, after ref. 4.4

on a reference vehicle, a Volkswagen 1600 with notchback prepared for comparative tests in various wind tunnels. In case A, in which the vehicle had no attachments whatsoever, approximately the same drag was measured as in case B with a rear spoiler. However, in the latter case the lift is less than half as great as in the first case. Configuration C with a pair of spoilers on the front fenders and configuration D with a normal front spoiler have exactly the same drag, although a considerable difference is present in the lift. If, finally, case A is compared with case D it is obvious that case A has a lower drag and simultaneously a higher lift than case D. Therefore in some cases the drag and lift increase simultaneously, while in other cases the relationship is exactly opposite. Therefore, that part of the drag of a car induced by the trailing vortices cannot be calculated with Eqns 4.1 and 4.2.

The drag is broken down into profile drag and vortex-induced drag for analysis of the drag with different rear end shapes in section 4.3.2.5. Here it is also explained how the lift of a solid body near the ground develops and that there is not a simple relationship between the overall lift and drag for this.


4.3.2 Components of drag

4.3.2.1 Procedure

The development of the drag on the individual components of a passenger car, for which the flow fields were shown in Figs 4.3 and 4.4, is described below. Attention is focused on two aspects: first, the mechanism of drag at the observed location itself is explained; second, the effect of the associated flow field upon the adjacent areas is investigated. In doing so it is not sufficient to examine the effects downstream of the specific location under consideration. Owing to the subsonic character of the flow field, disturbances at one point also have an effect upon the entire flow field—including upstream areas.

The pressure drag is explained by the deviations of the pressure distribution in actual flow from those in friction-free flow. The pressure distribution in friction-free flow can be calculated with procedures described in Chapter 13. This requires a great deal of work—particularly in preparing the geometric data. For this reason it is reasonable to proceed somewhat more pragmatically by changing the detail in question until the flow no longer separates around it. The associated pressure distribution is compared with that of the initial contour to obtain information on the pressure drag for the initial contour. Naturally, this is not exact, because the pressure distribution of the modified contour does not completely correspond to that calculated for the friction-free flow on the initial contour.

The frictional drag can be determined from the wall shear stresses or from the related momentum loss. Such measured results are available only for a few shape details. The reflections below are therefore more qualitative and in part more schematic. They are supplemented by numerous examples from real vehicle developments.

4.3.2.2 Forebody

Considering first the simpler case in which the cooling air inlet is closed, the flow over the forebody is distinguished by a stagnation point and a surrounding high pressure area (see Fig. 2.4, and also the plain stagnation point flow, Schlichting and Truckenbrodt4 12). Downstream of this point the flow is deflected strongly onto the hood, the fenders and the lower front panel. Figure 4.18 shows the case of a separation on the hood. In actual

p-P~

2 °°

- 2 - 1 1 cp

Figure 4.18 Pressure distribution along the centre line section of a forebody; schematic

125

°-<

^ Η ^ — ^ ^ — = ^ = - — 2

.S--

5 5 _ - 2 -1 1 PRESSURE COEFFICIENT, CP

- 2 - 1 0 1 PRESSURE COEFFICIENT, CP

s

F

— ο * - " * * \

1

. / <—

- 2 - 1 1

PRESSURE COEFFICIENT, CP


- 2 - 1 PRESSURE COEFFICIENT, CP

' <~»S

F

- ^ pJ-^X· fvTr L> n


Figure 4.19 Pressure distribution along the centre line section of various forebodies, after ref. 4.11


flow, the suction peak at the upper corner is very much less pronounced than for ideal, separation-free flow. On the other hand, the pressure above the stagnation point is slightly greater than for friction-free flow. At the stagnation point itself cp is equal to 1 in both cases. Therefore the force acting upon the forebody in the flow direction in actual flow is greater than in ideal flow.

Pressure distributions for various forebody shapes have been published by Carr;411 see Fig. 4.19. However, it is questionable to derive the forebody drag from such pressure distributions, even if a sufficient number of pressure taps are applied to provide adequate accuracy. None of the forebodies shown in Fig. 4.19 is likely to have a zero axial force in non-viscous flow. Only the difference between these axial forces in viscous and non-viscous flow is drag. Accordingly it does not make sense physically to cut models at the location of their largest cross-section, measure the axial forces on forebody and afterbody (measurement on each part of course done in the presence of the other section of the model) and quote forebody and afterbody drag (see Garrone and Costelli4 20).

The statements made based on the schematic of Fig. 4.18 are confirmed by the measured results shown in Fig. 4.20 (after Hucho421). The data

Figure 4.20 Pressure distribution along a horizontal line of a Volkswagen van; r/w = 0.085, well-rounded corner, flow attached: cD = 0.40; r/w = 0, sharp corner, flow separation: cD = 0.45

plotted here are the pressure coefficients cp, measured at beltline height, over the width of a Volkswagen van on which the radius between the front and side panels was increased in increments. The air flows around the well-rounded corner, r/w = 0.085, without separation although a strong suction peak is present. On the sharp-edged corner, r/w = 0, the flow separates. The suction peak is reduced and the pressure on the front wall increases. In the present example this leads to an increase in drag of AcD = 0.05, which is more than 10 per cent of the total drag for this model. The increase of the pressure in front of the separation point is a clear example that a downstream disturbance—here separation—has an effect upon the course of the pressure upstream.

Figure 4.18 and the diagrams in Fig. 4.19 also show that the separation on the front edge of the hood is not only disadvantageous for the drag. The pressure at the cowl, the point where fresh air is taken in for the heater and for ventilation, is reduced. The amount of this reduction depends on the size of the bubble and on the position of the reattachment line on the hood. As a rule, the pressure at the cowl is cp = 0.4-0.5. The steeper the angle of the windshield, the higher the pressure. When the flow separates at the


Figure 4.21 Drag reduction by front end shape modifications, after ref. 4.22

front edge of the hood and does not attach further downstream the pressure at the cowl is reduced to cp = 0 (see also section 6.2.2).

Figure 4.21 shows an example for a front end that was developed purely empirically; see Hucho and Janssen.4 22 Here the development of the longitudinal midsection is illustrated. The initial shape is designated 'forebody Γ and illustrated in each case for comparison. The bar graph shows the percentage change in drag in comparison with the initial shape. A small correction of the shape on the front edge alone reduced the drag by 6 per cent. The front end shapes 3, 4 and 5 represent equal variants; they provide an improvement of 10 per cent. Shapes 6 and 7 already show significant stylistic deviation from the initial shape; they are intended to show the maximum improvements possible. In the present example a drag reduction up to 14 per cent was achieved with this particular detail.

Figure 4.22a provides an example of the optimization of a complete front end (the term optimization is defined in section 4.4.1). This is the result from the development of the VW Golf I; see Janssen and Hucho.423 In order to determine the maximum drag reduction that can be achieved by optimum front end design, the flow around the front end was first improved with an attached 'nose', designed according to purely aerodynamic aspects without consideration of the external appearance. The stimulus for this approach (explained in greater detail later) came from the work of Carr.4 It is most practical to design this nose in several pieces in order to separate the influence of the upper hood transition from that of the lateral fender transitions. By attaching both parts Ml (hood transition) and Kl (fender transition) a maximum reduction in the drag of AcD = —0.05 was measured. This value represents the limit that can be achieved with the given front end main dimensions without taking into consideration the stylistic realization.

If the original fender transition is improved with part Kl, only a slight improvement in drag of —0.015 is achieved; i.e. with an optimum lateral


Centre line cross-section

Horizontal section, height of headlamps

KO ^ f %k K2 Jk . K3

-0 .05 A -0 .04 I -0.03

A c ° -0 .02 -0 .01

(a)

M1 +

K1

K1 M2 M2 +

K2

M3 +

K2

M3 +

K3

Figure 4.22 Detail optimization of the Volkswagen Golf I (Rabbit), after ref. 4.23: (a) drag reduction by small detail changes; (b) attached flow despite relatively sharp hood leading edge

transition only 30 per cent of the drag improvement of the 'ideal' attached front end is realized. With shapes M2 and K2, in which the contours were modified in such a manner that the circumferential surface strip remains as a stylistic element, a reduction in the drag of -0.02 is achieved,


corresponding to 40 per cent of the maximum possible improvement. Of the possible reduction in the drag, 90 per cent is achieved with shapes M3 and K3 with slightly rounded front end edges. This change in the front end shape results in only a slight modification of the styling without influencing the primary dimensions of the front end. A front end edge with rounded transition optimized in this manner was realized on the VW Golf I and VW Scirocco I. How perfectly the air flows around a front end shaped in this manner is shown by the smoke trails in Fig. 4.22b.

The attached front end used in Fig. 4.22a was designed in such a manner that the air flows around the forebody without separation. This shape is frequently designated as an 'optimum front end'. However, the condition of smooth flow can also be achieved with other shapes, which may have an even lower drag coefficient than the shape selected in Fig. 4.22a. The four different attached front ends shown in Fig. 4.23 (see Hucho, Janssen and Emmelmann4 25) indicate that the various shapes of this type differ only

v////////*

Basic shape

Detail X

Figure 4.23 'Ideal' front end and shape modifications, after ref. 4.25

slightly from one another in terms of drag improvement. Only the contour drawn with dots can be designated as 'optimum'; the other shapes are not quite as good. Therefore when an attached front end designed intuitively is frequently designated as the 'optimum front end' and its drag coefficient is specified as the target, this is not quite correct—although the differences may be slight.

It is not always possible to achieve the drag coefficient of the optimum front end with such small shape modifications as was the case for the VW Golf I and VW Scirocco I. An example of this is given in Fig. 4.24. Originally the Audi 100 II, model year 1975, was to be built with the front end shape designated A, which was based on the previous model in terms of style. By attaching the 'optimum' front end it was possible to show that an 11 per cent reduction in drag could be realized solely with a front end around which the air flowed well. It was not possible to achieve this value


Figure 4.24 Detail optimization of the front end of the Audi 100II, model year 1975, after ref. 4.4

with slight variations of shape A while maintaining its basic appearance. Thereafter shape C was developed, with which it was possible to approach the optimum value by rounding the hood radius. Hucho4 4 showed that an equally good result could also be obtained by chamfering the front edge of the hood.

Chamfering of the front edge of the hood was applied in the development of the front end of the 1978 model VW Passat. As shown in Fig. 4.25, and clearly visible in Fig. 4.26 at the left, the previous model had a separation bubble on the engine hood, which contributed significantly to its drag. The optimum front end indicated the possibility of a 15 per cent reduction in drag. This could be realized approximately with the adapted

A VW Passat (Dasher) B Ideal front end

Figure 4.25 Front end optimization, Volkswagen Passat (Dasher), model year 1978 (facelift)


Figure 4.26 Flow around the forebody of the VW Passat (Dasher); left: model year 1977, right: model year 1978 (top, optimum front end; bottom, improved front end)

hood. At the same time the lift at the front axle was reduced considerably. The smooth course of the flow on the improved front end can be seen at the lower right in Fig. 4.26. The contribution of the front end spoiler is explained in section 4.3.2.9.

On the other hand, the fact that very small modifications of the shape can often approach the flow pattern of the optimum front end is shown in Fig. 4.27 (after Hucho, Janssen and Emmelmann4 2 5). In comparison with

Figure ^.27 Front end optimization by matching the leading edge of the hood to the grill position, after ref. 4.25

the initial shape, the optimum front end, shape B, provides a 9 per cent lower drag. The same result can be achieved with shape D, in which the hood is slightly rounded and the grill is moved forward parallel to the initial position. By contrast, only slightly more than one half of the possible improvement in the drag can be achieved with the variants of shape C.

A further example of front end optimization is given in Fig. 6.9. To achieve a low aerodynamic drag it is not sufficient to design the front

end simply so that the air flows along it without separation. The position of

132

production car-

Zs = stagnation point height Z v = vehicle height e = ground clearance

0.02

0.01

zJCD

-0.01 Figure 4.28 Effect of the stagnation point position on drag, after ref. 4.26

0.5

CD

0.4

35° 45° 55° 65° 5° δ a

Figure 4.29 Effect of bonnet slope a and windscreen rake δ on drag, after ref. 4.27


the stagnation point determines which portion of the flow passes over the vehicle and how much air must flow between the bottom of the car and the road. Figure 4.28, after Buchheim, Deutenbach and Lückoff,4 26 shows that there is an optimum stagnation point position. This depends upon the shape of the vehicle and the design of the underside. Generally it can be stated that a low stagnation point is favourable for low drag.

The inclination of the engine hood also has an effect upon the drag. Figure 4.29, after Carr,4 27 gives an example of this. Once the slope is steep enough to keep the flow attached, further sloping does not reduce drag any further. The 'optimum' slope angle ocF depends on the leading edge radius and on the windscreen rake.

4.3.2.3 Windshield, A-pillar

If the air flows across the front edge of the hood without separation, separation may occur at the cowl, while further downstream the flow will reattach somewhere on the windshield; see Fig. 4.3. This phenomenon has been investigated by Scribor-Rylski.4 28 To date only the results on flat, i.e. non-convex, windshields are known. Figure 4.30 shows clearly how the

c ' d

Figure 4.30 Flow separation on the bonnet and reattachment on the windscreen, as a function of windscreen rake γ, after ref. 4.28

point of separation S is displaced toward the front and the point of reattachment R toward the rear as the angle γ of the windshield becomes steeper. Here the longitudinal midsection is shown. In planes outboard of this section, the separation point and the point of reattachment should be closer to one another. The location and the shape of the three-dimensional separation bubble is highly dependent upon the lateral curvature of the windshield. On the configurations (angle of inclination, lateral curvature) existing in practice, the examined separation bubbles are small in comparison to those measured by Scribor-Rylski on the flat screen model.

As the windshield becomes flatter, the aerodynamic drag decreases. This has been known since the investigation by Lay 29 (Fig. 1.20) and has been

134

0.03

en c σ

5 10 15 increase of windshield angle Δ9 [°]

Figure 4.31 Effect of windshield angle φ on drag, after ref. 4.30

,55

Windshield angle δ [°]

56 57 58 59 60 61

Figure 4.32 Effect of windshield angle 6 on drag, after refs 4.31 and 4.32


confirmed by several authors; see for instance Carr,4 27 (Fig. 4.29, left). Figure 4.31 shows this on the VW 2000 research automobile according to measurements made by Buchheim et al.4-30 The measured values according to Buchheim et al.4 31, 32 from the development of the Audi 100 III, model year 1982, are included in Fig. 4.32. From all these data it can be concluded that the direct influence of windshield inclination on drag is only moderate. The effect is assumed to be more pronounced the more the flow is routed over the vehicle.

Windshield inclination angles δ of more than 60° are not practical because of light diffusion. In addition, large, highly inclined windshields lead to increased solar heating of the passenger compartment.

Pressure tap position

20 25 30

AUDI 100 II

20 , , Ί2-5- - ^ 3 0

AUDI 100 III

Figure 4.33 Pressure distribution along the centre line section, comparison: Audi 100II, cD :

0.42 and Audi 100 III, cD = 0.30, after refs 4.31 and 4.32


Two effects are responsible for the favourable, though moderate, influence of a highly inclined windshield on drag. First, the excessive speed in the area of the A-pillar is reduced so that the momentum loss occurring at that point is smaller. Second, the deflection of the flow at the transition from the windshield to the roof is weaker. The low pressure peak occurring there is therefore smaller and the positive pressure gradient in the remaining flow is less steep. Hence the momentum loss in the boundary layer is lower, allowing greater pressure recovery in the area of the rear end. The pressure distributions illustrated in Fig. 4.33 along the longitudinal midsection of the Audi 100II and III indicate this very clearly. Therefore, even if a strongly inclined windshield does not contribute to a local drag reduction, it helps to improve the flow over the rear part of the car and thus to reduce the overall drag.

With the moderate lateral curvatures of windshields used today, separation occurs at the A-pillar in the form of a three-dimensional vortex train (Fig. 4.3), regardless of whether the A-pillar is provided with an edge flange acting as a rain gutter or whether it is smooth. The resulting flow pattern has considerable similarity to the flow around a delta wing at the angle of attack. The flow around the A-pillar has been investigated by Watanabe et al.4 33 on the simplified model shown in Fig. 4.34. However,

Figure 4.34 Vortex formation on the A-pillar, after ref. 4.33

the subject of this examination was the development of wind noise; this is handled in section 6.5.2. An interrelationship with drag was not made.

In the design of the A-pillars more must be examined than drag. Production technical requirements and functional aspects such as water accumulation on the side windows and the development of wind noise must also be considered.

Figure 4.35, after Janssen and Hucho,4 2 3 shows the effect of A-pillar design upon the aerodynamic drag of a VW Scirocco I. The initial shape (1) with an extended rain gutter represents an exceptionally favourable solution in terms of production technology. However, the high degree of separation behind the pillar leads to a high drag coefficient and loud wind noise. The water flow illustrated in the figure ends in the drip moulding so that, when the rain gutter is properly dimensioned, wetting of the foremost side window can be avoided.

Shape (2) without rain gutter has—with cD = 0.38—7 per cent less aerodynamic drag than shape (1) with rain gutter. The wind noise is lower than with the extended rain gutter. However, with shape (2) the rain water flows over the A-pillar and onto the side window unimpeded.

Shape (3) has a rain gutter which is recessed into the pillar, on which the


1 Separation

Figure 4.35 Development of the A-pillar of the Volkswagen Scirocco I, after ref. 4.23

edge flange runs parallel to the body sheet metal of the A-pillar. With a value of cD = 0.39 this design shape has 5 per cent less drag than shape (1) and 3 per cent higher drag than shape (2). Wetting of the side windows did not occur with this shape in light and medium rain. The rain gutter on the A-pillar of the VW Golf I corresponds approximately to shape (3).

If the rain gutter is integrated completely into the pillar, shape (4), a drag of 0.38 is obtained, which is the same drag coefficient as with the design without rain gutter. In comparison with the design without rain gutter, this shape has the advantage of better production possibilities and the side window is kept largely free of water. With regard to wind noise, there is no difference between the design without rain gutter and shape (4). The VW Scirocco I was equipped with an A-pillar corresponding to shape (4).

Shape (5) is distinguished by a long water trap pocket, and the side window is nearly flush with the outer surface. As a result of the flush side window, the drag coefficient of 0.37 is 3 per cent less than the design without rain gutter and 10 per cent less than the design with extended rain gutter. In contrast to shapes (3) and (4) this water trap pocket makes it possible to keep the side windows completely free of water even at high speeds and in heavy rain when the contours are designed optimally and there are good drainage possibilities. The disadvantage of shape (5) is the higher construction cost. A shape similar to this is used on the Porsche 924.

An effective measure for reducing the drag is to round off the A-pillar. One example of this is given in Fig. 4.36, after Buchheim et a l . 4 3 l A It is necessary to position the water trap pocket far to the front on the A-pillar, similar to case (5) shown in Fig. 4.35. The flow of air around the A-pillar is also improved when the side window is recessed as little as possible. The


8 -0.002

-0.010

_2a_

b 0.02 0.04 0.06 0.08 0.10

— — A-pillar

- — C-pillar

AUDI 100 III

rt-Üi AUDI 100 III

Figure 4.36 Development of the A-pillar and C-pillar of the Audi 100 III, after refs 4.31 and 4.32

greatest proportion of this effect can be obtained if only the triangular window is designed flush with the A-pillar. Such a solution was used on the VWGolf I I ;seeLincke.4 3 4

4.3.2.4 Roof

Roofs are designed with a convex shape to ensure sufficient rigidity. For stylistic reasons an attempt is made to keep the convexity as small as possible. If this convexity is increased the drag coefficient can be reduced. Figure 4.37 shows this for a medium-size notchback car. If the convex shape is designed so that the frontal area A of the vehicle increases, the


CD

0.47]

0.46

0.45

0.44 t \ . -5%

0.02 0.040.060.08 0.10 a/h

0.02 0.04 0.06 0.08 0.10 a/h

Figure 4.37 Effect of roof camber on drag of a notchback car

aerodynamic drag increases (D ~ Cr>4). On the other hand, if the original roof height is kept constant the front and rear windows must be curved into the roof contour to eliminate obstruction of the view. This leads to expensive windows but results in lower drag.

The measurements plotted in Fig. 4.38 (after Buchheim et al.426) show the same tendency for a car with a fastback. Here the chord length of the

Figure 4.38 Effect of roof camber on drag of a car with a 'high' fastback, after ref. 4.26


roof arch was used as the reference variable for the curvature instead of the vehicle height h, as in Fig. 4.37.

Aerodynamic drag reduces with increased convexity for two reasons. First, the higher convexity allows for a larger radius at the transition from the windshield to the roof. This results in a less pronounced suction peak at this location; see Fig. 4.33. The momentum loss in the boundary layer during the following less steep adverse pressure gradient is therefore smaller and the boundary layer itself is less endangered by separation. Second, the convexity provides for gentle deflection of the flow at the rear and the pressure rise at the rear end is therefore enhanced. The convexity of the roof and the rear end shape must be carefully matched.

4.3.2.5 Vehicle rear end

The two different forms of separation that occur at the rear end of the vehicle are shown schematically in Fig. 4.4: the quasi-two-dimensional shape in the form of a wake and the three-dimensional form as a longitudinal vortex pair (see section 2.3.3.4). Frequently both forms occur simultaneously; however, they are first discussed separately on simplified models.

Figure 4.39 Different rear ends, schematic: (a) squareback; (b),(c) fastback; (d) notchback

In Fig. 4.39 the primary rear end shapes are illustrated schematically. Shape (a), the full rear end, most commonly called 'squareback', is typical for the quasi-two-dimensional separation bubble. This is because the boundary layer cannot follow the steep pressure increase resulting at the rear edge according to potential flow theory and separates from the contour. This results in a considerably lower mean pressure coefficient cp than in friction-free flow on the rear vehicle surface. A classical example for this is the flow of air around a sphere; see Fig. 4.40. Contrary to normal practice, here the pressure is represented perpendicular to the direction of flow. In this manner the generation of the drag—almost wholly pressure drag on the sphere—from the difference of the pressures in ideal and actual flow is represented particularly clearly. This difference occurs only on the rear side of the sphere and the pressure drag therefore is generated only there.

On a prismatic body, the base pressure in real flow is dependent upon the fineness ratio l/dh, where the hydraulic diameter is selected as a


Front, non-viscous and viscous

D

Rear, viscous turbulent separation

Rear, non-viscous

Figure 4.40 Pressure distribution around a sphere; comparison of ideal, non-viscous and real, viscous flow

reference variable with dh = ACIA (C = circumference of the body perpendicular to the axis). The results for this have been compiled by Hoerner4 35 and further data are given by Nakaguchi.4 36 For vehicles with a blunt rear end—squareback passenger cars and vans—the mean base pressure is approximately cp = -0.2. The fineness ratio defined above is given by the vehicle design and is therefore not a variable during aerodynamic development. The base pressure also depends upon the angle at which the flow separates from the contour. Results for this are given by Tanner,4 2 and Roshko and Lau.4 37

Maull4 38 and Mair439 studied in detail the important case of boat-tailing of the rear end contours of vehicles. The effect of this measure is shown in Fig. 4.41. Here drag measurements are given, which were made by Mair440 on a cylindrical body with diameter d, the length of the cylindrical part 3d and an elliptical nose with a length of 1.3d. Mair found that the optimum boat tail angle was ß = 22°. When the angle ß is larger, the flow separates at the shoulder. The measurements in Fig. 4.41 indicate that not

0.2

Φ .

CD 0.1

Φ

* o ^ ο ^ °-r

- o - o - o - o -

0.5 1.0

Figure 4.41 Effect of boat-tailing on drag coefficient, after ref. 4.40


_ro ■ — — — *

cc I

500 1000 1500 mm

Rear elongation h

Figure 4.42 Boat-tailing applied to the Mercedes Benz C 111 III, after ref. 4.41

much is gained by extending the body to a point. This confirms the idea of the K rear end (Kamm-back).

The application of boat-tailing on a motor vehicle is shown in Fig. 4.42, after Liebold et al.4 41 This is the Mercedes Benz research vehicle C 111. Qualitatively, the effect of the length upon the aerodynamic drag is similar to that for the body of rotation in Fig. 4.41.

On mass produced vehicles, the application of boat-tailing is more difficult. An extension of the vehicle is not usually permissible. The internal space should not be reduced if possible (head room in the rear seat, trunk volume). The stylistic design of tapers is difficult to master. Boat-tailing must be accomplished separately for the basic body and the superstructure.

An example of drag reduction by tapering the rear end is illustrated in Fig. 4.43, after Hucho, Janssen and Emmelmann.4 25 On the notchback car shown in longitudinal section the lateral taper was increased in increments while holding the height of the trunk fixed. Starting with parallel side walls, i.e. y = 0, a generally monotonic reduction of the drag is achieved up to

Section A-A Initial shape

Figure 4.43 Boat-tailing applied to a notchback car, after ref. 4.25

143

Figure 4.44 Boat-tailing applied to the Mercedes Benz 190 (Baby Benz), MY 1983 (courtesy Daimler Benz AG)

diffuser length

· j = 0.21

— ■ τ = 0·50

IV \ ■

\ \

V

i i

. _ . -

* \ 12 16 20 24 L diffuser anale Ot [ ° I _*J

/ 1

\J s — · ^

\J\ /

-0.04I

Figure 4.45 Effect of underbody diffuser length and angle on drag, after ref. 4.26


shape B with increasing taper. Further tapering then no longer improves the drag. Apparently the flow remains attached up to the taper corresponding to shape B. The pressure recovery, which is accomplished in this manner, provides for a reduction of the drag. Unfortunately pressure distribution measurements to confirm this assumption are not available for such an example. One passenger car, on which this type of boat-tailing was accomplished consistently, is the Mercedes Benz 190 ('Baby Benz'); see Fig. 4.44.

The drag can also be reduced in the area of the superstructure by boat-tailing. Figure 4.36 illustrates how this can be achieved by rounding off the C-pillars.

Recovery of the pressure, such as can be achieved with boat-tailing, can also be obtained by tapering the bottom upwards. Figure 4.45, after Buchheim et al.,4 gives corresponding test data on the Research Car 2000 from Volkswagen. With a long diffuser, a notable reduction in drag can be achieved with a very small angle a. However, this effect is only assured with a smooth underside. Measurements made by Potthoff4 42 on the Unicar research automobile gave a similar result (Fig. 4.46). Here too the longer diffuser has the greater effect. Also of note is that the lift at the rear axle is reduced by the diffuser.

0° 2° 4° 6° 8° 10° 12° 0 10 20 mm 40 Diffuser angle aD Diffuser height hD ^ : 5

Figure 4.46 Effect of underbody diffuser geometry on drag and rear axle lift, after ref. 4.42


Extremely high underbody diffuser angles have been investigated by George.4 43 These produce a vortex formation similar to a fastback (see shape b in Fig. 4.39).

The three-dimensional separation—formation of a pair of longitudinal vortices—occurs on rear end shape (b) (Fig. 4.39), assuming a certain inclination of the rear end. Shape (b) is hardly used any more. Shape (c) is selected much more frequently. The flow relationships are similar in both cases. However, on shape (c) a quasi-two-dimensional wake is present at the perpendicular basis in every case. Therefore both types of separation can occur at the same time with this rear end shape.

The fact that two completely different types of flow occur depending upon the inclination of the rear end, which lead to different drag, was observed for the first time during the development of the VW Golf I. Janssen and Hucho4 23 varied the angle of inclination of the rear end φ (see Fig. 4.47) in increments. The drag coefficient cD is shown versus the angle of inclination φ in Fig. 4.47.

Figure 4.47 Influence of rear end slope angle φ on drag coefficient cD, separation line and wake, after ref. 4.23, measured on VW Golf I (Rabbit)

The development work in the wind tunnel began with a high angle of inclination at the rear end, φ = 45°. At this angle the flow separated at the end of the roof. The drag coefficient was 0.40. As the angle of inclination was diminished, the drag suddenly increased by 10 per cent at φ = 30°. The line of separation jumped down to the lower edge of the inclined rear end. Two strong inward-rotating longitudinal vortices were observed which induced very low pressure on the slanted part of the back. As the angle was reduced further, the drag dropped again. At φ = 15°, a very flat angle, such as is used on coupes, a drag minimum resulted. At still smaller angles the same flow forms were reached as with a squareback: cD = 0.40. In the area 28° < φ < 32° a bistable condition was observed. Depending upon the curvature of the rear edge of the roof, separation occurred at the top or bottom of the inclined rear end.

This effect, which was first published by Janssen and Hucho,4 23 has been studied in detail by Morel4 and later by Bearman and his students.4 45

These studies were first performed on bodies of revolution in free flow and then on prismatic bodies with more similarity to motor vehicles in ground proximity.


0.8 r

0.7

0.6

0.5

0.4

0.3

0.2

0.1

cD

°—®-o—s>

10° 20° 30° 40° 50° 60° 70° 80° 90° Ψ

cL

1.0

0.8

0.6

0.4

0.2

0

/

/ K L

30° 60° 90° φ

Figure 4.48 Effect of rear end slope angle φ on drag and lift of an axisymmetric body off ground, after ref. 4.45 — o — measurement T. Morel — x — measurement A.D. Stuart and A.T. Jones

Figure 4.48, after Bearman,4 45 shows the measurement of drag and lift on a cylindrical body in free flow. The dependence of the drag on the slant angle φ is similar to that observed on the Golf I (see Fig. 4.47). As the slant angle φ increases, a vortex pair is formed similar to that on a slender delta wing at the angle of attack; the drag and lift increase. At a limit angle φ, which is between 54° and 55° for this body, another form of separation results. A large wake is formed rather than the two tip vortices. Comparison of the measurements made by Morel with those made by Stuart and Jones4 46 allow the assumption that the critical slant angle is dependent upon the angle of attack of the body. The data from both


sources are in good agreement, with the exception of the numerical value of the said critical slant angle.

The pressure distribution measurements, which were made on the same body and are illustrated in Fig. 4.49, confirm the information on the vortex formation. At increasing slant angles φ higher pressures are induced at the outer area of the base. A characteristic pressure pattern develops as it forms under longitudinal vortices. If, conversely, a wake develops, the pressure is nearly constant over the entire base.

- C P

20 30 40 50 70

—x— —o— 1 - + -—&-—D—

Figure 4.49 Pressure distribution at the sloping rear end, measured along section YY, after ref. 4.45

Morel4 44 published corresponding measurements on a prismatic body in ground proximity; see Fig. 4.50. As determined by Janssen and Hucho4 23

on the Golf I, a critical base angle occurs at φ = 30° (according to Morel γ = 60°; γ = 90 — φ), at which the flow pattern changes from state I (squareback, wake) to state II (fastback, tip vortices). The two different types of flow—tip vortices or wake—can be clearly identified with the pressure pattern shown in Fig. 4.51.

Bearman et ^4.47,4.48,4.49 s u c c e e c i e ( j j n determining the vortex structure and in breaking down the drag into its components—'profile' drag and vortex-induced drag. This was done by traversing the velocity field in several yz-planes downstream of the model—similar to a vehicle, with


CD

0.5

0.4 0.3 0.2

1 r i

Janssen y. Hucho" l \ _ "

- * ; - i \Y

ail· 1 -0.5

0.4 0.3 0.2

0.1

-0.1 -0.2

ί 1

- i\n-1 \ 1 1

| 1 V ' 1/ \ mr-^\ 1 J

I 3^7 Squareback

Fastback

30° 60° 90°

Figure 4.50 Drag, lift and flow pattern for a body close to the ground with varying slope angle γ, after ref. 4.44

-0.5

V b

Figure 4.51 Pressure distribution on the sloping rear-end with vortex formation at the C-pillar (II) and with quasi-two-dimensional wake flow (I), after ref. 4.44

various base angles—very much in the same manner as did Ahmed4 6 ' 4 1 0

and, earlier, Howell.4 7

The formation of the vortex pair for a base angle of φ = 25° can be seen in Fig. 4.52 on the basis of the lines of constant total pressure. As the vortices approach the ground they move slowly to the outside, as a result of the induction effect of their mirror image. The vector diagram in Fig. 4.53 is comparable to that determined by Ahmed.4 6 4 10 The position of the vortex can be clearly identified.

From these measurements Bearman et al. calculated the 'profile' drag and the vortex-induced drag according to a method derived from the theorem of momentum outlined in detail in ref. 4.48 and compared these with the total drag determined by the balance; see Fig. 4.54. The agreement between the drag from the balance and the sum of the component drags determined from the velocity field measurements is very


Datum line

Figure 4.52 Total pressure contours in the wake of a sloping rear end, after refs 4.47, 4.48 and 4.49

good, thus confirming the approach taken to separate the drag components. The highest drag is reached at φ = 30°. Above all, the high increase in drag results from vortex drag. However, 'profile' drag is also not independent of the base angle φ.

Jones4 50 established why there is no simple relationship between the

0.15 h

VV/////////////////////////////////// Moving floor h-x/h = 6.5 I

z 120

80

40

0

0 IL

, ^ . > . V l ^ * * *»

-20 180 60 100 140 Vorticity

20 60 100 140 Cross flow velocity vectors

Figure 4.53 Transverse speed vector diagram and vorticity in the wake of a sloping rear end, after refs 4.47, 4.48 and 4.49

180

150

r x/h = 4.17

φ ^^777777777777777777777777777777777777777777777777777777,

cD, Uoch

Profile' drag

Vortex induced drag

o Total drag cD, sum of vortex and 'profile' drag

x Direct measurement of cD

Figure 4.54 Variation of circulation, of total drag, 'profile' drag and vortex-induced drag with rear end slope angle, after ref. 4.49

Squareback

20° 30° 40° 50° 60°

Figure 4.55 Variation of drag and lift—the entire change in lift is change of rear axle lift—with slope angle φ, after ref. 4.4


drag and lift corresponding to Eqn 4.2 for bluff bodies close to the ground. These considerations were further developed by Bearman et al. The flow around a body close to the ground can be described by that around the body and its imaginary mirror image beneath the ground. As a result of the high speed, a force of attraction develops between the body and its mirror image, which increases as the distance decreases. A negative lift therefore develops. Circulation develops on the body (and on its mirror image) owing to the effect of friction, which results in a positive lift component. In three-dimensional flow the lift induced by side vortices must also be considered. Therefore only a portion of the lift comes from the trailing vortices, and only this can be linked with the drag induced by these vortices according to a relationship such as Eqn 4.2. Confirmation of this is supplied by Fig. 4.55, after Hucho,4 4 which resulted from the development of the Volkswagen Polo I. As in the development of the Golf I, the angle of inclination of the rear end was varied. The change in drag was accompanied by a change in lift, which is exclusively a change in the lift at the rear axle, i.e. in the effective area of the side vortices.

o Total

□ 'Profile' + Vortex X Measured

0.2 k

0.1h

Figure 4.56 Effect of rear end modifications on total drag and its components, after ref. 4.47: (1) φ = 25°; (2) φ = 25°, underbody upswept by a = 10°; (3) as (2) but boat-tailed sides, δ = 10°; (4) as (3) but top edges chamfered

U.H

0.3


Bearman et al.4 47 also investigated the effect of upsweeping the rear of the underbody and of boat-tailing—for a fixed base angle; see Fig. 4.56. The reduction in drag that can be achieved by tapering the bottom upward is ascribed mainly to the reduction of the vortex drag, but the 'profile' drag is also reduced.

The change of the flow pattern from the squareback mode to that of a fastback, and vice versa, occurs only at a defined slant angle φ when the transition from the roof to the inclined rear end forms a sharp edge. However, if this area is rounded the transition in the range of slant angle 28° < φ < 32° is unstable. Pulsations of the separation may occur from top to bottom and up again. This was first observed during the development of the Volkswagen Golf I.423 Later it was confirmed independently by Morel4 44 and Ahmed;4 6 see remarks to Fig. 4.10.

In addition to the angle of inclination of the rear end, the edge design in the area of the rear end also influences the drag coefficient. The influence of the end of the roof and the end of the side (C-pillar) on the drag coefficient is given in Fig. 4.57, after ref. 4.23, for a vehicle with a squareback (VW Golf I). The squareback character of the flow at the rear end was not changed by this modification of the shape.

Figure 4.57 Influence of small rear end details on drag, after ref. 4.23

First, the influence of the contour design at the end of the roof was accomplished without modifying the side contour of the C-pillar. If the roof ends with a sharp edge Dl, the edge forms the separation line. With the curvature described with D2 the separation was shifted down to the hatch joint; however, cD remained unchanged. The highly rounded roof end D3 resulted in a 9 per cent reduction in drag. It can be assumed that the higher deflection of the flow combined with a further rearward displacement of the separation resulted in a slight increase of the base pressure.

The termination of the side also influences the drag coefficient. By


extending the C-pillar by the value a, it was possible to reduce the drag by 4 per cent for a = 20 mm and even 9 per cent for a = 40 mm. Surprisingly, no further improvement in drag was achieved with the combination of the two measures—rounding the roof contour to D3 and extending the C-pillar to a = 20 mm. The C-pillar extension of a = 20 mm was selected for the VW Golf I.

^ A

VW-Golf I (Rabbit)

Ac

Co JB- =-2%

1000

New contour /initial contour

Detail A Centreline cross-section

Figure 4.58 Integrated roof spoiler-lip, Volkswagen Golf I (Rabbit), after ref. 4.23

The small roof moulding, which is integrated into the rear hatch on the VW Golf I, reduces the drag by an additional 2 per cent; see Fig. 4.58. It can be assumed that this roof moulding has an effect similar to that of a rear spoiler on a fastback; see section 4.3.2.10. However, this reduction in drag is achieved only when this increased pressure is effective on a surface whose projected area perpendicular to the direction of motion is not zero. This is frequently overlooked in the attachment of such a roof spoiler. A precise clarification of the function of this roof moulding is not yet available.

The optimum rear end inclination angle φ, i.e. the angle that provides a minimum drag coefficient, depends upon the length of the rear portion of the car. This relationship, which was first established by Buchheim et

Fastback 0.04

0.02

£ _

-0.12 Figure 4.59 Effect of rear end parameters length /0 and slope φ on drag, after ref. 4.26


al.,4'26 is illustrated in Fig. 4.59. On long vehicles, where more length is available for the rear end length /r, a larger angle φ can be used resulting in a higher reduction of the drag than on compact vehicles. However, Buchheim et al. have shown that this effect is highly dependent upon the design of the C-pillar and is less pronounced on an optimized C-pillar.

If, instead of a transition with a sharp edge, a rounded rear end contour is selected (see Fig. 4.60, after Buchheim et al.)4·30 this results in a distinct minimum for the optimum rear end height z, which again is highly dependent upon the design of the C-pillar.

0.10r

-100 50 50 100 change of rear end height z [mm]

Figure 4.60 Effect of rear end height z on drag, after ref. 4.30

Width b

Aspect ratio of back lite b/l% « 3 to 4 Figure 4.61 Notchback configuration: (a) variable geometric parameters; (b) two-dimensional step model

The notchback (Fig. 4.39d) is the most common rear-end shape for passenger vehicles. As shown in Fig. 4.61, the number of geometric parameters that influence the flow pattern is very much larger than for


other rear-end shapes. This is why it is not possible to relate geometry to flow pattern as clearly for the notchback as it is for the fastback and the squareback. However, a series of parameter variations are available, which can be applied as guides for development of the shape—at least in terms of the method.

It is tempting to treat the inclined rear window of the notchback in the same manner as a fastback. However, in comparison to the latter there are two differences. First, the aspect ratio Λ = W/Ls of the inclination of the notchback is much higher than that of a fastback. The aspect ratio on a fastback is Λ ~ 1.5, but Λ = 3 to 4 on a notchback. At the same angle of inclination φ, smaller negative pressures and a weaker downwash are induced on the slanted part of a notchback in comparison to a fastback. Secondly, the subsequent step causes a positive pressure gradient, which may lead to bursting of the side vortices; see Hummel.4 Therefore the negative pressure on the rear window and the induced downwash velocities, which cause deflection of the flow in the rear-end area, become even smaller.

On the other hand, it is known that the flow becomes attached again at a point A after a step; see Fig. 4.61b. Vertical steps (γχ = 0) have been studied on two-dimensional models by Arnold.451 The point of reattachment of the flow in relation to the step height h was measured along with parameters of the boundary layer in front of the step. The thicker the boundary layer of the oncoming flow, the later the flow becomes reattached behind the step. Applied to a vehicle, this means that a thick boundary layer created by unfavourable flow around the front of the car (hood, cowl, roof) makes it most difficult for the flow to become reattached at the rear end. Results for the step angle γλ Φ 0 are not available. In the three-dimensional case, it can be assumed that the point of reattachment A will be moved forward due to the downwash induced by the side vortices at the slanted rear window.

Detail X .Shape B

-50 50 150 250 450mm 550

Figure 4.62 Effect of step height on drag of a notchback car, after ref. 4.25

The drag of a notchback can be influenced by the height of the trunk. One example of this is given in Fig. 4.62, after Hucho, Janssen and Emmelmann.4 25 If the height of the trunk is increased as shown, the drag initially remains unchanged. At a height of z ~ 100 mm a sudden drop in drag occurs. An increase beyond this provides no further improvement.


The sudden drag reduction according to Fig. 4.62 can be attributed to the fact that when the height z is too low the flow does not reattach on the lid. This reattachment was first achieved with shape A.

On notchback shapes with long trunks a continuous reduction of the drag with the lid height is usually observed. An example of this is given in Fig. 4.63, after Buchheim, Leie and Lückoff,4 3 1 ' 4 3 2 from the development

Change of trunk height z [mm]

20 40 60 80 100 Q Q , ■ 1 1 .

^ TV 1 1 1

< \ 0) \

^ \ o \

■σ X

^ ί ^N^T~ as I I ! o -0.021 1 1

Audi 100 II Audi 100 III

Figure 4.63 Drag reduction by increasing trunk height z, after refs 4.31 and 4.32

of the Audi 100 III. The possibilities offered by this measure have not been fully exploited due to the reduction of the view to the rear as well as the appearance of the vehicle from the rear. A high trunk has become a symbol of an aerodynamically designed notchback car.

The drag can also be reduced by extending the trunk length; see Fig. 4.64 after Buchheim et al.4 31'4 32

The inclination of the rear window also has a decisive effect upon the drag, as shown in Fig. 4.65, also after Buchheim et al. However, if the angle of inclination is too great, the achievable reduction in drag is counteracted by the disadvantage of high radiant heat gain from the sun.

The three parameters, step height z, step length x and angle of inclination of the window φ, must be carefully matched for each vehicle. It can be assumed that not just one single combination of the three parameters will lead to minimum drag. An additional influence can be expected from the roof curvature and the transition from the roof to the rear window. An example of this is given in Fig. 4.66, after Götz,4 52 from the development of the Mercedes Benz 190 ('Baby Benz'). Here the greatest effect was achieved by lowering the rear edge of the roof. This process is naturally limited by consideration of the headroom for the rear seat passengers.

Audi 100 II 157

Change of trunk length x [mm]

20 40 60 80 100

Q

-0.005

| -0.010

Audi

1 100 III·

120

Figure 4.64 Drag reduction by increasing trunk length x, after refs 4.31 and 4.32

Rear window inclination angle 7 [°]

A 56 58 60 62 64

o

U V

-0.01

0.02

Γ

Audi f

100 \ · 11 >

y///////////////.

Figure 4.65 Drag reduction by sloping the rear window, after refs 4.31 and 4.32

158

χ^ Increase of trunk height [mm]

<P -15 ° +5 +10 +15

Figure 4.66 Combined effect of roof height and trunk height on the drag of Mercedes Benz 190, after ref. 4.52

O 4 r O

10<

<fco tjo 15° 15'

k f u405·

,L)>. ./., wMss/sbw/sA

-1045- Category I

Category I Notchback Co and CLR fairly high CSH moderate Category II Squareback CLR low CSR fairly high cw moderate Category III Fastback cLR high cD and CSR low

10 20 30 40 50 60 70 80 90 a ►

Figure 4.67 Notchback: influence of the main geometric parameters on drag, rear axle lift and rear axle side force, after ref. 4.55


Carr also investigated the various rear-end shapes and published his results in a series of MIRA reports, refs 4.27, 4.53, 4.54. Figure 4.67 summarizes the most significant results.4 55 The step height z and step length x parameters are consolidated to one variable with the angle ß. Carr distinguishes three categories depending upon the angle of inclination of the rear window and the length of the trunk (notchback shape): I. Notchback; drag and lift at rear axle rather high, moderate rear lateral

force (for oblique oncoming flow). II. Squareback; moderate drag, low rear lift, rather high rear lateral

force. III. Fastback; low drag and rear lift, high rear lateral force. The data only give general guidelines and it is well known that there are fastbacks with significantly higher and others with lower cD values than squarebacks; see Fig. 4.47.

4.3.2.6 Sides

The flow of air around the vehicle can be improved, and the drag reduced, by curving the outline of the body in plan. On one hand, the deflection of the flow at the front of the car is not as high due to this curvature. On the other hand, a slow pressure increase is achieved in the rear area, which allows a higher degree of boat-tailing and therefore leads to a higher pressure at the back of the vehicle. Figures 4.68 and 4.69 show how the

0.04 0.06

Q * .

plan view camber —"r _0Ό2_ 0.04 0.06

a υ ^ i -0.01

c υ

s? υ " ° -0.03

-0.02

- W B -

__.i ^ 1 ^ rah

Figure 4.68 Effect of plan view camber on drag, fastback car, after ref. 4.26


Plan view camber ah

WB

0.005 0.010 0.015 0.020 0.025

1"" f -0.02

-0.03

0.01

n Audi 100 II Audi 100 III

-M-

Figure 4.69 Effect of plan view camber on drag, notchback car, after refs 4.31 and 4.32

drag decreases with increasing convexity. If the curvature can only be achieved by increasing frontal area (dotted line in Fig. 4.68) this can lead to an increase in drag despite a decrease in the cD value, because the product Cr>4 increases, as shown for roof curvature (Figs 4.37 and 4.38). If the curvature is achieved with no increase in frontal area (solid line in Fig. 4.68), the overall drag can be reduced. However, there are functional limitations such as integral fenders and general styling.

The top view is also characterized by the transition from the front end to the fenders, referred to in Figs 4.20 and 4.22. Boat-tailing also has a considerable influence (Figs 4.41 and 4.43).

Lateral air flow around the A- and C-pillars is also significant (Fig. 4.36). Rounded corners and convex surfaces must be matched to prevent high pressure variation along the flow path. In designing the outline of the body, care must be taken that no kinks are present in the curvature.

The flow of air around the sides is interrupted by the wheel openings (section 4.3.2.8), by the outside mirror (section 4.3.2.11) and by the window recesses. Hoerner4 35 and Wieghardt4 56 have already indicated the drag-increasing effect of transversely positioned strips or gaps, as well as pockets. This knowledge is being taken into account in the design of mass-produced automobiles more and more. Examples are the Audi 100


Side window inset t [mm] 10 5

-0.005

-C CJ

-0.010

Audi 100 III

Figure 4.70 Effect of side window inset on drag, after refs 4.31 and 4.32

III, the Volkswagen Golf II, the Ford Scorpio and the Opel Omega. Figure 4.70 from Buchheim et al.4·31'4·32 illustrates how the aerodynamic drag was reduced by filling up the window recesses in this case. The drag coefficient is reduced by AcD = -0.02 with fully flush window surfaces. This is considerably more than the -0.01 indicated by Carr.411 The greatest effect

Figure 4.71 Drag reduction by A-pillar guide vane, Peugeot Vera, after ref. 4.57


was obtained by filling window A. Filling up the last 5 mm only has a slight effect upon drag. However, the side windows on the Audi 100 III were designed completely flush to eliminate wind noise (see Chapter 6). In the light of Fig. 4.70, for the Volkswagen Golf II only the small triangular side window following the A-pillar was made flush to the contour of the body; see Lincke.4 34 A deflector at the front edge of the upper side window also proved very effective. Rousillon4 57'4 58 achieved a value of AcD = -0.015 with this on the research automobile Peugeot Vera (Fig. 4.71), though this solution is not really suitable for mass-produced vehicles.

4.3.2.7 Underside

The underside of the vehicle can be considered to be an extremely rough flat plate. The extent to which the drag of a plate is increased by moderate roughness is shown in Fig. 2.9. Reduction of drag by panelling the underside has been extolled by numerous authors (see Carr4 5 9), but is difficult to realize because of the need for access to the axles and engine compartment, cooling of the oil sump and exhaust system, etc. According to Buchheim et a l . 3 1 , 4 3 2 such efforts are justified (see Fig. 4.72).

AcD = -0 .010

AcD = -0.015 AcD = -0 .015

AcD = -0.005

Figure 4.72 Drag reduction by 'smoothing' the underpanel, Audi 100 III, after refs 4.31 and 4.32

Complete panelling of the underside provides a reduction of drag amounting to —0.045. Carr4 n cites a similar value. When the rear is designed as a diffuser, it is possible to achieve a value of AcD = -0.07. A portion of this effect can be realized by attaching a front spoiler (see section 4.3.2.9) and a further portion by carefully matching the individual recesses in the underside panelling and by profiling the axles.

4.3.2.8 Wheels and wheel wells

The air flow in a wheel well with a rotating wheel is extremely complicated, as recent studies have shown. The flow of air around an isolated rotating wheel has been investigated by Morelli4 60 and by Stapleford and Carr.4 ^ The latest data was presented by Cogotti,4 62 who also included a faired wheel in his studies, as did Scribor-Rylski4 28 earlier. Both cases are shown in Fig. 4.73.

Exposed wheels are found on racing cars, trucks and trailers. However,


Figure 4.73 Isolated wheel and wheel in wheel well

in these cases the wheels are not truly exposed. On one hand, the displacement effect of the vehicle body leads to oblique oncoming air flow at the wheel. On the other hand, on racing cars winglets are positioned in front of the wheel to increase the traction. The rear wheels are also in the wake of the front wheels.

Partially faired wheels are typical for passenger cars. Here the displacement effect of the vehicle body also provides for oblique oncoming air flow.

The measured results for a free rotating wheel with straight oncoming flow are summarized in Fig. 4.74, after Cogotti.4 62 The effect of rotation

2R cD = P 2

D

V 2 B 2 R

cD

C|_

cD

C|_

ω = 0

0.593

0.272

0.544

0.296

V

0.579

0.180

0.488

0.178

Remarks

Standard rim

Rim faired on both sides, flat cap

Tyre 145 SR 10 Cinturato Pirelli

Figure 4.74 Drag and lift of isolated wheel, after ref. 4.62

on drag and lift will be discussed in section 11.4.2 together with details of scale modelling. The drag coefficient of the exposed wheel of 0.5 < cD < 0.6 is considerably higher than that of a vehicle. According to Morelli4 60

this value does not change even when the wheel plunges partially into the wheel well, when only that part of the wheel that is not covered is selected as the projection area. Scribor-Rylski4 28 came to a similar conclusion; see Fig. 4.75. To what extent his results can be applied to full-size models is not known. His high measured drag coefficient for the exposed wheel, cD = 1.1, allows the conclusion that the Reynolds number based on the driving speed, Re = VO/v, was less than the critical value; see section 11.4.2.


Figure 4.75 Flow around a wheel in a wheel well; effect of vertical position h on drag and lift, after ref. 4.28

i—°-7i

Co

[—0.6

N — 0 . 5

1 1—<

■/

b — i

Λ

1

V »

1 1

i—°-7i

—0.6

CL

k-0.5

Γν>.4

[—Ό.3

—0.2

—0.1

— i — I \—i—

I

! !

I

i

-10° 10° 20° 30° 40° ß

-10° 10° 20° 30° ß

40°

Figure 4.76 Drag and lift of an isolated (not rotating) wheel in contact with ground under yaw, after ref. 4.62

With oblique oncoming flow the drag and lift increase, see Fig. 4.76, from ref. 4.62. Smoke trail photographs indicate a value of 10° < ß < 20° for the local angle of side slip at the position of the wheel.

Cogotti4'62 showed that the drag of a low drag configuration similar to a

165

|r^> WZ///////////////////////////////.

Qy—~<y >///////>////////////////?#//////

cD

0.073

0.157

C|_

-0 .044

-0.009

M 1:2

0.407

0.462

Figure 4.77 Drag and lift increase of a car-like body due to the addition of wheels, after ref. 4.62

V/////////////A

ω = 0

CO =

R +

0.25

0.20

0.15

CD

0.10

0.05

0.00 2 4 6

VH/VW

2 4 6 VH/VW

Figure 4.78 Effect of wheelhousing volume to wheel volume on drag and lift of a wheel, after ref. 4.62


car increases drastically when the wheels are added (Fig. 4.77). The drag coefficient of the Pininfarina research car CNR (1976) was more than doubled.

On the basis of measurements performed on a drop-shaped body with a rotating wheel, Cogotti4 62 proved that the smaller the volume of the wheel well in relation to the volume of the wheel itself, the smaller the total drag of the wheel and wheel well (Fig. 4.78).

From a series study on 14 passenger cars Cogotti deduced that flush panelling of the outer wheel naves would result in a drag reduction of AcD = -0.009 ± 0.003. Inclusion of the wheel and the wheel opening in the vehicle contour allows a certain degree of design freedom (Fig. 4.79). Of

Section A-A, simplified

Two-dimensional model

r; wfy/ww. ΤΎ - * A - —

1 i i I I I

Section A-A

I I

www»»?,.

L cpf* ^ Λ«Λ*Λ<Λ<Λ«Λλ<Λ I

'»WWW»»

Figure 4.79 Geometry of wheel and wheelhousing, schematic

course, both the tyre bead and secondarily the recesses hx and h2 must be selected so that the body is affected as little as possible (see section 6.4).

Covering the rear wheels reduces the drag only on already streamlined vehicles, and is effective only when the flow is attached upstream. On vehicles designed for extremely low aerodynamic drag (so-called concept cars) a 'spat' which moves with the steering may also be fitted over the front wheels, or, in more advanced cases, the body shell could flex with the steering motion of the front wheels (section 4.6.3).

4.3.2.9 Front spoiler

The friction drag along the underside of the vehicle is reduced with the aid of a front spoiler. This also reduces the lift at the front of the car and increases the volumetric flow through the cooling air duct. The

Forebody and underside

s = Equivalent roughness

Figure 4.80 Effect of front spoiler on drag, schematic


drag-reducing effect of the front spoiler is illustrated in Fig. 4.80. The drag Ds+U of the combination of spoiler and underside can be computed by adding the individual drags of the spoiler D s and the underside Dv.

Ds+v = Ds + £>u

The drag of the underside is mainly friction drag but the spoiler itself produces a pressure drag. If the spoiler is considered as a rectangular plate positioned vertically on a wall transverse to the oncoming flow, its drag coefficient can be assumed to be:

C'DS = — — « 1.2 (4.4) -?-V*A,

where the frontal area ^4S of the spoiler is initially selected as the reference area. The reference speed is the driving speed V. So the defined c'DS can be used regardless of the spoiler height zs. However, if the drag of the spoiler is computed in relation to the frontal area A of the vehicle with the equation

£>s ^ s c D s= = c'DS—— (4.5)

^-V2A A

2 this drag coefficient cDS increases linearly with the spoiler height zs; see Fig. 4.80. The spoiler height zs is related to the equivalent sand roughness s of the underside.

As usual, the friction drag Dv of the rough underside is first equated to the 'wetted' surface Sv and the velocity Vv at the edge of the boundary layer:

C'DU = QD U (4.6)

The value Ξυ for the surface of the underside has an almost fixed relationship to the frontal area A of the vehicle (Sv « 3A). The velocity νυ

is proportional to the vehicle speed V. Depending upon the shape of the vehicle and the ground clearance, the ratio Vv/V is greater or less than unity, see Hucho, Janssen and Schwarz.463 Generally νυ is also not constant over the length of the underside. It is assumed that the friction drag coefficient c 'D U of Eqn 4.6 is independent of the velocity VJJ. In fact, for high roughness, the friction drag coefficient cf of a plate is not dependent upon the Reynolds number Re = VIIv (/ = length of plate, v = kinematic viscosity of the air); see Fig. 2.9.

However, the velocity Vu is affected by the spoiler height. As the spoiler height zs increases the velocity Vv decreases. The function

(4.7)

is not known quantitatively.


Now the drag coefficient cD U of the underside, which is now related to the frontal area A of the car and to the driving speed V, is also entered in relation to zjs in Fig. 4.80.

cDu = c ' D u ^ f e V (4.8)

The curve of the function according to Eqn 4.8 was estimated. Addition of the corresponding Eqn 4.5 results in the total drag coefficient of the underside and spoiler:

CD(S + U) = CDS + CDU (4-9)

The friction drag cD U of the underside initially decreases more rapidly than the pressure drag cDS of the spoiler increases with its height zs. However, the longer spoiler then leads to an increase in the total drag cD(S + u ) . With a very long spoiler the drag is even greater than without a spoiler.

The reduction of the velocity Vv on the underside with a front spoiler is shown in the measurements of Kramer et al .4 6 4 in Fig. 4.81. Unfortunately

— — Without spoiler — — — With spoiler

wwwwwww

Road test

t 25 cm 15

f± ΠΓ -+~n— \ II

Ϊ H-P

tuz u 6—

\\ 1

1

i 1 1

La

I P \ \ J l

6—I—1—1—I I 6 1 1 iU

0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0

v v \ / oo

V V

\/oo

V

Voo

V

\/oo

Figure 4.81 Velocity distribution underneath a car, without and with front spoiler, after ref. 4.64

the correspondence between model and road measurements in ref. 4.64 is not good. Generally, the local speed underneath the car is lower than the vehicle speed. The reduction of the local speed by a spoiler is less pronounced on the road.

The effect of the front spoiler on the pressure distribution was worked out by Schenkel465 (Fig. 4.82). The pressure at the front part of the underside is greatly reduced. High velocities at these points must not be deduced from these high negative pressures under any circumstances. Separated flow is present behind the spoiler. The Bernoulli constant (see section 2.3.1) is different in this area from that for the intact outer flow. Only slight changes result in the pressure pattern on the upper side of the vehicle.


• No spoiler O 100 mm spoiler height Δ 150 mm spoiler height

Figure 4.82 Effect of spoiler height on the pressure distribution around a car, after ref. 4.65

The lift at the front of the car is reduced by the front spoiler. Moreover, the low pressure on the underside in the area of the engine compartment supports the flow of cooling air. The front spoiler causes a growth of the boundary layer on the underside of the vehicle. This can have the effect that an underbody which tapers up behind the rear axle cannot act as a diffuser, because the low energy flow cannot withstand a pressure increase and therefore separates from the contour. In this manner the drag reduction from the spoiler can be lost again. The interaction of the spoiler, rough underside and upward tapering diffuser-type rear underbody has not yet been examined systematically.

Front spoilers may either be attachments or integrated into the front skirt. In the first case there is considerable freedom with regard to the

40 80 120 160 mm 50 100 km/h 200

z s — ► v—► Figure 4.83 Spoiler development for the sports car VW do Brasil 1600 X, after ref. 4.66

1.0

t . 1 n


position, length and inclination of the spoiler, limited only by the overhang angle to be maintained. In the second case there is less freedom in the spoiler design, largely for production technical reasons (drawing depth of the sheet metal, engine installation from underneath).

A systematic spoiler design was carried out in the course of the development of the VW do Brasil 1600 X, a sporty coupe. A series of spoiler arrangements was studied; see Fig. 4.83 from ref. 4.66. Various optimum lengths zs result, depending upon the location of the spoiler. The measurements also show that the optimum spoiler length zs is greater when an attempt is made to achieve the minimum lift instead of the lowest possible drag. These results are confirmed by measurements made by Schenkel,4 see Fig. 4.84. While the lift at the front axle decreases

_ o 3 « i i i i i ■

0 50 100 150 200 250mm 300 Figure 4.84 Effect of front spoiler height on Spoiler height z, ► drag a n d lift o f a c a r > a f ter ref- 4.65

monotonically with the spoiler height zs, a minimum value for the drag results at approximately zs = 100 mm. At still greater spoiler height, the drag increases again; see also Fig. 4.80.

A front spoiler must be matched carefully to the shape of the front end. This is shown in the next two examples. The drag of a specific passenger car was reduced by 4 per cent by mounting an attachment front end (Fig. 4.85) with shape A or shape B. The two shapes are only slightly different. A spoiler was optimized for both. Front end A attained an 11 per cent reduction in the drag with spoiler a. Front end B provided reduction of 16 per cent with spoiler b.

Figure 4.86 shows how sensitively the flow reacts to slight changes in the shape. First the effective radius of the front edge of the hood was increased by attaching a well-rounded rubber moulding, resulting in shape B. With shape B the drag was reduced by 2 per cent and the lift on the front axle by 8 per cent. For shape C this moulding was removed again and a front spoiler attached. The change in the drag of 2 per cent was again only slight. The reduction of lift, on the other hand, was significant. Both measures were used simultaneously on shape D; the result exceeds the total of the individual results significantly. The high reduction in drag in case D can possibly be attributed to the generation of a low pressure peak on the front edge of the hood rounded with the moulding in interaction with the spoiler.


Front end B ^ \ fsr*

%.

spoiler b

itEH spoiler a

-20 %

Γ" 1-10

A*L

H 4% ■

9 i A | B Front end

1 without spoiler

-16%

-119

P w.

^^H

A + a B + b Front end

with spoiler

Figure 4.85 Matching of front end shape and spoiler geometry, after ref. 4.25

detail X

N\\\\\\\\\\\\\X^^sV;

Initial shape Shape B

AcD = -2% ACLF - - 8 %

Shape C

AcD = - 2 % AcLF = -30%

Shape D

AcD = -8% AcLF = -32%

Figure 4.86 Matching of front spoiler and leading edge of the hood, after ref. 4.25

This low pressure peak point could not form on the hood with a sharp edge corresponding to the initial shape. Proof of this explanation has still to be made with pressure distribution measurements.

One example for the development of a spoiler integrated into the front skirt is given in Fig. 4.87, after Emmelmann.4 67 A significant reduction in the drag was obtained in this manner on the compact Opel Corsa,


AC,

0 20 40 60 Figure 4.87 Development of an integrated front spoiler for the compact car Opel Corsa, after ref. 4.67

particularly on the sporty SR version on which the spoiler was extended down to the overhang angle.

4.3.2.10 Rear spoiler

The effect of the rear spoiler is basically different from that of the front spoiler. Its effect has been explained by Ohtani et al.4·68 who compared the rear spoiler with the trailing-edge flap of an aerofoil. On an aerofoil, the trailing-edge flap is moved downward to increase the lift, but in this case it is deflected upward to reduce the drag and lift. Figure 4.88 shows the two-dimensional model used by Ohtani et al. The wing or the slanted rear window respectively is simulated by a flat plate. This is very close to the outline of a fastback. The flap length l2 is small in comparison to the wing length / j . Even without the limitation l2ll\ < 1 this model can be evaluated theoretically; see Schlichting and Truckenbrodt.4 12 The pressure distribu-tion on the upper side for a given value pair consisting of angle of attack oc and flap angle δ is given in Fig. 4.88. The reduction of the negative pressure by the deflected spoiler is clearly recognizable. The lines of constant pressure in Fig. 4.89, which were measured on a sports car with

-1.0 -0.8 -0.6 -0.4 -0.2 X Figure 4.88 Two-dimensional 'wing-with-flap-model'

for the rear spoiler of a fastback, after ref. 4.68


CNOOCO

Figure 4.89 Static pressure on the slope of a fastback; pressure increase due to the spoiler, after ref. 4.68

and without rear spoiler (see also Ohtani et al.4 68), confirm the results obtained on this model. While negative pressure, cp < 0, is present on almost the entire rear end without a spoiler, the spoiler creates a positive pressure, cp > 0, over a large area. If the pressure is plotted against the vehicle height zlh (Fig. 4.90), the effect of the rear spoiler upon the drag becomes even clearer. The pressure at the front of the car remains unaffected by the rear spoiler. However, the pressure at the rear end is

o without spoiler • with spoiler

zs = 100 mm

= P -P -

-1 .0 -0 .5 0.5 1.0 -0.5 0.5

Figure 4.90 Effect of a rear spoiler on the pressure at the front and the rear of a fastback, after ref. 4.68

^ *

J \

t

i.u z |

0.8^

—·— 0 .6 -

ΟΛ^

0 .2 -

·-s

:ront end I

3

^ Γ I Rear |

end


increased even in the area of the wake. That the rear spoiler reduces the lift at the rear of the car can be concluded directly from Fig. 4.89. Rear spoilers can be used on fastback as well as notchback vehicles to reduce both drag and lift.

Figure 4.91, after Schenkel,465 shows the effect of a spoiler on a notchback vehicle. A reduction in drag can be obtained only with relatively low spoiler height z. As the spoiler height continues to increase, the drag

0.1

Ü

0.1

0.2

0.3

0.4

-AcLf

\ * " " ""^"Δθη

\ ^ A C L R

1 l .i i ^ SL 2 0 40 60 80 mm 100 Fig u r e 4.91 Effect of rear spoiler height on

Spoiler height zs — ► drag and lift of a notchback, after ref. 4.65

t 1.0

0.0

• without spoiler o 34 mm \ Δ 68 mm \ Spoiler height zs

n 100 mm >

-1.0

Figure 4.92 Increase of pressure at the back of a notchback with increasing rear spoiler height, after ref. 4.65

also increases again. However, significant negative lift coefficients were obtained at the rear axle. In this manner, the driving characteristics can be improved considerably. Surprisingly, the rear spoiler not only changes the pressure on the top of the vehicle, where it causes a pressure increase, but the pressure on the underside is decreased (Fig. 4.92). On the other hand,


the pressure on the vertical rear surface is not influenced by the spoiler—in contrast to the measurements made on a fastback by Ohtani et al.;4 68 see Fig. 4.90.

The development of a rear spoiler for a production vehicle is demonstrated with the Volkswagen Scirocco I (Fig. 4.93, after Janssen and Hucho4 2 3) . A series of formally different solutions was worked out, in order to allow the stylist the possibility of selecting the one best suited to his design. Of all the shapes in each case, only the one that produced the greatest reduction in the drag is shown. In all cases the separation line was at the lower edge of the car's rear end.

Figure 4.93 Development of a rear spoiler for a fastback car, VW Scirocco I, after ref. 4.23

The original styling shape (1) resulted in a drag coefficient of 0.41 after optimization of the front end region. By raising the upper rear edge by 40 mm (2), the drag coefficient was reduced by 5 per cent to 0.39. Simultaneously the lift was reduced by 15 per cent. Additional lifting of the rear edge (3) by a total of 55 mm resulted in a further reduction in the drag of 7 per cent overall to 0.38. The lift was also reduced further by a total of 30 per cent. The attached spoiler (4) with a height of 55 mm provided nearly the same drag and lift coefficients as raising the upper rear edge (3) to the same height. The same reduction in the drag as with raising the rear edge by 55mm was achieved with the spoiler versions (5) and (6), which, however, only had a height of 40 mm. The mass-produced Scirocco I was equipped with a rear spoiler according to shape (5), which had no negative effect upon the external appearance and simultaneously contributed to a high buckling strength of the rear lid.

4.3.2.11 Attachments

Attachments, such as outside mirrors or antennas, themselves have high drag coefficients if their drag is related to their individual frontal areas. The following equation can be used for the mirror, where DM is the drag of the mirror and AM is its frontal area:

D c DM —

M = 1.2 P V2 A

(4.10)


when it is similar to a flat circular disk. See Hoerner4 35 for other shapes. The velocity of the oncoming flow VM is not equal to the vehicle speed V. It must be determined by measurement. According to Carr,4'11 VM ~ 1.3V is a good approximation.

When DA is the drag of the antenna and AA its frontal area, the drag coefficient of the antenna is:

C ' D A - T J ^ 1.2 (4.11)

The following formula applies in the normal range of vehicle speeds:

Re = — ^ - < 3 x 105

so we can assume a case of laminar separation on a circular cylinder (d = diameter of antenna; see section 2.3.3.4).

The frontal areas of these attachments are, however, small in comparison with the frontal area of the vehicle. For example, the area of the outside mirror is less than 0.5 per cent of the frontal area of the car. Therefore the contribution of the mirror to the total drag coefficient can be described with the following equation when VM = 1.3 V:

cD M = c 'D M V y / ? M = 1.2 x 1.7 x 0.005 = 0.01 (4.12)

This corresponds to approximately 2 per cent of the total drag coefficient and is in good agreement with measurements on production vehicles. The contribution of the antenna to the total drag is in approximately the same range.

These estimates do not take into consideration the interaction of the flow field of the mirror and the antenna with the flow field of the car. Outside mirrors produce long and wide wakes, which disturb the flow on the side surfaces. Quantitative information on the effect of such disturbances—e.g. upon the effectiveness of boat-tailing—is not available. The disturbing effect of the mirror is more pronounced on smooth, low-drag vehicles than on high-drag cars, where the flow is more or less separated on the side walls. On vehicles with extremely low drag, integration of the outside mirror into the vehicle contour is given particular attention. A good example of this is the Unicar; see Potthoff4 42 and section 4.6.3

4.3.2.12 Drag from flow through the car

On passenger vehicles there are two flow systems through the car, one for the engine cooling and the other for the heater and ventilation. Only the flow through the radiator contributes significantly to the drag. The volumetric flow for the ventilation is considerably smaller than the volumetric flow of the engine-cooling air. As a rule, the ventilation air is taken in at the cowl. Here a separation bubble is formed in the concave corner (Fig. 4.3). Lower-energy air is extracted from this separation


bubble. It has not yet been possible to show that this extraction has any effect upon the airflow around the vehicle.

Considering only the cooling air, therefore, drag results on the one hand from pressure loss in the cooling-air duct, and on the other hand from the influence on the air flow around the outside of the vehicle, which generally leads to additional drag (interference drag). To date these two drag components have not been separated. There are indications, however, that the interference drag in some cases might even be negative; see Carr.4 6 9

The relationship between the internal losses of a flow system and its external drag has been investigated in great depth in the course of optimization of aircraft oil coolers. A summary of this research is given by Hoerner.4 35 The cooling-air drag has been calculated with the aid of the theorem of momentum (Fig. 4.94) for the limit case in which the entire

Theorem of momentum p f vdQ = — DQ

(k)

2 i—«I

Poo

H «Ά Poc

1 - 2

3 - 4

2 - 3 1 - 4

Mass f low

-pAV»

pÄV„

| -pAR vA

-PAR vA

Momentum flow

-pÄVj

pA Vj

-pAn vA V„

-p AR vA V„

\C'DC

Do

P 2

= P^R

Dc

VJAR

VA

=

V«,

Voo

Figure 4.94 Calculation of cooling airflow drag with momentum theorem

cooling air exits the system with the momentum in the direction of motion equal to zero. According to this, the cooling-air drag Dc in relation to the frontal area A of the vehicle is

Dr COC = 2

vA AR (4.13) -VIA


where AR is the frontal area of the radiator and vA is the mean radiator face velocity. In section 9.3.1 a relationship will be established between the internal drag (pressure loss) of the cooling-air duct and this radiator face velocity.

For typical values of vA/VOo and AR/A, see Emmenthal and Hucho.4 70

The cooling-air drag is in the following range, according to Eqn 4.13: 0.02 < COC < 0.06. This corresponds well with measurements on vehicles in production, as shown in Fig. 4.95a (after Hucho4 4) and Fig. 4.95b (after Emmelmann467).

30

A 25

2 20 CO o 0 15 a>

1 10 2 5

A— UAiii ^4S u ui —

-At

ΛΛΛΛ

N 76

: D C υ.υο-

■

ΕΞΞ3

C Q O ·>////////////////////

0.01 0.02 0.03 0.04 0.05 0.06

A c D C -

A ^ D C - cD - cD0

®

E 3

19 20

1

16 Λ/=70 ÄcDC = 0.04

1

0 .01 .02 .03 .04 .05 .06 .07

AcDC

Figure 4.95 Drag increase related to cooling airflow: (a) after ref. 4.4; (b) after ref. 4.67

According to this, a carefully designed cooling system increases the drag of a vehicle by only 2 per cent. However, the drag increase can amount to more than 10 per cent.

In the development of the cooling air duct, it must be ensured that only as much air flows into the body as is really required for cooling. Formerly, the radiator was located behind—but isolated from—the grill. Nowadays it


Figure 4.96 Alternative radiator arrangements to reduce cooling airflow drag, after ref. 4.26

is connected to the grill by an air passage. To what extent the design of the cooling-air duct can affect the radiator drag can be seen in Fig. 4.96, after Buchheim et al.4*26 With almost the same face velocity vA as the standard arrangement A it was possible to achieve a significantly lower radiator drag with air duct C. The disadvantage of arrangement C, however, is that the air heated by the radiator flows to the cowl where it is drawn into the fresh-air inlet. For this reason arrangement C is used only on racing cars and record vehicles.

4.3.2.13 Trailers and roof luggage racks

A car pulling a caravan/trailer has a considerably higher drag than the same car alone. Depending upon the size and shape of the trailer, the drag of the two is approximately three times as high. This is for two main reasons. Firstly, the caravan has approximately twice the frontal area of the passenger car pulling it. Secondly, its drag coefficient is higher because caravans are usually box shaped, for design reasons. Due to interference between the car and the trailer, the flow of air around both is changed so that the drag of the two together is less than the sum of the individual drags of the car alone and the trailer alone (see Chapters 2 and 8). This is shown clearly in Fig. 4.97, after Beauvais.4 In relation to the frontal area of the


Car without trailer

Car in front of trailer

Trailer without car

Trailer behind car

A [ft2]

24.6

24.6

54.2

54.2

CD

0.53

0.30

0.62

0.59

cD.A

13.0

7.4

33.6

32.0

c DACar

Λ Μ . « *y =1.6

20 Ft Travel Trailer r

Ford Galaxie 1965

Figure 4.97 Drag of car and trailer, after ref. 4.71

towing car, the two together have a drag coefficient of 1.6, whereas the total of the individual drags is 1.9.

If the shape of the trailer is matched to that of the towing car a considerable reduction of the aerodynamic drag of the two together can be achieved—as in the case of semi-trailer tractors. However, in practice the possibilities for accomplishing this are considerably more limited. Caravans are not designed to be towed by one specific car. In the design of their shape and the selection of the distance between the two vehicles, consideration must also be given to the stability of the combination—both without as well as with side wind.

Q

0.8

0.6

0.4

0.2

— * | Δ Χ | —

o MORRIS 1000 (notchback)

x TRAVELLER (Squareback)

Standard gap

0 0.1 0.2 0.3 0.4 0.5 0.6

Gap Ax/y/Ä2 Figure 4.98 Influence of gap between car and trailer on the drag of the car-trailer combination, after ref. 4.72. A2 is the frontal area of the trailer


The influence of several significant geometric parameters of the trailer upon the drag of the car/trailer together have been studied by Waters.4 72

The results cannot be generalized without reservations, owing to the special configuration of the car and trailer.

Figure 4.98 shows the effect of the distance between the two vehicles upon the drag. In this case the drag coefficient is based on the frontal area of the trailer. As the distance decreases, the drag of the two vehicles together is reduced. The effect is greater on a station-wagon than with a notchback car. For reasons of stability, it is important to ensure that, when the distance Ax is reduced, the tow bar length /D remains the same; see Zomotor et al.4 73 Increasing the front-edge radii produces a considerable reduction in the drag; see Fig. 4.99, after ref. 4.72. However, this also

1.2

1.0 V A 2

Rectangular block all corners radiused

_L J_ J_ 0.1 0.2 0.3 0.4 0.5

r

\fA~7 Figure 4.99 Influence of the leading edge radius of the trailer on the drag of the car-trailer combination, after ref. 4.72

greatly increases the yawing moment in side winds. To what extent the stability of the two vehicles is altered in side wind is not known. The studies made by Waters also showed that sloping the front end of the trailer was very effective in reducing the drag. Measurements, made later by Peschke and Mankau4 74 with a fastback passenger car as the towing car, have confirmed this effect.

However, more important than achieving a low aerodynamic drag is ensuring sufficient stability of the car/trailer combination. This is


influenced primarily by the tow-bar load, as shown by measurements made by Zomotor et al.4 73 This is the force that the trailer exerts on the trailer hitch. Even in the absence of cross-wind, oscillatory vibrations are induced in the trailer by unevenness in the road. At increasing cruising speed, damping of this vibration is reduced. As shown in Fig. 4.100, after ref.

Q c

0.5

0.4

0.3

0.2

0.1

t

F

I I

I I

I I

I I

I

p

1 I

N \ ;

1

Tow hitch load 1 — — ■ 1000 N

■ — ■ ^ or

S> sxl V

\l 1

sl 1

60 80 100 120 V[km/h]

140 160

Figure 4.100 Effect of tow hitch load on the stability of oscillatory motion of the trailer, after ref. 4.73

4.73, the degree of damping D is highly dependent upon the tow-bar load. At low tow-bar load, the value D = 0, the stability limit, is reached even at low cruising speeds.

As proved by Peschke and Mankau,4 74 depending upon its shape, the trailer is subject to a pitching moment, which changes the tow-bar load. Figure 4.101 clearly shows this. With a box-shaped trailer, the pitching moment of the trailer is positive (tow bar up), and the tow-bar load decreases at increasing speed, but the pitching moment is negative (tow bar down) and therefore the tow-bar load increases, on a trailer with a sloping front.

The measurements performed by Peschke and Mankau4 74 on a VW Passat with trailer at full scale in the climatic wind tunnel of Volkswagen AG are summarized in Fig. 4.101. The lowest aerodynamic drag of the car/trailer combination was achieved with an aerofoil on the roof of the towing car guiding the airflow in a similar manner to the deflector on top of the cab of a truck-semitrailer (see section 8.5.3.4). The trailer with a sloping front did not provide any advantage in terms of the drag. However, it did provide the best characteristics for stability against oscillatory vibrations. The tow-bar load proved to be independent of cruising speed.

183

cDcar + trailer1

Load change at the hitch (N) at V = 80 km/h (50 mph)

0.53 -3402

0.45 -3152

0.53 ±0

Figure 4.101 Flow around different car-trailer combinations, drag of the combination and variation of tow hitch load, after ref. 4.74. (1) Frontal area of the trailer is the reference area. (2) Negative sign means load reduction compared to V — 0

©

= 0.10 \

®

0.18

% 0.33 1

I©

0.38

Figure 4.102 Drag increase from ski-racks, after ref. 4.75; VW Golf GTI (I); cD = 0.40; A = 1.87 m2


Roof luggage carriers increase the aerodynamic drag of automobiles considerably. In Fig. 4.102 several measurements with ski racks are summarized, which were performed in the wind tunnel of Volkswagen AG on a VW GTI I.4·75 All the drag coefficients given here are related to the frontal area of the car without roof rack. Surprisingly, the large ski box C for four pairs of skis is no better than simple roof racks E, while the lockable racks F and G have even higher drag coefficients.

4.4 Strategies for aerodynamic development of passenger cars 4.4.1 Detail optimization

Three characteristic functions can be derived from the test results described in the previous section 4.3. They express the relationship between the aerodynamic drag and the vectors rt describing the various parameters of the body's shape and are illustrated schematically in Fig. 4.103. Each shape detail is described by at least one vector rh which can be

i

1

£D_ coo

I L >

V Mini murrt/

I Jump

I j i Saturation

i l l k i l l — 5 I

PiSopt |PiMopt P· I

PiJopt

Figure 4.103 Typical drag-geometry relationship, schematic

a radius, a height or a length, etc. Here the vehicle length / was selected as a reference value, yielding p, = r,//. However, other reference values are also possible, such as the width or height of the vehicle. The drag coefficient cD is equated to the value cD0 before starting variation of the corresponding shape details. If for instance the effect of the value of a corner radius upon the drag coefficient cD is examined, the value cD0 represents the drag of the initial shape rt = 0 with a sharp edge. The following three characteristic functions cD (p,·) result:

1. Saturation: this curve pattern is typical when an edge is rounded; see the front-end development of the Audi 100 II (Fig. 4.24). Another typical example is the radius on the corners between the front and sides of a van; see Hucho,4 2 1 and Hucho and Emmelmann.4 76 Yet another example is given in Fig. 8.50. When the corner is rounded to the point that the air flows around it without separation, a further increase in the corner radius does not provide any additional reduction in drag.

2. Jump (sudden transition): this characteristic is typical for sudden changes of the flow pattern from one type to another. Figure 4.62 shows such a jump. If the rear step is very large, the flow that separates at the end of the roof does not become reattached and the drag is high. At a

Strategies for aerodynamic development of passenger cars 185

certain height reattachment occurs and the drag decreases suddenly. The various flow patterns on fastbacks and squarebacks (see section 4.3.2.5) also have transitions with jumps. However, here an Overshoot' effect results in a departure from the curve in Fig. 4.62.

3. Minimum: this pattern occurs when two elements of drag are influenced in opposite directions by variations in the same parameter p,. An example of this is the height variation of the front spoiler; see Figs 4 80 and 4.84.

One procedure for the aerodynamic development of vehicles is to determine these functions cD(p,·) for all significant parameters on a given model. Owing to the interaction of the individual flow fields, this is in principle an iterative process as shown in section 4.2. Practice has shown that the vector designated as Optimum' according to Fig. 4.103 does not differ greatly from the initial vector for many shape details. A drag coefficient in the order of 0.40 can be achieved for almost any styling concept. Yet this drag figure is far better than that of most of today's cars; see Fig. 1.53.

Figure 4.104 Example of the 'detail optimization' of a passenger car, after ref. 4.66

An example of the optimization of a total vehicle is shown in Fig. 4.104, after Janssen and Hucho.4 66 The optimum vectors for the shape details A to E were determined experimentally by finding the function cD(p,) for each detail. Taking the interference into consideration, it was possible in this case to reduce the drag in comparison with the initial shape by 21 per cent. In terms of appearance the optimized model could not be distinguished from the initial model. By contrast, shape (7) deviated


greatly in terms of style. This was intended to show what could be reached over and above 'optimization' by departing from the stylistic concept.

The term 'detail optimization' has been recommended by Janssen and Hucho4 66 for this procedure, which assumes the stylistic concept of the vehicle to be given. Numerous detail optimization procedures.already carried out have shown that drag coefficients down to 0.40 can be achieved with this strategy. The lower cD value for shape (6) in Fig. 4.104 is attributable to the fact that the model was not as 'rough' in all details as a complete vehicle. Values lower than cD = 0.40 have hardly been achieved using the detail optimization method. However, 0.40 cannot be considered to be an absolute lower limit for this method. A favourable initial shape could lead to better results. Examples of cars developed according to this detail optimization strategy include the VW Golf I and VW Scirocco I (see ref. 4.23), the Audi 80 II and the Volkswagen light truck LT (see ref. 4.76 and Figs 1.41, 8.53 and 8.55).

4.4.2 Shape optimization

In contrast, the development of body shapes with low drag according to the strategy of shape optimization starts with a streamlined basic body developed according to the method described in section 4.6.2. This basic body already has the main dimensions (length, height, width) of the final vehicle. Frequently, scale models are used in this phase in order to save costs and to facilitate the mechanical processing of the model. The final vehicle shape is then derived step by step from this.

0.35

0.30

0.25

Co

0.20

0.15

Basic body | Basic shape | Basic model | Styling model

Figure 4.105 Example of the 'shape optimization' of a fastback passenger car, after ref. 4.77

The sequence of such a derivation is summarized in Fig. 4.105 (after Hucho4 77 and Buchheim et al.4 3 M 3 2). The basic shape is first generated from the basic body according to systematic parameter variation. This already includes all the primary shape characteristics of a passenger car body. It is characterized by a flat, well-rounded front end, a highly curved windshield, a heavy draw in the top view and—in this particular case—by

Strategies for aerodynamic development of passenger cars 187

the high fastback. The drag coefficient cD = 0.18 of this basic shape is only slightly higher than that of the basic body. The next step is to develop the basic model from the basic shape by incorporating all of the technical characteristics of a practical car. The flow of air around the body, which is no longer smooth (window recesses, joints, beads, suspension parts, exhaust pipe and muffler), as well as the flow of air through the radiator and the wheel wells, results in a further increase in the drag to 0.24. This basic model is then given to the designer.

During the course of the styling process increases in the drag are very highly dependent upon the ability of the designer and upon the cooperation between him and the aerodynamics engineer. An acceptable compromise was found for the VW Research Car 2000, resulting in cD = 0.25; see Fig. 4.106.478

Figure 4.106 Sahep-optimized Volkswagen Research Car 2000; cD = 0.25; A = 1.88 mz, after ref. 4.78

0.35

0.30

cD

0.25

0.20

0.15

0.17"

basic-body 1:4

basic-model 1:1

0.29 0.30

styling-model 1:1

production-car 1:1

Figure 4.107 Shape optimization of the Audi 100 III, model year 1982; cD = 0.30; A 2.05 m2, after refs 4.31 and 4.32

The development of a mass-produced passenger vehicle, the Audi 100 III, using the same strategy, is illustrated in Fig. 4.107. Since a notchback was required for this car, a corresponding basic body was first developed at a scale of 1:4; see Buchheim et al.4·31'4~2 With cD = 0.17, this value was


only slightly higher than that for the basic body of the VW research car. The transition to the basic model is accompanied by a rather high increase in drag. This comes from the fact that all the aerodynamically relevant details are now incorporated (detailed underside, cooling air flow, bumpers, joints, etc.). The individual parameters were optimized with a procedure similar to that of detail optimization. Stylistic refinement of this basic model led to a styling model, which again had a higher drag coefficient. On the other hand, the drag of the mass-produced vehicle was only insignificantly higher than that of the styling model. This is a sign that the styling model was in fact virtually identical geometrically to the mass-produced vehicle. With cD = 0.30, the lowest drag coefficient to that date for a mass-produced saloon was achieved with the Audi 100 III. Figure 1.55 shows that this did not lead to a shape unlike any other car's—with the concomitant risk to sales.

It is therefore possible to obtain a value of cD = 0.30 with the shape optimization strategy without too many concessions in terms of styling. There is no absolute limit to even lower drag. A value of cD = 0.25 is also achievable, as shown by the example of the VW Research Car 2000 and other concept cars; see section 4.6.3.

4.4.3 Drag reduction in the course of model improvement measures

The measures described in section 4.3.2 can also be used to advantage within a model improvement programme, a so-called face-lift. Naturally the success depends upon how far the modifications can go in comparison with the initial model. Figure 4.108 shows examples of the individual measures by which the drag of 0.45 of the Opel Rekord model year 1980 was reduced to 0.36 on the Opel Rekord model year 1983 (after Emmelmann4 7 9) . The greatest success was provided by optimization of the

A-PILLAR SHAPE ACD=-.007

FRONT END SHAPE A C D = " 0 2 4 REAR END SHAPE A C De - 0 l 3

L WHEEL CAPS A C D = - 0 0 3

L COOLING AIR FLOW A C D = " 0 4 1

Figure 4.108 Drag reduction in the course of improving the Opel Rekord, model year 1980, cD = 0.45 to model year 1983, cD = 0.36, after ref. 4.79

Drag of passenger cars in production 189

REKORD MY 80 cD =0.45 REKORD MY 83 cD =0.36

Figure 4.109 Comparison of centreline section Opel Rekord, model year 1980 and model year 1983, after ref. 4.79

cooling-air duct. The size of the cooling-air inlet was reduced significantly. The oncoming flow to the cooler was improved with an air guide. The reduction in size of the cooling-air opening was realized in part by lowering the hood, thus giving it a larger radius. The 20 per cent reduction in the drag was simultaneously combined with a welcome reduction in the lift of 48 per cent. The silhouette in Fig. 4.109 indicates how the greater curvature at the transition from the grille to the hood and a higher rear end were realized.

4.4.4 Adaptation of attachments

One method of reducing the aerodynamic drag on existing vehicles is the subsequent development of suitable attachments. The Motor Industry Research Association (MIRA) has completed a programme to discover the short-term possibilities for fuel savings; see Carr.4 ^° Above all, front and rear spoilers can be used. Their tuning is described in sections 4.3.2.9 and 4.3.2.10.

Attachments are offered by the accessory industry. Only parts which are carefully matched to the corresponding vehicle model fulfil their purpose. Side effects, such as possible reduction of the cooling of the oil pan or the brakes by a front spoiler, must not be overlooked.

For cost reasons, in the development of mass-production vehicles an attempt is made to integrate into the body parts which were initially introduced as attachments. For this reason the front spoiler is integrated into the front panel on a series of modern vehicles—one example of this is the Opel Corsa (Fig. 4.87).

