Empirical Combustion Modeling in SI Engines

FREDRIK LINDSTRÖM

Licentiate thesis Department of Machine Design Royal Institute of Technology SE-100 44 Stockholm

TRITA – MMK 2005:19 ISSN 1400-1179

ISRN/KTH/MMK/R-05/19-SE

Empirical Combustion

Modeling in SI Engines

TRITA – MMK 2005:19 ISSN 1400-1179 ISRN/KTH/MMK/R-05/19-SE

Empirical Combustion Modeling in SI Engines

Fredrik Lindström

Licentiate thesis

Academic thesis, which with the approval of Kungliga Tekniska Högskolan, will be presented for public review in fulfilment of the requirements for a Licentiate of Engineering in Machine Design. The public review is held at Kungliga Tekniska Högskolan, Brinellvägen 23 in room B1 at 13:00 on the 26th of September 2005.

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ABSTRACT

This licentiate thesis concerns the modeling of spark ignition engine combustion for use in one dimensional simulation tools. Modeling of knock is of particular interest when modeling turbocharged engines since knock usually limits the possible engine output at high load. The knocking sound is an acoustic phenomenon with pressure oscillations triggered by autoignition of the unburned charge ahead of the propagating flame front and it is potentially damaging to the engine. To be able to predict knock it is essential to predict the temperature and pressure in the unburned charge ahead of the flame front. Hence, an adequate combustion model is needed.

The combustion model presented here is based on established correlations of laminar burning velocity which are used to predict changes in combustion duration relative to a base operating condition. Turbulence influence is captured in empirical correlations to the engine operating parameters spark advance and engine speed. This approach makes the combustion model predictive in terms of changes in gas properties such as mixture strength, residual gas content, pressure and temperature. However, a base operating condition and calibration of the turbulence correlations is still needed when using this combustion model.

The empirical models presented in this thesis are based on extensive measurements on a turbocharged four cylinder passenger car engine. The knock model is simply a calibration of the Arrhenius type equation for ignition delay in the widely used Livengood-Wu knock integral to the particular fuel and engine used in this work.

Keywords: spark ignited engines, combustion modeling, knock, 1D simulation, Wiebe, divided exhaust period

iv

SAMMANFATTNING

Denna avhandling behandlar modellering av förbränning i ottomotorer med endimensionella simuleringsverktyg. Knackmodellering är av särskilt intresse vid simulering av turbomotorer eftersom dessa motorer oftast begränsas av knack vid höga laster. Det knackande ljudet är ett akustiskt fenomen som uppstår då den obrända bränsle-luftblandningen självantänder framför flamfronten. Knack kan skada motorn. För att förutsäga knack är det av största vikt att känna till tryck och temperatur i den obrända blandningen framför flamfronten, vilket leder till behovet av en förbränningsmodell.

Förbränningsmodellen som presenteras är baserad på beprövade korrelationer för laminär flamhastighet. Dessa används för att förutspå förändringar i förbränningsduration relativt en referensförbränning. Turbulensens påverkan på förbränningen fångas genom korrelationer mot tändvinkel och motorvarvtal. Med detta tillvägagångssätt blir förbränningsmodellen prediktiv med avseende på förändringar i temperatur, tryck, restgashalt och bränsle-luftförhållande. Ett referenstillstånd och kalibrering av turbulensens påverkan på förbränningen behövs dock fortfarande.

De empiriska modellerna som presenteras i denna avhandling baseras på utförliga mätningar på en fyrcylindrig turbomotor. Knackmodellen är helt enkelt en kalibrering av den Arrhenius-liknande funktionen för tändfördröjning i Livengood-Wu’s knackintegral med det bränsle och den motor som användes i testerna.

Sökord: ottomotorer, förbränningsmodellering, knack, endimensionell simulering, Wiebe

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ACKNOWLEDGEMENTS

Where am I to start this display of gratitude towards colleagues and friends? From the beginning of course! It all started with Emil Åberg, who had the patience to guide me, a complete novice in the world of engines and a stranger to essential skills such as welding and soldering, into the fascinating interior of the DEP engine. With the aid of Emil, I could eventually start discussing engines with Hans-Erik Ångström, who never stops to evolve his wonderful engine laboratory. The software support department, i.e. Hans-Erik, has been impeccable; we once clocked the time from failure detection in the Cell4 system to installed and working program update to just over 12 minutes!