4.5 Drag of passenger cars in production 4.5.1 Subdivision of the test results

It is usual to specify one single value as the drag coefficient cD for a given vehicle. In reality a drag range exists for every car, because drag does not depend solely upon the vehicle shape. The position of the vehicle relative to the road—ground clearance and angle of attack—also has an influence


Position

Effect of load

Function

Effect of external items

Effect of cooling air flow

Shape

Effect of shape details

Figure 4.110 Parameters influencing the drag of a car, after ref. 4.66

upon the drag. Finally, the state of the vehicle—e.g. windows open or closed—also influences the cD value. These variables, which have an effect upon the drag, are summarized in Fig. 4.110 (after Janssen and Hucho4 66) and subdivided into three categories—position, function and shape. They are dealt with in the following sections. Thereafter the drag coefficients for a large number of mass-production vehicles will be listed.

4.5.2 Vehicle position, side wind

The influence upon aerodynamic drag and lift of the various parameters characterizing the position of the vehicle has been studied by Janssen and Hucho.4 66 The following results were taken from this work. The variables

h*-7

T(D)

T(D))

Figure 4.111 Forces and moments acting upon the vehicle; definition of vehicle position

Drag of passenger cars in production 191

characterizing the position of the vehicle are defined in Fig. 4.111. The definition of the angle of attack a = 0 is arbitrary. In what follows a = 0 designates the design position of the vehicle.

The influence of the angle of attack upon drag and lift is shown in Fig. 4.112. The ground clearance e of each and every vehicle was held constant.

' S* 0.1 i j X J ( ^ j

_4° _3° _2° _i° +T° +2° +3°

Figure 4.112 Effect of angle of attack a on drag and lift, after ref. 4.66

A drag and lift increase with increasing angle of attack on the three vehicles is observed. A change of the angle of attack oc of 1° causes an increase in the drag of about 2 per cent. The influence of a change in the angle of attack when the underbody is held stationary and the body is moved relative to it has not yet been studied. However, it can be assumed that the effect of this change in the angle of attack would not be much less than in the previous case. If it is possible to accommodate a negative angle of attack of 1° to 2° stylistically, this would provide a good possibility of contributing to drag reduction.

The effect of the ground clearance e upon drag and lift is shown in Fig. 4.113. Only the Citroen ID 19 showed a similar increase in drag with


VW van

VW-PORSCHE 914

▼ Citroen ID 19

A

Competitor F2-2

100 150 200 250 mm 350

Figure 4.113 Effect of ground clearance e on drag and lift of cars and a van, after ref. 4.66

decreasing ground clearance, such as the measurements performed by Hansen and Schlör481 (Fig. 1.28) and those performed by Stollery and Burns4 82 (Fig. 4.125). The other vehicles, one of which was a van, showed a reduction in drag with decreasing ground clearance, with virtually unchanged lift. While the Citroen ID 19 had a smooth underside, those of the other vehicles are characterized by 'normal roughness'. A general tendency for the effect of the ground clearance for real cars can therefore not be given.

During operation of a vehicle, the angle of attack and the ground clearance do not vary independently. Both are changed simultaneously, depending upon the load. The large changes in drag when a vehicle is loaded extremely, taking into consideration the permissible maximum axle loads, are shown in Fig. 4.114. Here the reference value cD2 is that at full load, although today half load is selected as the normal load for fuel economy tests according to the specifications of DIN 70 300. Naturally, particularly large drag ranges result for vehicles with luggage compart-ments at the front and at the rear. As a rule (luggage compartment at rear) the drag increases with increasing load, owing to the change in the angle of attack.

193

F3-1 (M-SH) F1-4JK-VH)

§ Fi-3 (M-VH) S II 4-1 (K-VH) | l M - 3 ( K - F H ) o I 1-2 (M-SH)

D4-1 (M-SH) D2-4(M-SH) AUDI 1001 PORSCHE 91 IT

VW-PORSCHE914 gVW Variant 411 L J VW41TL' 2 £VW181 > VW 1302

VW 1200

I K - ^mal l

"■ " "1 "

M - Medium size car

ς|_Ι Notch ^^^g± back ^ ^ ^ ^ ^

f-H Hast back ^ ^ H

\/u Sauare -^^Λ^^^ —bac k w ^

1

j

] ~ a a ^ H H

- + -+ -i

1 I !

—-

I

^^^^^^^^^^

- -J —-

1

1

J

■

^ ^ ^ ^ ^ ^ ^ ^ e

^^^^ 1

^^^^^^^^^^^^^^H 1

-12 -10 - 8 - 6 - 4 - 2 4 6

Δ£ρΒ _ 8 10 % 12

CD2

Figure 4.114 Effect of load and load distribution on drag; cD2 is the drag coefficient of the car with full load; after ref. 4.66

in—(\r^ £T

AUDI 100

— ♦ — PORSCHE 911T

Competitor 11-2

t VW-Model VW-P1

1 VW-Model VW-P2

-10 Figure 4.115 Drag increase with yaw, cT(ß), after ref. 4.66


Generally, the natural wind speed is not zero. Hence the car is approached by the oncoming flow at an angle of yaw ß (Fig. 4.2). The case of ß = 0 is rare. A rough estimate indicated that for a passenger car in the speed range above V = 80 km/h (50 mile/h) the most probable angle of yaw is ß ~ 5°. For this reason care should be taken in the development of the shape to maintain a low drag coefficient achieved for straight oncoming flow (ß = 0) at least up to the most probable angle of yaw. Figure 4.115 shows a selection of measured patterns for cT(ß). The subscript T indicates that this is the force in the longitudinal direction of the vehicle. While the absolute cT values in the yaw-angle range up to 45° are compared in the upper diagram, the lower diagram shows the relative drag increase with the angle of yaw for the important range of small angles ß. Of particular note is the steep increase in the drag on prototype I. The observed decrease in the drag on prototype II at a very small angle of yaw—this was during an early development stage on the VW Golf I—is an indication of unfavourable air flow around the car at ß = 0, which was eliminated in the course of development.

To date, the drag coefficient for ß = 0 has always been the basis of the determination of the relationship between the aerodynamic drag and the fuel consumption; see Chapter 3. As Fig. 4.115 shows, this simplification should be permissible as a rule.

These relationships are different on commercial vehicles, because the angle of yaw of the oncoming flow is greater owing to their lower average cruising speed V (valid for Europe but not for the US). This is treated in section 8.4.3.

4.5.3 Equipment, function

Open windows, extended folding headlights, roof removed (hardtop) or folded back (convertible) change the flow around the vehicle and therefore

VW 1300 Beetle Saloon Convertible, Convertible,

closed I ° P e n

VW Karmann Ghia 1300 Coupe" Convertible, Convertible,

open | open

Figure 4.116 Comparison of drag for a saloon and an open and closed convertible, after ref. 4.66

Research in the field of vehicle aerodynamics 195

have an effect upon drag. This is shown by two examples (after Janssen and Hucho4·66). Figure 4.116 provides a comparison between saloons and their convertible versions. In both cases the formal difference between the saloons and the convertible is small. The differences in drag are correspondingly slight. However, increases in drag of up to 70 per cent resulted from opening the roof. If the open roof can be lowered into the body, or if it is smooth with the contour of the body, the increase in drag is considerably less. For the sake of completeness it must be mentioned that the open convertibles were measured without passengers. Tilling up' the hollow space behind the windshield with passengers should improve the flow of air around the car and therefore lessen the increase in drag.

Aerodynamic drag measurements must be made with fully functional cooling-air ducts. If the cooling-air inlet is closed the value obtained for the drag will be too low (Fig. 4.95). This must be taken into consideration— particularly on model measurements. On the other hand, the fresh-air inlet for the ventilation and heating system is usually sealed during drag measurements. As already established in section 4.3.2.12 the drag resulting from this flow of air through the car is negligibly small.

4.5.4 Drag coefficients of mass-produced vehicles

The drag coefficients of a series of mass-produced vehicles are summarized in Table 4.3. All measured data were determined in the climatic wind tunnel of the Volkswagen AG under uniform conditions. In Chapter 11 it will be shown that the drag coefficients measured in the VW wind tunnel correspond well with the measured data from other large wind tunnels. The test state of the vehicles was as follows: • Half-load (2 x 75 kg on the front seats, remaining load in middle of trunk). • Suspension free to move. • Standard external equipment (licence plate, one outside mirror, no antenna). • Open cooling-air duct. • Covered fresh-air inlet. In addition to the drag coefficient cD, the frontal area A is also given as well as the product CjyA.

Given here are only those drag figures that have already been published in other works; see Werner,4 83 and Heil.4 84 The classification of the cars tested is according to European standards.

4.6 Research in the field of vehicle aerodynamics 4.6.1 Potential and problems

Research and development in the field of motor vehicle aerodynamics continue to focus on aerodynamic drag. The potential possible here is shown in Fig. 4.117, after Hucho.4 85 Three bodies with the same solidity, i.e. same ratio of length to diameter or height, are compared. The isolated body of revolution has a drag coefficient of 0.05. Even smaller drag figures

< H

H z

s ?

. 2

2 2

3 <!

EL

~

öS °

§

D

X

OS

c*>

N <*>

CL

SO

OS

3

c

w

O <

oo

=T

-·

=·

cr r

O "

3 Ξ

Π Pö

o

os' 5

'

m

o o u> <-►

«-►

3<8

o

3 OS

O

a H

r

s'S

^^

w

^ ς

oa

^lg

n

og

" m

*>

~i

3§"

oo

-a -a

OS

? S w *

X

- 1

OS

OS

OS

^

O

> T3

o

— n

os g

£

*«

ft)

O-

~ 5*

0

3

*>2

E

K"

w

tö w

2 ~

<

<

*v o

v ~

e

.9

2 2

Ό

W

O

S

CO CD

W

£

Ξ

Γ^

-^ο

£ C/

5 '

S 3

ε?

—

^ n

Q H

<

gr

OS

CL

CO

H

ST. 3

S

. to

_

_

„,

n 2

Π

os

M

—

3 §

I pi

« 5

id

c

i. O

os

cro

-

«-►

c

Π)

os

3

- o

- 5-

a *

-

a ^

r £

a

r £

X

t-n

N)

55

g.O

~ K

-1

r :

n

0 OS

K>

3 m

in

n

0 C/5 OS

OO

*

o

oooooooooooooooooooooooooooo

ooMUiMN)\ooo^)i-'\£i'soooa)vjoNa\^vivjâiU)(7i^^K)MO

I I I I I I I I I I I I I I I I I I I I I I I I I I I I

oooooooooooooooooooooooooooo

0000000000000000000000000

OOMvJK)ÔNO^NlOOOO^ÔOv)ÔOvjâi(7iOM»J^

I I I I I I I I I I I I I I I I I I I I I I I I I

0000000000000000000000000

000000000000000000000000

fV>

- Ϊ

1

ΐ

- Ϊ

Ί

/- ^

Ί^

Ϊ-

Ί^

Ϊ^

Ί^

Ϊ /^

^.

/

^*

^*.

/

*-^v

/·**.

*·**.

***. Λ

*. ***.

_

w'

w'

W

W

W

W v—'

W

W

> '

v < ^

v

' O

O

O O

ι ι

ι ι

ι ι

ι ι

ι ι

ι ι

ι ι

ι VO

ON

Ό

L

/\

LAI

t—k

*sO 1

I

I I

I I

I '

I I

I I

I 1

1

1

1

1

1

1

I I

I I

I I

I I

I I

I Ί

I I

.

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

MH

MO

O^

^^

Lf

lN

lt

yi

Ui

WW

Ki

MO

OO

HO

O^

Ol

Xa

i-

ti

MO

VO

OO

OO

OO

OO

OO

OO

OO

OO

OO

OO

OO

OO

O

OO

OO

OO

^^

^^

^^

bN

Ô

NO

NO

Nb

Nb

NO

NO

NO

NO

NO

NO

Nb

Nb

Nly

i 0

\^

OO

OW

^H

M0

0O

vJ

s)

Nl

Ui

|k

Û

i|

kt

OW

Mt

OO

^

l l

1

l l

l l

1

l l

l l

1

1

l l

1

l l

l 1

1

l

1

l

OOOOOOOOOOOOOOOOOOOOOOOOO

οο

οο

οο

οο

^^

^^

^^

^^

σΝ

σΝ

σΝ

σΝ

σΝ

σΝ

θΝ

θΝ

θΝ

θΝ

σΝ

θΝ

θΝ

0

0O

\^

.N

)0

\O

IW

WW

MM

OO

00

-N

JV

JO

\0

0V

JU

I^

^^

K)

M

&

»>i. 1 **

1 s 3 ST

0 e n VI

^ 0 <*i w

3:

Table 4.3 continued

197

Vehicle type

Medium size Ford Sierra 1.8 Ford Sierra Turnier 2.3 D Renault 18 Turbo VW Passat CL Citroen BX 16 RS Opel Ascona GT 1.8i Mitsubishi Galant 1600 GLX Audi 80 CC Opel Ascona GT notchback Peugeot 305 GTX Mazda 626 GLX 2.0 Audi 90/2.0 E BMW 318i (320i) Toyota Camry GLi VW Passat notchback 2.0 E Honda Accord 1.8 EX VW Passat Variant CL Nissan Stanza SGL 1.8 Volvo 360 GLT Alfa Romeo Giulietta 1.6 Nissan Stanza notchback Nissan Bluebird 2.0 GL

Upper medium size Mercedes 200 D (250 D) Audi 100 1.8 Mercedes 230 E (new) Renault 25 TS Mercedes 190 E (190 D) Lancia Thema 2000 i.e. Mitsubishi Galant Royal Audi 100 Avant TD Opel Rekord 2.2i BMW 323i Audi 80 Quattro Audi 90 Quattro BMW518i(520i,525e) Citroen CX 25 GTi Alfa Romeo 90 2.0 VW Passat Synchro Opel Rekord Caravan TD Saab 900 GLi Citroen 25 TRD Break Peugeot 505 STI Mazda 929 2.0 GLX Mercedes 300 TD Turbo diesel Volvo 740 GLE Ford Granada 2.3 GL

Luxury cars Mercedes 300 E (260 E) Mercedes 190 E 2.3-16 Renault 25 V6 Audi 200 Turbo Audi Quattro

Drag coefficient cD

0.34-0.35 0.33-0.34 0.35-0.37 0.36-0.37 0.34-0.36 0.37-0.38 0.36-0.38 0.38-0.39 0.38-0.39 0.38-0.40 0.36-0.38 0.39-0.40 0.39-0.40 0.37-0.39 0.38-0.40 0.40-0.42 0.40-0.42 0.40-0.42 0.40-0.41 0.42-0.44 0.41-0.43 0.41-0.44

0.29-0.30 0.30-0.31 0.29-0.30 0.30-0.31 0.33-0.35 0.35-0.35 0.36-0.37 0.34-0.35 0.36-0.37 0.38-0.39 0.38-0.40 0.39-0.41 0.36-0.38 0.36-0.39 0.38-0.40 0.40-0.41 0.39-0.40 0.40-0.42 0.37-0.40 0.41-0.43 0.39-0.44 0.41-0.42 0.40-0.42 0.44-0.46

0.29-0.31 0.31-0.33 0.32-0.34 0.33-0.34 0.38-0.40

Frontal area A (m2)

1.94 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

00 88 89 91 87 88 86 87 84 92 87 86 94 91 88 91 88 95 87 88 86

2.05 2.05 2.06 2.04 1.90 2.02 1.89 2.05 1.97 1.86 1.89 1.90 2.02 1.99 1.95 1.92 2.06 1.95 2.16 1.97 1.93 2.11 2.16 2.13

2.06 1.92 2.04 2.07 1.86

cOA (m2)

0.66-0.68 0.66-0.68 0.66-0.70 0.68-0.70 0.65-0.69 0.69-0.71 0.68-0.71 0.71-0.73 0.71-0.73 0.70-0.74 0.69-0.73 0.73-0.75 0.73-0.74 0.72-0.76 0.73-0.76 0.75-0.79 0.75-0.80 0.75-0.79 0.78-0.80 0.79-0.82 0.77-0.81 0.76-0.82

0.59-0.62 0.62-0.64 0.60-0.62 0.61-0.63 0.63-0.67 0.71-0.71 0.68-0.70 0.70-0.72 0.71-0.73 0.71-0.73 0.72-0.76 0.74-0.78 0.73-0.77 0.72-0.78 0.74-0.78 0.77-0.79 0.80-0.82 0.78-0.82 0.80-0.86 0.81-0.85 0.75-0.85 0.87-0.89 0.86-0.91 0.94-0.98

0.60-0.64 0.60-0.63 0.65-0.69 0.68-0.70 0.71-0.74


Table 4.3 continued

Vehicle type

Saab 9000 Turbo 16 Mercedes 380 SEC Rover 3500 Vitesse BMW M 535i Porsche 928 S Jaguar XJ-S BMW 524 td Mercedes 280 SE Mercedes 500 SEL Opel Senator 3.Oi Mercedes 500 SL (Hardtop) Peugeot 604 STI Volvo 760 turbo Intercooler BMW 728i (732i/735i) BMW 745i

Sports cars Porsche 924 Honda CRX Coupe Porsche 944 Turbo Ford Sierra XR 4i Porsche 944 Opel Manta GSi Nissan 300 ZX Mazda RX-7 Chevrolet Corvette Opel Manta GSi CC Audi Coupe GT 5E Mazda 626 Coupe Renault Fuego GTX VW Scirocco GTX Mitsubishi Cordia Turbo Mazda 929 Coupe 2.0 GLX Opel Monza GSE Porsche 911 Carrera Toyota Celica Supra 2.8i Porsche 911 Carrera Cabrio Ford Capri 2.8i Honda Prelude Chevrolet Camaro Z 28 E Mitsubishi Starion Turbo

Drag coefficient cD

0.34-0.36 0.34-0.35 0.36-0.37 0.37-0.38 0.38-0.40 0.40-0.41 0.38-0.40 0.36-0.37 0.36-0.37 0.39-0.40 0.45-0.46 0.41-0.43 0.40-0.42 0.42-0.44 0.43-0.45

0.31-0.33 0.35-0.37 0.33-0.34 0.32-0.34 0.35-0.36 0.36-0.37 0.33-0.36 0.36-0.39 0.36-0.38 0.37-0.38 0.36-0.37 0.34-0.36 0.34-0.37 0.38-0.39 0.37-0.39 0.35-0.37 0.35-0.36 0.38-0.39 0.37-0.39 0.40-0.41 0.40-0.42 0.38-0.40 0.37-0.38 0.38-0.40

Frontal area A (m2)

2.05 2.10 2.06 2.04 1.96 1.92 2.04 2.15 2.16 2.00 1.85 2.05 2.16 2.13 2.14

1.80 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

72 90 98 83 78 82 69 80 80 83 88 82 74 78 87 95 78 83 77 81 84 94 84

cOA (m2)

0.70-0.74 0.71-0.74 0.74-0.76 0.75-0.78 0.74-0.78 0.77-0.79 0.78-0.82 0.77-0.80 0.78-0.80 0.78-0.80 0.83-0.85 0.84-0.88 0.86-0.91 0.89-0.94 0.92-0.96

0.56-0.59 0.60-0.64 0.63-0.65 0.63-0.67 0.64-0.66 0.64-0.66 0.60-0.66 0.61-0.66 0.65-0.68 0.67-0.68 0.66-0.68 0.64-0.68 0.62-0.67 0.66-0.68 0.66-0.69 0.65-0.69 0.68-0.70 0.68-0.69 0.68-0.71 0.71-0.73 0.72-0.76 0.70-0.74 0.72-0.74 0.70-0.74

are possible with special shapes (e.g. laminar profiles). If this body is moved close to the ground and shaped so that separation is prevented to the greatest extent possible by giving up the symmetry of rotation, a drag coefficient of 0.15 results. This drag is three times higher than that of the isolated body of revolution. In comparison to this, the average drag coefficient of mass-produced passenger cars (cD ~ 0.43) is again three times as great.

This results in two problems to be solved by research. The first, which is more in the field of basic research, is to clarify which mechanisms lead to the drastic increase in drag, when going from an isolated body to a body close to the ground. Basic bodies with drag figures of less than 0.15 can be


cD < 0.04 Body of revolution, optimized for low drag

cD = 0.05 Body of revolution

cD =0.15

Xvxbifa g £ g ? # # # # j ^ # 3 # g g ^ ^ ^

Basic body near ground

Co = 0.43 Average passenger car

Figure 4.117 Drag coefficients for bodies of revolution, a body close to the ground and an average car, after ref. 4.85

expected as a practical result of this research. These bodies can then be used as initial shapes for shape optimization according to section 4.4.2.

The second research problem is application-oriented. How does the flow change when a mass-produced vehicle is developed from the basic body, what are the associated drag mechanisms, and how can they be influenced favourably?

4.6.2 Basic bodies

The increase in drag that results when a given body is moved close to the ground (Fig. 1.28) can be explained by the fact that the effective solidity of the body increases as the ground clearance is reduced. If the solidity of an isolated body is dll, it becomes 2dll at zero ground clearance, e = 0. The

Figure 4.118 Increase of effective bluffness dll (inverse fineness ratio lid) with decreasing ground clearance ell, schematic


road

Re= 1.106

ARe= 1.107

SI 1

/ —

Total drag 1 — I

2 4 6 8 10

Figure 4.119 Total drag and friction drag of ellipsoids with different fineness ratio lid

body contacts its mirror image (Fig. 4.118) and merges with it to form (approximately) one single body. In Fig. 4.119, after Hoerner435 and Hucho,4 86 the drag of bodies of revolution is shown in terms of the fineness ratio lid, the reciprocal of the solidity dll. In the range lid < 4, where the drag is primarily pressure drag, the drag increases with decreasing fineness lid. The basic bodies, which have a fineness ratio of lid « 3 far away from the ground and an effective fineness ratio of lid « 1.5 at low ground clearance eld ~ 0, lie precisely in this range. A drag increase of

Q O

c o

o

0.3 p 0.4 ground clearance - r

Figure 4.120 Effect of ground clearance ell on drag of a low drag configuration, after ref. 4.26


approximately 50 per cent is connected with this reduction of the effective fineness ratio. A drag increase of the same magnitude in fact results when a body is moved from a very large to a very small ground clearance, as shown in Fig. 4.120, after Buchheim et al . , 4 2 6 as well as in Fig. 1.28.

For this reason it is not correct to compare a passenger car or its basic body, with IIh ~ 3 close to the ground, with a body of rotation with lid = 3 off the ground. On the contrary, a body with lid = 1 . 5 must be used for comparison. In comparison to this, the drag of the basic body close to the ground, cD = 0.15, is only approximately twice as high.

A considerable portion of the drag difference between the body of revolution in free air and the basic body close to the ground is also attributable to the presence of the wheels, as shown in Fig. 4.74. Therefore the lower limit for the drag coefficient of a basic body without wheels but with the dimensions of today's passenger cars can be considered to lie between 0.07 and 0.09.

A limit of between 0.14 and 0.16 results for the basic body with the same dimensions, but this time with wheels. A closer approach to the value of the basic body without wheels is only achievable through further integration of the wheels into the body.

On the other hand, the value of cD = 0.15 can be realized with more than one single body shape, as has been shown by Buchheim et al.4-26 (Fig. 4.121).

VW-Blunt Body cD = 0.15 - „ V W - B l u n t Body cD = 0,16

Figure 4.121 Alternative shapes for low drag configurations, after ref. 4.26

Lower drag can only be achieved by extending the length of the vehicle's body. Corresponding basic bodies have been developed by Morelli et aj 4.17,4.87 Q n e Qf these is compared with other well-known basic bodies in Fig. 4.122. With a drag coefficient of 0.05, this body has an extremely low drag close to the ground. To what extent basic bodies with high fineness ratios can be used as the starting point for vehicle development depends upon the value placed upon low drag in the future. The fact that such concessions are being considered is shown by several experimental vehicles discussed in section 4.6.3. The basic body shown at the top of Fig. 4.122


Basic body

' > / . v / / > A

■ > / / / / / / > ^ /.

'/////////

Reference

4.88

4.25

,4.17

4.16

cD

0.15

0.16

0.07

0.18

0.05

l/h

4.0

3.0

3.1

3.9

Configuration

With wheels modelled

With wheels modelled

Without wheels

With wheels

Without wheels

Figure 4.122 Comparison of drag of different basic bodies

cD

0.50 Y

0.48 V-

0.46h

0.44^-

0.42^

0.40l·-

0.38^

0.36 Y-

0.34 L-

• ■

# · · *

■ NOTCHBACK

• HATCHBACK

FASTBACK

3000 3500 4500 5000 4000

I [mm] Figure 4.123 Drag coefficient versus car length, after ref. 4.67

could be called the father of the streamlined cars of the 1930s, and that in the second line the origin of today's low-drag cars.

The drag coefficient for today's passenger cars may be plotted against vehicle length, as shown in Fig. 4.123 (from Emmelmann4 67) yet no correlation can be discerned between greater lengths and lower aerodynamic drag. However, if the evaluation is limited to vehicles that were developed for the lowest possible drag coefficient, this expected trend is in fact confirmed; see Fig. 4.124, also from ref. 4.67.

The drag and lift of a body depend strongly upon the angle of attack. This has been investigated by Stollery and Burns 82 for a bluff body close to the ground. The most important results are summarized in Fig. 4.125. As can be seen, at an angle of attack oc = 0 the drag of a symmetric body


0.38 h

0.36 h

0.34

0.32

CORSA I

CORSASR i ^

SUBCOMPACT ', COMPACT

" <

S. MEDIUM

0.30 h

0 %

iLARGE

_L 3500 4000 4500 5000

I [mm] Figure 4.124 Drag coefficient versus car length for aerodynamically developed cars, model year 1983, after ref. 4.67

£ - 0 . 0 4 1 >*> a 3

- 8 - 4

Section A-A Relative thickness t/c = 0.21 Aspect ratio s/c = 0.365

Figure 4.125 Drag and lift of a bluff body, effect of ground clearance hlc and angle of attack a, after ref. 4.82

increases as it approaches the ground. This corresponds well with the measurements made by Hansen and Schlör,481 see Fig. 1.28, as well as those of Buchheim et al.,426 see Fig. 4.120. However, at an angle of attack of oc > 0 this trend is not clear.

As the ground is approached, the lift decreases considerably (thickness influence) but the gradient dcA/da increases (circulation influence). At small or negative angles of attack, this trend is reversed. Unfortunately the measurements were not continued in this range. These trend reversals in the range of oc = 0 show clearly how difficult it is to draw general conclusions from these measurements for designing the shape of automobiles.

Stollery and Burns4 82 created asymmetrical bodies by modifications to


wmim^m^Wv Symmetrical nose

'sWWV'AVVVsVWVVVVWVv

Dropped nose

Raised nose

Figure 4.126 Effect of nose shape on lift and pitching moment of a bluff body close to the ground, after ref. 4.82

the nose. The influence of this upon lift is shown in Fig. 4.126. If the nose is tapered downward, the camber of the body is increased, giving an increase in lift, but the effective angle of attack is also reduced— a lift-reducing measure.

Both effects approximately compensate for one another, with the exception of the range near a = 0. There the lifted nose leads to the smallest lift, but also to the greatest positive (i.e. nose-up) pitching moment. Applied to vehicles, this implies the greatest load reduction on the front axle. For this reason sports cars are designed with a nose which slopes downward; see Fig. 7.29. The increase in total lift resulting from this front end shape is compensated by other measures such as winglets at the front and spoilers at the rear; see section 7.4.1.

Morelli et a l . 4 1 4"4 1 7 established that, at a fixed ground clearance typical of automobiles and at a fixed angle of attack, the drag decreases with increasing camber, while the opposite applies at high ground clearances. However, as Fig. 4.127 shows, the influence is small.

A systematic study on the influence of the thickness, the camber and the angle of attack upon the drag and lift of streamlined bodies was performed by Carr.4 54 The main results are summarized in Fig. 4.128. In comparison to passenger cars, the bodies tested are very slender. The relative

0.4

0.3 I C J ^

u L c »1 L^J T

Relative camber f

0.1 0.2 0.3

d=^ . b

Figure 4.127 Effect of camber and ground clearance,on the drag of a bluff body, after refs4.14 to 4.17


Rear axle lift cLR

Lift cL

Figure 4.128 Effect of camber, thickness and angle of attack on total drag, lift and lift distribution; axle positions 11 per cent and 65 per cent of body length, after ref. 4.54

thickness, that is the ratio of the thickness d to the length /, was varied within the limits 0.09 to 0.26. For passenger vehicles this value (height to length) is approximately 0.30.

Particular care must be taken when the information gained from basic bodies is applied to real vehicles. Direct transfer is only possible when the flow pattern is the same—or at least similar—in both cases. This is not the case for the bodies studied by Carr.4 54 However, the results in Fig. 4.128 can serve as a guideline in the development of sports cars and record vehicles (see Chapter 7).

It is very unfortunate that the numerous investigations on basic bodies are inconsistent. The effects of the various parameters (solidity, camber, ground clearance, angle of attack) on the aerodynamic properties (drag,


lift and pitching moment) have been studied by various authors on different bodies, which sometimes are too far away from cars. A more systematic investigation is needed to generate the basic knowledge on the aerodynamics of bluff bodies close to the ground. The value of the measurements performed on basic bodies is that they can be applied to the development of low-drag bodies, which can then be used as the starting point for shape optimization.

4.6.3 Concept cars

A concept car is a vehicle whose specifications correspond largely to a production model in the same class. However, to achieve characteristics such as exceptionally low fuel consumption, concessions are made in the shape, the materials and the production cost, which would hardly be accepted by the market. On such cars, the achievement of certain characteristics is the focal point and not their application in mass-production vehicles.

Recently it has been proved with a series of concept cars that the drag coefficient gap (Fig. 4.117) between present mass-produced passenger cars and basic bodies similar to vehicles can be closed. Depending upon the problem posed, drag figures can be achieved that are considerably below the present average and can even reach the value of 0.15 for the basic bodies shown in Fig. 4.121.

Figure 4.129 Drag coefficients of research cars exhibited at the 1981 Frankfurt International Auto Show (IAA) (* sponsored by German Ministry of Research and Technology, BMFT), after ref. 4.89

In Fig. 4.129, after Hucho,4 8 9 the research cars exhibited at the International Automobile Exhibition (IAA) in Frankfurt in 1981 are shown. Very low drag coefficients were realized with very different body shapes without having to make any significant concessions in their utility

207

(a)

(b)

Figure 4.130 (continued overleaf)

208

(d)

(e)

Figure 4.130 1983 concept cars: (a) Ford Probe IV, cD = 0.15 (ref. 4.92); (b) GM Aero 2000, cD = 0.23 (ref. 4.93); (c) GM Aero 2002, cD = 0.14 (ref. 4.93); (d) Opel Junior, cD = 0.31 (ref. 4.94); (e) VW Student, cD = 0.30 (ref. 4.95)


and styling. In the meantime, the shapes of two of these research cars were applied to a large extent to production vehicles. The Audi 100 III model year 1982 has basically the same shape as the Audi research car—the aerodynamic drag remaining unchanged at cD = 0.30. The shape of the Ford Sierra is basically similar to that of the Ford Probe III, whose particularly low aerodynamic drag of 0.22, see Bahnsen,4 90 could not be maintained on the Ford Sierra with cD = 0.34 because it was necessary to eliminate a number of the drag-reducing details on the production vehicle, such as the completely smooth underside.

Figure 4.130 provides a summary of the concept cars for the model year 1983. With the exception of the extremely compact cars, Opel Junior and VW Student, the value for the basic body of cD = 0.15 was achieved with these vehicles, with however greater vehicle length and with technically unusual measures, such as covered front wheels. Although the concept cars in 1983 are much further away from production vehicles than those exhibited in 1981, they do show that the drag of the basic body is achievable. To what extent this can be approached in the development of a production vehicle is therefore more a question of the balance of the requirements of the specifications than of technical feasibility.

4.6.4 Record breaking cars

The design of record-breaking cars and experimental vehicles goes considerably further beyond the state of mass-production technology than that of concept cars. Depending upon the experimental purpose, the ability to drive in public traffic is more or less limited. The vehicles with which absolute speed records have been established differ greatly from the technology of road vehicles. Hardly any information can be obtained for production cars from the aerodynamic characteristics of cars in the transonic speed range (see section 7.5.2).

Figure 4.131 Mercedes Benz record car C-lll III (Photograph by courtesy of Daimler Benz AG)


On the other hand, the limits of automotive technology can be recognized with those record-breaking cars which are designed for extremely low fuel consumption, extremely large cruising range or high average speeds over greater distances.

Figure 4.131 shows the record-breaking car O i l III (1978) from Mercedes Benz, after Liebold.441 The longitudinal and cross-section silhouettes (Fig. 4.132, from ref. 4.41) clearly show the difference between

Figure 4.132 Comparison of longitudinal and tranverse contour of Mercedes Benz record car C- l l l III with contemporary European full-size cars, after ref. 4.41

this car and production passenger vehicles in the upper European vehicle class. The passenger compartment corresponds to that of a two-seater sports car or racing car. In this aspect this car is still very similar to production cars. A very low aerodynamic drag of 0.18 was achieved. Because of its comparatively high fineness ratio of IIh = 4.94 an even lower drag should have been possible; see Table 4.4.

Table 4.4 Data for two record-breaking cars

Vehicle

DBC111III ARVW

cD

0.18 0.15

A (m2)

1.5 0.75

(m2)

0.27 0.11

lib.

4.94 5.53

Year

1978 1982

The record-breaking car ARVW (1982) from Volkswagen AG (Fig. 4.133, after Nitz et al.496) was designed with even less similarity to production vehicles. With a drag coefficient of 0.15 the limit for such a slender car has most probably not yet been reached; see Table 4.4.

The fineness ratio of the ARVW is llh = 5.53. According to Fig. 4.118 this corresponds to an effective fineness ratio in free air of 2.27. This approaches the drag minimum recognizable in Fig. 4.119. With a greater fineness ratio, the drag would increase again as a result of the increasing friction drag.

The development of both these record-breaking vehicles is described in

Notation 211

Figure 4.133 Volkswagen Aerodynamic Research Vehicle, 1982, after ref. 4.96

detail in refs 4.41 and 4.96. The individual measures for achieving not only a low drag but also better data for the longitudinal and lateral stability as well as the cooling provide valuable information for the development of body shapes for production cars.

4.7 Notation As far as possible notations were maintained from references. Some symbols are used for more than one item; they are explained either in the text or within the figures.

A A As

B D D DA

Dc

DF

DM

DP

Ds

Dv L M N R R Re S Sv T V Veff ^ Α , Μ

V , VH

frontal area of car; Fig. 1.3 wing area; Eqn 4.3 frontal area of spoiler width of tyre; Fig. 4.74 wheel diameter; Fig. 4.73 drag; Fig. 4.1 drag of antenna; Eqn 4.11 cooling-air drag; Eqn 4.13 friction drag; Fig. 4.13 drag of mirror; Eqn 4.10 pressure drag; Fig. 4.13 drag of spoiler; Eqn 4.4 drag of vehicle's underside; Eqn 4.6 lift; Fig. 4.111 pitching moment; Fig. 4.111 yawing moment; Fig. 4.111 rolling moment; Fig. 4.111 radius of wheel; Fig. 4.74 Reynolds number vehicle surface; Table 4.1 underside surface tangential force; Fig. 4.111 vehicle speed; Fig. 4.2 local speed local speed resulting air speed; Fig. 4.2 volume of wheel-well; Fig. 4.78


Vw Y a a öh b b CB

cD COA> c DA C D C COF c D i C D M J C DM c D o CDS> C DS C D U ? c DU

cL C L F

C L R C M C N

C P CR

C R c s C T

cY d e h Al ,2 I ha /o / D

/u P Poo r /

5 ί V

vA w W B

x, y, z ^s

volume of wheel; Fig. 4.78 side force; Fig. 4.111 wheel base; Fig. 4.111 roof camber; Fig. 4.37 plan view camber; Fig. 4.68 width span of wing; Eqn 4.3 base drag coefficient; Fig. 4.14 drag coefficient; Fig. 4.1 antenna drag coefficient; Eqn 4.11 cooling-air drag coefficient; Eqn 4.13 friction drag coefficient; Table 4.1 induced drag coefficient; Eqn 4.1 mirror drag coefficient; Eqn 4.10, 4.12 profile drag coefficient; Eqn 4.1 spoiler drag coefficient; Eqn 4.4, 4.5 underside drag coefficient; Eqn 4.6, 4.8 front drag coefficient; Fig. 4.14 lift coefficient lift coefficient, front axle lift coefficient, rear axle pitching moment coefficient yawing moment coefficient pressure coefficient; Fig. 4.13 rolling moment coefficient friction drag coefficient; Fig. 4.14 pressure drag coefficient; Fig. 4.14 tangential force coefficient side force coefficient diameter vehicle ground distance; Fig. 4.111 vehicle height recess depth; Fig. 4.79 vehicle length; Fig. 4.111 lengths; Fig. 4.88 slope length; Fig. 4.59 diffuser length; Fig. 4.46 diffuser length; Fig. 4.45 local pressure; Fig. 4.13 pressure in undisturbed flow; Fig. 4.13 radius of sphere; Fig. 4.40 local dimension; Fig. 4.103 roughness height; Fig. 4.80 side window inset; Fig. 4.70 local speed radiator face velocity; Fig. 4.94 width wheel base rectangular coordinates spoiler height

Γ Ax A Xo a αΌ

ß γ δ V

Ρ Pi φ ω

circulation car/trailer gap; Fig. 4.98 aspect ratio; Eqn 4.3 wall shear stress; Fig. 4.13 angle of attack; Fig. 4.111 diffuser angle; Fig. 4.46 yawing angle; Fig. 4.4 slope angle slope angle kinematic viscosity of air density of air non-dimensional local dimension; Fig. 4.103 local slope angle angular speed; Fig. 4.74

Chapter 5

Driving stability in side winds Hans-Joachim Emmelmann

5.1 Introduction When driving on the open road, the air 'flows over' the vehicle. This causes forces and moments along or about all axes, which affect the driving characteristics. Of these, aerodynamic drag has always attracted most interest.

The components in the other five degrees of freedom greatly influence the lateral dynamic characteristics of the vehicle. Lift and pitching moment occur along with the drag during motion of a vehicle through still air, whereas in side-wind conditions the additional components of side force and yawing and rolling moments develop (see Figs 2.14 and 4.111).

The resultant air forces and moments must be balanced by the reaction forces between the vehicle and the road, gripping through the tyres. The resulting tyre slip angles lead to a deviation from the required direction of travel which must be compensated for by the driver via the steering.

The above phenomenon, which is often referred to as side-wind sensitivity, must be considered from two different aspects. The driver is inconvenienced when continual compensation at the steering wheel is necessary to correct side-wind effects. This leads to stress, premature tiredness and increased risk.

When strong side winds occur from random directions a safety problem can rapidly arise. If the driver lacks the necessary skill or experience to correct for side wind, undesirable deviations from the required vehicle path result and incorrect reaction can lead to loss of control.

If a vehicle is to have good driving characteristics, both aspects of side-wind sensitivity must be considered during the design stage. What follows shows how this is achieved with the help of a general computer model, which establishes the main parameters and presents them as a simple equation. Emphasis is placed on illustrating the methods used rather than the establishment of quantitative results.

5.2 The origin of the forces and moments on a vehicle 5.2.1 Natural wind

The strength and direction of the wind is continuously measured and recorded at a number of geographical locations and at various heights

214

The origin of the forces and moments on a vehicle 215

above the ground, such as 10 to 15 metres. When time-averaged, this airflow profile reveals a normally turbulent boundary layer.

Close to the ground, the fluctuation of wind speed u' is approximately equal to the average value of the speed, i.e. the turbulence level is

,'2

Tu = 1

Depending on the condition ('roughness') of the ground, the wind speed at, for instance, half vehicle height, differs from that at a weather station, being either faster or slower. An impression of the form of the boundary layer is shown in Fig. 5.1, from Davenport.5Λ

In comparison to vehicle height, the boundary layer can be seen to be extremely thick. At vehicle level the wind speed gradient is especially

Figure 5.1 Natural wind boundary layers over various ground profiles, after ref. 5.1

a) Frequency of strong winds

800 Hours per year

600

400

200

\ \ \

\

^ - N orthc

Cem

»rn G

ral G

erma

erma

i y

ny

\ 1 1 1 1 \ Southern Germany

k v ' ' ' Λ Γ \

^J\ 12 16 m 20

s Wind speed ^ -

30 mph I

45

b) Wind boundary layer over smooth ground

1.8 |

1.6

1.4

1.2

I 0 · 8

h° 0.6

0.4

0.2

v ■ =(

0 ho

~*r*

n

/7 = e

A /

\

/

7 r

\

= 7

0.2 0.6

V0

1.0

Figure 5.2 Frequency of strong winds in various regions of Germany, and wind boundary layers over smooth ground, after ref. 5.2

1.4

216 Driving stability in side winds

steep. Over smooth ground Bitzl5 2 has shown (Fig. 5.2) that the boundary layer follows a potential function law. Fig. 5.2 also gives data on the frequency of occurrence of strong winds in Germany. Information about side winds—both artificial and natural—has been presented by Karrenberg.53 Some relevant wind speed measurements have been presented by Smith.5 4 A typical compass card, showing details of wind speed and directions, is shown in Fig. 8.12.

5.2.2 Wind forces due to steady side winds

A special case of side wind consists of a steady airflow which has a constant velocity profile regardless of height. Although hardly possible in nature, this case is in fact provided in the wind tunnel with the exclusion of a thin ground-floor boundary layer (Fig. 5.3). Under natural side-wind condi-tions, the relationship shown in the right-hand figure is present, whereby

c) Natural side wind

a) Wind funnel (without floor boundary layer)

Figure 5.3 Comparison of various side-wind profiles, after Hucho

the whole side-wind profile has boundary layer characteristics. When combined with vehicle speed the resultant air flow profile is strongly twisted. For comparison, the centre part of Fig. 5.3 shows the wind profile of a side-wind simulator, where it can be seen to be seriously distorted. The possibility of simulating side wind using such simulation apparatus is reported in section 12.4.2.

Aerodynamic side force results from the difference in pressure between the windward side and the leeward side of a vehicle. The right-hand side of Fig. 5.4 (after Barth5 5 and Squire56) shows the pressure distribution around a horizontal section of a vehicle. On the leeward side considerable negative pressure develops due to high airflow speeds over the vehicle's leading edge. On the windward side, except for a slight negative pressure at the leading edge, a slight positive pressure exists along the vehicle's side to the midpoint. On the rear half of the vehicle, steadily increasing negative pressure is observed. Comparison of the vehicle pressure distribution and that on a wing section shows good correlation, at least in principle. The angle of attack of the wing section was chosen so that the

b)Side wind simulator


Figure 5.4 Comparison of the pressure distribution around a wing section and a vehicle horizontal section, after refs 5.5 and 5.6

pressure level obtained was approximately similar to that on the vehicle. The pressures of the windward and leeward sides lead to a side force on the vehicle which is directed to the leeward side, and to a yawing moment which generally tends to turn the vehicle's nose to the leeward side.

5.2.3 Aerodynamic stability

The concentration of the negative pressures on the leeward side, at the front of the vehicle, is largely responsible for the aerodynamic yawing moment. This is the characteristic that causes instability. In other words, when side winds on a vehicle cause an angular deviation ß (yaw angle), the effect of this aerodynamic yawing moment tends to increase the angle ß further.

A clear illustration of the flow characteristics of standard production vehicles exposed to side winds is given by Sorgatz and Buchheim5 7 and shown in Fig. 5.5. For small yaw angles, very high negative (suction) pressures occur at the leeward side of the vehicle's front end and the leeward A-pillar, whereas further downstream the leeward side exhibits low negative pressures only. For larger angles of yaw, the air flow separates at the leeward front fender corner and at the A-pillar, which results in smaller negative pressure peaks in these areas. The kink in the curve of the frontal side-force coefficient indicates the beginning of the transition to separated flow.

At the windward side of the front end, low positive pressure exists which


QD Attached leeward front airflow. Q) Airflow is attached in C pillar area.

(2) Separated leeward front airflow. @ Completely separated leeward rear end airflow.

Figure 5.5 Airflow conditions and forces acting on the car exposed to side wind, after ref. 5.7

turns to low negative pressure further downstream. The magnitude and extent of the positive pressure region grow as yaw angle increases. For such yaw angles, vehicles exhibiting well-tapered and rounded rear ends and C-pillars exhibit a significant pressure increase at the leeward side at their rear ends and a corresponding pressure decrease at the windward side.

For further increased yaw angles this trend is reversed and it slowly diminishes until it disappears, due to a substantial change in the characteristics of separation at the rear end and vortex patterns at the C-pillars.

Fastback and notchback cars therefore show a different slope of the rear side-force coefficient from squareback vehicles. For small yaw angles, fastback vehicles show a slight slope of the rear side-force coefficient which changes to a steeper slope for larger yaw angles. At this stage the slope of the yawing moment coefficient becomes negative.

The question now arises of how the slope of the side-force coefficient or the yawing moment coefficient, respectively, can be influenced by contour changes.

From aerofoil aerodynamics it is known that an aerofoil section that is stalled, exhibiting separation on the upper side, has very low lift and a small pitching moment. When this principle is applied to a vehicle, it means that sharp edges on the front corners of the vehicle, although increasing vehicle drag, can reduce the side force and yawing moment on the vehicle.

The conflicting goals between designing for optimized drag and reduction of side-wind force and yawing moment are overcome by optimizing the vehicle front for separation-free flow for yaw angles between —10° ^ ß ^ + 10°, which is a region in which side winds cause relatively little concern. For larger yaw angles, where side winds cause more concern, separation of the airflow is permitted in order to reduce the yawing moment. The subsequent increase in drag can then be tolerated, because these larger yaw angles occur only briefly. The 'matching' for low


drag at small yaw angles and low yawing moments at higher yaw angles is to be seen in Fig. 5.6, after Hucho.5 27 This condition is simplest to realize during the optimization of box vans—as illustrated by Hucho.5 8

Figure 5.6 Reduction of yawing moment by controlled separation, after ref. 5.27


In vehicle dynamics, moments are usually related to a reference point at the centre of the wheelbase and centre of the track, at road level. With regard to side-wind sensitivity however, the yawing moment NSF is referenced to the vehicle centre of gravity, around which the yawing motion occurs, see Fig. 5.7. Aerodynamic yawing moment

N = xD-S

Yawing moment around the centre of gravity

A/OP = X n s - S

Centre of gravity

Aerodynamic reference point

Figure 5.7 Definition of centre of pressure

The two reference points for yawing motion are only identical if the vehicle's weight is equally distributed on the front and rear axles. Increased rear axle loading increases the mechanically induced yawing moment and increased front axle loading reduces it, compared with the aerodynamic yawing moment. The latter can even result in a change of sign of the stability expression.

The possibilities for influencing aerodynamic forces and moments by modifying the vehicle shape are shown in Fig. 5.8 and further detailed in

0.14

A0.10

cN 0.06

0.02

!

I l

& / ,#f l/fi

s >1

^ '

1 1 1

* I N ^

1.4

r 0.6

0.2 \£

J & *

— i —

~1y M Y< f \

1

71

kä*

30° 10° 20° 30° 10° 20°

Figure 5.8 Yawing moment and side-force coefficients for a vehicle with different rear end shapes

Fig. 5.9. From Fig. 5.8 it can be seen that yawing moment and side-force coefficients are extremely dependent upon the vehicle rear end configuration. The smallest yawing moment and the largest side forces are found with the squareback configuration, whereas the fastback exhibits the smallest side force and the largest yawing moments. The notchback configuration exhibits intermediate values for both side forces and yawing moments. The evaluation of the effect of the above forces and moments on the sideways deviation of a vehicle from its desired direction is discussed in section 5.5.3.

The lift forces shown in Fig. 5.9 are of similar magnitude to drag. However, they only affect directional stability at speeds above roughly 100 km/h (62mile/h) because at lower speeds they are small relative to vehicle weight and their 'unloading' effect on the tyres is small.


u _v

^

**

\l& 1 Ό

f?

^

10° 20° 30°

Type 31 fastback "M K

* — " ■ —*— t

Γ

A

J-n \^^ Type 31 notchback n i ^ Ι Ρ 10° 20° 30°

""*"" Type 36 $ ** squareback

Figure 5.9 Lift and rolling and pitching moment coefficients for a vehicle with different rear end shapes

In the case of fast coupes or sports cars, lift must be reduced by modification of vehicle shape or addition of supplementary spoilers at the front and/or the rear of the vehicle. To increase maximum cornering speeds of racing cars, spoilers or wings provide negative lift, even at the cost of increased drag and therefore reduced top speed (see section 7.4.1).

5.2.4 Wind forces resulting from non-steady side winds

As mentioned in section 5.2.1, speed and direction of natural side wind vary from place to place. In addition to the side-wind forces and moments, which generally are measured under steady state conditions in a wind tunnel, further components must be considered, as indicated schematically in Fig. 5.10. The components can be split into three parts: constant,

CN = CT = .

linearized:

oß op dwz

Variable Constant Quasi-constant

cN

Figure 5.10 Linearized view of stationary airflow forces and moments for variable side-wind profiles


quasi-constant (turning motion) and variable. The last are to be expected in steep wind gradients where the normalized frequency is

Ω ω/ V

> 1

According to Reichard,5 9 side-wind profiles vary relative to normal free airflow limits according to a cosine relationship. Hucho and Emmelmann5 10 have, by application of the Slender Body Theory (see also Hummel5,11 and Woolard512) calculated the development of yawing moments and side forces for such side-wind profiles. The results of these calculations are shown in Fig. 5.11.

I 1.0

Vs. 0.5 Rn-

/ 1

SI s% 5

0.1 0.2 0.3 0.4 0.5 0.6 sec 0.8

0.1 0.2 0.3 0.4 Ö.5 06 sec 0.8

1.5

t„ CM» 0.5

0.1 0.2 0.3 0.4 0.5 0.6 sec 0.8

Figure 5.11 Computed variable side-force and yawing moment coefficients for different side-wind profiles, after ref. 5.10

\k

f^ /

\A 3 ^ 2 s

■ —

^ ->

In the upper part of the figure, the applied wind profile can be seen in plan view. Vs is the local side-wind speed, Vsoo the constant speed of side wind following the transition. The parameter is based upon vehicle length /, relative to the transition length SM, of the wind profile from wind speed Vs = 0 up to the attainment of full wind speed Vsoo. From this it can be seen that, as a result of steep wind profiles, the variable portion leads clearly to an 'overshoot' situation, in terms of side force and yawing moments, during which these forces and moments approach those resulting from a flat wind profile. Measurements by Beauvais5 13 and Muto5 14 confirm this overshoot phenomenon, which results from spatially varying side winds. Measurements conducted by Emmelmann5 25 using a model side-wind simulator (Fig. 5.12) showed that, as expected, the theory outlined in ref.

Real side-wind problems 223

Figure 5.12 Model side-wind track for measurement of side forces and yawing moments, after ref. 5.25

5.10 only correlates with experiment in the case of vehicle bodies having what could be described as slender front ends.

5.3 Real side-wind problems 5.3.1 Traffic routes, wind protection

Traffic routes are normally established without regard for side-wind danger. Underpasses, embankments and bridges are particularly exposed. In contrast to the statement made in section 5.2.1, where it was said that lower wind speeds are normally experienced at vehicle level than at 10 to 15 metres above ground level, Fig. 5.13 shows that buildings and

Figure 5.13 Increased speed on embankments under side-wind conditions, after ref. 5.2

man-made features, i.e. embankments, can increase wind speeds above the speed of ambient wind. Gaps in bushes and tree spacing can cause a jet effect which raises local wind speeds above the normal wind speed in open spaces. These findings were taken from the work by Bitzl5 2 and are illustrated in Figs 5.13 and 5.14.


Figure 5.14 Side-wind jet effect from a gap in roadside bushes, after ref. 5.2

Impermeable hedges and wooden protective fences are equally effective in reducing wind speed, according to the Heppenheimer model (Fig. 5.15, from Blenk and Trienes5 15). However, wind speed can be accelerated by roadside trees, such as poplars, due to the displacement effect of the tree tops.

Ψ ΨΨ* Impermeable hedge . = 0)

-4 T 0 ll U 10 15 x/H

UMtmZmdmwkmM wmmmw%MW?Mm%m!^zw

Medium permeability hedge (λ = 0.48)

wWM Mb WMtmMwmwM^ a, mm».

Row of poplar trees

Figure 5.15 Wind profiles behind various types of hedges (model tests), after ref. 5.15

Good wind protection is offered on roads which pass through country areas (Fig. 5.16). Results to confirm this were obtained from tests conducted by the author on a 1:16 scale countryside model in the full-scale wind tunnel of Volkswagen AG.

5.3.2 Natural and artificial side-wind gusts

It was stated above that the turbulence level of natural wind is of the order of unity: Tu ~ 1. Thus when the side wind has the velocity V, the speed can suddenly increase to 2V or drop to zero. The effect of natural wind squalling seems to be the same regardless of whether the cause is building development or vegetation (bushes, etc.). Whereas the constant side-wind conditions indicated in Fig. 5.13 can be compensated for by a constant

Real side-wind problems 225

- 3 5 10 m/s 15

Figure 5.16 Wind speed distribution through a section of countryside (scale 1:16) • without trees o with trees

steering angle, the side-wind case shown in Fig. 5.14 cannot be anticipated and calls for sudden correction. It is therefore more dangerous.

The same applies to driving between bridge abutments under side-wind conditions. Initially the vehicle moves in a constant side-wind area (Fig. 5.17) with an appropriate constant steering angle towards the wind. It then comes into the sheltered area adjacent to the bridge abutment, and the driver must then steer to the left in order to avoid driving off the right-hand side of the road. With this new steering angle the vehicle is then again exposed to side wind from the right, which leads to a violent reaction by the driver.

Every driver is familiar with the problem of overtaking a truck under side-wind conditions. Due to the relative velocities of the two vehicles, the overtaking speed is small compared to the driving speed and a small wind frequency results. Non-steady wind effects are therefore not normally expected. It is therefore possible to simulate and measure this overtaking situation using constant side wind in the wind tunnel.

Figure 5.18, after Emmelmann,5 16 shows the effect on the vehicle yawing moment when it overtakes a container truck. Large yawing moments are found, endangering the driver/vehicle system, when the vehicle emerges from the sheltered side of the container truck, where it enters the displaced airflow field of the truck. This field exhibits increased airflow speed, relative to the normal side-wind speed, coupled with larger deflection angles. The amplitude AcN is dependent on the lateral distance


Figure 5.17 Schematic showing side-wind speed distribution in the vicinity of bridge abutments

Figure 5.18 Yawing moment change during the overtaking of a container truck by a car, after ref. 5.16

between the two vehicles during the overtaking manoeuvre. In principle the effect is the same for every shape of vehicle. However, the magnitude of yawing moment change can be reduced by rounding the front corners of the truck.

5.4 Vehicle dynamics under side wind

No general definition exists for the side-wind sensitivity of vehicles. In the majority of the many studies into this problem the effect of side winds on

Vehicle dynamics under side wind 227

vehicles has been established either from test results or with the help of computer models (Fiala,5 17'5 18 Gnadler,519'520 Mitschke,5 21'5 22

Sorgatz523). In order to represent the side-wind sensitivity phenomenon completely,

the driver must also be taken into consideration. The relationship between the driver and the vehicle, as shown in Fig. 5.19, must be fully understood.

Vehicle

Driver

Positional measures (steering, drive)

Disturbance measures (wind, surface irregularities, other vehicles)

Driving measures (course, speed)

Figure 5.19 Driver/vehicle control system

The necessary investigation is however complicated by the fact that the driver is an adaptive controller; that is to say, he or she adapts to the characteristics of the vehicle being driven. There are so many unknowns with regard to driver adaptability that the driver/vehicle system cannot yet be fully explained theoretically.

Various assumptions concerning the behaviour of the driver have been made for the purpose of the various test methods and computer models (see Niemann ); i.e. driver behaviour is defined by a number of different statements—each case then being investigated to establish the manner in which the vehicle reacts under the influence of side-wind disturbance.

Vehicle

* Disturbance i

Variable steering

Fixed control

Free control Ideal driver

Actual driver

Control

1

2

3 4

5

Figure 5.20 Possible representations of the driver/vehicle system

Figure 5.20 shows the various possibilities for consideration, whereby the vehicle can either be under 'fixed control' by the steering wheel being held firm, or under 'free control' by allowing the steering wheel to turn freely. Measurements have been conducted by Fiala5 17 to evaluate cases 2, 3 and 5.

The corresponding two diagrams (see Fig. 5.21) indicate the change in angular direction γ and lateral deviation yG of the centre of gravity of the vehicle as a result of the use of a hot water rocket mounted on the vehicle,


10°

8°

T6°

7 U°

2°

-V

/ /

/ /

/ /

j£'~~-L^ "χ

/ /

100 m 120

Figure 5.21 Slip angle and lateral deviation for various driver reactions. driver steers against deviation steering wheel held firm (fixed control) steering wheel allowed to move freely driver steers against deviation, and brakes

which simulates a side wind. These variables are plotted against time t. From tests it was discovered that the real driver, case 5, began to make steering corrections after a reaction time of approximately 0.2 seconds. Due to steering play, elasticity and the variable nature of the side forces it was however 0.8 seconds before the vehicle 'noticed' any effect from the driver's reaction.

Until this time, the yawing rate and resultant lateral deviation are similar for all cases investigated. For the specific case however, where a vehicle is under fixed control and its reaction to side-wind squalls is analysed, reasonable results are obtained by evaluating lateral deviation yG after a time lapse of 0.8 seconds. In the following section, calculations for the fixed control case are analysed with the aim of evaluating the effect of wind forces on lateral deviation. Representative test methods are described in section 12.4.2.

5.5 The effect of aerodynamic forces on lateral deviation 5.5.1 Reduction of the number of parameters

The lateral deviation of a vehicle from its intended path, under fixed control conditions, is dependent upon a number of factors additional to the actual wind profile that is causing the disturbance. These factors include

The effect of aerodynamic forces on lateral deviation 229

the weight G of the vehicle, the moment of inertia Izz of the vehicle about the vertical axis through the centre of gravity of the vehicle, the load distribution between front and rear axles and the design of the chassis. In this last factor the influence of the tyres, steering elasticity and type of suspension are reflected.

The extent of the disturbance is influenced by the aerodynamic side force and the associated yawing moment, and also by lift, roll and pitching moments. Because parameter tests in a side-wind simulator are very time-consuming it is worthwhile to use an accurate computer model. The data that follows have been calculated using the previously mentioned computer model by Sorgatz.5 23

This computer program allows for a full description of the vehicle to be entered in 23 degrees of freedom using a large amount of input data. In order to evaluate standard vehicles which are perhaps only modified in minor chassis characteristics, it is possible to use standard data so that observation can be concentrated only on the following important side-wind deviation parameters:

• Vehicle weight G • Weight distribution Gf/Gr (centre of gravity position) • Moment of interia Izz about a vertical axis through the centre of gravity • Yawing moment N • Side force S

As Fig. 5.22 shows, good correlation exists between vehicle weight G and the moment of inertia Izz about a vertical axis through the centre of gravity,

250

kgms2

200

1150

/zz

100

u

A /

• / · Approximation in observed range:

/ · /zz = 0.28G-145

800 1000 1200 kg 1400

^Kerb ^

Figure 5.22 Comparison of vehicle weight and moment of inertia around the vertical axis through the centre of gravity

for vehicle weight between 700 and 1500 kg. In this region the relationship is approximately a linear function.

lzz = 0.28G - 145 kgms2 (5.1)


A yawing moment exists around the zz axis, which passes vertically through the vehicle's centre of gravity. It results from the aerodynamic forces that act at the aerodynamic reference point adjacent to the centre of gravity of the vehicle (see Fig. 5.7):

N< SP xS (5.2)

When one divides this yawing moment by the side force, an aerodynamic lever arm length xOS is established (the distance from the so-called centre of pressure to the centre of gravity).

M •^DS —

SP N — xs — χΌ — x$ (5.3)

This expression 'centre of pressure' assumes that the yawing moment was the result of side force only.

In reality the yawing moment is generated by the side force and the drag (tangential force), because the latter is acting in the same plane as the side force and, of course, for yawed flow the tangential force will act with a lever arm from the aerodynamic reference point. Therefore the expression 'centre of pressure', taken from aerofoil aerodynamics where the influence of drag and its lever effect compared with the influence of the lift is negligible, is misleading in the case of automobiles.

The following evaluation of the effect of aerodynamic coefficients and the weight parameters on lateral deviation requires the choice of a wind profile along the virtual test track. The chosen profile, shown in Fig. 5.23,

Figure 5.23 Artificial wind profile

is trapezoidal, closely resembling the profile of the Volkswagen AG outdoor side-wind facility. With a driving speed of V = 26.7 m/s (60mile/h, according to RSV Specifications, RSV = Research Safety Vehicle) a yaw angle of β = 30° results. After time t = 0.8 s the vehicle is still exposed to constant side wind along its complete length.

5.5.2 Equation for evaluation of the influence of side force, weight and aerodynamic lever arm length

The previously mentioned computer model by Sorgatz was used to analyse two completely different vehicles by varying the side force, yawing moment and centre of gravity positions, with, as previously described, the remainder of the parameters all standardized. One vehicle was front wheel drive weighing 996 kg, the other was equipped with a rear mounted engine and rear wheel drive, and weighed 1506kg.

Following the calculations with these vehicles, a regression analysis was conducted for the computed lateral deviations, with a view to establishing

The effect of aerodynamic forces on lateral deviation 231

the influence of the parameters of weight, aerodynamic lever arm length xOS and side force, the latter substituted by the product csA.

The side force coefficient cs at the yaw angle ß = 30° was chosen to represent lateral deviation caused by the side-wind profile; this coefficient was then called cS3o· The following equation resulted:

yG = 1 (fci + k2xOS) + k3xOS + k4 cS3oA +

+ -77 (£5 + M D S ) + M D S + h (5.4)

where G is in kg, JCDS is in m and A is in m2, and the following constants for the particular side-wind case after time t = 0.8 s are valid:

* i = k2 --h -k4 -

0.8 m

0.7

0.6

58.820 135.290

0.028 0.014

k5 = h = k7 = k8 =

182.350 -279.410

0.215 - 0.095

Γ lo .

/ / V

/ /

*

λ / r

%

/

| z \ /

/ /

5!

4

§- 0.3 LU

0.2

0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7|m|0.8

KG ► Sorgatz's computer model [5.23]

Figure 5.24 Comparison of the results of Eqn 5.4 and those of the original calculations by Sorgatz5 23

As can be seen in Fig. 5.24, good correlation exists between the results of Eqn 5.4 and the deviation magnitudes calculated using the complete model of Sorgatz. Eqn 5.4 can therefore be used to calculate the lateral deviation of production vehicles under side wind.

5.5.3 Calculation of lateral deviation for production vehicles

Equation 5.4 was used to calculate lateral deviation for a range of 30 vehicles. Figure 5.25 shows plots of xOS versus respective side force coefficient cS30F. From this plot a trend can be seen, indicating that for vehicles with small side-force coefficients the aerodynamic lever arm is longer than for vehicles with large side forces.

The lateral deviations yG, calculated using Eqn 5.4 normalized to the


0.9 m

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

-0.1

M I

• • ·

•

• 4

i

• • • ·

•

•

• •

» • > ·

• •

•

• · • · *

4

•

1.0 2.0 2 Q 2 4 Q Figure 5.25 Side-force coefficients and centre of pressure distance for actual vehicles

KGmax

Figure 5.26 Frequency distribution of lateral deviation, computed using Eqn 5.4, for 30 production vehicles

largest lateral deviation yGmax of the vehicles 'tested', are shown in Fig. 5.26 as a frequency distribution. The arithmetical mean value is yG* = 0.63, with only 30 per cent of the vehicles tested exhibiting deviation larger than this mean, and approximately 50 per cent of the vehicles deviating less than yG* = 0.57.

5.6 Safety limit

The limit above which side-wind sensitivity becomes dangerous rather than just uncomfortable is not only dependent on the frequency distribution of side-wind deviation. With the help of an assumption, an attempt will be made to measure and specify the limit of safety.

A dangerously large side-wind deviation can be specified as one that causes the vehicle to deviate to the side of the driving lane. With a driving

Safety limit 233

lane width of 3.75 m (German Autobahn; USA highway is approximately 3.66 m) and a vehicle width of approximately 1.70 m, only about one metre of road width is available for course deviation from the optimum middle-of-the-lane driving position; see Fig. 5.27.

A 1

Figure 5.27 Vehicle course as a result of side wind (schematic)

10

^

1

3Π - v / ' \)

^max

Lo^ ^^^zÔJ

t t t t t t t t f t t t t t t t t t I 1/e I I

0.1 0.2 0.3 0.4 0.5

. . . 2KG

0.6 0.7 0.8 0.9 1.0

Figure 5.28 Danger level with increasing proximity to the side of the driving lane

As an initial assumption, one can say that a vehicle will deviate from its desired course by approximately twice the deviation yG, which occurs while the vehicle is under fixed control during the first 0.8 seconds after wind changes begin (see Fig. 5.21) and before driver reaction 'recovers' the vehicle.

Assuming that the original course is in the middle of the driving lane, the level of danger increases slowly as the vehicle deviates from this course and


is not significant until the vehicle approaches the side of the lane—when the level of danger increases rapidly. This situation can be represented by the following formula (see Fig. 5.28):

where

Y = - ^ (5.7)

Under the assumed distribution of level of danger (Eqn 5.6), the danger can be seen to increase rapidly from Y = 0.9. If this were defined as the danger limit, it would mean that for the example illustrated in Fig. 5.27 (flmax = 1 m) a maximum allowable deviation of yG = 0.45 is tolerable; i.e. minimum safe driving distance from the side of the lane is 0.1m.

5.7 Outlook

The side-wind sensitivity of motor vehicles represents a disturbance to the vehicle/driver system which can vary from being merely a loss of comfort to a dangerous vehicle characteristic. Whereas the vehicle is theoretically relatively easy to describe, the driver can only be simulated by an idealized model that does not have the adaptive qualities of an actual driver. Driver simulation is an area which must therefore be investigated in the future. Attachments on this theme are presented by Wallentowitz,5 26 who applied a frequency-dependent characteristic.

Until now, vehicle development has had to rely on simple evaluation methods; such a method has been described in this section.

5.8 Notation

A /zz N S Tu

u V Vs Y CL

cN CM

CR

cs CS30 CT

reference area moment of inertia about vertical axis yawing moment side force degree of turbulence wind speed driving speed side-wind speed relative lateral deviation, Eqn 5.7 lift coefficient yawing moment coefficient pitching moment coefficient rolling moment coefficient side force coefficient side force coefficient at ß = 30° tangential force coefficient

Notation 235

/ G degree of danger, Eqn 5.6 / length of vehicle q dynamic pressure χΌ centre of pressure distance xOS distance between centre of pressure and centre of gravity

(aerodynamic lever arm length) xs centre of gravity distance yG lateral deviation β yaw angle γ slip angle

Chapter 6

Operation, safety and comfort Raimund Piatek

6.1 Definition of themes

In Chapters 4 and 5 a relationship was established between the flow around a passenger car and the resulting forces and moments. In this context, separations are of interest in as much as they influence the integral force and moment coefficients. This global approach is no longer sufficient within the framework of this chapter.

The aim here is to illustrate that air flow around a vehicle should be developed also on the basis of factors that have nothing at all to do with the mechanics of motion, but which are of crucial importance in terms of operation, safety and comfort of the vehicle. Phenomena such as the accumulation of dirt on the vehicle, cooling of the brakes, the magnitude of forces on individual bodywork components, the fluttering of bodywork components and bolted-on parts and, finally, the occurrence of wind noise are directly connected with air flow around the vehicle. Treatment of these problems requires an exact picture of the character of local flow. Figures 4.3 and 4.4 give a qualitative illustration of the individual fields of flow. Quantitative results are available only by measuring individual local fields.

6.2 The field of flow around a vehicle 6.2.1 Air flow patterns

A distinction can be made between two basic types of flow around a vehicle: there are areas of attached flow as well as of separated flow. Further differentiation can be made between separated flow of quasi-two-dimensional type and of three-dimensional type (see section 4.2). The location of such areas of separation and the determination of their extent is possible by means of relatively simple test techniques. Figures 6.1 and 6.2 give examples of how vehicle air flow can be made visible. In Fig. 6.1 thin woollen threads have been fixed to the vehicle surface at set intervals. The orientation which the threads adopt during air flow gives an indication as to the local direction of flow. Three-dimensional separation behind the A-pillar is clearly visible in this figure.

Figure 6.2 shows an oil flow picture of a test vehicle. A thin emulsion of aluminium oxide, kerosene and petroleum, painted onto the vehicle, is

236

The field of flow around a vehicle 237

Figure 6.1 Air flow around a vehicle, made visible by using woollen threads, after ref. 6.17

Figure 6.2 Flow pattern of a delivery van with front edge radius r = 0 mm, angle of yawß = 0°, after ref. 6.6

dried by the air flow in the wind tunnel. The picture thus created is likewise only a limited indication as to local direction of flow, since the influence of gravity upon each particle of the liquid distorts its path. Thus, the lines formed on the surface of a body during this procedure always deviate downwards from the actual lines of flow. On the other hand, the illustration shows two clearly recognizable areas of separation, one behind the A-pillar, the other behind the vertical edge of the front end. Air flow in this illustration was frontal. Both techniques mentioned here give an idea of the course of lines of flow at the vehicle surface. Such investigations cannot give any indication as to air flow within the area surrounding the vehicle, but smoke flow can be of use.

The air flow around the front of a car made visible in Fig. 6.3 (after Hucho and Janssen6 6) illustrates an example of separation at the front edge of an engine bonnet. The introduction of smoke into the separated air flow (below in Fig. 6.3) is a particularly effective way of making separated air flow visible. Smoke, injected into a separation bubble, fills this bubble

238 Operation, safety and comfort

Figure 6.3 Separation bubble made visible by means of smoke, which is injected either as streaks into the undisturbed flow or into the separated flow, after ref. 6.6

completely because of the recirculating flow pattern inside the bubble. Therefore the separation line is clearly identified.

An exact, quantitative description of the flow field is possible only through the measurement of speed and pressure distributions by means of probes. However, during the development of a new car this precise information is hardly heeded. Flow visualization methods are adequate to identify problem areas.

Within the framework of the problems outlined in section 6.1, the following areas of separation occurring on a vehicle are of interest:

• Engine bonnet separation • Roof separation • A-pillar eddies • Longitudinal tail vortices • Wake.

Separation over the bonnet of a vehicle (see Fig. 6.3) is caused by the front edge being too sharp and, apart from the two side areas of the vehicle, can be regarded as being quasi-two-dimensional. Separation at the front roof edge is essentially identical to engine bonnet separation. The third important area of air flow separation occurs to the rear of the A-pillar, the A-pillar eddy. Eddy separation occurs at this pillar, the roof post between front and side windows, just as it does on angled delta wings. Figure 6.4, after Watanabe et al., shows air flow made visible in this area on a vehicle. This oil flow picture confirms the nature of air flow determined by model tests. A vortex is formed, with a secondary one to the side of the edge. Figure 6.5 is a schematic drawing, also after Watanabe. This type of separation has a three-dimensional character.

There are two forms of air flow separation in the rear region.


Separation line

Reattachment line Figure 6.4 Oil flow picture of the three-dimensional A-pillar separation, after ref. 6.5

Section A-A

Flow

Figure 6.5 Schematic drawing of an A-pillar vortex, after ref. 6.5

Figure 6.6 Schematic drawing of fully formed trailing vortices on a fastback vehicle, after ref. 6.3

Longitudinal vortices, after Hucho6 3 and highly simplified in Fig. 6.6, are caused by the static pressure difference between the upper and lower sides of the vehicle (Figure 4.4 corresponds rather more to the actual course of air flow). The pressure difference between the underside of the vehicle and the roof induces on both sides an upward flow which, together with the flow over the roof, forms trailing vortices.


Figure 6.7 Wake made visible behind a VW Golf (longitudinal vortices have not formed)

The second type of air flow separation in the rear area of a vehicle is the wake, which has been made visible in Fig. 6.7 by introducing smoke. Flow over the vehicle can no longer follow the contour, separating from the rear edge of the roof. Flow within the area of separation appears random. However, there is a tendency towards particular flow directions. This will be dealt with further in section 6.4.3. The immediate aim is to examine the influence of the air flow details dealt with here in the context of operation, safety and comfort.

6.2.2 Pressure distribution

When a vehicle is moving, a certain velocity distribution, and thus also pressure distribution, is set up. Figure 6.8 shows a comparison between the pressure distributions measured along the longitudinal centreline of three

Figure 6.8 Upper body surface pressure distributions of several vehicles

different types of vehicle: a van, a notchback car and a sports car. Pressure is represented in line with Eqn 2.8 as a dimensionless coefficient cp. Knowledge of local pressure distribution is important for three reasons (see also section 2.3.2): • Determining areas for air inlets to the passenger compartment • Determining areas for air outlets from the passenger compartment • Determining the forces acting upon bodywork components.


Two different concepts may be employed in order to supply air to and remove air from the passenger compartment (see also section 10.4.1):

• Speed-dependent volume flow • Speed-independent volume flow. Volume flow can be made independent of vehicle speed by locating air inlets and outlets in areas of equal pressure. There is then no pressure difference, and a constant air flow rate can be generated by means of a continuously operating fan. The extra noise generated, as well as higher production costs for the more powerful fan, have however led to a preference in practice for the second option, involving volume flow which is indeed dependent on vehicle speed, but with which the fresh air fan need not necessarily operate continuously.

Generally speaking, there is little freedom of choice as regards air inlets. In order to guarantee a sufficient supply of air with minimal fan power, the location chosen for the air inlet is in an area where pressure is highest. As shown in Fig. 6.8, there are two possibilities as far as a passenger car is concerned. First, in the front end of the vehicle, i.e. in an area near to the stagnation point where cp = 1. The drawback here is that exhaust gas from a vehicle in front enters the passenger compartment. Furthermore, a long air duct is necessary from the air inlet to the passenger compartment, meaning additional design outlay and thus greater expense. The second possibility is in the region in front of the windshield, the scuttle. The air inlets are generally located in the centre of this region. Static pressure at this point, which must be known in order to be able to design the ventilation system, can vary from vehicle to vehicle. It is influenced by the slope of the windshield, as well as by the nature of air flow on the front bonnet. If air flow separates at the front edge of the bonnet, the pressure depends upon where the air flow reattaches again.

0.40

* 0.30

|0.20

0.10

Complete separation

Separation and reattachment

No separation

Figure 6.9 The influence of bonnet air flow upon pressure in front of the windscreen, after ref. 6.2


Figure 6.9 shows the influence of the design of the front edge upon pressure just in front of the windshield (after Janssen and Hucho6 ). With design A, where flow separation above the hood is complete, only slight pressure of cp = +0.1 is set up. If a vehicle were to be built with this front end contour, it would need to have a continuously operating fan. With contour B, where air flow around the front edge is better, air flow separates at the edge and reattaches to the vehicle surface in front of the air inlet region. The pressure measured with this design rises to cp = +0.3. With a rounded hood edge, such as contour C, air flow does not separate from the hood. Pressure rises to cp = +0.4, thus providing for sufficient ventilation during cruise without an additional fan.

With vans (see Fig. 6.8) the front panel of the vehicle is the only possible position for air inlets. However, it must be placed as high up as possible, in order to prevent exhaust gas from entering the passenger compartment.

There is greater freedom of choice in the location of air outlets. At first sight, it would seem suitable to choose an area where pressure is lowest, i.e. the transitional area between windshield and roof. This solution does indeed generate the maximum pressure difference, and thus maximum air volume flow, though distribution of fresh air and warm air in the passenger compartment would be unsatisfactory (see Chapter 10) since there would be no air circulation through the rear of the passenger compartment. Furthermore, severe noise problems would be introduced, as tests have indicated. Bearing certain production factors in mind, satisfactory passenger compartment flow is most easily attainable if the air outlets are located further towards the rear.

There are various areas of lower pressure to choose from at the rear end. In Fig. 6.10, the results of pressure distribution measurements are given (after Hucho6·10), which were conducted with a view to the selection of air outlet locations on notchback vehicles. Measurements were made in four

Figure 6.10 Pressure distribution measurements with a view to the selection of air outlet locations on a notchback passenger car, after ref. 6.1

Forces acting upon bodywork components 243

areas of low static pressure potentially suitable in construction terms for the location of air outlets. The values featured are the mean values of the pressure coefficients measured in these areas. It can be clearly seen that there is a considerable rise in pressure in the event of side wind on the lee side. The yaw angle ß must be varied within the series of tests, in order to ensure that the air outlets work properly even when cross-winds act upon the moving vehicle.

Pressure conditions at an outlet are determined to a great extent by details of bodywork design. If, for instance, the outlet is located to the rear of the rain gutter on the C-pillar, pressure at this point is mostly dependent upon the geometrical shape of the rain gutter. Results comparable to those in Fig. 6.10 were obtained by Hucho and Janssen616 when developing air outlets for the Volkswagen 1300 (Beetle).

6.3 Forces acting upon bodywork components

The fact that pressure distribution around the vehicle results in air forces and moments has already been dealt with in Chapters 4 and 5. This chapter deals in more detail with the forces acting upon individual bodywork components. These forces can be either steady or non-steady. Using the front side window as an example, Fig. 6.11 shows that these forces can

40 10-1 N

35

30

t 2 5

I 20

15

10 5

ß-

w

^

-0

nd \ >

Wind 1 \ 1

owB

\ v «* "

ow

\

pr f

A

S s

β'-

\

= 1 5° LE

Vindow i ■ "V

Window B

S* 's , /

/

E

v / /

/ /

/

i r

J

r\

Window A

Support of open window

Window B

Centre of pressure of outside wind force

• 0 = 0 β 0=15° LEE

20 60 100 km/h 180 20 60 100 km/h 180

Figure 6.11 The influence of vehicle speed and yaw angle upon the resulting side window force

become quite considerable, necessitating appropriate design measures. The magnitude of the force depends of course upon the area of the window, but also to a considerable extent upon the direction of the oncoming air flow. The resulting force increases on the lee side because of the decreasing static pressure on the outside. This effect can lead to pulling away from the door seal, especially with frameless windows. Through this open gap a high-frequency jet is set up, caused by the pressure difference (see section 6.5.2). This causes great discomfort. A remedy is available in the form of an increase in the resistance of components to distortion, or, adopting the aerodynamic approach, by increasing exterior pressure by reducing local air flow speed.


Forces and moments acting upon movable bodywork components, such as hoods and lids, merit particular attention. Because of the high suction peak on the front edge of the hood (see Fig. 6.8) great forces are generated. If the front compartment is to hold luggage care must be taken to ensure that the lid is tightly sealed even at high speeds. Sloping the lid or increasing the radius of the front edge will reduce the suction peak in the front area of the hood.

Periodic flow, occurring for example in separated regions, leads to non-steady forces upon vehicle components, and can, if they are flexible, lead to so-called fluttering, see also section 2.3.4.2. Such effects have been observed on passenger car front hoods and van roofs. When developing the air flow around bodywork components which have a large surface the danger of such self-excited flutter motion cannot always be reduced by preventing separation. Very often the only measure is to design the related part to be more rigid. The tendency towards long, low vehicles, and thus to only slightly convex bodywork components, as well as to weight-saving construction, will mean that greater attention will have to be paid to the problem of flutter in the future.

This examination of non-steady forces acting upon bodywork compo-nents must also include the exterior rear-view mirror. Periodic air flow in the separation area to the rear of the rear-view mirror leads to a non-steady load upon the mirror. Since the very function of the mirror necessitates that it be mechanically movable, sympathetic movement of the component can occur. In order to counter this, the mirror geometry may be modified in such a way that the tendency to vibrate is prevented. The final geometry of the mirror is, however, determined by still further factors (see also section 6.4.2).

6.4 Dirt accumulation on the vehicle 6.4.1 Basic considerations

The accumulation of dirt on the surface of a vehicle is significant in two respects (see also section 8.6): first in terms of safety, i.e. the accumulation of dirt on the headlamps, direction indicators and windows, and secondly, in aesthetic terms, i.e. the problem of the accumulation of dirt over large sections on the vehicle sides, in particular near the sills and door handles. The very title 'Dirt accumulation on the vehicle' represents a whole new factor: air flow around the vehicle is now to be treated as a bearer of dirt (see also section 2.3.4.3). The particles carried by the air could be either liquid (water) or solid (dirt raised from the road surface). When driving, these two types can combine in the form of dirty water. However, for the sake of simplicity, a distinction will be made here between water flow around the vehicle and dry dirt deposits upon a vehicle.

6.4.2 Water flow

Because of the reduction in visibility it causes, the wetting of a vehicle's windows is treated as a problem in its own right during development work. The windscreen, the A-pillar and the side windows to its rear, the exterior

Dirt accumulation on the vehicle 245

rear-view mirror and the rear windows are involved. The development of water flow always takes place with a defined method of water guidance in mind. Water must be diverted and then got rid of before it can accumulate on a window and cause a nuisance.

Various approaches have been proposed as regards the windshield (Götz6 8), see also section 8.6.1. Flow guides and 'air curtains' from air sources located beneath and in front of the windshield have not, however, proved viable. As far as the windshield is concerned, further improvements will have to be made to conventional wash/wipe systems.

Water on vehicle side windows not only reduces lateral visibility but also restricts the usefulness of the exterior rear-view mirrors. This can be countered by appropriate design of the A-pillar. However, when developing appropriate A-pillar geometry, the influence of this geometry upon the vehicle's aerodynamic drag (see also section 4.3.2.3) and upon the generation of wind noise (see section 6.5.2) must be borne in mind.

Windscreen

Rain water

^ P " ^ v ^ § Figure 6.12 The influence of the design of Ρ £ ^ & # * ^ ^ Γ t n e windscreen pillar upon the drag

coefficient cD,water flow and air flow Separation separation, after ref. 6.2

Figure 6.12, from Janssen and Hucho, 6 2 shows the various stages in the development of an A-pillar. Design 1 could be easily manufactured, but would generate very great aerodynamic drag because of the intensive air flow separation it would bring about. Water flow from the front does not wet the side windows. Versions 2 to 5 represent further developments of this design. Contour 2 brings about a considerable reduction in aerodynamic drag because of the considerably smaller area of separation. However, this alternative is unacceptable since water spills out over the A-pillar and wets the side windows. In design 3, the side windows are indeed dry, but the drag coefficient is greater. In view of the greater outlay involved in the construction of alternative 5, contour 4 with integrated gutter is the most practical of those discussed here.


The exterior rear-view mirrors represent a further cause of water deposits on the side windows. The mirror wake can cause wetting not only of the side windows but also of the mirror surface. No general statements can be made concerning the shaping of the mirror. On the contrary, optimum mirror geometry has to be achieved on the basis of tests carried out during new development. In this context, optimum means that there is as far as possible no contact surface between mirror wake and side window, and that the flow guarantees a clear mirror surface.

Wetting of the rear windows of notchback and fastback vehicles is caused by air flow over the roof. A water trap situated above the rear window can prevent the overflowing water from reaching the window. The water flowing over the roof is intercepted above the rear window and drains away downwards to both sides of the window. Figure 6.13 shows a design solution formulated by Janssen6 17 for just such a water trap for a fastback vehicle. In this instance, the trap is represented by the gap between roof and tailgate.

The left-hand side of the figure represents an early vehicle development stage, while the right-hand side demonstrates the geometry as used in the

Figure 6.13 Wetting of the rear window and its prevention in the standard vehicle, after ref. 6.17

Trap strip Without trap strip

Optimized trap strip

Figure 6.14 Water flow over the rear window of a notchback passenger car; the effect of a water trap strip, after ref. 6.1


production vehicle. In the latter instance, the water is drained to the side between roof and tailgate.

Figure 6.14 (after Hucho6Λ) shows how water flow is kept away from the rear window of a notchback car. Water flowing over the roof is trapped by a strip integrated into the rubber seal. An experiment is necessary to match the geometry of this strip to the vehicle's contour.

6.4.3 Dirt accumulation

In the last section attention was paid to water flow on and around the vehicle windows. Water lying on the road and rain is seldom likely to be completely clean. Apart from the problems concerning water flow outlined above, there is thus the additional problem of dirt being deposited on the window. This source of dirt will not be dealt with again here, since the prevention of water flow over the windows will also prevent the depositing of dirt on the windows caused by this very water flow.

The shaping of a vehicle has hardly any influence at all upon the accumulation of dirt on the headlamps. There is as yet no aerodynamic alternative to the mechanical cleaning of headlamps.

Dirt on the rear window has two causes. The first, water flow over the vehicle roof, has already been dealt with in detail in section 6.4.2. It is observed on fastback and notchback shapes. Water and dirt on the rear window of squareback vehicles is caused by the accumulation of water droplets and dirt particles within the wake and the depositing of this matter upon the bodywork surface as a result of the swirling movement within this area of separated flow. Figure 6.15 shows the two basic forms of air flow separation already dealt with in Chapter 4. In the upper picture air flow

Figure 6.15 Separation patterns in the wake: (a) air flow separates at rear edge (squareback-type); (b) air flow remains attached until beneath the rear window (fastback-type), after ref. 6.3


separates at the rear roof edge. The rear window thus lies within the area of the wake, and is exposed to dirty water borne by air swirling at random. The lower diagram shows attached flow in the rear window area. In terms of a clean rear window, this is preferable, but in section 4.3.2.5 it is shown that attached flow at the rear window is not always desirable in the context of the minimization of aerodynamic drag.

Unless additional measures are taken, air flow separates at the rear roof edge of squareback vehicles. Thus, the rear window lies within the wake area and becomes very dirty. Figure 6.16, from Hucho6Λ shows how the

1 2 3 4 5 6 7 mg 8

Figure 6.16 The influence of an air guide vane upon the accumulation of dirt on the rear window of a squareback vehicle, after ref. 6.1

Figure 6.17 Variations to the guide-vane gap; the influence upon the accumulation of dirt on the rear window, after ref. 6.6: (a) without guide vane; (b) gap width 20 mm; (c) gap width 40 mm

rear window can be kept clean by means of a guide vane. The shape and position of such a guide vane must be determined on a vehicle-specific basis. The deflected air ensures that the upper part of the rear window remains almost completely free of dirt, though a considerable increase does take place in the lower third of the window.

In Fig. 6.17, after Hucho and Janssen6 6 it is clear that this phenomenon


can be countered by varying the guide vane gap. If there is sufficient distance between the guide vane and vehicle contour, the air screen remains attached as far as to the lower edge of the rear window. However, the increase in aerodynamic drag brought about by such bolted-on guide vanes disqualifies them from consideration as far as large-scale production is concerned. A guide vane integrated into the vehicle would cause production difficulties and would lead to a considerable increase in costs. However, an integrated guide vane is used in one range of buses, as illustrated in Fig. 8.94.

Vehicle rear lights are highly susceptible to dirt because they lie within the area of the wake. Measurements of dirt thickness which have been carried out (Götz68) have led to the conclusion that the heaviest accumulation of dirt on rear lights is observed on notchback vehicles, followed by fastback and squareback versions. One possible solution is represented by a flowing air screen between the rear-light level and the surrounding separated flow. The associated drawbacks and difficulties have already been illustrated in the discussion dealing with the squareback vehicle. When developing vehicles nowadays, efforts are made to minimize dirt deposits in this area by designing appropriate shapes for the rear lights. Ribbed rear lights have been shown to represent an effective solution, since the recessed areas are less heavily coated by dirt contained in the swirling air.

Delivery vans are often subject to dirt deposits on their sides. The dirty water swirled up out of the front wheel housing is deposited over large areas of the bodywork. Figure 6.18, from unpublished experiments carried out by E. Rohlf in the Volkswagen AG wind tunnel, shows how careful design can reduce this effect to a level no longer to be regarded as a nuisance. Design modifications to the bodywork are restricted in this case to a front apron and a divider on the edge of the wheel well. Design A gives a steep pressure gradient from the wheel well to the side wall above it. The result is an upward velocity component of the spray water emerging from

Figure 6.18 The accumulation of dirt on delivery van side walls, after E. Rohlf


the wheel well. Contour B gives rise to a smaller vertical velocity component as a result of a less steep pressure gradient, though dirt still stretches over an area which is often used for advertising purposes on such vehicles. Only design C, with a weak and reversed pressure gradient, can be regarded as satisfactory. As Fig. 6.18 shows, the reversal of the pressure gradient is achieved by reducing pressure in the wheel well. An increase in pressure on the outer skin above the wheel could be achieved only at the cost of major, unacceptable changes in shape.