Christel Elmqvist-Möller put me right into the business of research, as she gave me a good chunk of the knock model to bite into just weeks after my first close encounter with SI engines. I would also like to thank Christel for excellent project management throughout this entire project.

The mechanics Henrik Nilsson at KTH and Jon Nilsson at GM Powertrain Sweden kept the engines running even though we did our best to kill them (the engines of course) at times. I thank lab manager Eric Lycke especially for talking me out of disassembling the gear box of my car. As always, there was a much more straightforward solution to the problem…

Gautam Kalghatgi has contributed a lot to the work on combustion and knock modeling. Thank you for many interesting discussions and insights and for being such a joyful person. But who is there to talk about knock modeling when Gautam has left the building? Per Risberg and Fredrik Agrell! Thank you also Fredrik for having enough confidence in me to let me present your work in Rio.

All colleagues at KTH have made the time here very rewarding. Fredrik Westin’s immense knowledge of racing engines; Andreas Cronhjort for sharing knowledge in filtering and electronics; fellow sailor Fredrik Wåhlin; fellow musician Per Strålin. Thank you Ulrica and Niklas for finally taking the burden of being the department junior off my shoulders.

Some people at GM Powertrain Sweden have contributed with valuable comments and support along the way, in particular Börje Grandin, Eric Olofsson, Lennarth Zander and Raymond Reinmann. The link to GM Powertrain has made the work meaningful to me.

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And finally, thank you to friends and family, nieces and nephews, who encouraged me every now and then along the way. I’ll let you in on a secret. It actually started almost exactly 30 years ago on the outskirts of Rio de Janeiro, Brazil.

Fredrik Lindström Brasilia, August 2005

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LIST OF PUBLICATIONS

Paper I

Divided Exhaust Period – A Gas Exchange System for Turbocharged SI Engines by Christel Elmqvist-Möller, Pontus Johansson, Börje Grandin and Fredrik Lindström. SAE Technical Paper 2005-01-1150 presented by Christel Elmqvist-Möller at the SAE World Congress 2005 in Detroit, USA.

Paper II

Optimizing Engine Concepts by Using a Simple Model for Knock Prediction by Christel Elmqvist-Möller, Fredrik Lindström, Hans-Erik Ångström, and Gautam Kalghatgi. SAE Technical Paper 2003-01-3123 presented by Christel Elmqvist-Möller at the SAE Powertrain and Fluid Systems Conference 2003 in Pittsburg, USA.

Paper III

An Empirical SI Combustion Model Using Laminar Burning Velocity Correlations by Fredrik Lindström, Hans-Erik Ångström, Gautam Kalghatgi and Christel Elmqvist-Möller. SAE Technical Paper 2005-01-2106 presented by Fredrik Lindström at the SAE Fuels & Lubricants Meeting 2005 in Rio de Janeiro, Brazil.

All three papers are appended to the end of this thesis.

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TABLE OF CONTENTS

Abstract ..............................................................................................................iii Sammanfattning................................................................................................. iv Acknowledgements ............................................................................................. v List of publications ........................................................................................... vii Abbreviations, symbols and subscripts............................................................... x Chapter 1 Introduction ..................................................................................1

1.1 Motivation ................................................................................................................2 1.2 Contributions ...........................................................................................................3 1.3 Thesis outline ...........................................................................................................4

Chapter 2 Combustion in spark ignition engines......................................... 5 2.1 Gas Exchange ..........................................................................................................5

2.1.1 Residual gases ......................................................................................................6 2.1.2 Fuel........................................................................................................................6 2.1.3 Turbulence ...........................................................................................................6

2.2 Combustion ..............................................................................................................7 2.2.1 Laminar burning velocity ...................................................................................7 2.2.2 Cycle to cycle variations.....................................................................................8

2.3 Knock ........................................................................................................................9 2.3.1 Autoignition chemistry.......................................................................................9 2.3.2 Modes of Autoignition.....................................................................................11 2.3.3 Combustion Chamber Oscillation Modes ....................................................12 2.3.4 Measures of Knock...........................................................................................14