6.5 Wind noise 6.5.1 The fundamentals of noise generation on vehicles

Wind noise is generated by vehicle air flow. Wind noise must be handled in conjunction with the other sources of vehicle noise. Refer to Günther et al.6,9 and Zboralski610 for the fundamentals of acoustics.

Vehicle noise is generated essentially by the engine, the tyres and the air stream. The interior noise measurement in a subcompact car can give an idea of the relative magnitude of the three sources. At a vehicle speed of 150km/h (93.8mile/h), corresponding to an engine speed of 5500rpm (the microphone for recording measured data was located on a level corresponding to that of the driver's left ear), the following levels were recorded:

Engine 82.5 dB (A) Tyres 78.0 dB(A) Wind 78.5 dB(A)

From these, a total noise level of 85 dB (A) is calculated. The trend towards deluxe vehicles as well as legislation to protect the

environment necessitate efforts to reduce both interior and exterior noise levels.

Future exterior noise legislation will lead primarily to a reduction in engine noise by means of better noise absorption. A desirable spin-off of this will be a reduction in interior engine noise. This will mean that the relatively low tyre- and wind-noise levels will assume greater importance in terms of interior noise.

Vehicle wind noise is assessed using two criteria. The first is the limiting of the wind noise frequency spectrum. When deluxe vehicles are being developed, efforts are made to achieve so-called 'uniform' noise. Uniform here means that the noise frequency band is as far as possible speed-independent, so that the total noise level rises continuously and that there are no frequency peaks.

The second assessment criterion is the sound pressure level mentioned at the beginning of this section, i.e. sound volume. The noise level measured in the passenger compartment is dependent not only upon the noise generated but also on the sound conductance characteristics and resonance characteristics of the vehicle. Important in this respect are, for instance, acoustic insulating mats and acoustic absorption elements, such as are found in today's mass-produced vehicles, and which positively influence the sound conductance behaviour of the bodywork. Such acoustic

Wind noise 251

absorption is beset by major problems in terms of wind noise, since, for reasons of design, there is minimal scope for insulation between those points where wind noise occurs and the passenger compartment. Therefore the only alternative way of reducing wind noise is to reduce the intensity of the noise at the point of its generation, by means of design optimization.

6.5.2 The influence of air flow mechanisms

The various types of air flow illustrated in Figs 4.3 and 4.4, which were discussed in more detail in section 6.2.1, can be distinguished on the basis of the mechanism involved in noise generation, as Stapleford and Carr611

have demonstrated on a simple model, a rectangular cuboid. The following types of air flow are observed:

• Attached flow • Quasi-two-dimensional separation • Reattached air flow • Three-dimensional vortex separation

Figure 6.19, after Stapleford and Carr6 n shows these four types of air flow on a cuboid. The Reynolds number of air flow determined by the length of the cuboid was Rex = 9.2 x 105. Attached flow along the entire

Figure 6.19 Types of air flow generated on a cuboid in order to measure sound levels, after ref. 6.11

length of the cuboid can be generated by means of a rounded edge at contour point A. A sharp edge at this point brings about a separation bubble between A and B with subsequent reattachment of air flow. The fourth form of air flow to be examined can be brought about by oblique air flow over the sharp-edged object. The oil film pictures of the cuboid air flow thus generated are shown in Figs 6.20 to 6.22 (also from ref. 6.11). Within the separation bubble, a distinction can be made between area A with side air flow and area B with clearly reversed flow. Measurements of the sound pressure level were made with microphones flush with the surface.

Table 6.1 gives the maximum sound pressure level measured for each type of air flow, and the frequency range over which this level was measured. The maximum levels measured within the range 500 Hz to 1500 Hz are shown in Fig. 6.23 (after ref. 6.11) in the form of lines of constant sound pressure. This investigation showed that the areas of separated air flow were particularly noise-intensive, as was the reverse flow


Figure 6.20 Oil film picture of air flow in contact along entire length (front edge is rounded, see also Fig. 6.19), after ref. 6.11

Figure 6.21 Oil film picture of the quasi-two-dimensional separation bubble with reattached air flow (see also Fig. 6.19), after ref. 6.11

Figure 6.22 Oil film picture of cuboid with air flow under 30°, with formation of two three-dimensional vortices (see also Fig. 6.19), after ref. 6.11

area within the separation bubble and, particularly strikingly, the three-dimensional vortex separation. Both types of air flow together cover a very wide frequency range, in this instance from 200 Hz to about 800 Hz.

The measured values given in Table 6.1 are meant only as a guide, and should not be viewed as anything more. The measurements have shown

Wind noise 253

Table 6.1 Relation between character of flow, maximum sound pressure level and frequency range (after ref. 6.11)

Character of flow Max. sound pressure level Lm a x(dB(A))

Frequency range ofLmax (Hz)

All attached Separation bubble A Separation bubble B Reattached Vortex

111 108 115 113 130

800 to 1200 400 to 500 200 to 500 300 to 600 500 to 800

WIND

DIRECTION

(b)

ALL ATTACHED FLOW-

(— RE-ATTACHMENT ZONE -

ίτιτπ WIND I I / / Ί / / | _ j 105 107.5 110 I 112.5 115 ]112.5

DIRECTION rom ^•SEPERATION BUBBLE- RE-ATTACHMENT LINE

WIND DIRECTION

v V O R T E X ^ ATTACHED FLOW-

Figure 6.23 Surface sound pressure level in the frequency range 500 Hz to 1500 Hz, after ref. 6.11: (a) attached air flow; (b) two-dimensional separation with reattachment; (c) three-dimensional vortex

that the level measured in the separation area behind the A-pillar on a vehicle of normal size can be more than 30dB(A) higher than that measured in the centre of the roof, an area of attached air flow. Thus, it is also in the interests of the acoustic engineer to avoid air flow separation as far as possible.

Figure 6.24 shows the sound pressure measurement made by Watanabe et al.6"5 in the separation bubble of the right-angled step. The frequency at which measurement was made was 1kHz. The measurement underlines the evidence contained in Fig. 6.23 a and b. In a quasi-two-dimensional separation bubble, maximum noise intensity occurs in the area of


- 0 .4

100 200 300 400 mm 500

Figure 6.24 Pressure and sound pressure level measurement to the rear of a step, after ref. 6.5

reattachment of air flow. The level measured within attached air flow decreases as length of attached air flow increases.

There are, in addition, two extremely undesirable effects to be dealt with, which occur especially in motor vehicles: first, so-called 'booming' and second, leaking door seals. Booming occurs with open side windows or an open sliding roof. Effects are induced within the air column inside the vehicle by the exterior air flow, causing the passenger compartment to become a resonator. According to Aspinall6 14 there are two possible types of booming in the instance of an open side window. The first type occurs predominantly at low vehicle speeds (up to 80 km/h, 50mile/h) on the luff side, and the sound pressure has a periodic character. The second form occurs on the lee side at higher vehicle speeds, and the sound pressure is random in character. In the case of frontal air flow, the periodic type of air flow occurs.

For both types of low-frequency booming, whose frequencies lie beneath 60 Hz, scope was found for reducing wind noise. Deflectors located on the front side of the opening have proved effective in the case of periodic booming. Such ramps avoid unstable pumping effects on the rear edge of the opening and define a clear reattachment point of air flow. Reductions in local sound pressure level from over 120 dB to below 90 dB were recorded on vehicles equipped in this way.

However, this method of air flow guidance is difficult to integrate into vehicle design in the case of the side window. On the other hand, deflectors which are mechanically extended when the sliding roof is opened have gained acceptance in production.

The second type of booming can be reduced by a more sloping

Wind noise 255

windshield. The air volume flow around the A-pillar is thus reduced, i.e. lower air flow speeds are reached at the window opening.

No functional link can be quoted between, on the one hand, the geometry and location of the deflectors, or angle of slope of the windshield and, on the other hand, the sound pressure level and individual frequency spectra. Optimum solutions have been found on a vehicle-specific basis using different shapes, sizes and locations. In wind tunnel experiments, optimization must take place on a vehicle-specific basis.

As has long been known, passengers find the noise caused by leaking door seals most unpleasant. Imperfect seals can be caused by one of two things:

• Unsatisfactory workmanship • The great suction force on the door (see section 6.3) can lead to local lifting-off of the door from the seal in the area of the window.

0 = 0° 0=15° LEE fc^^j tgjgfl Partial vacuum

Q ^ Figure 6.25 Static pressure distribution in cp = 1 the door clearance of a passenger car

Figure 6.25 shows the measured distribution of static pressure in the front door joint of a passenger car. A considerable negative pressure is set up precisely in the area where the door is not supported. The pressure coefficients cp measured in this area, particularly on the lee side, are among the lowest over the whole vehicle. Similar measurements on a VW411 have been published by Hucho and Janssen.6 16 These measure-ments were used as a basis for the design of the door seals and for the formulation of a tightness test in quality assurance.

A leaking door joint is undesirable for two reasons:

• Damping of the intensive noise from the A-pillar vortex decreases and the open gap acts as a noise path.


• A high-frequency jet air flow is set up from the passenger compartment through the gap because of the great pressure difference. The door clearance becomes an additional source of noise. If a door seal remains tight under all driving conditions, the door clearance cannot be considered to provide scope for a reduction in wind noise.

6.6 Air flow around individual components 6.6.1 Windshield wipers

Air flow around the windshield wipers should be designed so that the wiper blades remain in contact with the windshield under all circumstances.

Because of the speed of air flow when the vehicle is on the move, a lift force is exerted perpendicular to the windshield. This lift force depends upon many parameters and changes continually during wiper operation. The only fixed parameter is wiper arm geometry. All other variables are of changeable character, such as vehicle speed and yaw angle of vehicle air flow. The movement of the wiper arms also continuously changes the effective flow direction of the windshield wipers, and thus also their lift. The body surface velocity, which contributes to this lift, becomes greater as the wiper approaches the horizontal neutral position, i.e. the wiper arms are most susceptible to lifting off from the windshield near the lower reversal point.

In Fig. 6.26, the turning-over of the wiper blades at the point of reversal in the wiper movement is investigated (Barth615). According to the

Figure 6.26 Influence of wiping direction upon the aerodynamic drag and lift of a wiper blade, after ref. 6.15

Air flow around individual components 257

direction of movement, angle ß is either positive or negative. During downward movement (ß < 0°) lift is clearly higher than when the wipers are moving upwards (ß > 0°). When ß < 0° the magnitude of the angle is of hardly any significance. Therefore maximum lift is to be expected during the downward movement, shortly before the lower point of reversal. In order to reduce this lift force, small pressure vanes are used that supplement the spring force.

-60'

Figure 6.27 Influence of pressure vane angle upon drag and lift of a windscreen wiper configuration, after ref. 6.15

Figure 6.27 (also after Barth6-15) shows the influence of the angle of attack of such a vane upon the coefficients of lift cL and drag cD. The precondition here is the critical case of air flow perpendicular to the wiper shaft. The angle of attack of a = -45° can be considered optimum in view of the lift. The determination of length, width and profile of such vanes must be based on experiments.

6.6.2 Brakes

An important consideration when undertaking aerodynamic optimization of a vehicle is the necessity to ensure sufficient brake cooling. Results will be given, originating from tests carried out with a view to improving the cooling of disc brakes (Fig. 6.28) from Hucho.6Λ The aim was to guide as large a flow of air as possible to the disc brakes by means of suitably located air inlets. The left-hand graph shows this air flow volume against the vehicle speed range.

The right-hand graph shows how this cooling air influences the temperature at the disc brake. The related test procedure is outlined in section 12.3.2. The vehicle was originally fitted with an apron at the front end. The temperature curve on the brake caliper over time is that


100

dm3

s

\ 60

V 40

20 y

\Δ /

Λ 1

/

Apron"

t 120 °C

80

t with cooling inlets

ι i »80 km/h

I 40 80 120 160 km/h 8 min 12

Figure 6.28 Improving brake cooling on a passenger car, after ref. 6.1

identified with 'as delivered' in the figure. To reduce the aerodynamic drag of this vehicle, an aerodynamically optimized apron was developed. The result was, however, an even higher brake temperature. Developing cooling air inlets and the fitting of hoses made it possible to achieve a far more favourable temperature curve, identified on the figure as 'with cooling inlets'. The aerodynamic drag of this model is identical to that of the model with the drag-optimized apron.

6.7 Future prospects

As has been shown in this chapter, the aerodynamics of a motor vehicle cannot simply be identified with the mechanics of vehicle motion. It is rather more a question of a number of problems associated with safety, operation and comfort, which must be solved by aerodynamic means. The solution to the problems outlined here must be formulated in future on a vehicle-specific basis. Tests are an absolute necessity in this context, since the air flow details dealt with in this chapter are dependent upon a whole host of geometrical and aerodynamic parameters. Numerical procedures, which have started to be used in the science of automobile aerodynamics (see Chapter 13), will perhaps make their own contribution in future to the rationalization of test procedures.

6.8 Notation

L,Ln

L w Re V V

sound pressure level, Table 6.1 force acting upon side window, Fig. 6.11 Reynolds number vehicle speed volume air flow, Fig. 6.28

oncoming air flow speed VH velocity components, Fig. 6.18

drag coefficient of windshield wiper lift coefficient of windshield wiper pressure coefficient as per Eqn 2.8 weight of dirt per unit of area, Fig. 6.16 step height, Fig. 6.24 vehicle length, Fig. 6.8 test duration, Fig. 6.28 brake temperature, Fig. 6.28 orthogonal coordinates angle of attack of pressure vane, Fig. 6.27 angle of yaw angle of inclination of windshield wiper, Fig. 6

Chapter 7

High-performance vehicles

Helmut Flegl and Michael Rauser

7.1 Introduction

High-performance vehicles are primarily vehicles that have a high power to weight ratio. High acceleration, deceleration and manoeuvrability can also be vital factors, particularly for sports and racing vehicles. This chapter considers three basic categories: sports cars, racing cars, and record vehicles.

Sports cars (Fig. 7.1) are designed for everyday use on public roads. High power to weight ratio, low centre of gravity and compactness are

Figure 7.1 Porsche 911 Turbo sportscar 1983, 221 kW (300 hp), 260 km/h (162mile/h) cD = 0.39

given priority over carrying capacity and, to some extent ride comfort, and the superior acceleration, manoeuvrability and braking, can be a positive factor in active safety.

Racing cars (Fig. 7.2) normally compete with similar vehicles on special tracks or roads closed to public traffic. They are designed within specific rules and regulations to provide maximum performance in terms of acceleration, top speed, braking, and cornering power. 260

Introduction 261

Figure 7.2 Porsche 935/78 'Moby Dick' racing car; Le Mans 1978, 552 kW (750 hp), 365 km/h (227mile/h),cD = 0.36

Record vehicles (Fig. 7.3) are even more restricted in their use, and are usually designed to achieve high top speeds, or combinations of speed and economy over measured distances (see also section 4.6.3).

Aerodynamics plays an important role in performance and safety of these vehicles. With record vehicles, low drag and straight line stability have top priority whereas racing cars have additional requirements, such as outstanding road holding and high cornering capability. Sports cars often combine all of these factors with everyday utility.

Figure 7.3 Blue Flame rocket-propelled record vehicle 1970,1.001.671 km/h (622.410 mile/h) (courtesy Auto -I- Technik Museum, Sinsheim)

262

^ « a f c w

Figure 7.4 Lotus 79 Formula I racing car. First to realize ground effect in 1977 (courtesy W. Wilhelm)

Figure 7.5 Pennzoil Chaparral 2K Indy-type race car 1979 (courtesy J. Fousel)

*;:?i

Figure 7.6 Porsche 936/78 racing car 1978; 427 kW (580 hp), 340 km/h (211 mile/h), cD = 0.40. Behind the driver above the engine is the so-called lair box'.

Introduction 263

/ T k FORSCHE

Figure 7.7 Porsche 917/30 racing car, 1973; 809 kW (1100 hp), 370 km/h (230mile/h), cD = 0.57. Clearly visible are front air dam and rear wing.

Within these three categories there is a broad spectrum of body configurations that meet particular rules and requirements, for example:

• Open cars—usually single seaters—with exposed wheels, see Figs 7.4 and 7.5 • Open cars with enclosed wheels, see Figs 7.6 and 7.7, see Flegl and Bez^1

• Closed cars with enclosed wheels, see Fig. 7.8 • Closed cars with exposed wheels, as used in record vehicles, see for example Fig. 7.3

Figure 7.8 Porsche 956 ground-effect racing car, Le Mans 1983; 456 kW (620 hp), 355 km/h (221 mile/h)

264 High-performance vehicles

7.2 Some historical milestones

The importance of aerodynamics to record vehicles was recognized very early in their development. The first car to exceed 100 km/h (62 mile/h) was 'La Jamais Contente' built by Jenatzy in 1899. Jenatzy used a cigar-shaped, airship-influenced body (see Fig. 1.9).

Its successors were designed with more or less streamlined bodies, often including rear fins to improve directional stability, the first example being Henry Seagrave's 'Golden Arrow', which achieved a speed of 372.456 km/h (231.433mile/h) in 1929 (Fig. 7.9).

Figure 7.9 Golden Arrow record vehicle 1929; 684 kW (930 hp), 372.456 km/h (231.433 mile/h) (courtesy Auto, Motor + Sport)

The Opel Rak 2 rocket car of 1928 was the first to be fitted with horizontal wings generating negative lift for better control, while a combination of streamlined body, rear vertical fins and wings generating negative lift was featured in the Mercedes Benz T80 of 1939 (Fig. 7.10). It was never used due to the outbreak of World War II.

After the war, John Cobb established a land speed record of 634.386 km/h (394.189 mile/h) in 1947, which remained unequalled until

Figure 7.10 Mercedes Benz T80 record vehicle 1939; 2200 kW (3000 hp) estimated top speed about 650 km/h (400 mile/h)

Some historical milestones 265

the 1960s. Between 1963 and 1970 the land speed record was increased to more than 1000 km/h (620mile/h) by rocket-driven vehicles, with The Blue Flame' (Fig. 7.3) reaching 1001.671km/h (622.410 mile/h) in 1970. The world record for wheel-driven vehicles was increased to 658.649 km/h (409.266mile/h) by the 'Goldenrod' in 1965.

A new land speed record was set by Richard Noble's 'Thrust 2' turbine vehicle to 1019.7km/h (633.6mile/h) in 1983. In 1979, Stan Barret broke the sound barrier with the 'Budweiser Rocket', which reached 1190.23 km/h (739.58mile/h) (Fig. 7.11), though not in accordance with land speed record rules.

Figure 7.11 Budweiser Rocket record vehicle, 1975, first to break the sound barrier; 1.190.23 km/h (739.58 mile/h) (courtesy J.G. Rettie)

Figure 7.12 Benz Tropfenwagen racing car 1923; 66 kW (90 hp), about 185 km/h (115 mile/h) (courtesy Daimler-Benz AG, Stuttgart)

The aerodynamic development of racing cars was somewhat slower. In 1923, the racing version of the Benz Tropfenwagen' was built on the basis of Rumpler patents (Fig. 7.12), and in the same year the Bugatti Tank' (see Fig. 1.14) was built with the body widened to accommodate the wheels. These, however, were isolated examples, as the manufacturers of racing and sports cars generally retained classical body configurations with large radiators mounted at the front, causing considerable air drag. Shortly before World War II, Auto-Union and Daimler-Benz brought the first streamlined racing cars to the track (Fig. 7.13).

Until the late 1960s, racing cars were primarily designed for low air drag,

266

Figure 7.13 Daimler-Benz streamlined racing car, Avus race track, Berlin 1937 (courtesy Daimler-Benz AG, Stuttgart)

Figure 7.14 Porsche Carrera 6 Long Tail racing car, 1966; 162 kW (220 hp), 265 km/h (171 mile/h), cD = 0.33

Figure 7.15 CD Peugeot 66, 1966; 78 kW (105 hp), 245 km/h (152 mile/h) (courtesy Automobiles Peugeot, Sochaux)


one example being the Porsche 906 of 1966 (Fig. 7.14). More extreme examples were the Panhard and Peugeot vehicles designed by Charles Deutsch for the Le Mans endurance race, which reached 220 and 245 km/h (137 and 152mile/h) with 63 and 105 hp respectively (Fig. 7.15). All these streamlined cars did attain high speeds, but they developed lift forces which affected stability and cornering speed.

In 1967, the Chaparral 2F was the first racing car to use a wing to provide downforce to increase lateral adhesion and thus improve handling and stability on the track. This idea led to the general introduction of negative-lift wings and air dams for racing cars, for example the Can Am Porsche 917/30 (Fig. 7.7), and for racing cars derived from production cars, such as the Porsche 935 'Moby Dick' (Fig. 7.2).

The development of racing cars with uncovered wheels followed a similar trend. The early single seaters were built with streamlined bodies as narrow as possible to reduce drag. Little consideration was given to improve the downforces. After 1968, negative lift wings were linked to the front and rear axles and mounted high above the road surface. In some cases they broke off and so were prohibited. In the following racing season, vehicles were equipped with body-mounted wings.

The Chaparral 2J of 1969 presented a new negative-lift concept: two motor-driven fans were used to draw in air from under the car, and thus increased the force between vehicle and road. This 'vacuum cleaner' (Fig. 7.16) was soon prohibited by regulations. A similar experiment, using a

Figure 7.16 Chaparral 2J racing car 1979. Visible are the two motor-driven fans to create a partial vacuum under the car

cooling fan for suction, was made with the Brabham Formula I car in 1978. This attempt also fell foul of regulations which, at the time, dictated that there should be no articulated aerodynamic devices on the car.

In 1977, the Lotus team developed the so-called 'ground effect' which was subsequently made use of in the Formula I Lotus 79 (Fig. 7.4). The fundamental idea of ground effect is that the shaped underbody creates a venturi effect with the ground (see also Fig. 4.125) enhanced by the use of lateral skirts. The resulting low pressure area creates high negative lift, inducing extreme lateral acceleration capability but exerting great strain on the driver. The skirts were therefore ruled out and, from the 1983 racing season on, the underbody panel between the wheels is required to be level.


Ground effect has also been made use of in other racing car types, such as the 1979 Pennzoil Chaparral 2K (Fig. 7.5) and the Porsche 956 of 1982 (Fig. 7.8).

The effect of negative lift on maximum lateral acceleration is shown in Fig. 7.17. Although between 1950 and 1970 only moderate lateral acceleration increases were achieved through chassis and tyre improve-ments, aerodynamic negative lift enabled lateral acceleration to increase dramatically.

3.0 i

c: .o

a

2.0 \

1.0 H

Aerodynamic / Downforce^^j ^**

pa; <M (Ä-

- Ground Effect-

Production Sports Cars

Sedans

ö H h r " ' ^ 1950 1960 1970

1 1

1980 1990

Year ■ Figure 7.17 Evolution of maximum lateral acceleration of sedans, sports cars, and racing cars

Table 7.1 shows the evolution of drag coefficients and frontal areas from the 1950s up to the present for Porsche racing cars. It becomes evident that both the drag coefficient and the frontal area have continued to increase, as greater emphasis was placed on negative lift and maximum track and tyre widths respectively.


Table 7.1 Evolution of drag coefficients and frontal areas from the 1950s to the present (examples from Porsche racing cars)

Type Year cD A (m2) COA (m2)

Porsche Porsche Porsche Porsche Porsche Porsche Porsche Porsche Porsche Porsche Porsche Porsche Porsche Porsche Porsche Porsche Porsche Porsche Porsche Porsche

550 Coupe 550 Spyder ABARTH Formula II Formula I 904 Carrera GTS Carrera 6 910 908/02 Spyder 917 (short tail) 914/6 GT Coupe 908/03 Spyder 917 (long tail) 917/10 917/30 911 Carrera RSR 936 935/78 936 924 Carrera GT

1953 1954 1960 1960 1962 1964 1966 1966 1969 1970 1970 1970 1971 1972 1973 1974 1977 1978 1978 1980

0.36 0.45 0.37 0.53 0.60 0.33 0.34 0.35 0.49 0.44 0.45 0.56 0.36 0.60 0.57 0.43 0.40 0.36 0.40 0.34

1.13 1.03 1.43 0.89 0.72 1.32 1.33 1.32 1.27 1.55 1.66 1.40 1.57 1.85 1.86 1.91 1.75 2.00 1.65 1.94

0.41 0.46 0.52 0.47 0.43 0.44 0.45 0.46 0.62 0.68 0.75 0.78 0.57 1.11 1.06 0.82 0.70 0.72 0.66 0.66

Production sports car development followed a similar pattern to that of racing vehicles. In the pre-war years the manufacturers of sports cars persisted in building to the classical configurations with large radiators and separate mudguards. Immediately after World War II, the producers of sports cars concentrated mainly on reducing the drag coefficient. An example of this is the Porsche 356 (Fig. 1.30) with a frontal area of 1.61 m2

(17.3 sq.ft) and a drag coefficient of 0.34—very respectable even by today's standard.

In the following years, efforts to increase road holding through improved suspensions, wider tracks and tyres, and more comfort through roomy

Figure 7.18 Porsche 911 Group B sportscar prototype 1983; 293 kW (400 hp), 300 km/h (186 mile/h), cD = 0.32 depending on negative lift


interiors resulted in larger frontal areas and higher drag coefficients. The seventies saw the application of aerodynamic aids in the form of front air dams and rear spoilers further to reduce drag and improve road holding by reducing lift. The Porsche 911 Turbo (Fig. 7.1) illustrates this point.

Today the designers are applying race car aerodynamics to the basic body configurations of competition sports cars—the Porsche 911 Group B (Fig. 7.18) with its redesigned underbody and integrated rear wing is an example.

7.3 The influence of aerodynamics on high-performance vehicles

Good aerodynamic properties are basic requirements for high-performance vehicles to obtain both high speeds and superior handling characteristics.

7.3.1 Drag and lift

Increased top speeds for a given engine power are obtained by reducing drag. Drag, which increases as the square of the speed, is determined by the vehicle's drag coefficient cD and frontal area A. Figure 7.19 shows how sports cars reached low levels of cÂ in the 1950s but these could not be further reduced because of roomier interiors, wider tyres and track. The

01 . 1960 1970 1980 1990

Year —► Figure 7.19 Development of air drag (cD A -values) of sedans and sports cars

CO φ υ

c

1350 τ 6000

lbs

1000 _ 4000

£ 500 ο ϋ

2000

The influence of aerodynamics on high-performance vehicles 271

>

\ l ^ y^

^ s

A 0 ^

/ ,

£ A

A y\ ^λ

0 2000 4000 N 60

4° * c < a

0 500 lbs 1000 1350

Wheel Load P —► Figure 7.20 Cornering force as a function of wheel load and slip angle

development of sedans was slower, but recently they have reached comparable drag levels. Record vehicles of recent years are well below these values.

The true wheel transferred load of the vehicle can be influenced by the air stream passing around it. The resulting lift forces involved, whether negative or positive, vary as the square of the vehicle speed. Any change in the wheel load influences the adhesion of the tyres (Fig. 7.20) and therefore the handling of the vehicle.

7.3.2 Handling

Vehicle handling is primarily influenced by the chassis and tyres but can be significantly improved by aerodynamic means—especially at high speeds.

7.3.2.1 Driving tests

Road tests carried out by Flegl7 2 showed that in vehicles with negative lift the maximum lateral acceleration increases with speed (Fig. 7.21). The favourable influence of negative lift forces at the rear axle is illustrated in Fig. 7.22. The test vehicle was fitted with winglets and flaps to generate negative lift at the front and/or rear axle. The steering angle increased with rising lateral acceleration as soon as the rear flaps were extended to create negative lift at the rear. This meant that the vehicle understeered and therefore was more easily controlled. By extending the front winglet, the vehicle tended to oversteer. It is interesting to note that these results were obtained on a 190 m (616 ft) diameter skid pad, which corresponded to a driving speed of only about 120 km/h (75mile/h).

Tests performed by Braess et al.7 3 showed that by reducing lift forces,

272

2.0

O* 1.6

.8

.Qj

"αΐ

5;

12

0.8

0Λ

0

£>~>

rrc

Racing Car

eduction S portscar ^ 'IL· Ci-u-ii"//-»

viIn Spoilei I I

--■£ without Spoiler

50 100 150 km/h 200

0 25 50 75 100 125 mph 150 Velocity u —*■

Figure 7.21 Influence of aerodynamic aids (spoilers) on maximum lateral acceleration

5SW

DEGIm

2-

WINGLETS

FLAPS

WINGLETS AND FLAPS

ClF

-0,22U

0,163

-0,069

CLR

0,060

-0,363

-0,320

^ ^ hs^=STEER/NO WHEEL ANGLE

I = OVER ALL STEER/NO RAT/0

L =WHEELBASE

0,5 15

Figure 7.22 Steady-state cornering behaviour as a function of front and rear lift coefficients


Figure 7.23 Porsche 911 Carrera sports car 1973 with front air dam and rear spoiler to reduce aerodynamic lift

u=202 km/h (125mph)

With without Aerodynamic Aids

Figure 7.24 Vehicle response to steering-step input taking the example of a Porsche 911 Carrera, after ref. 7.3

vehicle response under transient driving conditions such as overtaking could be improved. Driving tests using a Porsche 911 Carrera (Fig. 7.23) showed that by reducing lift forces steering response was more direct (Fig. 7.24).


Reduced lift forces also have positive effects on braking in a turn, where adhesion of the tyres to the road surface as well as other effects of driving dynamics (particularly wheel load transfer) play an important role. The lower graph in Fig. 7.25 shows the deceleration values obtained during braking in a marked-off narrow lane.7 3 The initial trial speed was 145 km/h

With

m u=0 . ,-J.L A Aerodynamic Aids Without J

+±-

u=%Ukm/h(90mph)

Figure 7.25 Braking behaviour of a Porsche 911 Carrera in a turn, after ref. 7.3

(90mile/h). It can be seen that the car equipped with aerodynamic aids to reduce lift forces would brake more effectively and come to a standstill one second earlier than the non-equipped vehicle. In addition the vehicle is easier to control since fewer steering corrections are required.

7.3.2.2 Angle of attack and yawed air flow

Up to now, conclusions have been based on the assumption that the aerodynamic coefficients are constant. During most manoeuvres, e.g. driving over the crest of a hill, the suspension system alters the angle of attack of the vehicle and thus also its aerodynamic qualities. Figure 7.26 represents front lift coefficient as a result of front axle bump and rebound. It has been found that the commonly used front end configurations intensify these movements: during rebound negative lift decreases, thus increasing the bump travel. The opposite reaction would be desirable, in which the bump movement would be lessened. At present, this characteristic can be reversed only by mechanical means, such as wheel-travel control devices (see section 7.4.2).

Yawed air flow conditions are caused by both side wind and cornering. Vehicle tyres require a slip angle to generate a cornering force. This means


0.3 τ

&CLF 0.2

0.1 \

-1.0 in. -0.5

Bump

-30

0.14-

-0.2

-0.3-

^t\CLF MCLAREN CAN AM ^l\CLF 917 LONG TAIL 1971

ΔΓ^ 917/10 FRONT WINGS

0.5 in. 10 Rebound

ΔΖ? — REAR AXLE CONSTANT HEIGHT

Figure 7.26 Variation of front axle lift as a function of angle of attack

that the vehicle can have a yaw angle of the same magnitude, up to about 10° for normal road tyres and up to about 8° for racing tyres. The resulting yaw angle normally causes an increase in drag and a decrease in negative lift (Fig. 7.27). In this situation the increase of lift forces at the vehicle nose should be higher than at the rear, in order to improve stability and consequently safety (higher negative lift at the rear axle causes the vehicle to understeer, see section 7.3.2.1). In addition, the yawed airflow produces side forces. If the centre of pressure is located in front of the centre of gravity of the vehicle, the resulting yawing moment causes the vehicle to turn away from the direction of air flow, having a destabilizing effect, see also section 5.2.3.

Figure 7.27 Variation of drag and negative lift as a function of yaw angle


In the opposite situation, where the centre of pressure is located behind the centre of gravity, the resulting yawing moment attempts to turn the vehicle into the direction of the air flow, as it would a weather-vane, thus increasing stability.

During cornering, the aerodynamic side forces act towards the inside of the corner and thus have a stabilizing effect. This however can be counteracted by the loss of negative lift.

7.3.2.3 Draughting

So far the study has been based on the idea that the vehicle moves in an undisturbed air flow, but in events such as 'stock car' racing the competitors often drive in close formation—so-called 'draughting'. Tests reported by Romberg et al.7 4 with models of such vehicles have proved that the air drag is reduced by up to 30 per cent for the leading car and by 37 per cent for the following vehicle (see also section 8.6.1).

Draughting also has a considerable influence on the vertical forces at the axles, altering the lift coefficients and causing a tendency in both vehicles to oversteer (Fig. 7.28). A study by the Jim Clark Foundation7 5 on the effectiveness of wings on single-seat racing cars driving behind one another

0.5

0.4

0.3

0.2

0.1

I CLF

0

CAR 1

-HI

0Λ

0.3-

0.2

0.1

0

0.1-

0.2-

k A

CAR 1

cLF

*^^ , CLR

H 1 1

|| ,

II 1

CAR 2

Figure 7.28 Aerodynamic forces of two cars draughting, after ref. 7.4


in a straight line showed that lift did not change at the front axle of the following car. However, if the cars were offset by 42 per cent of the vehicle width—a normal racing situation—the following vehicle experienced reduced overall lift, accompanied by reduced negative lift at the rear axle, causing it to oversteer.

7.3.2.4 Theoretical investigation

The basic influence of aerodynamic forces on vehicle handling was examined in 1975 by Scribor-Rylski.7 6 A recent study from Assmann and Witte7 7 on the influence of varying aerodynamic coefficients on various driving manoeuvres was performed by driving dynamics simulations and corresponding computations.

Table 7.2 Influence of aerodynamic coefficient variation on vehicle handling (after ref. 7.7)

Driving manoeuvre

Steady-state cornering

Power-off in a turn Steering step input Cross-wind attack

Effect: + + Very positive,

i Less under-steer ( - )

0

1 +

+ +

-1- Positive, 0 Neutral,

Coefficient variations CL R CS CS R

1 i t More under-steer (+) + + + + +

- Negative, -

0

0 0 +

0to +

+ + + + +

t O t o -

0

■ - Very negative

1 0

0 0 0

Driving manoeuvres such as steady-state cornering, power-off in a turn, steering step input, and cross-wind attack were calculated by varying the aerodynamic coefficients (see Table 7.2), and led to the following conclusions:

• By reducing the lift coefficient cLF at the front axle, the tendency to understeer is diminished and the stability margin at the rear axle is lowered, which has negative effects during power-off and steering step input. • By increasing the negative lift cLR at the rear axle, the stability margin is improved, giving better control under all driving conditions. • Lowering the overall lift cL increases the lateral acceleration potential, which greatly improves handling. • A reduction of the lateral force coefficient cs improves handling in cross-winds, without significant influence on other manoeuvres. • An increase of the rear lateral force coefficient cSR results in improved handling characteristics under all driving conditions, which is attributable to the stabilizing aerodynamic side forces. • An increasing yawing moment cN tends to destabilize the vehicle, mainly under the influence of cross-wind, while a rolling moment cR M reduction has no measurable effects.

7.3.3 Cooling and ventilation

Power unit cooling and cockpit ventilation require a certain amount of air to flow through the vehicle. Sports cars must comply with the same general requirements as other vehicles used on public roads.


Racing cars and record vehicles are usually fitted with simple ventilation systems and in general do not have any heating, but a great deal of attention is given to unit cooling due to the extreme engine powers involved. Some examples of units that require air for cooling purposes are:

• water cooler • oil cooler • intercooler • engine • transmission and other drive train components • brakes • turbo charger, supercharger • exhaust system

In all cases, cooling must be achieved with a minimum air drag, and without affecting the negative lift coefficients.

7.4 Design alternatives

To summarize section 7.3, the aerodynamic requirements for high-performance cars are as follows:

• low drag coefficient and a small frontal area to achieve minimum air drag; • high negative lift-to-drag ratio. Priority is given to either drag reduction or negative lift increase, depending on intended purpose; • higher negative lift at the rear than at the front axle. No lift should occur from yawed air flow up to about 10 to 15 degrees yaw angle, depending on intended use; • in the case of yawed air flow, generation of a stabilizing yawing moment about the vertical axis; • sufficient cooling and ventilation without significant deterioration of the aerodynamic coefficients.

In most cases these requirements can be adequately fulfilled by the following design alternatives:

7.4.1 Drag and lift

The drag force is proportional to the product of drag coefficient and frontal area. Minimizing both factors in a high-performance car often has conflicting results.

It is not always possible to lower the drag coefficient because regulations might stipulate uncovered wheels, wide tyres must be mounted for improved traction, high negative lift forces are required, or a large volume of cooling air is necessary. All these requirements tend to increase the drag coefficient. The reduction of the frontal area is limited by the wide track required for handling reasons, and the large diameter wheels necessary for racing brakes.

Body design has a decisive influence on air drag. Some particular features can be noted, according to Flegl.78 For example, a tapered

Design alternatives 279

slender front end reduces air drag. It is not sufficient, however, to taper the upper and lower sides identically, as pressure builds up under the front end thus producing lift forces. For this reason the front end should be sloped down, to create a low drag coefficient and negative lift.

CD = 0.21*0 CLF = 0.198

CD = 0.223 r = 0.022

CD= 0.224 CLF =-0.094

Figure 7.29 Aerodynamic coefficients of different front end configurations

4 .

0Λ

-0.2·

-0.U

-0.6+

-OjBi

-1.0·

HI H 0.5 0.6

—\ 1

Variation: Angle of Wing

917/10

917/30 Figure 7.30 cjc^ graphs for different racing cars


The data shown in Fig. 7.29 were determined from a 1:5 scale model with a smooth underbody. It can be seen that lift decreases as the front end is inclined. Minimum drag conditions are achieved as the lift approaches zero, as shown in Fig. 7.30 (see also Morelli7 9).

Today's vehicles rarely have a smooth underbody, because certain chassis components cannot be easily incorporated and other elements, such

150τ

(bs\

100

50]

0J

υ.αυ

kN

0.60

0A0

0.20

Air Dam

—

I I I With . . Without Aerodynam,

ΛΓ

^-^^

REAR SPOIL

I

I ^ 4.

/ "

:R

/ •

c Aids

/

/

A /

/

20 40 m/s 60

0 50 100 mph 150

u Figure 7.31 Front axle lift as a function of driving speed and the use of aerodynamic aids (Porsche 911 Carrera)

0.03T

REAR AXLE CONSTANT HEIGHT

-0.03

Figure 7.32 Variation of drag coefficient as a function of front end height


as the exhaust system and ancillaries, need to be exposed to an air stream. Air drag can however be minimized by deflecting the air away with an air dam (see also section 4.3.2.9). This also reduces the lift forces (Fig. 7.31), as does reducing the ground clearance (see also Fig. 4.125). By lowering the vehicle front the air drag diminishes, because the effect of the front air dam is intensified (Fig. 7.32).

Figure 7.33 compares different separation cross-sections at the rear end. A small wake area is desirable, and can be obtained either by tapering the rear end abruptly or by tapering it moderately—thus increasing the overhang. Steep tapering, though, is limited as the resulting flow separation increases air drag, as has been confirmed by Hucho7 10 (see also section 4.3.2.5).

Figure 7.33 Aerodynamic coefficients of different rear end configurations

It has been found that all drag-reducing measures have an influence on the lift forces. For driving safety and handling, high-performance cars must have negative lift, so the most efficient aids must be selected, i.e. those with the maximum cL/cD ratio.

There are three main ways to generate negative lift:

• variation of the basic vehicle configuration • mounting of negatively inclined wings • built-in ground effect.

The basic vehicle configuration for minimum lift or negative lift has a low concave nose, a smooth upper surface, and an elevated tail section. As shown in tests by Braess et al.7 3 (Fig. 7.34) it is also possible to use a rear spoiler, the decisive feature being the relative height of separation in relation to the rest of the body. Another way of inducing negative lift is to


f 300

LR lbs

200\

100

kN

1.00

OSO 1

1

I Air Dam

I I 1 1 ^houf Aerodynamic Aids

1 \REAR SPOILER

^^Γψ^ Si 10 ■■/ \J

^

i / y

y y

A y

'-L-L-

/ / / /

/ /Ί

20 40 m/s 60

0 50 u

100 mph 150

Figure 7.34 Rear axle lift as a function of driving speed and the use of aerodynamic aids (Porsche 911 Carrera)

obtain a negative angle of attack by lowering the front end of the car or raising the rear.

High negative lift values of up to about cL = - 1 are obtained with negatively inclined wings, the effect of which increases with clearance above the body surfaces as they enter the undisturbed air flow. Additional

PORSCHE 917/30

0.5

-0.65

0.55 0.6

-0.74

WING: NACA 63-412 1.95m *0.75m

(6M*2.5ft.)

= -10°

-0.75

Figure 7.35 ^κ/εΌ graphs of a Porsche 917/30 race car equipped with a rear wing


force can be obtained by positioning the rear wing(s) far behind the rear axle and the front wing(s) as far in front of the front axle as possible (regulations permitting) thereby producing a greater leverage about the centre of gravity.

Figure 7.35 shows the angle of attack graph of a Porsche 917/30 rear wing with which an average AcLR/AcO ratio of 1.83 was obtained. Figure 7.36 illustrates the increase of the drag coefficient as a result of increased negative lift. The rear wing gives a better C^CD ratio than lifting the break-off edge.

0Λ 0.5 0.6

-0.11

-0.2-

-0.3{

-0Λ

-0.5-

Figure 7.36 c^lc^, graphs of different rear end configurations

REAR WING SIDEPOD FRONT WING

- VENTURI CHANNEL

Figure 7.37 Schematic drawing of the underbody of a ground effect single-seat racing car, after ref. 7.21


The ground effect is based on the theory that the vehicle underbody and the track surface constitute a venturi nozzle producing a low pressure area below the car and thus creating negative lift forces. The negative pressure is maintained by lateral skirts fixed to the car and preferably touching the

c,

-0.1

-0.2

-0.3

-0.4

Ground Clearance b tn. I

50 mm 100

^—ΛΊ\

Ο^^ΞΓθ ///7?7///;///;//////;/77////

-0.7 L Figure 7.38 Negative lift coefficient of a ground effect car as a function of ground clearance, after ref. 7.11

SKIRT GAP s — 0 0.5 1.0 in. 2.0 I I I I i

A 0 10 20 3Q mm 50

Q -0.7-

-0.2

-0.3

-0Λ

-0.5

-OS

-0.7* GROUND

Figure 7.39 Negative lift coefficient of a ground effect car as a function of skirt gap, after ref. 7.11


ground (Fig. 7.37). The advantage of ground effect is that it allows very high negative lift forces with favourable drag values.

According to Wright7 n the negative lift coefficients of Formula 1 racing cars reached cL = —2.6, corresponding to a negative lift force of 16 kN (3600lbs) at 290km/h (180mile/h). The vehicle weight was 6.5kN (1460lbs). The ground effect accounts for about 80 per cent of the overall negative lift; the negative pressure between the ground and the underbody can achieve local values of up to cp = -2 .0 . Negative lift will peak at a given ground clearance (Fig. 7.38) and is strongly dependent on the skirt gap (Fig. 7.39).

When wind tunnel testing a similar type of racing car (see Faul7 1 2), a cJcO ratio of approximately 300 was measured for the ground effect, a very high efficiency and far in excess of that realized with negatively inclined wings. Here again, the influence of the gap between the skirts and the ground was confirmed (Fig. 7.40).

-0.5

-1.0

-1.5

OS 1.0

i© NO FRONT AND REAR WINGS

Q)=®

V)N0 SI DE PODS

pSKIRTS S= 87mm (342in.) k)SKIRTS S= 52mm(2.05in.)

SIDEPOD

kDSKIRTS S = 2mm(0.08in.)

Figure 7.40 cjc^ graph of a ground effect single-seat racing car with different body configurations, numerical data after ref. 7.13

The Porsche 956 (Fig. 7.7) demonstrates that a considerable amount of negative lift can be produced with a profiled underbody without using skirts.

7.4.2 Handling

Vehicles reaching very high speeds, such as racing cars but in particular record vehicles, are required to have inherent directional stability to enhance safety and to reduce stress on the driver. The vehicle should have


a relatively long wheelbase and negative lift should be present at all axles, being more pronounced at the rear than at the front to produce more understeer as speed increases.

Cross-wind sensitivity can be minimized by locating the pressure centre behind the vehicle's centre of gravity, thus creating a counteracting moment under the influence of a yawed air flow. This can be achieved by a vertical tail fin, which generates a yawing moment about the vertical axis (see Fig. 7.41).

7—FIN

Figure 7.41 Influence of a rear vertical fin on yaw moment

Another method of dynamically stabilizing the vehicle by using movable aerodynamic devices is described by Mezger.7 13 Movable flaps or ailerons are fitted to the suspension in such a way that each flap swings upwards as the corresponding wheel rebounds and vice versa (Fig. 7.42). For example, in a left-hand turn, as the vehicle is forced to roll to the right about its longitudinal axis, the inner left wing will rise to create a rolling moment until the vehicle reassumes a horizontal position. Correspondingly, the flaps go up as the vehicle passes over the crest of a hill with all wheels in rebound condition. The resulting negative lift forces press the vehicle back onto the road surface.

Another system is to fit the struts of the wings directly to the wheel hubs. This avoids the reduction of spring travel with increasing negative lift, thus improving the vehicle's handling properties.

Unfortunately, these safety devices fall within the scope of moving aerodynamic aids, which are prohibited by current race regulations.

7.4.3 Cooling and ventilation

Although there are general guidelines for the optimum design of air inlet, cooler location or air outlets, each vehicle requires its own solutions according to the special conditions, vehicle layout, and function.


Position of Flaps in a Left Turn

I !

Effect of Flaps over a Hump Figure 7.42 Movable wheel-travel controlled flaps for stabilizing purposes, after ref. 7.13

A large volume of air flow through a radiator is achieved by creating the highest possible pressure difference between the cooling air inlet and outlet, so that the air is conducted through a closed channel (see sections 4.3.2.12 and 9.3.1).

Larrabee714 recommends as large a radiator as possible, air flow controlled by graduating the inlet duct cross-section. To minimize the increased drag due to cooling air flow, a radiator with a small inlet combined with a diffuser for relatively slow flow velocities through the radiator matrix is suggested by Bosnjakovic.7 15 The warmed air is then accelerated and expelled (Fig. 7.43). According to Amato7 16 this system could be used to produce thrust if the air were to be sufficiently warmed. In practice, though, such conditions are unlikely to be realized because of lack of space.

The most convenient position for the cooling unit is at the front of the vehicle. Positioning the intake at the stagnation point and the outlet on the negative pressure area on the top surface of the nose produces a large airflow due to the high pressure difference (see also Fig. 4.96c). A further advantage is that the negative pressure under the vehicle underbody—and therefore negative lift—is not affected. One of the main drawbacks is the


Figure 7.43 High-efficiency radiator arrangement

restricted amount of space in the nose, which limits the possibility of optimizing the air ducting.

An air intake system known as the 'NACA inlet' has proved to be very effective since it has only minor influence on overall air drag (see Reilly717).

The Porsche 956 air ducts (Fig. 7.44) illustrate these design guidelines. The air inlets required for front brake cooling are arranged in the vehicle nose. The oil cooler, intercooler, engine air induction and water radiator are located in lateral sills close to the engine. Engine cooling air is taken in through a NACA inlet in the roof and carried away through louvres in the underbody. Three NACA ducts located on the rear upper side of the car are air intakes for the rear brakes and the transmission radiator. The cockpit is ventilated through a slot in front of the windshield.

COCKPIT VENTILATION

WATER ENGINEÎNTERCOOLER COOLER AIR

Figure 7.44 Air inlets and outlets of the Porsche 956

Special problems 289

The specification for the Porsche 956, which stipulated a maximum vehicle height of 1.1m (43.3 in), precluded the installation of an 'airbox'. This device, which can be seen in Fig. 7.6 on a Porsche 936, is often used to supply the engine with pressurized cooling or intake air. By selecting such a design the drag coefficient of the Porsche 936 was reduced by 18 per cent, while cÂ was lowered by 11 per cent when compared with the previous model. In addition, these measures doubled the pressure in front of the fan and the intercooler, thus reducing the cylinder temperature by 15°C (27°F) and the intake air temperature by 17°C (31°F).

Record vehicles intended for short runs only may function without any air cooling, thus permitting a reduction of the drag coefficient. Instead it might be feasible to fill the cooling system with ice to ensure sufficient unit cooling during a record attempt.

7.5 Special problems 7.5.1 Lap time and fuel economy

One of the main goals of a racing car is to attain the shortest possible lap time. Without considering engine and chassis, the lap time is strongly

HIGH SPEED CIRCUIT TYPICAL RACE CIRCUIT

1.00

0.97

0.9U

0.91 A

Figure 7.45 Fuel economy and lap time as a function of negative lift


determined by the cJcO ratio. Maximum speed can be increased by reducing the air drag coefficient, but this is usually accompanied by less negative lift forces and thus reduced cornering speeds.

Road tests or calculations are required to obtain an optimum vehicle layout for a particular race track. As can be seen from Fig. 7.45, the negative lift cannot be great enough for a short and twisting race track, whereas on a high-speed course with long straights, a low drag coefficient is advantageous.

High negative lift results in increased air drag causing low fuel economy, more refuelling stops and, consequently, loss of time. In the worst case it may be impossible to comply with fuel consumption regulations, allowing only a certain amount of fuel for the race. For this reason it must be determined what degree of negative lift is acceptable for a given fuel allowance. The most economical measures must be taken to develop negative lift, i.e. the cL/cD ratio should be as high as possible.

7.5.2 Near-sonic speeds

When designing record cars intended to reach near-sonic speeds, air compressibility can no longer be neglected. Special design measures are required, which have been discussed by Torda and Morel,7 18 taking the example of the 'Blue Flame'.

In 1970, the rocket propelled Blue Flame (Fig. 7.3) reached a record speed of 1001.67 km/h (622.41 mile/h). Increasing the speed from M = 0.5 to M = 1.2 raised the drag coefficient by 200 per cent (Fig. 7.46). Therefore extreme care was given to a low drag body design and an extremely slender basic body with an ogival nose shape was chosen. The front wheels were integrated into the body contour in order to reduce the frontal area.

i

r 0.6

0Λ

0.2

—ESTIMATE —MEASURED IN ACTUAL

RUNS

0 0A OJS 0.8 W U M

Figure 7.46 Drag coefficient increase of the Blue Flame as a function of Mach number, after ref. 7.18

Special problems 291

To ensure controllability at all speeds, lift forces were absolutely avoided. However, when breaking the sound barrier an interesting phenomenon occurs: the negative pressure existing under vehicles in the vicinity of the ground is inverted to produce positive lift forces. This is explained by the fact that in the subsonic range the air between the vehicle underbody and the ground is accelerated, thus creating low pressure. At supersonic speeds, however, the shock wave caused by the vehicle nose is reflected by the ground, producing a pressure increase which is transformed into lift forces. So when passing from subsonic to supersonic speeds, the inverted vertical forces change the vehicle's angle of attack and may result in instability.

As this phenomenon is particularly marked with flat underbodies, the vehicle was provided with a cross-section in the shape of a triangle standing on its apex and with rounded corners. Further, the longitudinal axis was inclined negatively by 1.5° and a slight nose droop incorporated. The vehicle was trimmed by means of small 'canards' or flippers at the nose. Longitudinal stability was increased by installing a vertical fin at the rear, shifting the centre of pressure behind the vehicle's centre of gravity (see section 7.4.2). In this way the Blue Flame displayed stable handling up to near-sonic speeds.

7.5.3 Uncovered wheels

Single-seat racing cars (see section 7.1) are equipped with uncovered wheels, freely exposed to the air flow.

Wind tunnel tests by Cogotti7 19 with uncovered wheels furnished the following information (see also section 4.3.2.8):

• the drag coefficient of a rotating passenger car wheel, which is about 0.6 can be reduced to 0.5 by providing the rim with a smooth cover; • rotating wheels have a slightly lower drag coefficient than stationary ones; • wheels produce lift forces, being greater for stationary than for rotating ones.

When considering the whole vehicle, the four wheels interfere with the body thus creating quite complicated effects, which have not yet been fully investigated in wind tunnel tests due to the ground simulation problems involved (see section 11.4.1). To minimize these effects, deflectors ahead of the wheels and between front and rear wheels can be used to guide the air flow and so to avoid excessive turbulence.

7.5.4 Development methods and simulation

The development of high-performance vehicles in the wind tunnel poses problems that are more acute than when developing road vehicles for the following reasons:

• Wind tunnels available for vehicle investigation are usually not designed for speeds of 250-400 km/h (150-250 mile/h) for sports cars and racing cars or over 1000 km/h (620 mile/h) for record vehicles. So special effects such


as the actual attitude of the freely suspended car relative to the ground and possible distortion of the outer panels under the influence of wind forces cannot be recorded under all driving conditions. • The boundary layer, building up on the test section floor (see section 11.3.2), affects the flow conditions below the vehicle underbody and cannot be neglected, because of the significantly lower ground clearance of racing and record cars as compared to more usual road vehicles. The boundary layer reduces the air flow rate under the car and does not equate with conditions on the road. So the forces involved, particularly the vertical forces, cannot be determined with precision. • The simulation of wheel rotation in wind tunnel testing is difficult due to severe problems in measuring the forces transferred between rotating wheel and ground. Correct reproduction of the flow conditions around the wheels is of special importance for evaluation of vehicles with uncovered wheels.

In an attempt to eliminate the two latter problems, special model wind tunnels were developed. There the balance is mounted above the test section suspending the car body by means of struts. The test section floor is equipped with a moving belt running at air speed. The wheels are not connected to the body but supported from outside and driven by the moving belt (see e.g. Fackrell ). The disadvantages of this solution are that the forces acting on the wheels cannot be measured, the data evaluated are affected by the suspending gear connecting the model with the balance, and yawed air flow can only be simulated by complicated technical means.

Figure 7.47 Examples of a panelled sports car body (above) and a racing car body (below), after ref. 7.22

Trends in future high-performance vehicle development 293

A feasible solution seems to be a boundary layer suction system under the test section floor, not taking wheel rotation into account, see Figs 11.15 and 11.16.

Numerical methods will find increasing application in future aerodyna-mic development, not only because of simulation problems in the wind tunnel. The panel/boundary layer calculation can be a useful tool to determine air flow conditions. Figure 7.47 shows two panelled vehicles as needed for calculation purpose. This procedure, however, does not permit precise analysis of the flow separation areas as a result of the mathematical model of the air flow. More precise simulation methods are under development and details are to be found in Chapter 13. In view of some of the wind tunnel simulation problems described and numerical methods still under development, road tuning is of particular importance when developing a high-performance car.

As far as cars for closed circuit racing are concerned, tuning on a skid pad with circles of different diameters has proved to be helpful. A small circle of about 50 m (160 ft) in diameter serves to tune the chassis, while a bigger circle of more than 200 m (670 ft) in diameter can be used to adjust the aerodynamics. After this basic adjustment, the vehicles are tested on a track. Final tuning for the racing event is carried out on the particular race track.

7.6 Trends in future high-performance vehicle development

Socio-economic factors as well as technical advances will play a decisive role on future development in the automobile industry. On the basis of past history and the present state of technology, it is possible to identify some trends in the future application of aerodynamics on high-performance cars.

Sports cars To improve fuel economy, further efforts will be made to decrease drag, which is attainable by reducing frontal area as well as drag coefficient.

For production cars, zero overall lift is desirable, which basically is in compliance with low drag, yet rear axle lift should always be somewhat lower than at the front to help handling and stability at high speeds.

The best possible solution of the conflicting aims of minimum drag and low cross-wind sensitivity will be a stringent design goal for the future. Racing cars Obviously development will be strongly affected by future racing regulations. The present trend places emphasis on fuel economy. This factor might put an end to the emphasis on negative lift observed during recent years.

Record vehicles Reaching the sound barrier has been a goal long sought after and finally achieved. Further increase in speed will be limited because sufficiently long test tracks are not available to allow such vehicles to accelerate, be measured and come to a stop. Emphasis might instead be placed on


realizing fuel economy records at high average speeds, thereby providing incentives to production car development.

7.7 Notation

A FE L LF

LR M P S T ax

ay

b CO

CL

C L F CLR CP CRM

cs CSR CYM d g i s t u A oc

ß Osw

î

frontal (cross-sectional) area fuel economy wheelbase lift at the front axle lift at the rear axle Mach number (speed of sound M = 1) wheel load cornering force lap time lateral acceleration lateral acceleration ground clearance drag coefficient lift coefficient lift coefficient at the front axle lift coefficient at the rear axle pressure coefficient rolling moment coefficient side force coefficient side force coefficient at the rear axle yawing moment coefficient distance between two vehicles acceleration due to gravity overall steering ratio distance between skirt and road surface time air flow velocity difference between two adjacent values angle of attack yaw angle steering wheel angle distance coefficient

Chapter 8

Commercial vehicles Hans Gφtz

8.1 Introduction

Rising fuel prices and the need for profitable operation encourage the commercial vehicle manufacturer to exploit all opportunities for minimiz-ing fuel consumption. One such opportunity is aerodynamic efficiency.

Although aerodynamics is of no significance for construction site and agricultural vehicles etc., for high-speed inter-city and long-distance transportation it is increasingly important. High-bodied commercial vehicles, touring coaches and delivery vans are therefore the targets for improved aerodynamic design to reduce fuel consumption (Fig. 8.1).

Figure 8.1 Variety of commercial vehicles. The traffic signs indicate the related speed limits in Germany in km/h

8.2 Tractive resistance and fuel consumption

Fuel savings through aerodynamic refinement must be viewed in the context of the energy necessary to overcome each element of resistance, such as rolling resistance, air drag and climbing resistance (Fig. 8.2). At

295

296 Commercial vehicles

Drag and Rolling Resistance

Tyre Rolling Resistance

> * 0.2

'"§ = CO

1 20 40 60 80 100 km/h

Figure 8.2 Components of tractive resistance

constant speed on a level road, rolling resistance usually exceeds air drag. Even at medium speed, air drag only exceeds rolling resistance in the case of light trucks and vans, and, in heavy truck combinations, only above 100km/h (62mile/h). Nevertheless, air drag must not be ignored even for heavy units when one considers that the power required by a high-bodied 38-tonne truck train to overcome air drag is 25 kW at 60 km/h (37 mile/h) and 60kW at 80km/h (50mile/h).

In practice, climbing and accelerating modify the idealized constant-speed level-road relationship, as shown in Fig. 8.3 for the main categories of utility vehicles. Aerodynamic drag is however still significant.

^w

Q

ñéééééâ i

�� | —

H i

� �

0 20 40 60 0 20 40 60 80

1/100 km Fuel Consumption

► Drag

l H Rolling Resistance

I | Acceleration - and Climbing Resistance

Figure 8.3 Percentage of fuel consumption of different vehicles related to components of tractive resistance

297 /0 Components in Fuel Consumption

1001 U M

Level Moun- Federal Moun-Road tainous Highway tainous

Average Motor- Average Route Speed way Speed

72 km/h 57 km/h

► Drag

[ H I Rolling Resistance

[ I Acceleration - and Climbing Resistance

Figure 8.4 Fuel consumption of a 38-tonne tractor-semitrailer to overcome tractive resistance components for different route profiles

Components in Fuel Consumption

H Drag

f i l l Rolling Resistance

[ I Acceleration - and Climbing Resistance

► I Stops (Idling) 100 km/h 80 km/h

Level Road Partly City Bus hilly

Motorway Intercity Bus

Figure 8.5 Fuel consumption to overcome components of tractive resistance for city and intercity buses

Ξ1

TO

' c 00

Fue

l S

avi

ng

ro

ro

ro

o

^'

.'"

^

>'

o Φ < J3

O

03

Q.

O o 3

.''

1

o o IS

a "

3E

\ n>

\ r

o \ °

"

\ 1

v\y

\ /

\

Hilly way —

<7>

1 tr

*Zr^

n

^y

I..

o

* if

a>

1

·α>

... t*<

1

o T

φ7

1

/ o'

1

ro

o

CO

o -&>

o

CJl

o

Γ)

σ 71

ù

c o

o

D

TO

* e 00

O

N

Fu

el

Sa

vin

g

no

o

3 C —

o

O

3 C

/2 3 -a o

3 O

CO

00 o

3 3 ft»

O

o H

Ö

Q.

C

O

'±

o

D

ai

ro

o

ro

en

CO

o

CO

en

o^

1 1

! 1

/ r~

f

CD < Ö

O

0)

Q.

1

1

l/ 1

-i i

" 1

'=lf

CQ

·

i 1

I;

j &

r//

. 1

i |

Aerodynamic drag coefficients of different commercial vehicles 299

Figure 8.4 shows how the contribution of aerodynamic drag varies from 2.5 to 35 per cent, with road profile and speed, for a 38-tonne tractor-semitrailer combination.8Λ Figure 8.5 shows similar resistance components for a bus. Tests up to 100 km/h (62mile/h) showed that air drag dominates on level road. At the lower average speeds of city traffic the acceleration component predominates.

8.3 Drag reduction and fuel consumption

The effect of drag reduction on fuel consumption in actual operation can best be shown with typical vehicles in typical driving conditions, as in Fig. 8.6. Here the fuel savings are based on overall consumption in real conditions such as 'very difficult route' or 'highway', as opposed to idealized level-road constant-speed driving.

The reduction in consumption of the bus (Fig. 8.7) is modest in city traffic, though a separate bus lane provides definite fuel economy advantages. Light trucks or vans are less dependent on set routes (Fig. 8.8).

Reduction of Drag

Figure 8.8 Influence of drag on fuel consumption of light van

Thus reductions in drag are worth while for heavy trucks and buses on motorways, and for light trucks, minibuses and vans even on more 'difficult' routes.

8.4 Aerodynamic drag coefficients of different commercial vehicles

It is not solely the appreciably larger frontal area in comparison with the car that is responsible for the high aerodynamic forces acting on the commercial vehicle. The frontal areas of a high-bodied truck, bus, light van


Figure 8.9 Vehicle frontal area

and car are in the ratio of about 9:7:4:2 (Fig. 8.9). A decisive influence is the aerodynamic quality of the vehicle shape, the drag coefficient cD.

8.4.1 Operation in still air

With their many different shapes and sizes, commercial vehicles have a wider range of drag coefficients (Fig. 8.10). Buses have drag coefficients cD

Figure 8.10 Drag coefficients of different commercial vehicles

about IV2 times those of cars and tractor-semitrailer units, and trucks and trailer units about double. Only light vans, which lend themselves more readily to aerodynamic improvement, have drag figures close to those of cars.

8.4.2 Drag as a function of yaw angle

The drag coefficient at zero yaw angle, equivalent to driving in still air, gives insufficient indication of aerodynamic characteristics in real operation, where the tangential force coefficient cT (due to yaw) must be taken into account (Fig. 8.11). All vehicle types—with the exception of the light van—show a marked increase in cT with increasing yaw angle.

Aerodynamic drag coefficients of different commercial vehicles 301

b'r*l i I 1 113

30° Yaw angle

Figure 8.11 Drag versus yaw of different vehicle types

8.4.3 Wind influence—definition of yaw angle

The magnitude of the angle of yaw is related to road wind conditions, though the wide ranges of wind speed and direction mean that we have to content ourselves with a rough estimate.

If we base our estimate on the wind conditions at international airports, presented as wind 'compass cards' (Fig. 8.12), we find that wind forces of Beaufort 4-5 (20-39 km/h, 12.5-24 mile/h) and above only occur about 20 per cent of the time on an annual average basis,83 lighter winds predominating. Aerodynamic drag tests at maximum permissible speed are therefore adequately covered by a yaw angle of ø < 14°.

Frequency

20 15 10

Beaufort scale

0-11 16 20-39 >41 km/h 0-8 11 14-26 ^ 2 7 Ø° at VT = 80 km/h

Figure 8.12 'Compass card' illustrating frequencies and directions of winds of different strengths


8.4.4 Characterization of air resistance in actual operating conditions

To make allowance for the influence of cross-winds, various formulae have been proposed to represent a wind-averaged drag coefficient cD. According to Ingram, the wind-averaged drag coefficient, cD, is defined as

2ð

cO = if Jo Jo

cD(i|0{l + (V/VT)2 + 2(V7VT)cos cp}/?(V,cp)dcpdV

where ñ( í ,ö) is the probability that a wind of speed V is blowing at an angle ö relative to the vehicle (see Fig. 8.13). This averaging process takes into account that the velocity of the air relative to the vehicle (upon which the aerodynamic drag depends) is different from the road speed of the vehicle.

Figure 8.13 Relative wind vector diagram

C = 1.09

band of yaw angle according to SAE-J 1252

^DSAE-JT252 { B f ^DzEROYAW

C,

0° 5° 10° 15°

Yaw angle

Figure 8.14 Wind-averaged drag coefficients cD of different aerodynamic tractor-trailer devices according to the SAE-1252 procedure

Reducing aerodynamic drag 303

The equation can be evaluated by a computer program incorporating a numerical integration, using measured data of cT for a range of values of ö, and data on the distribution of wind speeds. The distribution of ö is evaluated from wind direction data and data on the usage by heavy goods vehicles of motorways orientated in different directions.

On comparatively compact bodies the wind-averaged drag cD at 30 m/s is less than 10 per cent greater than the drag at zero yaw, but for more complex shapes the increase is much greater, according to Naysmith.8 5 A road speed of V = 55 mile/h (89 km/h) and a typical wind velocity of VT = 7mile/h (11 km/h) are used as a basis for evaluations in the USA (SAE-J 1252).

Typical cD graphs representing different body configurations are shown in Fig. 8.14. According to SAE-J 1252 we find wind-averaged cD figures 6 to 19 per cent higher than those at zero yaw.

8.5 Reducing aerodynamic drag 8.5.1 Scope for aerodynamic changes on commercial vehicles

Unlike the car, the shape of a commercial vehicle is determined mainly by the cargo space. Cuboid, sharp-edged bodies predominate. Statutory size limits impose restrictions on this requirement (Fig. 8.15). Little scope

! 1 P '

I ! I

I

10 20 30 t Gross weight

Figure 8.15 Permissible vehicle lengths and gross weights

remains to the aerodynamicist for changing the shape of the load-carrying part of the vehicle. However, there is some freedom in designing the front end of the vehicle or the cab and developing drag-reducing add-on devices.

8.5.2 Optimization in the wind tunnel—problems of model measuring techniques

The wind tunnel is the ideal location for systematic development work. However, tunnel dimensions for commercial vehicles are problematic. Precise aerodynamic measurements can just about be made on full-size

0 5 10 15 m

Vehicle length


small trucks and buses in the large wind tunnels available today. Larger vehicles create too large an obstruction in the test section, both lengthwise and crosswise. They must therefore be studied in scaled-down form. But how safely can the results on models be applied to the original vehicles?

The prerequisite for this is similarity in geometry and flow dynamics; that is, precise and detailed replicas of the originals and identical Reynolds numbers for model and full-size version, see Chapters 2 and 11.

A loss of surface detail is inevitable in small models (scale 1:10). Moreover, in spite of the high speeds (250km/h, 155mile/h) of some automotive wind tunnels, Reynolds numbers are still lower than with corresponding vehicles travelling at a road speed of, say, 80km/h (50mile/h). Allowance must therefore be made for the differences in airflow between model and full-scale vehicle, which are manifested, for example, in a different location of the transition from laminar to turbulent boundary layer and/or the flow separation points. Thus in measurements on a one-tenth scale tractor-semitrailer model (Fig. 8.16) dependence on

cD

0.7

0.6

0.5

0.4

0.3 1/5-scale model (passenger car)

full scale passenger car

2 4 6 8

Figure 8.16 Influence of Reynolds number on drag

10.10 6 Re= U o o ' l

Reynolds number is obvious. Only at airstream velocities about 300 km/h (186mile/h), at which compressibility effects are no longer negligible (see section 11.4.2), does the drag coefficient approach its value for the appropriate Reynolds number (dotted line).

On commercial vehicle models—unlike car models—this behaviour is essentially dependent on the shape of the vehicle front end. On a bus with critical front radii, for example, quite different curves result depending on radius. The studies by Pawlowski8 6 and Hucho et al . 8 7 led to similar results, see section 11.4.2.

Measurements on small-scale models, apart from those with complicated boundary layer corrections, can only approximately reproduce real conditions. In many cases, therefore, they are only used for qualitative, preliminary studies.


Most model studies are with 1:2.5 scale models, which more closely represent true flow conditions as well as air flow through radiator, engine compartment, etc. The aerodynamic force coefficients obtained on these models agree well with those measured on full-size vehicles. Soiling simulation can also be performed on them remarkably well.

8.5.3 Drag minimization on trucks

8.5.3.1 Characteristic flow and pressure conditions

If we look at the airflow conditions on the most common group of high-bodied truck and trailer and tractor-trailer units, photographs of flow using smoke (Fig. 8.17) indicate strong interaction between cab and body. The gap width s, measured from the cab rear end to the body front end, and the projecting body height h, measured above the cab roof, are essential parameters in this relationship.

The pressure distribution over the vehicle (Fig. 8.18), with high positive pressure zones at the front of cab and body and negative pressure at the

306

Center Line

Belt Line

Pressure ratio Cp

Figure 8.18 Pressure coefficient cp on cab and bodies, centre section, zero yaw angle, for truck (top) and tractor-trailer train (bottom)

Cab _ t Front rprd

or β· β· Ö _·

Pressure ratio CD

Velocity ratio Vx/Uoo ?e3S «S3 oSS

S ,

Distance from front of vehicle

5 § § E | I 2

Figure 8.19 Velocity ratios Vx/U^ of the flow about the vehicle and pressure coefficient cp in the centre section for a symmetrical flow on a semitrailer with box-like body (height 3.67 m), after ref. 8.8


rear of the vehicle due to separation of flow, is characteristic of blunt, sharp-edged bodies having high aerodynamic drag.

Further information about the quality of a vehicle shape is provided by the near-field velocity distribution. Figure 8.19 (see ref. 8.8) shows the horizontal velocity component Vx, related to the velocity ßË» of the undisturbed free airstream, along the centre cross-section of the vehicle.

On top of the sharp-edged vehicle roof, areas of reverse flow are visible (indicated by non-shaded areas), which characterize the turbulent zone with recirculation flow in the separation bubble. On top of the trailer a fairly thick boundary layer is developing. At the rear the typical large wake is formed.

8.5.3.2 Partial resistance—interference problem

From an aerodynamic viewpoint, tractor-semitrailers and truck and trailer units in an airstream are 'formations' made up of various sub-bodies which interact with each other (the problem of interference, see refs 8.8, 8.9, 8.10). To get a better understanding of individual aerodynamic measures, the forces on the sub-bodies have to be treated separately.

Gap width S Yaw angle

Figure 8.20 Partial drag-components for 8-ft container semitrailer unit

Figure 8.20 shows an example of such a drag breakdown. The total drag of a semitrailer unit has been divided into the partial drag for cab, chassis and body. With relative wind from straight ahead, the partial drag of body, cab and chassis are in the ratio of about 4:3:2. With increasing gap s, a slight increase in drag is observed. With relative wind from an increasing yaw angle, the drag coefficient cD 'body' and 'chassis' rise distinctly. This results from the leeward separation of flow and the flow of air about the cleft chassis. By contrast, the drag coefficient cD of the 'cab' in yaw is hardly increased by side wind.

308

H = 3.97 m

0 * ► i 1 0° 5° 10° 15°

H = 3.97 m

U � | | | 0° 5° 10° Yaw angle 15°

Figure 8.21 Partial drag coefficients of tractor and semitrailer (top) and motor truck and trailer (bottom), after ref. 8.8


In a similar way, the drag coefficient of a semitrailer can be divided into the constituents of tractor and semitrailer according to Fig. 8.21.8 8 In the range of yaw angles relevant for trucks (see section 8.4.3), the drag of the tractor is fairly constant with yaw. The increase of the total drag with yaw is solely caused by the semitrailer. The main reason for this is the cross-flow of air through the cab-trailer gap with subsequent flow separation on the lee side. This increases the forebody drag of the semitrailer. Other reasons are the change of the flow at the rear end of the semitrailer (compared with symmetric conditions), with enlargement of the turbulent wake (larger semitrailer base drag), as well as the increased flow of air into the unshielded side chassis area.

The partial drag coefficients of motor truck and trailer on a truck train are divided in the ratio of 70:30. Both drag coefficients rise at about the same rate with increasing angle of yaw, so that motor truck and trailer contribute approximately equal parts to the appreciable rise of the total drag coefficient of this train configuration. The causes are the leeward separation of flow at the vehicle's front and the direct flow against the projecting motor truck body, with enlarged frontal drag of the same. Air flow from the side through the gaps between cab, motor truck body and trailer increases with increasing angle of yaw, inducing additional leeside separation of flow. This results in rising frontal and base drag of the body sections concerned. As on the tractor-semitrailer, the changed flow (compared with directly oncoming wind) from the trailer rear end, with enlarged turbulent wake, contributes to the increase of the overall drag coefficient of the truck train, as does increased flow of air into the gap and unshielded chassis area.

8.5.3.3 Cab shape

From Fig. 8.22 almost the same drag coefficients are to be seen for a tractor-semitrailer with sharp-edged cab and one with a streamlined cab, both with identical overall dimensions and identical body and chassis. This might lead to the conclusion that the shape of the cab has only minor influence on air drag. But looking at the partial 'body' and 'cab' drags for symmetric flow, it becomes evident that the sharp-edged cab takes the full air drag and completely shields the body behind it because of the distinct separation of flow, so that the body may have zero or even negative partial drag. This 'redistribution of drag' is also evident from the measured pressure distribution across the centre section of the vehicle front, see Fig. 8.23 after ref. 8.8. This result indicates the significant influence of the grouping of cab and trailer.

By varying the gap width s and projecting body height h for three cabs with different shapes but otherwise identical external dimensions, Götz8 2

achieved the results plotted in Fig. 8.24. The results for the sharp-edged cab (C) show:

• A very small influence of gap width s • A drag minimum with a projecting body height h = 1.0 m • Smaller drag coefficients than for streamlined cabs with projecting body heights h > 1.0 m


CD

0.5

0.4

0.3

0.2

0.1

Distance above cab h = 1.1 m

Gap width s = 0.7 m

5° 10° 15° 20°

Yaw angle

5° 10° 15° 20°

Yaw angle 5° 10° 15° 20°

Yaw angle

Figure 8.22 Influence of cab shape on partial drags of cab and body for semitrailer

Pressure distribution CP

Figure 8.23 Flow interference: cab-body front, after ref. 8.8

For the streamlined cab (B): • A broadening of the range of drag coefficients with increasing gap width s, while the band itself also rises with increasing projecting body height h • Lower drag compared with sharp-edged cabs for projecting body heights h < 1.0m.


0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 m

Distance h above cab

Figure 8.24 Influence of cab shape on aerodynamic drag coefficient taking into account different body heights h and gap widths s

For the production cab (A): • A well-designed cab is very close to an ideal' streamlined cab. • Higher drag than for streamlined cabs with small projecting body heights h < 0.6m, resulting from the compromise with interior space, which is made as large as possible, whereby smaller external bend radii and edges and steps required by the production process are tolerated.

These studies show that, at least in symmetric relative flow, favourable drag coefficients are obtainable even with sharp-edged cabs with a certain body height h. Basically, conditions are favourable when the 'flow separation line' from the cab (divides separated region and 'sound' outer flow) attaches smoothly to the following, generally sharp-edged, body.

This situation is changed when yaw is considered. As can be seen from Fig. 8.25, the drag of a sharp-edged cab increases dramatically with yaw. The body, which is shielded by the cab under zero yaw, is now exposed to the oncoming flow. In contrast, trucks with streamlined cabs suffer only slight drag rise due to yaw.

^CrV"""

Distance above cab h = 1.1 m

Gap width s = 0.7 m

20° 30° Yaw angle

Figure 8.25 Influence of cab shape versus yaw for a semitrailer unit


8.5.3.4 Drag-reducing add-on devices for trucks

Tractors are operated with a variety of different trailers. Low drag of the cab alone does not guarantee low drag for all truck-trailer combinations. For high bodies, therefore, a whole range of add-on devices for reducing air drag have been developed. Some of those to be seen on the road are compared in Fig. 8.26.

AC« . 9 7 . ACn »W7. ACD � 307·

Figure 8.26 Drag reduction through add-on devices with head-on air flow

Figure 8.27 Influence of air shield on pressure distribution

For cab mounting, head and side wind deflectors or adjustable air shields have proved to be effective. The latter are easy to fit, effective and cheap. The pressure distribution in Fig. 8.27 illustrates the effect of an air shield. Devices mounted on the body, for instance fin-like vortex stabilizers on the front wall, which by vortex formation reduce the flow of air between cab and body in cross-winds, or half-balloon-shaped aerofoils, help to reduce overall drag.

Similar results have been achieved by Berta et al . 8 1 1 with a tractor-semitrailer carrying a ribbed container, see Fig. 8.28. The various airshields on the left column of Fig. 8.28 result in almost the same drag


CD CD CL, Reduction CD Reduction

o/0 %

0656 24

0 6 2 9 271

0 820 4.2

0673 22

0 568 34 1

0 609 29 4

Figure 8.28 Tractor-trailer configuration: add-on devices and body-details study, after ref. 8.11

Gap width s = 0.7 m

Y 10° 20° 30° Yaw angle

Figure 8.29 Drag reduction versus yaw through add-on devices on a semitrailer unit

reduction. A further improvement is obtained with a smooth-walled trailer, as would be expected.

As can be seen from Fig. 8.29 (after ref. 8.2), for trucks with sharp-edged cabs wind-deflecting devices can reduce drag by up to about

0.663 23 2

0.660 23 5

0.657 2 3 8

0.668 2 2 6

0.680 21


10 per cent, while for low drag versions up to 30 per cent reductions are possible with relative wind from directly ahead.

With increasing angle of yaw, appreciably smaller drag coefficients are realized with bulbous fairings on the front of the body than with an air shield. Figure 8.30 shows these add-ons on a full-size tractor-trailer.

Figure 8.30 Air shield and container front end fairing on full-size vehicles

Similar configurations are described in refs 8.12 and 8.13. The first steps have been further improved by integrating the air shield and side cab flaps into a cab fairing design as shown on various production semitrailer tractors, see Fig. 8.31.

Further drag reductions of about 5 per cent can be obtained with an underbumper apron, similar to the fairings for cars, by which the airflow underneath the vehicle is improved.

Chassis fairings, which may also incorporate underride protection from the sides and the rear, Fig. 8.32, are only effective against cross-winds. With increasing yaw angle the improvement in the drag coefficient increases, becoming about 13 per cent at a yaw angle of ø = 15°, see Fig. 8.33.

8.5.3.5 Full trailer

The interaction between the motor truck and the 'full' trailer of a truck-train is, to some extent, similar to the cab-semitrailer interference mentioned above. Several measures have been developed to improve the flow pattern in the gap between the two bodies.

According to Gilhaus and Hau8 14, a low-drag cab causes both reduction of overall drag and redistribution of drag between truck and trailer, as becomes evident from the drag breakdown in Fig. 8.34. Consequently, the gap between the two becomes more and more important from an aerodynamic viewpoint.

The development of the devices that reduce the gap-related drag follows the same lines as for the cab-semitrailer interaction.815 A way of

315

Figure 8.31 'Integrated' air shields on actual semitrailer tractors

316

ù ï ï ó) ù �σ

ï

c �ο ï

<

Figure 8.32 Completely faired chassis

20° 25°

Yaw angle Figure 8.33 Influence of chassis fairings on drag versus yaw angle

CD

.2 0.7 [ o

0.61-

0.5[

0.4 |

0.3[

0.2[

Oi l

ol-Figure 8.34 Drag reduction and redistribution of drag caused by improvements at the front of the truck train, after ref. 8.14

º 1

I

S x

s

3

δ 5

!

317

ACD = -5.5% Rounded trailer front

ACD = -6.5% Vortex-stabilizer

^ ACD = -10% Rounded trailer front

-I- Vortex stabilizer

ACD = -12% Gap sealed

Figure 8.35 Drag reduction of truck and trailer by means of add-on devices on trailer, after ref. 8.8

Baseline

Leading edge radii on semitrailer

dragfoiler Frontal air dam

Chassis fairings

Cab side flaps (low drag configuration)

15°

Yaw angle

Figure 8.36 Influence of aerodynamic improvements to a 15 m semitrailer unit as shown in Fig. 8.37

318

Figure 8.37 Semitrailer unit with complete aerodynamic fairings, concept vehicle


approximating the drag of the 'ideal', i.e. gapless configuration, is shown in Fig. 8.35.8·8

It should be mentioned that the drag of the motor truck is reduced most of all by the vortex stabilizer, while rounded edges on the trailer front chiefly reduce the trailer's own drag. The obvious route is to combine the two features, which brings a reduction almost equal to the sum of their individual effects.

8.5.3.6 Future trends in tractor-trailer design

The aerodynamic knowledge from the various individual studies has been integrated in a body concept for a tractor-trailer designed for long-distance haulage (Figs 8.36 and 8.37). The goal was to obtain similar drag improvements for both head and side winds. By the sequence of improvements in Fig. 8.36—leading edge radii on body front, 'dragfoiler' on cab roof, frontal air dam, chassis fairings for tractor and semitrailer, and cab side flaps—cD was reduced from 0.65 in the original condition to 0.42 (35 per cent) at 0° yaw and from cT = 1.0 to 0.67 (33 per cent) at 15° yaw.

The simultaneous demand for more cargo space and improved aerodynamics has led to the so-called 'high-cube' truck train design as in Fig. 8.38. Cargo space was enlarged by about 10 per cent by placing the

( r o·—(TU 18 m

M.75-

\¢ -6.15- 0.7

-6.1 m-

feQ

-9.4-

9.3 m-

ÃÔÃÔÔ ΠΠ Figure 8.38 'High cube' truck train design

sleeper box over the cab and halving the gap between truck and trailer by new steering geometry of the trailer front axle. A production truck train is shown in Fig. 8.39.

What can be achieved if aerodynamics are pushed to their limit is seen from Fig. 8.40. The prototype FEV 2000 achieves a reduction of drag by as much as 57 per cent, fuel savings (including rolling resistance improvement and weight reduction) of up to 40 per cent, and at the same time a 39 per cent larger cargo space.816 An optimal underride protection was obtained at the front and rear and on both sides in the process.

Because of smoother airflow, the suction effect of large commercial

320

•TOS^V · ί

Figure 8.39 Production truck train

Fruehauf's Aerodynamic, Truck of The Future,

Speed-sensitive gap seal deploys at high speeds and folds to tractor for

►speed maneuverability.

Frontal-dam directs surface air upward.

Lightweight panels provide more cube space.

Aluminum coupler, floor, crossmembers and rear frame lighten the load.

Boattail maintains a streamlined afterbody.

Retractable side skirts restrict airflow from underbody.

integral wheel with radial tires promote stability with wider track and added cube.

Figure 8.40 Design studies for aerodynamically advantageous future long-haul trucks


Figure 8.41 The Cargo Concept of Ford Europe

vehicles on passing cars is noticeably reduced (see section 5.3.2), as is the sheet of spray normally produced on wet roads, so that the visibility of other road users is less impaired.

On the ordinary rigid truck (Fig. 8.41), too, energy-saving, perform-ance-improving aerodynamic features are gaining ground. They are particularly effective on light trucks with relatively large bodies which regularly average high speeds; cD was improved here by 36 per cent from 0.78 to 0.5.

8.5.3.7 Reduction of aerodynamic drag on 'truckaway' units

Car transporters present a rather special aerodynamic situation. Wind tunnel tests using a one-tenth scale model demonstrate high drag figures from cD = 0.94 (trailer empty; cÂ = 8.9 m2). Side panels are the most effective way of reducing drag. In Fig. 8.42 the drag dropped from cD = 0.82 to 0.70 (a 14 per cent decrease). As an experiment, a full fairing, Fig. 8.42 bottom, shows a reduction in drag of 40 per cent.

Glas8 1 7 performed tests with panels on only one side of the vehicle. With a complete panel on only the windward side, the drag at 20° yaw angle was cT = 1.20 as compared to the baseline figure of cT = 1.66—a reduction in drag of 27.7 per cent. However, panels on only the lee side reduced the drag by only 15.7 per cent. Clearly, panels on only one side of the truck would be much less effective, on average, than panels on both sides. However, the drivers can leave and enter the cars more easily when loading and unloading.

8.5.4 Minimizing drag of buses and delivery vans

8.5.4.1 Boundary conditions

The constraints on optimum design of commercial vehicle shapes are generally more severe than for cars. Apart from aspects of styling and

322

Figure 8.42 Truckaway unit fairings (model studies)

Figure 8.43 Scope for development of shape of delivery van, after ref. 8.22


manufacturing, functional requirements dominate, with the result that designers must deviate as little as possible from the basic cuboid shape. The scope for design is indicated in Fig. 8.43822. Some freedom exists for shaping the vehicle front end. Tapering of the side panels, very conducive to smooth airflow, has disadvantages for production (parts for left and right sides not identical) and reduces cargo space. Tapering must therefore be restricted to short sections at the front and rear ends. The windshield and the roof leading edge on touring coaches, for example, allow more latitude for design.

8.5.4.2 Characteristic flow conditions on simple geometric bodies

Photographic flow studies with smoke on cuboid bodies,8 18 Fig. 8.44, indicate strong separation of flow at the leading edge, amplified by reverse flow (rear to front) close to the surface of the body in the case of bodies

L / W - 0 . 5 L / W - 1 . 2 L / W = 1 . 6

Figure 8.44 Separation of flow on cuboids with different length width ratios L/W, after ref. 8.18: (a) smoke from the front; (b) smoke from the rear

with small length/width ratios L/W < 1.6. When a specific relative length L/W is exceeded (L/W = 1.6 to 1.8), the separated flow reattaches on the rear of the side panels. There is a distinct drag minimum for the relative length, see Fig. 8.45, which also exists for bodies with no separation at the front, see Fig. 4.119.

Similar but earlier results from Barth8 19 are shown in Fig. 8.46. A definite correlation between drag coefficient cD and body shape and relative length lid exists. The considerable reduction of drag from rounding the leading and longitudinal edges is particularly noticeable. Measured pressure distributions as well as detailed flow visualization (see Figs 8.47, 8.48 and 8.49) clearly indicate how important a well-designed front end is for low drag. The basic findings demonstrated hereafter on the bus can be directly applied to the delivery van.

8.5.4.3 Optimization of the front end

The size of the leading edge radii has a substantial influence on the drag of a bus. In Fig. 8.50 the leading edge radius has been successively enlarged, starting from a sharp-edged front end shape. It is evident that a radius of about 150 mm is sufficient to reduce the drag of the bus so far that further

324

-3 0 3 6 9 12 15

Yaw angle, deg.

1.4

1.2

1.0

° ' -3 0 3 6 9 12 15

Yaw angle, deg.

Figure 8.45 Drag coefficient cD of a cuboid against yaw angle for different length/width ratios L/W, after ref. 8.18

L^ j

L/W I O 1.6 j Ä 1 . 8

D 2.4 D 3.2 V 4.2

2 4 6 8 10 12 Length ratio l/d, l/d*

Figure 8.46 Drag coefficients cD of geometric bodies against length ratio l/d, after ref. 8.19

325

Figure 8.47 Characteristic flow conditions on bus. Top: zero yaw angle Bottom: 15° yaw angle

Center Line «

Belt Line f +0.5

-0.5

-1.0

^

Figure 8.48 Pressure distribution cp on bus with symmetric flow

326

Figure 8.49 Pressure distribution cp in different horizontal and vertical planes with 20° angle of yaw

R

0.10 R/b 0.15 0.05 R = Front End Radius

R/b = Front End Radius in Relation to Width b

Figure 8.50 Influence of front radii on drag

1. Sharp-edged front

2. Front with rounded leading edges CD = 0.36

3. "Stromform"-front CD = 0.34

Figure 8.51 Relationship between shape of vehicle front and drag coefficient, after ref. 8.20


Based on Carr (1967)

h/ f=0 .4

Red

h—h-H r/h = 0.1- 0.4f-|

i .