2.4 Combustion simulation ........................................................................................14 2.4.1 The Wiebe Function.........................................................................................17 2.4.2 Knock Simulation .............................................................................................17

Chapter 3 Experimental Method ................................................................ 23 3.1 Measurements ........................................................................................................23

3.1.1 Measurement system ........................................................................................23 3.1.2 Pressure measurement......................................................................................24 3.1.3 Temperature measurement..............................................................................25

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3.1.4 Other measurements ........................................................................................27 3.2 Data Acquisition ....................................................................................................29

3.2.1 Signal Conditioning ..........................................................................................30 3.2.2 FIR Low Pass Filter..........................................................................................32 3.2.3 FIR Band Pass Filtering ...................................................................................35 3.2.4 IIR Filtering for Knock Onset Detection.....................................................35

3.3 Heat release calculation.........................................................................................36 3.3.1 Thermodynamic properties of mixture .........................................................37

3.4 Experiment engines...............................................................................................42 3.4.1 Divided Exhaust Period...................................................................................42 3.4.2 Engine specifications........................................................................................43

Chapter 4 Knock Modeling......................................................................... 45 4.1 Experiments ...........................................................................................................45 4.2 Data Evaluation .....................................................................................................46 4.3 Knock Model Calibration.....................................................................................47 4.4 Discussion...............................................................................................................49

Chapter 5 Combustion Modeling Using the Wiebe Function.....................51 5.1 Existing Wiebe models .........................................................................................51

5.1.1 Structure of Existing Models ..........................................................................52 5.1.2 Model Identification Procedure......................................................................53 5.1.3 Csallner ...............................................................................................................53 5.1.4 Witt......................................................................................................................55

5.2 Experiments ...........................................................................................................55 5.3 Data Evaluation .....................................................................................................59

5.3.1 Wiebe Parameter Identification ......................................................................60 5.4 Combustion model calibration ............................................................................62

5.4.1 Modeling Speed Influence ...............................................................................63 5.5 Results .....................................................................................................................64

Chapter 6 Conclusions ................................................................................ 65 6.1 Future work ............................................................................................................66

References ......................................................................................................... 69

x

ABBREVIATIONS, SYMBOLS AND SUBSCRIPTS

Abbreviations SI Spark Ignition HCCI Homogenous Charge Compression Ignition PFI Port Fuel Injection CA Crank Angle TDC Top Dead Center aTDC crank angles after combustion TDC bTDC crank angles before combustion TDC EVO Exhaust Valve Opening IVC Inlet Valve Closing IMEP Indicated Mean Effective Pressure, 720 CA PMEP Pumping Mean Effective Pressure EGR Exhaust Gas Recirculation MBT Maximum Brake Torque spark timing CFR Cooperative Fuels Research octane rating engine RON Research Octane Number MON Motor Octane Number PRF Primary Reference Fuel, iso-octane/n-heptane blend NTC Negative Temperature Coefficient FIR Finite Impulse Response filter IIR Infinite Impulse Response filter FS Full Scale, in measurement system errors A/D Analogue to Digital Symbols A scaling factor in ignition delay correlation and cylinder heat transfer area Ai constant in AVL expression for temperature dependent cp/cv

a scaling factor in Wiebe functionB cylinder bore and temperature coefficient in ignition delay correlation Bm, Bλ constants in laminar burning velocity correlations c speed of sound

Cp, CV molar heat capacity at constant pressure / volume cp, cV specific heat capacity at constant pressure / volume Fi, Gi, Hi influencing functions in Wiebe correlation fi, gi, hi normalized influencing functions in Wiebe correlation fLP low pass filter cutoff frequency in Hz fm,n,k combustion chamber natural frequencies hc heat transfer coefficient in Woschni equation for heat transfer Jm Bessel’s function of the first kind Kf number of periods of sinc function in FIR-filter kernel m combustion mode parameter in Wiebe function M molar mass N engine speed in rpm n pressure exponent in ignition delay correlation p pressure pm motored pressure PR pressure ratio Qch chemical energy released from fuel q0 , q1 normalized cutoff frequencies in filters R universal gas constant, 8.314 kJ/molK SL laminar burning velocity

pS

rx

piston mean velocity

T gas temperature Tu unburned zone temperature V volume, cylinder volume Vd displaced volume xb mass fraction burned ~ burned gas mole fraction

α, αg temperature exponent in laminar burning velocity correlations

αm,n zeros of Bessel’s function of the first kind

β, βg pressure exponent in laminar burning velocity correlations

β exponent for air/fuel ratio dependence in ignition delay

γ ratio of specific heats, cp/cv

xi

xii

λ normalized air/fuel ratio

λm constant in laminar burning velocity correlations

θ crank angle and cylindrical angle coordinate

θ0 start of combustion aTDC

θd flame development period

∆θ total combustion duration

τ ignition delay time Subscripts EOC end of combustion ,ref SOC start of combustion b burned exh exhaust k longitudinal mode number m circumferential mode number n radial mode number norm normalized u unburned 0 and ref reference condition

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Chapter 1

INTRODUCTION

The internal combustion engine as we know it today was invented over a hundred years ago by the likes of Otto and Diesel. Still today, however, there is progress and improvements in the design and operation of internal combustion engines. One of the key factors for the success of the internal combustion engine in the transport of people is the reliability and flexibility as a mobile power source.

The focus for research and development has shifted over the years, depending on trends and demand from society as a whole as well as on new enabling technologies. From society, focus has shifted from reductions of the local emissions towards the reduction of greenhouse gas emissions, i.e. CO2 or the fuel efficiency. Introduction of the three way catalyst and close loop fueling control basically solved the problem of local emissions of unburned hydrocarbons, carbon monoxide and nitrogen oxides for spark ignited engines. Today, with the introduction of direct fuel injection with stratified charge to improve part load fuel economy, emissions of nitrous oxides are again coming into focus since the three way catalyst doesn’t work in the overall fuel lean conditions. A rising concern today is the future availability of energy resources suitable for transportation which also brings focus to renewable energy sources and efficiency in using the available energy.

State of the art spark ignited engine of today can benefit from technologies such as: variable valve timing, which can replace throttling and reduce part load gas exchange losses and also maximize power output by improving volumetric efficiency; fuel injection with feedback control to maximize after treatment system efficiency; knock sensors for optimal combustion phasing; turbocharging which increases power


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density and enables downsizing of the engine with less friction losses and improved part load efficiency as a result. Evolution in the fields of electronics and sensors gives new opportunities to optimize the operation of internal combustion engines. Developments in auxiliary units such as water pumps and oil pumps reduce parasitic losses. New manufacturing methods and materials reduce the weight of engines. Electric hybrid systems enable recovery of breaking energy in the vehicle. Many more examples exist of parts of the engine or vehicle where improvements are being made today, all serving to improve fuel efficiency. However, the general trend in passenger cars is that passenger safety and comfort requirements lead to an increased vehicle weight with increased need for power and higher fuel consumption as a result. Statistics from the European Union [1] shows that during the period 1995 to 2002 the average vehicle weight increased by 10 %, average power by over 20 % while average vehicle CO2 emissions decreased by 12,1 % in new vehicles. The average CO2 emissions per kilometer is lower for diesel powered vehicles than for the equivalent gasoline powered vehicle owing to higher average efficiency of the diesel engine An increasing share of diesel powered vehicles explains some of the improvements in average CO2 emissions. The gasoline powered vehicles did however decrease average CO2 emissions per kilometer by 9,1 % in the EU statistics mentioned above.

Today, the fuel cell is put forward as an alternative for the internal combustion engine in automotive applications. The technology still has some hurdles to pass before it is a competitive alternative to internal combustion engines. In a recent presentation at SAE Fuels & Lubricants Meeting and Exhibition in Rio de Janeiro by Mitchell [2] the fuel efficiency of a fuel cell powered vehicle with on board fuel reformer was stated to be approximately 46 %, some percentage points over the best diesel powered vehicles. The cost for the fuel cell alone would however be several thousand US dollars per kilowatt of power. The average EU car had 78 kW of power in 2003. The conclusion from this has to be that efforts must be made to improve the currently working technology, i.e. the internal combustion engine, parallel to investigating new and perhaps better alternatives.