= 1 x 1 0 6

^ r / h = 0.1

~ 1 h

mrrflrrmr ////////////////hz/M/i////// ' H = 0 . 1 7 h

Front view S i de elevation

I Baseline: CD = 0.22 * | * with leading-edge B.L trip wires;

C0 (W/O wiresjTä£2iL

ÚÌ c

////////////// /77777777777777777777777777777T7 m

0.25 h S

Streamlined front-end medium leading-edge: CD = 0.23

Streamlined front-end low leading-edge: CD = 0.21

Elliptical in plan

//////)}/////7 ///////////////I}/////////////// TM 7777T77TTT7777ffrn7777777777TT

Streamlined front-end vertical leading-edge: CD = 0.22

Streamlined front-end high leading-edge: CD = 0.40

Figure 8.52 Effect of streamlined front ends on the drag coefficient of rectangular bodies in ground proximity, after ref. 8.21

appreciable improvement cannot be obtained even with so-called streamlined front-end shapes, which have been investigated by Gilhaus,820

see Fig. 8.51. Almost identical results have been achieved by Carr,8 21 as can be concluded from Fig. 8.52.

On actual vehicle front ends the potential for drag reduction can be exploited with often only slight modification to the previous design. Figure 8.53, from Hucho and Emmelmann,8 22 shows drag-reducing modifications

A-pillar, section 1400

— Baseline — Shape change A: ACD = -0.02 — Shape change B: ACD = -0.02

Figure 8.53 Drag reduction and A-pillar design, after ref. 8.22

to an A-pillar design as an example. An only slightly enlarged radius at the front end of the same vehicle prevented the flow separation. The lower photograph in Fig. 8.54 (after ref. 8.22) shows flow separation at the sharp leading edge; the upper photograph displays attached flow due to the rounded leading edge, see also section 1.2.6.

From Fig. 8.55 (after ref. 8.22) it becomes evident just how small


Figure 8.54 Flow around side of front end, after ref. 8.22. Top: attached due to shape A or B. Bottom: separated due to sharp-edged flange

Baseline

Figure 8.55 Drag reduction by improved roof leading edge, after ref. 8.22

changes sometimes need be to improve flow quality. The slight change in roof design, see thick lines, yields a drag reduction of AcD = -0.02 with no loss of interior space or any noticeable change in styling.

Even a production-originated drip rail at the windshield/roof transition can be positioned for clean air flow. Moving the drip rail down (Fig. 8.56) keeps the flow attached; see Fig. 8.57.

When a brand-new vehicle is being designed, the opportunity can be taken to select the overall dimensions properly. Figure 8.58, from Buchheim,8 23 shows the influence of several important front-end design parameters on the cD of vans. The following are evident:

• Front-end taper ä is very effective with steep windshields. • Raked windshields oc are very effective if there is no front-end taper.


ACD

CD

Ü

�0 Ö cc

D Ü

/o

16

14

12

10

8

6

4

2

I

/ ^

V - / × /

" l I

5 10 15 20 2 5 30 a mm

Positioning of a frontal drip moulding

Figure 8.56 Drag-reducing drip moulding configuration

Figure 8.57 Air flow over centre section

With properly matched taper, windshield rake has only minimal influence. • Radii on the front edges are also effective up to certain dimensions.

In future, aerodynamic design is likely to influence production vehicles through parameters shown in Fig. 8.58 consistent, of course, with engineering requirements, cab space, entrances, visibility and other safety aspects. Even so, we can expect to see substantial aerodynamic improvements over today's vehicles.

That ram-effect edges necessary for ventilation can also be designed for low drag is shown by Fig. 8.59.

The drag breakdown in Fig. 8.608 24 shows how far drag can be reduced with an optimum front end and what can be expected from the other sections of the vehicle. Once the front end is optimized, the rear end is the main contributor to drag.

330

Enlargement of front end radii

0° 10° 20° 30° 40° 50° 60° Figure 8.58 Influence of front end shape Windshield slope angle a on cD, after ref. 8.23

ACD = - 1 2 %

Figure 8.59 Low drag ram edge on bus

CD = 11 CD = 1

Rear end -

Bodywork

Rear end-"

Bodywork Front end

Front end-

Vehicle length Vehicle length

IVo-oshjhJ Figure 8.60 Air drag distribution over vehicle sections for a rounded and sharp-edged front

L - O


8.5.4.4 Optimization of the rear end

Any measures which would reduce the useful interior space have little chance of being adopted in practical bus design. The low-drag buses of the Thirties, with tails based on the ideas of Jaray, Fig. 8.61, and Kamm, Fig. 8.62, call for tapering to an extent that no longer makes them a match for present-day design in terms of user requirements (convenient boarding, seat access, luggage racks, seat comfort) and operator requirements (economy, capacity, manoeuvrability).

Figure 8.61 Jaray—bus rear end design

Figure 8.62 Kamm—bus rear end design

Realistic features, however, appear to be moderate trailing edge radii, a slight drop at the end of the roof, and slight tapering of the side panels. The results are shown in Fig. 8.63. One-tenth scale model studies on a simplified bus shape (wheelless, smooth underside) once again point to the dominant influence of the bus front end (sharp-edged or rounded), since the extent of drag reduction possible by better rear end design depends on it.

Along with a certain reduction -of transport capacity, cD reductions of 4-8 per cent result from trailing edge radii, of 6-20 per cent from side panel and roof taper, and of 9-22 per cent with additional trailing edge radii. The remaining 14-35 per cent potential for drag reduction with a


► Front Roof and Vertical Edges Rounded ■ Square Front 0 1

R/B = 0.122

U';"V Vehicle direction

2

l^\

" >

3

u sh-

Figure 8.63 influence of bus rear-end design on air drag

s ^ s ^ ±E

Schnitt A-B

Figure 8.64 Extensible trailing air foil

boat-tailed rear end cannot be exploited without radically reducing transport capacity or exceeding statutory length restrictions.

Perhaps an approach from the Thirties (Fig. 8.64), with an elastic trailing envelope—perhaps extensible and inflatable only at high speeds, rolling up again at low speeds (city traffic)—should be reconsidered.

8.5.4.5 Add-on devices on the rear end

Further measures are conceivable to reduce negative pressure on the rear end. A horizontal (/ = d) or vertical (/ = 0.5d, l.Od) splitter panel extending from the surface of the rear end, which has been investigated by Mason and Beebe,8,25 see Fig. 8.65, results in little or no change in air drag. With guide vanes, proposed by Frey8·26 as early as 1933, the added drag of the vanes was evidently larger than any base pressure-related drag reduction. All attempts to apply the results which Frey achieved on two-dimensional aerofoils (Fig. 8.66) to three-dimensional bodies in close ground proximity have so far failed. The only drag reductions achieved were by the addition of non-ventilated cavities. The best geometry, with a cavity depth of 0.13d, reduced the drag coefficient by 5 per cent. Similar

333

Splitters

Vanes Cavities Figure 8.65 Base-flow modification devices

Red = 0.06 x 106

CD based o n b x d l/d = 3.3, b/d = 3.3

r = 0.07d

Figure 8.66 Reduction of pressure drag by means of staggered guide vanes, after ref. 8.26

?o

0.10 ACD

0.06

0.04

0.02 •

0.1 0.2 X 0.3 I

Figure 8.67 Drag reduction with rear-end extension panels


improvements have also been found on light vans8 22 (see right of Fig. 8.67) and trucks (Fig. 8.67, left). But again this is not a very practical measure because it elongates the vehicle without contributing to interior space.

An unexpected drag increase was observed by Mair827 while investigating the drag-reducing capability of a circular disk placed concentrically in the near-wake of a blunt-based body of revolution. In general, drag is reduced by such an added disk, see Fig. 8.68, but in one very particular position a steep drag increase occurred.

Axisymmetric Body C j r c u | a r D j s k

Figure 8.68 Effect of a circular disk on afterbody drag, showing the occurrence of critical behaviour atx/D = 0.3, after ref. 8.27

Figure 8.69 Effect of vortex generators on base pressure along the span of a bluff-based body, after ref. 8.28. o with vortex generators + without vortex generators

The arrangement of vortex generators on the side surfaces at the rear, see Fig. 8.69, causes a reduction of pressure in the base area, according to investigations by Young.8 28 Whether this also holds for three-dimensional configurations is not yet known.

8.5.4.6 Future bus design trends

A number of aerodynamic solutions have been realized in the research project for high-decker buses by the Fachhochschule, Hamburg. The

Taking advantage of aerodynamic effects 335

Figure 8.70 High-decker bus designed by Fachhochschule Hamburg, after ref. 8.29

high-decker bus, used mostly for long-distance travel, has a drag coefficient of cD = 0.6, which can be reduced at least to 0.3 according to ref. 8.29. The smooth airflow pattern around the bus is shown in Fig. 8.70. This large reduction in drag of about 50 per cent reduces fuel consumption at 80 km/h (50mile/h) by 15 per cent and at 100 km/h (62.5mile/h) by more than 20 percent.

8.6 Taking advantage of aerodynamic effects 8.6.1 Driving in convoy

Driving in convoy reduces drag. Increasing traffic density often leads to formation of convoys of commercial vehicles, because of speed limits and limited opportunities for passing. High average speeds are possible on motorways, and definite interference phenomena occur between the vehicles. Each vehicle trails a distinct wake, which reduces the dynamic pressure on the following vehicle. This effect, known as slipstreaming or draughting in racing, is particularly pronounced in the case of commercial vehicles, so that clear-cut drag improvements still result even with larger intervals between vehicles (Fig. 8.71).

If a convoy of several vehicles has formed and the drivers maintain the safe following distance of 40 m at a cruising speed of 80 km/h (50mile/h), a cD improvement of about 20 per cent is obtained for the second vehicle and about 30 per cent for the third and every additional vehicle. The same is true for trucks and tractor-trailer trains.8 It is not necessary to stay exactly in the track of the preceding vehicle. The vehicles can be staggered up to


40 50 60 m Vehicle Distance in Convoy

Figure 8.71 Influence of convoy driving on air drag

half a vehicle width. However, since air drag reduces with decreasing intervals between vehicles, drivers must be made aware of the dangers of 'fuel-saving euphoria'.

8.6.2 Driving through tunnels

There are even greater advantages in bus convoys in narrow tunnels, equal at least to the drag reductions for convoy travel on the open road. The drag coefficient cD of a bus driving through a tunnel is up to six times higher compared with a bus in the open.

One solution to city and regional traffic problems is the expansion of public transport. The bus is the most economical means of transportation for most requirements. It operates on normal roads and is flexible in response to new transportation needs, but during peak periods buses in the inner cities are hampered by private vehicles using the same lanes as buses.

One suggestion for reliable, fast and comfortable transit in the future is the ¼-Bahn' bus transit system which has its own tracks (Fig. 8.72) partly routed through narrow tunnels, wherever there is not enough room for bus lanes on the streets. Following the system's successful introduction on the occasion of the 1979 Hamburg International Transportation Show, the City of Essen (Germany) initiated ¼-Bahn' operation on one section of a route in 1980.8 b o

Generally speaking, air drag is one of the most basic concerns of tunnel and propulsion system design in tube-bound transportation systems. To solve these problems, tests were carried out on a linear motor system, normally used for crash testing, with 1:20 scale cylindrical bus-shaped


concrete cross beam

safeguard

longitudinal girder

ESCAPE WAY MADE OF PREFAB CONCRETE ELEMENTS

REINFORCED CONCRETE PIPE

(b) ADJUSTABLE TRACK ELEMENT WITH HIGH ABRASION RESISTANCE

Figure 8.72 Bus tracks: (a) elevated track; (b) underground track

Figure 8.73 Arrangement of bus convoy models on a linear motor

Figure 8.74 Tunnel entrance (left) and tunnel exit

bodies. Figures 8.73 and 8.74 show the test set-up for bus convoy measurements in tunnels. A short tunnel (L1:1 = 180 m) and a long tunnel (L1:1 = 2200m) were available. For technical reasons, in the long tunnel precise measurements could only be obtained on the first 180m. The models attained speeds up to 70 km/h (43.8 mile/h). The blockage ratio ö = 0.54 (bus cross-section/tunnel cross-section) was selected to be very close


rear end area

Figure 8.75 Development of pressure on the front and rear surfaces of a blunt cylindrical body with bus-like essential dimensions

to practical requirements. The first tests were pressure measurements on the front-end and rear-end surfaces of a single bus. The pressure recordings from both the front and the rear end of the bus are shown in Fig. 8.75.

The high pressure gradient on the front surface during the entry phase, caused by the impulse-like acceleration of the tunnel air mass, stands out. A rapid drop in front surface pressure drag even below that of the free atmosphere (tunnel air mass is already accelerated) follows shortly after,

^ 5 * 5 10 15 20 x/l

Figure 8.76 Typical development of drag coefficient cD for body inside a tunnel


so that the overall pressure drag following the entry phase is determined chiefly by the amount of base drag.

The air drag itself was measured by means of a force sensor mounted within the model. During the tunnel passage, the drag coefficient cD and the overall pressure on front- and rear-end surfaces follow similar curves, see Fig. 8.76. The shorter the tunnel, the more rapidly cD decreases. This corresponds to the acceleration of tunnel air mass. In the exit phase, the cD curve exhibits a brief decline beneath the value in the open. This is due to the rise in pressure from the wake behind the cylinder because of the sudden break-up of the ring stream which encompasses the wake in the tunnel and reduces pressure in the way of an injector.

Compared with the single bus, more or less pronounced drag reductions (depending on number of buses and position in the convoy) result during the entry phase for both the short and the long tunnel. The cD of the leading bus drops distinctly when the bus following enters the tunnel. It

lii j

� � � �

φ = 0.54

HHÜ Measuring bus

a = 15 m

I = 11 m

v = 50 km/h

Tunnel length 180 m

tunnel exit

-5 » 5 10 15 20 x/l Figure 8.77 Influence of sequence on drag coefficient of bus convoys in a tunnel. Top: short tunnel L1:1= 180 m. Bottom: long tunnel L1:1 = 2200 m


drops again, but to a lesser degree, when the third bus enters, Fig. 8.77, top. The negative pressure on the rear-end surface is reduced.

The drag peak in the tunnel entry phase is smaller, the more buses are in front intensifying the suction effect on the following bus. During the tunnel passage, all buses—in whichever position—show a cD curve only about half as high compared with the single bus.

In the long tunnel (L1:1 = 2200 m), the changes in air drag follow a similar pattern as in the short one, but take place on a higher level following the initial phase, at least over the measured section L1:1 = 180m (Fig. 8.77, bottom).

Figure 8.78 shows that drag improvements of up to 50 per cent are

I tunnel length 180 m j 1 1 1 1 1

100%

| 57% j 1 67% |

| 47% | j 47% |

| 78% |

| 60% 1 | 69% 1

58% I

100%1

75% |

86% |

I tunnel length 2200 m I l l l l l l lHll l l l l l l

Figure 8.78 Reduction of air drag with bus convoys in tunnel

City Bus, 16 t, 147 kW Engine Power

B [1/100 km] v [km/h]

80 \-

70 \-00

6 0 1 — -

50 a E CO

§ > 40

201 10

÷ Speed Top Gear (i = 1.0)

Þ Initial Speed 80 km/h

L Speed Second Top Gear (i = 1.348)

/ \ ^ Fuel Consumption Top Gear (i = 1.0)

-+J—j£- ^ Initial Speed 80 km/h

ë N Fuel Consumption Second Top Gear (i = 1.348)

1 8 3 4 5 6 Drag Coefficient CD

Figure 8.79 Influence of drag coefficient on speed of travel and fuel consumption with a given engine power

Vehicle soiling 341

possible with bus convoying. With a blockage ratio of ö = 0.54 and a tunnel length of 180 m, three buses in convoy at intervals of 15 m (Vmax = 50 km/h, 31.3mile/h) together have only half the air drag of three buses travelling singly.

For reasons of cost, the tendency is to keep the tunnel cross-sectional area as small as possible. This obviously results in a high cD curve during tunnel passage, so that the question arises as to whether the speed outside the tunnel can also be maintained in the tunnel. From Fig. 8.79 it follows that for a city bus with 147 kW engine output and 16-tonne GVW it is possible to maintain a speed of 60 km/h (37.5mile/h)—adequate for track-guided buses—up to a drag coefficient of cD = 5.7, albeit at the expense of distinctly higher fuel consumption.

8.7 Vehicle soiling

Visibility is impaired by the soiling that occurs in driving on wet roads, particularly in heavy traffic. Vehicle wheels raise particles of dirt that settle on the vehicle in question (self-soiling) or mix with the turbulent wake and precipitate on following and oncoming vehicles (foreign soiling). The result is the impairment of visibility due to dirty headlights, windshields, side windows and backlights, obstruction of vision by the fog effect of spray in vehicles' wakes, poorer recognition of rear light cluster signals and of the number plate, soiling of guardrails, markers, signs, etc.

The elimination of soiling has therefore long been more than just a question of comfort. It is an important contribution to safety—perceptual safety; see also section 6.4.

Measures against soiling must either remove deposited dirt to clean up soiled surfaces, or direct or divert the dirt-laden airstream so that it does not come in contact with surfaces that should be kept clean; or, ultimately, prevent muddy water from being whirled up.

8.7.1 Foreign soiling

In order to prevent the deposition of dirt in the high pressure regions of the vehicle (headlights, windshield), transparent air deflectors for cars and Ocl. 26, 1965 „ v. HANSEN 3.214,215

A U DcrucTOR ro* �IHOSNICLDS

ri\«4 Oct. 14. 1944 2 Sh..t»-Sh..t > JF2lC?.'4'.

Figure 8.80 Earlier approaches to keeping windshield free from dirt

342

Figure 8.81 Drip rail keeps side free of dirt

Figure 8.82 Dirty side window due to influence of external rear-view mirror

Figure 8.83 Reduced side window soiling through suitable shaping of the mirror and mud-water diverting moulding

Vehicle soiling 343

commercial vehicles were brought out in the years 1950 to 1955, see Fig. 8.80. However, experience in use made it clear that dirt particles of high density or insects cannot follow the deflected airstream (see section 2.3.4.3) and are thrown out of the streamline due to inertia, soiling the air deflecting devices themselves.

Studies with 'air curtains' produced by blowers to keep dirt off the windshield likewise showed that such solutions are impractical for reasons of space and because of their large power requirement and the noise they develop. ' It is therefore necessary to continue using and improving wiping and washing devices.

The side windows may be kept free from dirt at all speeds by aerodynamically shaped mouldings, drip rails, or trim strips along the windshield pillars, continuing downward along the door opening. These devices must be matched to the airflow characteristics of the particular vehicle shape, as shown by the mud-water deflecting truck cab in Fig. 8.81.

The soiling of the side window on commercial vehicles is caused particularly by the projecting side mirror and its bracket (Fig. 8.82). Through suitable shaping of the side mirror and mud-water deflecting mouldings it is possible to have a clean mirror and appreciably reduced spattering of the side window (Fig. 8.83).

8.7.2 Self-soiling

Self-soiling results from the vehicle's own motion over a wet and dirty surface. On the one hand, the rolling tyre displaces water from its contact area to the front and side (splash); on the other hand, the tread picks up water and, after leaving the tyre contact area, spins it off again due to centrifugal force (spray), essentially at an angle of 0 to 30°. This has already been sketched by Koessler,8 33 see Fig. 8.84. No effective remedy

Figure 8.84 Spray/splash of mud-laden water from free-rolling wheel, after ref. 8.33 has been found thus far against splash, which comes in relatively large drops and shoots out at a low angle. On the other hand, for reducing spray different solutions have been developed for trucks and buses.

8.7.2.1 Reduction of soiling of bus sides

Air flow and pressure distribution at the front of the body have a large influence on the spray coming out of the front wheel wells; see also Fig 6.18. The flatter the surface of the vehicle front end and the sharper the


mi Sp«Sto

m wm i r\^m\

Figure 8.85 FFG first prototype VÖVII

P. « ·,« l/CVî/SH .5·' .*-*..«·É.Ô' bt j:Jit. |[ΦÊ1ΖΖΙ31

Figure 8.86 Soiling of sides with sharp-edged front end design

Figure 8.87 Mercedes-Benz prototype city bus S 80

vertical edges, the greater the lateral negative pressure zone with high negative pressure values at front axle height.

This gives rise to an air flow which is directed out of the wheel well and which carries much of the spray. This phenomenon leads to heavy soiling of the sides of buses designed with sharp-edged fronts. A typical example of this, and a subject of controversy from the beginning, was the

Vehicle soiling 345

Figure 8.88 Left: previous city bus. Right: actual version

Vehicle Direction

Figure 8.89 Air dam in front of front axle reduces side-wall soiling

sharp-edged design of the outer skin of a city bus for the Eighties (Fig. 8.85). The first prototype, developed by the German Verband öffentlicher Verkehrsbetriebe (VOV), sponsored by the Federal Government's Research and Technology ministry and built by Fahrzeugwerkstätten Falkenried (FFG), was inconsistent with the twin requirements of low cD and minimal vehicle soiling (Fig. 8.86).

The now-revised city bus shape (S 80) with optimum radii at the front end (Fig. 8.87) was shown for the first time at the Hamburg International Transportation Show in 1979. Compared with the previous city bus (VÖV I), on the left in Fig. 8.88, the actual version (S 80, VÖV II), on the right in Fig. 8.88, has been substantially improved by numerous changes in engineering, design and frontal air flow characteristics.

The efflux of spray from the wheel wells can be reduced by flexible mouldings that reduce the size of the wheel openings and by a dam spanning the full width of the vehicle in front of the front axle and extending to within 10 cm of the roadway, see Fig. 8.89. The flow of air directed outwards from the wheel housing is diminished by the negative pressure generated behind the apron, which is effective into the wheel housing. Improved frontal flow, smaller wheel openings, and a flexible dam in front of the front axle result in a very small amount of side panel soiling (Fig. 8.90). This also applies to touring coaches (Fig. 8.91).

Another measure is full fairing of the wheel with a shell attached to the wheel hub and reaching to the bottom rim flange. This limits the efflux of

346

BUT STADT BUS SO

ß#Λß$*»*? -*<*«!«*? (5

Figure 8.90 Minimal side-wall soiling on city bus because of optimum front radii, smaller wheel openings and air-dam before front axle

^ n Square Front End

^W Rounded Front End

Figure 8.91 Influence of shape of bus front end on soiling of side surfaces

li

� Qft:S^B

.^SlsllilHl . nrîiiimS^H

Figure 8.92 Reduced side soiling with full wheel fairings

Vehicle soiling 347

mud-laden water to the lowest part of the side wall (Fig. 8.92). However, implementing this measure poses problems, for example higher cost of production, limited off-road capability, requires additional tyre and brake cooling, and will result in increased accumulation of dirt and ice inside the shell.

8.7.2.2 Reduction of bus rear-end soiling

Compared to the other surface panels of the vehicle, heavy and more rapid soiling of the rear window and rear panels is particularly observed on

)))))))))))))))!) Ã)))Ð)Ã))) ))))>) ))))))) ))))))))))))))))))))))

Figure 8.93 Near-wake flow field behind a bus, after ref. 8.25

Figure 8.94 Wing-type spoiler for keeping rear window free of dirt

Figure 8.95 Rear skirt reduces accumulation of dirt on rear


q rn

1 h = 0.8s

D Square Front End D Rounded Front End

30 i

%

q> 20 \

O 10

Figure 8.96 Influence of airdam and rear skirt on cD 1 2 (model test, smooth underbody)

buses. The mechanism of the related flow in the near field of the rear of a blunt-ended vehicle has been investigated by Mason and Beebe.8 25 Their findings are shown in Fig. 8.93. The dirt particles in the turbulent wake are not able to follow the sharp reversal of flow in the upper section of the rear surface and are flung out of the stream, covering the rear window, for example, with dirt.

By locating a wind-deflecting wing at the end of the roof it is possible to utilize roof air flow in such a way that the dirt-particle laden turbulent flow is forced away from the rear window by a curtain of clean air. This is demonstrated in Fig. 8.94.

Another alternative for reducing rear-end soiling is a rear apron (Fig. 8.95). But the higher drag coefficient (7-27 per cent depending on the front end and underfloor design) must be taken into account compared with a roof-end spoiler with a drag increase of only 4 per cent, see Fig. 8.96.

8.7.3 Reduction of truck soiling The large clearance angles of current truck mudguards neither limit splash nor do much to impede the spray spun off to the rear.

1.5 Tyre h- width -H Vehicle direction

Mudguard

Trough

Frontal drainage hole

Figure 8.97 Anti-spray mudguard, after ref. 8.34

Mudflap tray

Drainage hole at end

Vehicle soiling 349

Figure 8.98 Mudguard with air-permeable mudflap

Figure 8.97 shows a proposal for a more effective anti-spray mudguard by Braun.8 34 Water sprayed by the tyre strikes the easily wettable inside surface of the mudguard at a low angle, then collects in gutters of sufficient cross-section along all longitudinal edges and is channelled to the centre of the vehicle, where it is released in a continuous stream to a point of low relative wind velocity to the roadway. Figure 8.98 shows a mudguard improved even further. The spray whirled off directly behind the tyre contact patch ('tread throw' area), which the mudguard cannot trap, is caught by a flexible, large-pored mudflap, permeable to air, at the rear of the wheel housing. The influence of vehicle shape, road speed, tyres and road surface on the degree of soiling is largely eliminated by this device.

8.7.4 Impingement of spray on following vehicles Measures that result in reduction of self-soiling of commercial vehicles also serve to reduce the spray falling on following vehicles. Close-following

Thickness of the Water Film (Mean): 2.36 mm

> o c Q)

ù

high

low

intermit, no wiping

E (N Ö ó> �σ 3 o _ù "ä û co a.

CO

"o !> ¸ CO ZJ

σ

Ü U'

40

30

20

14

10-

6

2

\CP

f \| 1

7?

3

l —

) \

\

"1

H 1 - L ^ n

-a

CiXr-

� P i 1

10 20 30 40 50 Following Distance m

Figure 8.99 Effect of truck spray control devices on following car at various distances, after ref. 8.35


cars, in particular, are hit in the windshield area by billows of spray, thus reducing safety. Yamanaka and Nagaike8 35 have studied the effectiveness of different mudguards and chassis fairings against spray action on a following car.

The dirt-laden water is collected on a 0.2 m2 surface in front of the car at about the eye level of the driver, and is evaluated quantitatively. Qualitative assessment is facilitated by the necessary windshield wiper speed for safe driving. Figure 8.99 shows the influence of various mud-water shielding devices, depending on road speed. Figure 8.100 shows the influence of following distance. υ c Φ

ù

0)

a

High

Low

intermit.

I | no wiping r 4 0 50 60 70 80 90

Velocity km/h Figure 8.100 Effect of truck chassis fairings on s'pray striking a following car versus speed, after ref. 8.35

12m

Figure 8.101 Underbody baffle plus splitter panel concepc, after ref. 8.36

The quantity of splash and spray has been determined by optical laser systems and photometers by Weir. Visibility through the sheet of spray for a following vehicle is improved by 15 to 60 per cent (compared to the condition with a production vehicle) by the various add-on devices in Figs 8.101 to 8.106. The purpose of the longitudinal baffle, Fig. 8.101, is to

Vehicle soiling 351

45-

f—1.07 m - ç [—l.07r

•-K ïóá¼

Upper position Lower position

Figure 8.102 Gap filler panel concept for full-scale tests, after ref. 8.36

Figure 8.103 Angled side vane concept, plan view, after ref. 8.36

inhibit air flow under and through the truck in cross-wind conditions. In doing so, it reduces both truck drag and the splash and spray in a cross-wind. The gap filler panel, Fig. 8.102, blocks the air flowing down in the gap, and keeps the flow from striking the tractor driving wheels and contributing to the formation of spray. Angled side vanes, Fig. 8.103, were installed to duct air towards the centre of the truck, thereby carrying the spray under the truck and away from the adjacent car. The European type fender, Fig. 8.104, covers both wheels in a dual pair, and can be long enough to cover a tandem set. The lips along the edges, and the overhangs at the front and rear, are designed to trap the splash and spray. The Roberts fender, Fig. 8.105, has a corrugated and slotted inner liner which collects the splash and spray droplets and drains the water to the roadway inside the wheel. The Reddaway fender, Fig. 8.106, is made of a plastic 'grass' material bonded to a hard plastic backing. It collects and contains the splash and spray around the wheels which runs down the 'grass' and drips off the bottom onto the roadway. The grass-like liner is on the inside of these flaps, facing the tyre.

Forward

Figure 8.104 European fender

352

Trough

Figure 8.105 Sketch of Roberts fender on semitrailer

Figure 8.106 Sketch of Reddaway fender

Cab mounted Plate

Rear Board

TO I r

? ?&=&

Valance.

Mudflap Tray ___ Iff \ U 33 Mudguard

Rubber Flap Extension

Mudflap Tray

Rubber Flap Extension

Plastic Grass or Reticulate Foam inserted here above gutter

Drainage hole at end of gutter near vehicle centre line not shown

Figure 8.107 University of Southampton spray-reduction devices, after ref. 8.37

Notation 353

Spray behind and alongside the vehicle has been measured using a similar technique by Allan and Lilley.8 37 A combination of different collecting and diverting devices for splash and spray, arranged around the wheel as in Fig. 8.107, improves visibility from initially 4 per cent to 35 per cent (where visibility on a dry road is 100 per cent).

Most fender devices have some inherent problems which ne6d design or operational solutions, especially in the harsh physical environment of winter where mud, ice, and the presence of tyre chains might damage the flaps or fenders. At the moment, there does not appear to be one fender design suitable for all truck types. Whether one principle can be adopted universally remains to be seen. But the technical know-how is available to reduce significantly splash and spray from trucks and buses.

8.8 Notation

A •^bus -^tunnel D H L R Re i/oo V VR VT

vx w a a b cO

CO

CP CT

d d d* h h I I I r s X

Ø

frontal area frontal area of bus, Fig. 8.75 cross-section of tunnel, Fig. 8.75 aerodynamic drag overall height, Fig. 8.21 length, Fig. 8.44, 8.45 radius, Fig. 8.16, 8.50, 8.59, 8.60 Reynolds number, Fig. 8.16 undisturbed flow speed wind speed, Fig. 8.13 relative wind speed, Fig. 8.13 tangential windspeed, Fig. 8.13 local speed, Fig. 8.19 width, Fig. 8.44, 8.45 ground clearance, Fig. 8.96 coordinate, Fig. 8.56 spanwidth, Fig. 8.66 drag coefficient side-wind-averaged drag coefficient pressure coefficient tangential force coefficient diameter, Fig. 8.46 thickness, Fig. 8.66 equivalent diameter, Fig. 8.46 body height, Fig. 8.22, 8.24 apron height, Fig. 8.96 body length, Fig. 8.46 vehicle length, Fig. 8.67 tunnel length, Fig. 8.76 local radius gap width, Fig. 8.20, 8,22, 8.24 coordinate yaw angle, Fig. 8.13


oc windshield slope angle, Fig. 8.58 ä front end taper angle, Fig. 8.58 ö wind angle, Fig. 8.13 ö tunnel blockage ratio, Fig. 8.75

Chapter 9

Engine cooling system Klaus-Dieter Emmenthal

9.1 Introduction

Much of the energy available in fuel is converted into heat during the working cycle of an engine. Although this heat can be used to warm the vehicle interior, most is transferred to ambient air, either by air cooling or more often by water cooling. From a practical standpoint, water cooling is still a form of air cooling, but using water as a transfer medium. This chapter is solely concerned with water cooling systems for passenger cars.

Specifications have changed markedly in recent times for systems of this type. Traffic density demands compact, high-performance vehicles that meet safety standards for body design and structure. This poses the problem of how to transfer the relatively large amount of engine heat to ambient air by means of a radiator, for which there is generally very little room, and in a space which is further constricted by the various auxiliary power and servo units. Furthermore, aerodynamics, body styling and visibility considerations have led to steeply sloped hoods (bonnets), so that the air inlet has become smaller, thus emphasizing the importance of cooling fan design. Either the space problem or transverse mounting of the engine/transmission assembly will necessitate the use of an electric cooling fan, and the fan's performance is limited in turn by electrical system capacity.

Certain things must be considered before designing the cooling system. The available cooling air inlet cross-section and the maximum available space for the radiator and cooling fan are determined by vehicle styling and engine placement. The effect of ram air can be roughly estimated from the road performance map and heat rejection to coolant can be estimated from engine output. To minimize fuel consumption and noise, as well as electrical demand when the fan is switched on, cooling fan power consumption should be minimized, and the cost of the radiator and the fan with its drive must also be considered.

Finally, the problem of cooling fluid to ambient air heat transfer must be solved before the design of the radiator, water pump and cooling fan can be finalized: the total effect of radiator size and cooling fan power is of particular importance. These data plus, for example, coolant flow data can be found experimentally, through computation, or through a mixture of both.

355

356 Engine cooling system

Experimental testing is both time-consuming and expensive: yet calculation alone is an inadequate foundation for design. Calculation must be supported by experimental data so that the precise effects of any factor that may influence the size of the radiator, cooling fan, or water pump can be determined during the initial design stage.

The following section is concerned with steady-state heat- and flow-related problems of water cooling systems in passenger cars. Heat transfer problems during engine start up and idling, and technical details such as thermostats, hose connections, etc., will not be considered.

9.2 Cooling system requirements The cooling system, consisting of the radiator, cooling fan and water pump, must be designed so that the cooling fluid temperature stays below boiling point, or below an upper temperature limit for the cooling fluid, during all practical operating conditions. From Fig. 9.1 it is clearly

1301

Figure 9.1 Coolant temperature map of a 1.6 litre passenger car (wind tunnel measurements)

apparent that coolant temperature decreases with increasing vehicle speed for a specific cooling system layout; it approaches boiling point in the first-gear range.

The maximum coolant temperature requirements can lead to completely different engineering approaches within a given class of vehicles. For example, the radiators and cooling fans of vehicles ¢ ' and 'Â' , both having the same engine power, are compared in Fig. 9.2. One system has a wide mesh matrix with a cooling fan driven by the crankshaft, the other a dense mesh radiator with an electric cooling fan. Both require virtually the same installation space.

Other requirements must be fulfilled along with the cooling function:

• Low total manufacturing cost • Low overall weight • Low operating cost (i.e. low energy consumption of fan, good drag coefficient, reliability) • No annoying noises, from high cooling fan tip speeds, etc.

Cooling system requirements 357

Vehicle A Pressure drop Coefficient of heat transfer per unit of frontal area Radiator material Frontal area Cooling fan power

fic-3

6.5kW/m2/°C Cu-Ms 0.15 m2

1.1 kW

Vehicle B Pressure drop Coefficient of heat transfer per unit of frontal area Radiator material Frontal area Cooling fan power

* k = 6

10kW/m2/°C Steel 0.11 m2

0.08 kW

Engine power 85-90 HP Displacement 1.6 £

Figure 9.2 Radiator and cooling fan systems for vehicles with the same engine power

For example, Fig. 9.3 shows the qualitative curves for manufacturing cost, operating cost, and fan noise against radiator frontal area. As radiator frontal area increases, cooling fan noise decreases, since ram air provides most of the heat transfer. Manufacturing cost would be minimized if an expensive cooling fan were not required, and if the radiator size were limited, thus limiting the associated technical problems of installation. Operating cost would be high if the power required to drive the fan were high. A large radiator frontal area could increase the cooling system's contribution to overall air drag and result in increased fuel consumption. The 'optimum' result can be found within the shaded area in Fig. 9.3.

Manufacturing costs Operating costs Cooling fan noise Optimum results

Radiator frontal area Figure 9.3 Optimizing a water cooling system

The target values for the individual components of the cooling system are established in a so-called 'Specification Catalogue' for the particular vehicle.

What follows mainly concerns cooling system aspects of thermal safety, cooling fan power consumption requirements, manufacturing cost, and weight.


9.2.1 Design goals in the road performance map

In practice, very large, and therefore expensive, radiators would result from the need to run the vehicle at steady state for all operating points in the road performance map. Extreme gradients in the order of 20 per cent, which must still be negotiable by the vehicle according to the map, are only encountered for such short distances that they are meaningless as design criteria. Studies completed by Haas9 * aimed to define criteria in the road performance map, so that the cooling system would handle all conditions that occur in normal vehicle operation. Accordingly the cooling system must be sized for two specific operating points that have crystallized out of long-term observations made of the traffic scenario in Europe:

1. The vehicle must be able to drive continuously up a 10 per cent gradient at a speed of 25 km/h (15.6mile/h) while fully loaded and towing maximum trailer weight.

2. The vehicle must be able to run at top speed without constraints.

The following specifications apply to the temperature differences between the cooling air inlet and coolant fluid inlet, in addition to the conditions for the technical aspects of driving: while climbing hills and while at top speed, this difference may not be greater than 80°C or 65°C respectively. This applies for 'European' operating conditions and when pressurized systems with water and antifreeze are used,9 2 as is common practice today.

Figure 9.4 shows the road performance map for a vehicle with a 66kW

N 6400

5600

4800

[4000

3200

2400

1600

800

120 km/h 160

VD~ Figure 9.4 Design targets for the cooling system in the road performance map

Cooling system requirements 359

(88 hp) engine towing a trailer. The resistance curve for level road operation without a trailer has been included: design targets are identified as Á÷ and A2. A drag coefficient was assumed (as per Beauvais,9 3 see also section 4.3.2.13) and the towing vehicle cross-section served as the reference frontal area. It can be seen in Fig. 9.4 that a power of around 23 kW is required for hill climb Al5 using first gear with the engine under partial load. The full power level is 66 kW at design target A2.

9.2.2 Heat rejection to coolant by the engine

The heat rejected to the coolant by the engine is the next item of interest, since the required power levels have been established in the previous section. Various attempts have been made to calculate this heat with greater precision than that provided by the raw figure of 30 per cent of the input fuel energy, which was mentioned in section 1.1.1. Thus, for example, Drucker9 4 gave an equation for computing the heat rejected to coolant fluid. Work by Cramer9 5 concerning the influence of engine thermal efficiency on heat flux to the coolant should also be mentioned here. However, since the amount of heat transferred to the coolant depends on such items as cylinder head design, precise test stand measurements with a sample engine are indispensable for optimum cooling system design. Such test data are compiled in Fig. 9.5 for various engines in

Engine data

Figure 9.5 Rejected heat to coolant for various engines under full load

the form of heat rejected to the coolant at full load, plotted against engine speed as a fraction of the engine speed at peak power.

Three aspects are of special interest: • The dependence of heat rejection upon engine speed is very slight. • The ratio of heat rejection to output power is between values of 0.5 and 0.7, and thus is less than unity.


• The ratio of heat rejection to output power decreases with an increase in engine displacement for the same number of cylinders, due to the variations in combustion chamber volume and surface area for heat transfer.

1.61

1.4

A.1 0 p 0.8

0.6

:'$m%

•y.v ,>».■>; I

o 1.4 litres-70 HP/51 kW a 1.4 litres-75 HP/55 kW . � 1.6 litres-85 HP/62 kW A 1.7 litres -75 HP/55 kW -• 2.8 litres -125 HP/92 kW

A? = 3000 1/min

1 i ''••�•W»v^<vΔ,.,i(.vj

! 0.25 0.50 0.75 1.00 1.25

PPam* ** Figure 9.6 Rejected heat to coolant for different engines under part load

Engine heat flow under part load must be known for sizing a radiator for hill climbing. Figure 9.6 shows measurements for a series of 4-cylinder engines, and one 2.8 litre, 6-cylinder engine (the latter from Haas9 ). The relationship of heat flow to power clearly increases to values above one as the power ratio P/Pmax decreases.

9.3 Elements of the cooling system 9.3.1 Cooling air inlet

The design-related preconditions for installing a radiator in a vehicle are unfavourable, as compared to those for designing a ducted radiator for an aircraft (see Linke96). Available space is defined and limited by cross-members, the engine, and auxiliaries, and air flow is constricted by car body design and auxiliary headlights. Figure 9.7 shows that the air

Figure 9.7 Cooling air flow and the pressure characteristic in the cooling system passenger car

of a

Elements of the cooling system 361

C v / / / / ,

Renault 16 fG = - ^ £

ReQ =3.104

10° 20° 30° 40° 50°

Figure 9.8 Loss coefficient of various radiator grills for angular air inflow

stream does not approach the inlet grill parallel to the road surface as is frequently assumed.9 25 This flow pattern must be considered when the radiator grill is designed. Figure 9.8 shows that the pressure drop coefficient æá of the radiator grill is largely dependent upon the angle of attack aG of the radiator grill to the local air flow.9 25 According to Eqn 2.53 the following definition applies for the grill:

ζο = (9.1)

The flow in front of a porous wall (analogous to a radiator) was studied by Taylor.9 7 For a vehicle speed VO the cooling air face velocity vA can be calculated for two different radiator arrangements (with or without shroud baffling of the air leaving the radiator) as a function of the pressure loss coefficient æé of the air duct, including the radiator. This assumes that all components that cause a pressure loss are represented as a single item by the pressure loss coefficient æ^ Figure 9.9 depicts curves for the functions:

(9.2)

(9.3)

vA

Vu

vA

= 1

'4 1

vD V(l + ζ,)

The case of an unbaffled air flow from the radiator corresponds approximately to that of a 'free-flying' oil cooler installation in a racing car (tt = æ0> while the shroud-baffled air flow from the radiator is the general radiator arrangement in a passenger car. Individual elements such as radiator, grill, air baffling and engine compartment, have varying effects on system pressure loss. Limits are at approximately æé = 4 for a very porous system and æé = 8 for a severely constricted system. In this range of pressure loss coefficients, experiments with scale models and full-size vehicles agree well with theory; the difference between the two limiting radiator arrangements is only small. As shown in Fig. 9.9, higher cooling

Figure 9.9 Ratio of cooling air face velocity to vehicle speed against different cooling system loss coefficients

air face velocities can be achieved with a 'free-flying' radiator arrangement only for small pressure drop coefficients æ{.

The cooling system should contribute as little as possible to total drag. Assuming that air flows into and out of the cooling system at the same velocity, and that static pressure at the outlet corresponds to ambient pressure,9

CDR — 2

9.8 then: 1

_ V(i + æ,) 1

1 + æ._ (9.4)

for the resistance due to cooling air flow through the system. The drag coefficient of the cooling system cD R can be converted to the cooling system's share of the vehicle drag coefficient through the ratio of radiator frontal area AR to vehicle frontal area A:

Ac] DR C D R (9.5)

For example, for a very porous cooling system (æé = 3) and a frontal area ratio of 0.1 of the vehicle cross-section, the radiator system adds to the vehicle's drag coefficient AcDR = 0.05 according to Eqns 9.4 and 9.5. Most current passenger cars have a drag coefficient in the range 0.35 ^ cD ^ 0.45. Thus the cooling system's share of the drag coefficient could amount to more than 10 per cent for a very porous system.

The drag due to cooling can only be approximately determined from Eqn 9.4, since it does not consider the resistance due to the change to the air flow around the nose of a vehicle caused by air through the radiator system (interference drag). Schenkel" examined the influence of front-mounted spoilers on flow relationship within the engine compart-ment; see also section 4.3.2.9.

9.3.2 Radiators for passenger cars

All current radiators are of the cross-flow type, though different materials are used, e.g. heavy metal radiators (iron, brass, copper) and light metal radiators (aluminium). Five different aluminium radiator designs are

Elements of the cooling system 363

� Soldered � Adhesively bonded O Mechanically joined

Δ Welded T Skyve-fin

Figure 9.10 Aluminium matrix designs

shown in Fig. 9.10.9 26 They are a soldered core of VW manufacture, the standard VW-Sofica radiator core, the adhesive bonded AED-Covrad core, the laser welded core design of Union Carbide, and the Skyve Fin core design of Schmöle.

Low manufacturing cost and minimum fan power are the most important factors in the development of car radiators. Here the work of Dehn,910

Lorenz,911 and Kays and London9 12 should be mentioned.

9.3.3 Radiator cooling fan

Axial fans are used in almost all cars to increase the cooling air flow. Low cost and power consumption and low noise are the main advantages. Belt drive from the engine crankshaft is the cheapest, but optimum matching of the fan to the various load conditions is best realized by an electric fan.

Figure 9.11 Cooling fan map


Cooling fan data must be known before designing a cooling system. Fan characteristics should be presented as the relationship between pressure coefficient and volume coefficient (Fig. 9.11), since the cooling fan map would then shrink to a single curve. Extensive work has been done in this field by Eckert9 1 3 - 9 1 5 and Marcinowsky.9 16

9.3.4 Water pump

Centrifugal (radial) pumps are used exclusively in vehicle cooling systems to circulate the coolant, partly because of cost. They are usually crankshaft-driven.9 17 Dimensionless presentation of the characteristics is recommended (Fig. 9.12).

*F

Ί.0

0.8

0.6

0.4

0.2

TîZ

~7 Vehicle F

^

Vehicle S

^ " ^ rpm

a nf - 1900 1 /min Ä 3000 o 4500 � 1500 A 3000 • 5000

4 6 810-

Figure 9.12 Water pump map

9.4 Designing the cooling system

To design a cooling system, the following must be known: heat rejection by the engine, vehicle road speed (road performance map), and the flow rate and composition (glycol additive) of the coolant. A procedure for designing and computing has been developed by Emmenthal.9 18

9.4.1 The radiator as a cross-flow heat exchanger

Nusselt919 described the laws of heat transfer in cross-flow. Bosnjakovic et al.9,20 expressed the relationships in the form of radiator efficiency Ö, which is dependent upon the flow capacity rates of the fluid WF and the air WL, and the product of the overall coefficient of heat transfer and heat transferring surfaces. The average coefficient of heat transfer can also be referred to other surface areas since the overall coefficient of heat transfer is, by itself, not of importance in this context, but only in the previously mentioned combination with heat-transferring exchanger surface areas. The frontal area of the radiator is taken as a reference surface since it is of decisive importance in passenger car construction. Also, since it is more easily measured than surface areas within the radiator core, errors due to imprecise surface measurement become negligible when this reference is

Designing the cooling system 365

used. The drawback, that the overall coefficients of heat transfer kA will be solely device-dependent, can be accepted in this case.

The function:

Ö (kAA

wL/wF) = ^LE ~ ^LA

ß Å ~~ ^FE (9.6)

is reflected in Fig. 9.13 for the case where the coolant flow will be compensated for with respect to the temperature profile for each heat exchanger element (WF is well mixed transverse to its own flow direction).

to. 0

1.0!

0.8

•6|

0.4

0.2|

^ffi 0 = *VL(fLE-fFE)0

0.2 0.4 0.6 0.8 1.0 1.2 Nu* ^

Re*Pr

Figure 9.13 Radiator efficiency of the cross-flow heat exchanger

The radiator efficiency Ö that achieves the uppermost limit of unity if the air leaves the radiator at the coolant fluid inlet temperature, could assume values of Ö = 0.8 for very densely packed radiators and low air velocities (hill climbing). The ratio of WL/WF is between limits of 0.05 and 0.5.

An enclosed term is given in ref. 9.20 for the function 0(A:AA/WL, WL/WF). This is used in the following for the calculation of heat transfer.

Φ = * L Γΐ - exp exp (9.7)

The coefficient of heat transfer kA of the radiator must be known for evaluation of Eqn 9.7. With a metal radiator, the thermal resistance of the material between air and coolant fluid will have subordinate importance: the overall coefficient of heat transfer is primarily a function of the air and coolant-related heat transfer coefficients aL and aF.

Various approaches have been used to compute the overall air-related coefficient of heat transfer. First of all the flow within the matrix must be examined (see Beauvais9 21 and Paish9 22 and more recent results from Wong and Smith9 2 3) .

None of the methods of computing coefficients for heat transfer and pressure loss is precise enough for radiator sizing and for predicting the operating behaviour. Also, since turbulators are sometimes used in the coolant tubes to improve heat transfer per unit of frontal area in compact radiators, knowledge of the coolant related coefficient of heat transfer aF is also required: this, as will be shown later, is a primary co-determinant of the value of the overall coefficient of heat transfer during vehicle


operation. Hence precise measurements of the radiator characteristic data are used for calculating heat transfer.

9.4.2 Measurement of radiator data

Radiator data can be determined at a test stand, as in Fig. 9.14. This involves use of a small wind tunnel. Measurements are made of air temperature rise (air side At), due to heat rejection by the heated core, and coolant temperature drop (coolant At), for different coolant flows. Air and

Air Circuit: Power: />=40kW Test section i W s 30m/s /4=0.115m2

Contraction 11:1 Turbulence level 0.5% Coolant fluid circuit: Heating power: 0 = 75 kW Fluid flow: V'p = 250 l/min

Figure 9.14 Schematic of a test stand for measuring radiator data

Nu

104

8

'i «

3

2

103

fF =90°C^ V

X X

> Nu

*

kv 1

7 K ^ 1 r

*>>

*T

>

*m

«*

*

·-

¾" Jr Ί

Jr

Matrix S L = 0.03

\ s V V ^ %*r ] ^ -r^-cr Γ\, J Matrix F t~Z.=0.03

2

^ > ~^

>^

5

«*r * T V

-^ο,

^ - o . •^

101

8 6 5 4

3 fK

10° 103 2 3 4 5 6 8 104

Re* —

2 3 4 5 6 8 105

Figure 9.15 Heat transfer and air-side pressure loss of two different matrix designs

coolant flow-related pressure losses are also determined. Results are plotted in non-dimensional form. Heat transfer and air-related pressure losses of two different designs are shown versus Reynolds number, based on face velocity and radiator matrix depth, in Fig. 9.15.

Figure 9.16 shows the dependence of heat transfer upon coolant Reynolds number within the tubes of the radiator. From the characteristics of the curves it can be seen that heat transfer is strongly dependent upon coolant velocity, particularly at high air velocities.


2000 4000 6000 8000

ReF �

Figure 9.16 Heat transfer of a radiator matrix

9.4.3 Sizing the radiator

Calculations for radiator layout must take into consideration the fact that in practice air flow through a radiator is not uniform over its surface. Since parts of the radiator are frequently obstructed by bumpers or bodywork, the velocity profile of the incoming air is non-uniform. The cooling fan may act on the whole radiator or only part of it, so that its share in the velocity profile may also be non-uniform.

The heat flow to be rejected to the coolant by the engine is known from measurements for the previously mentioned engine loads: this can be expressed as:

O F = WF (ipE - rFA) (9.8)

Therefore, the coolant flow capacity rate WF is established for a chosen reduction in coolant temperature (iFE — iFA) at the radiator and the coolant flow of the pump is established for a known specific heat cF of the coolant, or the reverse.

In practice, one would aim for the lowest possible temperature difference to achieve higher values of radiator efficiency (see Fig. 9.13), good coolant fluid-related heat transfer coefficients in the radiator, cylinder head and engine block, and low thermal stress levels within the engine. However, water pump power consumption will increase markedly with increasing coolant fluid flow, and so the advantages gained in heat transfer have to be set in relation to increased power expenditures.

The following applies for relationships between the heat flow, the radiator efficiency and the air and coolant inlet temperatures:

O F = WL (iLE - ßÑÅ)Ö (9.9)


From Eqns 9.9 and 9.7, one obtains:

Ö = i L E - i F E WL

1 exp exp * A ^

WLJ )!] (9.10)

In Eqn 9.10 the temperature tLA of the air leaving the radiator is a disruptive factor in further use of the equation. This quantity can be eliminated by combining Eqns 9.6, 9.7, 9.8 and 9.9.

'LE - U FA

*LE — ^FE exp É-ÀÇ'-¹ïÉ] (9.11)

In solving Eqn 9.11 for coolant outlet temperature iFA at the radiator, one obtains:

'FA *LE - OLE " *FE) e x P 1 - exp (9.12)

The following quantities and interdependences are known in both Eqns 9.8 and 9.12:

Eqn 9.8 ÖF Known from measurements at the engine; see Figs 9.5 and

9.6 Defined by the coolant fluid flow and the dependence of the data of the fluid upon coolant temperature: achievable at a defined temperature difference (iFE - tFA) Defined by design guidelines: calculated at a given coolant flow rate

Defined by the maximum ambient temperature or the temperature of the air leaving from a front-mounted condenser for an air conditioner Defined by design criteria Known from Eqn 9.8 Known from measurements of the dependence of the coefficients of heat transfer upon coolant and air flow

Equation 9.12 is evaluated by increasing the air flow capacity rate WL for the given radiator frontal area A of a known matrix design, until the coolant fluid outlet temperature according to Eqn 9.8 sets in. At least a portion of the air side capacity rate will be provided by available ram air in a front-mounted radiator arrangement; the remainder must be provided by the radiator cooling fan.

There is a set procedure for radiator sizing. The radiator is calculated, section by section, as shown in Fig. 9.17. For a non-uniform fan velocity, the sections are broken down further into, for example, square radiator elements. The core depth L is established when the matrix design is selected. In the example cited, the core height H is governed by design limitations. Calculation starts with the first section: this is treated initially as if it had to effect the entire heat transfer by itself. Cooling air velocity vA

^FE — ^FA

Eqn 9.12

^FE

WF

kA


H I Radiator section � i Radiator element Figure 9.17 Subdividing the radiator frontal area for Õ77Λ Oversizing radiator sizing

is increased step by step until the coolant fluid temperature tFA required by Eqn 9.8 is achieved. The required cooling air velocity is designated vAE. A second section is added to the first. Both of these together now represent the radiator. A smaller vAE velocity is now sufficient for heat transfer. This procedure continues until the width bmax that was prespecified by design is reached. Heat cross-transfer within the matrix is not considered.

Cooling air velocity vAD due to ram air can be determined for a prescribed driving speed and for the previously measured resistance characteristic æ, (íÁ) of the grill, radiator, and engine compartment as air ducting elements, by specifying a starting value for cooling air velocity vA, followed by iterative calculation of the function:

ÉΔ- = I (9 13) VD V[l + æ,(íÁ)] V'LO)

The consistent decrease in required cooling air velocity vAE is entered over the radiator width ft in Fig. 9.17; at a specific width, it equals that of the velocity vA D supplied by ram air.

The radiator is over-sized to the right-hand side of this abscissa value; on the left-hand side, a cooling fan must be provided to bring the air velocity from vA D to vAE(f>), in order to handle cooling tasks.

The air flow that the cooling fan must supply can be calculated, since the width b and height H constitute the radiator's frontal area: the pressure loss that has to be overcome by the cooling fan can then be determined from the velocities and resistance characteristics of the individual components. For example, required cooling fan power has been entered over the radiator width in Fig. 9.18 for different degrees of fan efficiency. These computations for the cooling system of a Volkswagen K 70 passenger car show that a reduction in radiator width leads to very high levels of required cooling fan power, particularly with an unshrouded cooling fan.


IU kW

9 8

Operating point: 2nd Gear range-wide open throttle 5000 rnin"1

56 cm 64

Point A: VW-K70 Figure 9.18 Cooling fan power versus radiator width, for different degrees of fan efficiency

Segmenting the radiator frontal area in individual elements can also respond to a very non-uniform face velocity profile due to car body components in front of the radiator. Velocity distributions at the radiator frontal area for a given vehicle are shown in Fig. 9.19 for a driving speed of 170km/h (106mile/h). Calculation of the coolant fluid temperature reduction for the mean velocity and for the given profile shows that averaging the face velocity leads to incorrect results (Fig. 9.20).

10 i m/s

"A

VD =170 km/h P = 62 kW

v Radiator

Figure 9.19 Cooling air flow profile of a passenger car with a 1.5 litre engine


12 m2 14-10"2

Figure 9.20 Computed coolant temperature curve of a passenger car with a 1.5 litre engine with mean air flow value and with differentiated face velocity

Since heat transfer is proportional to íÁå, where å assumes values <1,

heat transfer is poorer in the velocity 'valleys', which, compared to the mean value vA, are not compensated for by the higher excess velocities. Accordingly, for a non-uniformly shaped face velocity profile, less heat is transferred than at the average velocity vA computed from volume flow and frontal area.

9.4.4 Recomputing the system

The temperature curve should be computed for various speeds, otherwise the size would be valid for only one point in the road performance map. The coolant fluid temperatures in the 'off-design' points are also of

100 120 140 km/h 180

VD

Figure 9.21 Measured and computed coolant temperatures


interest. For example, prior to the final, costly tests on the vehicle, a picture of the operating behaviour of the system can be obtained with the aid of computation procedures, as described in ref. 9.18. The results of computation and measurements are compared in Fig. 9.21. The data predicted by the method of Emmenthal9 18 are in good agreement with the experimental results.

9.5 Experimental testing of the cooling system

The vehicle should be run at different loads on a chassis dynamometer in a full-scale wind tunnel for these measurements. The heating system should be disconnected; the thermostat is locked open. Depending upon the engine load, it takes about 20 minutes to reach thermal equilibrium. Results obtained from two different cooling systems in the same vehicle are given in Fig. 9.22.925 The coolant temperature curve shows the marked

A- 1500 cm2

Unbaffled air passage

/* = 1000 cm2

120 km/h 160 Baffled air passage

Figure 9.22 Comparison of coolant temperatures of two systems

dependence of the temperature on vehicle speed for the system with unbaffled air inlet and larger radiator frontal area, compared with the cooling system with a baffled air inlet and smaller radiator frontal area, which gives a more uniform temperature versus speed characteristic.

9.6 Evaluating the cooling system

The development of a radiator matrix for a specific application is relatively expensive, mainly because of the high cost of constructing and testing the prototype. It is therefore desirable to have an evaluation procedure that allows preliminary selection from the many types of possible radiator matrix designs, and thus reduce expenditure on prototypes and testing. Equations listed in Fig. 9.23 describe the performance of the radiator in a vehicle during driving. The engine rejects heat to the coolant fluid which must be transferred to ambient by the radiator. For a specific project, it can be assumed that this heat flow Q as a function of engine output power and speed is known. Even so, the temperature of the ambient air iLE and that of the coolant entering the radiator rWE must be viewed as 'given' by the

Evaluating the cooling system 373

operating conditions. The flow stream capacity rate WL of the air passing through the radiator, meaning the volume of cooling air flow, and the efficiency Ö of the radiator (both quantities are also defined in Fig. 9.23) must be adjusted to satisfy the equation for heat flow.

The velocity of the inflowing air vA is dependent upon the speed VO at which the vehicle is being driven, and upon the radiator cooling-fan operating data. The evaluation process is clearer in the case without cooling-fan operation. The aerodynamic efficiency ç, meaning the ratio of face velocity vA to driving speed VO (see Fig. 9.23), is, for its part, a function of the pressure drop coefficient æ of the cooling air path.

Heat flow

Q = WL ( f L E - t F E ) 0

WL=pvAA CPL

0 = fl - E - fLA ,

iLE " fFE

Face velocity

Radiator frontal area A

■¢ - T? * VL Required radiator frontal area

1 - Ö

Vb P cp L (f LE - - * F E )

m J_ çφ P 2

�7Ã- KA

2 A

Figure 9.23 Heat flow, cooling air velocity, and required radiator frontal area

£Τ7777,

Figure 9.24 Evaluation of different radiator matrix designs, after ref. 9.25

From the equations listed in Fig. 9.23 for a specific radiator design, which is characterized by its aerodynamic and heat transfer properties in the form of É/çÖ, the magnitude of the necessary frontal area can be derived. This frontal area is

1 ç ö

(9.14)

This relation has been used to compare and evaluate different radiator matrix designs by Hucho.9 25 The higher the product çÖ, the better the radiator performance.

An evaluation of different radiator designs is shown in Fig. 9.24. The


product çÖ has been plotted against ReO, the Reynolds number at the driving speed. It is evident from Fig. 9.24 that pronounced differences in heat transfer occur at higher vehicle speeds (ReD ~ 105).

This evaluation method indicates some of the targets for future radiator development, such as lower air-related pressure losses and improved heat transfer. Improvements to heat transfer alone could too easily be nullified by higher air resistance.

Since the only item of real importance is cost per unit of heat transferred, the selection of material and manufacturing process is of predominant interest. The radiator of the future must therefore provide increased heat transfer with a cheaper material and be capable of manufacture by an even more cost-effective process.

9.7 Notation

Geometric A B D F

Dv H L b dhyd

oc

variables frontal area core width diameter of the water pump impeller diameter of the cooling fan core height core depth linear width hydraulic diameter angle of incidence of the radiator

Engine!vehicle variables F z tractive force P, Pmax engine power output (*PS = DIN horsepower) n speed in revolutions per minute np speed at rated output power

Heat flow and air flow fluid variables Qc R A B heat flow from convection (C), radiation (R), exhaust (A),

and fuel (B) O F heat flow UF tip speed, water pump impeller Uv tip speed, cooling fan VO vehicle speed VF coolant flow rate WL flow stream capacity rate cF specific heat of the fluid cpL specific heat of the air kA coefficient of heat transfer as referenced to the radiator

frontal area p0 ambient pressure /FE fluid temperature, radiator inlet tFA fluid temperature, radiator outlet iLE air temperature, radiator inlet iLA air temperature, radiator outlet

Notation 375

boiling temperature vA = VJA mean cooling air velocity velocity of cooling air flow (face velocity) required cooling air velocity velocity of cooling air flow due to ram air velocity in the radiator tube air velocity in front of the radiator grill static pressure loss thermal conductivity of ambient air inflow density of the air and of the fluid kinematic viscosity of ambient air inflow kinematic viscosity of coolent fluid

*2 vA VA

V A E

V A D

VF

Ap

p and pF

v vF Dimensionless expressions CO

Re* = vAL/v ReG = vGLG/v ReF = vFdhydT/vF

ReO* = VOLN = ReGV(l + æ<)

Nu* = kAL/XL æ* = 2Äñ/ñíÁ

2

ζó = 2Ap/pvG2

St

öÑ = 4VF/UFKD2F

ö í = 4VJUvnD2v

Ö = (iLE - ' L A ) / ( ' L E " ^FE) øÑ = 2Ap/pFUF

2

øí = 2Ap/pFUv2

air drag coefficient Reynolds number, air side Reynolds number, radiator grill Reynolds number, coolant (watertube) Reynolds number of the operating condition Nusselt number pressure drop coefficient, radiator, air side pressure drop coefficient, grill pressure drop coefficient, total air passage, as referenced to vA fan efficiency volume coefficient, water pump volume coefficient, cooling fan radiator efficiency pressure coefficient, water pump pressure coefficient, cooling fan

Chapter 10

Heating, ventilation and air conditioning of motor vehicles Werner Gengenbach

10.1 Climate

The climate of a region usually means the typical atmospheric conditions and characteristics of the weather. Climate influences the quality of life and even the possibility of maintaining life at all. It comprises the following factors: air temperature air ionization air humidity partial pressure of oxygen air circulation electrostatic fields radiation radioactivity air pressure

In addition to the broad definition of climate, we also speak of a climate on a small scale, such as the passenger compartment of a car. Much has been written about 'climate control' in buildings, living and working areas, and reference will be made to some of these studies, since there is very little literature available on climate control in cars. Nor is any work known on the physical effects of electrical phenomena. Therefore neither electrostatic fields nor ionized air is considered.

As the term 'climate control' implies, the climate is not only defined but is regulated to provide optimum comfort, though it is not possible to influence all climatic factors in a motor vehicle. In the main, air temperature, air humidity and speed of air flow can be changed.

Climate control enhances safety in traffic in two ways. It enables the driver to concentrate better, thus reducing the risk of an accident. Also, by directing the air flow properly, the car's windows can be kept free of moisture, thus guaranteeing good visibility.

10.2 Physical aspects of climate

Several investigators have studied comfort and climate in living and working areas, but their work cannot be applied unconditionally to the motor vehicle, where volume occupied and duration of occupancy are so different.

The climatic factors that particularly affect comfort are dealt with in the following sections. 376

Physical aspects of climate 377

10.2.1 Interior temperature

Figure 10.1 shows the suggestions of various authors for a comfortable car interior temperature. Stolz10 21 suggests 26-30°C, regardless of ambient temperature, whereas Müllejans and Illg1016 recommend 25-33°C for an ambient temperature of -20°C. Veil10 suggests an interior temperature of 22°C regardless of outside temperature, a value also recommended for motor vehicles by DIN 194610 4 in the range from -18 to +20°C.

Average-interior temperature f j

-30 -20 -10 0 +10 +20 +30 °C +40 Ambient temperature ra �

Figure 10.1 Specifications given in the literature concerning comfortable temperature in the interior of a motor vehicle, related to ambient temperature; compiled by J. Temming

In the author's opinion, the temperature range for comfort should be related to ambience. During winter one feels comfortable at a somewhat higher temperature than in summer. When the body is accustomed to very high outside temperatures, the temperature experienced as comfortable also rises. There are also medical reasons for raising the temperature of the interior; given for instance an ambient temperature of +40°C and an interior temperature of 22°C, the risk of cold infection is increased by the temperature difference.

The author's recommendation ('Audi' curve in Fig. 10.1) shows a rough range of temperature which is considered comfortable. Clothing, the time of day, state of health of the passengers, etc. will influence these figures, and it is important that the interior temperature can be finely adjusted over a wide range.

The data given in Fig. 10.1 are based on many years of experience. It will be noted that interior temperatures of motor vehicles are somewhat higher than for living or working areas. This is because the temperature of radiation from the walls of a building is considered the same as the room temperature, which is correct. In a motor vehicle, however, the relatively large glass areas may be cooler than the passenger compartment. Therefore the radiation from the windows has to be compensated for in winter by a higher interior temperature, the more so when the outside temperature—and consequently the temperature of the window surfaces— falls. In summer the opposite is the case. In cars with air conditioning the delivery of cold air has to compensate for the heat of the sun through the large, inclined glass areas typical of modern cars.

378 Heating, ventilation and air conditioning of motor vehicles

In buildings, it is sufficient to specify a standard temperature for the indoor space. In a motor vehicle, however, it is necessary to specify a difference in temperature between head and foot level, referred to as temperature stratification. Miura10 15 describes tests on 50 individuals in a climatic chamber to determine the most comfortable temperature stratification. Figure 10.2 shows that a temperature difference of approximately 7°C between the foot and head areas was found to be the most comfortable.

20 25 30 35 40 °C 45 Air temperature for maximum comfort � -

Figure 10.2 Statistical investigation to find the most comfortable temperatures in foot and head areas inside a motor vehicle, after ref. 10.15

Similar figures can be found in other literature dealing specifically with temperature distribution in motor vehicles. None of these articles mentions the sources used, so it can be taken that they are the result of extensive experience of engineers from the automotive industry concerned with heating and climate control.

Figure 10.2 shows clearly the wide range of temperatures found comfortable by various persons under the same conditions. Differences of up to 14°C were recorded for the foot wells as well as for the head area.

The results referred to so far indicate comfortable temperatures in the steady-state condition. Tests involving 3000 people carried out by Rohles and Wallis10 19 established that the time necessary to reach a comfortable temperature after switching on the air-conditioning unit in a car left standing in the sun depends only on the air delivery rate, the temperature of the cooled air and the seating position (front or rear). With a constant air delivery rate, the size of the outlets and therefore the air speed are of no importance.

The conditions for heating-up are much more complex, as the passengers' response is masked by the warm-up phase of the engine, etc.

10.2.2 Air speed

It is well known that people experience the temperature of still air differently from that of moving air. When the ambient temperature is lower than skin temperature, the temperature has to be raised with increasing air speed to give the same subjective feeling of temperature as in

Physical aspects of climate 379

still air. The literature is divided regarding the relationship involved. Figure 10.3 shows a compilation by Temming of data from the literature (refs 10.4, 10.7, 10.13, 10.14, 10.22). Notably, the graph by Fänger107

shows the existence of a temperature limit where the subjective feeling of temperature no longer changes even if air speed is increased above about 1.5 m/s. This is in accordance with practical observations, at least as far as qualitative results are concerned.

1.4 m/s

11.2 1 i.o

fo.8 £ 0.6 <

0.4

0.2

0 Â- /

Fδnger I 1970 1

Lies« / 1 9 7 0 /

S

^

/ 1

A 'S

b /

À

T 7Lutz 7 /1970/

C^

Π

Effective temperature (Yaglou 1927) Limit temperature

\U1 >l 1 9 «tu/

0v 18 19 20 21 22 23 24 25 26 °C 28 Air temperature �

Figure 10.3 Influence of air speed (air flow directed at occupants) on subjective feeling of temperature. Comparison of publications by various authors; compiled by J. Temming

When the air temperature exceeds the skin temperature, as in hot desert areas, the gradient of the graph is reversed, i.e. the moving air feels hotter than still air. Therefore, when driving without air conditioning in temperatures above 40°C all windows and all air outlets should be closed.

Similarly, when heating the passenger compartment a direct air stream onto the passengers should always be avoided. The outlets for heated air therefore require very careful location and an optimally directed air flow, regardless of air delivery rates.

In summer, however, at higher ambient temperatures, a direct air stream to the body enhances comfort. It is best to direct the flow to the chest area at an air speed of up to 3 m/s, but the throat and uncovered wrists should not be subjected to a direct air flow due to the risk of cold infection. The face, too, and especially the eyes, must be protected from faster air flows. For medical reasons, high air speeds should be avoided completely, even though they bring about a local feeling of intensive cooling. It is preferable to direct large quantities of air towards the passengers over a wide area. When outside temperatures are low or when air conditioning is used, it should be possible to introduce slightly warmed-up air (reheat system with completely integrated air con-ditioning).

Today, this knowledge is widely utilized in every modern car equipped with different air outlets for heating and ventilation. It should be possible to adjust the outlets individually for air delivery and direction.

10.2.3 Air humidity

The control mechanism that stabilizes the temperature of the human body at approximately 37°C uses, amongst other things, the latent heat of


evaporation of perspiration on the surface of the skin. Even in neutral thermal conditions, the human body releases perspiration at the rate of about 25 g per hour. This quantity increases as surrounding temperature rises. The evaporation of moisture on the skin surface and thus the feeling of comfort depends of course on the vapour pressure of the surroundings and thus on the relative humidity of the ambient air. It is not easy to stipulate exact limits of conditions still felt to be comfortable, or which may become uncomfortable, for many factors have a large influence, e.g. solar radiation, physical stress and minor day-to-day health variations, etc.

The literature very often indicates a water vapour pressure of 1.87 x 103Pa as the limit where conditions are felt to be 'close', or oppressive. This water vapour pressure results in a relative humidity of

80 per cent at an ambient temperature of 20°C 60 per cent at an ambient temperature of 25°C 45 per cent at an ambient temperature of 30°C

Figure 10.4 Comfort ranges in h-x graph, distinguished for summer and winter

How climate can be influenced 381

When these limits of humidity are exceeded, the only way of preventing the atmosphere becoming oppressive is to dry the air in the vehicle by means of an air-conditioning system.

On the other hand, air that is too dry is not necessarily uncomfortable, although health can be impaired due to the higher infection risk, rough skin, chapped lips, etc. In such cases the air in fully air-conditioned buildings is humidified artificially. No such conditions are known for motor vehicles, especially since there is no source of data for the relatively short periods spent travelling in vehicles with extremely dry air.

Comfort at varying temperatures and humidity conditions is shown in the h-x graph (Fig. 10.4), which also distinguishes summer and winter operation.

10.2.4 Requirements for climate control in motor vehicles

The requirements for a comfortable climate in a motor vehicle can be summarized as follows: • Temperature must be adjustable over a wide range; fine adjustment is important. • Temperature should vary as little as possible during driving. • Warm air should not be blown directly onto the passengers. • Headroom should be about 7°C cooler than the footwells (temperature stratification). • Relative air humidity should be between 30 and 70 per cent. • It must be possible to direct ventilating air towards the occupants at the required temperature. Direction and air delivery must be adjustable. The air flow to the body should cover a large area at not too high a speed. Air speed should be low on the face, neck and wrists.

10.3 How climate can be influenced

Figure 10.5 shows two examples of how the climate in the passenger compartment can be influenced when the interior is heated. The first example assumes a foggy day at an ambient temperature of about 10?C with 100 per cent relative humidity; the air must be heated to about 45°C in the heater so as to obtain a mean temperature of about 25°C in the vehicle. Assuming that 2 g of water per kilogram of air are absorbed from the moist air exhaled by the passengers and possibly from damp clothing, the resulting humidity is about 45 per cent, which is still within the range of comfort.

The second example assumes that air is heated from — 10°C with 100 per cent relative humidity up to about 28°C in the interior. Here, too, we can take it that 1kg of air entering the car absorbs about 2g of water. The result is a relative humidity of 16 per cent, which means that the air is too dry. The possibility of chapped skin and the increased infection risk have already been pointed out.

At high outside temperatures and air humidity levels, ventilation alone cannot produce a comfortable climate in the car. However, in this case the


Figure 10.5 Effect on variables when air is heated to warm car interior: (a) at 10°C with saturated air; (b) at -10°C with saturated air

installation of air conditioning can be of considerable advantage. Figure 10.6 shows the changes in variables when air conditioning is used. Fresh air operation is assumed, with outside temperature 40°C and a relative air humidity of about 30 per cent. Such climatic conditions prevail for instance in Colorado, USA, and are very uncomfortable and oppressive.

The air entering the air conditioner is cooled to about 8°C by the evaporator. Here, about 7g of water are lost for each kilogram of air fed into the compartment. The resulting interior temperature of about 27°C results in a relative humidity of 40 per cent, again assuming that about 2g of water are absorbed per kilogram of air. Thus the conditions obtained are within the range of comfort. It is obvious that the cooling effect of the air conditioner is all taken up in condensing the water and thus is no longer available for cooling the air.

How climate can be influenced 383

Figure 10.6 Effect on variables when air is cooled by air conditioner. Ambient air: 40°C and 30 per cent relative humidity

These examples show that, especially when only heating and ventilation are employed, climate control in the vehicle interior is not possible to the full extent desirable. Only the temperature of the air can be so influenced, and then only by heating. The resulting relative drying effect cannot be avoided. At outside temperatures only slightly above the comfort range, air directed towards the passengers over as wide an area as possible will restore comfort. Excessive air humidity cannot be influenced.

Only by installing an integrated air conditioner (or refrigeration system) can the climate in the vehicle be influenced further, and the uncomfortable air humidity at higher temperatures be reduced. Furthermore, the temperature in the vehicle can be lowered as well as raised in relation to the outside temperature.


10.4 Components of a heating and ventilation system

Climate control in the passenger compartment is usually effected by means of a heating and ventilation system, with which every modern vehicle is equipped. Greater demands for climate control can only be satisfied by an air conditioner. Although air conditioning does not fall within the scope of this chapter the comments on heating can basically be applied to air conditioning if the state of the air fed to the heater is altered accordingly, i.e. if the temperature is lowered and (as in most cases) if the air is saturated with water vapour.

The main components of a heating and ventilation system are: car body, heat exchanger, fan, and controls.

10.4.1 Car body

The requirements for producing a volume flow are a pressure difference and an open area allowing through flow. Firstly, the pressure difference provided by the fan itself is used for producing an air flow, and secondly the body itself plays a most important part. (See also sections 2.3.2, 6.2.2 and 12.3.3.1.)

By reason of its design the passenger compartment of a vehicle can never be quite airtight. There are always air leaks at weatherstrips, window frames, welding flanges, grommet holes, etc. through which the air in the passenger compartment can be exchanged with the outside air. Following the definition in section 12.3.3, the cross-sectional area of these leakage points can be determined relatively easily by blowing air into the interior by means of a test fan with an airtight duct and flow measuring equipment, and by recording the amount of air leakage in relation to the pressure in the passenger compartment. Having obtained this graph, we can assume the same flow rate through a nozzle with an area Ae, working without loss. This area can be taken as the effective cross-sectional area passed through by the air leaking out of the body (like an 'equivalent nozzle'). The advantage of this procedure in comparison with other methods is that the

Figure 10.7 Distribution of equivalent leakage cross-sectional areas related to the pressure coefficient at closed air outlets of the cabin. (The author thanks Dipl.-Ing. Holger Grossmann, Audi AG Ingolstadt, for kindly letting him have this so-far unpublished material)

Components of a heating and ventilation system 385

leakage area is represented clearly and simply, and if there is any alteration the change can be directly added or subtracted.

The air flow around a moving vehicle gives rise to high pressure areas at points where the air flow is retarded, and low pressure areas at points where the flow is accelerated, as shown in section 2.3.2. The air leaks from the body described above are distributed at various positions on the vehicle, so the pressure coefficient for the various leakage points will also be different. Generally, this results in a distribution curve which is characteristic for a particular vehicle, but which does not differ greatly from vehicle to vehicle. Figure 10.7 shows a distribution curve of this kind. The equivalent cross-sectional area is shown as a distribution related to the effective pressure coefficient cp. The resulting leakage air flow can be derived from the sum of the individual leakage cross-sectional areas with the appropriate pressure drop.

As can be concluded from Fig. 10.7 the leaks are generally concentrated at locations where the pressure is below ambient (cp < 0), whereas the air intake is always at a position of pressure higher than ambient (cp > 0). This explains why even cars with no special provision for air extraction have a through flow of air. Its mass flow can be calculated from Eqns 2.50 and 2.51.

The random leakage areas of a body shell depend largely on the quality in production. It has therefore been general practice for several years not to leave air extraction from the passenger compartment to chance, but to provide extraction apertures for the purpose. The intensity of the low pressure area at the extraction aperture location enables the air flow through the compartment to be related to road speed with a steeper or flatter gradient. If a point with slight negative pressure is chosen with an appropriately large cross-sectional area, the air flow does not vary greatly with road speed; if a position is chosen with greater negative pressure, the air flow rises sharply as road speed increases. The best arrangement appears to be one where air flow does not vary greatly with road speed, and where high air flow rates are obtained at low road speeds and when the vehicle is stationary.

In practice it is difficult and time-consuming to determine the individual leakage cross-sections and the appropriate pressure coefficients. A practical method is to measure the air extraction characteristics of the vehicle by blanking off the extraction vents and determining the air flow with a test blower in relation to the interior pressure in the vehicle, see section 12.3.3. It is now possible to determine the extraction curve for the leakage areas and the extraction openings together, either mathematically or by measurement, both for the stationary vehicle and for a constant road speed. A diagram of this kind is shown schematically in Fig. 10.8. The diagram also shows the characteristics of the incoming air flow, which are partly determined by the characteristics of the heater fan employed. Operation without the fan, using ram air only, is also represented. The points of intersection of the curves give information concerning the air flow and how this varies with road speed.

This technique provides useful information about air flow at an early stage of development, and makes it possible to optimize the position and effectiveness of the extractor vents on the car. For this purpose it is


Air leakage (hardly influenced by body design)

Lo

Air extraction (influenced by body design)

Figure 10.8 Characteristic curves for ventilation air intake and extraction from the vehicle interior, and—at intersections—determination of air throughput; index 0, speed V = 0, index 100, speed V = 100 km/h (62.5 mile/h)

necessary to know the equivalent leakage area Ae, for which data of sufficient accuracy are usually available from the previous model, or which can at least be estimated if the design of the body shell is changed. It is also necessary to know the pressure distribution on the external surfaces from wind tunnel tests with models, see Fig. 6.10.

10.4.2 Heat exchanger

The heat exchanger in a vehicle heating system is of special importance, as it not only has to provide the required amount of heat for warming up the passenger compartment, but is also to a large extent responsible for the function of the heating in maintaining an even and constant temperature.

Only a few years ago it was normal practice to construct heat exchangers similar to car radiators, see section 9.4.2. They consisted, for example, of flat tubing made of brass with copper or steel fins between the tubing. The tubes ended at each side in base plates enclosed in water chambers. The whole heat exchanger was soldered in one operation by passing it through an oven. Usually, the inlet and outlet connections were both in the same water chamber; the water flow was routed so that with the two-row heat exchangers the water flow in the upper row was supplied in reverse direction to the lower row. A partition in one of the water chambers prevented a short circuit.

Heat exchangers are nowadays frequently made of round aluminium tubing (see Fig. 10.9), which is much cheaper because no soldering is necessary. The aluminium tubing of about 0.4 or 0.5 mm wall thickness is assembled with the stamped air fins and then expanded with a mandrel. In this way, the close contact between the air fins and the tubing carrying the water is achieved by direct metal-to-metal contact, and not as with a


Figure 10.9 Modern aluminium heat exchanger with round aluminium tubing: surface of pipe matrix 42.6cm2, depth 42 mm

conventional heat exchanger by solder, which has poor heat conductivity. The disadvantage of round tubing over flat tubing, the reduced turbulence at the water-carrying surface, can be compensated for either by specially shaped turbulators or by using multiple passes on the water side to give higher water flow speeds. The sealing of the tubing in the base plates is achieved either with rubber seals or by metal contact with the aluminium tubing pressed into the base plate. The plastic water chambers are injection mouldings, sealed to the base plates with a rubber seal. The joint is effected by flanging the edges of the base plates. The routing of the water circuits is virtually unrestricted since partitions can be located in the injection moulded water chambers as required. Many car manufacturers nowaday use the same construction for their radiators as well; see section 9.3.2.

Figure 10.10 shows the characteristic curve of this kind of heat exchanger. On the left-hand side the heat flow Q100 (for a 100°C

rfiL = 7 kg/min

mL = 6 kg/min 136

mL = 5 kg/min N/m2

32 28 A 24^

o 20 7

3 4 5 6 7 kg/min 10

Air flow mL — �

0 250 500 1000 l/h 1500

Coolant flow C i —^" Figure 10.10 Characteristic curve showing heat flow of a heat exchanger


temperature difference between entering water and entering air) and the air resistance are shown as a function of air flow. The right-hand graph again shows the heat flow Qioo and the flow resistance in the water circuit as a function of water flow. The two graphs comprise all the data needed for the development of the heat exchanger and heating system design; a similar representation in dimensionless form for a car radiator is shown in Fig. 9.16. Different driving conditions are characterized by particular air and water flow rates, so it is possible to determine the attainable heat flow for any driving condition. This diagram is referred to again below in different form when describing possible regulating and control systems.

However, one such system is mentioned here since, in combination with the heat exchanger, there are certain effects which are important for the design and development of a vehicle heating system. This concerns the control of the heat flow by altering the water flow with a control valve. At maximum heat output, i.e. maximum water flow, the water remains at virtually the same temperature when passing through the heat exchanger, so that with a uniform air flow through the heat exchanger (the same air speed at all points in the heat exchanger), a uniform temperature distribution can also be expected downstream of the heat exchanger.

The situation is different when the heat requirement is low, i.e. with a small water flow. In this case the water does not remain at constant temperature when it passes through, but cools down noticeably. So with a uniform air velocity, the temperature distribution downstream of the heat exchanger will no longer be uniform. The air is warmer in the area where the water enters the heat exchanger.

j Air flow 4kg/min I Water flow 100 l/h I Water inlet temp. 82°C Air intake temp. 4°C Temp, diff: right/left 3.3°C

Figure 10.11 Temperature distribution and temperature difference between left and right halves of a heat exchanger with stratified flow and low liquid flow rate

Figure 10.11 shows four operating points of a heat exchanger with low water flow. The diagram is a view of the heat exchanger surface looking in the direction of the air flow. In all cases the air flow rate was a constant 4kg/min. The temperature of the incoming air is chosen so that in all four cases the average interior temperature obtained is 25°C. Water flow rate is raised in steps from 15 to 100 litres per hour and the temperature of the water intake is a constant 82°C. The two-row heat exchanger is made of

Air flow 4 kg/min Water flow 15 l/h Water inlet temp. 82°C Air intake temp. 18°C Temp. diff. right/left 5.1 °C

Air flow 4 kg/min Water flow 30 l/h Water inlet temp. 82°C Air intake temp. 15°C Temp. diff. right/left 4.8°C

Air flow Water flow Water inlet temp. Air intake temp.

4 kg/min 50 l/h 82°C 12°C

Temp. diff. right/left 3.8°C

� 4 Γ � �

+ + ·


round aluminium tubing with turbulators and a stratified flow, i.e. the water in the rear row of pipes, as seen in the diagram, flows from right to left, and the water in the front row flows in the opposite direction.

The temperature of the air leaving the heat exchanger is measured with a grid of 16 thermocouples. The examples show the line of the mean outlet temperature. Areas with temperatures above the mean value are shaded and marked ' + '. The maximum temperature difference of the air leaving the two halves of the heat exchanger is shown for each diagram.

At the very low water flow rate of 151/h = 0.251/min the temperature difference in this example is only about 5°C between the left and right halves. The temperature is higher on the water inlet side. With increasing water flow rates the difference in temperature becomes smaller.

A difference in the air temperature between the left and right side outlets of about 5°C will not be noticed by the passengers, because the heater outlet air will be mixed with the air of the cabin and so the average air temperature of the left and right side of the cabin will differ only very little. However, there exists the possibility of heating up the non-driver side of a car a little more than the driver's side, as recommended by some specialists in car-climatization. This is because the driver is in action and his body produces more heat than that of his passenger.

With a uniform air velocity, the temperature difference between various points on the surface of the heat exchanger can be influenced considerably by the routing of the water circuit, in this example a stratified flow. Apart from the water routing, the distribution of the air velocity also significantly influences the uniformity of the outgoing air temperature. A high air speed results in a low outgoing air temperature, and vice versa. Thus it is possible when developing a vehicle heating system to obtain an even temperature distribution at the heater outlets, even at low and very low water flow rates, by suitable routing of the water flow and distribution of the air velocity over the heat exchanger surface.

10.4.3 Fan

Both axial and radial (centrifugal) fans are used to produce the air flow for vehicle heating and ventilation. Axial fans are simpler and more robust than radial fans, but more noisy in operation. With increasing standards of comfort there is at present a clear tendency in favour of the quieter but more complex and expensive radial fan.

Figure 10.12 shows the characteristic curves for an axial and a radial fan. The design of both fans is such that they provide the same air flow operating with the vehicle stationary (point of intersection with the resistance curve). The characteristic difference between the two types of fan is clearly to be seen. Back pressure Ap varies only moderately with air flow m for the axial fan, but considerably for the radial fan, i.e. the axial fan is able to deliver large quantities of air with a low back pressure, and that air delivery is reduced sharply when back pressure increases by only a slight amount. The radial fan, on the other hand, is still able to deliver large quantities of air even with increasing back pressure. The diagram also shows that with the additional effect of ram pressure with the vehicle


6 8 10 kg/min 12 Air flow m �

Figure 10.12 Characteristic curves of axial and radial fans set up to produce the same air flow with the vehicle stationary

moving, air delivery increases much less with the radial fan than with the axial fan.

The two types of fan differ in current consumption. The speed of rotation of the axial fan increases as the back pressure drops, and current consumption decreases. The opposite is the case with the radial fan, where the speed of rotation decreases with rising current consumption. This means that special attention must be paid to the thermal load on the motor of a radial fan running without resistance from back pressure. The motor must be designed to withstand long periods of driving at maximum speed, possibly with an open sun roof, and the fan at the fastest setting. It may be necessary to provide special air cooling for the motor. In some cases, thermal safety circuits may be provided to protect the motor when the fan is running without back pressure.

10.4.4 Temperature control

When developing a vehicle heating system, particular emphasis must be placed on the control of the heater output and thus of the average temperature in the vehicle interior. An effort must be made to obtain a fine temperature adjustment; once set, the temperature should preferably remain stable, even under widely varying driving conditions. When describing the characteristics of the heat exchanger it was shown that these are very much non-linear, so that variations in water flow (i.e. changing road speed in different gears) and air flow (dependent again on road speed


and the fan setting) can have a great effect on the air temperature at the heater outlet and thus inside the compartment.

Two different systems are mainly used for temperature control. In water-flow controlled heating, as already described, the amount of water passing through the heat exchanger is restricted to a greater or lesser extent by a water flow control valve, according to the heat requirement.

This valve is normally operated from the vehicle interior via a Bowden cable. The regulating characteristics of this valve must meet very stringent requirements, as can be seen from Fig. 10.13, which shows water flow as a function of valve operating travel, as is required for fine control, i.e. linear temperature rise in relation to the operating travel.

100 1 %

1 80

| 6 0 %Af\ jo 40 o o ü

20

/

/

20 40 60 80% 100 Heater control travel a " * ·

Figure 10.13 Required water flow rate through heat exchanger to obtain a linear temperature increase with the operating travel of heater control

Up to about 70 per cent of its operating travel the valve must restrict water flow to only about 10 per cent of the maximum flow rate through the heat exchanger. Over the last part of the operating travel the water flow must then rise steeply up to the maximum value. The difficulties of achieving this lie not only in the geometry of the valve, but also particularly in the fact that only a very tiny gap must be opened for such small water flow rates, and this gap can easily be obstructed by impurities in the cooling system. One possible design for such a valve is a quadrant plate gate valve. This employs a control plate as a sliding regulator which, in the version proposed by the author, has wedge-shaped slots to control the cross-sectional area of the opening for small water flow rates.

Figure 10.14 is a schematic diagram of a gate valve of this kind. The relative position of the circular regulator opening is shown for five different settings. In the first setting the regulator opening is completely covered and the valve is closed. In the second setting a small quantity of water can flow through the opening exposed by the slots. The steep rise in the flow characteristics starts in the third position where the crescent-shaped opening is exposed. The valve is fully open in position 5.