1.1 MOTIVATION

Simulation tools are becoming increasingly important in the development and improvement of internal combustion engines. One dimensional simulation tools have been used within this project to evaluate a new gas exchange system for SI engines, the Divided Exhaust Period system. In one-dimensional simulation, equations for conservation of mass, momentum and energy are solved in time and in one space dimension along the main flow direction in the engine pipes. However, many

Chapter 1 - Introduction

3

phenomena in engines are three-dimensional in their nature. Additional models, correlations or measurements are needed in one-dimensional codes to capture three-dimensional phenomena such as flow in pipe bends and junctions, flow over valves and combustion. [3][4]

One might think that the increasing use of simulation would decrease the need for expensive engine prototypes and tests. This is not the case today since the simulation models rely on test data to calibrate the sub-models describing three dimensional phenomena. This is especially true for turbocharged engines, where modeling of the turbine is singled out as one of the most difficult tasks [5]. In fact, engine simulation has put new demands on the engine measurement technique, requiring more crank angle resolved measurements of pressures at various positions and more detailed measurements on components that the one dimensional flow calculations fail to describe. For example Westin [5] and Gamma Technologies [4] describe the measurement data needed for calibrating a simulation model.

The key focus of this work has been to improve the simulation models for combustion and especially knocking combustion. Knock can be described as an acoustic phenomenon where autoignition of the unburned gas ahead of the propagating flame front triggers pressure oscillations in the combustion chamber. The pressure waves give rise to the characteristic, potentially disturbing, sound which has given knock its name. The pressure pulses can however also damage the engine, why knock must be avoided. The Divided Exhaust Period concept is in part aimed at improving the knock resistance of turbocharged spark ignited engines by reducing the amount of hot residual gases that are trapped in the cylinder when the exhaust valves close. Hot residuals increase the charge temperature and reduce the knock resistance of the engine. To be able to investigate the potential improvement by using the Divided Exhaust Period system, a knock model had to be used in the simulation software. To be able to simulate knock, the in cylinder temperature and pressure have to be predicted accurately which lead to the work with the empirical combustion model. The overall target for this work has been to make the one dimensional simulation model more predictive.

1.2 CONTRIBUTIONS

The main contribution of this work is the combustion model presented in Paper III. The presented model combines the empirical approach of using the Wiebe function to describe the heat release in SI engines with established correlations for laminar burning velocity. This makes the presented model predictive in terms of changes in


4

gas properties such as temperature, pressure and composition. The model is still very intuitive and easy to interpret or compare with engine tests.

As for the appended papers, my contributions to Paper I and Paper II have been the experimental investigations involved in those papers along with analysis of the experimental results. Paper I concerning Divided Exhaust Period was originally written in two parts, a theoretical and simulation part with fellow licentiate candidate Christel Elmqvist-Möller as main author, and an experimental part with me as main author. In Paper III, I carried out all experiments and analysis with very valuable input regarding how to model combustion from the co-authors. A fruitful team work was developed between the simulation part of the project, i.e. Christel Elmqvist-Möller, and the experimental part of the project.

1.3 THESIS OUTLINE

First of all, this thesis contains a short introduction to combustion in SI engines, which serves as a background to the work presented in Paper II and Paper III. Some factors influencing combustion are presented. The knock phenomenon is explored both from an autoignition chemistry viewpoint and from the combustion chamber acoustic viewpoint to help in understanding the measurement technique as well as the knock model presented in Paper II.

Description of the measurement technique and measurement data processing tools follows. Signal processing is an important part of combustion engine data analysis. Measurements in internal combustion engines can easily produce several megabytes of data in only a few seconds. With this amount of data automated analysis is preferred. When performing this automated analysis it is important to know what can go wrong and how to handle errors in the measured data. Therefore digital filtering is explored. The algorithm used for calculating in cylinder heat release, i.e. the release of chemical energy from the fuel, from measured cylinder pressure data is also described.

Some additional comments to the appended papers are found last in the thesis. These two works give simplified but practical descriptions of how combustion and knock can be simulated in SI engines. With the lack of physical models which are easy to use and calibrate, an empirical approach as in this work can give at least partly predictive simulation tools.

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Chapter 2

COMBUSTION IN SPARK IGNITED ENGINES

The following paragraphs contain a brief overview of the combustion in port fuel injected spark ignition four stroke engines. This overview serves as a base for understanding the simplifications made in the models presented later in this thesis. Parameters that influence the combustion event and cycle-to-cycle variations are summarized. The knock phenomenon is explored. Finally, combustion simulation is discussed.

2.1 GAS EXCHANGE The gas exchange process plays a major role for the combustion in spark ignition engines. The mixture composition in the combustion chamber is set once the inlet valves have closed. Residual gas fraction and air/fuel ratio are important parameters affecting the combustion event. A large part of the residual gases are evacuated from the cylinder during the blow-down phase of the exhaust process, during which the cylinder pressure drops to the pressure in the exhaust manifold. The remaining exhaust is pushed out from the cylinders by the piston during the exhaust stroke. Scavenging of the cylinder is controlled by the pressure difference from intake to exhaust system during the valve overlap period. A positive pressure difference, i.e. higher pressure in the intake system than in the exhaust system, can be accomplished at high load by exhaust and intake system tuning and design and by proper turbocharger matching [6].


6

2.1.1 Residual gases Residual gases that are trapped in the cylinder when the exhaust valves closes affect the cylinder charge in several ways. The hot residual gases increase charge temperature thereby decreasing charge density and volumetric efficiency. The increased charge temperature reduces the knock resistance of the engine, since knock is highly temperature dependent. Residual gases also have a minor effect on the ratio of specific heats, γ. Residual gases have slightly lower γ than pure air. Vaporized hydrocarbon fuel, on the other hand, has very low γ. Increased residual gases with constant air/fuel ratio decreases the relative amount of fuel in the mixture. The overall result for premixed SI engines is a slight increase in γ when residual gas content increases, according to the frozen mixture gas model described in Chapter 3.1.1. Increased γ leads to increased charge temperature during isentropic compression, but this effect is very small compared to the temperature rise associated with the mixing of hot residual gases with the fresh charge. Calculation of isentropic maximum temperature with the heat release algorithms and assumptions described in Chapter 3 reveal that a 10% increase of residual gases at one high load operating condition cause an increase from 683 K to 803 K in maximum temperature. Only 4 K, or 3,5% of the total increase in temperature, is associated with the increase in γ.

2.1.2 Fuel Fuel is usually injected in the inlet runner towards the inlet valves in port fuel injected engines. Some of the injected fuel is deposited on the inlet runner walls, on the valve stems and on the back face of the inlet valves to form a fuel film and puddles. Fuel enters the cylinder during the intake stroke in vapor phase and in liquid phase. The fuel evaporates and mixes with air and residual gases during the intake and compression stroke.

2.1.3 Turbulence The flow over the inlet valves creates turbulence. Large scale rotating charge motion is created from the intake jet in the form of tumble, swirl or combinations thereof. As shown for example by Söderberg [7], turbulence increases close to top dead center due to tumble breakdown in tumbling engines. Late inlet valve closing combined with low valve lift creates more turbulence around top dead center in the same work. Piston motion during the compression stroke also creates a vortex near the cylinder wall which further increases turbulence at TDC [8].

Chapter 2 – Combustion in spark ignited engines

2.2 COMBUSTION The mixture in the combustion chamber is ignited by the spark discharge between the electrodes of the spark plug and a flame kernel is formed. Exothermic chemical reactions take place in the flame kernel. Diffusion of heat and radicals from the flame kernel surface makes the kernel expand and start propagating in the combustion chamber. A thin, smooth reaction sheet, with thickness in the order of 0.1 mm, separates the burned gases from the unburned gases [8]. See Glassman [9] for a thorough discussion about laminar flame propagation. The early flame has been shown to propagate with a speed close to experimentally determined laminar burning velocity [10].