The second method of temperature control uses air-flow controlled heating, in which the unrestricted water flow, dependent only on the engine speed, passes through the heat exchanger at all times.

The required outlet temperature is adjusted by mixing cold and warm partial air flows. The amounts of air passing through or bypassing the heat exchanger are normally controlled via two temperature mixing flaps, one

392

Free opening

Control surfaces

Position 1 closed

2 Flat portion of curve (Fig 10.13)

3 Beginning of steep portion of curve (Fig 10.13)

4 Steep portion of curve (fig 10.13)

Fully open (Fig 10.13)

Figure 10.14 Principle of a quadrant plate gate valve for regulating the heater of a passenger car


upstream and the other downstream of the heat exchanger. Theoretically, one mixing flap upstream of the heat exchanger would be sufficient, but then turbulence and convection currents in the area downstream of the heat exchanger would always permit the addition of undesired warm air, even with the warm air flap closed. This would mean that even at the 'cold' setting, the air would still be noticeably warmed as it passes through the heater. With the arrangement employing two temperature control flaps in the Audi 100 II, the residual heating effect in the heating system at the 'cold' setting is below 2°C, even with low air flow rates. The temperature mixing flaps are controlled via a Bowden cable from the passenger compartment.

Apart from these two control systems, there are also mixed systems which work with a bypass duct as well as a water valve, as for example the Audi 100 I.

The two types of temperature control in the passenger compartment are discussed by Frank.10 ä The advantages and disadvantages of the two systems can be explained with the aid of Fig. 10.15.

2501 500 1500 1000 l/h Coolant flow V *~

Figure 10.15 The air outlet temperature from a heat exchanger as a function of water and air flow

In this graph the temperature of the air leaving the heat exchanger is plotted against the water flow (which is proportional to engine speed) for different air delivery rates. The example assumes an ambient temperature of 0°C, and water supplied at a temperature of 92°C. Air delivery when stationary should be about 5m3/min = 6kg/min, which is about twice the required fresh air delivery rate of 0.5 m2 per person per minute for a car with five occupants. In order to achieve a comfortable interior temperature


under the assumed conditions, approximately half the air flow is routed through the heat exchanger. This means that with the vehicle stationary about 3kg/min pass through the heat exchanger. The air flow and the corresponding water flow are shown as open circles in the diagram for road speeds of 64, 96 and 128 km/h (40, 60 and 80mile/h respectively) in 4th gear. It can be seen that the air outlet temperature at 64 km/h (40 mile/h) is just under 1°C higher than the temperature at 128km/h (80mile/h). This difference is halved since the hot air, heated to about 87°C, is mixed with the same quantity of air at 0°C, so the temperature fluctuation drops to about 0.5°C.

It can also be seen that the maximum temperature difference between the driving modes mentioned above and the idle condition is about 4.5°C in the outlet temperature from the heater. This means that the mean interior temperature will only vary by about 2°C, a value which is on the limit of perceptible temperature difference.

If the same heater system were controlled by restricting water flow, and if, for example, it is assumed that at 96 km/h (60mile/h) the same air outlet temperature of about 43°C is achieved as in the case of the air-flow controlled heater, then the temperature at 128 km/h (80 mile/h) rises to about 48°C, and falls to 35°C at 64km/h (40mile/h), and to as low as 22°C at idle. The effect on the interior temperature of these temperature variations between idling and the various driving modes is that the temperature setting has to be altered if road speed is changed for any period of time. Short speed changes, as for example during overtaking, cause no perceptible temperature difference due to the heat capacity of the heat exchanger and the associated response delay of the system, so it is not necessary to readjust the temperature controls.

At lower air delivery rates (this example deliberately assumes a high air delivery rate) the temperature variations are also smaller. The same applies as the heater output is increased, when the points for the different driving modes are no longer on the steep section of the heat exchanger characteristic curve. At maximum heat output there is no difference between the two systems.

A further advantage of the air-flow controlled heater system is its fast response to a new setting. The occupants notice the change in temperature more quickly than with the slower response of the water-flow controlled system, and are therefore able to find a comfortable setting more quickly. For the same reason it is easier to make temperature adjustments with air-flow controlled heater systems than with water-flow controlled systems, which respond more slowly and are subject to much greater variations in the outlet temperature.

10.5 Example of a production heating system Recent developments in the engineering of passenger car heating systems can be seen from the example of the Audi 100 II. Bauer10 3 has described the heating system of the Audi 100 I (1969 model). It is intended here to describe the system used in the Audi 100II, which is a further development of this design. Very much the same system was applied for the Audi 100 III (1982 model).

Example of a production heating system 395

Figure 10.16 shows a cross-section of the Audi 100 II heater, and also illustrates connection to defroster ducts, ventilation outlets and heater ducts for the rear passengers. The heater is arranged symmetrically about the centre line of the vehicle, with the exception of the blower intake, which is located to one side. The heater housing is made in two halves, which are joined along the centre line of the vehicle. Control flaps, heat exchanger and fan are installed in the halves of the housing. The heater is installed from outside in a chamber which is separate from the engine compartment.

The blades of the single-entry radial fan are curved forwards. The drive motor is completely sealed from the outside, and is mounted in the left half of the heater housing. The motor is cooled by air diverted from the fan volute. The fan has three speed settings controlled via resistances. When the controls are set to 'ventilation', one series resistance is short-circuited to raise the fan speed by an amount corresponding roughly to one speed setting. The fan volute widens both radially and axially.

Air can be directed either through the heat exchanger or through the bypass by means of two interlinked temperature mixing flaps. This makes it possible to set any desired air outlet temperature. The cold and warm air is not mixed completely at the point where the two flows merge. The upper part of the air duct is cooler than the lower part when the air is mixed. This feature is used to give the air emerging from the wide-section ventilation outlets a lower temperature than the air for the footwells. The air channelled to the defrosters is also cooler than the air at footwell level. This arrangement meets the requirement for temperature stratification as described in section 10.2.1, i.e. air at head level is cooler than the air supplied to the footwells. Since the system is air-flow controlled, temperature remains constant regardless of road speed.

Air distribution in the Audi 100II is adjusted by a single lever among the heater controls. The two distribution flaps, which move in opposite directions, are therefore similarly interconnected. In the 'defrost' setting, with the distribution lever at the extreme right, all the air is directed through the defroster outlets in the facia. This setting gives optimum


windshield demisting and de-icing. With the distribution lever in the other extreme position, 'ventilation', the air flow (increased by shorting out one of the series resistances) emerges from the many large outlets of the full-width ventilation. At intermediate settings the air is distributed between the various outlets. The air distribution giving best results under normal conditions is identified by a detent on the heater controls.

Some of the specifications of this heater system are:

Heat output with -20°C standard heat exchanger, approx. 8.9 kW Heat output with -30°C cold-climate heat exchanger, approx. 10.4kW Area of heat exchanger 280 x 152 mm2 426 cm2

Depth of heat exchanger 42 mm Maximum air flow on ventilation setting with vehicle stationary, windows etc. closed 11.6 kg/h

10.6 Summary

Physical well-being is not a matter of course. It is dependent on certain factors that influence the climate. The requirements for climate control in vehicles are as follows. • When the interior is heated, temperature must be easily adjustable over a wide range, and must remain constant regardless of road speed. • The warm air stream must not be aimed directly at the occupants. • The air at head level should be about 7°C cooler than the air in the footwells. • Relative air humidity should be between 30 and 70 per cent. • For ventilation and air conditioning, it should be possible to aim cool air directly at the passengers. The direction and quantity of air flow should be adjustable. Air delivery should be over a wide area, and air speed should not be excessive. The flow rate should be kept low at the face, neck and wrists.

It has been shown that the scope for influencing climate factors by heating and ventilation for enhanced comfort is limited: in winter because of the relatively dry air, and in summer because it is not possible to reduce humidity levels. These can however be reduced with air conditioning.

The principal components of a heating and ventilation system have been discussed. In addition, the level of sealing or the amount of leakage from a car's body is of special importance—together with the air flow around the car—for the flow of air through the car, whether moving or stationary. The arrangement of air extraction outlets and the type of fan chosen both influence the air flow characteristics.

The characteristic curves of heat transferred by a heat exchanger explain the temperature variations of the heated air occurring with a water-flow controlled heater at small water flow rates. Temperature fluctuations when road speed is varied are much higher with water-flow controlled systems than with air-flow controlled systems, since in the latter case the heat exchanger operates constantly with almost saturation water flow, so an increase in water flow means only a small increase in heater output.

The actual heater configuration used in the Audi 100 II is described by way of an example.

Notation 397

10.7 Notation

Ae equivalent leakage cross-section ßioo heat flow, Fig. 10.10 yFL coolant flow, Fig. 10.10 / current, Fig. 10.12 U voltage, Fig. 10.12 a relative heater control valve travel, Fig. 10.13 h enthalpy, Figs 10.4, 10.5, 10.6 m, mL air mass flow n revolutions of the fan, Fig. 10.12 Pi pressure inside the passenger compartment ti averaged temperature inside the passenger compartment ta temperature of ambient (external) air x water content of air, Figs 10.4, 10.5, 10.6 pL density of air

Chapter 11

Wind tunnels for automobile aerodynamics Wolf-Heinrich Hucho

11.1 Introduction 11.1.1 Requirements for a vehicle wind tunnel

Much development work is required to achieve the aerodynamic qualities and thermal characteristics of vehicles, as described in the previous chapters. In this work, the road is an important test instrument and in the final analysis this is where the results must prove themselves. The wind tunnel is however an essential development tool, with which reality is simulated—but not duplicated. Before attempting simulation of this type it is necessary to analyse the original phenomenon.

Figure 11.11 1 1 shows variables for air flow and thermal load. The air flow is composed of two fields, one resulting from the forward motion of the vehicle, the other from the natural wind (see Fig. 4.2). As indicated in Fig. 11.1 this natural wind field is similar to a boundary layer and causes a

Sidewind v . , , ^ - (

1 ^ R a i n \ S u n , ' ' , 7

Figure 11.1 The vehicle in its true environment

twisted oncoming flow profile to develop (see Fig. 5.3). Gusts continuously change the wind speed and angle ß of oncoming flow. The ground boundary layer of the wind is turbulent; the dimensions of the turbulence eddies are of the same magnitude as the length of the vehicle. For an observer moving with the vehicle, the gustiness appears to be increased by the fact that the vehicle drives through wakes resulting from bridges, houses, trees, etc. and through the flow field of vehicles driving in front and in the opposite direction. The flow field approaching the vehicle is therefore largely inhomogeneous and non-stationary and is considerably

398

Introduction 399

more complex than that of an aircraft flying at high altitude. The requirements for the flow quality of an automobile wind tunnel therefore cannot be borrowed uncritically from aeronautics.

The temperature field above the road is also not always homogeneous. Intensive sunlight will heat the roadway more than the surrounding air so that a temperature boundary layer forms above the road.

The flow and temperature fields on the road can be simulated in a wind tunnel only in a highly idealized form; homogeneous fields are used. However, it is worth considering, from time to time, the much more complex real-life situation during the evaluation of test results.

The performance specification of the air conditioner in a vehicle is highly dependent upon the radiation from the sun, including diffuse radiation. The former may be simulated in simplified form in the wind tunnel in terms of the spectrum and direction; the diffuse radiation is usually not considered.

Much development work is done to channel rain water and spray, and to prevent the deposition of dirt, or to limit it to areas where safety will not be affected (see section 6.4). The simulation of rain in the wind tunnel is in fact relatively simple, but flow simulation of the soiling process is imperfect—due particularly to the expense of reproducing wheel rotation in the wind tunnel.

With the exception of model testing, all the above-mentioned development work can be performed on the road. The disadvantage of using the road as a test instrument is that conditions are seldom repeatable. It is also extremely difficult to find roads with a given gradient long enough to achieve a state of equilibrium for thermal tests. On the other hand, the acquisition, storage and processing of data during a road test now presents less of a problem, due to advances in electronics.

11.1.2 Simulation of road driving

Motor vehicle aerodynamics can be subdivided into four categories, both in regard to its objectives and, as explained below, in regard to the requirements it places on simulation techniques. These are illustrated in Fig. 11.2 for passenger vehicles,112 and in Fig. 11.3 for commercial vehicles.11 3

Performance, directional stability

Engine cooling

Flow details

Heating, ventilation, air conditioning

Figure 11.2 The main objectives of vehicle aerodynamics, passenger cars

400 Wind tunnels for automobile aerodynamics

Performance, directional stability | Flow details

Engine cooling Heating, ventilation, air conditioning

Figure 11.3 The main objectives of vehicle aerodynamics, commercial vehicles

For the forces and moments which determine driving performance and directional stability it is important to represent the actual air flow around the vehicle as closely as possible. Since the pressure p at every point (and therefore the effective forces and moments as integral variables) is proportional to the local flow speed v in the relationship

errors in the velocity distribution of the simulated flow field have a significant effect upon the test results. Within the limitations mentioned above—a homogeneous flow field—the air flow around the vehicle can be simulated quite well in a wind tunnel and close agreement between wind tunnel measurements and road tests has been achieved (see section 11.3).

In the wind tunnel the vehicle remains stationary and the wind blows by—the reverse of the situation on the road. Tests with towed vehicle models (common in naval architecture) are used when examining the non-stationary effects of side wind. (Section 5.2.3 describes some of the test equipment.) Towing systems are also used to simulate driving through tunnels (see section 8.5.5.2), and here there are parallels with railway

u Observer at rest Jj~~

Figure 11.4 Change of the relative motion between road driving and wind tunnel testing

Introduction 401

aerodynamics (see section 1.13). When performing wind tunnel tests, one must remain aware of the reversal of the motion sequence (Fig. 11.4).

The same requirements as regards forces and moments have to be placed on the quality of air flow around the vehicle when studying flow details. However, the wind tunnel alone is not sufficient for this purpose. For example, research on wind noise generation is limited by the high noise level in the wind tunnel. Also, tests on spray soiling must take into consideration the relative motion between vehicle and road and the rotation of the wheels, both of which present technical difficulties during wind tunnel tests.

Although less stringent requirements are placed on the quality of the air flow for development work on the cooling system, the tractive effort and the speed of the driving wheels as well as the air temperature must be simulated precisely. Air flow around the front of the car can be simulated relatively easily in combination with several correlation measurements. Special rigs are used for the development of cooling systems, which might be better described as 'climatic wind chambers' or 'chassis dynamometers with cooling air' rather than wind tunnels. Such systems are described in section 11.5.

For testing the heater, ventilation and air conditioning, simulation requirements are part way between those for purely aerodynamic tests and those for component cooling. The primary climatic parameters such as air temperature, humidity and solar radiation, as well as the influence of the engine, must be simulated precisely. The heat balance of the vehicle is highly dependent on the flow of air around and through it, so the convective heat flux, which is directly proportional to the quantity of air flowing through the passenger compartment, must also be simulated precisely. However, the heat flux Qc resulting from conduction through the various parts of the body and heat transfer to its interior and exterior surfaces is

Qc ~ v0·5 to v0·8

The effect of an error in the local velocity of the simulated flow field is therefore less than proportionate. This is why 'climatic' wind tunnels with smaller jet dimensions and consequently greater velocity flow field deviations are acceptable.

As an alternative to simulating one main parameter and only approximating the others, all primary parameters may be simulated simultaneously and as closely as possible in a so-called 'large climatic wind tunnel'. Practical examples of all these possibilities are given in section 11.5.

Vehicle development work is usually shared among the above-mentioned test facilities. However, for this to be successful, precise information must be available on how the individual test results relate to driving on the road and how they can be compared with one another. In aeronautical research and ship testing much effort has been expended to discover and quantify the shortcomings of simulation by comparing wind tunnels, towing tanks, etc. using standardized calibration models. Corresponding research in automobile aerodynamics is described in sections 11.3.2 and 11.5.7.


11.2 Principles of wind tunnel technology 11.2.1 Recommended reading

Wind tunnel technology is dealt with in detail in standard works such as Pankhurst and Holder114 and Pope.1 1 5 Wuest116 provides a short introduction to the most important details of wind tunnel technology. Details of recent research results, for example rational nozzle design or the execution of wind tunnel corrections (the so-called 'blockage corrections'), have to be sought in the journals; they have not yet been published in book form.

11.2.2 Design and function

The two types of wind tunnel are distinguished by the type of air guidance. In the Göttingen type tunnel with closed air return (Fig. 11.5, bottom) the fan drives the air in a closed circuit. The top illustration shows the Eiffel type tunnel, which takes in air from the surroundings and expels it to the

Figure 11.5 Wind tunnel with closed return (Göttingen type) and with open return (Eiffel type), after ref. 11.6

surroundings. In addition to these types there is a 'compromise' type with 'open return', often also connected with the name Eiffel. On this type the air from the outlet diffuser is returned to the inlet of the settling chamber upstream of the nozzle within a building surrounding the entire wind tunnel. In newer wind tunnels of this type the building is designed to return the air with the lowest possible losses. There are also some 'closed return' wind tunnels with two return ducts, but this approach can hardly be recommended. In addition to the higher cost of two return circuits and two drive units, they have the inherent problem of uncontrollable flow split and thus flow distribution in the test section. Examples of the first three types of construction are given in section 11.5. All types have intrinsic advantages and disadvantages, which can be compared quantitatively with one another only for a specific application.

The main advantage of the Göttingen type tunnel is its low power requirement, which reduces the operating cost due to the lower energy consumption itself as well as the lower electric power connection cost—a

Principles of wind tunnel technology 403

considerable sum for larger wind tunnels. The cost of the drive unit (motor, fan, control) is lower, though that for the tunnel duct is considerably higher than for the pure Eiffel type. Most automobile models are made of plastilina, which loses its stability at higher temperatures. For this reason a cooler must be provided for the closed air return. The pressure loss resulting from the cooler requires additional power, thus some of the advantage of the lower drive power is lost. The closed return tunnel is the only type suitable for air-conditioning, and climatic work.

The Eiffel tunnel, set up outdoors, has a considerable disadvantage in that operation is dependent upon the weather; for this reason it is only practical in countries with moderate climates. Particular difficulties are presented in keeping the quality of the flow in the test section free from wind effects where the air is sucked in from outdoors. In the case of one large Eiffel tunnel in the automobile industry, it is known that on average one test day per week is lost due to unfavourable wind conditions. Screens in front of the intake nozzle, which also prevent leaves and birds etc. from being sucked in, eliminate the influence of the wind only when they are suitably designed. Their pressure loss has to be overcome by additional fan power. A further disadvantage of the outdoor Eiffel tunnel is its excessive noise.

However, the primary advantage of the Eiffel tunnel is its economical construction. If it exhausts outdoors, an exhaust gas extractor is not required for tests with the vehicle engine running. It is simple to construct an Eiffel tunnel with a test section closed on all sides, although an open test section is possible at slightly higher construction cost.

11.2.3 Construction elements

The size, performance and quality of a wind tunnel are mainly determined by the following elements:

• test section • nozzle and settling chamber • fan and drive.

In climatic wind tunnels a fourth significant construction element, the cooler, is added. Only these four elements are considered here; the reader is referred to the literature for details such as diffuser, deflection baffles, screens and flow straighteners, etc.1 1·4 1 1 5

The overall size of a wind tunnel is determined, above all, by the dimensions of the test section. The governing parameter is the cross-section AT of the wind tunnel's nozzle. The ratio of the frontal area A of the vehicle to the cross-sectional area AT of the wind tunnel air stream, also called the blockage ratio ö, should be as small as possible. On the road the blockage ratio is zero. If the frontal area for a car is assumed to be 2.0 m2 (see Fig. 1.48), and if, as in aircraft aerodynamics, the blockage ratio should not exceed 0.05, a nozzle exit cross-section of AT = 40 m2 is required. Of all automobile wind tunnels this requirement is fulfilled only by the wind tunnel at General Motors (AT = 65.9m2). None of the other wind tunnels used in automobile engineering meets this requirement, with the only exception of the Deutsch Niederländischer Windkanal (DNW),


which was designed for aeronautical purposes and is now also used for automobile testing. Comparative measurements between wind tunnels of different sizes (see section 11.5.7) indicate however that a considerably higher blockage ratio is permissible for automobile aerodynamics.

For economic reasons attempts are to be made to construct wind tunnels as small as possible. Two approaches are used, often simultaneously. In the first, attempts are made to simulate the flow in the open air by suitable shaping of the air stream boundaries of the smaller test section; in the second, the limits of the air stream dimensions are taken into consideration by applying empirical corrections to the measurement results. These corrections are described in section 11.3.3.

- 2 ¿ " * < ^ _

a) Open b) Closed parallel walls

c£ZS

c) streamlined walls d) slotted walls

Figure 11.6 Classification of test sections according to the type of test section boundaries

In Fig. 11.6 four test sections are compared according to the type of the jet boundary; they all have a level floor, which represents the road. (The questions in relation to simulation of the road are discussed in section 11.3.2.) In the free jet ('open') test section, Fig. 11.6a, the air stream has three free boundaries, at which the air from the test stream mixes with the quiescent surrounding air as a free jet. This mixing leads to dissipation of the jet's core, that portion of the stream which contains the desired oncoming flow velocity V. This mixing limits the usable length of the test section.

The great advantage of the open test section is that, with a correctly matched collecting cone, the gradient of the static pressure along the axis of the tunnel is negligible. When measuring the drag of long bodies with large vertical surfaces at the front and rear, even small axial pressure gradients can lead to notable errors (buoyancy effect). Another considerable advantage is the lower absolute value of the blockage correction in comparison to closed parallel test sections. Finally, the accessibility of the open test section facilitates experimenting with and photographing the flow. Disadvantages are the higher loss coefficient of the free jet and the unimpeded sound radiation. For climatic tunnels with free jet test section, the chamber surrounding the test section must be included in the air-conditioned area.

The advantage of a closed test section, Fig. 11.6b, is its large usable length; the core of the air stream is dissipated much more slowly along a closed duct than in an open jet. However, the friction loss along the walls results in a pressure decrease along the axis of the stream. This pressure


decrease must be compensated for by slightly widening the tunnel cross-section in the flow direction. However, this compensation is only correct for one configuration, for example in the case of an empty test section; in all other cases it is only an approximation and where necessary must be further corrected through computation.

One disadvantage of the closed test section is its sensitivity to blockage; the absolute blockage correction value is approximately double that of a free jet. At a higher angle of yaw ß, separation may result along the walls of the wind tunnel due to the high degree of deformation of the air stream; a correction for the angle of yaw is then no longer possible.

One way of overcoming the large blockage correction for the closed test section is to streamline the test section walls. In this case it is assumed that the flow pattern at a certain distance from the vehicle,^the so-called far field, is no longer highly dependent upon the individual details of its shape. The far field is determined mainly by the primary parameters length, height and width (and thus the fineness ratio which can be derived from these).

There is little variation in the principal dimensions for passenger cars. The frontal area of an average family car is approximately 1.85 m2, and the deviation between large and small cars is no more than ±15 per cent, if we neglect subminiature cars. If the tunnel walls are shaped according to the flow pattern of an average car in the open air, the flow around smaller and larger vehicles will only be slightly distorted.

Figure 11.7 Comparison of the far flow fields of different passenger cars, using a selected streamline in the longitudinal midsection

A comparison of flow patterns using smoke to show the streamlines confirms this concept. As shown in Fig. 11.7, the flow pattern for various vehicles is very similar even at a height of only approximately 2 m above the roadway. Stafford11 8 was able to show that with streamlined walls the same result could be obtained with blockage of 20 per cent as in a test section with parallel walls with blockage of only 5 per cent. Streamlined test sections are particularly recommended for climatic chambers with wind with a nozzle area of Α¾ ~ 10 m2. This is because it is not desirable to attempt a subsequent correction for an imperfect pressure distribution in this case, but rather to have a flow state during the test that corresponds to the climatic load on the vehicle while driving on the road.

Instead of having streamlined tunnel walls with a fixed contour the tunnel walls can be designed to be adaptive. A related concept has been developed by Whitfield et al.11 9 In an iterative process, using a potential flow model for the far field ('exterior flow field'), the tunnel walls are

406

Position at converged value

'Frontal areal

/Converged 'non-interference' position

Straight wall Model Blockage, %

5

- 3 0

Wall Ground plane

Model blockage %

5

10 -20

^

Converged 'non-interface' position

(b) Model blockage, % 5 \ .

'ss//}/^/fM/^/s/y}S/S//SS/SSS)////s V////////M,

Model blockage, % 5

QO

Figure 11.8 Adaptive tunnel walls at converged value for blockage ratios of 10, 20 and 30 per cent: (a) zero yaw; (b) yaw angle ß = 10°; after ref. 11.9


streamlined such that flow angularity at the walls is the same as for the related streamline in an infinite flow field. According to ref. 11.9 this procedure will compensate in 8 to 10 iteration steps for blockage ratios up to 30 per cent, even for a yaw angle of 10°. Figure 11.8a, from ref. 11.9, shows the contours of the tunnel walls at converged value for blockage ratios of 10, 20 and 30 per cent for zero yaw, Fig. 11.8b for 10° yaw.

The slotted wall test section, Fig. 11.6d, is an attempt to combine the advantages of the open and closed test sections, and eliminate the disadvantages of both. This idea is attributed to Vandrey and Wieghardt.1110'1111 Slotted walls are used in water tunnels and wind tunnels in marine hydrodynamics, to allow research on particularly long bodies with a sufficiently large Reynolds number. The automobile wind tunnels at the Institute Aerotechnique in St. Cyr, France (see Peters1112), and at the Bayerische Motorenwerke AG (BMW) in Munich, Germany, also have test sections with slotted walls. The wind tunnels opened in 1986 by Volvo AB, Göteborg, Sweden, and Dr.-Ing. F. Porsche AG, Weissach, Germany, are also equipped with slotted walls. The open area ratio (free surface to covered surface) must be matched with calibration tests so that the pressure distribution corresponds closely to that in the open air. In the St. Cyr tunnel, an open area ratio of 28 per cent was established; see ref. 11.12. Flay et al.1 found an open area ratio of 30 per cent to be an optimum for a blockage ratio of 14 per cent up to a yaw angle of 30°. This is confirmed by systematic measurements carried out by Waudby-Smith and Rainbird.11·*5

The contraction ratio and contours of the wind tunnel nozzle have a decisive effect upon the quality of the air stream and the required fan power. The contraction ratio K (Fig. 11.9) is the area ratio of the nozzle

A

/teci

Contraction ratio K -

A 3.2

Ra 2· 4

n 2 4 6 8 10 v 22

Contraction ratio K ^ *

4 %o 6

" ^ Tu=-^- .100-

Figure 11.9 Critical Reynolds number and turbulence level of existing wind tunnel nozzles, after ref. 11.7


inlet to the nozzle outlet, K = ASIAT. Assuming a suitable nozzle contour, a larger contraction ratio provides a more uniform velocity distribution over the air stream cross-section and a lower turbulence level. In order to achieve these objectives, wind tunnels for aircraft aerodynamics are designed with a large contraction ratio (Bradshaw and Pankhurst1114

recommend K = 10 to 12). Automobile wind tunnels usually have a smaller contraction ratio: K = 4. For Eiffel type wind tunnels, a considerably smaller contraction ratio is sufficient; K = 2 to 3 is often selected.

The tendency towards larger contraction ratios in vehicle work is more attributable to the attempt to minimize the power requirement. If a fan drive power of P0 corresponding to a contraction ratio of K0 is assumed, the decreasing power requirement with increasing contraction ratio shown in Fig. 11.10 results, according to an estimate made by Piatek.1115 Here it is assumed that the jet power remains constant. Therefore, to a first approximation, the losses in the nozzle, test section and collecting cone remain the same while the losses in the remaining parts of the wind tunnel decrease when the geometric similarity is maintained at (lAKnew : K0)

2. The maintenance of the geometric similarity naturally results in an increasing volume for the tunnel for increasing contraction ratios. If the short diffuser recommended in ref. 11.14 is attached in front of the settling chamber the construction volume can be reduced, but the reduction of the required drive power is then not as great as shown in Fig. 11.10.

1.0 i 1 1 1 1

0.8 h-V

4θ.6 fv

P ^ Ã * ^ ^ ' n e w � ^ l

Po | J JJZj I Afivv- = o.3 + 0.7 · ß £ ω * } -2

° · 2 | Po \K0 J Vo. = const | I

Q| Λ ñ = const 1.0 1.5 2.0 2.5 3.0

Ko Figure 11.10 Reduction of required fan power for a wind tunnel with increasing contraction ratio K of the nozzle. In wind tunnels with coolers approx. 30 per cent of the total losses are generated in the nozzle, the test section and the collecting cone. Jet power remains constant* after ref. 11.15

In addition to the contraction ratio, the contour of the nozzle also determines the quality of the wind tunnel flow field. The velocity should be uniform at the nozzle exit yet for reasons of cost the nozzle should be as short as possible. The local velocity vector should also be as near parallel as possible to the axis of the tunnel. Of the numerous recommendations for calculation of the nozzles to date, that proposed by Witoszynski1116 was preferred, though it applies only to axially symmetrical flow and does not


provide any information on the selection of nozzle length. Good results have been achieved with nozzles whose length corresponds approximately to the inlet diameter, particularly when the recommendation of Prandtl is followed and the nozzle is widened slightly at the outlet. Recently published numerical procedures have been based upon the principle of iterative computation of the potential flow and the boundary layer: a contour is prescribed and then varied until the desired uniform velocity distribution results at the nozzle outlet. A procedure of this type was presented by Borger11 17 for two-dimensional and axially symmetrical flow; the formation of the boundary layer is also taken into consideration in the computation of the contour. Figure 11.11 shows the contour computed by

A 1.50

1.25

1.00

0.75

0.50

0.25

I E

ü

. Witoszyn ski ^ \

G. Bφr

* \

ger

y*

Φ> / A

KA

1.0 1.5 2.0 2.5 3.0 3.5

Figure 11.11 Comparison of nozzle contours according to Witoszynski and Borger, axial symmetry, after ref. 11.17

Borger compared with that according to Witoszynski; the slight widening of the contour at the outlet is a result of the computation from Borger. Borger designs the nozzle shorter than Witoszynski with better (computed) velocity distribution at the outlet. No experimental confirmation of these results has yet been published to the knowledge of the author.

A procedure for designing axially symmetrical nozzles by Morel1118

leads to contours very similar to those of Borger. The nozzle design is accomplished on the basis of draft diagrams; but again experimental confirmation is lacking.

The air stream velocity in the wind tunnel must be continuously controllable. In automobile work precise tests at very low wind speed are important. As explained in Chapter 9, driving slowly up a long steep gradient represents a critical case for the dimensioning of the radiator. In such cases the relative wind as well as the radiator fan contribute to the cooling effect; precise control of the relative wind is essential.

Two basic solutions are available for control of the wind velocity: variable-pitch blades at constant fan speed or variation of fan speed with fixed blade angle. Variable pitch has the advantage that the velocities can be changed very quickly and the drive is simple. The disadvantage is the high noise level at all wind speeds, even at zero wind speed. With the use of pole-changing asynchronous motors, a second lower fan speed is possible for wind noise tests. Further disadvantages of blade pitch control are the


mechanical complexity and sensitivity of the blade pitch-changing mechanism as well as the high inertia of the rotor. The latter disadvantage has now been overcome by the use of light-weight technology from aircraft construction.

Fan speed control is used for newer wind tunnels. The fan blades are of light construction; wood or fibre-glass laminates are used. Thyristor controls have generally replaced the Ward-Leonard system. The possibility of driving the fan directly with a heat engine, such as a propeller turbine, has yet to be explored.

The layout of the wind tunnel cooler must accommodate other aspects than steady-state operation. It is important that the cooler performance is sufficient to allow the desired temperature to be reached quickly. In order to keep the pressure loss through the cooler as small as possible, it should be installed at a point with a large cross-section. A position at the end of the large diffuser downstream of the fan appears to be more suitable than a location inside the settling chamber (see also section 11.3.1).

11.2.4 Equipment

A six-component balance is required for force measurements (see section 12.1.1). In full-scale automotive wind tunnels, balances mounted underneath the test section are preferred.

In addition to the simple model assembly, these balances offer the great advantage that no corrections are necessary for suspension wires or struts. It is only necessary to correct for the lift on the wheel support plates. This takes into consideration the fact that, as a result of the displacement flow around the wheel, a low pressure field is formed on the plate, which results in lift acting upon the plate surface not covered by the wheel.

The traditional beam and lever balances with moving balance weights are being replaced by balances with load cells in combination with preload weights.

The test equipment in an automotive wind tunnel also includes high-performance pressure and temperature measuring instruments. In view of the pressures of time and cost an on-line, real-time process computer is nowadays considered essential.

Other typical features of motor vehicle wind tunnels are an engine cooling water simulation unit, to allow development of the radiator even during the model phase, as well as a device for measuring the volume of air passing through the passenger compartment (see section 12.1.5).

Climate simulation is required for thermal tests; air temperature, solar radiation and relative humidity to tropical rain levels must all be simulated. During tests the propulsion system of the vehicle can be loaded with a chassis dynamometer, but the lost tractive force at the drums must be considered, and also the fact that the rolling resistance of the tyres on drums is different from that on a level road.

Good lighting is required for flow observation. Smoke or oil vapour can be made easily visible in a darkened room, under proper illumination. Wakes are generally illuminated over a large surface (see Fig. 1.2); for photographing flow patterns with individual smoke trails, a planar light source (or slit) is more suitable, as in Fig. 1.1 (see Hucho and Janssen, 9

andTakagiet al.1 1 2 0).

Limitations of simulation 411

11.3 Limitations of simulation 11.3.1 Air flow quality

A uniform velocity distribution over the cross-section of the air stream is not only important for simulation but also to facilitate comparison between tunnels. With a contraction ratio of K = 4 and correct nozzle design, a velocity distribution can be achieved in which the local velocity does not deviate more than ±1 per cent from the mean velocity except at the edge of the jet.11 21 This is sufficient for automobile aerodynamics purposes.

It is important that the wind tunnel air stream be aligned precisely relative to the test vehicle. In automobile wind tunnels, the boundary layer which forms on the ground plane increases the effective angle of attack. As shown in Fig. 4.112, the angle of attack has a considerable influence upon the drag, particularly when edge radii are optimized using the procedure described in section 4.4.1. Asymmetries in the chamber surrounding the test section of an open-jet wind tunnel can produce an angle of yaw in the wind tunnel stream. As long as this remains small it has only a slight influence upon the drag (Fig. 4.115). However, a precisely directed jet is required for exact determination of the lateral forces and moment. Despite the extra cost it is best to make the wind tunnel nozzle adjustable so that the air stream can be set to the exact direction.

In climatic wind tunnels attention must be given to uniform temperature distribution over the cross-section of the air stream. Due to the cross-flow characteristics of the heat exchanger and the resulting non-uniformity in the temperature distribution it is worth installing the heat exchanger as far as possible upstream from the wind tunnel nozzle in order to allow any temperature non-uniformity to decay by mixing over a longer flow path.

11.3.2 Ground plane boundary layer The relative motion between the road and vehicle is simulated only in exceptional cases. As a rule, the level floor of the test section is used as the

Figure 11.12 Possibilities for simulation of the road in the wind tunnel, after ref. 11.22


road. As a matter of principle the boundary layer that forms on the floor of the test section results in a different flow field than during driving on the road. A series of suggestions have been made to improve the simulation of the road in wind tunnels. These are summarized in Fig. 11.12 (from ref. 11.22).

One solution to this simulation task is the use of a running belt. As shown in Fig. 11.13, from ref. 11.23, the floor boundary layer can be virtually eliminated in this manner. This has also been confirmed with measurements performed by Rose and Carr.11 24 However, the support of

Suction

Figure 11.13 Simulation of the road with a moving belt, after ref. 11.23

the model over the moving belt presents difficulties, particularly with large and heavy models. Moreover, Beauvais et al.11,23 have shown that the error in drag and particularly in lift, resulting from the flow in the gap between the wheels and belt, is greater than the influence of the ground boundary layer. Conversely, Ohtani et al.1 1 2 5 state that lifting of the vehicle by the amount of the displacement thickness of the ground boundary layer has no effect upon the flow around the vehicle and the effective forces.

Potthoff suggested limiting the width of the running belt to the space between the wheels. The vehicle can then be supported with its tyres on the pads of the balance underneath the tunnel floor. However, no test results using this technique have yet been published.

The mirror image technique, which was preferred in the early days of automotive aerodynamics, is not practical. In addition to the difficulties listed in ref. 11.22 a second model and, if the blockage is not to be changed, a wind tunnel with double the nozzle cross-section are required.

Suction of the boundary layer is a practical method of reducing the boundary layer thickness. If accomplished as described in ref. 11.22, only suction through a slit or through a narrow strip of porous floor plate upstream of the model need be used.


.1.0

* - äíè.5

Suction volume flow: 0 = vS'b-s Z

Volume flow deficit within the boundary layer:

* - * . . £ > · 6 l x . 0

s: slot width b: slot length

K I x - const.

>

o

C Q *

Suction parameter

CQ* = · Ê » · ä À ÷ - ï

Figure 11.14 Reduction of the displacement thickness 6j of a turbulent boundary layer by slot suction, after ref. 11.22

Figure .11.14, from ref. 11.22, shows the relationship between the volume Q which is sucked off and the reduction of the displacement thickness ä÷ of the floor boundary layer for slot suction; this diagram is based on the tests performed by Arnold.11 26 A slot suction system for the Volkswagen AG climatic wind tunnel was designed (but not installed) for the largest suction parameter considered here of CQ = 7. The suction slot was to be positioned in front of the vehicle, and a reduction in the displacement thickness of 60 per cent was expected for the empty test section at the middle of the balance turntable (see Fig. 11.15). Approximately the same results were obtained with the boundary layer suction system in the Fiat wind tunnel in Turin by Antonucci, Ceronetti

**-*z Nozzle Average car length Balance pivot

k Chassis-dynamometer

Figure 11.15 Possible reduction of the displacement thickness bi of the floor boundary layer, Volkswagen climatic wind tunnel, by slot suction; suction parameter cQ = 7; after ref. 11.22


Figure 11.16 Test section floor boundary layer in the General Motors wind tunnel ESAL, after ref. 11.21: (a) velocity profiles without and with suction; (b) boundary layer growth at 80.5 km/h (50.3 mile/h)

and Costelli11 27 and in the large wind tunnel of General Motors in Warren, Mich.; see Kelly, Provencher and Schenkel11 21 (Fig. 11.16).

Blowing air into the retarded flow near the ground plane is another way of reducing the boundary layer thickness. Figure 11.17, from ref. 11.28, shows the blowing device used in the Lockheed Georgia wind tunnel. At about 2 m downstream from the row of nozzles the momentum loss of the boundary layer was almost completely compensated.

According to Gould11 29 the boundary layer thickness can be reduced by one-half with trip mouldings placed on the floor in the form of an arrow


0.91 m h * - 2 . 1 3 m - H Traversing plane

r ^^)//////////M//^^^^

t 1.3 cm | f j >SV?»»A Τ77777777Τ τã,

z

150

mm

100

50

i

Nozzle diameter 13 mm

Distance between nozzles 127 mm H

o o o o

φ without aO

° O r with o </

D O o o

a o

0.7 0.8 0.9 1.0 v

blowing

Figure 11.17 Reduction of boundary layer thickness by blowing air into the boundary layer, after ref. 11.28

(see Fig. 11.12). However, as Carr and Hassel1130 established, this measure has no notable effect upon the forces and moments acting upon vehicles with normal ground clearance.

Comparative measurements between wind tunnel and road performed by Hucho, Janssen and Schwarz11 22 (Fig. 11.18) show that the velocity profile underneath the vehicle is only influenced by the ground plane boundary layer of the wind tunnel in the immediate vicinity of the test section floor. The displacement flow around the vehicle completely changes the velocity distribution in the channel formed by the vehicle's underside and the floor of the test section in comparison to that with an

— · — Wind tunnel —o— Road

Empty test section

Vehicle floor

250

mm

200

[150

100

50

Front

0.5 1.0 1.5 v 0.5 1.0 1.5 ~ 0.5 1.0 1.5 _y ^ v_ _v V- V„ K»

Figure 11.18 Velocity profiles beneath a car, wind tunnel versus road; after ref. 11.22


+1.0 140-Figure 11.19 Pressure distribution along the longitudinal midsection of a passenger car, wind tunnel versus road; after ref. 11.22

empty test section; a comparatively thin boundary layer forms. As shown in Fig. 11.19 there is very good agreement between wind tunnel and road results for pressure distribution. This shows that the forces and moments measured in the wind tunnel are the same as those on the road if the prerequisite stated in ref. 11.22 is fulfilled, i.e. the ratio of the displacement thickness δλ to the ground clearance e of the vehicle is at least

äé 0.1

Other measurements given in ref. 11.22 on a sports car (less ground clearance) show that there is no significant boundary layer influence even for values of bê ~ 0.05 (see also section 11.5.7). Thus, for passenger cars and vans, the need to improve road simulation by control of the boundary layer of the wind tunnel floor is eliminated. For vehicles with very low ground clearance, such as racing cars, the influence of the boundary layer has not yet been examined but a higher influence can be expected. The method suggested by Williams11 28 of re-energizing the boundary layer by blowing in air appears to be particularly well suited for this type of application.

11.3.3 Air flow blockage, streamline deformation, pressure gradient

The flow of air around a vehicle in the wind tunnel is influenced by the flow conditions existing at the boundaries of the jet. The closer these boundaries are to the model the more the flow around the model is changed, compared to an infinitely large jet cross-section. In a closed test section the streamlines around the vehicle are forced closer together, in an open test section they widen out (see Fig. 11.20 from Wuest11 6). In the first case, the effective approach velocity is greater, in the second less than


© ©

Figure 11.20 Effect of the flow boundary on the flow field, after ref. 11.6: (a) narrowing in a closed test section; (b) widening in an open test section

that at the nozzle. Without correction, this leads to drag coefficients which are too large in a closed test section and too small in an open test section. The same applies for all of the other force and moment coefficients.

Through corrections an attempt is made to take the finite character of the air stream dimensions into consideration and to convert the measured data to road conditions. In ref. 11.6, Wuest summarized how these corrections can be performed in aircraft aerodynamics. The correction formula for the drag contains the blockage ratio ö (they are therefore designated blockage corrections) and the drag of the test body as the primary variables. The corrections are only applicable when their magnitude is small, i.e. with small blockage and low drag figures. However caution is required in applying aircraft correction formulae to motor vehicle aerodynamics. In comparison to aircraft, motor vehicles are bluff bodies with high drag and large zones of flow separation, particularly in the wake. Motor vehicles therefore 'disturb' the wind tunnel stream much more than aircraft at the same geometric blockage ratio. Carr1131

attempted to take this into consideration by working out empirical correction formulae for motor vehicles. A recent survey on wind tunnel blockage corrections has been presented by Buchheim et al.11 32 The corrections have been derived from comparative measurements among major European and North American automotive wind tunnels. A generally valid solution for the blockage correction for measurements on motor vehicles has not yet been found.

Wuest11 6 showed that, for a wind tunnel whose jet has three free boundaries and one rigid boundary—the tunnel floor—the value of the blockage correction is small. For a large full-scale wind tunnel (see section 11.5) correction factors of maximum 2 per cent result for passenger cars. As the blockage correction itself is unreliable, this correction is generally neglected for large free jet wind tunnels. In contrast, closed test sections need relatively high correction factors. Moreover, these have the opposite sign, which must be taken into consideration when comparing measured results from wind tunnels with open and closed test sections.

When performing thermal tests, for which the effective wind speed must usually be equal to the circumferential speed on the drums of the chassis dynamometer, other procedures must be used for the application of correction factors than for aerodynamic tests. Here the measured data cannot be corrected after completion of the test according to correction


formulae; the corrected wind speed must prevail during the test. As a rule, the reference velocity is selected or adjusted for which the pressure coefficient at the stagnation point is cp = 1 (see section 2.3.2 and Iwase, Yamada and Koga11 3 3) .

If the vehicle is yawed to the oncoming flow the wind tunnel flow is deflected. In an open test section the jet can deflect laterally. The high curvature of the flow lines compared with those in the open air influences the field upstream of the vehicle. The effective angle of yaw is therefore smaller than the geometric angle of the vehicle relative to the axis of the working section.

In a closed test section the relationships are reversed. At large angles of yaw there is also the danger that the flow will separate from the test section walls.

Since the lateral force created by the wind passing a yawed car is equivalent to the lift on an aerofoil of low aspect ratio at an angle of attack (see Hucho and Emmelmann11 3 4) , the correction mode for angle of attack could be used to correct for yaw angle in vehicle measurements, but in practice no yaw correction is applied. This is justified as long as the further processing of the vehicle aerodynamic derivatives is associated with further and very much greater uncertainties, such as the mechanical models used and the characteristics of tyres and other components.

The effect on vehicle drag of a pressure gradient along the axis of the air stream has already been discussed in section 11.2.3. A 'buoyancy' correction based on the pressure gradient in the empty test section must be considered questionable.

11.4 Tests with scale models 11.4.1 Model techniques

Even today, many tests are still performed on scale models. These tests are comparatively inexpensive; a further advantage is the handiness of smaller models for transport and for shape modifications. The most common scale in Europe for passenger cars is 1:4, though in small model tunnels 1:5 is also used. In the USA the '3/8 scale' is most common. For commercial vehicles a scale of 1:10 is popular. If a large wind tunnel is available, 1:2.5 is selected, see section 8.5.2.

However, in the development of passenger cars the use of reduced scale models is decreasing because the transferability of model tests to full-scale is uncertain; this is discussed in greater detail in the next section. Also designers prefer working on full-size models; judging the shape of scale models is very difficult. Details in the shape such as indentations, curvatures, window recesses, tyre beads and welts are overemphasized as a rule on scale models. On full-scale models, which represent the basis for model selection and later design, these exaggerations are reduced. Therefore one of the basic prerequisites for performing tests on scale models, the geometrical similarity to the full-scale version, is not fulfilled. However, if the wind tunnel model is produced by reducing the size of an existing full-scale model this problem is eliminated. A scale of 1:4 is then just large enough to reproduce all of the primary details to scale.

Tests with scale models 419

Since the underside of the vehicle has a great influence upon the flow of air around the vehicle (see section 4.3.2.7) all of its significant parts must also be represented.

Full-size models are generally built on an existing (reinforced) chassis; in this manner the flow of cooling air through the vehicle can also be simulated, an absolutely necessary prerequisite for optimization of the front of the vehicle.

Since the vehicle position has an influence upon the flow of air around the vehicle, it must be fixed precisely and adjusted for reproducibility. There are two possibilities for testing a vehicle in the ready-to-drive state: either the suspension is fixed in a given position, or the suspension remains free. In the latter case the vehicle is loaded with one half of the maximum permissible load so that it is in the design position. According to the aerodynamic forces and moments, the vehicle will adopt a similar attitude in the tunnel as when driving on the road. However, as a rule the suspension is fixed for tests on full-scale models. Models are considerably heavier than the finished vehicle, so that the effect of the air forces and moments on the vehicle position would be unrealistic.

The rotation of the wheels is usually not taken into consideration in wind tunnel testing; testing is carried out with the wheels stationary. When the wheels are integrated into the body the rotation of the wheels appears to have a negligible influence upon the forces and moments acting upon the vehicle. For soiling tests the 'spray pattern' of the rotating wheel can be reproduced by blowing in water drops or talcum (to simulate dust) at the appropriate points. When the wheels are not integrated into the body, as in single-seat racing cars, the forward displacement of the separation resulting from the rotation of the wheel can be taken into consideration by attaching a trip moulding (Williams,11 35 see Fig. 11.21). The flow pattern is then very similar to that of a rolling wheel.

Trip moulding

�0 * ^ | | i =£-<+ _ ω = 0 ωΦÏ ω = 0

Figure 11.21 Simulation of the wheel rotation for a free rolling wheel by attachment of a trip moulding, after ref. 11.35

For force measurements on trucks with uncovered wheel sets, the rotation of the wheels is also neglected. Since the flow in the area of the chassis is largely separated, this should be permissible.

The simulation of the wheel and its rotary motion has been investigated by Cogotti.11-36 His pressure measurements, reproduced in Fig. 11.22, clearly show the effects of ground clearance and wheel rotation. High negative pressures are induced on the tunnel floor and on the lower surface of the wheel as well, when the wheel is off the ground. These negative pressures increase sharply with decreasing ground clearance, causing


ω

0

V R

- - + - -

Figure 11.22 Pressure distribution on the floor beneath a wheel for different ground clearances, after ref. 11.36

negative lift. The effect of rotation on the pressure underneath the wheel is small. When the wheel just touches the ground, the pressure in front of the wheel is changed to a positive value, causing a significant change in lift from negative to positive, see Fig. 11.23. While the effect of rotation is small on drag, it is remarkable on lift. From Cogotti's experiments it can be concluded that for correct simulation of the flow around the wheel it is more important to maintain its contact to the ground than to reproduce its


0.80

0.60

CD

0.40

0.20

Π^Ξ^-""* "i � · · -�— -f*"

0.60

0.40

0.201

7 CLW m.x - best wheel to ground sealing j Range of CLW for different wheel to ground sealings

CL

-0.20

e/2R

0.05 0.10 e/2R

Figure 11.23 Drag and lift of a wheel, rotating and stationary, for different ground clearances; after ref. 11.36. — · — ù = 0; — + — ù = V/R

rotation. The drag of the non-rotating wheel is only slightly higher than that of the rotating wheel. But as soon as the wheel is shielded by a fairing, rotation starts to play an important role. Cogotti found that fairing a fixed wheel resulted in a drag reduction of AcD = -0.049, whereas this value

-ΚΪ /?<? = V2R

>A»iW!Wß»»SSM*»jy, ω e

• o

V

= 0 = 0

Standard rim Faired rim

cD\

U.DU

0.55

0.50

\

[ ·

^

i 1 1 m i

•

o

\

1 L - L l l i u x

T8" L__

3 5 1.105 3 5 1.106

Re

0.8

0.6

0.4

0.2

[-

L·

L . l l i i n

1

1 1 1 1 1 111 1 3 5 1.10s 3 5 1.106 3

Re Figure 11.24 Drag and lift of a stationary wheel versus Reynolds number, after ref. 11.36


was AcD = -0.091 for the rotating wheel. The optimization of the flow around the wheel has to be done with the rotating wheel.

The Reynolds number has a significant influence on the flow around a wheel. This is to be seen from Fig. 11.24 for an isolated, stationary wheel. The plot of the drag coefficient cD versus Reynolds number Re is similar to that for the circular cylinder. A drastic drag reduction occurs in the range of

105 < Re < 106

When small-scale models are tested, especially those with exposed wheels like single-seat racing cars, provision has to be made to be beyond the 'critical' wheel Reynolds number of 106.

11.4.2 Influence of the Reynolds number

In addition to the requirement for geometric similarity, the flow around the model and the full-scale version must be mechanically similar. For incompressible flow this condition is fulfilled when the Reynolds numbers for the scale model and full-scale version are equal, see Schhchting and Truckenbrodt11 37 for example. The Reynolds number is defined as

Re= —

see also section 2.2.1. V«, is the velocity of the undisturbed oncoming flow, / the length of the vehicle and v the kinematic viscosity of the working fluid. Mechanical similarity is therefore present when the following equation is true:

V\h _ V2k Vl V2

Since, as a rule, model testing is accomplished in air (tests in water tunnels are seldom performed on vehicle models) the requirement for mechanical similarity is satisfied when the products of the velocities and lengths are equal. This condition is generally not maintained in tests on models with a scale of 1:4; the Reynolds numbers amount to one-quarter to one-half of the value of the full-scale version.

Since the drag resulting from friction is small in comparison to the drag resulting from pressure for motor vehicles (see section 4.3.1) it could be assumed that the influence of the Reynolds number is small within the stated Reynolds number range. In fact, drag measurements on vehicles exist that show hardly any Reynolds number influence. However, the following two examples show that serious errors can result through violation of the Reynolds law of similarity:

Figure 11.25 (after Hucho, Janssen and Emmelmann11 38) shows a series of measurements obtained during optimization of the front end of two vans. In both cases the objective was to find that radius between the front wall and side wall around which the air could just flow without separation, and which is therefore 'optimum' within the sense of the definition according to section 4.4.1. Van A had a relatively highly cambered front


0.55

0.50

t 0.45

Co 0.40

0.35

£-i 0.05 0.10

Figure 11.25 Influence of Reynolds number on 'optimum1 radius at the transition from the front end to the sidewall of two different vans, after ref. 11.38

end; on the model with the scale of 1:4 the optimum radius in relation to the vehicle width was found to be rib = 0.06. On van B, which was characterized by a very flat front end, the optimum radius on the 1:4 model was found to be rib « 0.14. This radius was so large that it was rejected by the designers. The 'optimum' radii established for the models with a scale of 1:4 were checked on the full-scale versions. In both cases, optimum radii were found for the full scale versions that were considerably smaller than those found on the models. In the case of van B, the optimum radius for the full-scale version resulted in a stylistically acceptable solution.

The fact that air flows around considerably 'sharper' corners without separation on the large versions than is the case with small models is

A

Co

A

0.25

0.20

0.15

0.10 >t

0.05

0.05 0.10 0.15 0.20 0.25 «V—

Re V

S

„·/ V

N N.

Ί

0.9 1.0 1.1 1.2 1.3 1.4

b Figure 11.26 Influence of Reynolds number on the 'optimum' front end radius of a cuboid, after ref. 11.39


obviously traceable to the Reynolds number effect. It is known that the separation of the turbulent boundary layer is influenced by the Reynolds number; with increasing Reynolds number the location of the separation on a given body moves downstream. With larger Reynolds number the turbulent boundary layer can sustain greater adverse pressure gradients than with a small Reynolds number. This means that when the Reynolds number is large the air can flow around sharper bends without separation.

The measurements performed by Pawlowski,11 39 which are reproduced in his original version in Fig. 1.38 and which are replotted in non-dimensional form in Fig. 11.26, confirm this. Further details on the influence of Reynolds number on optimum radii have been published by Cooper.11 64 Similar Reynolds number effects have also been observed on other vehicle details. They are, as has been discussed in section 11.4.2, significant for wheels. Quantitative results—and only these count in the development of a vehicle—can therefore only be expected with the correct Reynolds number.

There are two ways to achieve the Reynolds number of the large version with scale models. Frequently the suggestion is made to increase the model scale but this would require a larger model wind tunnel. The advantage of the easy-to-handle model and the ease of quickly modifying the shape are rapidly lost with increasing dimensions. Limits therefore exist in this direction. In practice the largest model scale used for passenger vehicles is the 3/8 scale.

On the other hand, a frequent suggestion is to increase the air stream velocity in the model wind tunnels. Figure 11.27 (after ref. 11.38) shows that there is little scope for this either. Due to the bluntness of the vehicle body, greatly increased velocities are reached at individual points of the vehicle contour. As calculations and measurements on elliptical bodies of revolution and cylinders show, the critical Mach number, i.e. the Mach number for undisturbed oncoming flow, at which the speed of sound is first

Afak = 1

A

Co

Elliptical cylinder, exact solution, 0.1 ace. to C. Kaplan

0.2 0.4 0.6 0.8

Figure 11.27 Critical Mach number and drag for bodies whose bluntness is comparable to that of passenger cars, after ref. 11.38

Existing automobile wind tunnels 425

reached locally at the contour of the body, is reduced to very low values with increasing bluntness. Even below the critical Mach number the drag begins to increase due to compressibility effects. For vehicle shapes, this is probably much more difficult to calculate than the influence of the Reynolds number upon the local separation.

In wind tunnel tests on aircraft models a higher Reynolds number is sometimes simulated by artificially increasing the turbulence level of the wind tunnel air stream. In this manner, flow separation on a wing can be displaced to higher angles of attack, an effect that also occurs with increasing Reynolds number. This may possibly offer a solution. However, for the time being, quantitative information such as how great the turbulence level of the wind tunnel must be to simulate a certain Reynolds number, is not available. Artificial generation of turbulence also presents difficulties, because once produced, the turbulence decays along the flow. This procedure can therefore not yet be recommended for application in motor vehicle aerodynamics.

11.5 Existing automobile wind tunnels 11.5.1 Synopsis

The wind tunnels, climatic tunnels and climatic wind chambers used in industry and research centres for automobile aerodynamics are listed in Table 11.1. The tunnels are arranged according to the cross-section of the nozzle, without regard to the type of test section boundaries.

Wind tunnels with a nozzle cross-section of over 30 m2 can be used for passenger car aerodynamics without limitations. Even small vans can be tested at full scale. For large commercial vehicles a scale of 1:2.5 is recommended. With low blockage, the Reynolds numbers for the full-scale version can still be achieved.

Tunnels with a nozzle cross-section between 15 and 25 m2 are unnecessarily large for climatic engineering for passenger cars and small vans. For aerodynamic testing on vehicles at full scale they are suitable with limitations. Tunnels of this size can be improved with slotted or streamlined test section boundaries.

For climatic tunnels, a nozzle cross-section between 10 and 12 m2 is sufficient. The prerequisite is that an empirical blockage correction factor be determined through calibration measurements in a large wind tunnel or on the road, which is then taken into consideration for the adjustment of the oncoming flow velocity. In part, an attempt is made to trim the air flow with the aid of baffles so that the pressure distribution on the vehicle corresponds as precisely as possible to that on the road. This would lead ultimately to a streamlined test section boundary, which, however, has not been practically applied to date.

Climatic wind chambers with a nozzle cross-section of 5 m2 and smaller are suitable for climatic testing only with limitations, but can be used without limitations for cooling system development. The smaller the nozzle cross-section, the greater the effort that must be expended for calibration and flow guidance (baffles) for each new vehicle shape.

Tab

le 1

1.1

Win

d tu

nnel

s, c

limat

ic t

unne

ls a

nd c

limat

ic w

ind

cham

bers

in a

utom

obile

aer

odyn

amic

s

DN

W

Gen

eral

Mot

ors

Vol

ksw

agen

Lo

ckhe

ed-G

eorg

ia

MIR

A

Dai

mle

r-B

enz

Fiat

V

olvo

Fo

rd (

Col

ogne

) M

azda

M

itsub

ishi

Fo

rd (

Dea

rbor

n)

FKFS

Po

rsch

e N

issa

n B

MW

To

yota

N

ippo

n So

ken

Inst

. Aer

otec

hniq

ue S

t. C

yr

Fiat

(2

x C

limat

e)

JAR

I Pi

ninf

arin

a Fo

rd (

Col

ogne

Clim

ate)

So

fica

FKFS

V

olks

wag

en I

I C

hrys

ler

Vol

vo

Beh

r O

pel

Aud

i Po

rsch

e

A T

(m2 )

90.2

5 48

.0

65.9

37

.5

35.1

35

.0

32.6

30

.0

27.0

6 24

.0/8

.6

24

24

23.2

22

.5

22.3

21

.0

20.0

17

.5

17.5

/12

15.0

12

.0

12.0

11

.75

11.0

11

.0/4

.3

6.0

6.0

4.74

4.

32

5.24

4.

30

1.5

1.5

^-M

(m

)

15.0

16

.0

23

10.0

0 13

.10

15.2

4 10

.00

10.5

0 15

.8

10.0

12

.0

12.0

9.

15

9.5

12.0

10

.00

12.5

8.

00

12.5

/8.5

10

.00

11.6

0 10

.00

9.5

9.00

16

.5/1

4.0

15.8

7.

2/6.

0 8.

6 8.

6 14

.00

- 11.0

7.

5

v ma*

(k

m/h

)

220

400

240

180

406

133

270

200

200

182/

298

230

216

201

220

230

119

160

200

120/

200

144

160

205

185

180

80/1

70

200

170/

180

190

190

120

120 95

168

TS

c c c o c c 0 0 sw

0 c/o

c/o

c 0 sw

c sw

c c sw

o c o c c 0 o o o o c 0 0

K

4.8

9.0

5 4.0

7.02

1.4

5 3.

53

4.0

6.0

4.0

6 7 3.80

4.

41

6.06

2.

86

3.66

3.

66

3.66

5.

0 4.

0 4.

06

6.2

6.0

9 4.16

6.

0 5.

56

6.60

6.

0 7 4.

3 5.

0

L (m)

320

303

114.

0 23

8.0

50.5

12

5.0

144.

0 16

5.3

124.

0 9 7 7 15

0 14

9.9

7 45

95.0

10

4 39.2

99

.0

83.3

27

.3

113.

4 7 84

73

.4

58.8

93

.2

48.0

7 21

.0

30

P (kW

)

1270

0 29

50

2600

67

00

970

4000

18

65

2300

16

50/1

960

1600

23

50

1865

25

50

2200

7 16

76

1500

14

50

516

560

1200

10

80

1120

38

0 10

00

460

560

500

147

460 60

16

0

Ref

eren

ce

11.6

6 11

.21

11.4

1 11

.51

11.5

2 11

.40

11.2

7 11

.71

11.6

2 11

.63

11.6

3 11

.53

11.6

7 11

.68

11.2

5 11

.61

11.5

4 11

.63

11.1

2 11

.27

11.5

5 11

.42

11.5

6 11

.45

11.6

9 11

.70

11.5

7 11

.58

11.6

0 11

.59

11.6

8

Noz

zle

cros

s-se

ctio

n Le

ngth

of t

est s

ectio

n M

axim

um w

ind

spee

d

TS

Type

of

test

sec

tion:

o

— o

pen

c =

clos

ed

sw =

slo

tted

wal

ls

K

Con

trac

tion

ratio

L

Leng

th o

f tun

nel

axis


All-purpose wind tunnel VOLKSWAGEN-AG Wolfsburg

Climatic tunnel FORD Werke AG Cologne

Climatic chamber with wind CHRYSLER Corporation Chelsea, Michigan/USA

^ Climatic chamber with wind AUDI-AG Ingolstadt

Figure 11.28 Size comparison between a large all-purpose wind tunnel, a climatic tunnel and two types of climatic chambers with wind

Figure 11.28 provides a pictorial comparison of the sizes of the various types of automobile wind tunnels. Figure 11.29 shows how the pressure distribution around the front of a car can approach reality even in a small climatic wind chamber by calibrating the wind velocity. Agreement of the pressure distribution in the area of the cooling air inlet is sufficient for cooling system development.

11.5.2 Large full-scale wind tunnels

Figure 11.30 shows the oldest full-scale automobile wind tunnel at Daimler-Benz AG in Stuttgart-Untertürkheim (see Kuhn11 4 0) . This wind tunnel was designed under the direction of W. Kamm, opened in 1939 as part of the Forschungsinstitut für Kraftfahrwesen und Fahrzeugmotoren (FKFS), Stuttgart, Germany, and was completely overhauled in 1977, when it was taken over by Daimler-Benz AG. This wind tunnel is distinguished by an exceptionally high blowing velocity of Vmax = 270 km/h. Such a high velocity is an advantage for the development of fast vehicles; it is then possible to examine directly the position of the vehicle resulting from the air forces and moments, and the effect of such changes upon the aerodynamics even at top speed.


VW-all-purpose wind tunnel

ö = 5%

P o r c t e ^ ^ ^ ^ ^ ^ ^ Climatic chamber with wind v?=124% Γ " - 1 ö =

Figure 11.29 Comparison of the pressure distribution around the front of a car according to measurements in a large wind tunnel, a climatic chamber with wind and a blower, after R. Unger

For comparison, Fig. 11.31 shows the large climatic wind tunnel at Volkswagen AG in Wolfsburg, Germany. This tunnel (see Mörchen11 41) can be fully air conditioned; it is exceptionally well suited for all motor vehicle aerodynamic purposes. The limitation of the wind speed to Vmax = 180 km/h is reasonable for a manufacturer of passenger cars and small vans, particularly as Reynolds number influences are unlikely and have never been observed for such high velocities.

The advantages and disadvantages of an all-purpose system, such as is represented by the Volkswagen AG climatic wind tunnel, in comparison to a 'wind tunnel centre', consisting of a large wind tunnel and climatic tunnels11 27 are described in detail in ref. 11.7. For the time being, the Fiat concept of having separate tunnels for pure aerodynamic development work and for climatic tests can be said to be superior compared to the earlier approach of Volkswagen AG—having a general purpose climatic wind tunnel.

In any case, a large car manufacturer with a complete model line-up needs more than one aerodynamic test facility to do the large amount of

429

Nozzle cross-section: 32.6 m2

Maximum wind speed: 270 km/h Fan power: 4000 kW

Figure 11.30 Large full-scale wind tunnel of Daimler Benz AG, Stuttgart, Germany (earlier belonging to FKFS); after ref. 11.40

All dimensions in m


Maximum wind speed: 175 km/h Fan power: 2600 kW Temperature range: -35°C to +40°C

Figure 11.31 Large full-scale climatic (all-purpose) wind tunnel of Volkswagen AG, Wolfsburg, Germany; after ref. 11.41


related development work. This implies specialized devices for aerodyna-mic and climatic tests. Each facility can be optimized to its purpose. Investment cost and operating cost are lower while flexibility is much higher.

11.5.3 Small full-scale wind tunnels

Small full-scale wind tunnels are those with test section cross-sections in the range 10 to 20 m2. They either have open test sections or slotted walls. Blockage corrections have to be studied for each individual tunnel. Figure 11.32 shows the wind tunnel at Pininfarina, Turin, Italy, as an example of a small wind tunnel for testing full-size vehicles (see Morelli,1142

Cogotti1147).

Nozzle cross-section: 11.75m2

Maximum wind speed: 185km/h Fan power: 1080kW

%37m Figure 11.32 Small full-scale wind tunnel of Pininfarina, Turin, Italy; after ref. 11.42

This tunnel is a good example of the Eiffel type with air return in the test building, which is shaped to reduce the pressure loss in the return air path.

The aerodynamic development of models with a scale of 1:1 is subject to certain risks in such a small wind tunnel. The study of small changes, the basic idea of the detail optimization procedure, is only possible when the local flow fields are similar to those in the open air. The use of blockage corrections, which apply to overall forces and moments, is less certain. However, as will be discussed in section 11.5.7, a measurement comparison with large full-scale wind tunnels resulted in surprisingly favourable results for the Pininfarina wind tunnel.

11.5.4 Wind tunnels for scale models

Wind tunnels for scale models are not listed in Table 11.1; many such tunnels are occasionally used for vehicle aerodynamics. The MIRA model wind tunnel shown in Fig. 11.33, see Carr,11 43 is intended to demonstrate how little expenditure is required for such a testing unit.

Smoke tunnels have been developed especially for flow observations on vehicles and their components. Isuzu Motors operates a i m 2 smoke tunnel, which allows three-dimensional phenomena to be made visible; Oda and Hoshino11 44 have reported on this. Nissan has a smoke tunnel,



Maximum wind speed: 160 km/h Fan power: 37.3 kW.

È L—3.8 m—J

L » 15 m mi

Figure 11.33 Quarter-scale model wind tunnel at MIRA, Nuneaton, UK; after ref. 11.43

which is used mostly for examination of details such as the cooling air duct on two-dimensional models.

11.5.5 Climatic tunnels

Figure 11.34 shows a typical climatic tunnel represented by that of Sofica, see Chenet.1145 An exchangeable nozzle allows the air stream cross-section to be adapted for testing passenger cars and small vans. Climatic tunnels of this type represent a very good, economical solution for the development of heaters and cooling systems. Climatic tunnels of this size are also operated by Fiat in Turin and by Ford in Cologne, see Table 11.1.

Nozzle cross-section: 11/4.3 m2

Maximum wind speed: 80/170 km/h Fan power: 280 kW Temperature range: —50°C to +50°C

Figure 11.34 Climatic tunnel of Sofica, Paris, France; after ref. 11.45

11.5.6 Climatic wind chambers

In the construction of the climatic wind chamber shown in Fig. 11.35, the objective was to install the unit in a narrow room and simultaneously to allow easy access for the vehicle. Engine cooling tests performed in this chamber showed good agreement with tests performed in the climatic wind



Maximum wind speed: 100 km/h Fan power: 60 kW Temperature range: -40°C bis +60°C

Figure 11.35 Climatic chamber with wind, Audi AG, Ingolstadt, Germany

tunnel at Volkswagen AG. This chamber is also used successfully for heater development by adjusting the test section boundaries with baffles. Climatic wind chambers of the size shown in Fig. 11.35, but with various different designs, are used in many places all over the world—mainly for cooling system development.

11.6 Comparative measurements between European and North American automobile wind tunnels

In order to assure the comparability of test data from different wind tunnels, an intensive correlation test programme has been performed between automotive wind tunnels in Europe, the US and Canada. The programme was started in Europe and results have been reported in detail by Buchheim et al.,11·46 Cogotti et al.,1147 Costelli et al.,11·* and Carr.11 49

It was later extended to the North American wind tunnels, see ref. 11.50. The same car, a Volkswagen 1600 notchback (Type 31) (see Fig. 4.17) was tested in the following wind tunnels (see Table 11.1) with open test section: Volkswagen AG (VW), Daimler-Benz (DB), Fiat (CRF), all large full-scale tunnels in the sense of section 11.5.2, and Pininfarina (PF), a small full-scale tunnel; with closed test section, the tunnels of Motor Industry Research Association (MIRA), Lockheed-Georgia, National Research Council Canada (NRC), General Motors (GM-ESAL), German-Dutch Wind Tunnel (DNW), all large full-scale tunnels; and, finally, the tunnel of the Institute Aerotechnique de St. Cyr (IAT), a small full-scale tunnel with slotted side walls. Details from the wind tunnels, the test procedure, the model and the corrections applied are to be found in refs 11.46 to 11.50. The results for the drag measurements are summarized in Fig. 11.36.

The measured drag coefficients are in a narrow band with a standard deviation of ±2.2 per cent, corresponding to AcD = ±0.009. In view of the large technical differences among the wind tunnels considered this may be called a good agreement in drag data. On the other hand, the largest

433

o VW Ü DAIMLER BENZ 0 CRF

Ä PININFARINA T MIRA • LOCKHEED

NRC GM-ESAL DNW

� I.A.T. S4

· · · · ·

Q -

3

2

1

0

-1

2

CD —O

§ -4 CD

*- - 5

- 6

- 7 cD -

k^y^^^jAJ |

: mt£m [ooocd

DaDOIT

��] SU***]

T

AAAAik] ' 4i

^ Α Λ Λ Α

ô ô ^ ô ô | V T V T T

DDPDD �� T T T T V DDDDG I

W W T

0.338 0.381

^ ^

® ®

0.382 0.396

© Configuration

0.327

© i ©

0.493 0.368 0.430

© ® "c^"= Drag coefficient mean of 10(8) wind tunnels Elfffffl Standard deviation from mean of 10(8) wind tunnels

Figure 11.36 Comparison of drag measurements in major European and North American automobile wind tunnels, after ref. 11.50

spread of data, which was 9.3 per cent on configuration F, shows that occasionally significant differences may occur.

The data show some systematic differences: St. Cyr and Daimler-Benz data are always below mean value (not that the mean is necessarily the true value). Lockheed and NRC data are above the mean; DNW, GM-ESAL, VW and CRF are close to the mean. Despite the applied corrections the drag figures from the tunnels with closed test section are generally higher than those from open test sections (for which no corrections at all are applied). Surprisingly, the data of the smallest tunnel, the Pininfarina, are well within the standard deviation of the large tunnels.

A more systematic way to look at comparative data is to compare drag changes due to minor or greater modifications of individual body details, see Fig. 11.37, after Buchheim et al.11·50 For example, the drag reduction due to a rear spoiler was 1.3 per cent in one tunnel and 5.1 per cent in another. The first figure may well be considered not to justify the expense of a rear spoiler, while the latter may suggest the opposite. No explanations have been offered to explain these discrepancies. Further-more, Buchheim et al.11,50 emphasize that comparing data from cars other than the tested one—e.g. fastbacks and squarebacks with their related rear flow characteristics—may lead to somewhat different results, see Cogotti et a l . 1 1 4 7 andCos te l l i e ta l . 1 1 4 8

As reported by Buchheim et al. in ref. 11.50, the agreement between the lift figures obtained in the tunnels is not as good. Whether the measured differences result from the different flow patterns (angle of attack of the air


O VW

D DB

OCRF

APININFARINA

• LOCKHEED

� NRC

� GM ESAL

A DNW

V MIRA

Sf I.A.T. S4

B Standard deviation from mean value

56

52

c? 48

�M

.§ 44

^ 16 o u CO �o 12

Uli sfe

ßi;5

«J 4h -^

-â Δ

e-rah Δ

wSfc

Configuration change

Figure 11.37 Change of drag subsequent to shape modifications, comparison between wind tunnels; after ref. 11.50

stream) in the individual wind tunnels or from the measurement techniques (consideration of the lift on the wheel support plates of the balance), has yet to be clarified.

In the Fiat tunnel, which has a floor boundary layer suction device, comparative measurements were performed with and without floor boundary layer suction. These confirmed the findings of Hucho, Janssen and Schwarz11 22 and model tests performed by Carr and Hassell:11 30

suction of the floor boundary layer has no measurable influence upon the aerodynamic drag of passenger cars.

11.7 Final comments and prospects

The large number of testing facilities for research and development in the area of automobile aerodynamics indicates the high priority placed on this area of specialization by motor vehicle engineering. Of particular note is the multiplicity of types and sizes of such facilities. In spite of the nearly identical objectives, the various vehicle manufacturers have arrived at solutions which differ considerably from one another. This is in part

Notation 435

attributable to the fact that particular objectives in the field of automobile aerodynamics are not given the same significance by all, and in part to the fact that, over time, the objectives have changed.

The rapidly increasing significance of fuel economy is bringing the aerodynamic drag of vehicles more and more to the fore. This makes it all the more important to be able to measure this figure reliably in a wind tunnel.

Reliable wind tunnel corrections must be derived from the results of comparative measurements—both existing and those still outstanding. Inclusion of further wind tunnels will make it possible to confirm these correction factors on a wider basis.

It is known that the individual users of one large wind tunnel in the US use different, company-specific wind tunnel correction factors for the test data obtained in this tunnel. The result is that various cD values are derived from one set of uncorrected test data, depending upon the user. By computing and agreeing upon standardized wind tunnel correction factors, this situation, which makes it difficult for the arguments of automotive aerodynamic engineers to be taken seriously, must be surmounted.

11.8 Notation

A As Áτ

D K A n e w 5 L LK M Ma P p ßc Q Re Tu U V V

vx VB

CO CP co d e h I

K0

Po

frontal area of the vehicle cross-sectional area of settling chamber cross-sectional area of wind tunnel air stream drag, Figs 11.2 and 11.3 contraction ratio, Fig. 11.9 contraction ratio, Fig. 11.10 lift, Figs 11.2 and 11.3 length of test section pitching moment, Figs 11.2 and 11.3 Mach number, Fig. 11.27 drive power of wind tunnel drive power of wind tunnel, Fig. 11.10 heat flux suction volume flow Reynolds number, Eqn 2.4 turbulence level flow velocity vehicle speed wind velocity oncoming flow velocity belt speed drag coefficient, Eqn 1.2 pressure coefficient, Eqn 2.8 suction parameter diameter, Fig. 11.9* ground clearance, Fig. 4.111 height above ground vehicle length


p static pressure /?oo static pressure in undis turbed flow (free s t ream) r contour radius s width of suction slot, Fig. 11.14 u' turbulent velocity variat ion vs velocity in suction slot, Fig. 11.14 w vehicle width x, y , z orthogonal coordinate system a angle of attack, Fig. 11.1 ß angle of yaw, Fig. 11.1 ä boundary layer thickness δι displacement thickness of boundary layer v kinematic viscosity of the air p air density ö blockage ratio, Fig. 11.29 ù angular velocity of the wheel

Chapter 12

Measurement and test techniques Gφrgün A. Necati

12.1 Objectives

Objective assessment of vehicle performance necessitates the use of appropriate measuring equipment and testing methods. This chapter describes the instrumentation widely used in vehicle aerodynamics and related vehicle engineering problems. This is followed by a description of testing procedures carried out both in the wind tunnel and on the road.

12.2 Measuring equipment and transducers 12.2.1 Measurement of aerodynamic forces and moments

The precise measurement of the aerodynamic forces and moments acting on a vehicle body is usually done in a wind tunnel. An aerodynamic balance is commonly used to measure the forces and moments. This is a stationary high-precision measuring instrument.

An axis system most widely used is the right-hand orthogonal system (Fig. 4.111). It has its origin at the centroid of the contact points of the wheels with the ground and is fixed in the vehicle. The jc-axis is horizontal, pointing forward and in the longitudinal plane of symmetry. The v-axis points to the driver's right and the z-axis points downwards; this is in accordance with SAE Vehicle Dynamics Terminology.12Λ Confusion may arise if other axis conventions are used and the test results gained with different axis systems are compared by mistake. For example, the axis system commonly in use in flight aerodynamics is shown in Fig. 2.14 and has the x and z axes in the opposite directions.

The axis system used in vehicle aerodynamics has the advantage of coinciding with the axis system commonly used for vehicle handling investigations. This enables wind tunnel data to be used directly with vehicle handling data if the aerodynamic effects on vehicle dynamics are investigated.

12.2.1.1 Wind tunnel balances

A wind tunnel balance measures three aerodynamic force components in the x, y and z directions and three aerodynamic moment components

437

Hyd

rost

atic

be

arin

g

Flo

atin

g

fram

e

Ro

tati

ng

ba

se f

ram

e

Figu

re 1

2.1(

a) (

see

oppo

site

)

Lev

er-l

inka

ge

mec

han

ism

to

m

easu

re d

rag

fo

rce

To

p p

late

P

latf

orm

Lev

er-t

are

wei

gh

t m

ech

anis

m t

o

mea

sure

lif

t fo

rce

Lev

er-l

inka

ge

mec

han

ism

to

m

easu

re s

ides

fo

rces

H

ydro

stat

ic

bear

ing

Measuring equipment and transducers 439

tending to rotate the vehicle body about the x, y and z axes of the reference axis system. If the aerodynamic yaw angle is zero, the measurement of only three components is sufficient, namely the force components in the x and z directions and the moment about the y-axis. Hence, for tests at 'straight ahead' position only, a balance of simpler design can be used.

To enable precise force and moment measurements to be made, the wind tunnel balances have to satisfy a number of requirements: • The balance equipment should not disturb the air flow near the test vehicle. If a support system has to be used (e.g. during small-scale wind tunnel tests) the influence of this system on the test results has to be determined for subsequent elimination. • No changes in vehicle set-up position should occur during the measuring procedure. • The lift forces to be measured are only fractional compared with the initial wheel loads; hence, for accuracy, tare weights have to be used to compensate the pre-loading in the z direction. • If the tests are to be carried out at varying yaw angles, provision must be made for the yawing of the balance equipment up to a desired maximum yaw angle. • Friction and hysteresis must be kept to a minimum in the force transmission mechanisms between the test object and the load sensing systems. The use of special precision components is therefore essential, e.g. knife-edge and groove combinations, elastic hinges, hydrostatic and pneumatic bearings, etc.

12.2.1.2 Resolving the forces and moments into components

The separation method of the three force and three moment components depends on the design of the balance. The six-component balance

i Virtual centre

\ i-Supporting strut —

Vertical link

Inclined link

Frame no. 3

Frame no. 2

Frame no.1

(b) /

Rotating base frame

^Mmmmimmms. v»mJH'\vvvvuJt}

Fixed base frame

Figure 12.1 Wind tunnel balances, (a) Six-component balance equipped with hydrostatic bearings, base frame and floating frame. The lift force, rolling and pitching moments are calculated from the four lift forces Zu Z2, Z3 and Z4. Õλ and Y2 enable the side force and yawing moment to be calculated, (b) Working principle and main components of a pyramidal balance

440 Measurement and test techniques

constructions that have been realized for vehicle wind tunnel testing are outlined in the following paragraphs.

One approach to separating the aerodynamic force and moment components is to support the vehicle with four wires parallel to the z-axis, two parallel to the y-axis and one parallel to the x-axis. The force and moment components are then calculated using the measured forces read at all seven wires. This type of force and moment resolution is no longer used in full-scale wind tunnel testing. However, wire type balances are still used in small-scale wind tunnels.

In the second method, the vehicle is positioned on one platform, which is supported on a main frame below the test section by means of three (or four) vertical supports. The horizontal restraint of the platform is provided by three links. The vertical restraint of the platform is provided by three links. The vertical and horizontal supports are connected to load cells to measure the forces transmitted from the vehicle onto the platform. The required vehicle aerodynamic forces and moments can not be immediately read, but are derived from the measured force measurements. This system is applied in the MIRA wind tunnel.

In another construction, each wheel of the test vehicle is positioned on a separate platform, which is instrumented to measure the force components in three directions parallel to the vehicle reference axis system. The resulting aerodynamic force and moment components are then calculated using the 12 signals measured. Such a system is employed in the environmental wind tunnel of Ford-Germany (Cologne), because it is easily removed during environmental tests, when it is replaced by a dynamometer.

Another design often used to separate the aerodynamic force and moment components is shown in Fig. 12.1a. The test vehicle wheels are supported on four platforms, each supplied with a hydrostatic bearing to ensure minimum friction in the vertical direction for immediate lift force measurement. These are mounted on a frame (floating frame) which is supported by four further hydrostatic bearings carried on a second frame (base frame). By means of the hydrostatic bearings, the friction is reduced to a minimum in the horizontal direction. The floating frame is held relative to the base frame in the x-axis direction by means of a linkage lever mechanism to measure the drag force. Two similar mechanisms hold the floating frame in the y-axis direction to measure the side forces. Using all seven force measurements, the required three force and three moment values are calculated. This balance system is most widely used by Volkswagen, Mercedes, Ford (Germany), Fiat, Pininfarina, Saint Cyr (France), and BMW.

The final method has the test vehicle supported on four struts mounted on a frame beneath the test section (see Fig. 12.1b). This frame is attached to a second frame by means of four inclined links (pyramidal balance), as shown. A third frame, which is connected to the second frame via four vertical links, is finally supported by the rotating base frame. The axes of the inclined links have a common intersection point (virtual centre) which coincides with the centre of the vehicle axis system (see Fig. 4.111). As this point is also the moment resolution centre, all three aerodynamic forces and moments can immediately be read on appropriately positioned


linkages without any calculations. The forces in the x and z directions are measured by means of linkage-lever mechanisms which support frame number 2 on the rotating base frame. The force in the y direction is read similarly by means of a double linkage-lever mechanism that supports the second frame on the first frame. For further details on pyramidal balances see Pope and Harper.12 2 Pyramidal balances are used in the wind tunnels of General Motors and Lockheed Georgia.

Automatic beam balances are often used to measure the forces transmitted from the test vehicle to the force separation system of the wind tunnel balance. This type of balance consists of a weighing beam that has an electrically driven jockey weight. When the beam drops, a driving motor automatically moves the jockey weight in the direction that will balance the beam. The final jockey position represents the magnitude of the force to be measured.

A cheaper way to measure the required forces is to use electrical load cells. These are usually transducers of capacitive or inductive type or strain gauges. However, they need more maintenance than the beam balances and frequent recalibration is necessary.

The upper faces of the platforms on which the vehicle wheels are supported are usually subjected to a decreased static pressure level due to the local air flow regime near the wheels. The static pressure difference between the upper and lower faces of a platform results in an additional force component, which is measured by the balance, and thus to incorrect lift force measurements. The area of the top plates of the platforms must therefore be kept as small as possible. At the same time, provisions have to be made to enable adjustment of the wheelbase and tread width to suit test vehicles of various sizes. Figure 12.1 shows one way of solving this problem. The top plates attached to the platforms can be moved fore and aft to match the desired wheelbase. The remaining areas above the platforms are covered with movable plates supported on the test section floor (not shown in the figure). The lateral position of each of the top plates can also be varied and a belt consisting of a number of slats and supported on the test section floor covers the remaining face. In this way, a flat test section floor is achieved. The top plates, which transmit the forces to be measured to the balance, are isolated from the surrounding turntable by a narrow gap.

Another way of achieving these adjustments is by the use of a system of three eccentric circular plates for each wheel, the smallest being the top plate of balance. The outer two plates are supported by the test section floor. The rotation of these plates allows the desired positioning of the top plate. This enables any combination of tread width and wheelbase to be used. Details are to be found in Kelly et al.12 23

If the top plate areas have not been designed sufficiently small, a lift force measurement error is inevitable. In this case, an average static pressure value has to be determined by measuring the static pressure distribution on the upper face of each plate. The difference between the static pressures acting on the upper and lower faces is then multiplied by the plate area to find the lift force component to be taken into consideration as the lift force measurement error.


12.2.2 Pressure measurements

During wind tunnel tests, the most frequent data collected involve the measurement of dynamic or static pressures relative to a free airstream. Measurements are also made of the static pressure distribution created by the air flow over a solid surface.

The measurement of dynamic pressure is usually required to calculate air flow velocity, while static pressure measurement is used to detect the different pressure zones on the vehicle body. These zones are used to determine the air inlet and outlet areas for ventilation and the risk of fume ingress. They are also used to investigate and understand the effects of various aerodynamic proposals (e.g. front end and rear end spoilers) on aerodynamic coefficients.

12.2.2.1 Pressure probes

A common way of measuring the dynamic and static pressure in a free airstream is to use a Pitöt-static tube (Fig. 2.5). The total head g is measured by the orifice at the tip and the static pressure p is measured by the holes or slots in the Pitöt-static tube. If both pressures are connected across a manometer, the pressure difference g - p will represent the dynamic pressure and Eqn 2.11 describes the calculation of free air speed w using the dynamic head (see also Eqn 12.1).

Various types of Pitöt-static tubes are used, the difference being in the head shape. Hemispherical, ellipsoidal and tapered-nose tubes are the most common.

A Pitöt-static tube delivers precise results if it is subjected to a free airstream without large-scale turbulence and swirl. Furthermore, the tube axis must coincide with the air flow direction, otherwise the pressure measurement error rate will vary with the yaw angle. Figure 12.2, from Pope and Harper,12 2 shows the error versus yaw angle for a Pitöt-static

c > T3

6

4

2

0

- 2

A —H

- 6

- 8

Tot

^ S

al head

Static _, pressure

} 1

X1 vj

\ \

>

1 Dynami ares.

\ \ \

\ \

c sure

4 8 12 16 Yaw angle (degrees)—^»

20

Figure 12.2 Error of a Pitöt-static tube (hemispherical head shape) due to airflow yaw, after ref. 12.2. (Note: the static pressure is plotted with negative sign)


tube with a hemispherical head, where up to 12° yaw angle gives less than 1 per cent variation in dynamic pressure which is an acceptable accuracy for most measuring tasks.

The yaw sensitivity of a Pitot-static tube is strongly influenced by its head shape. The yaw performance of an ellipsoidal nose-type tube, which is also in widespread use, is comparable with the hemispherical head tube. The yaw sensitivity of an N.P.L. tapered-nose standard tube is however considerably higher, as can be seen from Gorlin and Slezinger12 4 and from Pankhurst and Holder.12 ^ Therefore correct alignment during measure-ments is particularly essential for this type.

The static pressure distribution on body surface is usually measured by using a small, thin, disk-shaped device, which is sketched at the top of Fig. 12.3a, from Wuest.12 3 It can be stuck to the vehicle body by means of double-sided adhesive tape. A 0.8 mm diameter hole at the centre of the sensor is connected by means of a radial hole to a tapping soldered on the side of the device and this in turn is connected to a manometer by a plastic tube.

o a 0.2 2>

S.2 o.i £ E a c 8-Ö o

1I ì-200-J

"-

(a) 200 400 600

Dynamic pressure (Pa)—� 800

Vehicle body panel Static pressure hole

0.8 mm dia.

Tufnol· cup

bonded to panel

(b)

1mm bore

plastic tubing to

manometer

Figure 12.3 (a) Static pressure measuring device and its error after ref. 12.3. (b) Static pressure measurement on body panel without disturbing the local airflow characteristics, after ref. 12.6

Figure 12.3a shows that the error rate of this sensor is negligible if it is used on a flat surface. If the static pressure on a well-rounded surface has to be measured, the error rate of the sensor will however be unacceptably high.

If several sensors are used simultaneously, care should be taken to avoid disturbing the air flow with the plastic tubing, which could result in faulty static pressure results.

Another method of measuring the static pressure on a surface, proposed by Carr and Rose,12 6 is to drill a 0.8 mm diameter hole in the body panel and to bond a Tufnol cup to the underside. A hole is drilled into the cup


Figure 12.4 Static pressure measurement error caused by the hole diameter of the probe or the hole drilled in the body panel, after ref. 12.4

and a plastic tube is stuck into it to enable the static pressure to be read by a manometer, see Fig. 12.3b.

The incorrect choice of hole diameter may lead to spurious results. Figure 12.4 shows how static pressure error rate depends on the sensor hole diameter. Hole diameters up to 1 mm are considered accurate enough for most measuring applications.

12.2.2.2 Pressure transducers

The pressure probes are usually connected to pressure transducers by a plastic tube. The pressure range in most cases is low (10-1000 Pa) and usually the measurement of differential pressures rather than absolute values is required.

The pressures measured during wind tunnel testing are very seldom steady. Measuring equipment possessing a good damping ability is therefore advantageous. Liquid-column manometers (e.g. U-tube and vertical-tube manometers) are widely used, being uncomplicated instru-ments with sufficient damping due to the inertia of the liquid column. An inclined-tube version combined with a low density liquid (e.g. alcohol) enables the measurement of the lower pressure ranges.12,2' '

The projection manometer (after Betz12 312 5) is a further development of fluid-column manometers and is fitted with special reading equipment; a magnified image of a floating scale, which moves proportionally to the measured pressure difference, enables pressure readings to be made with a high degree of resolution.

Further commonly used types of pressure transducers are mechanical or electrical types. The mechanical devices use a diaphragm or bellows device to convert the pressure signal to a linear movement and then transfer it to a gauge. With the electrical type, the physical displacement is converted to an electrical signal. Most transducers rely on capacitive, inductive, piezo-electric, potentiometric or strain gauge equipment to generate their signal.124

The electrical transducers enable continuous data recording on chart recorders or magnetic tape. Moreover, they offer the advantage of computerized data handling, which has advanced sufficiently to make them the most widely used types of pressure transducers.

"8

1.6

1.2

3

£θ.8 a

a- I 0.4

\y

A] 77;

I I 3 1 2 Diameter d (mm)-


The mechanical and electrical type pressure transducers exhibit a higher frequency response range than the liquid-column manometers; for most wind tunnel measurements additional damping is therefore required. This can be effected either on the pneumatic side (i.e. between pressure probe and transducer input) or on the electric side (i.e. between transducer output and data recording).

To damp the pressure oscillations and pulsations prior to converting pressure into an electric signal, either resistance or volumetric damping (or both) can be used: the first usually consists of a long plastic tube of small diameter (e.g. 1mm or less) and the length can be varied to produce the required damping. Volumetric damping is performed by introducing large diameter sections into the connection line between the probe and transducer. The combination of both damping types is advantageous if very small pressure values have to be measured, as for instance during the measurement of air flow through the passenger compartment, see section 12.3.3. If signal damping on the electrical side is preferred, an active filter between the transducer and data recording device enables the desired damping to be obtained.

For certain measuring tasks, the measurement of pressure oscillations and pulsations may be required (e.g. if airflow-induced noise problems are the subject of investigation). In this case, no damping of the pressure signal is desired. The use of a small, highly sensitive pressure transducer located directly at the measuring point without any connecting tubing is effective. Piezo-electric pressure transducers are convenient devices for this type of application.

If the measurement of several pressures in a flow field or the static pressure distribution on a body surface is required, then a pressure scanner combined with one single pressure transducer can be used to measure multiple pressures by 'time-sharing' the single transducer. Test pressures from individual pressure probes are connected to the pressure scanner with plastic tubing and the scanner selects and connects each pressure probe in turn to the pressure transducer. The advantage of using a pressure scanner is the possibility of reading a great number of pressure signals at the lowest cost with only one pressure transducer.

12.2.3 Air flow velocity measurements

The main velocity measurement tasks in a wind tunnel include the determination of wind tunnel operational speed and the air flow speed outside or inside the test car. In some special tests the measurement of the turbulence intensity is also required.

The most common device to measure air flow velocity is the Pitöt-static tube. In the preceding section a method was described of measuring the dynamic pressure of a free airstream using a Pitöt-static tube. From the dynamic pressure, the air flow velocity is calculated as follows:

where v is the air flow velocity in m/s, p is the air density in kg/m3, and Apdyn is the dynamic pressure in pascals.


The air density varies with temperature, atmospheric pressure and humidity as follows:

349/700 - 131/7e P = ψ (12.2)

11

where Tl is the absolute temperature in K, poo is the atmospheric pressure in bar, pe = UE/100 is the partial water vapour pressure in air (bar), U is the relative humidity (%), and E is the saturation vapour pressure at Tx in bar.

12.2.3.1 Determination of wind tunnel operational speed

A Pitot-static tube may be used to measure the wind tunnel operational speed by positioning it at the nozzle exit. However, due to the air flow stagnation in front of the test vehicle, the measured wind speed does not correspond to the same wind speed on the road. Hence the wind tunnel operational speed must be calibrated. In doing this, advantage is taken of the fact that above a certain wind speed the static pressure coefficient cp usually does not vary.

To calibrate the wind tunnel operational speed, one or several cars should first be subjected to road tests to measure the static pressure distribution at several characteristic body areas. The same test procedure must then be repeated in the wind tunnel. From the result of these tests the static pressure coefficient for each body area can be calculated using Eqn 2.9:

P ~ Poo n i ^ cp = (12.3)

2 Vac

and the graph of the static pressure coefficients from the wind tunnel against those from the road test can be plotted.

As long as the test wind speeds were above the minimum speed at which cp stays constant, the graphs should be a straight line inclined at 45° and passing through the origin. However, the graph will most likely not be of this form. It may deviate in three ways: 1. The plotted points are scattered from a straight line due to imperfect air

flow simulation in the wind tunnel. A first degree polynomial approximation must then be fitted to the curve.

2. The inclination of the fitted line is not 45°. This is caused by the discrepancy between the wind tunnel speed measured with the Pitöt-static tube and the equivalent road speed. From the gradient of the graph, and from the definition of the static pressure coefficient, the correction factor which should be applied to the measured wind tunnel speed V^ can be found, according to Carr,12 7 and thus the wind tunnel operational speed is calibrated.

3. The line does not pass through the origin. This enables the additional information of the relation between the wind tunnel static reference pressure poo and the equivalent atmospheric pressure of the road test to be found. The meaning of this correction has already been discussed in section 12.1.2.2.


The calibration of wind tunnel operational speed with the above method also allows the wind tunnel blockage correction to be taken into account at the same time (see also section 11.3.3).

A further method of calibrating the wind tunnel operational speed is based on measuring the static pressure drop Ap between the nozzle inlet and the nozzle outlet. The dynamic pressure Apdyn caused by the wind tunnel operational speed V«, can be considered proportional to Ap as:

Apdyn = -^Vj = kAp (12.4)

which enables the calculation of wind tunnel speed by measuring Ap. The constant k has to be determined from airspeed measurements in the empty test section. This calibration should be performed through the whole speed range of the wind tunnel to check any Reynolds number dependencies. It is recommended that wind tunnel speed calibration be determined by comparing the static pressure distribution on a vehicle body measured on the road and in the wind tunnel, in a similar way to the method described earlier.

12.2.3.2 Measurement of air flow speed outside or inside the test car

The Pitöt-static tube can generally be used for all airspeed measuring tasks if the air flow character in the measuring area is steady and the air flow direction coincides with the axis of the Pitöt-static tube head. The accuracy of this device is, however, not satisfactory at low air flow velocities and if the airspeed is lower than 3 m/s other types of instrumentation are required. Miniature vane-type anemometers are the typical measuring devices used at low speeds.

A vane anemometer consists of a small vane (diameter: 15 mm upwards), mounted coaxially in a cylindrical housing. The rotational speed of the vane is a measure of the wind speed. The operational conditions needed for a correct reading are the same as for the Pitöt-static tube: the air flow mode should be steady and the vane axis has to coincide with the air flow direction. The tolerable yaw until 1 per cent accuracy deterioration is approximately 5 to 7° for an anemometer furnished with a cylindrical housing. This limit can however be increased up to 15 to 20° yaw angle through the aerodynamic optimization of the anemometer housing. On the other hand, special housing shapes have also been developed to read only the wind vector component which coincides with the vane axis up to a certain yaw angle.

The principle behind hot wire anemometers is based on the fact that the heat loss of an electrically heated wire subjected to air flow increases with increasing wind speed. Since the electrical resistance of the wire depends on its temperature, the resistance variation of the exposed wire can be used to measure the air flow velocity. Fig. 12.5 shows schematically the design of a hot-wire anemometer. The wire has a diameter of about 0.005 mm and is welded to two electrodes, which form a fork. The wire is positioned at right angles to the flow direction during the measurements.

One method to determine the air flow velocity is to hold the voltage applied to the wire constant, with the hot wire forming one arm of a


Wheatstone bridge. The bridge unbalances as soon as the electrical resistance of the hot wire changes through air flow application. The amount of bridge imbalance is a measure of air flow speed. This method enables precise measurement of very low air velocities; the measurement sensitivity decreases, however, with increasing air flow speed.

Figure 12.5 Hot wire probes for velocity measurements in one-, two- or three-dimensional flow regimes

A second and more widely used method is constant temperature anemometry: the bridge imbalance due to resistance change of the hot wire is eliminated by changing the electrical current through the sensor with an electronic feedback control circuit. In other words, the temperature of the wire—and consequently its electrical resistance—is held at the same level by changing the current through the sensor. The current change (or voltage change) is a measure of air flow velocity.

In addition to measuring low airspeeds, hot wire sensors are particularly suitable for measuring fluctuating velocities (i.e. turbulence measure-ments) due to their low inertia. A further advantage is that they can be incorporated in very small probes, which enable measurements to be conducted on rounded body areas or in narrow ducts and gaps without appreciably disturbing the air flow. If multi-sensor type probes are used, two or all three components of the air velocity vector can be measured simultaneously; see Fig. 12.5.

12.2.3.3 Measurement of flow direction

The correct air flow speed measurement in a free air stream requires the air flow direction at the measuring point to be known, so that, as already mentioned, the flow direction sensitivity of the speed measuring equipment can be taken into consideration. The easiest way to position a speed measuring device in the air flow is to detect the flow direction at the concerned area by means of a wool tuft attached to the end of a thin stick.

If the measurement of air flow direction is required to understand or to judge the air flow characteristics in a velocity field (e.g. in the wake of a vehicle), special measuring equipment (yawmeters) can be used for this purpose. The different types of yawmeter for measuring the angular position of the air flow velocity vector in a two- or three-dimensional flow are described in detail in refs 12.3 and 12.4. Two main types of yawmeter are identified: the first group operates on the basis of measuring the pressure difference at symmetrically positioned orifices; the second main type is the hot wire anemometer with multi-sensor probes.

For the pressure difference measurement method, either symmetrically


fitted tubes are used or the differential pressures of orifice pairs positioned on a streamlined symmetrical body are measured. The measurement principle is based on the fact that the pressure difference between two symmetrically positioned tubes or orifices is zero if the flow direction coincides with the symmetry plane of both measuring points. Otherwise a pressure difference is measured, which can be related to the air flow yaw angle through calibration. One pair of tubes or orifices is sufficient for the measurements in a two-dimensional flow. If flow direction measurements in a three-dimensional flow is required, four tubes or orifices are needed, which should be located in pairs in two mutually perpendicular planes. Figure 12.6 shows a spherical yawmeter for three-dimensional flow

0 5 10 15 20 a (degrees)

z Figure 12.6 Spherical yawmeter and its characteristics (orifice no. 2 for total pressure), after ref. 12.4

direction measurements from ref. 12.4. In addition to the two orifice pairs (nos. 1, 3 and 4, 5) a further orifice (no. 2) at the intersection of the planes serves for measuring the total pressure. If the spherical yawmeter is mounted rigidly in the air flow field, a set of calibration curves is needed for the different combinations of the angular values oc and ß. However, if the yawmeter is constructed so as to be rotatable about the z-axis, the value of ß (in the x-y plane) can first be determined by the null method, i.e. the yawmeter is turned until the pressure difference between points 4 and 5 disappears; the determination of angle a can now be done with the aid of only one calibration curve, as shown in Fig. 12.6.

Flow direction measurements using multi-sensor hot wire probes are done by using specially designed probes consisting of two (or three) mutually perpendicular sensors for use in a two (or three) dimensional flow field. In reality, all two (or three) mutually perpendicular components of the required airspeed vector are measured so that the flow direction and the resulting wind speed can be read simultaneously (see Fig. 12.5).

12.2.4 Temperature measurement

Along with the measurement of air flow characteristics, temperature measurements are often required during wind tunnel tests on a vehicle.


These measurements aim to meet one of the two following objectives: 1. Tests to define vehicle systems performance. The systems mainly

concerned are engine cooling, engine starting and fuelling, air conditioning, passenger compartment heating, and defrosting and demisting.

2. Tests to investigate the temperatures of vehicle components. These include all vehicle parts—especially plastics—that may be damaged if subjected to high temperatures, and all vehicle parts which could cause human injury. The brakes, the exhaust pipe, body areas close to the exhaust system, and components in the engine compartment are the most critical parts.

Two different temperature values may be required: (a) Temperature level at a single measuring point. (b) Temperature difference between two measuring points. The first type usually covers most test requirements. If, however, an energy balance has to be established during a performance test, it is necessary to measure the temperature difference of the air or coolant with greater accuracy.

12.2.4.1 Temperature sensors

(a) Thermocouples Thermocouples are the most common temperature sensors used for vehicle wind tunnel testing. Figure 12.7 shows schematically the electrical circuit for a typical thermocouple probe.

A thermocouple is a pair of wires, made of dissimilar metallic conductors, connected (e.g. welded) at both ends. When the two junctions are subjected to different temperatures, an electrical potential is set up between them (also termed electromotive force, EMF), which is approximately proportional to the temperature difference. A voltmeter in the circuit (see Fig. 12.7) can thus measure the temperature difference. If one of the junction points is maintained at a standard reference temperature (e.g. 0°C) the second junction point can be used to measure the absolute temperature at a desired location. Pair of dissimilar metallic conductors

Thermocouple extension cable

ft Lead wire (Cu) Voltmeter (mV)

Thermocouple junction (measuring point)

L.

<^> Xd . _ J

Thermocouple cold lunction (reference point)

Figure 12.7 Temperature measurement using a thermocouple


The reference junction (also termed the cold junction) can be replaced by an electrical compensation circuit so that the equipment for accurately maintaining a reference temperature can be removed.

The most commonly used thermocouples and their ISA (Instrument Society of America) identification codes are:

Base metal thermocouples ISA Type Copper-Constantan T Iron-Constantan J Chromel-Alumel (Equivalent to Nickelchrom-Nickel) K

Noble-metal thermocouples Platinum—10 per cent Rhodium Platinum S

Keeping the reference temperature at 0°C, the EMF values to be expected at different temperatures are standardized. Table 12.1 shows some EMF figures defined by three different national standards.

0 400 800 1200 1600

Temperature (°C) Figure 12.8 Characteristics of different thermocouples (cold junction maintained at constant temperature of 0°C)

Figure 12.8 compares the thermocouple characteristics of the thermo-couple types. Iron-constantan and copper-constantan thermocouples are preferred in the temperature ranges of -200°C to +500°C and 700°C respectively. Both these thermocouples produce high EMFs but they tend to oxidize at high temperatures. Chromel-alumel (equivalent to nickel-chrom-nickel) thermocouples can be used beyond 1000°C, and are resistant to oxidation. They exhibit an almost linear characteristic and produce high EMF values. They are therefore very suitable devices for wind tunnel use.

The measured temperature may deviate from the true temperature due to the production tolerances of the thermocouple. The deviation limits for each type of thermocouple are also defined in the national standards. The tolerance band for chromel-alumel type thermocouples is shown in Fig. 12.9. The tolerance bands for noble metal thermocouples are smaller than for base metal thermocouples.

to

Tab

le 1

2.1

Rev

iew

of

som

e st

anda

rd E

MF

val

ues

of t

herm

ocou

ples

def

ined

in

Ger

man

, Am

eric

an a

nd B

riti

sh s

tand

ards

Tem

pera

ture

(°

C)

-100

0 10

0 50

0 10

00

1500

Cop

p

DIN

437

10

-3.4

0 0 4.

25

27.4

1

er-C

onst

anta

n

AST

ME

BS4

937

230-

72

-3.3

78

0 0

4.27

7 4.

227

Iron

DIN

437

10

-4.7

5 0 5.

37

27.8

5

EM

F

\-C

onst

anta

n

AST

ME

230-

72

-4.6

32

0 5.26

8 27

.388

BS4

93

0 5.26

8 27

.388

(mV

)

Chr

omel

-A

lum

el

DIN

437

10

0 4.09

5 20

.640

41

.269

AST

ME

230-

72

0 4.09

5 20

.640

41

.269

BS

4937

0 4.09

5 20

.640

41

.269

Pla

tinum

-

DIN

437

10

0 0.64

5 4.

234

9.58

5 15

.576

-10%

R

h-

AS

TM

E 23

0-72

0 0.64

5 4.

234

9.58

5 15

.576

Pla

tinum

BS

4937

0 0.64

5 4.

234

9.58

5 15

.576


±10

500 1000 Temperature (°C)

1500

Figure 12.9 Tolerance band for chromel-alumel (or nickelchrom-nickel) thermocouples, as defined by different national standards

(b) Resistance temperature sensors Resistance temperature sensors are usually used during wind tunnel tests if a higher accuracy is required than can be achieved with a thermocouple. The measuring principle is based upon the change of electrical resistance of metals and semiconductors with temperature. The measurement of resistance change will therefore represent the desired temperature measurement.

There is an almost linear relationship between the change in resistance of metals and temperature change (see Fig. 12.10). Semiconductors, however, usually show a non-linear relation and their resistance may either increase or decrease if temperature is increased. They are therefore termed

o

4

3

2

1

\ / N

^"^

I re

=*H

P T C ^

I

r~ l

Ni > ^

T"" �Pt —

-100 -50 0 50 100 Temperature (°C)

Figure 12.10 Change of electrical resistance of various materials appropriate for use as resistance temperature probes


NTC (negative temperature coefficient) or thermistor (thermal sensitive resistor) probes if a decreasing curve is observed, and PTC (positive temperature coefficient) probes if the resistance increases with tempera-ture.

The change of resistance versus temperature curves of two commonly used metals, platinum and nickel, are given in Fig. 12.10. Very precise temperature measurements in the temperature range of -200°C to +750°C can be made by using platinum of high purity. In practice, the nominal resistance of the platinum sensors at 0°C is usually defined and this resistance is often also used for identifying the probe, e.g. Pt 100 or Pt 500 for probes with nominal resistance values of 100 or 500 ohms at 0°C. As with thermocouples, platinum and nickel resistance temperature sensors are also standardized and their characteristic data are defined in national and international standards. The resistance of the probes at different temperatures and the ratio of the probe resistance at 100°C to the resistance at 0°C (R100/Ro) are compiled. The standards also include information about the tolerances of the probes. Table 12.2 gives an extract

Table 12.2 Extract of characteristic data for Pt 100 defined in the German and international standards

Temperature C Q

-100 o

100 500

1000 ^éïï/^ï

from the standardized characteristic data for platinum and nickel probes with a nominal resistance of 100 ohms at 0°C and Fig. 12.11 illustrates the error range for a Pt 100.

The sensor resistance changes can be measured by including the sensor in a voltage divider circuit or in a Wheatstone bridge. The measurement error caused by self-heating of the sensor due to the current flowing through it (approx. 10mA) is usually negligible.

12.2.4.2 Typical temperature measurement errors

Temperature measurement may appear to be very uncomplicated, but through bad handling and by disregarding the rules considerable measurement errors may arise. During measurement heat transfer between the sensor and the object usually occurs, and this may result in intolerable errors in temperature readings. Heat transfer by conduction takes place if the surface or material temperature of a solid object has to be measured.

During temperature measurements of a fluid or a gas, heat transfer between the medium and the sensor is by convection. If a high-

F

DIN 43760 (ohms)

60.20 100.00 138.50 280.93

1.385

Hatinum

ISO (ohms)

59.65 100.00 139.10 283.80 438.2 1.391

Nickel

DIN 43760 (ohms)

100.0 161.8

1.617


3

2

1

0

-1

2

-200 600 0 200 400 Temperature (°C)

Figure 12.11 Tolerance band for platinum resistance thermometer—Pt 100 (DIN 43 760)

temperature device is located close enough to the sensor, a measurement error due to the radiation from the hot object will occur.

The error due to conduction or convection will be high if a high temperature gradient exists through the sensor and its connection cable. As an example, the surface temperature measurement on a solid object using a thermocouple is shown in Fig. 12.12a, after Lindorf and Marchevka:12 8 due to heat transfer (conduction) through the sensor the

Isotherms

a) High measurement error b) Low measurement error

Figure 12.12 Error due to the heat transfer between test object and thermocouple during a surface temperature measurement, after ref. 12.8


isotherms of the object are distorted. Consequently, the temperature monitored by the thermocouple differs from the true surface temperature.

The error increases with a lower thermal conductivity coefficient of the object, higher thermal conductivity and convective heat transfer coef-ficients (with reference to air) of the sensor, and poorer contact between the sensor and the object. Any or all of these unfavourable conditions may occur if surface temperatures of plastic or rubber devices are measured. Figure 12.12b demonstrates how this error can be eliminated. If a certain length of the tip (and cable) is glued on the surface, the thermocouple junction point, which actually measures the temperature, is thus still subjected to the true surface temperature; the longer the glued piece, the lower the error. Figure 12.13 shows an example of how the error changes with the glued length of a thermocouple. Figure 12.13 also demonstrates the deterioration in accuracy with increasing thermocouple diameter since the thermal conduction of the sensor increases.

\

v •

0.3 mrr

Cu-Con 1.0 mm

\ N

•0.5 mrr

v \ %

1* I

stantan Φ

^ C\

� " " — ~ • * 0 20 40 60 80

Length of glued cable (mm)

Figure 12.13 Variation of temperature measurement accuracy with glued cable length on the surface and cable diameter, after ref. 12.8

No major alteration in the performance of the test object should be allowed while taking measures to increase temperature measurement accuracy. If for example the thermocouple cable is glued on a surface, the convective heat transfer coefficient of the cable and glue should be comparable with that of the test object. This is important if the test object is small.

If the temperature in a solid object has to be measured, similar means as described for surface temperature measurements should be used to minimize any disturbance of the initial isotherms of the test object.

During temperature measurements of air (e.g. in ducts, etc.) or a fluid (e.g. coolant in hoses, engine oil, etc.) care should be taken to avoid the temperature sensors touching the boundary walls. Furthermore, if a temperature probe is mounted on a wall or on a hose by using fittings,

Wind tunnel testing methods 457

precautions should be taken to minimize the heat losses through the fittings and thermocouple leads to ensure a true measurement.

Incomprehensible temperature values from thermocouples are usually caused by using wrong thermocouple leads and extension cables or wrong polarity.

Thermocouple material characteristics may change due to oxidation or other chemical influences. Further change in the calibration of thermo-couples is caused by ageing, which may result in drifting of several degrees Kelvin per year.

Most of the errors occurring with resistance temperature sensors are caused by faulty insulation of the probe.

12.3 Wind tunnel testing methods

12.3.1 Measurement of aerodynamic coefficients

The aerodynamic forces and moments are measured in a wind tunnel using a wind tunnel balance. The various types of wind tunnel balance are discussed in section 12.2.1. The aerodynamic force and moment figures obtained are then used to calculate the aerodynamic force and moment coefficients as described in section 2.3.3.5.

At the start of the test, the vehicle is set up on the balance top plates and fixed, preferably by locking its driven wheels. High standards of wind tunnel air flow quality are important for obtaining reliable aerodynamic data, but attention should also be paid to some simple test details for good test results.

One important point is the correct loading of the test vehicle to its test weight. Not only the total weight must be checked but also its distribution between front and rear axles. If this is not correct, the riding heights at front and rear will be incorrect and the angle of attack of the vehicle body will not be representative of the intended test case. As the aerodynamic coefficients vary with angle of attack (see section 4.5.2) the test results will be incorrect.

As a result of the lift force components at front and rear axles, the effective axle loads decrease with consequent changes of the front and rear riding heights. However, with independent wheel suspension, the bounce or rebound motions cause simultaneous tread width changes. But, because the wheels are not rotating in the wind tunnel, no tread width change can occur. This results in reduced vertical body movements and therefore to riding heights which do not completely correspond to driving conditions. Measures have therefore to be taken to enable the vehicle tread to change freely during wind application. The easiest way to achieve this is to apply steering wheel motions by a 'driver' prior to every data reading. Thus the riding heights at vehicle front end are truly adjusted. A similar compensation at the rear end is not easy, and as the error is generally small compared with the front end, it can be neglected.

As a result of flow separations and vortices at various points, the vehicle body is subjected to pulsation and the test signals are consequently not steady. The test data reading should therefore be made for long enough to


gain a representative mean value of the parameters measured. The minimum measuring time has to be determined experimentally and is also dependent on the force sensing system of the aerodynamic balance. If the measuring system contains weigh beams instead of electrical load cells, the reading time can be kept shorter due to the higher inertia and thus to the higher damping ability of these devices.

12.3.2 Air flow management tests

Optimization of the air flow characteristics at certain points on the body may be required to develop the performance of various vehicle systems. For this purpose, the flow characteristics around these areas must be identified in order to enable any modifications to be done.

To improve the engine heat rejection through the radiator, the air flow velocity through the radiator core should be increased as much as possible. As has been outlined in sections 4.3.2.12 and 9.3.1, this can be achieved with body front end modifications or by varying the radiator position. To judge the effectiveness of the tested variations, the velocity distribution over the radiator has to be measured. The air flow velocity through the core cannot, however, be easily measured. The reason for this is that the air flow undergoes a swirling motion between grill and radiator. Most anemometers can only measure air flow in the direction for which they have been set up. The continuously changing direction of air flow around the radiator makes the use of these anemometers questionable (see also section 12.2.3.2). If the measurement is carried out at the rear of the radiator, similar measuring difficulties occur due to turbulence caused by the fan. One possibility however is to use hot wire anemometers, suitable for measurements in three-dimensional flow regimes (see Fig. 12.5). These sensors make it possible to determine the air velocity component normal to the core. Moreover, due to their small dimensions, positioning close to the radiator is possible without disturbing the prevailing air flow characteris-tics. By moving the sensor with a traversing device, continuous tracings of the air velocity distribution across the radiator core can be recorded (see Fig. 9.19).

Another air flow measurement task is the optimization of the brake cooling air flow. A qualitative evaluation of the air flow characteristics can be done by using a smoke generator. A mirror positioned beneath the brake assembly enables the observation of the air flow patterns to be made easily. Furthermore, the air velocity distribution in the area in question can be measured using a hot wire anemometer.

A brake cooling performance test, however, delivers quicker informa-tion if the wind tunnel is equipped with a dynamometer facility capable of applying a motoring torque; see section 6.6.2. Using the dynamometer, braking is applied at a representative driving speed (e.g. 100km/h; 62.5mile/h) to heat up the brake system. Typical temperatures (e.g. brake fluid, brake disc or drum) are measured. After reading a temperature level representative of severe braking on the road, the brake force is released and the braking system is subjected to tunnel wind until all components have cooled down. The time needed to achieve a selected lower temperature level can be taken as a representative figure to assess the


effective cooling capability of the brake assembly. The effectiveness of different measures to improve brake cooling performance can be investigated by performing successive cooling tests.

12.3.3 Measurement of air flow rate through the passenger compartment

The volumetric rate of air passing through the passenger compartment has to be measured to judge the ventilation performance of the vehicle. Air flow rate measurements are also required for some thermal tests (e.g. passenger compartment heating) to enable the establishment of an energy balance.

The air flow passing through the vehicle interior usually enters the passenger compartment at the cowl inlet and leaves through the extraction openings and leaks in the seals around doors, windows and rear boot lid. The air flow rate is a function of the wind speed V«,, the yaw angle, and the position of the ventilation/heater flaps and blower speed.

12.3.3.1 Air flow rate measurement by means of 'extraction curves'

This method is often used in vehicle wind tunnel testing (see also section 10.4.1) and consists of two steps:

• establishment of 'extraction curves'; • determination of air flow rate using these curves.

To establish the extraction curves, the air inlet at the cowlhas first to be sealed (e.g. by using adhesive tape). The air input into the passenger compartment will now be achieved externally by using an air blower (see Fig. 12.14a). The blower outlet is connected to the car interior by a flexible hose.

Hose

Flow rate measurement External

blower

a) Figure 12.14 Wind tunnel test to measure the air flow rate through the passenger compartment: (a) arrangement to establish the 'extraction curves'; (b) airflow test

The air flow rate is variable and is measured at the air blower exit using an appropriate flowmeter. Measures have to be taken so that the air pumped by the blower flows into the vehicle interior without leaks. The easiest way is to prepare a plywood plate with the contours of a window and then mount and seal it into the opened window. A cylindrical connection piece fitted to a hole i n the wooden plate facilitates the connection and sealing of the hose coming from the blower.

To establish the extraction curves, the air flow rate of the blower is changed and the air flow rate V and the static pressure increase


Δρχ = Pi - Poo at the vehicle interior are measured simultaneously. The pressure difference to be measured is usually low; attention should therefore be paid to positioning the measuring point in the passenger compartment at a place where no error can occur due to local dynamic pressure.

The test is first done without wind and then repeated at different windspeeds. All the curves obtained are plotted on a graph as shown on Fig. 12.15. These curves are termed 'extraction curves' of the test vehicle body.

Body leakage characteristics

Figure 12.15 Determination of the air flow rate V by measurement of the interior static pressure increase Äñ;

Each extraction curve shows the rate of air flow extraction against interior pressure, where the only deviation from real driving conditions is the replacement of the real air intake system by an external air blower. In other words, if the external blower is removed and the air inlet is again opened, the air flow rate occurring under driving conditions can now be determined by using the extraction curves, knowing the wind speed and then measuring merely the vehicle interior pressure.

The above method can be extended to define the amount of air extraction occurring through body leakages. For this purpose the test with the external blower has to be repeated, but with the body air extraction ducts also closed. The remaining air openings are the body leakages and the established curves at various wind speeds show the proportion of the extraction air flowing through the body leaks (see Fig. 12.15).

Once the extraction and body leakage characteristics have been established, the test vehicle is returned to its original conditions by re-opening the air inlet and extraction ducts and removing the external air


supply device (Fig. 12.14b). The required operational position of the heating/ventilation system can now be defined through various flap positions and blower speeds. After setting up the system to a desired position, the vehicle interior pressure is measured at the wind speeds already used to establish the extraction curves, and these points are marked on each corresponding extraction curve, see Fig. 12.15. For each pressure measurement A/?j and windspeed combination a corresponding air flow rate V{ can now be read on the x-axis. Extending all marked points to a curve, a graph is obtained characterizing the performance of the selected heating/ventilation system in the selected operational position. Finally, to show the results more clearly, a further graph can be drawn of the determined air flow rate V versus windspeed K, see Fig. 12.16. To give an example, three different operating positions are shown on the graph: curve n indicates the ram air condition while curves a and b show the blower operation at high and low speeds respectively.

160

5 120

g 80

40

0 V, 50 V2 100 V3 150

Wind velocity (km/h) Figure 12.16 Final presentation of airflow rate test results derived from Fig. 12.15

1 1 1 1 1 1

^^""^^ 1— 1 1

1 — � ""*! 1

^ ú ^ 1

1 1 1 1 1

Γ

^ 1 ^

^ — i n 1

1 ... _ 1 .

^

Plotting the test results for all the required operating positions of the heating/ventilation system on a graph as shown in Fig. 12.16 is very informative and enables a rapid assessment of the heating/ventilation system.

A further application of the graph illustrated in Fig. 12.15 is to find out which portion of the measured air flow rate flows through the body extraction ducts and which share flows through the body leakages. If the interior pressure Δρλ at the wind speed Vx is measured, a horizontal line at A/?i is drawn and the intersection points of this line with the body leakage and extraction curves are marked (see Fig. 12.15). The total air flow rate Vx

is divided into two components Vx' and V" at the intersection point with the body leakage curve, where V{ is the air flow share flowing through the leaks and V" is the share of the extraction ducts.

The body leakage is the result of many small openings. According to Eck12'10 an 'equivalent leakage cross-section' can however be defined to express the leakages with one single figure (see also section 10.4.1). Using


the body leakage characteristic curve without wind application (V = 0) and reading the flow rate Vfor a selected vehicle interior pressure level Ap{

the equivalent leakage cross-section Ac is defined as

A< = V ( 2 ^ ( 1 2 · 5 )

where all of the leakage openings are assumed to be replaced by one single opening with cross-section Ae. It is usually of interest to check the value of Ae at different A/?j levels. An 'equivalent cross-section for body extraction ducts' can also be defined, which enables the engineer to assess the effectiveness of the ducts.

The method described is easily carried out and is therefore widely used. It is, however, of limited accuracy due to the assumption that the air intake into the vehicle interior occurs exclusively through the air intake ducts in the cowl and that air exits at every body leak. Consequently, if air intake instead of air exit occurs at some leaks the method will give incorrect results. This situation may occur if the flaps of the vehicle heating/ ventilation system are positioned to allow very low air flow rate by ram air while the test car is subjected to wind.

Alternative test methods using different measurement principles can be applied to measure the air flow rate through the vehicle interior, where this shortcoming is eliminated.

12.33.2 Alternative methods of measuring the airflow rate through the passenger compartment

A vehicle interior heating test using the vehicle heating system enables the calculation of the air flow rate through the passenger compartment by establishing an energy balance for the heated air passing through the vehicle interior.12 n A very good knowledge of the heat loss characteristics at every body area and precise temperature measurements are required to obtain precise test results. This method is therefore impractical.

Another method of air flow rate measurement is to insert a defined volume of an isotope gas (e.g. Krypton 85) as a tracer into the vehicle interior and to measure the concentration while the vehicle is subjected to wind.12"11 The concentration measurements enable the calculation of the exact ventilation rate through the passenger compartment. C 0 2 may also be used as a tracer, which has the advantage that the special precautions necessary for an isotopic tracer are not needed.

Finally, it should be noted that the air flow rate measurement tasks in the wind tunnel are usually performed at a straight ahead position of the test vehicle. The results, however, may change considerably if the test car is yawed to the wind direction, which would correspond to natural cross-wind effects on the road.

12.3.4 Passenger compartment heating and air conditioning tests

A temperature-controlled wind tunnel equipped with an adjustable chassis dynamometer is an ideal facility to conduct passenger compartment heating or air conditioning tests. Because the dimensions of the


temperature-controlled wind tunnels are usually smaller than the aerodynamic wind tunnels (see section 11.5.5), the suitability of the wind tunnel for such tests has to be verified. This validation can be done by examining the correlation between the static pressure distribution on a representative vehicle body measured on the road and in the wind tunnel. This correlation ensures realistic air inlet and outlet rates at body openings and consequently true air flow rates through the heat exchanger of the heating system and through the vehicle interior, which are significant parameters for heating and air conditioning tests.

Figure 12.17 shows a typical recording of a heating test. Prior to the test the test vehicle is usually soaked at the test temperature until all engine and passenger compartment components reach this temperature. The test is then started and the engine is loaded by means of a chassis dynamometer, which for each wind speed is capable of simulating the corresponding tractive resistance. After a predetermined time (e.g. 1 hour) of constant driving, the test speed and corresponding dynamometer drag is increased to a higher level. A third test phase with further increased test speed and engine load follows. During the test the air temperature distribution at several locations in the passenger compartment is recorded. Figure 12.17

Rear foot level (mean) Front foot level (mean)

- ^ Τ ^ _ Γ 3 ^ £ ^ Γ _ Γ : Overall ^ mean

105 120 min

Test time

7-Ambient

Figure 12.17 Typical vehicle interior heating test recording

shows only the average values of the temperatures at foot, chest and head levels as well as their overall average. The final judgement of the heating system performance is made by comparing the overall average temperature values with 'minimum performance' figures, which are usually set according to practical experience.

The procedure of an air-conditioning system performance test is very similar to the heater performance test: the test vehicle is first soaked at high test temperatures and then the test is carried out with successively increased driving speeds. In addition to the high test temperature level, solar radiant heating by means of special lamps and an increased level of


humidity are applied to simulate the most severe operational conditions for the air-conditioning system. Typical test conditions for an air-conditioning system test are, for example, 40°C or higher, 40 per cent humidity and 1 kW/m2 solar radiation intensity. The solar simulation lamps should emit parallel rays and possess a spectrum similar to sunlight. Satisfactory correlation with field tests has also been observed if infra-red lamps are used to simulate solar radiation. However, the absorption and reflection of the radiation energy falling on (tinted or clear) glass surfaces are not identical for infra-red and sunlight-similar radiation. Therefore the heating effect on the vehicle interior will also be different and deviations from field test results may be observed.

The evaluation of the air conditioning is done against a minimum performance limit for the average air temperature of the passenger compartment for transient and steady-state behaviour.

12.3.5 Windshield defrosting and demisting tests

Defrosting performance of the heating system is an important requirement for cold climate operation of a vehicle. Several countries require a minimum performance level for windshield defrosting; e.g. FMVSS 1031212 j s a t e s t standard for North American countries and 78/317/ EEC12·13 is currently being introduced as an acceptance requirement for European countries.

The defrosting test is preceded by a soaking phase until all vehicle components are cooled down to the test temperature. Standard test temperatures are -3°C and — 18°C. The test begins with the application of an ice layer on the vehicle glass surfaces of defined thickness (e.g. 0.044 g/cm2) by spraying water from a spray gun. After the car is soaked for a further 30-40 minutes the engine is started and warmed up, either at a defined idling speed or through driving the vehicle at a partial load. The defrosting system is brought into operation and the defrosted areas of the glass surfaces are marked on their inner faces at five-minute intervals. The defrosting pattern is photographed or traced onto paper on completion of the test. The patterns can be used to assess the performance level of the defrosting system. The judgement of the windshield defrosting capability is especially important and special areas on the windshield are specified in standard test procedures to enable a realistic assessment.1212, 3

Figure 12.18 shows the defrosted pattern on the windshield. The dotted lines indicate the special areas of the windshield. The minimum performance requirement for a defroster system is established in terms of percentage of defrosted areas in a defined time period for each windshield zone.

During the demisting test, the moisture rejection of passengers (approx. 70g/h per passenger) is simulated by using a specially designed steam generator.113 The test temperature is slightly below freezing point (e.g. —3°C). After the soaking period, the steam generator is brought into operation for 5 minutes to form a moisture layer on the glass surfaces. The engine is then started and the defrosting/demisting system is put into operation to remove the moisture on the glass surfaces while the steam generator is kept in operation until the test is completed. Patterns of


Figure 12.18 Windscreen defrosting test result: patterns show the defrosted windscreen areas at five-minute intervals. The significant windscreen zones are indicated by dotted lines

demisted areas are outlined and documented for evaluation much as for defrosting tests.

12.3.6 Wind tunnel engine cooling tests

The performance of the engine cooling system is usually investigated and developed in a wind tunnel. The tunnel must be equipped with a chassis dynamometer to simulate the vehicle aerodynamic and mechanical resistance. The climbing resistance may also be added if hill climbing simulation is required. The tests are usually carried out at high air temperatures to simulate severe operating conditions. Sun load and tailwind simulations may also be introduced to make the testing conditions even more severe.

A good correlation is observed between engine cooling tests carried out in a wind tunnel and those on the road. As long as the air flow simulation is good at the front end of the vehicle this correlation applies. In other words, reliable cooling test results can be gained in wind tunnels with small nozzle exit areas. Wind tunnel facilities can therefore be designed exclusively for engine cooling tests. Being smaller, they have lower investment and operating costs. Attention should however be paid to the correct calibration of the wind tunnel operational speed since its accurate determination usually becomes more difficult as the nozzle exit area is decreased (see also section 12.2.3.1).

Three main test procedures are applied to check the engine cooling performance in a wind tunnel (see also section 9.2.1): (a) Simulated top-speed test on level road; (b) Simulated hill climb test while towing a trailer; (c) Idling or switch-off of the engine at the completion of (a) or (b).

The dynamometer roll speed and torque can be adjusted to simulate the speed and driving resistance of the test vehicle. The driving resistance must either be computed from test data or read from a traction force-speed diagram, see Fig. 9.4.


The simulated top speed and hill climb tests are continued until the coolant and engine oil temperatures are stable. The most important temperatures to be measured are the radiator coolant in the top and bottom hoses, engine oil and ambient air. For the evaluation of the cooling system, the difference between the radiator top hose coolant temperature tT and the ambient air temperature ta is considered to be the most significant parameter as

At=tr- ta (12.6)

The value of At is found to be approximately constant at various ambient temperatures, as long as the thermostat valve opening and the engine fan switch on/off (electric fan) or engagement/disengagement (visco fan) behaviour remain unchanged.

The ambient temperature may be increased up to a limit tATB where the coolant at the radiator top hose begins to boil. The coolant boiling temperature tcb depends on the cooling system pressure level, which is determined by the opening pressure of the radiator cap.

Extending Eqn 12.6 to the critical boiling case:

At = tr — ta = tcb — tATB

hence

'ÁÔÂ = 'cb - (*r - 'a) = (*cb " 'Ã) + k (12 .7 )

tATB is termed the 'air-to-boil temperature' and represents the ambient air temperature at which the engine coolant would begin to boil if the test car were subjected to similar driving conditions as simulated during the cooling test. The air-to-boil temperature tATB is therefore considered to be a significant figure in the judgement of the cooling system performance: the higher the air-to-boil temperature, the higher the engine cooling system performance.

It is clear that the engine cooling performance becomes more critical at high ambient temperatures. If the temperature of the wind tunnel is controllable it is better to choose high test temperatures. This is to ensure that the operation of the thermostat and fan is the same as during severe environmental and driving conditions. Otherwise, the air-to-boil tempera-tures found with relatively low testing temperatures in a wind tunnel may deviate from the corresponding tATB figures representative of field operating conditions with high ambient temperatures. This problem may, however, be overcome by using a thermostat blocked to its maximum opening and with the fan switch shortcircuited or the fan visco-clutch continuously engaged, whichever is applicable.

If similar operation of the thermostat and engine fan is ensured at two different test temperatures, there is still a minor difference between the air-to-boil temperatures calculated for the two environmental temperature levels. The reasons are the changed volumetric and combustion efficiencies of the engine and the changed density of the cooling air. Using the practical experience gained on various engines, the following correction can be applied to estimate the air-to-boil temperature at other ambient temperatures:

ßÁÔÂ = ßÁÔÂ + 0 . 1 6 ( ß ß - ß ! ) (12.8)


where iATB is the measured air-to-boil temperature at an ambient temperature of tx and ^ÁÔÂ is the estimated air-to-boil temperature for another ambient air temperature of t[.

The air-to-boil temperature of an engine cooling system, calculated after a top speed test, does not necessarily coincide with the air-to-boil temperature established after a hill climb test using the same vehicle. The /ATB figures can therefore be compared only for similar driving conditions.

For each type of cooling test the acceptance level can be defined in terms of air-to-boil temperatures. These limits are based on practical experience. The acceptance limit for top speed tests can be chosen as ÂTB = 48 to 55°C, whereas the limit for the hill climb tests may be lower (/ATB = 28 to 35°C). This is because of the lower ambient air temperatures usually prevalent in higher altitude regions. The road gradient for the hill climb tests are usually chosen as 10 to 12 per cent, which corresponds to alpine pass driving conditions.

12.3.7 Flow visualization techniques

Visualization of the flow on the vehicle body, the spatial flow close to the vehicle and the air flow pattern in the passenger compartment is an effective method of investigating and understanding the flow field in and around the vehicle. A survey has been given by Hucho and Janssen12 14

and by Takagi et al.11 20 The flow patterns adjacent to the vehicle body surface can easily be made visible by using wool tufts (Figs 6.1, 8.59) and the regions of attached and separated flow can thus be clearly detected. Another method for surface flow visualization is the application of a surface oil film containing coloured or luminescent pigments. Figure 6.2 demonstrates this type of flow visualization. However, attention should be paid to the air flow separation regions because these regions are not always clearly indicated by the oil film method.

The visualization of spatial flow near to the vehicle body helps significantly in understanding and interpreting the aerodynamic effects of interesting body areas and contours. The most widely used tool for this is a smoke generator. Emitting smoke into the air flow enables the flow patterns to be made visible. The smoke generators most widely used are based on heating a mineral oil derivative (e.g. Shell Ondina G17) until evaporation occurs and a dense white inoffensive smoke is provided. The smoke is then injected into the air flow with the aid of a long thin stem. The pictures in the preceding chapters of this book showing flow pattern visualization using smoke filaments demonstrate the widespread use of this technique. A further application of smoke generators is the filling of the separation bubbles and wake zones with smoke to illustrate their form and size (Figs 1.2, 6.3, 6.7, 6.15). In this case the smoke has to be injected directly into the bubble or wake to fill them.

If information about the secondary motion within the separated flow is required, a bubble generator can be used to illustrate the flow patterns within the superimposed flow regimes. Helium-filled soap bubbles are injected into the air flow and their paths are photographed. If the exposure time is well chosen, the superimposed flow patterns can be clearly distinguished on the photograph. This technique is especially suited to flow visualization during small-scale wind tunnel testing, see ref. 12.14.


12.4 Road testing methods 12.4.1 Aerodynamic drag force measurements on freely coasting vehicles

Drag coefficient measurements are usually performed in a wind tunnel. However, test methods have been developed to measure the drag coefficient of a vehicle on the road, though the reliability of these measurements is limited, mainly due to uncontrollable environmental conditions prevailing during the road test. Furthermore, the variability of several parameters causes difficulties and uncertainties during isolation of aerodynamic drag from mechanical drag.

One widely used test method to measure the drag factor on the road is the coast-down test procedure (see Bez12 15). The test is performed on a long straight track, which must also be level. Although negligibly low natural windspeed is normally required, Walston et al .1 2 1 6 have described a method to determine the drag factor of a vehicle from a coast down test in a windy environment.

The test vehicle is first brought up to a high speed (if possible close to its top speed) and then is made to coast freely by disengaging the vehicle engine. The vehicle speed change is recorded continuously. The deceleration of the car is caused by the mechanical and aerodynamic drag acting on the vehicle, which can be expressed as follows:

m{\ + f) ^ =DM + DA (12.9)

where m is the vehicle mass in kg, / is the effective mass increase due to the inertia of rotating vehicle components, V(t) is the vehicle speed in m/s, DM

is the mechanical drag including the drag shares of tyres, driveline, bearings etc., in newtons, and DA is the aerodynamic drag in newtons.

/ i s derived from the equations of motion of the rotating components and is found as

/d + /o

f=I« i°_ (12.10) m

where Id is the total rotational inertia of the driveline, including the wheels of the driven axle, in Nms 2 , IQ is the total rotational inertia of the non-driven axle in N m s2, and rdo is the dynamic roll radius of the tyres on the driven and non-driven axle respectively, in metres.

The aerodynamic drag is

DA = COA^r V\t) (12.11)

where p is the air density in kg/m3, A is the vehicle projected frontal area in square metres, and cD is the drag coefficient.

Equation 12.9 contains the total drag, which is made up of two different components: mechanical drag and aerodynamic drag. As the deceleration of the vehicle during coast-down is continuously recorded and vehicle effective mass can easily be determined, the sum of both drag forces can be calculated for any desired vehicle speed. The main problem now is the

Road testing methods 469

determination of the mechanical drag, so that the aerodynamic drag can be isolated and the drag factor can be calculated.

One method of determining the mechanical drag is to conduct laboratory tests to measure the dependence on speed of the tyre rolling resistance and the driveline friction torque and then use these to find the total mechanical drag. The confidence level of this procedure is however low, mainly due to the difficulty of accurately measuring the tyre rolling resistance. The common way to measure this is to drive the tyre on the outer (or inner) surface of a drum at the desired speeds. However, a number of test parameters differ from road driving conditions, and therefore the rolling resistance figures obtained on a rig test are usually different from the true road values. The main differences are in the different surface materials of drum and road, the cylindrical driving surface on the drum instead of the flat surface on the road and the difficulty of exact road and ambient air temperature simulation during the drum tests. Furthermore, the additional tyre drag caused by vehicle suspension geometry (i.e. wheel camber, toe-in, toe-out) has also to be estimated.

Another method of determining the mechanical drag is to carry out a road test immediately after the coast-down test where the aerodynamic drag is artificially eliminated. This can be performed by using a 'shrouding trailer', which is a plywood box with no bottom and is large enough to hold the test vehicle; see Carr and Rose,12 6 and Kessler and Wallis. Figure 12.19 illustrates the test set-up.

Shrouding trailer

Rubber Rubber

Figure 12.19 Determination of the rolling resistance of a vehicle using a 'shrouding trailer', after refs 12.6 and 12.17

The shrouding trailer is supported by two wheels at the rear and by the trailer hitch of the towing car at the front. The test car is towed by the shrouding trailer by means of a link, instrumented to measure the towing force. The trailer is equipped with a rubber seal around the bottom which is always in contact with the road so that the aerodynamic drag of the test car is eliminated when the combination of shrouding trailer and test vehicle is towed on the road. The force measured on the link between the test vehicle and shrouding trailer is therefore only mechanical drag. This method eliminates all the disadvantages of the previous one, if the measurement of the mechanical drag is performed back-to-back with the coast-down test. However, on the other hand, the driver of the test vehicle has to carry out some steering corrections to stay on course with the towing car, which consequently results in increased mechanical drag. Further-more, for safety reasons, the combined driving of two vehicles requires the test speed to be limited. This is a disadvantage because at lower driving


speeds the share of the aerodynamic drag within the total drag is smaller, resulting in lower drag factor accuracy.

Several driving speeds are used from the coast-down test in the evaluation of the aerodynamic drag coefficient. The shrouding trailer test has therefore to be repeated at each of the required speeds to determine the corresponding mechanical drag value. The drag factors corresponding to various speeds can then be plotted against vehicle speed to check any Reynolds-number dependencies. To obtain reliable results the whole test procedure should be repeated several times and the results should be averaged.

The above test method enables the determination of the total drag by measuring the vehicle deceleration during a free-coasting manoeuvre. The measurement of total drag can also be done by pushing the test vehicle with another car by means of a link bar, as has been performed by Romani.12 18

The link bar should be long enough to keep the air flow interference between the vehicles small. The pushing force measured on the bar is equivalent to the total drag. The isolation of the aerodynamic drag has then to be performed as before.

12.4.2 Cross-wind tests

The cross-wind sensitivity of a vehicle can be judged and compared with other vehicles if the vehicle is subjected to an artificially created cross-wind gust during a straight-ahead drive on the road. Figure 12.20 shows

Figure 12.20 Cross-wind test, after ref. 12.20

schematically the performance of a cross-wind test. The lateral deviation of the vehicle from the initial straight-ahead direction is usually considered the most significant parameter in assessing the cross-wind sensitivity of the vehicle.


Cross-wind tests can be performed in two ways (see also section 5.4): 1. The driver does not apply steering correction. The steering wheel of the

vehicle is held either constant at its initial position (fixed control) or remains untouched by the driver (free control) throughout the test.

2. The driver attempts to minimize the lateral deviation of the vehicle by steering wheel corrections.

The first method considers only the vehicle response on cross-wind gust and is therefore suitable for comparative tests on one or more vehicles. The second method also includes the driver's response; the test outcomes are therefore primarily influenced by the driver. This method is applied mainly to study driver behaviour or to determine traffic safety performance.

The vehicle lateral deviation can be measured in two ways: (a) The driver enters the cross-wind gust at a defined point and with zero

yaw angle. This is usually done with the help of an 'orientation line', parallel to the battery of the cross-wind generators (see Fig. 12.20). The position of the vehicle during or at the end of the test is defined by markings on the road (e.g. bollards) or sensors under the road surface.

(b) Instrumentation mounted in the test vehicle measures the path curve before and during the test. The equipment to measure the vehicle lateral motion is based on exact measurement of the vehicle lateral acceleration perpendicular to the initial plane of symmetry of the vehicle. Through two successive integrations of the acceleration signal, the lateral deviation of the vehicle is found. Precautions have to be taken to ensure that an exact measurement of the lateral acceleration is made to eliminate the errors caused during the test. This can be done by positioning the accelerometer on a gyroscopically stabilized platform, which maintains the accelerometer in its initial horizontal position in an earth-related coordinate system throughout the test. Finally, the vehicle forward speed has also to be measured for a complete definition of the vehicle path.

Method (a) is quick, easy to carry out and does not need complicated equipment. It is, however, less precise than the second method. One source of error is the difficulty in entering the cross-wind gust with zero yaw angle, due to the steering corrections of the driver immediately beforehand. This error can be allowed for if the gyroscopic instrumenta-tion is used and the test recording is started before the car enters the cross-wind gust.

Although the cross-wind test results enable assessment of the cross-wind sensitivity of a vehicle in general, it is however not possible to derive the aerodynamic coefficients (i.e. side force and yawing moment coefficients) directly from the test results. The reason for this is that the response of a vehicle to a cross-wind gust is affected by two different properties of the vehicle: one is the above mentioned vehicle aerodynamic coefficients and the other is the overall handling characteristics of the car. The significance of the vehicle handling characteristics in cross-wind sensitivity can be demonstrated easily by conducting successive cross-wind tests on a vehicle where the handling behaviour of the car is changed by varying the tyre

4^

Tab

le 1

2.3

Tec

hnic

al d

ata

for

vari

ous

cros

s-w

ind

faci

litie

s1

Cro

ss-w

ind

gust

len

gth

Max

imum

cr

oss-

win

d sp

eed

Num

ber

of

nozz

le u

nits

Pow

er

Vol

ksw

agen

47 m

80 k

m/h

36

VW

pet

rol

engi

nes

44 k

W e

ach

Mer

cede

s-B

enz

35 m

70 k

m/h

16

Elec

tric

mot

ors

100-

125

kW

each

Mot

or

Indu

stri

es

Res

earc

h A

ssoc

iatio

n

36 m

72 k

m/h

3 Gas

tur

bine

ai

rcra

ft en

gine

(R

olls

-Roy

ce A

von

45 k

N t

hrus

t)

Inst

itute

for

R

oad

Veh

icle

s,

TNO

11m

120

km/h

5 Petr

ol e

ngin

es

147

kW e

ach

Toyo

ta

44 m

35 k

m/h

70

km

/h

15

Elec

tric

mot

ors

95 k

W e

ach

Nis

san

Mot

or

Co.

12 m

80 k

m/h

2 V8

petr

ol

engi

nes

132

kW e

ach

Japa

n A

utom

obile

R

esea

rch

Inst

itute

15 m

48 k

m/h

80

km

/h

106

km/h

5 Elec

tric

mot

ors

320

kW e

ach


pressures of the front and rear wheels. Although the aerodynamic coefficients remain unchanged, the lateral deviation of the vehicle due to cross-wind increases considerably if the vehicle becomes more prone to oversteering (i.e. the tyre pressures of the front wheels are high and of the rear wheels are low).

A number of cross-wind facilities are in operation in different countries. Their characteristic data are outlined in Table 12.3. The comparison shows great differences in gust lengths and wind velocities; consequently only test results obtained in one facility are comparable. Because of the changing wind speed profile and magnitude at different distances to the nozzle units, care should be taken to ensure that the test vehicle always enters the cross-wind test section at a defined distance from the units.

The effective wind velocity vector acting on the vehicle consists of the vehicle driving speed and the cross-wind component. Considerable differences are observed if the effective velocity vector profiles of wind tunnel cross-wind tests and cross-wind facility tests are compared with the profile obtaining during normal road driving. Figure 12.21 illustrates

Natural

Figure 12.21 Comparison of the effective wind velocity vector profiles prevailing in the wind tunnel, on a cross-wind test track and under natural driving conditions, after ref. 12.20

schematically the differences between the three cases, demonstrating the difficulty in the correlation of cross-wind sensitivity tests with driver assessments under real driving conditions. An actual velocity profile of a cross-wind facility measured at 2 m distance from the nozzles and over a length of 4 m (corresponding to the length of two nozzle units) is illustrated in Fig. 12.22.

If the cross-wind deviations of several vehicles are measured and a ranking is established (see section 5.5), that ranking may change if the test is repeated at another cross-wind or driving speed. The reason for this is


Figure 12.22 Velocity profile of a cross-wind facility

the changed aerodynamic yaw angle ß, which results in changes in the side force and yawing moment.

A change in vehicle ranking usually occurs if the test results performed with lower aerodynamic yaw angles (e.g. ß = 30°) are compared with those at extremely high values. However, because accident danger is higher at higher driving speeds, the yaw angle for cross-wind tests should generally be chosen to be less than 30°. Moreover, the maximum of the yawing moment coefficient is usually in this region. In other words, the driving speeds of the vehicle should be high enough to ensure that the test results can be related to real driving conditions.

In the technical literature, methods have been described of investigating vehicle cross-wind response by simulating the road test in a small-scale version (see section 5.2.4). The required parameters of motion are measured as a small-scale vehicle model is moved through a cross-wind gust (see Fig. 5.12). This type of testing is especially useful in the investigation of vehicle transient motion as it enters a cross-wind gust, and so contributes to a better understanding of cross-wind sensitivity problems.

12.4.3 Engine cooling tests on the road

The performance of engine cooling tests in the wind tunnel has already been described in section 12.3.6. Although the same tests can also be carried out on the road, continuously changing environmental conditions


make a systematic investigation and tuning of an engine cooling system impossible. Therefore the road tests are usually performed simply to validate the results gained with wind tunnel testing.

The cooling tests at top speed are usually possible without any major complications if a long level track test or a high-speed loop is available. The performance of hill climbing tests on the road is however not easy, due to the difficulty in finding a test track with a constant gradient, and long enough to enable the engine coolant and oil temperatures to stabilize. This problem can however be overcome by performing a towing test on a level road with a specially designed trailer that can be programmed to dissipate a defined rate of energy during towing. The towing force can thus be adjusted to simulate hill climbing. As with the wind tunnel cooling tests, the results of the road tests are usually presented in terms of air-to-boil temperatures (for definition see section 12.3.6).

The environmental air temperature during road tests changes from one test to another and is often lower than the test temperatures usually chosen in a temperature-controlled wind tunnel. If any comparison between wind tunnel and road test results is intended, attention should be paid to the fact that the air-to-boil temperatures for a given engine cooling system may vary with ambient temperature (see section 12.3.6).

Not all the conditions affecting engine cooling performance are easily simulated in a wind tunnel. One important instance is the effect of altitude while hill-climbing. Due to the decreasing atmospheric pressure and air density at high altitude, the performance and thermal behaviour of the engine change. Therefore it is necessary to correct the cooling system performance by calculating the coolant boil temperature tch due to the decreased atmospheric pressure. For instance, the pressure at 2500m altitude is 0.74 bar. An easy simulation of this condition in a wind tunnel is obviously not possible. Therefore the most reliable way to check the engine cooling efficiency in these conditions is to conduct road tests in high altitude regions.

12.4.4 Soil deposits on glass surfaces and body areas

Test methods have been developed for qualitative and quantitative judgement of soil and mud deposits on body and window areas. By performing successive tests, the effectiveness of body contour change can be checked with comparative tests. A reference car can also be used as a basis for comparisons.

In a real driving situation, dirt is deposited on the vehicle by splashing either from the vehicle's own wheels or from other vehicles, see section 8.7. Dirt deposition tests can, in principle, be carried out in a wind tunnel. However, an exact simulation of self-initiated dirt deposition is not possible since the vehicle wheels are not rotating.

A road test method has been described by Hucho12 20 to investigate the self-initiated soil deposit on a vehicle body. First a test track has to be prepared using a specific soil. The test vehicle body areas under investigation are fitted with small plates. Their weights are measured prior to the test. The test car is then driven on the test track several times. At the end of the test, the plates are removed and weighed again to find the


ZbU mm

• 200

T 150

zs100

50

-50

-100

-150

-200

-250

> \ • 1 1 • . ) — •

. 1 \.

—__.

4 \ ^—

\ \ • \ V

1 without airfoif

V Λ

; é : * /

» — · — .

^ ^ - ·

!

with - — ^ a i r f o i l

1

5 (

V S

—

"~" ·—.1

1 mg 8

Airfoil

Figure 12.23 Soil deposition test results after driving the test car on a test road covered with dirt, after ref. 12.20

weight increase due to soil deposition. Figure 12.23 shows an example of the test results gained with this test method. The test vehicle, a VW Variant 1600, was tested with and without an aerofoil, as shown on the figure. The results illustrate the ability of the method to highlight the effectiveness of a body modification aiming to decrease dirt deposits on the rear window. The disadvantage of the modification can also be seen: increased soil deposits on the body area beneath the rear window.

An attempt can be made to simulate this test in a wind tunnel by replacing road mud splashed by the wheels with water sprayed at vehicle wheel areas. In this case the small plates used to measure the soil deposits should preferably be covered with thin dry sponge pieces. A further test procedure can be applied in the wind tunnel by spraying water ahead of the test vehicle to investigate the soil deposits caused by dirt thrown up by a preceding car.

Another road test method to investigate soil deposition is to apply a thin layer of oil on the required body areas and then to feed talcum into the airstream in a manner similar to the way the wheels kick up mud or dust from the road surface. The talcum concentrations found on the car surfaces represent the soil deposits to be expected under natural driving conditions. Figure 6.17 shows the test results gained with the talcum method, showing the effectiveness of using an aerofoil to keep the rear window free from dirt.

The talcum method can be applied in a wind tunnel too, but it has the disadvantage that the wind tunnel becomes dirty. This is not only annoying because of the dirt but it may also disturb sensitive wind tunnel instrumentation.

12.4,5 Wind noise measurements

The sources of the wind noise heard in the vehicle interior are mainly the vortices caused by the air flow separations at various body areas. Due to the unsteady character of these vortices, the air in the separation bubbles is subjected to pressure oscillations (see also sections 2.3.4.1 and 6.5.2). If


these are transmitted to the vehicle interior they will be experienced by the passengers as noise. The pressure pulsations may reach the passenger compartment after being more or less attenuated by body materials. Another possibility is a direct link to the vehicle interior due to defective door or window seals or through ventilation openings.

Considerable success has been achieved in the reduction of mechanical and combustion noise in modern cars. It can therefore be very annoying if the wind noise level, which increases rapidly with vehicle speed, is too high. The first step to reduce the wind noise is the isolation of this component out of the total sound level measurement (SLM).

The SLM recordings usually contain the superimposed noise of combustion, mechanical, tyre and wind noise components. Hence direct identification of the wind noise component from a SLM trace recorded during a road test is not possible. One major noise component, the combustion noise, can be eliminated if the engine is switched off at a high driving speed. The mechanical noise is also partially mitigated if the transmission is shifted to neutral. But tyre noise is still present with the wind noise. All noise components except wind noise are eliminated if the vehicle is subjected to airstream in a wind tunnel. However, in this case the wind tunnel noise, which is usually high, is superimposed on the vehicle wind noise.

Although absolute isolation of wind noise is not possible, testing methods have been developed to investigate and reduce wind noise problems. These methods can however only be applied efficiently if the wind noise is the dominant component of a SLM recording. This requirement is met if the SLM difference between the wind noise and remaining noise components is at least 5 to 7 dB. If tested in a wind tunnel, the same SLM difference between wind tunnel noise and wind noise must be attained.

Under certain environmental conditions, a road test can be conducted to check compliance with this requirement. The test is performed on a road where a steady breeze blows with almost constant velocity and direction. Two successive sound level measurements, one with headwind and the other with tailwind, have to be carried out while the engine is switched off and the vehicle coasts. The compliance of the resulting wind speed

dB

+ 10

With headwind

90 km/h 120km/h

With tai lwind (base level)

90 and 120 km/h

Windspeed difference Headwind/Tailwind : 20 km/h

Driving speeds: 90 and 120 km/h Figure 12.24 Determination of wind noise and tyre noise contributions in road tests, after ref. 12.22


direction with vehicle symmetry plane can be ensured by using an appropriate yawmeter device (see section 12.2.3.3), preferably attached on the roof of the car. Both sound level measurements have to be done at the same road speed. If the recordings are compared, the difference between them is due exclusively to the air flow speed difference of the two tests.

Figure 12.24 shows the SLM difference between two headwind/tailwind tests, one carried out at 90 km/h (56.3mile/h) and the other at 120 km/h (75mile/h) on the same vehicle, according to Grosshäuser and Brunkhorst.12 22 Air flow speed difference between both cases is 20 km/h. The required 5 to 7 dB level variation is not present throughout the whole frequency range. The wind noise is observed to be dominant in the range above 315 Hz. In other words, the efficiency of any measures to reduce the wind noise level can be judged by comparing the SLM patterns in this frequency range.

Another thing that must be known is the maximum achievable wind noise reduction. This is important as it enables the judgement of the improvement that can be achieved with a proposed feature, bearing cost in mind. To find the maximum wind noise reduction level, all the potential wind noise sources have to be eliminated to make a basic SLM recording: for this purpose the windshield wipers and outside mirrors are removed, the drip rail and edges are modified to give smooth edges and all door and hood gaps and ventilation openings are sealed with adhesive tape. The wind noise in a vehicle prepared in this way is barely audible and a noise level measurement performed with this vehicle can be considered as the

dB

90

80

70

60

50

40

ß

\ \

a

l·' K • —-\

16 31.5 125 500 2000 8000 Hz

Figure 12.25 Determination of maximum achievable wind noise reduction level, (a) vehicle in initial condition, (b) prepared vehicle, after ref. 12.22

Notation 479

lowest possible level. Figure 12.25 shows the highest achievable noise reduction level compared with the vehicle's initial condition.

The most widely used method of tackling wind noise problems is to take successive sound level measurements on the road or in the wind tunnel. Using the SLM curves, the effectiveness of the proposed body or component detail variations is then compared within the representative frequency range, which has been already ascertained. This enables an objective evaluation of wind noise.

12.5 Notation

A Ae

DM

DA

E h

/ o

¢ u V V

vx

cD CP

f k m P Pc Poo

'd.o

t *a ¢ Ô Â 'cb

<r V

ß Ap Apdyn P

vehicle projected frontal area (m2) equivalent leakage cross-section (m2) mechanical drag, including the drag shares of tyres, driveline, bearings, etc. (N) aerodynamic drag (N) saturation vapour pressure at 7\ (bar) total rotational inertia of the driveline, including the wheels of the driven axle (N m s2) total rotational inertia of the non-driven axle (N m s2) absolute temperature (K) relative humidity (%) airflow rate (1/s) vehicle speed (m/s) wind tunnel operational speed (m/s) (or vehicle driving speed during a road test) drag coefficient static pressure coefficient effective mass increase due to the inertia of rotating vehicle components wind tunnel speed calibration factor vehicle mass (kg) static pressure (Pa) partial water vapour pressure in air (bar) wind tunnel static reference pressure (bar) (or atmospheric pressure during a road test) dynamic roll radius of the tyres on the driven and non-driven axle respectively (m) temperature (°C) ambient air temperature (°C) air-to-boil temperature (°C) boiling temperature of engine coolant (°C) radiator top hose coolant temperature (°C) airflow velocity (m/s) aerodynamic yawing angle (degrees) static pressure difference between two points (Pa) dynamic pressure (Pa) air density (kg/m3)

Chapter 13

Numerical methods for computation of flow around road vehicles Syed R. Ahmed

13.1 Introduction

The traditional predictive tools used in the automobile industry to evaluate aerodynamic performance are the wind tunnel and road tests. Full-scale vehicle wind tunnels are expensive to build and operate whereas scale model test results are subject to numerous doubts associated with realistic simulation of Reynolds number, surface and underbody details, engine cooling and passenger compartment flows, tunnel wall boundary layer and model support interference effects, model and wake blockage effects, effects of flow-intrusive probes, etc.

Road tests represent the most realistic simulation of the environment in which a vehicle operates. However, the difficulties associated with the ever-changing environment often make the results obtained open to debate. Great care is needed to make the results meaningful and conclusive.

Computers, and with them computational fluid dynamics (CFD), are slowly emerging as additional basic tools in aerodynamic design. Wind tunnels and computers are both simulators—wind tunnels analogue, computers digital. Their characteristic differences make them com-plementary rather than directly competitive. The relative role of the two simulation techniques is however changing.

In future, wind tunnels may be used more for validation and refinement of theoretical predictions or global simulation of the entire flow field rather than for extensive parameter studies as in the past.

Numerical simulation is well suited to the analysis of a wide range of shape options—for example during an early design stage—thus increasing the prospect that an optimum shape will be identified. Sometimes a numerical simulation permits the investigation of situations that cannot be realistically duplicated in a wind tunnel. The aerodynamics of two vehicles in the passing or overtaking mode, for example, poses a difficult problem for wind tunnel tests.

Numerical simulations are most useful in predicting trends of how shape changes will affect flow field features. Absolute performance value prediction is usually poor. Computer size and speed limitations, and the lack of information about the physics involved, often limit the predictive capacity of numerical methods. 480

Introduction 481

An interesting application of numerical methods is the effectivity enhancement of wind tunnel tests through pre-test planning, on-line test diagnosis and post-test validation. Although this may not lead to a reduction in wind tunnel testing, it can help to ensure that the time spent is used more intelligently.

All numerical methods to compute fluid flow are based on approxima-tions to the full Navier-Stokes equations. These are second order non-linear partial differential equations which govern all fluid motion. Except for the simplest approximations, they are solved by techniques such as finite element, finite volume or finite difference to achieve the spatial and temporal detail needed.

In these techniques the physical region of interest is divided up (or discretized) by a two- or three-dimensional grid. Such grids are in practice complicated orthogonal or non-orthogonal networks that may originate from the body contour envelope and have a flow physics oriented spacing. The vast amount of detail needed to analyse the flow around a real vehicle will limit the use of computational methods for quite some time to come. Only flow simulation around basic vehicle-like configurations appears to be feasible at present.

Numerical methods to solve the Navier-Stokes equations can be classified into the following four categories, depending on the degree of approximation made: 1. Linearized inviscid flow methods 2. Non-linear inviscid flow methods 3. Methods based on Reynolds-averaged Navier-Stokes equations 4. Solutions of full Navier-Stokes equations.

Linearized inviscid flow methods are used routinely in aircraft design and have reached maturity. They are applicable to subsonic, contour-attached flow. Vortex-lattice and panel method codes belong to this category. Use of these methods to compute the flow field around cars, whose predominant feature is the large separation region at vehicle rear, remains severely restricted.

The non-linear inviscid flow methods based on the solution of the Euler equations have established themselves as accurate design tools for the prediction of trans-sonic flow around a class of aircraft components, e.g. wings. The 'automatic' simulation of flow kinematics in the subsonic separated flow computations claimed by developers of these code needs further substantiation. Provided this simulation capability turns out to be general, a coupling of these methods with boundary layer approaches may mean a significant advance also of benefit to vehicle aerodynamicists.

Category three methods, based on the Reynolds-averaged Navier-Stokes equations, are still undergoing extensive research and develop-ment. These equations need a turbulence model for closure. The difficulty of modelling turbulence with sufficient generality and the complex mesh generation needed to resolve flows such as those around road vehicles are the principal difficulties that have to be overcome.

Methods to solve the full Navier-Stokes equations, which belong to the last category named above, are practically non-existent. Only very preliminary research is under way here.

482 Numerical methods for computation of flow around road vehicles

In this chapter some current developments in the application of numerical methods to computing the flow around road vehicle-like bodies are mentioned. The choice of the methods treated is conservative. Mostly those approaches have been detailed whose direct applicability to vehicle-type flows has been demonstrated by more than one user in the open literature. Briefer mention is made of methods that have not yet found wider usage but display innovative ideas which may help further development of the first mentioned approaches.

A comprehensive picture of the application of computational fluid dynamics (CFD) to road vehicle flow has to remain incomplete as this technology is in the preliminary stage of emergence. The more modest aim of what follows is to introduce these techniques which bear the promise of developing into a complementary design tool besides the wind tunnel to engineering staff from the automotive industry who have had little experience with CFD in the past.

13.2 Nature of flow around road vehicles

The flow generated by the movement of a road vehicle is extremely complex. In contrast to the flows around aeronautical configurations, the road vehicle flow field is characterized by regions of separation both small and large. These can be of open or closed type and may exhibit quasi-two-dimensional or fully three-dimensional structures.

The smaller regions of local separation occur at body appendages such as headlights, mirrors, door handles, windscreen wipers etc. Large areas of separated flow are present at the trailing perimeter of the vehicle body and on the underside where the flow is disturbed by mechanical and structural elements and by the rotating wheels.

A feature of the environment in which a road vehicle operates is the ambient wind that is almost always present. The speed and path of the vehicle differ from that of the wind. In the resulting yawed flow, the wake and the local regions of separation are asymmetrically deformed, thus adding to the complexity of the flow field. Temporal changes in ambient conditions superimpose a time history on the phenomena in addition to the inherent unsteadiness of separated flows.

Figures 1.6, 4.3 and 4.4 give a schematic impression of the flow separations that may occur at the various locations. As in an actual situation, some or all of the separation phenomena may be present; the flow field is not known a priori. Mutual interference of the various separated flow regions, often triggered by minor changes in body geometry, are known to induce abrupt changes of the overall flow field. Air drawn from or exhausted into the external flow for the purpose of engine and brake cooling and ventilation of the passenger compartment links aero-thermodynamically the external flow with these internal flows.

Road vehicles move in close proximity to the ground and share common pathways, so that interaction between the overall flow fields of vehicles of different shape and size during the passing and overtaking phases is a common occurrence.

Flow passing over the vehicle underbody is restricted by the presence of

Some difficulties of numerical simulation of the road vehicle flow field 483

the ground. Interaction between flows generated by the rough vehicle underbody, wheels and the ground result in a complex viscous flow in this region.

13.3 Some difficulties of numerical simulation of the road vehicle flow field

Computational fluid dynamics, which has established itself as an effective design tool in many aeronautical applications, is based on idealized models of the overall flow. These models possess sufficient generality for their application to a broad range of similar components, for example a wing profile, to be frequently a routine exercise.

The successful abstraction of idealized flow modules from real flow situations in many aeronautical applications is a consequence of the prime requirement to avoid, minimize or control the separation phenomena in these cases. With the shape design margins available to the aeronautical engineer, this is achieved to a good degree, at least for the designed cruise conditions.

With separation then playing a less crucial role, the viscous effects can be hypothesized to act in the immediate vicinity of the body surface, in the so-called 'boundary layer'. Except where this boundary layer separates, its main effect is a particular outward displacement of the 'inviscid' flow away from the body surface. A possibility for numerical simulation of this flow phenomenon caused by viscosity is increasing the local body thickness by an amount equal to the displacement thickness of the boundary layer. This can be done in a 'correction' step performed after computing the inviscid flow.

In this simple example of flow modelling, only one set of governing equations is needed for the single flow module used for the entire flow field. More often a set of flow modules is blended together to simulate the significant part of the flow. Each of these idealized flow modules is then treated with a different approximation of the Navier-Stokes equations.

Regions of separated flow being the key features of a road vehicle flow field, an analytical approach of the type mentioned above is extremely difficult. Even simplified, basic vehicle-like configurations free of all appendages and having smooth surfaces create 'closed' separation regions and a large wake. One of the main difficulties encountered in modelling such flows is the lack of generally applicable information about three-dimensional separated flows. The variety of separation phenomena that can occur in three-dimensional flows is a subject of continuing research. Factors governing the initiation of different types of three-dimensional flow separation, kinematics of the structures in separated flow, unsteady behaviour of bluff body wakes, turbulence, etc., are all phenomena not well understood. Modular or sequential approaches similar to those used in aircraft applications remain inadequate since computational methods to treat three-dimensional boundary layers, in an adverse pressure gradient and strong cross-flow environment, which is typical of road vehicle flows, are not yet available.


As noted earlier, use of Reynolds-averaged Navier-Stokes equations needs a turbulence model to close the system of equations and make them amenable to solution. Standard mixing length and eddy viscosity concepts cannot be used to model complex real turbulent flows. Higher order turbulence models, currently not available, are therefore needed.

13.4 Relative magnitudes of the forces in a flow field

The force on a body arising from its motion relative to a surrounding fluid depends on the geometric shape and orientation of the body and the physical properties of the fluid. In general, it is immaterial whether the fluid moves and the body is stationary or vice versa, provided the nature of relative motion remains identical. In what follows, the body is considered to be stationary and the fluid moves.

For a rigid body, the geometric shape can be characterized by a length /. The orientation is specified by two angles oc and ß, which the velocity vector V of the fluid forms with a body-centred coordinate system. Road vehicle flow being of interest here, the surrounding fluid, air, is considered to extend over an infinite region. Fluid properties of importance are density p, viscosity ì and compressibility.

Considering a fluid element of volume dx dy dz = äíïÀ in the flow field (Fig. 13.1), the forces acting on the element are the inertial force, gravity force, pressure force and the viscous force.

Figure 13.1 Forces acting on a fluid element

The time rate of change of momentum is equal and opposite in sign to the inertial force. The change of momentum of the volume element having a velocity V is proportional to ñ^äíïÀ. This change may be assumed to take place in a characteristic time interval; for example, the time needed by the element to traverse a distance equal to the characteristic length /. Inertial force F{ acting on the element is given by the proportionality

Criteria for consideration of viscous and compressibility effects in a flow field 485

pVövol pVföyol ( F>~ ~lv Γ " (13'1}

The balance of pressure forces on the opposite faces—dx apart—of the fluid element (Figure 13.1) gives a net pressure force equal to

^ · ck ay Üζ = ^- · äíïÀ (13.2) dx y dx v J

Assuming all components of the pressure force are of same magnitude, the pressure force Fp can be set proportional to

bp

I Fp ~ -L . äíïÀ (13.3)

Here bp is a 'representative' pressure change and the length x in Eqn (13.2) has been replaced by the characteristic length /.

The viscous force can be estimated in a similar manner. Considering only one component acting in the jc-direction (Fig. 13.1), the balance of viscous forces acting on the faces—ay apart—of the fluid element delivers a viscous force acting in the x-direction equal to

| i - · dx ay Üζ = | 1 · bvol (13.4) By y dy v '

The shear stress x, can be expressed in terms of the velocity gradient in the ^-direction (see section 2.1.2, Eqn 2.1) as

ô = ì · ^- (13.5) dy

where ì is the coefficient of viscosity and u the velocity component in the x-direction. Replacing u and y with characteristic quantities V and / and assuming, as earlier, equality in magnitude of all shear force components, it follows

— ovol ~ ì —z dy μ I2

The relative magnitudes of the inertial force, pressure force and viscous force acting on the fluid element can be expressed as

pV2 bp V

~ Γ : Ô :ì T2

— äíïÀ ~ ì — äíïÀ (13.6)

F{:Fp:Fy= ^— : - f : ì - _ (13.7)

13.5 Criteria for consideration of viscous and compressibility effects in a flow field

The ratio of inertial force to viscous force is a non-dimensional parameter of fundamental importance in fluid mechanics. Called the Reynolds number Re, its value is given by (see Eqn 13.7)


Re,<^L,JLvl=YL (13.8) μν/l2 ì v V '

where v denotes the kinematic viscosity ì/ñ. The proportionality

Re ~ i n e r t i a l ! ° r C e (13.9) viscous force

enables an estimation of the relative roles that these forces play in a flow regime.

With the average length and maximum speed of current road vehicles, the Reynolds number of the flow field varies between 105 and 108. Accordingly, the inertial forces in the major part of the attached flow field are some orders of magnitude larger than the viscous forces. In the immediate vicinity of the body surface the flow is retarded and the velocity on the surface itself reduces to zero ('no slip' condition). In this thin 'boundary layer' region the viscous forces play a key role. The 'thin' boundary layer is a consequence of the low value of the kinematic viscosity of air. Thus the assumption of a 'perfect fluid' behaviour for the flow outside the attached boundary layer represents a good approximation of the real flow.

The decision whether or not compressibility effects in a flow are significant is related to the change in volume effected by the pressure changes due to motion of the fluid. For a perfect gas

bp äíïÀ p vol

(13.10)

with bp/p and äíïÀ/íïÀ denoting the relative changes in pressure p and volume 'vol'. Using the law of conservation of mass, the relative change in volume can be replaced by the change in density as

bp _ äñ

~P~ P (13.11)

The pressure change due to fluid motion can be estimated from the Bernoulli equation (see section 2.3.1, Eqn 2.6) as

bp ~ -H- V2 (13.12)

Substituting this value in Eqn 13.11, it follows

-V2 (13.13) ä Ñ 1 P v2 p 2 p

p and p denote here some value of pressure and density in the undisturbed region of flow, and may be considered as a set of constant reference values.

In physics textbooks it is shown that the speed of sound in a perfect gas is given by

a2 = JL (13.14) P

Inviscid flow methods 487

From Eqn 13.13 it follows

A p - L Ü ^ i ^ (13.15) p 2 a 2

The abbreviation Ma for the ratio of flow velocity to the velocity of sound is called the Mach number. From Eqn 13.15 one can state that the effects of compressibility are negligible if the ensuing density change

^ « 1 (13.16) P

In other words, compressibility effects can be neglected if the Mach number of the flow remains small compared to unity. At normal temperature, the speed of sound in air is about 1332 km/h. Assuming the maximum speed for a utility road vehicle of 250 km/h, the resulting Mach number for the flow field is 0.19. From Eqn 13.15 the change in density amounts to about 2 per cent. In aeronautical practice, compressibility effects are usually ignored for flows with a Mach number below 0.3.

13.6 Two approximations for the fluid air

Some of the difficulties encountered when describing the vehicle flow field analytically have been indicated in the preceding sections. To render the problems of aerodynamics tractable, the physical properties of air have to be approximated. The approximations relevant to vehicle aerodynamics lead basically to two types of fluid namely, a perfect fluid and a viscous, incompressible fluid.

The perfect fluid is a homogeneous, inviscid and incompressible medium. From Eqns 13.9 and 13.15 it follows that, for an inviscid incompressible flow, the Reynolds number is infinite and the Mach number equals zero. Independence of such flows from Reynolds number means that, with this approximation, the scale effects cannot be considered in the analysis. Such flows are also termed 'potential' flows and are a good simulation for flow regions outside the boundary layer and wake.

Assuming the fluid to be a homogeneous, viscous and incompressible medium is an almost complete description of air for problems of vehicle aerodynamics. The Reynolds number is then finite and Mach number is zero. Viscous laminar flow is amenable to accurate numerical analysis. Treatment of viscous turbulent flow is difficult and tractable mostly with the help of semi-empirical formulations.

13.7 Inviscid flow methods 13.7.1 Governing equations

The equations of motion for an inviscid, incompressible perfect fluid can be derived from the Navier-Stokes equations. For an unbounded, homogeneous, viscous and incompressible fluid, the Navier-Stokes equations express the balance between inertial force, pressure force and


du —- + u dt

dv — + u dt dw —- + u dt

du

dx

dv

dx

dw

dx

du

ay 3v 3y dw

+

+

+

du

dv

dw

viscous force, see e.g. refs 13.1 and 13.2. For a perfect fluid, as mentioned in the preceding section, the viscous force is absent and the set of equations of motion for a three-dimensional flow in cartesian coordinates is

| (13.17a)

| (13.17b)

7T (1 3-1 7 c) az

The terms on the left-hand side express the inertial force and on the right-hand side the pressure force acting on a fluid element. In the above equations u, v, w are components of the velocity vector Fin the directions x, y and z, p the density and p the pressure.

For an incompressible fluid, from the law of conservation of mass, the equation of continuity follows as

du dv dw ,«„ «^ — + — + — = 0 13.18 dx dy dz

The four unknowns w,v,w and/? may be determined from the set of Eqns 13.17a,b,c and 13.18. Equations 13.17a,b,c are known in the literature as Euler's equations.

13.7.2 Irrotational flow field as a solution of the Euler equations

In spite of their seeming complexity the Euler equations can be integrated for an irrotational flow. A flow is said to be irrotational if the components of the vorticity vector ä? are equal to zero everywhere in the flow field. With

(13.19) ù = \ùχ +

and 1

1

1

]ùγ + koo2

dw dv dy dz

du dw dz dx

dv du dx dy

the irrotationality of flow implies that

ùχ = ù^ = ùæ = 0

(13.20)

(13.21)

The condition of irrotationality can be derived directly from the Euler equations (13.17) with the help of the continuity equation (13.18), see e.g. refs 13.1 and 13.2. To restate the problem of integration of the Euler equations: if a flow field satisfies the condition of irrotationality, Eqn


13.20, and the condition of continuity, Eqn 13.18, it represents a solution of the Euler equations.

13.7.3 Consequences of irrotational motion

A flow whose velocity field is irrotational can be expressed as the gradient (denoted by grad) of a scalar potential function Φ(χ,γ,ζ), see e.g. refs. 13.1, 13.2 and 13.3. The velocity potential Ö is defined as continuous and differentiable throughout the entire flow regime. It is

—K x 3Ö 3Ö 3Ö V(x,y,z) = grad Ö = i 1 - + j J g - + k - ^ (13.22)

With V = \u + jv +kw, the components of the velocity are given by

3Ö 3Ö 3Ö n a ^ v = ^—\ H > = - — (13.23) dx By 3z

For the x-component of vorticity vector ù*, it follows from Eqns 13.20 and 13.23

32φ - o dydz

Similarly

(oy = ù2 = 0 Thus the condition of irrotationality if fulfilled by the potential function

Ö. Substituting Eqn 13.23 in the continuity equation (13.18), one obtains 32ö 32ö 32ö dx2 By2 dz2 v '

Using the Laplace operator

V2 _ a2 + 32

+ 32

Eqn 13.24 can be expressed as

í 2 Ö = 0 (13.25)

Eqn 13.25 is known in the literature as the Laplace or potential equation. The introduction of the concept of a potential function considerably

simplifies the problem of integration of the Euler equations. Instead of seeking a solution of the three non-linear partial differential equations 17a,b,c together with the equation of continuity, Eqn 13.18, it is sufficient to find a solution for the potential function Ö which fulfils Eqn 13.25. From a mathematical viewpoint, the solution of the linear Laplace equation (13.25) is much simpler than the non-linear set of Euler equations. Linearity of the Laplace equation allows the generation of a family of solutions from a set of known basic solutions using the principle of superposition. If


Öé (x,y,z) Ö2 (x,y,z)

Ö« (x,y,z) represent n basic solutions of the Laplace equation, then

Φ(χ, y, z) = αλΦχ + α2Φ2 + ... + αçΦç (13.26)

also represents a solution of the Laplace equation.13 2 Through proper choice of the constants a1? a2, ... an, particular solutions can be 'constructed'.

Since each of the solutions Ö1? Ö2, ... Ö„ is linear, the velocity components and therefore the velocity vectors are also additive. This means that, with (see Eqn 13.23),

3Ö 3Ö v = dx ' dy

3Ö× 3Ö÷ "i = ^ ô ; íé = dx ' l dy

3Ö2 3Ö2 U2 = -^Ã \ V2 =

w

W\

= 3Ö dz

3Öé dz

3Ö2 3x ' Vl dy ' rvz dz

3Ö„ 3Ö„ 3Öç - - � w„ =

(13.26)

dx ' n 3y ' " 3z the resultant velocity field vfyt,;y,z) can be expressed as

V(x,y,z) = i(fliW! + #2^2 + . . . + anun) +

j(fliVi + a2v2 + ... +flnvr t) +

From the velocity field, the pressure field p(x,y,z) can be evaluated using the Bernoulli equation (Eqn 2.7)

p + -γ V2 = const. (13.27)

It is important to note that the pressures pi,p2,...,pn of the basic flows cannot be superimposed because of the quadratic relation between pressure and velocity (Eqn 13.27).

13.7.4 Stream function

A useful concept in the treatment of irrotational flows is that of a stream function. As seen in section 13.7.3, the potential function Ö fulfils the condition of irrotationality. The equation of continuity (13.24), is then used to evaluate the potential function. Alternatively, it is possible to


define a function ø, which fulfils the equation of continuity. The condition of irrotationality can then be used to determine the function ø.

The function ø is termed the stream function. A unique definition of the stream function is possible for two-dimensional flow. Such a function can also be found in three dimensions for the case of axially symmetric flows, see for example refs 13.3 and 13.4.

For the sake of simplicity, we consider below a two-dimensional flow. The stream function ty(x,y) can be expressed in terms of the velocity components u and v as

3ø 3ø u - —— , v = -3y 3JC

(13.28)

Substituting this in the continuity equation for two-dimensional incom-pressible flow

^ + ^ = 0 (13.29) 3* 3y v '

it is seen that Eqn 13.9 is fulfilled. For a two-dimensional flow, with only velocity components u and v

present, the condition of irrotationality (Eqn 13.20) reduces to ù æ = 0

3v du n ,Λ~ . n , or ——-—— = 0 (13.30)

dx 3v v ' Equation 13.30 can be used to determine the stream function ø(÷,í).

Substituting for u and v from Eqn 13.28 32ø 32ø —ß- + _ v - = 0 (13.31) dx2 dy2 K }

The stream function can be utilized to map the streamlines in a flow field. A streamline is a curve whose tangent at every point in the flow coincides with the direction of the velocity vector.

From Eqn 13.22 a two-dimensional potential flow is given by the velocity field

VW) = grad [Ö(*ï0] = i -H- + j ^ - (13.32)

and grad Ö = \u + jv (13.33)

The gradient of the stream function is given by Eqn 13.28 3ib 3ø

grad ø = é ^L + j _T = _ iv + j M (13.34)

A comparison of Eqns 13.33 and 13.34 shows that the vectors grad Ö and grad ø are perpendicular to one another (Fig. 13.2). It can be shown that the vectors grad Ö and grad ø point in the direction normal to the curves Ö = const, and ø = const, respectively.133 The vector grad Ö, which

Ö=c

onst

S

trea

mlin

es

Ø=

con

st

Equ

ipot

entia

l lin

es

Ö=

con

st

Figu

re 1

3.2

Stre

amlin

es a

nd e

quip

oten

tial l

ines

are

orth

ogon

al


represents the velocity vector, is thus tangential everywhere to the curve ø = const. Therefore the curves ø = const, represent the streamlines of the flow. From the above it also follows that streamlines (ø = const.) and equipotentials (Ö = const.) are orthogonal (Fig. 13.2).

13.7.5 Some basic potential flows

In this section some well-known basic potential flows are treated briefly. Using the principle of superposition, complicated potential flows of practical interest can be 'constructed' with these basic solutions. Use is made of this technique in the vortex lattice and panel methods, to be treated later in this chapter.

13.7.5.1 Uniform flow — �

A uniform flow with the velocity vector V = \u + jv + kw, constant everywhere in a flow region can be represented by the potential function

(13.35) Ö(÷

with

u =

>y>z) =

3Ö dx

ux

?

+

V

vy + ]

3Ö -º37"

wz

and 9Ö

Since u, v and w are also constant in the flow field, the potential function defined by Eqn 13.35 fulfils the continuity equation (13.24). The streamlines of the uniform flow are straight lines oriented in space such that their intercepts with a cartesian axis system are given by

dx : ay : Üζ = u : v : w (13.36)

13.7.5.2 Point source or sink flow

If the streamlines of a flow emanate radially from a point, the flow field created is said to be a source flow. The potential function of a three-dimensional source flow is given by

ö(÷'ã'æ) = ~ º Γ T ( 1 3 · 3 6 )

with r = V(x2 + y2 + z2). The velocity components of the source flow in cartesian coordinates are obtained from Eqn 13.36 as

v = -¥- ^j (13.37)

w =

<J 4ð

Q 4ð

Q 4ð

X

P

y r3

Z

r3


The equipotential surfaces Ö = const, are spheres of radii r with the origin at x = y = z = 0. The resultant velocity V of the flow is directed radially outwards, i.e. normal to the surface of the spherical equipotential surfaces. It is

V{r) = V(u2 + v2 + w2) = — 4 " (13.38) An r

The outflowing volume of fluid through a closed spherical surface of radius r is given by

Volume = V · ^Jtr2 = — - i - · inr2 = Q (13.39) 4ð r

Since the chosen value of r is arbitrary, it follows from Eqn 13.39, that the outflow of fluid through any closed spherical surface with its origin at the origin of the axes is constant and equals Q. Q is termed the strength of the source, or simply source strength.

For positive values of Q, we see from Eqn 13.38 that fluid is being continuously 'created' at the point r = 0. In the case of Q being negative, the velocity V(f) is directed radially inwards and the fluid continuously 'disappears' at the point r = 0. A radially inwards-directed flow, analogous to the source, is called a sink flow. The corresponding potential function and the velocity components can be readily obtained from Eqns 13.36, 13.37 and 13.38 by putting Q = -Q.

It is important to note that the velocity V(r) becomes infinite at the point r = 0 (Eqn 13.38). The origin, r = 0, represents a singular point, also characterized by 'creation' and 'disappearance' of fluid there. As this is not possible in nature, the source or sink flow described above has relevance to reality only when the immediate vicinity of the singular point r = 0 is omitted from consideration.

13.7.5.3 Plane source or sink flow

In a two-dimensional (plane) flow with only the velocity components u and v present, the potential function for a source or sink flow is

<P(x,y)=^\nr (13.40)

with

r = V(JC2 + y2)

Source flow is represented by positive and sink flow by negative values of the strength Q.

The equipotential lines for a plane source or sink are concentric circles about the origin of the xy-axes (Fig. 13.3). Radially outward or inward directed straight rays from the origin represent the streamlines for a plane source or sink. The velocity components in cartesian coordinates are obtained from Eqn 13.40 as


Figure 13.3 Streamlines and equipotential

U =

V =

Q_ 2ð

Q_ 2ð

X

~7

y r2

lines for i ι point source flow

(13.41)

and the resultant radially directed velocity Q_ J_ 2ð r

V(r) = V(u2 + v2) =

The stream function for the plane source or sink flow is

ø(÷,)>) = ——arctan 2ð

�� ( * ) · 2ð φ

(13.42)

(13.43)

with ö denoting the polar angle (Fig. 13.3). As noted earlier in section 13.7.5.2, the origin r = 0 represents a singular

point. Solutions of the Laplace equation (13.25) which contain such singular points are called singular solutions.

13.7.5.4 Point doublet and plane doublet

Another interesting singular solution of the Laplace equation (13.25) is obtained when a source of strength Q, and a sink of equal strength, situated at a distance / apart, are brought together by letting / go to zero. The resulting flow has the potential13

Φ(χ,γ,ζ) = M -? (13.44)


with r = V(x2 + y2 + z2)

Ql (13.45)

and M - 4ð

The product M = Ql/Αð is referred to as the doublet strength and also as the moment of the doublet.

Velocity components in the x, y and z-directions are obtained from Eqn 13.44 as

u = M

v = -M-

w = —M-

r 2 - ^ 2

r5

xy

r5

xz

(13.46)

r5

In a spherical coordinate system defined by R, È and ö, the streamlines are given in a plane ö = const, by (see e.g. ref. 13.3)

- ^ - = constant (13.47) iV

Figure 13.4 Streamlines for a point doublet


Figure 13.4 shows the streamlines for a point doublet. The streamlines are obtained by choosing different values for the constant in Eqn 13.47.

Similar considerations lead to the derivation of potential and stream functions for a plane doublet.13Λ

In terms of cartesian coordinates, the potential function is

Φ(χ,γ) = Mpjz (13.48)

and the stream function

ôÊ*èÏ = -Mp^T (13.49)

As before, Mp = QU2n, is termed as the doublet strength or moment of the plane doublet.

Figure 13.5 Streamlines and equipotential lines for a plane doublet


The components of velocity u and v follow from Eqn 13.48, as

u = —M. y

v = -M 2xy

p~7~

(13.50)

Equipotential lines and streamlines for a plane doublet can be readily derived from Eqns 13.48 and 13.49 and are shown in Fig. 13.5. Streamlines and equipotential lines are represented by a family of circles tangent to the jc-axis or the y-axis respectively.

13.7.5.5 Point vortex and vortex filament

A potential flow of great importance in aerodynamics is that of a vortex. The potential function

Ö ( ^ ) = ^ ^ ç ( ^ = É _ ö ( 1 3 .5À)

with the corresponding stream function

n*,y) = - - ^ i n (*2 + y2) = ■ 2 ð · -lnr (13.52)

is that of a point vortex of 'strength' Ã situated at the origin x = v = 0 (Fig. 13.6). The equipotential and streamlines of a vortex flow are straight

wv(r)

Ö = const Ø=const

Figure 13.6 Streamlines, equipotential lines and circumferential velocity distribution of a point vortex


outward rays emanating from the origin and concentric circles about it, respectively. The velocity component of the flow along an outward ray

3Ö wr= = 0 (13.53)

or

i.e. the radial component of the velocity for a vortex flow is equal to zero. (It can be shown that the velocity component of a potential flow in a direction n is given by the derivative ΒΦ/dn; see e.g. ref. 13.3.) Components of the velocity in x- and ^-directions are given by

u = —

v =

JLiL 2ð r2

(13.54)

2ð r2

The velocity vector V is

V(x,y) = \u + jv

and

V = — -f- (13.55) r 2ð

As the streamlines are concentric circles and no radial component of velocity is present, the resultant velocity V from Eqn 13.55 is the circumferential velocity in the circulatory vortex flow.

It is customary to speak of the flow defined by Eqns 13.51 and 13.52 as that of a point vortex. The two-dimensional velocity field described by Eqn 13.54 is that of a vortex flow in the xy plane with the point vortex at the origin x = y = 0. Two-dimensional flow implies that the flow pattern is identical in all planes parallel to the xy plane. The line connecting the origins of the vortex flow in these parallel planes is a straight vortex filament.

In three-dimensional flow, a line coinciding with the axis of rotation of successive fluid elements is termed a vortex filament. This flow too possesses a singularity at the point r = 0 (see Eqn 13.55) where the velocity becomes infinite and thus is physically impossible. However, vortex flows occur in a viscous fluid, outside the central core of the flow field, which conform closely with that described by Eqns 13.51 and 13.52.

From Eqn 13.55 it can be seen that

2nrV = Y = constant (13.56)

irrespective of the chosen radius r. The product of circumference (= 2nr) and velocity V, is called the strength of the vortex filament and denoted by Ã.

13.7.6 Some concepts common to vortex-lattice and panel methods

Before dealing with the vortex-lattice and panel methods in more detail, some common features of these inviscid flow approaches as applied to


computation of vehicle flow fields are presented in this section. The analytical concept for the simulation of a potential flow around an arbitrarily shaped body is to consider the flow to be formed by the superposition of two flow fields: A uniform 'onset' flow jjeld of constant velocity V^ and a 'perturbation' flow field with velocity Vp(x,y,z).

The uniform onset flow is defined as the one which would exist in the absence of the body. Perturbation flow is so structured that at every point in the flow field the actual velocity vector v(x,y,z) is given by the resultant of both flow fields:

V(x,y,z) = F . + Vp(x,y,z) (13.57)

In the vehicle flow problem considered here, the onset flow is known. For a vehicle moving witji a constant speed this is, for example, a field with a constant velocity V^ equal to the vehicle velocity.

Given the geometry of the vehicle and the onset flow, the problem is therefore to find the appropriate perturbation velocity field Vp(x,y,z). Relevance of the solution to the specific nature of a particular case is obtained by imposing boundary conditions on the solution. From physical considerations, it is plausible that an inviscid fluid glides past the body surface without being decelerated. The resulting flow appears tangentially attached everywhere on the body surface. In other words, on the body surface, the normal component of the resultant flow velocity Vcan be set equal to zero.

A further boundary condition also following from physical observation concerns the perturbation flow. The perturbation of the onset flow is strongest on the body surface. This effect diminishes as the distance from the body surface increases. If Ö, Ö0 and Öñ denote the potentials of the resultant flow, onset flow and the perturbation flow respectively, the two boundary conditions stated above can be expressed as

8Ö _ 3Ö0 + 3ÖÑ _ Q

dn dn dn

(13.58) Öñ -> 0 with r -> °o

In Eqn 13.58 n is the direction normal to body surface and r is the distance away from a point on the body surface.

The flow around a bluff-based ground vehicle is characterized in the real flow by the presence of a wake which emanates from the rear part of the body surface. It is also known that ground vehicles can experience a sizeable amount of lift.

The wake and the trailing vorticity shed by a lifting body are simulated by an artifice in potential flow methods. This consists of an infinitely thin tubular surface which extends downstream in direction of the onset flow, starting from a postulated flow separation line round the rear end of the body. Shed vorticity is assumed to be concentrated in this infinitely thin surface which now represents the wake in the analytical model.

In the real flow, the wake 'surface' is aligned in the direction of the local velocity; i.e. the wake 'surface', in contrast to the body surface, cannot carry a load; instead it deforms until its surface is load-free. For a given


body and flow conditions, the geometry of the wake boundary surface is not known in advance. This non-linear problem is often linearized in practice by the assumption of a certain geometrical shape for the wake surface.

In the case of a road vehicle, the ground plane simulation is effected by introducing an image of the road vehicle symmetrically below the notional position of the ground plane. The inviscid flow produced by the vehicle and its image is symmetrical to the ground plane. The plane of symmetry is a stream surface and represents the inviscid flow over the plane ground surface.

13.7.7 The vortex-lattice method

The fundamental ideas underlying the vortex-lattice approach are derived from the concept of a 'lifting surface', which is well known in aerodynamics. * 135

Considering the flow around a road vehicle, its 'wetted' surface is approximated by flat area elements, each of which is simulated in the flow model by a discrete 'horseshoe' vortex. A horseshoe vortex consists of a 'bound' leg filament and two 'trailing' leg filaments. The bound leg of the horseshoe vortex is placed on the upstream element edge, and its trailing legs are positioned along its sides as illustrated in Fig. 13.7. The trailing

Figure 13.7 (a) Surface discretization for vortex lattice layout (schematic), and (b) arrangement of horseshoe vortices on a surface strip

legs are positioned in the plane of their originating element, and are deflected so that they lie in the plane of each surface element downstream of the originating element. From the last surface element contacted, i.e. at the edge of the flat vehicle base, the trailing legs extend downstream. The


trailing legs of the individual horseshoe vortices are placed coincident with the element side edges and are consequently contiguous with adjacent horseshoe vortices. The strength of a trailing leg is thus the vector sum of adjacent horseshoe vortex strengths. Figure 13.7b shows the vortex-lattice arrangement for a surface strip (shaded) of Fig. 13.7a.

The boundary condition, expressing flow tangency to body surface, is satisfied at a number of 'control points' which, for example, can be the centroids of area elements.

The geometry of the wake surface that emanages from the vehicle base is not known. To render the problem linear, its shape has to be assumed. To impose the flow tangency condition on this wake surface implies that it should represent a stream surface in the computed flow. A stream surface of the assumed wake shape may however not exist in the computed flow. The error involved depends on the accuracy with which wake geometry can be determined. Wake simulation thus remains inadequate in the linear theoretical model under consideration here.

Stafford,13 6 1 3 7 in applying the vortex-lattice method to compute the flow around a motor car, excludes the base area, which is covered by the wake, from the surface simulation. Through the open rear end an outflow is generated by placing a point source within the body. The strength of this source is given by the product of the open base area and the onset flow velocity. The position of the source within the body is adjusted to satisfy a flow tangency condition on an area element of body surface. This tubular wake of constant cross-section extends downstream to infinity. According-ly, the trailing legs of vortex filaments coming off the vehicle base also extend to infinity. The surface of the wake is not discretized and no boundary conditions are imposed on it.

As noted earlier, the resulting flow field is obtained through superposition of a uniform onset flow and the perturbation flow created by the horseshoe vortices placed on the body surface. The total velocity at a point is the vector sum of the onset flow velocity and induced velocity contributions of all vortex filaments on the body and the trailing filaments. The induced velocity through a vortex filament at a point is given by the Biot-Savart law (see e.g. refs 13.2 and 13.3).

In Fig. 13.7 Ã!,Ã2 ... Ã„ denote the vortex strengths of horseshoe vortices placed on n area elements of the surface. Let a^ represent the velocity induced by a horseshoe vortex of unit strength, placed on the ;th element, at the control point of the area element i. If Atj is the component of this induced velocity in a direction normal to the surface of the area element /, then

n

Σ AtjTj (13.59)

is the total normal velocity induced by all vortex filaments at control point of area element /. For a body in ground proximity, the terms αß} and Ay-include the influence of vortex-lattice body 'image' arranged below the ground; see section 13.7.6. To satisfy the boundary condition of flow tangency, i.e. no flow across the surface of the element /, this velocity


should equal the normal component R( of the onset velocity at the control point:

(13.60)

Since the flow tangency condition is to be applied at the control points of n surface elements, repeated use of Eqn 13.60 results in a system of linear equations:

¢çΑ12 ...Aln

A2\A22 ··· A2n

ÃÃéº r2

-Ã».

_

[~Rl~\ -R2

.-Rni

(13.61)

nn J L x n J L. LAnlAn2 ...A

Equations 13.61 are solved by the standard techniques available to deal with systems of linear equations, such as the Gauss-Seidel iterative solution scheme, which is well suited for calculations on a computer.

Both accuracy of the solution and computing time depend on the number of surface elements used to simulate the vehicle surface. No general rules can be given for the most appropriate surface discretization. The decision is closely related to an a priori knowledge of the probable flow. Critical regions, where rapid curvature changes, interference between neighbouring areas etc. is present or expected, need a finer discretization than relatively flat areas where the velocity gradients are small.

With vortex strengths Ãé,Ã2, ... Ã„ known, the induced velocities at each control point are determined by applying the Biot-Savart law. The vector sum of the tangential components of these induced velocities together with the tangential component of the onset velocity gives the net tangential velocity acting at the control point. Substituting the value of this velocity in the Bernoulli equation (2.6), the pressure at the control point is found. This pressure is taken as the mean value prevalent over the surface of the area element. The forces and moments acting on the body are then given as the sum of those acting on the individual area elements.

In the vortex-lattice model used in ref. 13.6, the base area (covered by the wake) is not simulated. As in the case of the wake surface, it is difficult to define appropriate boundary conditions here. Due to this missing area the pressure drag of this 'open' body cannot be estimated.

13.7.7.1 Some results obtained by the vortex-lattice method

Stafford13·6'13·7 used the vortex-lattice approach to compute the flow around wind tunnel models of a saloon and a GT car. Figure 13.8 shows the wind tunnel model of the saloon car. The model with flat side panels had a rectangular plan-form of aspect ratio 0.375. All the longitudinal edges were sharp.

In the theoretical model, the car body was simulated by 480 area elements. Ground simulation was also provided. Figure 13.8 also illustrates


^ ^ ^ ^ — ^ — Theory

I »J — — — — Theory ( Separation bubble model )

O Experiment

0 0.2 (K 0.6 0.8 x/l 1.0 Figure 13.8 Pressure coefficient distribution along centreline of saloon model (top surface), after ref. 13.6

the pressure distribution along the centre line of the upper surface. In general the agreement with experimental results is satisfactory in spite of the coarse surface discretization. Discrepancies at grille/hood and windscreen/roof junctions are probably due to insufficient surface element density. The main deviation of the theoretical results from experiment is however visible at the roof rear edge, where the flow separates in the wind tunnel experiment. The inviscid theoretical model obviously cannot simulate this phenomenon. By changing the model contour to follow the dotted line from roof rear edge to the boot edge, an improved pressure prediction is obtained. The dotted line in Fig. 13.8 can be assumed to represent crudely the 'separation bubble' contour. A separation bubble exists in the real flow between the rear window and boot lid region. It is interesting to note that the pressure computed at the assumed 'edge' of this separation bubble gives a better estimate of the pressure values measured on the model surface.

In a further study, Stafford13 7 demonstrated that some improvements in pressure prediction are possible through a more adequate wake modelling.

13.7.8 The pane! method

Some of the difficulties involved in 'constructing' a perturbation flow model for the road vehicle problem were evident in the preceding section. In textbooks of fluid mechanics it is shown that to simulate the flow about a lift-generating body of finite thickness both sources/sinks and doublet/ vortex types of singularities must be present in the theoretical model, (see e.g. refs 13.2, 13.3, 13.5). To circumvent this difficulty of the vortex-lattice approach to vehicle flow problem, Stafford13 6 employed a point source, placed within the body, which was otherwise represented only by a vortex lattice.


The panel method, discussed in this section, generates the perturbation flow by a source/sink singularity sheet placed on the surface of the body (Fig. 13.9a). For lifting bodies, doublet or vortex sheets are introduced to provide circulation. The strength of the singularity sheet varies over the surface in a manner such that at every point on the solid body (and wake) surface the normal velocity generated by the singularity sheet(s) just balances the component of the onset flow velocity. It is not necessary that the singularity sheets coincide with the surface on which the boundary conditions themselves are applied.

® r r r dSw

Wake Surface Sy

(Doublet Panels)

Body Surface S8

(Source/Sink Panels)

Wake

Ground Plane

Body and Wake Image

Figure 13.9 Numerical simulation of a vehicle model by the panel method

The essential features of the panel method formulated to compute a vehicle flow field are illustrated in Fig. 13.9 (from ref. 13.8). Let o(SB) be the local strength of the source sheet placed on the body surface SB and ì(5÷í) the local strength of the doublet sheet representing the assumed wake surface 5W. If Q is a point in the flow field at a distance r from a characteristic point ('control point') of the body and wake surface, then the potential at Q due to source/sink sheet can be expressed as


«fc<ß> = - -hffl^r1 d5B ( 1 3 · 6 2 ) 4ð

sB and the potential due to a doublet sheet as

9D(ß) = ^ K V > J ; (A d5w (13.63)

The integration in Eqns 13.62 and 13.63 is to be performed over the body and wake surface. The expression d/dn in Eqn 13.63 is the derivative in the direction normal to the surface.

The total perturbation potential cp(Q) at point Q is given by the sum of the potentials cps and cpD:

<P(G) = <Ps(G) + <PD(Q) (13.64)

It is worth while noting that, with ground simulation through the image technique (see section 13.7.6), every body and wake point has a counterpart in its image below the ground. Each of the terms in Eqn 13.64 is thus to be interpreted as a sum of the contributions from a point and its image counterpart.

The resultant flow^ around the vehicle is obtained by superposing a uniform onset flow ^ ( ÷ , í , æ ) and the perturbation flow defined by o(SB) and ì(5\í)· In ref. 13.8, the flow tangency condition is applied on both body and wake surface. The wake surface geometry was evaluated by means of smoke visualization in a wind tunnel. This provided a better basis for assuming the wake surface to be a stream surface (see section 13.7.7). Considering a point q on the body surface, the flow tangency condition implies that the normal component of the perturbation velocity there just balances the normal component of onset velocity; i.e.

grad Mq)]n(q) = -%X(q) (13.65)

Substituting for ö(#) from Eqns 13.64, 13.63 and 13.62, it follows that

grad Ý#^+Ü#^>Ý(4-Η"<<> = ~Voon(q)

The source and doublet strength functions o(SB) and ì(5\í) are unknown, so that Eqn 13.66 is non-linear. This equation links the unknowns ó and ì with the known body and wake surface geometrv expressed through the surface normal vector n. The onset velocity field Voo(x,y,z) is also known.

13.7.8.1 Numerical solution procedure

For the numerical solution, the continuous body and wake surface is replaced by flat quadrilateral or triangular area elements called panels (Fig. 13.9a). The source or doublet strength over the area of a panel is assumed constant. Consequences of this approach are: (1) through surface discretization, the surface integration in Eqn 13.66 is reduced to evaluation of a finite number of integrals, one for each panel, and (2) since ó and ì are


set constant over a panel surface, these can be taken out of the integral and the term becomes linear.

If m panels are used for the body and n panels for the wake surface discretization, then the integrals in Eqn 13.66 can be expressed as

sB sf

id

sw s,

Introducing the abbreviations

Xj = ó;·/(4ðí„)

Yj = IV(4OTV.)

(13.67)

dSj (13.68)

Aqj [-grad dS,]n(q) (13.69)

ß, <u - [ - f^(vH **>� Eqn 13.66 reduces to:

2 XjAqj + 7 = 1

y A ; ~ <7 (13.70) 7 = 1

Equation 13.70 is a linear algebraic equation expressing the flow tangency condition at point q. Xj and Yy express in dimensionless form the source and doublet strength of panel y. Aqj and Bqj can be interpreted as the normal component of the induced velocity at point q by a singularity distribution of unit strength placed on panel/. Aqj and Bqj are often termed the 'influence coefficients'. Repeated application of Eqn 13.70 to satisfy the flow tangency condition at m body and n wake surface control points leads to the linear system of (m + n) equations:

Α\\,Α12 --Aim A2\, • ••A2m

,Βιι,Βγι -Bin , # 2 1 , . . · #

1 ml> ^ ( m + l ) l ^ ( m + l ) m >^(m + l ) l

1 ( m + n ) n)l —A (m+n)m ?^( ra+/ i ) )1 · · · # !

1« 2n

mn

(m + l)n

(m + n)n

x2

Xm Yi

_Yn_

L

~Rx º Δ 2

Rm R(m + l)

R(m+n)\

(13.71)

Standard procedures, such as the Gauss-Seidel and Gauss-Jordan iteration schemes are employed to solve the equation system (13.71). With the


singularity strengths Xj and Y, known, the perturbation potential at a surface point is evaluated from Eqns 13.67, 13.68 and 13.64.

Since the singularity strengths Xj and Yy were determined by satisfying the flow tangency condition, the vector sum of perturbation velocity vp(q) = grad ö (q) at a control point q and the onset velocity V«, gives the tangential velocity at q. Using the Bernoulli equation, the pressure can now be evaluated. The force acting on a panel is then the product of this pressure (taken to be constant over the panel) and the panel area. The forces and moments acting on the body are given as the sum of those acting on the individual panels.

13.7.8.2 Examples of vehicle flow computations using the panel method

Ahmed and Hucho13 8 used the panel method to compute the inviscid flow around an idealized van. The theoretical simulation of both the body and the wake surface is simpler for this type of vehicle than a normal passenger car.

A quarter-scale wind tunnel model of the van was equipped with pressure taps and tested in the 7.5 by 5 metre wind tunnel of the Volkswagen AG at a model-length-based Reynolds number of 2.9 x 106. All external surface details, such as headlights, bumpers, mirrors, window pockets etc. were removed and the surface smoothly faired. The wheel cavities were also filled and the underside was flat. Wheels were used to fix the model on a ground board. The numerical model in the panel method simulated the body and wake surface at the same height above the ground as the wind tunnel model. Not simulated were the wheels and the flat base surface covered by the wake. Cross-wind effects were investigated by yawing the uniform onset flow in the theoretical model. A total of 1652 panels was used to describe the body and the wake. The wake surface was modelled only up to one vehicle length behind the vehicle base. The results obtained showed that the errors caused by ignoring rest of the wake surface were insignificant.

Instead of simulating the ground by image technique as described in section 13.7.6, it is also possible to simulate the ground surface by 'panellizing' it and satisfying the flow tangency conditions on a road surface. A sufficiently large road area, ahead, behind and laterally, must be chosen to minimize the road area edge-interference effects. The advantage of this type of model is that the pressure distribution on a road surface can also be computed; see Fig. 12 of ref. 13.8.

Figure 13.10 illustrates the surface discretization used and the velocity distribution on the surface of the van obtained by computation for zero and non-zero cross-wind conditions. The length and orientation of the line segments corresponds to the magnitude and orientation of the velocity vectors. A stagnation region at the blunt front end, and high velocity at regions where front, side and upper surface blend together are visible. With cross-wind present, the stagnation region is shifted windwards, causing high velocity on windward-facing roof and side flank edges. Flow over the roof aligns itself mainly with the onset flow.

An impression of the accuracy of the numerical prediction is conveyed by the results shown in Fig. 13.11. As the numerical model is applicable

509

Figure 13.10 (a) Surface discretization of vehicle surface, and (b) computed velocity distribution on vehicle surface without and with cross-wind (â = 20°), after ref. 13.8


lection MM

105 96 96 105 115

Figure 13.11 (a) Pressure distribution on VW van, longitudinal section without cross-wind, (b) Pressure distribution in longitudinal and horizontal sections with cross-wind (ß = 20°). (c) Pressure distribution in a transverse section AA, after ref. 13.8

only for attached flow, the pressure distribution on the van base, which is immersed in the separated flow of the wake, cannot be predicted. Considering the no-cross-wind situation (ß = 0°, Fig. 13.11a), the numerical and experimental results are in good agreement, except in the stagnation region and near the vehicle base. The deviation in the vicinity of the base is mainly due to inaccurate representation of the wake. The wake geometry was determined from photographs by illuminating the smoke-filled wake in the wind tunnel. Only a mean side and plan view of the wake was determined by this method.

Experimental results for flow with cross-wind represent a critical test for the theory as, under yaw, in addition to the flow separation at vehicle base, separation occurs also over parts of leeward surface. As was to be expected, a large discrepancy between computation and experiment is to be seen in the pressure plot of the horizontal section (Fig. 13.11b) and in


the transverse section AA (Fig. 13.11c). However, the pressure prediction on the windward side of these sections agrees closely with the experiments.

Using the same methodology, the inviscid flow field around a Mercedes C-lll research prototype car was computed by Ahmed.139 A surface geometry simulation of the vehicle, shown in Fig. 13.12 and employing

Figure 13.12 Mercedes C-lll research vehicle and its surface discretization, after ref. 13.9

1826 panels, exhibited the surface velocity distribution of Fig. 13.13. The pressure distribution shown in Fig. 13.14 for a tapered rear end version of the vehicle shows poor agreement between computation and experiment on the underside. Visualization of flow between model underside and ground plane showed extensive flow separation in the diffuser region formed by the rear of the model and ground.

An impressive demonstration of the complex surface details which can be handled by the panel method is illustrated in Fig. 13.15, which is due to Strieker.1310 Surface discretization of this type is conveniently realized in an automobile manufacturing environment, where refined computer aided design systems (CAD) are available to design complicated surface geometries. As panel methods in principle place no restrictions on surface geometry, very realistic vehicle shapes, with the ensuing computer storage and time requirements, can be simulated. However, one has to bear in mind that the computed flow is an inviscid one; detailed reproduction of surface geometry is meaningful only as long as attached flow can be expected. Figure 13.15 illustrates the isobar plots for pressure on the vehicle surface for the zero cross-wind situation. Road surface has been modelled by fulfilling the flow tangency condition on its surface.

Losito et al.13·11 report results of panel method calculations for real shape car bodies and comparison with full-scale wind tunnel tests. The numerical model was without wheels, wheel arches, bumpers, mirrors and other surface projections. The underside of vehicle was a smooth plane surface. The complete surface of the body, i.e. including the base surface, was panellized. The numerical model was thus that of a closed body. Wind tunnel tests on full-scale configurations were done without engine and

Side

vie

w

Fron

t vi

tw

..^

^

v V

\

\

M\\

fM\

HI

^^

itip

-p^

ÃÃ

Ð,

I'

ll,

,

»Wif

e

Plan

vie

w

2 V

/V

Fig

ure

13.1

3 C

ompu

ted

velo

city

dis

trib

utio

n on

a M

erce

des

C-1

11 v

ehic

le, a

fter

ref.

13.9


Figure 13.14 Comparison of numerical and experimental results, three-dimensional panel method; Mercedes C-lll vehicle, after ref. 13.9

passenger compartment flow present. Fig. 13.16 illustrates a typical result for a Fiat 124 passenger car under cross-wind flow conditions (ß = 15°). The nature of agreement between computed and experimental results is very similar to that already observed in Figs 13.11 and 13.14. The effect of 'closing' the body at the base leads to the sharp pressure peaks predicted at the base edge in the plane of symmetry and horizontal section. Also the computed base pressure, as was to be expected, bears no resemblance to the experimental results.

The application of the panel method to evaluate interference effects between two vehicles in the overtaking mode is investigated in ref. 13.8. The non-steady process has been treated as quasi-steady in the theoretical model. At two stages during the overtaking process, the pressure


Figure 13.15 Surface discretization and computed isobars on a passenger car, after ref. 13.10

distribution on the inside flank of the overtaken vehicle is shown in Fig. 13.17. As the overtaken vehicle is approached, it experiences an anticlockwise turning moment about the vertical axis. When both vehicles are abreast, they are drawn towards each other.

A higher order panel method was applied by Stafford13 12 to a vehicle configuration to evaluate the flow field. The merits of using fewer panels with this scheme is coupled with the penalty of the complex numerics involved; this may, in adverse cases, obviate the advantage.

13.7.9 Non-linear inviscid flow methods

13.7.9.1 Solution of the Euler equations for incompressible flow

The main inadequacy of the inviscid incompressible (potential) flow treated in the previous section is that regions of separated flow, for example at the base of a vehicle, cannot be simulated. Also longitudinal vortices, which form at the A-pillar or at the side edges of the slanted base, are not predicted. To incorporate these real flow features in potential flow methods, at least kinematically, a phenomena modelling approach has to be employed. This may, for example, consist of discrete or distributed singularities, so arranged as to generate kinematically the flow in the 'separation' region. Plausible boundary conditions, derived from real flow physics, need to be imposed on this arrangement of singularities, whose strength and location in space can then be determined iteratively. The difficulties involved in this approach are the definition of proper boundary conditions, and advance knowledge of where and what type of phenomena modelling should be resorted to.

An interesting alternative to phenomena modelling is to consider the formation of the separation region (wake) as a time-dependent process.

O ·

ß

= +1

5°

Ä

Á

â=

-15

° •

A

me

asu

red

O

Ä

com

pu

ted

Figu

re 1

3.16

Com

paris

on o

f thr

ee-d

imen

siona

l pan

el m

etho

d re

sults

with

full-

scale

win

d tu

nnel

test

s; F

iat 1

24 p

asse

nger

car

, afte

r ref

. 13.

11


- 3 . 0 T

-£ÎÎ3-

30 35 40 £5

-3.0

-2.0

-1.0 \ A ) I l/j I I 1— =^-

C -f

ÜT.!_-!

2

" 1 -

u-i_J

I I_

15^/20 30 35 40 45 Ô-1—^ PressureTapNo.

Figure 13.17 Variation of pressure on side flank of a vehicle during overtaking; VW van, three-dimensional panel method, after ref. 13.8

This method, proposed by Chometon,13 13 is based on the solution of the Euler equations for an incompressible, inviscid and unsteady flow (Eqn 13.17). The pressure terms in equation system 13.17 are eliminated by differentiating, for example, Eqn 13.17a with respect to y and Eqn 13.17b with respect to x. Subtraction of the two equations gives results in an equation free of pressure terms. Proceeding in a cyclic order with all three equations (13.17a, b and c), three further equations are obtained, which contain only terms of velocity components w, v and w. With rearrangement of the terms and introduction of the vortex vector

W = curl V

which, from Eqns 13.19 and 13.20, can be expressed as

3v \ . / du dw\ I dv du

dy dz I \dzdxl \ dx dy

one obtains the Euler equations as in ref. 13.13:

W = il¥-

—+(V-V)W- (W-V)V = 0

(13.72)

(13.73)

(13.74)

Together with the continuity equation (Eqn 13.18), this system of equations represents a purely kinematic expression containing only the components u, v and w of the velocity vector V. The boundary conditions which are imposed on the solution of Eqn 13.74 are

V-n = 0

and Vx for r � (13.75)


where n denotes the surface normal vector, the velocity vector of the undisturbed flow, and Û the position vector. Physically the boundary conditions imply that the flow is tangential to the body surface, and the flow perturbation disappears as the distance away from body increases (see section 13.7.6).

The technique employed for solving Eqn 13.74 is, starting from an initial solution (which can be obtained by the panel method—see section 13.7.8), to obtain subsequent solutions after small time steps of At. To account for wake flow, for example at the side edges of the slanted base of a fastback

5 Steps

10 Steps

15 Steps

Figure 13.18 Wake simulation in inviscid flow. Development of wake after various time steps, after ref. 13.13: (a) 5 steps, (b) 10 steps, (c) 15 steps


car, vortex filaments are emitted from an assumed or known line of separation. As the time-stepping progresses, the length of the emitted discrete vortex filaments increases and these distort, due to the boundary conditions imposed, to form trajectories that show similarities to those observed in real flow. More details about how the strength of these vortices is determined and the discretization procedure are given in ref. 13.13.

Figure 13.18 depicts results obtained by Chometon on a Renault R20 automobile. The body surface was discretized by 375 plane panels, each overlaid with a dipole distribution, which is equivalent to the arrangement of a vortex filament around the panel periphery.

The separation line was assumed to be the perimeter of the rear end with the exception of the roof rear edge. Along this line, vortex filaments are emitted, which grow in length with each time step. Figures 13.18a, b and c show the development of the side edge vortex and the 'shear layer' roll-up at the lower edge of the vehicle base after 5, 10 and 15 time steps.

-�— Experiment

D 15 Steps

Ä 20 Steps Theory [13]

0 2.0

SECTION 2

-J I 1 L

[ I I I I I

I ^ — '

Γ SECTION 3

L. i i i , i i

' 9

Hi i.,,., ,J 1

A1 Pr. Tap No. A9 A1 Pr. Tap No A9 Figure 13.19 Comparison of computed and measured velocity on the slanted base surface, after ref. 13.13


Velocities computed on the slanted base surface with this technique are compared with experimental results in Fig. 13.19. Fair agreement is obtained in the mid area, becoming increasingly poor as the side edge or the trailing edge of the slant surface is reached. As visible in Fig. 13.18, with progressively increasing time steps and the coiling up of the vortex filaments, the stability of the numerical technique employed is endangered. Chometon mentions the introduction of a 'viscous core' concept to avoid these difficulties, which are an inherent characteristic of wake roll-up techniques employing discrete vortex filaments.

As shown in Fig. 13.18, the rear end surface of the vehicle is also represented. However, base pressure results obtained were, according to Chometon, not satisfactory.

13.7.9.2 Solution of the Euler equations for compressible flow

A promising feature of the non-linear inviscid methods being developed for aeronautical use is claimed by the developers of these codes to be the inherent ability to simulate regions of 'separation' such as those mentioned above. The governing equations for these methods are the inviscid compressible Euler equations in the time-dependent form.13 14 These are a system of non-linear partial differential equations of hyperbolic type.

Regions of separation in real flow are characterized by a non-zero value of circulation. The mechanism of generation of circulation in the solutions of compressible Euler equations is explained as follows13 15 (see also ref. 13.16).

The marching coordinate for solving the time-dependent Euler equations being the time t, the procedure involves a number of time steps. After this transient phase, a converged solution is obtained, which is accepted as that describing the steady state. During the transient phase, the inviscid compressible flow creates a shock, with an accompanying entropy production, at sharp corners or at points where abrupt contour changes take place. This entropy production generates flow kinematics bearing strong similarity to that observed in separation regions of real flow.

Another explanation, also offered elsewhere, is that to make the underlying system of equations numerically stable, 'artificial viscosity' terms are introduced in the codes which are in current use. These then produce the observed circulation.

It is unclear however how far, with the introduction of these terms, the governing equations can still be termed Euler equations and whether their hyperbolic character remains unchanged. Even if the introduction of artificial viscosity is so conditioned that it is effective only during the transient phase and its influence diminishes with the solution converging to steady state, it must be made clear what system of equations is being solved to start with, and what effect a progressively changing governing system of equations can have on the final solution.

These considerations may be of less interest to users primarily concerned with the actual predictive capability of these codes. Bearing in mind that the codes treat air as being compressible, the question arises, from the viewpoint of a vehicle aerodynamicist, how these methods could be applied to the very low Mach number flows. Progressive decrease in Mach number


invariably leads, in the existing codes, to analytical and numerical difficulties (see ref. 13.17). To circumvent these, it may be necessary to introduce artifices such as 'artificial compressibility' terms. The impression one gains is that, even though these approaches signal significant advances in computational fluid dynamics as far as aeronautical applications are concerned, the physics involved is not sufficiently understood to enable a straightforward extension to the incompressible, separation-dominated vehicle flow fields.

An example of a two-dimensional Euler equations solution, of interest to vehicle aerodynamicists, is that of a backward facing step, reproduced from the work of Schmidt et al.1 3 1 5 in Fig. 13.20.

M = 0.50

Figure 13.20 (a) Streamlines, and (b) velocity distribution for a backward-facing step. Two-dimensional Euler equation solution results from ref. 13.15

The velocity vector plot for the Mach-number of 0.5 clearly indicates a region of separated circulatory flow behind the step—as is commonly observed in a real flow. A comparison with experimental data, especially for very low values of Mach number, is not available. The results of Fig. 13.20 are thus essentially of a qualitative nature. Three-dimensional solutions for Euler equations around vehicle bodies have not yet been published.

Coupled inviscid flow—boundary layer methods 521

13.8 Coupled inviscid flow—boundary layer methods

The classic approach when considering viscous effects in attached high Reynolds number flow is to view them as confined to a thin boundary layer in the vicinity of body surface. The governing equations for the flow in this layer are the so-called boundary layer equations, which represent a simplification of the Navier-Stokes equations (see ref. 13.1). Outside this viscous layer, the flow is considered to be inviscid. The main effect of the viscous boundary layer is a retardation of the flow in surface proximity, with the velocity becoming equal to zero on the surface itself ('no slip' condition). Compared to the inviscid flow around the body, the boundary layer in the real flow appears to displace the inviscid flow outwards and away from body surface.

The usual approach is first to perform an inviscid computation for the flow on the body surface, using, for example, the panel method. The pressure, velocity and streamline data obtained on the body surface is assumed to exist slightly above the body surface, i.e. outside the boundary layer. With this as input, a boundary layer code is employed to compute the boundary layer and displacement thickness. Using an equivalent source or displacement thickness concept to account for the boundary layer, a new inviscid calculation is then done. This iterative process is repeated till no significant change in the computed boundary layer values is present.

However, the artifice of equivalent source to create the boundary layer displacement effect is preferable, in the attached flow regime, to the displacement thickness concept, because the latter involves a new geometry generation after each iteration step in the panel method program and consequently more computational effort. The equivalent source concept involves the arrangement of a source distribution on the body surface which is so determined that it 'pushes' the inviscid flow away from body surface by an amount equal to the local displacement thickness.

Subdivision of the flow field into a viscous boundary layer and an inviscid flow region implies a weak interaction between the two flow regimes. This may be justified in regions of attached flow and weak transverse flow gradients, but is inadequate in the wake region of a vehicle flow field. Losito et al.13,11 have applied a simplified approach when considering the boundary layer effects on a car body. Instead of using a three-dimensional boundary layer code, they apply a two-dimensional boundary layer method along three-dimensional streamlines obtained through an inviscid (panel method) calculation.

Investigation of integral and finite difference methods of calculating the boundary layers in ref. 13.11 show that, even though the displacement thickness obtained by both methods is about the same, momentum thickness and friction coefficient are generally overestimated by the integral methods. Losito et al. state further that, with their approach, realistic prediction of separation was possible only by using a finite difference scheme for the boundary layer calculations. An illustrative example of this effect is shown in Fig. 13.21 for a Fiat 124 car.13 n The separation line predicted by the finite difference scheme agrees with the experimental results, whereas the integral boundary layer method indicates a more downstream location of the separation line.


Streamlines

Isobars

SEPARATION LINES

EXPERIMENTAL

— * - COMPUTATIONAL INTEGRAL METHOD —o— COMPUTATIONAL F D METHOD

Figure 13.21 Potential isobars and streamlines—computed and experimental separation lines for a Fiat 124 (top view), after ref. 13.11

Figure 13.22 Schematic of body surface coordinates xa (a = 1,2), and Cartesian reference coordinates x1' (/' = 1, 2, 3), after ref. 13.19

Bretthauer13 18 and Hirschel13 19 applied a three-dimensional turbulent boundary layer integral method to evaluate the boundary layer develop-ment over simplified ground vehicle type bluff bodies. Figure 13.22, reproduced from ref. 13.19, illustrates schematically the surface discretiza-tion and the body-centred coordinate system used, which is described in more detail in ref. 13.20.

Figure 13.23 shows the distortion of the surface streamlines (dotted) caused by the boundary layer for the automobile-like body.13 19 The tendency of the flow to separate is indicated by the convergent behaviour of the (dotted) streamlines on the upper rear end surface. It is important to

-1.1

9 I

1 1

1 1

1 1

1 r

0.0

0.34

0.

68

1.02

1.

36

1.70

2.

04

2.38

2

72

3.06

3.

40 m

3.7

4 4.

08

Figu

re 1

3.23

Stre

amlin

es a

t the

edg

e of

the

boun

dary

laye

r (

) and

on

the

body

surfa

ce (

),

afte

r re

f. 13

.19


Section

Section E Section F

/ /

if

1 1 J

ll li

/ / ^

2' / V^"^

\ \ T "

D.05-

loj-^ — ^ [m]j

5

l x 3 '

/ l

\

ΓÇ&

" " Ί ' — º -0.05

B /

-0.1

[mj

«1

Figure 13.24 Distribution of computed boundary layer ä and displacement thickness oj over the body contour, with and without ground, after ref. 13.19

note that, since the wake at the vehicle base is not simulated, an interaction between wake flow and body flow is not considered in the flow calculation. Thus a separation line, evaluated as the locus of points where the wall friction tends to zero, may not represent the actual situation of a real flow. The results obtained serve as a guide to localize regions of flow separation.

Also shown in Fig. 13.24 is the effect of the ground on boundary layer development. Mainly the rear part and undersurface of the body are influenced by the presence of the ground; a thicker boundary layer is computed on the undersurface with ground simulated. A bulge near


0.12

m

0.10

0.08 h

0.06

0.04

0.02

x3'·

^ ^ x 1

Ö

I

I 0

oo IJ-U

I ®

>

^ã

x ' = , /

X 2 : 0

cor � exp

► Ö

np. ).

(2 = const

m π^ ~ i

;

I

Ö ! I 1

1 stparation 1

1 1 0.2 0.4 0.6 0.8 1.0

Figure 13.25 Measured and computed boundary layer thickness on the body upper surface, in the plane of symmetry, after ref. 13.19

roof/side flank and side flank/undersurface edges indicates a separation tendency with vortex formation.

Figure 13.25 illustrates a comparison of the computed boundary layer thickness with the experimental data obtained on a full-scale wind tunnel model. Computations were done for a body length based Reynolds number of 9 million. Experiments done in the Reynolds number range of 7.5 to 12.6 million were corrected to correspond with the computations using the 1/7 power law representation of the boundary layer velocity profile. The theoretical boundary layer thickness results agree reasonably well at three stations on the upper surface centre line, but deviation is noticeable at the foot of the windscreen. Some explanation of this behaviour is offered in ref. 13.19.

Losito13,11 and Hirschel13 19 have attempted to calculate the total drag of the vehicles they considered by making simple assumptions about the base pressure in the region of separated flow. The results are however to be considered as of a preliminary nature.

An improvement on the approaches discussed above has been proposed by Summa and Maskew.13 21 A panel method is iteratively coupled with an integral boundary layer code. The wake at the vehicle base is simulated by enclosing it with a doublet sheet in a similar fashion to that done by Ahmed and Hucho in ref. 13.8. The wake surface emanated from an assumed separation line on the body surface. The shape of this wake surface is determined iteratively by requiring it to be a stream surface. In the actual


Figure 13.26 Surface discretization and wake simulation for a Porsche 924 vehicle, after ref. 13.21

computation, the wake surface is left open after a certain downstream length; this is stated to have little effect on the results.13 8 The boundary layer displacement is accounted for by the previously mentioned technique of 'equivalent sources' placed on the surface.

Following the panel method solution, the surface streamlines are traced from the computed surface velocity distribution. The boundary layer is calculated along each streamline, first as laminar and then, after transition, as turbulent. Turbulent boundary layer separation on a given streamline is

-2 h

-1 h

o h

1 u

300

-100 100 200 300 £00 500

Figure 13.27 Comparison of numerical and experimental pressure distribution in the plane of symmetry for a Porsche 924, after ref. 13.21


predicted when the value of skin friction reaches zero. The location of the separation line is considered to be the locus of these separation points. As the iteration proceeds, the location of the separation line may shift, which means that the location of the doublet sheet representing the wake has to be adjusted accordingly.

The results obtained in ref. 13.21 for a simplified Porsche 924 automobile are shown in Figs 13.26, 13.27 and 13.28. The surface

-1.50-1

-1.25

-1.0(H

-0.75H

-0.50

-0.25-I

X = 223.7

-1.0

-0.8 H : p

-0.6

-0.4

-0.2

120

100 7

80

60

40

2 0

-40 -20 0 20 40 60 80 100 y

X = 368.0 Figure 13.28 Comparison of numerical and experimental pressure distribution over the body contour at two transverse sections of a Porsche 924 vehicle, after ref. 13.21

-

-

-1 T

/ " 1

"T

""â

1

T *L? 1 r ^^m<r^

1

_Ù _J * "v

1

V i

^ ^ Ί

BODY VCON

'

TOUR

l - !


discretization and wake representation of the vehicle is depicted in Fig. 13.26; in all, 314 panels were used on the half-body and 156 panels on the wake. Ground simulation was provided by the image technique. Wheels and surface details were not represented in the numerical model. The rear end of the body, as indicated in Fig. 13.26, was also discretized, so that a pressure prediction on this surface, wetted by the wake, is in principle possible. The wake geometry was prescribed in the computations.

In Fig. 13.27 the computed pressure distribution in the longitudinal central plane is compared with full-scale experimental results. Except for a slight underestimation of peak suction at windscreen/roof junction, the agreement is good, especially so in the vicinity of the rear end. No experimental results are available for the body undersurface. The experimental results indicate that over the body centreline attached flow prevailed up to the rear end, which may, at least in part, be responsible for the close agreement obtained.

Figure 13.28 illustrates the comparison of the predicted pressure distribution and experimental results over two transverse sections. Here again the agreement between the two results is exceptionally good.

Good results obtained by the method of ref. 13.21 for the Porsche 924 vehicle, as the authors also state, are not necessarily representative of other vehicle shapes. More refinement of wake simulation is needed to improve the prediction capability of this promising approach.

13.9 Methods based on solution of Navier-Stokes equations

The Navier-Stokes equations (see ref. 13.1) for a homogeneous, incompressible medium, together with the continuity equation, can be used to describe adequately the laminar flow around a road vehicle. As these equations represent, in principle, all the physics involved, no additional assumptions and modelling, as in the methods of preceding sections, are needed.

However, the flow around actual road vehicles is mainly turbulent, and Navier-Stokes equations for turbulent flows need a turbulence 'model', to make the system of equations amenable to numerical analysis. The basic equations employed are averaged over a time interval. This interval is chosen so as to make the equations independent of the random eddy fluctuations, yet permit a resolution of the unsteady macro-structures which may be present.

The main problems encountered are of turbulence modelling and of finding a suitable numerical solution scheme. Much attention is currently devoted to the modelling of turbulence but models of sufficient generality and applicable to complex flows—such as around bluff vehicle type bodies—are not yet available.

The method often used to solve the Navier-Stokes equations in aeronautical practice is the finite difference technique. According to this approach, the Navier-Stokes equations are discretized in a domain around the body into a set of finite difference equations. The flow region itself is partitioned by overlaying it with a cartesian grid. In this grid the solution of the discretized equations is sought iteratively through standard solution

Methods based on solution of Navier-Stokes equations 529

techniques. The irregular shape of a road vehicle does not allow proper representation through a rectangular grid, so that in the numerical representation the grid lines cannot be made to coincide with the body contour and consequently the surface of the vehicle is serrated. Obviously this is a drawback. As is well known, seemingly insignificant surface details can trigger major changes in the overall vehicle flow field. To improve the body surface representation, a special treatment of the near-wall flow region is therefore necessary.

Haase13 22 used the finite difference technique to solve the laminar steady Navier-Stokes equations for the flow around a basic road vehicle like body. His results, quoted in refs 13.10 and 13.16, are reproduced in Figs 13.29 and 13.30. Figure 13.29 illustrates the grid of 55 x 25 x 35 (=48125) points arranged in one half of the cartesian computation domain around the vehicle. To achieve sufficient resolution a denser grid is employed near the body surface, in regions of high curvature and in the

+ � + � t - f l l l l l t + t - H I H M M t t t l l tHMHHHH + + + + � � + � -�� +

Figure 13.29 Computational grid for the laminar three-dimensional Navier-Stokes equations solution, after ref. 13.22

Figure 13.30 Velocity distribution in the plane of symmetry; solution of three-dimensional laminar Navier-Stokes equations, after ref. 13.22


wake. This density of the grid needs to be retained over the computation domain, even when a finer resolution of flow details further away from body surface is not of prime interest. The demands on computer storage and time are consequently high.

Figure 13.30 depicts the velocity distribution obtained in the longitudinal central plane. Retardation of flow in the vicinity of the base and the formation of recirculation zones are visible. The region of retarded flow behind the vehicle is apparently much longer than that observed in real flow (see ref. 13.23).

Demuren and Rodi13 24 presented a finite difference solution of the three-dimensional, turbulent, time-averaged steady Navier-Stokes equa-tions for the flow over an idealized notchback type of vehicle. (Results of a two-dimensional calculation for a fastback type of vehicle are also presented in ref. 13.24. The authors state that comparison of the numerical results with measurements at the central plane of a three-dimensional model show that essential features of the flow are not captured by a two-dimensional treatment of the problem.) The method uses a cartesian grid so that the inclined vehicle contour is approximated by steps (Fig. 13.31). Closure of the system of equations was obtained by using the k-z turbulence model of Rodi1325 (see also ref. 13.26). The car half-body

\{ ' ' ' ' '/ ' / '. ' ' ' ' / ' ' ' ' '

Distances in meters

Figure 13.31 Body contour discretization with a Cartesian grid; solution of three-dimensional turbulent Navier-Stokes equations, after ref. 13.24

considered is enclosed in a box-like computational domain. This consists of top, side and bottom 'wind tunnel walls' as well as an inflow and outflow plane. Together with the plane of symmetry, boundary conditions are specified for the dependent variables in these six planes. As mentioned above, due to the step-like numerical representation of the body surface, a special wall-function procedure is employed for the near-wall region. More details of the boundary conditions imposed are given in ref. 13.24. The computational grid had 45 x 26 x 17 (= 19 890) points distributed in the x, y and z directions.

Figure 13.32 presents results of the computed velocity distribution,13 24

in three x-z planes. The enlarged representation of the computed flow in

531

y/b = 0

z 1.6 4

-5

y/b = 0.30 3,0 m/s

*3.2 m/s

Z

1.6

-i 1 1 1 1 r

-1 X

y/b = (U5

Figure 13.32 Velocity distribution in longitudinal planes; solution of three-dimensional turbulent Navier-Stokes equations, after ref. 13.24


the plane of symmetry shows separation from the roof and the boot rear edge. A circulatory flow region forms over the boot and another, with the same sense of rotation, behind the upper edge of the flat base. The reverse flow obtained on the upswept rear undersurface is probably incorrect. The length of the separation bubble at the vehicle base, at both stations ylb = 0

1 2 3

t t f / / / / / / -� / / / / / / / / U / / / / / / x

«IΔ«=2

/

~^

2 r

1m& 1 x'/L.-O.ÖZ" x'/L = 1.02 1

f f / / / / / X X A \ f / / / x ^ s \ \ f f/ / ^ ^ ^

= S ^ : ^ S

^ χ ^< —

>te-^-^Z-^Z. — |

Y

^

_

-

\\i / / / / / / \\l / / / / / y

l / //ss / y 1 / Sr~- / y 1 / yzz^y ^ lim~ I s / N -

/ y y * y

^ ^-^

— Zi ~z

y

s y

^ ^ *r~

^ ~-n - ~ i

x ' /L = 0.33 I x'/Lx1.29

M / / / / / / \\ / / / / / y *

- -^ * >

Γ

t » ' * * ' '

>- f ß f 0 0 * »

I / - - - - >

A \ 'ft \ ^ - I v y / » - -

i Ξ 2 ί ί i ί

> 0

0

0

»

_c

* 0

0

0

+

;

# ß

0

Λ

-.

: i

| xVL.rO.5A | I xVL=1.8A |

Figure 13.33 Cross-flow velocity distribution in various transverse planes; solution of three-dimensional Navier-Stokes equations, after ref. 13.24

http://xVL.rO.5A

Methods based on solution of Navier-Stokes equations 533

and 0.3, appears to be the same, indicating a weaker simulation of three-dimensional effects in the lateral direction. Also the flow near the rear window, at station ylb = 0.45, deviates from the real flow behaviour (see ref. 13.23).

The series of results shown in Fig. 13.33 (reproduced from ref. 13.24), illustrates the macro-structure of the cross-flow developing around the vehicle. Outward displacement of the flow in the front sections and formation of vortices on the side flank up to xll = 0.54 can be observed in the velocity vector plots. The transition of the cross-flow downstream of this station cannot be inferred from the data presented.

Using a finite difference scheme developed by Patankar and Spalding,13 26 Markatos13'27 computed the flow field around a vehicle body of notchback type. The iterative solution procedure used to solve the time-averaged Navier-Stokes equations for steady flow is similar to that of Demuren and Rodi.13 24 The results presented by Markatos, with only 15 x 9 x 25 (=3375) grid points in the computation domain, serve mainly to demonstrate the basic capability of the approach. A sample result, Fig. 13.34, shows the pressure isobars, computed at a y-z plane just

® Figure 13.34 (a)Computation domain and (b) isobar plot for a notchback vehicle; solution of three-dimensional turbulent Navier-Stokes equations, after ref. 13.27


downstream of the body. Some qualitative similarity to the real flow situation can be observed.

The results obtained by the solution of Navier-Stokes equations, as shown in Figs 13.30, 13.32, 13.33 and 13.34 show that the macro-structure of the complex three-dimensional turbulent flow around a car-like body is qualitatively correctly simulated. Separation and the formation of longitudinal vortices is indicated and bears similarity to the phenomena observed in real flow. Due to lack of available data, it is difficult to make a statement about the quantitative accuracy of the prediction but it does not seem to be very high. Inadequacies of the turbulence model, the coarse grids used, inaccurate representation of body contour, inadequate boundary condition in the near-wall region, and other factors, lead to results which differ, even qualitatively, from real flow behaviour. Both Demuren and Markatos note that the numerical accuracy of the results or the results themselves may vary with grid refinement.

Results for vehicle flow fields, using time-dependent Navier-Stokes equations, are not available in the open literature. Computations employing the finite volume technique have appeared since the time of writing: see refs 13.28,13.29.

13.10 Concluding remarks Many of the numerical methods treated in the preceding sections are used routinely as design tools in the aerospace industry. Similar success has not yet been achieved in their application to the computing of vehicle flow fields. No calculation scheme is presently available which can both qualitatively and quantitatively describe the real flow field around even a basic vehicle-type body. One of the reasons for this was the less pressing need in the past, on the part of automobile manufacturers, to apply these techniques in the design of automobiles and utility vehicles. On the other hand, aerodynamicists engaged primarily in design of aircraft had sufficient margins in shape design to avoid or minimize separation and thus were less concerned with the physics of such flows. The majority of the computational techniques developed for aeronautical use are based on the premise of attached flow.

Linear inviscid flow methods, such as the panel method, very often constitute the first step in the computation of a vehicle flow field. The main advantage of the panel method is its extreme flexibility to represent complicated and realistic body geometry with relatively modest effort. At present this capability is unsurpassed by other numerical methods. The computation effort is, compared to other techniques, also small. One of the main reasons for this is that only a discretization of body surface is needed in the panel method approach. As often pressure and velocity distribution on body surface alone are of interest, the computational effort is directly related to this objective. In other methods, such as solution of Euler and Navier-Stokes equations, the whole flow domain around the body has to be discretized. The solution delivers a large amount of data, even for regions far away from body surface. In a parametric design study, the computation of this far field, which is of less interest, amounts to a penalty.

Concluding remarks 535

The major limitation of the panel method is that it can simulate only attached flow. Separation, at least kinematically, has to be considered by phenomena modelling. This involves a vast experimental basis to model correctly the separated flow macro-structure, for example in the wake of a vehicle. As the panel method does not compute the pressure in the separated flow regime, prediction of the pressure drag is not possible. Unless suitable modelling is employed in the computation scheme, interaction effects, such as between attached flow and the wake, remain unconsidered. A reasonable prediction of lift experienced by a vehicle is,however, possible by the panel method even in the absence of a refined separated flow modelling.

On a short-term basis, the coupled panel method/boundary layer computation schemes combined with refined phenomena modelling of the vehicle wake have the chance of maturing into cost-effective design tools. Much of the success of this approach depends on how well the vortical and 'separation bubble' type of wake phenomena are modelled.

The status of the boundary layer computer codes currently available is that they fail near the region of flow separation. Lines of flow separation can be determined only approximately in view of the complex nature of three-dimensional flow. The flow data at these 'separation' lines is of some help in modelling the separated flow regions. In the attached flow regime, the boundary layer computations enable an estimation of the friction drag. However, for vehicle-type bodies, this accounts for only a small portion of the total drag. The more realistic surface streamlines resulting from such a calculation are helpful in proper location of ventilation vents and in the analysis of rainwater flow, dirt accumulation etc. on the vehicle surface. As the coupled panel method/boundary layer codes are also unable to predict pressure in the separation zone, a rational basis to evaluate the pressure drag, and thus total drag, is at present not available.

Non-linear inviscid flow schemes, based on the solution of compressible Euler equations, avoid the need for phenomena modelling. This very significant advantage, based on results obtained with aeronautical configurations, needs substantiation for the incompressible vehicle flow problems. The analytical and numerical aspects of this approach are in process of rapid development.

By treating the medium of air as inviscid, solutions of the Euler equations do not include viscous effects such as boundary layer displacement, total pressure loss etc. These results therefore need to be corrected with a boundary layer code. The question which arises is how far this approach then remains short of a solution of the full Navier-Stokes equations.

The Navier-Stokes equations represent, in principle, the true simulation of the physics of viscous flow. The main drawback of the methods currently employed to solve these equations is the cartesian grid, which allows the body contour to be only crudely represented. Special treatment of the near-wall region limits the generality and can introduce incorrect physics in the computed flow. A body-centred grid may bring improvements in the discretization.

Finite volume techniques to solve the Navier-Stokes equations avoid the disadvantages of a cartesian grid and are flexible in the generation of a


general body contour. The key problem of turbulence modelling remains open, however, irrespective of which of the two solution procedures mentioned above is adopted. A long-range effort is necessary before appropriate turbulence models for vehicle-type flow fields become available. Solutions of three-dimensional Navier-Stokes equations, em-ploying the finite volume technique to compute vehicle flows, have been reported only recently.

With the provision of a correct turbulence model, the Navier-Stokes equations describe completely the physics of the viscous flow. Accuracy of the prediction is then basically dependent on grid density. As the present numerical schemes have to retain this grid density over a major portion of the computation domain, the computation effort becomes very large. Use of Navier-Stokes solutions must therefore remain restricted to investiga-tions in a late design stage, when more detailed information may be required.

13.11 Notation

Aij component of a^ normal to surface of element / Aqp Bqj influence coefficients, (Eqn 13.69) Fj, Fp, Fy inertial, viscous and pressure force M, Ma Mach number M, Mp strength of a point or plane doublet (Eqns 13.45,13.48) Q source strength or volume (Eqn 13.39); also a point in flow

field R radial coordinate in spherical coordinate system

VI Re = — Reynolds number (Eqn 13.8) v Ri component of onset flow normal to surface of element / ^B» ^w body and wake surface Vj V^ velocity vector and its magnitude V«,, Vp onset flow and perturbation flow velocity vector (Eqn 13.57 _^ and Fig. 13.9a) W vortex vector (Eqn 13.73) Xp Yj dimensionless source/sink or doublet strength of panel; a speed of sound ax, a2 ... constants (Eqn 13.26) üij velocity induced by a horseshoe vortex placed at element/, at

control point of element / b body width, Fig. 13.32

mp-p° P-V <

pressure coefficient

2 grad gradient (Eqn 13.22) / body length m, n number of panels n surface normal vector, Fig. 13.9a p, poo local and ambient pressure

Notation 537

q a point on body surface r, Û radial distance and position vector s coordinate along body contour, Fig. 13.14 t, At time and time interval vol volume _ u, v, w velocity components of vector V in x, y and z direction x, y, z Cartesian coordinates, Fig. 13.1 Ã vortex strength (Eqn 13.56) È polar angle in spherical coordinate system Ö potential function Ø stream function oc angle of incidence ß angle of yaw (angle between direction of motion and wind),

Fig. 13.11 ä, δ1 boundary layer and displacement thickness bp pressure change äíïÀ volume of an element (= dx dy dz); also change in volume äñ change in density ì viscosity; also local strength of doublet sheet

v = — kinematic viscosity P

p density ó local strength of source/sink distribution ô shear stress (Eqn 13.5) ö cone angle in spherical coordinates; also potential function ö (Q) potential at point Q due to source/sink distribution on body

surface Öï(â) potential at point Q due to doublet distribution on wake

surface ù vorticity vector = ico* + )ùγ + ka)z ùχ, ùγ, ùζ components of vorticity vector V 2 Laplace operator (Eqn 13.25)

References

Chapter 1

1.1 Schlichting, H., Truckenbrodt, E., Aerodynamics of the Airplane. McGraw-Hill, New York, 1979.

1.2 Hoerner, S., Fluid-Dynamic Drag. Published by the author. Midland Park, NJ, 1965. 1.3 Ackeret, J., 'Anwendung der Aerodynamik im Bauwesen'. ZfW, Vol. 13, 1965, pp

109-122. 1.4 Sachs, P., Wind Forces in Engineering. Pergamon Press, Oxford, 1972. 1.5 Houghton, E.L., Carruthers, N.B., Wind Forces on Buildings and Structures. E.

Arnold. London, 1976. 1.6 Peters, J.L., 'Aerodynamics of very high speed trains and Maglev vehicles: state of the

art and future potential. Impact of aerodynamics on vehicle design'. Int. J. of Vehicle Design, SP3, London, 1983, pp 308-341.

1.7 Gawthorpe, R.G., 'Train drag reduction from simple design changes. Impact of aerodynamics on vehicle design'. Int. J. of Vehicle Design, SP3, London, 1983, pp 342-353.

1.8 Neppert, H., Sanderson, R., 'Untersuchungen zur Schnellbahn Aerodynamik'. ZfW, Vol. 22, 1974, pp 347-359.

1.9 Steinheuer, J., 'Calculation of unsteady pressures during passing and tunnel entrance of trains. Aerodynamics of Transportation. ASME-CSME Conference, Niagara Falls, June 18th to 20th 1979, pp 177-191.

1.10 Thieme, H., 'Beitrag zur Schornstein-Aerodynamik'. Schiff und Hafen, 1952, pp 453-455.

1.11 Gould, R.W.F., Measurements of the Wind Forces on a Series of Models of Merchant Ships. NPL Aero Rep. 1233, 1967.

1.12 Kuechemann, D., Weber, J., Aerodynamics of Propulsion. McGraw Hill, London, 1953.

1.13 Hucho, W.-H., Janssen, L.J., Emmelmann, H.-J., The Optimization of Body Details—A Method for Reducing the Aerodynamic Drag of Vehicles. SAE Paper 760 185, Detroit, 1976.

1.14 v. Koenig-Fachsenfeld, R., Aerodynamik des Kraftfahrzeuges, Vol I and II. Umschau-Verlag, Frankfurt, 1951.

1.15 Ludvigsen, K.E., The Time Tunnel—An Historical Survey of Automotive Aerodynamics. SAE Paper 700 035, Detroit, 1970.

1.16 McDonald, A.T., ¢ historical survey of automotive aerodynamics'. Aerodynamics of Transportation, ASME-CSME Conference, Niagara Falls, June 18th to 20th 1979, pp 61-69.

1.17 Kieselbach, R.J.F., Streamline Cars in Germany, Aerodynamics in the Construction of Passenger Vehicles 1900-1945. Kohlhammer Edition Auto & Verkehr, Stuttgart, 1982.

538

References 539

* 1.18 Kieselbach, R.J.F., Streamline Cars in Europe/USA, Aerodynamics in the Construction of Passenger Vehicles 1900-1945. Kohlhammer Edition Auto & Verkehr, Stuttgart, 1982.

1.19 Kieselbach, R.J.F., Aerodynamically Designed Commercial Vehicles 1931-1961 Built on the Chassis of: Daimler Benz, Krupp, Opel, Ford... Kohlhammer Edition Auto & Verkehr, Stuttgart, 1983.

1.20 v. Franckenberg, R., Matteucci, M., Geschichte des Automobils. Sigloch Service Ed. Künzelsau, 1973.

1.21 Riedler, A., Wissenschaftliche Automobilbewertung. Verl. Oldenburg, 1911 and Automobiltechn. Handbuch, 10. Edition, Verlag M. Krayn, Berlin, 1921.

1.22 Aston, W.G., 'Body design and wind resistance'. The Autocar, August 1911, pp 364-366.

1.23 Heller, A., 'Der neue Kraftwagen von Dr.-Ing. Rumpier'. ZDVI, Vol. 39, 1921, pp 1011-1015.

1.24 Eppinger, E., 'Tropfenwagen—Anwendung der Flugzeug-Aerodynamik'. Zeitschrift f. Flugtechnik u. Motorluftschiffahrt, Vol. 12, 1921, pp 287-289.

1.25 Rumpier, E., 'Das Auto im Luftstrom'. Zeitschrift f. Flugtecknik u. Motorluftschiffahrt, Vol. 15, 1924, pp 22-25.

1.26 Klemperer, W., 'Luftwiderstandsuntersuchungen an Automobilmodellen'. Zeitschrift für Flugtechnik u. Motorluftschiffahrt, Vol. 13, 1922, pp 201-206.

1.27 Jaray, P., 'Der Stromlinienwagen—Eine neue Form der Automobil-Karosserie'. Der Motorwagen, No. 17, 1922, pp 333-336.

1.28 Bröhl, H.P., Paul Jaray—Stromlinienpionier. Published by the author, Berne 1978. 1.29 Jaray, P., 'Grundlagen für die Berechnung des Leistungsaufwandes von Kraftwagen'.

ATZ, Vol. 37, 1934, pp 86-92. 1.30 v. Koenig-Fachsenfeld, R., 'Luftwiderstandsmessungen an einem Modell des Tatra-

Wagens Typ 87'. ATZ, Vol. 44, 1941, pp 286-287. 1.31 Lange, A., 'Vergleichende Windkanalversuche an Fahrzeugmodellen'. Berichte

deutscher Kraftfahrzeugforschung im Auftrag des RVM, No. 31, 1937. 1.32 Mauboussin, P., 'Voitures aerodynamiques'. VAeronautique, Nov. 1933, pp 239-245. 1.33 Lay, W.E., 'Is 50 miles per gallon possible with correct streamlining?' SAE-Journal,

Vol. 32, 1933, pp 144-156; pp 177-186. 1.34 Kamm, W., 'Einfluss der Reichsautobahn auf die Gestaltung von Kraftfahrzeugen'.

ATZ, Vol. 37, 1934, pp 341-354. 1.35 v. Koenig-Fachsenfeld, R., Rühle, D., Eckert, A., Zeuner, M., 'Windkanalmessungen

an Omnibusmodellen'. ATZ, Vol. 39, 1936, pp 143-149. 1.36 Everling, E., 'Die Stromlinie sitzt vorn'. Neues Kraftfahrzeug Fachblatt, Vol. 1,1948, pp

19-22. 1.37 Dörr, E., 'Vergleichsmessungen an einem Fahrzeug mit Everling-Aufbau und einem

Fahrzeug mit üblichem Aufbau'. Deutsche Kraftfahrtforschung, Zwischenbericht No. 33, 1938.

1.38 White, R.G.S., A Rating Method for Assessing Vehicle Aerodynamic Drag Coefficients. MIRA-Rep. No. 1967/9.

1.39 Kamm, W., 'Anforderungen an Kraftwagen bei Dauerfahrten'. ZVDI, Vol. 77, 1933, pp 1129-1133.

1.40 Sawatzki, E., 'Die Luftkräfte und ihre Momente am Kraftwagen'. Deutsche Kraftfahrtforschung. No. 50, VDI-Verlag, Berlin, 1941.

1.41 Huber, L., 'Die Fahrtrichtungsstabilität des schnellfahrenden Kraftwagens'. Deutsche Kraftfahrtforschung. No. 44, VDI-Verlag, Berlin, 1940.

1.42 Fiedler, F., Kamm, W., 'Steigerung der Wirtschaftlichkeit des Personenwagens'. ZVDI, Vol. 84, 1940, pp 485-491.

1.43 Schmitt, H., 'Der Leistungsbedarf zur Kühlung des Fahrzeugmotors und seine Verminderung'. Deutsche Kraftfahrtforschung, No. 45, VDI-Verlag, Berlin, 1940.

1.44 Eckert, B., 'Das Kühlgebläse im Kraftfahrzeug und sein betriebliches Verhalten'. Deutsche Kraftfahrtforschung, No. 51, VDI-Verlag, Berlin, 1940.

540 References

1.45 Persu, A., 'Luftwiderstand und Schnellwagen'. Zeitschrift für Flugtechnik u. Motorluftschiffahrt, Vol. 15, 1924, pp 25-27.

1.46 Fishleigh, W.T., The tear-drop car'. SAE-Journal, 1931, pp 353-362. 1.47 Heald, R.H., Aerodynamic Characteristics of Automobile Models. US Dept. of

Commerce, Bureau of Standards, Res. Paper RP 591, 1933, pp 285-291. 1.48 Reid, E.G., 'Farewell to the horseless carriage'. SAE-Journal, Vol. 36 1935, pp

180-189. 1.49 Hansen, M., Senior, K., Der AVA-Versuchswagen. AVA-Bericht 43 W 26, Göttingen,

1943. 1.50 Hucho, W.-H., 'Die optimale Karosserieform'. Volkswagen-Workshop. Das Auto der

Wer Jahre. Wolfsburg, Nov. 28th, 1978, pp 17-23. 1.51 Buchheim, R., Deutenbach, K.-R., Lueckoff, H.-J., 'Necessity and premises for

reducing the aerodynamic drag of future passenger cars'. SAE Paper 810 185, Detroit, 1981.

1.52 Pawlowski, F.W., 'Wind resistance of automobiles'. SAE-Journal, Vol. 27, 1930, pp 5-14.

1.53 Möller, E., 'Luftwiderstandsmessungen am VW-Lieferwagen'. ATZ Vol. 53, 1951, pp 153-156.

1.54 Schlichting, H., Boundary Layer Theory, 6th Edition, McGraw-Hill, New York, 1968. 1.5^ Hucho, W.-H., Emmelmann, H.-J., 'Aerodynamische Formoptimierung, ein Weg zur

Steigerung der Wirtschaftlichkeit von Nutzfahrzeugen'. Fortschr.-Ber. VDI-Z, Reihe 12, No. 31, pp 163-185.

1.56 Saunders, W.S., US Patent 3,241,876 (1966), US Patent 3,309,131 (1967), US Patent 3,348,873 (1967).

1.57 Frey, K., 'Verminderung des Strömungswiderstandes von Körpern durch Leitflächen'. Forschung Ing. Wesen, March 1933, pp 67-74.

1.58 Hucho, W.-H., 'The aerodynamic drag of cars—current understanding, unresolved problems, and future prospects', pp 7-44 in: Aerodynamic Drag Mech. of Bluff Bodies and Road Vehicles. Ed. by G. Sovran, T. Morel, W.T. Mason, Plenum Press, New York, 1978.

1.59 Gφtz, H., The Influence of Wind Tunnel Tests on Body Design, Ventilation and Surface Deposits of Sedans and Sportscars. SAE Paper 710212. Detroit, 1971.

1.60 'Entwicklung in Europa angebotener Personenkraftwagen'. Edition 1978, VW-FE-Dokumentation, Report D07801/4.

1.61 Costelli, A.F., Aerodynamic Characteristics of the Fiat Uno Car. SAE Paper 840297, Detroit, 1984.

1.62 Flegl, H., Bez, U., 'Aerodynamics—conflict or compliance in vehicle layout?' Impact of Aerodynamics on Vehicle Design. Int. I. of Vehicle Design, SP3, London, 1983, pp 9-43.

1.63 Hucho, W.-H., 'Bringt uns die Aerodynamic die Einheitsform für den Personenwagen?' Automobil Revue No. 37, Berne, 1983, pp 39-43.

1.64 Hucho, W.-H., 'Will aerodynamic design make all cars look alike?' Int. J. of Vehicle Design, Vol. 5, No. 3, 1984, pp 364-373.

1.65 Buchheim, R., Leie, B., The Development of the AUDI 100—A New Approach in Passenger Car Design. Int. Symp. on Vehicle Aerodynamics, Wolfsburg, December 2nd-3rd, 1982.

1.66 Ahmed, S.R., 'Experimentelle und theoretische Untersuchungen zur Aerodynamic von Strassenfahrzeugen'. DFVLR-Nachrichten, No. 31, Nov. 1980, pp 4-7.

1.67 Szigethy, N.M., 'Aerodynamics: slippery cars and slippery numbers'. Automotive Industries, Dec. 1981, pp 87-89.

1.68 Hucho, W.-H., Versuchstechnik in der Fahrzeugaerodynamic. Koll. Industrieaerodyna-mik, Aachen, 1974.

1.69 Buchheim, R., Piatek, R., Walzer, P., 'Contribution of aerodynamics to fuel economy improvements for future passenger cars'. First Int. Automotive Fuel Economy Conf. Washington D.C. Oct. 30th-Nov. 2nd, 1979.

References 541

Chapter 2

2.1 Schlichting, H., Grenzschicht-Theorie, 8th Edition, Braun, Karlsruhe, 1982. 2.2 Becker, E., Technische Strömungslehre. Teubner, Stuttgart, 1971. 2.3 Eck, B., Technische Strömungslehre, 7th Edition, Springer, Berlin/Heidelberg/New

York, 1966. 2.4 Gersten, K., Einführung in die Strömungsmechanik. Bertelsmann, Düsseldorf, 1974. 2.5 Prandtl, L., Oswatitsch, K., Wieghardt, K., Führer durch die Strömungslehre, 7th

Edition, Vieweg, Braunschweig, 1969. 2.6 Richter, H., Rohrhydraulik. Springer, Berlin, 1962. 2.7 Truckenbrodt, E., Fluidmechanik, Vol. 1 and 2. Springer, Berlin, 1980. 2.8 Akad. Ver. Hütte (Hrsg.), 'Hütte'. Des Ingenieurs Taschenbuch. 28. Aufl., Ernst.

Berlin, 1960. 2.9 Hoerner, S., Fluid-Dynamic Drag. Midland Park, New Jersey. Published by the author,

1965. 2.10 Hucho, W.-H., 'The aerodynamic drag of cars—current understanding, unresolved

problems and future prospects'. In: Sovran, G., Morel, T., Mason, W.T. (Ed.): Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles. Plenum Press, New York, 1978, pp 7-44.

2.11 Hummel, D., 'On the vortex formation over a slender wing at large angles of incidence'. AGARD CPP—247 (1978), pp 15-1-15-17.

2.12 Thwaites, B. (Ed.), Incompressible Aerodynamics. Clarendon Press, Oxford, 1960. 2.13 Janssen, L.J., Hucho, W.-H., 'Aerodynamische Formoptimierung der Typen VW Golf

und VW Scirocco'. Kolloquium über Industrieaerodynamik, Aachen, 1974, Part 3, pp 46-69.

2.14 Morel, T., The effect of base slant on the flow pattern and drag of three-dimensional bodies with blunt ends'. In: Sovran, G., Morel, T., Mason, W.T. (Ed.): Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles. Plenum Press, New York, 1978, pp 191-226.

2.15 Hucho, W.-H., 'Einfluss der Vorderwagenform auf Widerstand, Giermoment und Seitenkraft von Kastenwagen'. ZfW, Vol. 20, 1972, pp 341-351.

2.16 Verein Deutscher Igenieure (Hrsg.), VDI-Wδrmeatlas, 2nd Edition, VDI-Verlag, Düsseldorf, 1974.

2.17 Heller, H.H., Dobrzynski, W.M., ¢ comprehensive review of airframe noise research'. Proceedings of the 11th Congress of ICAS, Lisboa, Portugal, 1978, pp 42-60.

2.18 Forschung, H., Grundlagen der Aeroelastik. Springer, Berlin/Heidelberg/New York, 1974.

2.19 Brun, E.A. (Ed.), Icing Problems and Recommended Solutions. AGAR-Dograph 16, 1956.

2.20 Schlichting, H., Gersten, K., 'Berechnung der Strömung in rotationssymmetrischen Diffusoren mit Hilfe der Grenzschichttheorie'. ZfW, Vol. 9, 1961, pp 135-140.

2.21 Sprenger, H., 'Experimentelle Untersuchungen an geraden und gekrümmten Diffu-soren im inkompressiblen Geschwindigkeitsbereich'. Mitt. Nr. 27 des Inst. Aerodyna-mik Zürich, 1959.

2.22 Ahmed, S.R., 'Wake structure of typical automobile shapes'. Transactions of the ASME, Journal of Fluid Engineering, Vol. 103, 1981, pp 162-169.

2.23 Ahmed, S.R., Ramm, R., Faltin, G., Some Salient Features of the Time-Averaged Ground Vehicle Wake. SAE-Paper 840 300, Detroit, 1984.

Chapter 3

3.1 Buckley, F.T., Marks, C.H., Walston, W.H., An Evaluation of the Aerodynamic Drag Reductions Produced by Various Cab Roof Trailer Trucks. SAE Paper 760 105, Detroit, 1976.

542 References

3.2 Schubert, K., 'Bewertung unterschiedlicher Antriebsaggregate in Lkw und Omnibussen durch rechnerische Methoden'. VDI-Vortragsreihe 100 Jahre Ottomotoren, Cologne, 26-28th April 1976.

3.3 Bussien, Automobiltechnisches Handbuch. Technischer Verlag Herbert Cram, Berlin, 1965.

3.4 Hucho, W.-H., Emmelmann, H.-J., 'Aerodynamische Formoptimierung, ein Weg zur Steigerung der Wirtschaftlichkeit von Nutzfahrzeugen'. Fortschr. Ber. VDI-Z. Vol. 12, No. 31, pp 163-185, Düsseldorf, 1978.

3.5 Hucho, W.-H., Janssen, L.J., Emmelmann, H.-J., The Optimization of Body Details—A Method for Reducing the Aerodynamic Drag of Road Vehicles, SAE Paper 760 185, Detroit, 1976.

3.6 Emmelmann, H.-J., 'Fahrleistung von PKW und Schnelltransportern'. In: W.-H. Hucho (Ed.): Aerodynamik des Automobils, Vogel-Verlag, Würzburg, 1979.

3.7 Janssen, L.J., Emmelmann, H.-J., 'The effect of aerodynamic drag on the fuel economy of passenger cars'. 4th International Symposium on Automotive Propulsion Systems, Washington DC, Vol. V, Session 14.

3.8 Emmelmann, H.-J., 'Aerodynamic development and conflicting goals of subcompacts— outlined on the Opel Corsa'. International Symposium Vehicle Aerodynamics, Wolfsburg, 1982.

3.9 Emmelmann, H.-J., 'Aerodynamische Entwicklung und Zielkonflikte von Klein-wagen—Am Beispiel des Opel Corsa'. Automobil Revue 26, Berne, 1983.

3.10 Sovran, G., Tractive Energy Based Formulae for the Impact of Aerodynamics on Fuel Economy Over the EPA-Driving Schedules. SAE Paper 830 304, Detroit, 1983.

3.11 Sovran, G., Bohn, M.S., Formula for the Tractive Energy Requirements of Vehicles Driving the EPA Schedules. SAE Paper 810 184, Detroit, 1981.

3.12 Hucho, W.-H., Janssen, L.J., Schwarz, G., The Wind Tunnel's Ground Plane Boundary Layer—Its Interference with the Flow Underneath Cars. SAE Paper 750 006, Detroit, 1975.

Chapter 4

4.1 Schlichting, H., Boundary layer theory, 6th Edition, McGraw-Hill, New York, 1968. 4.2 Tanner, M., 'Ein Verfahren zur Berechnung des Totwasserdruckes und Widerstandes

von stumpfen Körpern bei inkompressibler, nicht periodischer Strömung'. Dissertation, T.H. Braunschweig, 1967.

4.3 Hirt, C.W., Ramshaw, J.D., 'Prospects for numerical simulation of bluff-body aerodynamics', In: Sovran, G., Morel, T., Mason, W.T. (Ed.): Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles. Plenum Press, New York, 1978, pp 313-355.

4.4 Hucho, W.-H., 'The aerodynamic drag of cars, current understanding, unresolved problems and future prospects'. In: Sovran et al (see ref. 4.3), pp 1-44.

4.5 Ahmed, S.R., Baumert, W., The structure of wake flow behind road vehicles'. Aerodynamics of Transportation, ASME-CSME Conference, Niagara Falls, June 18th to 20th, 1979, pp 93-103.

4.6 Ahmed, S.R., 'Wake structure of typical automobile shapes'. Transactions of the ASME, Journal of Fluids Engineering, Vol 103, 1981, pp 162-169.

4.7 Howell, J., Wake Properties of a Saloon Car. Koll. Industrie Aerodynamik, Part 3, Aerodynamik von Strassenfahrzeugen, Aachen, 1974, pp 85-95.

4.8 Hummel, D., 'On the vortex formation over a slender wing at large angles of incident'. AGARD CPP—247 (1978) pp 15-1-15-17.

4.9 Ahmed, S.R., Influence of base slant on the wake structure and drag of road vehicles'. Transactions of the ASME, Journal of Fluids Engineering, Vol. 105, No. 4, Dec. 1984, pp. 429-434.

References 543

4.10 Ahmed, S.R., Ramm, R., Faltin, G., Some Salient Features of the Time-Averaged Ground Vehicle Wake. SAE Paper 840300, Detroit 1984.

4.11 Carr, G.W., 'Potential for aerodynamic drag reduction in car design'. Impact of Aerodynamics on Vehicle Design. Int. J. of Vehicle Design, SP3, London, 1983, pp 44-56.

4.12 Schlichting, H., Truckenbrodt, E., Aerodynamik des Flugzeuges, I and II, 2nd Edition, Springer-Verlag, Berlin, 1967/69.

4.13 Wieselsberger, C., Über den Flügelwiderstand in Bodennähe. Zeitschrift für Flugtechnik und Motorluftfahrt, Vol. 12, 1921, pp 145-147.

4.14 Morelli, A., 'Metodo teorico per la determinazione della distributione di portanza sul di un veicolo'. ATA, Vol. 17, 1964, pp 599-606.

4.15 Morelli, A., 'Principali influenze sul coefficiente di resistenza aerodinamica dei veicoli'. ATA, April 1960, pp 123-131.

4.16 Morelli, A., 'Low drag bodies moving in proximity of the ground'. Aerodynamics of Transportation, ASME-CSME Conference, Niagara Falls, June 18th-20th, 1979, pp 241-248.

4.17 Morelli, A., Fioravanti, L., Cogotti, A., The Body Shape of Minimum Drag. SAE Paper 760186, Detroit, 1976.

4.18 Potthoff, J., Einfluss des Auftriebes auf den Luftwiderstand in Abhängigkeit vom Bodenabstand und vom Anstellwinkel'. Diplomathesis TH Stuttgart, 1960.

4.19 Muto, S., 'The aerodynamic drag coefficient of a passenger car and methods for reducing it'. Impact of Aerodynamics on Vehicle Design. Int. J. of Vehicle Design, SP3, London, 1983, pp 37-69.

4.20 Garrone, A., Costelli, A., 'Contribution of car forebody and afterbody to drag resistance—methodology and measurement technique in wind tunnel'. Internat. Symp. Vehicle Aerodynamics, Wolfsburg, 1982.

4.21 Hucho, W.-H., 'Einfluss der Vorderwagenform auf Widerstand, Giermoment und Seitenkraft von Kastenwagen'. ZfW, Vol. 20, 1972, pp 341-351.

4.22 Hucho, W.-H., Janssen, L.J., 'Beiträge der Aerodynamik im Rahmen einer Fahrzeugentwicklung'. ATZ, Vol. 74, 1972, pp 1-5.

4.23 Janssen, L.J., Hucho, W.-H., 'Aerodynamische Entwicklung von VW Golf und VW Scirocco'. ATZ, Vol. 77, 1975, pp 1-5.

4.24 Carr, G.W., Aerodynamic Effects of Modifications to a Typical Car Model. MIRA-Rep. No. 1963/4.

4.25 Hucho, W.-H., Janssen, L.J., Emmelmann, H.-J., The Optimization of Body Details—A Method for Reducing the Aerodynamic Drag of Road Vehicles, SAE Paper 760185, Detroit, 1976.

4.26 Buchheim, R., Deutenbach, K.-R., Lückoff, H.-J., Necessity and Premises for Reducing the Aerodynamic Drag of Future Passenger Cars. SAE Paper 810185, Detroit, 1981.

4.27 Carr, G.W., The Aerodynamics of Basic Shapes for Road Vehicles, Part 2, Saloon Car Bodies. MIRA-Rep. No. 1968/9.

4.28 Scibor-Rylski, A.J., Road Vehicle Aerodynamics, 2nd edition. Pentech Press, London, 1984.

4.29 Lay, W.E., Is 50 miles per gallon possible with correct streamlining?' SAE Journal, Vol. 32, 1933, pp 144-156 and 177-186.

4.30 Buchheim, R., Piatek, R., Walzer, P., 'Contribution of aerodynamics to fuel economy improvements for future passenger cars'. First International Automotive Fuel Economy Conference, Washington, October 30th to November 2nd, 1979.

4.31 Buchheim, R., Leie, B., 'The development of the new AUDI 100—a new approach in aerodynamic passenger car design'. Internat. Symposium Vehicle Aerodynamics, Wolfsburg 1982.

4.32 Buchheim, R., Leie, B., Lückoff, H.-J., 'Der neue Audi 100—Ein Beispiel für Konsequente aerodynamische Personenwagen-Entwicklung'. ATZ 85, 1983, pp 419-425.

4.33 Watanabe, M., Harita, M., Hayashi, E., The Effect of Body Shapes on Wind Noise. SAE Paper 780266, Detroit, 1978.

544 References

4.34 Lincke, W., 'Der neue Golf. ATZ Vol. 85, 1983, pp 515-526. 4.35 Hoerner, S., Fluid-Dynamic Drag, published by the author. Midland Park, N.J., 1965. 4.36 Nakaguchi, H., 'Recent Japanese research on three-dimensional bluff-body flows

relevant to road-vehicle aerodynamics'. In: Sovran et al. (see ref. 4.3), pp 227-252. 4.37 Roshko, A., Lau, J.C., 'Some observations on transition and reattachment of a free

shear layer in incompressible flow'. Proc. Heat Transfer and Fluid Mech. Inst., Stanford University Press, 1965.

4.38 Maull, D.J., 'Mechanisms of two and three-dimensional base drag'. In: Sovran etal. (see ref. 4.3), pp 137-159.

4.39 Mair, W.A., 'Drag-reducing techniques for axi-symmetric bluff bodies'. In: Sovran et al. (see ref. 4.3), pp 161-187.

4.40 Mair, W.A., 'Reduction of base drag by boat-tailed afterbodies in low-speed flow'. Aeronautical Quarterly Vol. 20, Nov. 1969, pp 307-320.

4.41 Liebold, H., Fortnagel, M., Götz, H., Reinhard, T., 'Aus der Entwicklung des C l l l , ÉÐ'. Automobil-Industrie, No. 2, 1979, pp 29-36.

4.42 Potthoff, J., 'The aerodynamic layout of UNICAR research vehicle'. Int. Symp. Vehicle Aerodynamics, Wolfsburg, 1982.

4.43 George, A.R., 'Aerodynamics of simple bluff bodies including effects of body shape, ground proximity, and pitch'. Aerodynamics of Transportation, ASME-CSME-Conf. Niagara Falls, June 18th to 20th, 1979, pp 71-81.

4.44 Morel, T., 'The effect of base slant on the flow pattern and drag of three-dimensional bodies with blunt ends'. In Sovran et al. (see ref. 4.3), pp 191-226.

4.45 Bearmann, P.W., 'Bluff body flows applicable to vehicle aerodynamics'. Aerodynamics of Transportation, ASME-CSME-Conf. Niagara Falls, June 18th to 20th, 1979, pp 1-11.

4.46 Stuart, A.D. , Jones, A.T., 'The drag of an upswept fuselage'. Undergraduate Project, Dept. of Aeronautics, Imperial College, 1977, quoted in ref. 4.45.

4.47 Bearman, P.W., Davis, J.P., Harvey, J.K., 'Wind tunnel investigation of vehicle wakes'. Internat. Symp. Vehicle Aerodynamics, Wolfsburg, 1982.

4.48 Bearman, P.W., Davis, J.P., 'Measurement of the structure of road vehicle wakes'. Impact of Aerodynamics on Vehicle Design, SP3, London 1983, pp 493-499.

4.49 Bearman, P.W., Some Observations on Road Vehicle Wakes. SAE Paper 840301, Detroit, 1984.

4.50 Jones, R.T., Discussion of ref. 4.4. 4.51 Arnold, K.O., 'Untersuchungen über den Einfluss der Absaugung durch einen

Einzelschlitz auf die turbulente Grenzschicht in anliegender und abgelöster Strömung'. Unpublished Report of Institut für Strömungsmechanik, TH Braunschweig, 1965.

4.52 Götz, H., private communication, 1984. 4.53 Carr, G.W., The Aerodynamics of Basic Shapes for Road Vehicles, Part 1, Simple

Rectangular Bodies. MIRA Rep. No. 1968/2. 4.54 Carr, G.W., The Aerodynamics of Basic Shapes for Road Vehicles, Part 3, Streamlined

Bodies. MIRA Rep. No. 1970/4. 4.55 Carr, G. W., Influence of Rear Body Shape on the Aerodynamic Characteristics of Saloon

Cars. MIRA Rep. No. 1974/2. 4.56 Wieghardt, K., 'Erhöhung des turbulenten Reibungswiderstandes durch Oberflächen-

störungen'. Techn. Berichte, Bd. 10, Heft 9, 1943, see also Forschungshefte Schiffstechnik, Vol. 1, 1953, pp 65-81.

4.57 Roussillon, M.G., 'Etude de l'optimisation aerodynamique du vehicule Peugeot V.E.R.A. ' Ingenieurs de Ãautomobile, 82-3, pp 69-77.

4.58 Roussillon, M.G., 'Aerodynamic optimization of the Peugeot V.E.R.A. Impact of aerodynamics on vehicle design'. Int. J. of Vehicle Design, SP3, London 1983, pp 114-131.

4.59 Carr, G.W'., Aerodynamic Effects of Underbody Details on a Typical Car Model. MIRA Rep. No. 1965/7.

4.60 Morelli, A., 'Aerodynamic actions on an automobile wheel'. Paper 5; Proc. 1st Symp. Road Vehicle Aerodynamics, London, 1969.

References 545

4.61 Stapleford, W.R., Carr, G.W., Aerodynamic Characteristics of Exposed Rotating Wheels. MIRA Rep. No. 1970/2.

4.62 Cogotti, A., 'Aerodynamic characteristics for car wheels. Impact of aerodynamics on vehicle design'. Int. J. of Vehicle Design, SP3, London, 1983, pp 173-196.

4.63 Hucho, W.-H., Janssen, L.J., Schwarz, G., The Wind Tunnel's Ground Plane Boundary Layer—Its Interference with the Flow Underneath Cars. SAE Paper 760066, Detroit, 1965.

4.64 Kramer, C , Gerhardt, H J . , Jäger, E., Stein, H., Windkanalstudien zur Aerodynamik der Fahrzeugunterseite. Koll. Industrie Aerodynamik, Part 3, Aerodynamik von Strassenfahrzeugen, pp 71-83, Aachen, 1974.

4.65 Schenkel, F.K., The Origins of Drag and Lift Reductions on Automobiles with Front and Rear Spoiler. SAE Paper 770389, Detroit, 1977.

4.66 Janssen, L.J., Hucho, W.-H., 'The effect of various parameters on the aerodynamic drag of passenger cars'. Advances in Road Vehicle Aerodynamics; British Hydromech. Ass. Cranfield, UK, 1973.

4.67 Emmelmann, H.-J., 'Aerodynamic development and conflicting goals of subcompacts— outlined on the Opel Corsa'. Internat. Symp. Vehicle Aerodynamics, Wolfsburg, 1982.

4.68 Ohtani, K., Takei, M., Sakamoto, H., Nissan Full Scale Wind Tunnel—Its Application to Passenger Car Design. SAE Paper 720100, Detroit, 1972.

4.69 Carr, G.W., 'Reduction of cooling system aerodynamic power losses in road vehicles'. Part 3 of Vehicle Fuel Economy: Effects of Aerodynamics and Gearing. Dept. of Industry, London 1976.

4.70 Emmenthal, K.-D., Hucho, W.-H., A Rational Approach to Automotive Radiator Systems Design. SAE Paper 740088, Detroit, 1974.

4.71 Beauvais, F.N., Aerodynamic Characteristics of a Car-Trailer Combination. SAE Paper 670100, Detroit 1967.

4.72 Waters, D.M., 'The aerodynamic behaviour of car-caravan combinations'. Proc. of the 1st Symp. on Road Vehicle Aerodynamics, London, 1969, Paper 4.

4.73 Zomotor, A., Richter, K.-H., Kuhn, W., 'Untersuchungen über die Stabilität und das aerodynamische Störverhalten von PKW-Wohnanhängerzügen'. Automobil-Industrie, 3/1982, pp 331-340.

4.74 Peschke, W., Mankau, H., 'Pendel-Zug, Auftriebskräfte am Wohnanhänger beeinflus-sen die Stabilität von Wohnwagengespannen. 'Automobil-Revue 18, Berne, 1982, pp 51-53.

4.75 Hart am Wind. Auto Motor Sport, No. 20, Oct. 6th, 1982, pp 126-130. 4.76 Hucho, W.-H., Emmelmann, H.-J., 'Aerodynamische Formoptimierung, ein Weg zur

Steigerung der Wirtschaftlichkeit von Nutzfahrzeugen'. Fortschrittsberichte der VDI-Zeitschriften Series 12, No. 31, 1977, pp 163-185.

4.77 Hucho, W.-H., 'Die optimale Karosserieform'. Volkswagen-Workshop. Das Auto der 80er Jahre, Wolfsburg, November 18th, 1978, pp 17-23.

4.78 Volkswagen AG, Öffentlichkeitsarbeit, Presse: 'Automobil und Technik: Volkswagen Auto 2000', Wolfsburg, 1981.

4.79 Emmelmann, H.-J., Private communication, 1984. 4.80 Carr, G.W., Reducing Fuel Consumption by Means of Aerodynamic 'Add-On' Devices.

SAE Paper 760187, Detroit, 1976. 4.81 Hansen, M., Schlör, K., Der A VA-Versuchswagen, AVA-Bericht 43W26, Göttingen,

1943. 4.82 Stollery, J.L., Burns, W.K., 'Forces on bodies in the presence of the ground'. Paper 1;

Proc. 1st Symp. Road Vehicle Aerodynamics, London, 1969. 4.83 Werner, H., 'Die Wahrheit aus dem Windkanal'. Stern, No. 38, 1978, pp 144-150. 4.84 Heil, B., 'Stromlinie hilft Benzin sparen', mot, No. 26, 1978, pp 42-45 and mot, No. 1,

1979, pp 30-35. 4.85 Hucho, W.-H., Contribution to 'General Discussion and Outlook for the Future'. In:

Sovran et al. (see ref. 4.3), pp 357-367. 4.86 Hucho, W.-H., 'Untersuchungen über den Einfluss einer Heckschraube auf die

Druckverteilung und die Grenzschicht schiffsähnlicher Körper'. Ing. Arch., Vol. 37, 1969, pp 288-303.

546 References

4.87 Morelli, A., 'Aerodynamic basic bodies suitable for automobile applications'. Impact of Aerodynamics on Vehicle Design. Int. J. of Vehicle Design, SP3, London, 1983, pp 70-98.

4.88 Klemperer, W., 'Luftwiderstandsuntersuchungen an Automodellen'. Zeitschrift für Flugtechnik und Motorluftschiffahrt, Vol. 13, 1922, pp 201-206.

4.89 Hucho, W.-H., 'Designing cars for low drag—state of the art and future potential'. Impact of Aerodynamics on Vehicle Design. Int. J. of Vehicle Design, SP3, London 1983, pp 1-8.

4.90 Bahnsen, V., Airflow Management in Future Design. Int. J. of Vehicle Design. Vol. 3, 1982, pp 40-47.

4.91 Hack, A., Faul, R., Die Aerodynamic des Mercedes-Benz Forschungs-PKW. Automobil-Industrie 3, 1983, pp 379-385.

4.92 Ford Motor Company: The Ford Probe IV Programme, Geneva 1983. 4.93 Five GM Concept Models. Car Styling 44, Autumn 1983, pp 6-23. 4.94 Opel Presseinformation: 'Opel Junior auch in Genf. Das junge Auto voller

Design-Ideen'. Genf, 1984. 4.95 Volkswagen AG—Forschung und Öffentlichkeitsarbeit: 'Design-Studien—Vom Chico

bis zum Student'. 4.96 Nitz, J., Deutenbach, K.-R., Poltrock, R., 'ARVW—Konzept eines Luftwiderstandsar-

men Rekordfahrzeuges'. ATZ 84, 1982, pp 211-219. 4.97 Onorato, M., Costelli, A., Garonne, A., Drag Measurement Through Wake Analysis.

SAE Paper 840 302, Detroit, 1984. 4.98 Hackett, J.E., Williams, J.E., Patrick, J., Wake Traverses behind Production Cars and

their Interpretation. SAE Paper 850 280, Detroit, 1985. 4.99 Emmelmann, H.-J., private communication, 1985. 4.100Cogotti, A., Wake Survey of Different Car Body Shapes with Coloured Isopressure

Maps. SAE Paper 840 299, Detroit, 1984.

Chapter 5 5.1 Davenport, A.G., 'Some aspects of wind loading'. Transactions of the Institute of

Canada. Paper No. EIC 63-CIV-3. 5.2 Bitzl, F., 'Die Einwirkung von Seitenwindkräften auf den Strassenverkehr. Zeitschrift

für Verkehrssicherheit, No. 3, 1961, and No. 2, 1962. Dr. Arthur Tetzlaff-Verlag, Frankfurt/M.

5.3 Karrenberg, H., 'Der Einfluss von Wind auf die Sicherheit im Strassenverkehr'. PhD Thesis TH Aachen, 1973.

5.4 Smith, N.P., Wind Gusts Measured on High Speed Roads. MIRA Rep. No. 1972/7. 5.5 Barth, R., 'Der Einfluss unsymmetrischer Strömung auf die Luftkräfte an Fahrzeug-

modellen und ähnlichen Körpern'. ATZ, Vol. 62, 1960, pp 80-95. 5.6 Squire, H.B., Pankhurst, R.C., ARC CP 80, 1952. 5.7 Sorgatz, U., Buchheim, R., 'Untersuchungen zum Seitenwindverhalten zukünftiger

Fahrzeuge'. ATZ, 84, 1982, pp 11-18. 5.8 Hucho, W.-H., 'Einfluss der Vorderwagenform auf Widerstand, Giermoment und

Seitenkraft von Kastenwagen'. ZfW, 20, 1972, pp 341-351. 5.9 Reichard, H., 'Gesetzmässigkeiten der freien Turbulenz'. VDI-Forschungsheft 414,

1942, 2nd Edition, 1951. 5.10 Hucho, W.-H., Emmelmann, H.-J., Theoretical Prediction of the Aerodynamic

Derivatives of a Vehicle in Cross Wind Gusts. SAE Paper 730232, Detroit, 1973. 5.11 Hummel, D., Berechnung der Druckverteilung an schlanken Flugkörpern. ICAS Paper

No. 68-44. 5.12 Wollard, H.W., Slender Body Aerodynamics for High Speed Ground Vehicles. AIAA

Paper No. 70-139, New York, 1970.

References 547

5.13 Beauvais, F.N., Transient Nature of Wind Gust Effects on an Automobile. SAE Paper 670608, Detroit, 1967.

5.14 Muto, S., Yoshida, Y., Imaizumi, T., Transient Aerodynamic Forces and Moments of Vehicle Passing Through Cross-Wind. SAE Paper 770391. Detroit, 1977.

5.15 Blenk, H., Trienes, H., 'Strömungstechnische Beiträge zum Windschutz'. Grundlagen der Landtechnik. VDI-Verlag, No. 8, 1956.

5.16 Emmelmann, H.-J., Einfluss der Luftkrδfte auf Fahrdynamik, unfalltrδchtige Fahr-situationen, In Technologien für die Sicherheit im Strassenverkehr (BMFT) TÜV Rheinland GmbH, Köln 1976, pp 308-311.

5.17 Fiala, E., 'Lenkreaktionen bei Seitenwind'. VDI-Zeitung, Vol. 108, 1966, pp 1333. 5.18 Fiala, E., 'Die Wechselwirkungen zwischen Fahrzeug und Fahrer'. ATZ, 69, 1967, pp

345-348. 5.19 Gnadler, R., 'Umfassendes Ersatzsystem zur theoretischen Untersuchung der

Fahreigenschaften von vierrädrigen Kraftfahrzeugen'. Automobil Industrie, Vol. 16, 1971, pp 75-84.

5.20 Gnadler, R., 'Beitrag zum Problem Fahrer-Fahrzeug-Seitenwind'. Automobil Industrie, Vol. 18, 1973, pp 109-135.

5.21 Mitschke, M., 'Fahrer—Fahrzeug—Windböen'. ATZ, Vol. 71, 1969, pp 347-351. 5.22 Mitschke, M., 'Zur Auswertung von Versuchen zum Verhalten von Fahrern in

Kraftfahrzeugen bei Seitenwind'. Institut für Fahrzeugtechnik TU Braunschweig. Report No. 420, 1975.

5.23 Sorgatz, U., 'Simulation of directional behaviour of road vehicles'. Vehicle Systems Dynamics, Vol. 5. Swets & Zeitlinger BV, Amsterdam, August 1975.

5.24 Niemann, K., 'Messungen und Berechnungen über das Regelverhalten von Auto-fahrern'. PhD Thesis, TU Braunschweig 1972.

5.25 Emmelmann, H.-J., 'Messungen von Seitenkraft und Giermoment mit einer Modellseitenwindanlage'. unpublished.

5.26 Wallentowitz, H., 'Fahren bei Seitenwind'. Automobil Industrie, Vol. 2, 1981, pp 163-171.

5.27 Hucho, W.-H., Patentschrift DE 2218300, 1980.

Chapter 6

6.1 Hucho, W.-H., 'Versuchstechnik in der Fahrzeug-Aerodynamik'. Kolloquium über Industrieaerodynamik, Part 3: Aerodynamik von Strassenfahrzeugen, pp 1-48, Aachen, 1974.

6.2 Janssen, L.J., Hucho, W.-H., 'Aerodynamische Formoptimierung von VW Golf und VW Scirocco'. ATZ, Vol. 77, 1975, pp 309-313.

6.3 Hucho, W.-H., 'The aerodynamic drag of cars—current understanding, unresolved problems, and future prospects'. Sovran, G., Morel, T., Mason, W.T. (Ed.): Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles. Plenum Press, New York, 1978.

6.4 Howell, J., 'Wake properties of a saloon car'. Koll. Industrie Aerodynamik, Part 3, Aerodynamik von Strassenfahrzeugen, pp 85-95, Aachen, 1974.

6.5 Watanabe, M., Harita, M., Hayashi, E., The Effect of Body Shapes on Wind Noise. SAE Paper 780266, Detroit, 1978.

6.6 Hucho, W.-H., Janssen, L.J., 'Flow visualization techniques in vehicle aerodynamics'. The International Symposium on Flow-Visualization, pp 99-108, Tokyo, 1977.

6.7 Koessler, P., 'Kotflügeluntersuchungen'. Deutsche Kraftfahrtforschung und Strassenver-kehrstechnik, No. 175, VDI-Verlag, Düsseldorf, 1965.

6.8 Götz, H., 'Schüttguttransport, Verschmutzung und Abgasgeruch bei Kraftfahrzeugen— Auswirkungen und aerodynamische Abhilfemassnahmen'. Koll. Industrie Aerodyna-mik, Part 3, Aerodynamik von Strassenfahrzeugen, pp 97-108, Aachen, 1974.

548 References

6.9 Günther, B.C., Hansen, K.-H., Veit, I., Technische Akustik. Kontakt + Studium, Vol. 18, Lexika-Verlag, Grafenau, 1978.

6.10 Zboralski, D., 'Geräuschbekämpfung im Fahrzeugbau. Eisenbahn—Kraftfahrzeug— Schiff. Dr. Arthur-Tetzlaff-Verlag, Frankfurt, 1963.

6.11 Stapleford, W.R., Carr, G.W., Aerodynamic Noise in Road Vehicles. MIRA Rep. No. 1971/2.

6.12 Stapleford, W.R., Aerodynamic Noise in Road Vehicles. Part 2: A Study of the Sources and Significance of Aerodynamic Noise in Saloon Cars. MIRA Rep. No. 1972/6.

6.13 Jagtiani, H., The Objective Method of Evaluating Aspiration Wind Noise. SAE Paper 720506, Detroit, 1972.

6.14 Aspinall, D.T., An Empirical Investigation of Low Frequency Wind Noise in Motor Cars. MIRA Report No. 1966/2.

6.15 Barth, R., 'Über aerodynamische Eigenschaften von Scheibenwischern'. ATZ, Vol. 66, 1964, pp 329-329 and 349-352.

6.16 Hucho, W.-H., Janssen, L.J., 'Beiträge der Aerodynamik im Rahmen einer Fahrzeugentwicklung'. ATZ, Vol. 74, 1972, pp 1-5.

6.17 Volkswagen AG (Herausgeber): Der Wind, der Autos besser macht. VW AG, Wolfsburg, 1977.

Chapter 7

7.1 Flegl, H., Bez, U., Aerodynamics—conflict or compliance in vehicle layout?' Impact of Aerodynamics on Vehicle Design, Int. J. Vehicle Design, SP3, 1983, pp 9-43.

7.2 Flegl, H., 'Die Fahrleistungsgrenzen heutiger Rennwagen—erläutert am Beispiel des Porsche 917/10 Can Am'. Kolloquium über Industrieaerodynamik, Part 3: Aerodyna-mik von Strassenfahrzeugen, pp 141-152, Aachen, 1974.

7.3 Braess, H.-H., Burst, H., Hannes, R., Hamm, L., 'Verbesserung der Fahreigenschaften von Personenkraftwagen durch Verringerung des aerodynamischen Auftriebs'. ATZ, Vol. 77, 1975, pp 119-124.

7.4 Romberg, G.F., Chianese, F., Lajoie, R.G., Aerodynamics of Race Cars in Drafting and Passing Situations. SAE Paper 710213, Detroit, 1971.

7.5 Jim Clark Foundation, London: Aerofoil Report. Research Report 1969. 7.6 Scribor-Rylski, A.J., Road Vehicle Aerodynamics. Pentech Press Limited; London,

1975. 7.7 Assmann, W., Witte, L., 'Einfluss der Aerodynamik auf das Fahrverhalten eines

PKW'. Vehicle Aerodynamics Symposium, Wolfsburg, December 1982. 7.8 Flegl, H., 'Die Aerodynamische Gestaltung von Sportwagen'. Christophorus, No. 98,

1969, pp 18-19. 7.9 Morelli, A., 'Low drag bodies moving in proximity of the ground'. Aerodynamics of

Transportation. ASME-CSME-Conf. Niagara Falls, June 18th to 20th, 1979, pp 241-248.

7.10 Hucho, W.-H., 'The aerodynamic drag of cars, current understanding, unresolved problems, and future prospects'. In Sovran, G., Morel, T., Mason, W.T. (Ed.): Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles. Plenum Press, New York, 1978.

7.11 Wright, P.G., 'The influence of aerodynamics on the design of Formula One racing cars'. Impact of Aerodynamics on Vehicle Design, Int. J. of Vehicle Design, SP3, London, 1983, pp 158-172.

7.12 Faul, R., 'Ein Rennwagen steht im Windkanal'. Automobil Revue, No. 41, Berne, Oct. 2, 1980, pp 37 and 39.

7.13 Mezger, H., 'Der Porsche 4,5-1-Rennsportwagen Typ 917'. Part 2. ATZ. Vol. 71, 1969, pp 417-423.

References 549

7.14 Larrabee, E. , 'Aerodynamics of road vehicle or aerodynamics as an annoyance'. Second AIAA Symposium: The Aerodynamics of Sports and Competition Cars, Los Angeles, May 1974.

7.15 BoSnjakovic, F., Technische Thermodynamik, Part 1, Verlag Theodor Steinkopff, Dresden, 1967.

7.16 Amato, G., 'Reaction thrust from a vehicle radiator'. Automotive Engineer, December 1980, pp 67-68.

7.17 Reilly, D., 'NACA-ducts—what they are and how they work'. Road & Track, March 1970, pp 71-74.

7.18 Torda, T.P., Morel, T.A., 'Aerodynamic design of a land speed record car'. / . Aircraft, Vol. 8, No. 12, December 1971, pp 1029-1033.

7.19 Cogotti, A., 'Aerodynamic characteristics of car wheels'. Impact of Aerodynamics on Vehicle Design, Int. J. of Vehicle Design, SP3, London, 1983, pp 173-196.

7.20 Fackrell, J.E., The Simulation and Prediction of Ground Effect in Car Aerodynamics. Imperial College of Science and Technology, Department of Aeronautics; I.C. Aero Report 75-11, London, November 1975.

7.21 Auto-Jahr No. 27, Edita, Lausanne, 1979/80. 7.22 Bott, H., 'Entwicklungsziele bei Rennwagen, Sportwagen und Limousinen'. Gemein-

samkeiten und Unterschiede. FISITA-Kongress, Wien, 1984.

Chapter 8 8.1 Journal Le Poids Lourd, No. 772, October 1979, pp 14-25. 8.2 Götz, H., 'Die Aerodynamik des Nutzfahrzeuges—Massnahmen zur Kraftstoffeins-

parung'. Fortschr.-Berichte der VDI-Zeitschriften, Series 12, No. 31, 1977. 8.3 Deutscher Wetterdienst, 'Die flugklimatischen Verhältnisse an den internationalen

Flughäfen in der Bundesrepublik Deutschland', Offenbach a. M. 1963. 8.4 Ingram, K.C., The wind-averaged drag coefficient applied to heavy goods vehicles.

Department of the Environment, Department of Transport, Transport and Road Research Laboratory Report SR 392, Crowthorne, 1978.

8.5 Naysmith, A., Aerodynamic drag of commercial vehicles. Department of the Environment, Department of Transport, Transport and Road Research Laboratory Supplementary Report 732. Crowthorne, 1981.

8.6 Pawlowsky, F.W., 'Wind resistance of automobiles'. SAE-Journal, Vol. 27, 1930, pp 5-14.

8.7 Hucho, W.-H., Janssen, L.J., Emmelmann, H.-J., The Optimization of Body Details—A Method for Reducing the Aerodynamic Drag of Road Vehicles. SAE Paper 760185, Detroit, 1976.

8.8 Gilhaus, A., Hau, E., Künstner, R., Potthoff, J., 'Über den Luftwinderstand von Fernlastzügen, Ergebnisse aus Modellmessungen im Windkanal'. Automobil-Industrie, 3/1979, pp 125-137, 3/1980, pp 45-64.

8.9 Morel, T., Bohn, M., 'Flow over two circular disks in tandem'. Aerodynamics of Transportation, ASME-CSME-Conf. Niagara Falls, June 1979, pp 23-32.

8.10 Roshko, A., Koenig, K., 'Interaction effects on the drag of bluff bodies in tandem'. In Sovran, G., Morel, T., Mason, W.T. (Ed.): Aerodynamic Drag mechanisms of Bluff Bodies and Road Vehicles. Plenum Press, New York, 1978, pp 253-286.

8.11 Berta, C , Bonis, B., On Shape Experimental Research of Ideal Aerodynamic Characteristics for Industrial Vehicles. SAE Paper 801402, Detroit, 1980.

8.12 Choulet, R., 'Quelques aspects de l'aerodynamique des poids lourds'. Le Poids Lourd, No. 738, December 1976.

8.13 'Im Kampf dem Luftwiderstand', Zeitschrift Nutzfahrzeuge, August 1978, pp 39-41. 8.14 Gilhaus, A., Hau, E., 'Drag reduction on trucks by aerodynamic parts and covers'. Int.

Symposium on Vehicle Aerodynamics, Wolfsburg, December, 1982.

550 References

8.15 'Mehr Nutzraum für den Lastzug', Zeitschrift Fahrzeug und Karosserie, October 1979, pp 12-14.

8.16 Zeitschrift Automobil Revue, No. 16, Berne, April 14th 1983. 8.17 Glass, D.R., 'Reduction of aerodynamic drag on truckaway units'. 320707-F, The

University of Michigan, August 1978. 8.18 Nakaguchi, H., 'Recent Japanese research on three-dimensional bluff bodies flows

relevant to road-vehicle aerodynamics'. In Sovran et al (see ref. 8.10), pp 227-252. 8.19 Barth, R., 'Luftkräfte am Kraftfahrzeug'. Deutsche Kraftfahrtforschung und Strassen-

verkehrstechnik, No. 184, VDI-Verlag Düsseldorf. 8.20 Gilhaus, A., 'The main parameters determining the aerodynamic drag of buses'.

Colloque Construire avec le vent. Vol. 2, Centre Scientifique et Technique du Bätiment, Nantes, June 1981.

8.21 Carr, G.W., The Aerodynamics of Basic Shapes for Road Vehicles, Part I, Simple Rectangular Bodies, MIRA Report No. 1982/2.

8.22 Hucho, W.-H., Emmelmann, H.-J., 'Aerodynamische Formoptimierung, ein Weg zur Steigerung der Wirtschaftlichkeit von Nutzfahrzeugen'. Fortschr.-Berichte der VDI-Zeitschriften, Series 12, No. 31, 1977.

8.23 Buchheim, R., 'Aerodynamik bei leichten Nutzfahrzeugen—heute und morgen'. Pressemappe VW-Transportertage, 1983.

8.24 Lastauto Omnibus, Stuttgart, No. 10, October 1977, p 121. 8.25 Mason, W.T. Jr., Beebe, P.S., 'The drag-related flow field characteristics of trucks and

buses'. In Sovran et al (see ref 8.10), pp 45-93. 8.26 Frey, K., 'Verminderung des Strömungswiderstandes von Körpern durch Leitflächen'.

Forschung Ing. Wesen, March 1983, pp 67-74. 8.27 Mair, W.A., 'The effect of a rear-mounted disk on the drag of a blunt-based body of

revolution', The Aeronautical Quarterly, Vol. XVI, 1965, pp 350-360. 8.28 Young, R.A., 'Bluff bodies in a shear flow'. PhD Thesis, University of Cambridge. 8.29 'Forschungsprojekt Hochdeckerbus'. Fachhochschule Hamburg, Fachbereich Fahrzeug-

technik, 1981. 8.30 Daimler-Benz, Omnibus-Verkehrssysteme, Mercedes-Benz-Schriftenreihe No. 1. 8.31 Götz, H., 'Schüttguttransport, Verschmutzung und Abgasgeruch bei Kraftfahrzeugen—

Auswirkungen und aerodynamische Abhilfemassnahmen'. Kolloquium über Industrie-aerodynamik, Part 3: Aerodynamik von Strassenfahrzeugen, pp 97-108, Aachen, 1974.

8.32 Götz, H., The Influence of Wind Tunnel Tests on Body Design, Ventilation and Surface Deposits of Sedans and Sports Cars. SAE Paper 710212, Detroit, 1971.

8.33 Koessler, P., 'Kotflügeluntersuchungen'. Deutsche Kraftfahrtforschung und Strassen-verkehrstechnik, No. 175, 1965.

8.34 Braun, H., 'Neue Erkenntnisse über Radabdeckungen'. Deutsche Kraftfahrtforschung und Strassenverkehrstechnik, No. 223, 1972.

8.35 Yamanaka, A., Nagaike, N., Measurements and Control of Truck Spray on Wet Roads. Mitsubishi Motors Corp., Japan.

8.36 Weir, D.H., 'Truck splash and spray—full scale tests and alleviation devices'. AIAA 18th Aerospace Sciences Meeting, Pasadena, January 14-16, 1890.

8.37 Allan, J.W., Lilley, G.M., 'The reduction of water spray from heavy road vehicles'. Impact of Aerodynamics on Vehicle Design. Int. J. of Vehicle Design, SP3, 1983, pp 270-307.

Chapter 9

9.1 Haas, W., 'Strömungsprobleme an der Kühlanlage wassergekühlter Kraftfahrzeuge'. PhD Thesis, Darmstadt, 1967.

9.2 'Athylenglykol', Badische Anilin und Soda Fabrik AG. 9.3 Beauvais, F.N., Aerodynamic Characteristic of Car-Trailer Combination, SAE Paper

670100, Detroit, 1970.

References 551

9.4 Drucker, E., 'Kühlwasserwärme raschlaufender Verbrennungsmotoren'. VDI-Z Vol. 77, 1933, pp 912-913.

9.5 Cramer, R., Heat Rejection and Cooling Requirements of Internal Combustion Engines. SAE Paper 670524, Detroit, 1967.

9.6 Linke, W., 'Systematische Messungen über die Einflüsse der Öffnungsverhältnisse und der Kühlerbeheizung auf Durchfluss und Widerstand von Düsenkühler'. Lilienthal-Gesellschaft für Luftfahrtforschung, Sondertagung Kühlungsfragen, April 1937, Abhandlungen aus dem aerodynamischen Institut, No. 16.

9.7 Taylor, G.I., 'Air resistance of a flat plate of very porous material'. ARC R.u.M. No. 2236, 1948.

9.8 Hoerner, S., Fluid Dynamic Drag. Published by the author, Midland Park, NJ, 1965. 9.9 Schenkel, F.K., The Origins of Drag and Lift Reductions on Automobiles with Front and

Rear Spoiler. SAE Paper 770389, Detroit, 1977. 9.10 Dehn, K., 'Untersuchungen von Automobilkühlern'. VDI-Forschungsheft 342, 1931. 9.11 Lorenz, H., 'Wärmeabgabe und Widerstand von Kühlerelementen'. Abhandlung AIA

(Aachen) 13, Springer, Berlin, 1933. 9.12 Kays, W., London, A.L., Compact Heat Exchanger, 2nd Edition. McGraw-Hill, New

York, 1964. 9.13 Eckert, B., Axialkompressoren und Radialkompressoren. Springer, Berlin, 1953. 9.14 Eckert, B., 'Das Kühlgebläse des Kraftfahrzeuges und sein betriebliches Verhalten'.

Deutsche Kraftfahrtforschung 51, Berlin, 1941. 9.15 Eckert, B., 'Kühlgebläse für Verbrennungskraftmotoren'. MTZ 2, 1940, pp 316-327. 9.16 Marcinowski, H., 'Einfluss des Laufradspaltes und der Luftführung bei einem

Kühlgebläse axialer Bauart'. MTZ 14, 1953, pp. 259-262. 9.17 Pfleiderer, C , Die Kreiselpumpen für Flüssigkeiten und Gase, 4th Edition. Springer,

Berlin, 1955. 9.18 Emmenthal, K.-D., 'Verfahren zur Auslegung des Wasserkühlsystems von Kraftfahr-

zeugen'. PhD Thesis RWTH Aachen, February 1975. 9.19 Nusselt, W., 'Eine neue Formel für den Wärmedurchgang im Kreuzstrom'. Techn.

Mech. Thermodyn, Vol. 1, 1930, pp 417-422. 9.20 Bosnjakovic, F., Vilicic, M., Slipcevic, B., 'Einheitliche Berechnung von Rekuper-

atoren'. VDI-Forschungsheft 432, Edition 8, Vol. 17, 1951. 9.21 Beauvais, F.N., An Aerodynamic Look at Automotive Radiators. SAE Paper 650470,

Detroit, 1967. 9.22 Paish, M.G., 'Airflow measurements through vehicle cooling systems'. MIRA Bulletin

No. 6, 1966. 9.23 Wong, L.T., Smith, M.C., Airflow Phenomena in the Louvered-Fin Heat Exchanger.

SAE Paper 730237, Detroit, 1973. 9.24 Emmenthal, K.-D., Hucho, W.-H., A Rational Approach to Automotive Radiator

Systems Design. SAE Paper 740088, Detroit, 1974. 9.25 Hucho, W.-H., 'Strömungsmechanische Probleme an Fahrzeug-Kühlsystemen'. Fest-

schrift zum 65. Geburtstag von Professor H. Schlichting, Bericht 72/5 des Institutes für Strömungsmechanik der TU Braunschweig, 1972.

9.26 Emmenthal, K.-D., Hucho, W.-H., 'Optimierung von Aluminiumkühlern unterschied-licher Bauart'. International Conference, Aluminium und Automobil, Düsseldorf, March 1976.

Chapter 10

10.1 Amano, Y., Imai, H., 'Eine Kraftfahrzeugklimaanlage'. Jidosha Gijutsu {Vehicle Technology) Vol. 25, 1971, pp 1096-1101.

10.2 Asakai, U., Sakai, Y., 'Cooling effect of car ventilators'. SAE Journal 1974, pp 75-82. 10.3 Bauer, K., 'Entwicklung einer neuen Heizungs- und Lüftungsanlage für den Audi 100'.

ATZ, Vol. 71, 1969, pp 6-10.

552 References

10.4 DIN 1946, 'Lüftungstechnische Anlagen (VDI-Lüftungsregeln)'. Blatt 1: Grundregeln (1960), Blatt 2: Lüftung von Versammlungsräumen (1960), Blatt 3: Lüftung von Fahrzeugen. Beuth-Verlag, Berlin/Köln, 1962.

10.5 Diebschlag, W., Müller-Limmroth, W., Mauderer, V., 'Klima im Auto'. Arzt und Auto, July 1974, pp 2-10.

10.6 Fanger, P.O., 'Beurteilung der thermischen Behaglichkeit des Menschen in der Praxis'. Arbeitsmedizin, Sozialmedizin, Prδventivmedizin, Vol. 9, 1974, pp 265-269.

10.7 Fanger, P.O., Thermal Comfort, Analysis and Application in Environmental Engineering. Danish Technical Press, Kopenhagen, 1970.

10.8 Frank, W., 'Fragen der Beheizung und Belüftung von Kraftfahrzeugen'. ATZ, Vol. 13, 1971, pp 369-376.

10.9 Frank, W., 'Die Bedienung von Klimaanlagen in Kraftfahrzeugen'. Vortrag beim VDI Arbeitskreis Fahrzeugtechnik, April 25th, 1974.

10.10 Green, G.H., 'Die Wirkung der relativen Luftfeuchtigkeit auf Abwesenheit und Erkältungen in Schulen'. Klima und Kδlte-Ing. 1975, pp 51-56.

10.11 Hettinger, Th., Müller-Limmroth, W., Gesund und fit am Steuer. G. Thieme Verlag, Stuttgart, 1970.

10.12 Leusden, P., Freymark, H., 'Darstellungen der Raumbehaglichkeit für den einfachen praktischen Gebrauch'. Gesundheits-Ing., Vol. 72, 1951, pp 271-273.

10.13 Liese, W., 'Über den jahreszeitlichen Gang der Stirntemperatur und ihre Bedeutung für die objektive Behaglichkeitsbeurteilung'. Gesundheits-Ing., Vol. 62, 1939, pp 345-350.

10.14 Lutz, H., 'Thermische Behaglichkeit in Wohn- und Arbeitsräumen'. Gesundheits-Ing., Vol. 91, 1970, pp 338-350.

10.15 Miura, T., 'Studies on the optimum temperature. On some factors affecting the shift of optimum temperature'. / . Science of Labour, Vol. 44, 1968, pp 431-453.

10.16 Müllejans, H., Illg, M., 'Probleme der Klimatisierung von Strassenfahrzeugen'. Kδlte-Klima-Ing., 1975, pp 99-104.

10.17 Nitz, J., Hucho, W.-H., The Heat Transfer Coefficient of a Passenger Car's Body. SAE Paper 790399, Detroit, 1979.

10.18 Rohles, F.H., Nevins, R.G., 'Thermische Behaglichkeit: neue Richtlinien und Normen'. Klima- und Kδlte-Ing., 1975, pp 205-212.

10.19 Rohles, F.H., Wallis, S.B., Comfort Criteria for Air Conditioned Automotive Vehicles. SAE Paper 790122, Detroit, 1979.

10.20 Roose, H., 'Neue Untersuchungen über die Wandtemperatur im Raumklima. Schweizerische Blätter für Heizung und Lüftung'. Vol. 5, 1938, pp 49-54.

10.21 Stolz, H., 'Heutige Anforderungen an die Heizung, Lüftung, Scheibenentfrostung und -trocknung im Personenwagen'. VS-Bericht 69/583 (Sindelfingen). Internal Report, Daimler Benz AG, 24th October 1969.

10.22 Temming, J., Hucho, W.-H., Passenger-Car Ventilation for Thermal Comfort. SAE Paper 790398, Detroit, 1979.

10.23 Veil, W., Lüften, Heizen und Kühlen in Personenfahrzeugen. VDI-Verlag, Düsseldorf, 1965.

10.24 Wenzel, H.G., Müller, E.A., 'Untersuchungen der Behaglichkeit des Raumklimas bei Deckenheizung'. Int. Z. Physiol. einschl. Arbeitsphysiol., Vol. 16, 1957, pp 335-355.

10.25 Yaglou, C.P., 'Temperature, Humidity and Air Movement in Industries: The Effective Temperature Index'. The Journal of Industrial Hygiene, Vol. 9, 1927, pp 297-309.

Chapter 11

11.1 Hucho, W.-H., The Aerodynamic Drag of Cars—Current Understanding, Unresolved Problems and Future Prospects. In G. Sovran, T. Morel, W.T. Mason (Ed.): Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles. Plenum Press, New York, 1978.

References 553

11.2 Hucho, W. -H., Von der Stromlinienform zum Optimierungsverfahren. A utohaus, Vol. 18, 1976, pp 1093-1096.

11.3 Hucho, W.-H., Emmelmann, H.-J., 'Aerodynamische Formoptimierung, ein Weg zur Steigerung der Wirtschaftlichkeit von Nutzfahrzeugen'. Fortschr.-Ber. VDI-Z, Series 12, No. 31. Düsseldorf, 1977, pp 163-185.

11.4 Pankhurst, R.C., Holder, D.W., Wind Tunnel Technique. Sir Isaac Pitman & Sons, London,1965.

11.5 Pope, A., Wind-Tunnel Testing. John Wiley & Sons, 2nd Edition, New York, 1964. 11.6 Wuest, W., Strömungsmesstechnik. Verlag F. Vieweg, Braunschweig, 1969. 11.7 Hucho, W.-H., 'Versuchstechnik in der Fahrzeugaerodynamik'. Kolloquium über

Industrie-Aerodynamik, Part 3, Aerodynamik von Strassenfahr-zeugen, pp 1-48, Aachen, 1974.

11.8 Stafford, L.G., A 'Streamline', Wind Tunnel Working Section for Testing at High Blockage Ratios. Preliminary copy received from the author, 1979.

11.9 Whitfield, J.D., Jacocks, J.L., Dietz, W.E., Pate, S.R., Demonstration of the Adaptive-Wall Concept Applied to an Automotive Wind Tunnel. SAE Paper 820373, Detroit, 1982.

11.10 Vandrey, F., Wieghardt, K., Experiments on a Slotted Wall Working Section in a Wind Tunnel. ARC CP No. 206, 1955.

11.11 Vandrey, F., Further Experiments with a Slotted Wall Test Section. ARC CP No. 207, 1955.

11.12 Peters, J.-L., 'Windkanal S4 im Institut Aerotechnique, Saint-Cyr'. ATZ, Vol. 80, 1978, pp 333-343.

11.13 Flay, R.G.J., Elfstrom, G.M., Clark, P.J.F., Slotted-Wall Test Section for Automotive Aerodynamic Tests at Yaw. SAE Paper 830302, Detroit, 1983.

11.14 Bradshaw, P., Pankhurst, R.C., 'The design of low speed wind tunnels'. Progr. in Aeron. Sc. Vol. 5, Editors D. Küchemann and L.H.G. Sterne, Pergamon Press, London,1964.

11.15 Piatek, R., Windkanalantriebsleistung und Kontraktionsverhδltnis. Unpublished. 11.16 Witoszynski, E., 'Über Strahlerweiterung und Strahlablenkung'. Vorträge über

Hydro- und Aeromechanik, Innsbruck, 1922, Editor Th. v. Kärmän, T. Levi-Civita, Berlin, 1924, pp 245-251.

11.17 Borger, G.-G., Optimierung von Windkanaldüsen für den Unterschallbereich'. ZfW, Vol. 23, 1975, pp 45-50.

11.18 Morel, T., Comprehensive Design of Axisymmetric Wind Tunnel Contractions. ASME Paper 75-Fe-17, New York, 1975.

11.19 Hucho, W.-H., Janssen, L.J., 'Flow visualization techniques in vehicle aerodynamics'. Proc. Internat. Symp. on Flow Visualization, Tokyo, 1977, pp 99-108.

11.20 Takagi, M., Hayashi, K., Shimpo, Y., Uemura, S., 'Flow visualization techniques in automotive engineering'. Impact of aerodynamics on vehicle design. Int. J. of Vehicle Design, SP3, London, 1983, pp 500-511.

11.21 Kelly, K.B., Provencher, L.G., Schenkel, F.K., The General Motors Engineering Staff Aerodynamics Laboratory—A Full Scale Automotive Wind Tunnel. SAE Paper 820371, Detroit, 1982, SP 515, pp 1-18.

11.22 Hucho, W.-H., Janssen, L.J., Schwarz, G., The Wind Tunnels Ground Plane Boundary Layer—Its Interference with the Flow Underneath Cars. SAE Paper 750066, Detroit, 1975.

11.23 Beauvais, F.N., Tignor, S.C., Turner, T.R., Problems of Ground Simulation in Automotive Aerodynamics. SAE Paper 680121, Detroit, 1968.

11.24 Rose, M.J., Carr, G.W., Wind Tunnel Tests of Vehicle Models Using a Moving Ground Surface. MIRA Rep. No. 1966/13.

11.25 Ohtani, K., Takei, M., Sakamoto, H., Nissan Full-Scale Wind Tunnel—Its Application to Passenger Car Design. SAE Paper 720100, Detroit, 1972.

11.26 Arnold, K.O., 'Untersuchungen über den Einfluss der Absaugung durch einen Einzelschlitz auf die turbulente Grenzschicht in anliegender und abgelöster Strömung'. Unpublished report, Institut für Strömungsmechanik, TH Braunschweig, 1965.

554 References

11.27 Antonucci, G., Ceronetti, G., Costelli, A., Aerodynamic and Climatic Wind Tunnels in the FIAT Research Center. SAE Paper 770392, Detroit, 1977.

11.28 Williams, C , private communication. 11.29 Gould, R.W.F., Measurements of the Wind Forces in a Series of Models of Merchant

Ships. NPL Aero Rep. 1232, 1967. 11.30 Carr, G.W., Hassell, T.P., A Simple Device for Reducing Wind Tunnel Boundary

Layer Thickness. MIRA Bulletin, No. 5, 1968, pp 12-16. 11.31 Carr, G.W., Wind Tunnel Blockage Corrections for Road Vehicles. MIRA Rep. No.

1971/4. 11.32 Buchheim, R., Unger, R., Jousserandot, P., Merker, E., Schenkel, F.K., Nishimura,

Y., Wilsden, D.J., Comparison Tests between Major European and North American Automotive Wind Tunnels. SAE Paper 830301, Detroit, 1983.

11.33 Iwase, H., Yamada, S., Koga, H., ¢ new approach to measuring road load by chassis dynamometer and wind tunnel tests'. Automotive Wind Tunnel Design, Test Results and Correlations, SAE-SP-515, Detroit, 1982, pp 99-107.

11.34 Hucho, W.-H., Emmelmann, H.-J., Theoretical Prediction of the Aerodynamic Derivatives of a Vehicle in Cross Wind Gusts. SAE Paper 730232, Detroit, 1973.

11.35 Williams, C , private communication. 11.36 Cogotti, A., 'Aerodynamic characteristics of car wheels'. Impact of Aerodynamics on

Vehicle Design. Int. J. of Vehicle Design. SP3, London, 1983, pp 173-196. 11.37 Schlichting, H., Truckenbrodt, E., Aerodynamics of the Airplane, McGraw-Hill, New

York, 1979. 11.38 Hucho, W.-H., Janssen, L.J., Emmelmann, H.-J., The Optimization of Body

Details—A Method for Reducing the Aerodynamic Drag of Road Vehicles. SAE Paper 760185, Detroit, 1976.

11.39 Pawlowski, F.W., 'Wind Resistance of Automobiles'. SAE Journal, Vol. 27, 1930, pp 5-14.

11.40 Kuhn, A., 'Der grosse DB-Windkanal'. ATZ, Vol. 80, 1978, pp 27-32. 11.41 Mörchen, W., The Climatic Wind Tunnel of Volkswagenwerk AG. SAE Paper 680120,

Detroit, 1968. 11.42 Morelli, A., 'The new Pininfarina wind tunnel for full-scale automobile testing'.

Advances in Road Vehicle Aerodynamics. Cranfield, UK, 1973, pp 335-366. 11.43 Carr, G.W., The MIRA Quarter Scale Wind Tunnel. MIRA Rep. No. 1961/11. 11.44 Oda, N., Hoshino, T., Three-Dimensional Airflow Visualization by Smoke Tunnel.

SAE Paper 741029, Toronto, 1974. 11.45 Chenet, M.J., 'Reflexions sur l'exploitation d'une soufflerie climatique'. Ingenieurs de

ÃAutomobile, Vol. 5, 1974, pp 375-382. 11.46 Buchheim, R., Unger, R., Carr, G.W., Cogotti, A., Garone, A., Kuhn, A., Nilsson,

L., Comparison Tests between Major European Automotive Wind Tunnels. SAE Paper 800140, Detroit, 1980.

11.47 Cogotti, A., Buchheim, R., Garrone, A., Kuhn, A., Comparison Tests between Some Full-Scale European Automotive Wind Tunnels—Pininfarina Reference Car. SAE Paper 800139, Detroit, 1980.

11.48 Costelli, A., Garrone, A., Visconti, A., Buchheim, R., Cogotti, A., Kuhn, A., FIAT Research Center Reference Car: Correlation Tests between Four Full Scale European Wind Tunnels and Road. SAE Paper 810187, Detroit, 1981.

11.49 Carr, G.W., Correlation of Aerodynamic Force Measurements in MIRA and Other Automotive Wind Tunnels. SAE Paper 820374, Detroit, 1982.

11.50 Buchheim, R., Unger, R., Jousserandot, P., Merker, E., Schenkel, F.K., Nishimura, Y., Wilsden, D.J., Comparison Tests Between Major European and North American Automotive Wind Tunnels. SAE Paper 830301, Detroit, 1983.

11.51 Low Speed Wind Tunnel—User Manual. Lockheed-Georgia Company, Marietta, Georgia, 30060.

11.52 Fosberry, R.A.C., White, R.G.S., The Mira Full Scale Wind Tunnel. MIRA Rep. No. 1961/8.

References 555

11.53 McConnell, W.A., Climatic Testing Indoors—FORD's Hurricane Road. SAE-Preprint 22S, Detroit, 1959.

11.54 Kimura, Y., Toyota's All Weather Wind Tunnel. Company brochure. 11.55 Muto, S., Ishihara, T., The JARI Full Scale Wind Tunnel. SAE Paper 780586, Detroit,

1978. 11.56 Bengsch, H., 'Der neue Klima-Windkanal bei Ford, Köln. ATZ, Vol. 80, 1978, pp

17-26. 11.57 Lindsay, J.P., Lauktree, H.E., The New Chrysler Wind Tunnel. SAE Paper 730239,

Detroit, 1973. 11.58 Christensen, F.M., 'Die Klimaversuchsanlage von Volvo'. ATZ, Vol. 75, 1973, pp

42-45. 11.59 Bartsch, Der Rüsselsheimer Universalprüf stand. Motor-Rundschau G/1965. 11.60 Veil, W., 'Ein temperierter Windkanal zur Untersuchung strömungs- und wär-

metechnischer Fragen an originalgrossen Kraftfahrzeugen'. VDI-Bericht, Vol. 34, 1959, pp 39-45.

11.61 Egle, S., Herzum, N., Hofele, G., Konitzer, H., Wind Tunnel for Aerodynamic Research. SAE Paper 820372, Detroit, 1982, SP 515, pp 19-26.

11.62 Volkert, R.H., Ford-Windkanal-von der Planung bis zur Inbetriebnahme. Aerodyna-mik des Kraftfahrzeuges, Essen, 1984.

11.63 Shibakawa, H., private communication, 1985. 11.64 Cooper, K.R., The Effect of Front-Edge Rounding and Rear-Edge Shaping on the

Aerodynamic Drag of Bluff vehicles in Ground Proximity. SAE Paper 850 288, Detroit, 1985.

11.65 Waudby-Smith, P.M., Rainbird, W.J., Some Principles of Automotive Aerodynamic Testing in Wind tunnels with Examples from Slotted Wall Test Section Facilities. SAE Paper 850 284, Detroit, 1985.

11.66 Seidel, M. (Editor), Construction 1976-1980, Design, Manufacturing and Calibration of the Deutsch-Niederlδndischer Windkanal DNW. Publ. by DNW. Noordoostpolder, 1982.

11.67 Emmelmann, H.-J., private communication, 1986. 11.68 Flegl, H., private communication, 1986. 11.69 Esser, U., Thiel, E., Institut für Verbrennungs-motoren und Kraftfahrwesen der

Universität Stuttgart in neuem Gebäude. ATZ Vol. 83, 1981, pp 9-14. 11.70 Buchheim, R., Schwabe, D., Rohe, H., Der neue 6m2-Klimawindkanal von

Volkswagen. ATZ Vol. 88, 1986, Part 1, pp 211-218, part 2, pp 389-392. 11.71 Christensen, F.M., private communication, 1986.

Chapter 12

12.1 'Vehicle dynamics terminology'. SAE J. 670e, 1976. 12.2 Pope, A., Harper, J.J., Low Speed Wind Tunnel Testing. J. Wiley & Sons, New York,

1966. 12.3 Wuest, W., Strömungsmesstechnik. Vieweg, Braunschweig, 1969. 12.4 Gorlin, S.M., Slezinger, I.I., Wind Tunnels and their Instrumentation. Jerusalem, 1966. 12.5 Pankhurst, R.C., Holder, D.W., Wind Tunnel Technique. Pitman, London, 1968. 12.6 Carr, G.W., Rose, M.J., Correlation of Full-Scale Wind Tunnel and Road

Measurements of Aerodynamic Drag. MIRA Report, 1963. 12.7 Carr, G.W., Correlation of Pressure Measurements in Model and Full-Scale Wind

Tunnel and on the Road. SAE Paper 750065, Detroit, 1975. 12.8 Lindorf, H., Marchevka, F., Der richtige Einbau von Berühungs- und Strahlungs-

thermometer. Technische Akademie Esslingen, 1973. 12.9 Merz, L., Grundkurs der Messtechnik. Oldenburg Verlag, 1968. 12.10 Eck, B., Ventilatoren. 5th Edition, Springer-Verlag, Berlin, 1972.

556 References

12.11 Krämer, W., Maisch, G., Sailer, S., Schanzer, H.-P., 'Lufttechnische Messungen in Kraftfahrzeugen mit Hilfe der Isotopenmesstechnik'. ATZ, Vol. 78, 1976, pp 439-442.

12.12 Motor Vehicle Safety Standard (FMVSS) No. 103. Federal Register, 33 F.R. 6469, 40 F.R. 12991, 40 F.R. 32336.

12.13 Council Directive of 21 December 1977 (78/317/EEC). Official Journal of the European Communities, L 81 of 28 March 1978, pp 27-48, Brussels, 1977.

12.14 Hucho, W.-H., Janssen, L.J., 'Flow visualisation techniques in vehicle aerodynamics'. Int. Symposium on Flow Visualisation, Tokyo, 1977, pp 99-108.

12.15 Bez, U., 'Bestimmung des Luftwiderstandsbeiwertes bei Kraftfahrzeugen durch Auslaufversuch'. ATZ, Vol. 76, 1974, pp 345-350.

12.16 Walston, W.H., Buckley, F.T., Marks, C.H., Test Procedures of the Evaluation of Aerodynamic Drag on Full-Scale Vehicles in Windy Environments. SAE Paper 760 106, Detroit, 1976.

12.17 Kessler, J.C., Wallis, S.B., Aerodynamic Test Techniques. SAE Paper 660464, Detroit, 1966.

12.18 Romani, L., 'La Mesure sur piste de la resistance a I'avancement'. Paper 15, Road Vehicle Aerodynamics, 1. Symposium, London, 1969.

12.19 Klein, R.H., Jex, H.R., Development and Calibration of an Aerodynamic Disturbance Test Facility. SAE Paper 800143, Detroit, 1980.

12.20 Hucho, W.-H., 'Versuchstechnik in der Fahrzeugaerodynamik'. Colloquium on Industrial Aerodynamics, Aachen, 1974, pp 1-48.

12.21 Götz, H., The Influence of Wind Tunnel Tests on Body Design, Ventilation and Surface Deposits of Sedans and Sport Cars, SAE Paper 710212, Detroit, 1971.

12.22 Grosshäuser, E., Brunkhorst, R., Wind Noise Measurements, Cologne 1978 (report not published).

12.23 Kelly, K.B., Provencher, L.G., Schenkel, F.K., The General Motors Engineering Staff Aerodynamics Laboratory—A Full Scale Automotive Wind Tunnel. SAE 820371, Detroit, 1982, SP 515, pp 1-18.

Chapter 13

13.1 Schlichting, H., Boundary Layer Theory, 6th edition. McGraw-Hill, New York, 1968. 13.2 Kuethe, A.M., Chow, C.Y., Foundations of Aerodynamics, 3rd edition, John Wiley

and Sons, New York, 1976. 13.3 Karamcheti, K., Principles of Ideal Fluid Aerodynamics. John Wiley and Sons, New

York, 1966. 13.4 Batchelor, G.K., An Introduction to Fluid Dynamics. Cambridge University Press,

1967. 13.5 Schlichting, H., Truckenbrodt, E., Aerodynamics of the Airplane. McGraw-Hill, New

York, 1979. 13.6 Stafford, L.G., ¢ numerical method for the calculation of the flow around a motor

vehicle'. Advances in Road Vehicle Aerodynamics. BHRA Fluid Engineering, pp 167-183, 1973.

13.7 Stafford, L.G., 'An improved numerical method for the calculation of the flow around a motor vehicle'. Kolloquium über Industrie-Aerodynamik, pp 109-118, Aachen, 1974.

13.8 Ahmed, S.R., Hucho, W.-H., The Calculation of the Flow Field Past a Van with the Aid of a Panel Method. SAE Paper 770390, Detroit, 1977.

13.9 Ahmed, S.R., 'Experimentelle und theorethische Untersuchungen zur Aerodynamik von Strassenfahrzeugen'. DFVLR-Nachrichten, pp 4-7, Cologne, 1980.

13.10 Stricker, R., 'Möglichkeiten der Berechnung in der Kraftfahrzeugaerodynamik'. VDI-Berichte No. 444, pp 121-131, Düsseldorf, 1982.

References 557

13.11 Losito, V., de Nicola, C , Albertoni, S., Berta, C , 'Numerical solutions of potential and viscous flows around road vehicles'. Impact of aerodynamics on vehicle design. Int. J. Vehicle Design, SP3, pp 429-440, 1983.

13.12 Stafford, L.G., ¢ higher-order boundary integral equation technique for the computation of vehicle flow fields', (see ref. 13.11), pp 401-428, 1983.

13.13 Chometon, F., 'Calculating three-dimensional flow around road vehicles', (see ref 13.11), pp 374-386, 1983.

13.14 Jameson, A., Schmidt, W., Türkei, E., 'Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes'. AIAA-81-1259, Palo Alto, 1981.

13.15 Schmidt, W., Buchheim, R., 'Evaluation of different approaches in computational aerodynamics for passenger cars'. Int. Symposium Vehicle Aerodynamics, Wolfsburg, 1982.

13.16 Salas, M.D., 'Recent developments in transsonic Euler flow over a circular cylinder'. Mathematics and Computers in Simulation, North Holland, pp 232-236, 1983.

13.17 Briley, W.R., McDonald, H., Sharnroth, S.J., ¢ low Mach number Euler formulation and application to time-iterative LBI schemes'. AlAA Journal, Vol. 21, No. 10, pp 1467-1469, 1983.

13.18 Bretthauer, N., Hirschel, E.H., 'Erste Rechenergebnisse zum Problem der abgelösten Strömung an Kraftfahrzeugen'. Symposium 'Abgelöste Strömungen', Stuttgart, DGLR-81-270, 1981.

13.19 Hirschel, E.H., Bretthauer, N., 'Theoretical and experimental boundary-layer studies on car bodies'. Int. Symposium Vehicle Aerodynamics, Wolfsburg, 1982.

13.20 Hirschel, E.H., 'Ein Verfahren zur Aufbereitung der Anfangs-, Rand- und metrischen Daten für die Berechnung dreidimensionaler Grenzschichten mit den COUSTEIX-Verfahren'. MBB/FE122/S/R/1530, 1982.

13.21 Summa, J.M., Maskew, B., Predicting Automobile Characteristics using an Iterative Viscous/Potential Flow Technique. SAE Paper 830, 303, Detroit, 1983.

13.22 Haase, W., 'Ergebnisse numerischer Untersuchungen zur Kfz-Aerodynamik', (see ref 13.18).

13.23 Ahmed, S.R., 'Wake Structure of Typical Automobile Shapes'. ASME Journal of Fluids Engineering, pp 162-169, Vol. 103/1, 1981.

13.24 Demuren, A.O., Rodi, W., 'Calculation of three-dimensional flow around car bodies'. Int. Symposium Vehicle Aerodynamics, Wolfsburg, 1982.

13.25 Rodi, W., 'Examples of turbulence model applications'. Proceedings of Ecole d'Ete d'Analyse Numerique-Modelisation numerique de la turbulence, Breau sans Nappe, 1982.

13.26 Patankar, S.V., Spalding, D.B., ¢ calculation procedure for heat, mass and momentum transfer in parabolic flows'. Int. J. Heat Mass Transfer, Vol. 15, pp 1787-1806, 1972.

13.27 Markatos, N.G., 'The theoretical prediction of external aerodynamics of road vehicles', (see ref 13.11), SP3, pp 387-400, 1983.

13.28 Rawnsley, S.M., Tatchell, D.G., 'Application of the PHOENICS code to the computation of the flow around automobiles'. SAE SP-656, pp 139-147, Detroit, 1985.

13.29 Rawnsley, S.M., 'PHOENICS - A numerical wind tunnel for aerodynamic simulation of road vehicles'. Automotive Engineer, 1985.

Subject index

A-pillar, vortex, 112,136, 239, 327 acceleration resistance, 83, 86 add-on devices, 189, 312, 332 aerodynamic drag, 13, 83, 84, 94, 96,117,

296 aerodynamic noise, 67 aerodynamic stability, 217 aerodynamics

of aircraft, 6 of buildings, 8, 9 of constructions, 9 of ships, 9 of trains, 9

äerolastic effects, 68 aerofoil, 57, 172 aileron, 286 air box, 289 air conditioning, 382 air dam, 281 air flow rate, 459, 460, 461 air flow tests, 458, 459 air flow velocity, 445 air humidity, 379,380 air inlet, outlet, 52, 240, 241, 242, 288, 360 air leaks, 384 air resistance, 106 air shield, 312 airspeed, 378,379 air-to-boil temperature, 466,467 airframe noise, 68 airship form, 11,12 angle of attack, 60, 191, 202, 203, 204, 274

283 angle of yaw, 63, 107,194,275,301 antenna, 176 apron, 314, 345, 348 aspect ratio, 122 asymptotic law, 57 attachments, 175 axis system, 62, 190, 437

balance, six components, 410,437, 439, base pressure, 19, 140, 141

basic body, 15, 186,187,190, 202 basic model, 187 basic shape, 186 Bernoulli's equation, 51,190 blockage correction, 404, 405, 406, 447 blockage ratio, 337, 403 bluff body, 14,106,203 blunt body, 57, 58 boat tail, 11,13,141,142,332 body of revolution, 14, 15,106,195 bonnet slope, 132 booming, 254 boundary layer, 49, 53, 54, 215, 292, 412,

415,483,521 suction 412, 413, 414 thickness, 54

brake cooling, 257 brake temperature, 258 bridge, 225 bubble generator, 467 bus, 30, 299, 323, 331, 334, 336

C-pillar, vortex, 112, 113,152 cab shape, 309 calibration, 446, 447 camber, 204 caravan, 179,180 cartesian grid, 528, 530 centre of pressure, 230 chamfer, 130 circular cylinder, 58 climate, 376

control, 381 climatic tunnel, 425, 431 climatic wind chamber, 425, 431 climbing resistance, 83,85 coast down, 20, 468 combination form, 15,16, 18 Combined Fuel Economy, 94 comfort, 6, 236, 376, 377 commercial vehicles, 295 compass card, 301 compressibility, 47, 425

558

Subject index 559

computational fluid dynamics, 480 concept cars, 206, 209 contraction ratio, 407,408 controlled separation, 219 convertible, 195 convoy, 335, 339 coolant temperature, 356 cooler, 403,410 cooling, 10, 21,79, 277, 278

air duct, 178,179,287,288 air flow, 177 system, 4, 5, 22, 80,356, 364 tests, 465,460

correlation tests, 432 cost-benefit, 105 cross-section enlargement, 77 cross-wind, 3,4, 21, 22,63,64, 286, 302,

470 facilities 473 tests 470, 471

cuboid body, 31, 34,106, 251, 323,423 curved pipe, 75, 76

d'Alembert's paradox, 52 damping, 69,182 deflector, 162 defrosting test, 464 demisting test, 464,465 density, 47 design, 6, 39,41 detail optimization, 27, 29,184,185,186 development, cost, 45,46 diesel engine, 102,103 diffuser, angle, 78,79,144 dirt accumulation, 1, 244, 247, 249 dirt deposition tests, 475 displacement thickness, 413,416, 524 doublet flow, 495,496,497 downwash, 109,112 drag, 2, 26, 57,62,106, 270, 278, 279

area, 99 breakdown, 119,122, 307,329 coefficient, 2, 38, 39,40, 56, 58,62,195,

269, 300 reduction, 104, 299

dragfoiler, 319 draughting, 276, 335 driving cycles, 92 driving lane, 232, 233 droplets, 70

eddy conductivity, 66 eddy viscosity, 66 Eiffel tunnel, 402 elastic body, 68,69 elasticity, 87, 88 embankment, 223 engine cooling tests, 2,474 engine noise, 250

engine power, 4, 37 EPA driving cycles, 93 equivalent nozzle, 384 Euromix cycle, 93 Everling car, 20 exchange coefficient, 66 experimental vehicles, 209 extraction curves, 459,460

far field, 405 fastback, 18, 34,150,159 fender, 351 fineness ratio, 200 finite difference technique, 528, 530 finite volume technique, 534 fins, 22 fixed control, 227, 471 flap valve, 76,77 flaps, 286 flat plate, 56, 58, 64,65,172 flight path, 70, 71 flow field, 1 ,4 ,8 ,107,108,398,482,483 flow rate, 76, 77 flow visualization, 238,467 flutter, 69, 244 fore-body, 18, 32,124, 279,323 foreign soiling, 341 free control, 227,471 friction drag, 55, 72,106,117 frictional resistance, 74, 75 front end, 127,323,327,328 front spoiler, 166,167,168 frontal area, 2, 3,36, 37,63, 299 fuel consumption, 2, 83 ,88,92,93,94,97 ,

99,100,101,102,103, 293, 295, 299 full trailer, 314

gate valve, 391 gear ratio, matching, 90,91 geodetic height, 73 Göttingen tunnel, 402 grill, 4, 361 ground clearance, 15, 24,191,192,199, 202,

204, 416 ground effect, 267, 268, 284, 285 ground simulation, 411, 508 guide vane, 34, 248, 249, 332 gust, 22

half body, 15,16,22,23,24 handling, 271, 277, 285 heat conductivity, 66 heat exchanger, 386, 387, 388 heat flux, 4 ,48 ,65,66, 67 heat rejection, 359 heat transfer, 67,365, 366 heating system, 394

tests, 462,463

560 Subject index

heavy truck, 296 hedge, 224 high cube truck, 319 history, 10, 11 horseshoe vortex, 113, 501 hot wire anemometer, 447

ideal body, 13 idle consumption, 90 induced drag, 120 inertial force, 484, 488 influence coefficients, 507 inhomogeneities, 70 interaction, 8,185, 305, 521 interference, 80,179, 513 interference drag, 177, 362 interior temperature, 377 internal flow, 71,72, 79 irrotational flow, 488

Jaray shape, 17,18, 26, 30, 331 jet effect, 223, 224 jump, 184

Kamm-back, 19, 20, 21, 30, 331 kerb weight class, 34, 35, 36, 94

laminar, 53, 529 landscape, 22, 223 Lange car, 18, 23, 26 lap time, 289 Laplace equation, 489 lateral acceleration, 271 lateral deviation, 227, 228, 231, 232, 471 lateral taper, 142,144 leading edge radius, 30, 31, 32,130, 326 leakage area, 385, 462 leaking, 254, 255,460 lever arm, 230, 231 lift, 3, 62,122,146,169,174, 271, 274, 277,

279,281,285,439 light truck, 296 local contraction, 76, 77 loss coefficient, 73, 74, 75, 76, 77, 78, 79,

361,366 low drag configuration, 164,165, 201

Mach number, 50, 290, 424, 487 mass flow, 79, 80 matching, 218 mean effective pressure, 89 minimum, 185 mirror, 185 mirror image, 151,199, 411, 501, 505 model tests, 11,49,62, 71, 304, 418 moment of inertia, 229

motive force diagram, 86, 87 mud particles, 70, 71 mudguards, 348, 349

natural wind, 214, 301, 473 Navier-Stokes equations, 481, 487, 528 Newton's law, 50, 73 noise generation, 251 nose shape, 127, 204 notchback, 34,154,155,159 nozzle contour, 403, 407, 408, 409 numerical methods, 8, 46, 292, 480 Nusselt number, 66, 366

O-Bahn, 336 oil flow picture, 236, 238 operating points, 358 optimum front end, 129 orifice meter, 77 oscillation, 69,182 overshoot, 222 overtaking, 225, 516

panel method, 481,499, 504, 508 panelling, 162, 292, 505, 509, 511 particle, 70, 71, 247, 341 performance, 1, 83,86 periodic flow, 68,69 perspiration, 380 perturbation flow, 500 petrol engine, 102,103 pipe flow, 72, 73, 74, 75 pitching moment, 3, 62,190, 439 Pitot static probe, 52, 53, 442 plan view camber, 159,160 point vortex, 498, 499 potential equation, 489 potential flow, 487 potential function, 489 Prandtl number, 65,66 pressure, dynamic, 51,442 pressure coefficient, 52 pressure distribution, 51, 57,126,135, 136,

168,172, 216, 217, 240,305,416,443, 446,504,510,511,513,528

pressure drag, 57, 58, 59,107,117 pressure force, 485, 488 pressure gradient, 54, 75 pressure loss, 72, 73, 77, 80, 361, 366 pressure probe, 442 pressure recording, 338 pressure vanes, 257 pressure transducer, 444, 445 profile, 15,18 'profile' drag, 149,150

Subject index 561

racing cars, 3,14, 260, 265, 293 radiator, 4, 356, 362, 364, 367

drag, 179, 362 efficiency, 365, 367 flow, 176 performance, 373

rain, 1, 70,137, 245, 398 ram air, 357 rating method, 26 rear end, 18,19, 20,140, 281, 331, 332

spoiler, 172,173,174,175 reattachment, 155 record vehicles, 11, 205, 209, 261, 264, 290,

293 rectangular box, 31, 34,106, 251, 323,423 reference point, 62,190, 220,439 research cars, 195, 206 resistance temperature sensors, 453,454 resonator, 254 resultant air speed, 84,107,190, 216, 302,

473 Reynolds analogy, 66 Reynolds number, 49, 50, 54,62, 71, 73,

304,366,422,485 road performance map, 358 rolling moment, 62,190, 221,439 rolling resistance, 83, 84, 94, 96,469 roof camber, 138,139 roof moulding, 153 roof rack, 184 roughness, 54, 57, 75 Rumpler car, 14

safety limit, 232, 236 saturation, 184 Schlör-car, 23, 24 self-soiling, 343 separation, 2, 8, 55, 59,60,67, 75, 76,109,

145, 218, 236, 238, 305, 323, 482,483, 517

separation bubble, 109,112,130 separation line, 251, 253, 524 shape factor, 11,12, 36, 37,190 shape optimization, 29, 186,187 shear stress, 48, 54,65, 66, 73,117, 485 shrouding trailer, 469 side force, 62,190, 216, 275, 439 side wind, 21, 216, 217

deflector, 312 sensitivity, 214, 227 track, 223,472

simulation, 399, 401 sink flow, 493,494, 495 ski racks, 184 skirts, 267, 284, 285 slant (slope) angle, 34,113,145 sleeve valve, 76, 77 slender body theory, 222 slotted walls, 407,426

smoke flow picture, 1, 2,13,17, 28, 33,131, 211, 238, 240, 305, 323, 325, 328, 329, 335,405

smoke generator, 467 smoke trail, 129 smoke tunnel, 430 sou, 4, 245, 341,475 soil deposition tests, 475 solidity, 199 solids, 70 sound, speed of, 47,486 sound level measurements, 250, 477 sound pressure, 250, 251, 253 source flow, 493,494, 495 specific fuel consumption, 89, 91 specific heat, 64 speed record, 37, 38, 265 splash, 343 spoiler, 3, 34,123,166,172, 272, 312 sports cars, 26, 205, 260, 293 spray, 321, 343, 345, 349, 350 squareback, 34,140,150,159 stability, directional, 1, 3,4, 22,181,182 stability limit, 182 stagnation point, 4, 51,124,132,418, 509 step angle, 155 stream function, 490,491 streamline, 2, 61,109,491 streamlined automobiles, 14, 25 streamlined bodies, 13, 204 streamlined shapes, 11,13,17 Strouhal number, 67,68 styling, 39,41 superposition, 500 surface discretization, 506, 511, 528

tau fin, 286, 291 tangential force, 21, 84,193, 219, 300, 439 temperature control, 391, 393 temperature field, 65 temperature measurement, 449,450 temperature sensors, 450 temperature stratification, 378, 395 test section, 403, 404 theorem of momentum, 177 thermal boundary layer, 64 thermal conductivity, 48 thermocouples, 450,451 top speed, 37, 83, 87, 96 torpedo shape, 12 total resistance, 96 tractive energy, 100 tractive resistance, 295 tractor-trailer, 305, 319 trailer, 179,180,181 trailing-edge flap, 172 tram-bus, 30 transition, 54, 55 truck soiling, 348 truckaway unit, 321

562 Subject index

trucks, 30, 295 trunk height, 155,156 trunk length, 156,157 tunnel, 336 turbulence level, 215, 224, 407 turbulence model, 481, 530 tyre noise, 250

underbody, 280 underside, 115,162,167,168 uniform flow, 493, 500 upwash, 109

vans, 32,102,249, 296, 323 vane anemometer, 447 vehicle weight, 36, 94, 229 velocity distribution, 530 velocity fluctuation, 54 velocity profile, 55, 215, 216, 222, 224, 412,

474 ventilation, 4, 22, 52, 79, 241, 276 viscosity, 47, 48 viscous force, 485 volume rate, 80, 241 von Karman's vortex street, 67 vortex, 59,60,67,109,145, 239, 251 vortex burst, 60,120 vortex generator, 334 vortex filament, 498,499 vortex flow, 498,499 vortex-induced drag, 122,150

vortex-lattice method, 481, 499, 500, 501 vortex pair, 112,148 vortex pattern, 114,116 vortex stabilizer, 312, 319 vorticity, 114

wake, 2, 4, 59,109,112, 240, 508, 517, 528 water droplets, 4,137, 245 water flow, 244, 245 water pump, 356, 364 water trap pocket, 137, 246 weight reduction, 98 wheel, 162,163,166, 291, 419 wheel opening, 160 wheel well, 162,164,165,166,419,420, 421 wind gradient, 222 wind noise, 1,67,136, 236, 250,476 wind profile, 222, 230 wind protection, 224 wind tunnel, 11, 303, 398, 402,425, 427 window recess, 160 windshield angle, 133 windscreen wipers, 2, 256, 257 wing area, 3,4, 60,122, 216, 264, 267, 276,

282,283,348 winglets, 271 woollen threads, 236

yaw angle, 84, 218, 474 yaw meter, 448,449 yawing moment, 62, 63, 217, 218, 275 yawing rate, 228

Author index

A.ckeret J 9 Ahmed,'s. R., 61,109,112,114,115,119,

148,152,508,511,525 Albertoni, S., 557 Allan, J .W, 353 Amano, Y., 377 Amato, G., 287 Antonucci, G., 413 Arnold, K.O., 155,413 Aspinall, D. T., 254 Assmann, W., 277 Aston,W.G., 13

Bahnsen, U , 209 Barret, S., 265 Barth, R., 216, 256, 257, 323 Bartsch, 555 Batchelor, G. K., 556 Bauer, K., 394 Baumert, W., 109,112 Bearman, P. W., 145,146, 147,151,152 Beauvais, F. N., 179, 222, 359, 365, 412 Beebe, P. S., 332, 348 Bengsch,H., 555 Bernoulli, D., 51,72 Berta,C, 312 Betz, A., 444 Bez, U , 36, 263,468 Bitzl,F.,216,223 Blenk, H., 224 Borger, G.-G., 409 Bonn, M. S., 102 Bonis, B., 549 Bosnjacovic, F., 287, 364 Bradshaw, P., 408 Braess,H.-H.,271,281 Braun, H., 349 Bretthauer, N., 522 Briley,W.R.,557 Bröhl,H.P, 14, 16 Brun, E. A., 70, 71 Brunkhorst, R., 478 Buchheim, R, 14,17, 20, 29, 45, 133,135,

137,139,144,153,154,156,161,162, 179,186,187, 201, 203, 217, 328,417, 432,433

Buckley,FT., 556 Burns, W. K., 192, 202, 203, Burst, H., 548 Bussien, R., 80

Carr, G. W., 118,119,126,127,133,135, 159,161,162,176,177,189, 204, 205, 251, 327, 412, 415,417, 430, 432, 434, 443, 446,469

Carruthers, N. B., 9 Ceronetti,G.,413 Chenet,M.J.,431 Chianese, F , 548 Chometon,F,516,518,519 Chow, C Y , 556 Christens, F.M., 555 Clark, P. J .F , 553 Cobb,J.,264 Cogotti, A., 162,163,164,166, 291, 419,

420,421,432,433 Cooper, K. R , 424 Costelli, A., 36,126,414, 422, 433 Cramer, R., 359

dAlembert, J., 52 Davenport, A. G., 215 Davis, J. P., 544 Dehn, K., 363 Demuren, A. O., 530, 533, 534 Deutenbach, R., 133 Deutsch, C , 267 Diebschlag, W., 552 Dietz,W.E.,553 Dobrzynski, W. M , 68 Dörr, E., 20 Drucker, E., 359

Eck, B., 461 Eckert, A., 539 Eckert, B., 22, 364 Egle,S.,555 Eiffel, A. G., 13,402 Elfstrom, G. M , 553

563

564 Author index

Emmelmann, H.-J., 10, 27, 93, 96, 98,102, 129,131,142,155,171,178,184,188, 202,222,225,327,418,422

Emmenthal, K. D., 5,178, 364, 372 Eppinger, E., 13 Esser, U., 555 Everling,E., 19,21,22

Fackrell, J. E., 292 Faltin, G., 541 Fänger, P. O., 379 Faul, R., 285 Fiala, E , 227 Fiedler, F , 22 Fioravanti, L., 543 Fishleigh,W.T.,22,23 Flay, R.G.J., 407 Flegl ,H,36,263,271,278 Försching, H., 69 Fortnagel, M , 544 Fosberry,R.A.C.,554 Fourier, J.-B., 48 Frank, W, 393 Frankenberg, R. v., 12 Frey, K, 34, 332 Freymark, H., 552

Garrone, A., 126 Gaubschat, F , 30 Gawthorpe, R. G., 9 George, A. R., 145 Gerhardt, H. J , 545 Gersten, K., 78 Gilhaus,A,314,327 Glas, D.R., 321 Gnadler, R, 227 Götz, H., 156, 245, 249, 309 Gorlin, S. M., 443 Gould, R. W. E, 414 Grosshäuser, E., 478 Grossmann, H., 384 Günther,B.C., 250

Haas, W., 358, 360 Haase,W., 529 Hack, A., 546 Hacket, J. E., 546 Hamm, L , 548 Hannes, R., 548 Hansen, K.-H., 548 Hansen, M , 23, 192,203 Harita, M., 543 Harper, J.J., 441,442 Harvey, J. K., 544 Hassel, T. P., 415, 434 Hau, E., 314 Hayashi, E , 543 Heald, R. H., 22, 23

Heil,B., 195,196 Heller, A., 13 Heller, H.H., 68 Herzum, N., 555 Hettinger,Th.,552 Hirschel,E.H.,522,525 Hirt, C. W., 107 Hoerner, S., 9,19,141, 160,176,177, 200 Hofele,G.,555 Holder, D. W, 402,443 Hoshino, T., 430 Houghton, E. L , 9 Howell,J.P, 112, 148 Huber, L., 22 Hucho, W.-H., 10, 27, 36, 45, 59, 61, 64, 96,

102,123,126,127,129,130,131,136, 142,145,147,151,155,167,175,178, 184,185,186,190,195, 200, 206, 216, 219, 222, 237, 239, 242, 243, 245, 247, 248, 255, 257, 281, 304, 327, 373, 410, 415, 418, 422, 434, 467,475, 508, 525

Hummel, D , 60,112, l l4 ,155, 222

Illg,M,377 Imai,H.,377 Imaizumi, T., 547 Ishihara, T., 555 Iwase,H.,418

Jacocks, J. L., 553 Jäger, E., 545 Jagtiani, H., 548 Jameson, A., 557 Janssen, L. J., 10, 27, 98,102,127,129,131,

136,142,145,147,155,167,175,185, 190, 195, 237, 242, 243, 245, 246, 248, 255,410,415,422,434,467

Jaray, P., 10,14,15,16,17,18, 22,41, 331 Jenatzy,C., 11,12,264 Jex,H.R.,556 Jones, A. T., 146,544 Jones, R. T., 149 Jousserandot, P., 554

Kamm, W., 10, 19, 21, 22, 331, 427 Karamcheti, K., 556 Karman, T. v., 67 Karrenberg, H., 216 Kays, W., 363 Kelly, K. B., 414, 441 Kessler, J. C , 469 Kieselbach, J. R. E, 11,16, 190 Kimura, Y., 555 Klein, R.H., 556 Klemperer, W., 14,15,16,17, 18,19, 21, 22,

39 Koenig,K.,549 Koenig-Fachsenfeld, R. v., 11, 19, 30

Author index 565

Koessler, P., 343 Koga, H., 418 Konitzer,H.,555 Kramer, C , 168 Krämer, W., 556 Küchemann, D., 10 Kuethe,A.M.,556 Kuhn, A., 427 Kuhn, W, 545 Künster, R., 549

Lajoie, R. G., 548 Lange, G., 17,18 Larrabee, E. E., 287 Lau , J .C , 141 Lauktree, H. E., 555 Lay,W.E., 18,19,22,23,133 Ledwinka, H., 17 Leie,B., 156 Leusden,R, 552 Liebold,H., 142,210 Liese,W.,552 Lüley,G.M.,353 Lincke,W., 138,162 Lindorf,H,455 Lindsay, J. P., 555 Linke, W., 360 London, A. L., 363 Lorenz, H., 363 Losito,V.,511,521,525 Ludvigsen, K. E., 11 Lückoff, H.-J, 133,156 Lutz, H., 552

Mair,W. A., 141,334 Maisch, G., 556 Mankau,H., 181,182 Marchevka, F., 455 Marcinowski, H., 364 Markatos,N.G.,533,534 Marks, C. H., 541 Maskew,B.,525 Mason, W.T., 332, 348 Matteuchi, M., 12 Mauboussin, P., 18 Mauderer,V.,552 Maull,D.J., 141 McConell,W.A.,555 McDonald, A. T, 11 McDonald, H., 557 Merker, E., 544 Mezger, H., 286 Mitschke, M., 227 Miura,T.,377,378 Möller, E., 30, 32 Mörchen, W., 428 Morel, T., 61,145, 146,147,152, 290, 409 Morelli, A., 122,162,163, 201, 204, 280,

430

Müllejans, H., 377 Müller, E. A., 552 Müller-Limroth,W.,552 Muto,S., 123,222

Nagaike,N.,350 Nakaguchi, H., 141 Naysmith, A., 303 Neppert, H., 9 Nevins,R.G., 552 Newton, I., 13,48,50,72 Nicola, C. de, 557 Niemann, K., 227 Nilsson, L., 554 Nishimura, Y., 554 Nitz,J.,210 Noble, R., 265 Nusselt, W., 364

Oda, N , 430 Ohtani,K., 172,173,175,412 Onorato, M., 546

Paish,M.G.,365 Pankhurst, R. C , 402, 408, 443 Patankar,S.V.,533 Pate, S.R., 553 Patrick, J., 546 Pawlowski, F. W., 30, 31, 32, 304,424 Persu, A., 22 Peschke,W., 181,182 Peters, J.-L., 9,407 Piatek, R., 408 Pitot,H.,52,53 Poltrock, R., 546 Pope, A , 402, 441, 442 Potthoff,J., 122, 144,176,412 Prandtl,L., 13,17,23,409 Provencher, L. G., 144

Rainbird, W. J., 407 Ramm, R., 541 Ramshaw, J. D., 107 Rawnsley, S. M., 557 Reichard, H., 222 Reid, E. G., 22, 23 Reilly, D , 288 Reinhard, T., 544 Richter, K.-H., 545 Riedler, A., 13 Rodi,W.,530,533 Rohe, H., 555 Rohles,F.H.,378 Rohlf, E , 249 Romani, L., 470 Romberg, G. E, 276 Roose,H., 552

566 Author index

Rose, M.J., 412, 443, 469 Roshko, A., 141 Rousillon, M. G., 162 Riihle,D.,539 Rumpler,E., 10,13,41,265

Sachs, P., 9 Sailer, S., 556 Sakai,Y.,551 Sakamato, H., 545,553 Salas,M.D.,557 Sanderson, R., 9 Saunders, W. S., 34 Sawatzki, E., 22 Schanzer,H.-R,556 Schenkel, F. K., 168,170,174, 362,414 Schlichting, H., 30, 48, 54, 59,68, 74, 75,

122,124,172,422 Schlör, K., 10, 23, 24, 25, 41,192, 203 Schmidt, W., 520 Schmitt, H , 22 Schubert, K., 85 Schwabe, D., 555 Schwarz, G., 102,167,415,434 Scibor-Rylski, A. J., 133,162,163, 277 Seagrave, H., 264 Seidel, M , 555 Shamroth,S.J.,557 Shibakawa,H.,555 Shimpo,Y, 553 Slezinger, I. L, 443 Slipcevic, B., 551 Smith, M.C., 365 Smith, N. P., 216 Sorgatz, U , 217, 227, 229, 230, 231 Sovran, G., 100,102 Spalding, D. B., 533 Sprenger, H., 78 Squire, H. B , 216 Stafford, L. G., 405, 502, 503, 504, Stapleford,W.R.,251 Stein, H , 545 Steinheuer, J., 9 Stollery, J. L., 192,202,203 Stolz, H , 377 Strieker, R., 511 Stuart, A.D., 146 Summa, J. M , 525 Szigethy, N. M., 540

Takagi,M.,410,467 Takei, M., 545 Tanner, M , 107,141 Tatchel, D. G., 557 Taylor, G. I., 361 Temming,J.,377,379

Thiel, E., 555 Thieme, H., 9 Thwaites, B , 60 Tignor,S.C.,553 Torda,T.R,290 Trienes, H., 224 Truckenbrodt, E., 78, 122,124,172, 422 Türkei, E., 557 Turner, T.R., 553

Uemura, S., 553 Unger, R., 428

Vandrey, F., 407 Veil, W., 377 Veit, I., 548 Vilicic,M.,551 Visconti, A., 554 Volkert,R.H.,555

Wallentowitz, H., 234 Wallis, S.B., 378, 469 Walston, W.H., 468 Walzer, P., 543 Watauabe, M , 136, 238, 253 Waters, D.M., 181 Waudby-Smith, P. M , 407 Weber, J., 10 Weir,D.H., 350 Wenzel, H.G., 552 Werner, H., 195 White, R. G. S., 20, 26 Whitfield,J.D.,405 Wieghardt, K., 160, 407 Wieselsberger, C., 122 Williams, C , 416,419 Williams, J.E., 546 Wilsden,D.J.,554 Witoszynski, E., 408 Witte, L., 277 Wong, L.T., 365 Woolard,H.W,222 Wright, P. G., 285 Wuest, W, 402,416, 417, 443

Yaglou,C.P.,552 Yamada,S.,418 Yamanaka, A., 350 Yoshida, Y, 547 Young, R. A , 334

Zboralski, D., 250 Zeuner, M., 539 Zomotor,A., 181,182

Documents

Aerodynamics of Road Vehicles. From Fluid Mechanics to Vehicle Engineering