The time between spark discharge and any measurable increase in pressure due to combustion is sometimes referred to as the ignition delay period. The term ignition delay is misleading because the flame kernel will usually have grown to a significant size by this time. For example, Tagalian and Heywood [11] measured flame radiuses of about 5 mm when 0,1 % of the charge mass was burned. A more correct term would be flame development period. When the flame kernel has reached the size of the smallest turbulent eddies, the reaction sheet is wrinkled, resulting in increased surface area of the flame and increased burning velocity. The flame extinguishes when the flame eventually reaches the relatively cold combustion chamber walls

2.2.1 Laminar burning velocity Several correlations exist for laminar burning velocity SL of hydrocarbon/air mixtures. Heywood [8] summarizes the findings of Metghalchi and Keck [12][13] in the equation:

βα

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

000, p

pTT

SS uLL (2.1)

where T0 = 298 K and p0 = 101,3 kPa is reference temperature and pressure. The exponents α and β are functions of equivalence ratio, i.e. the inverse of the normalized air/fuel ratio λ:

( )

( )122,016,0

18,018,21

1

−+−=

−−=−

−

λβ

λα (2.2)

7


8

rxThe reference laminar burning velocity SL,0 is a function of equivalence ratio and burned gas mole fraction ~ :

( ) ( ) ( ) ⎟⎠⎞⎜

⎝⎛ −+⋅⋅−= −− 21177,0

0,~06,21~, mmrrL BBxxS λλλ λ (2.3)

Values for the constants in Equations (2.2) and (2.3) are found in Table 2.1.

Table 2.1 Constants for the laminar burning velocity correlations in Equations (2.2) and (2.3) from [8].

Fuel λm Bm [cm/s]

Bλ [cm/s]

Methanol 1/1,11 36,9 -140,5

Propane 1/1,08 34,2 -138,7

Isooctane 1/1,13 26,3 -84,7

Gasoline 1/1,21 30,5 -54,9

An additional correlation for the temperature and pressure exponents in Equation (2.1) for gasoline from the same source as the other correlations is:

(2.4) 77,2

51.3

14,0357,0

271,04,2−

−

⋅+−=

⋅−=

λβ

λα

g

g

2.2.2 Cycle to cycle variations Variations in the local and global air/fuel ratio, residual gas content, mixing and turbulence characteristics between cycles produce cycle to cycle variations. Turbulence during the intake and compression strokes affects the mixing of air, fuel and residual gases. The charge properties in the vicinity of the spark plug are of particular importance [14]. Air/fuel ratio and residual gas content affect the laminar burning velocity which in turn affects the ignition delay time. The time for developing a turbulent flame is also affected by local variations in turbulence length scales and intensity. Differences in ignition delay affect the turbulent flame speed during the rapid combustion period, since the turbulence varies with time. The large scale charge motion can move the flame in the combustion chamber, affecting the flame interaction with the cylinder walls, hence affecting the flame area and unburned gas temperature.


2.3 KNOCK The knock phenomenon has been extensively studied in the past. Grandin [15] gives an interesting historical review of the evolution of knowledge in the field of knock from the 1920’s an onwards. Knock is initiated by autoignition of the unburned charge ahead of the flame front. Autoignition of the end gas leads to a pressure disturbance in the combustion chamber which induces pressure oscillations. The knocking sound associated with the combustion chamber pressure oscillations have given knock its name. It is also the pressure oscillations, together with an increase in heat transfer, that are potentially damaging to combustion chamber components.

2.3.1 Autoignition chemistry The recent interest in HCCI combustion, where a homogenous air/fuel mixture is compressed until it ignites, has caused renewed interest in autoignition research. HCCI related research also improves the understanding of the knock phenomena, since knock and HCCI combustion are practically the same.

Westbrook [16] describe the chemical mechanisms leading to end gas autoignition in SI engines. Hydrogen peroxide, H2O2, is singled out as the most important species for autoignition chemistry. The dominating reaction in autoignition chemistry at typical engine temperatures below 1200 K is:

MOHOHMOH 22 ++→+ (2.5)

where M is a third body. H2O2 is accumulated during compression from low temperature reactions. Ignition occurs as a result of the chain branching reaction when H2O2 decomposes into two OH radicals. The decomposition of H2O2 is highly temperature dependent and occurs at 900 to 950 K at typical engine conditions. The rapid increase in concentration of the OH radical causes the remaining hydrocarbon to react and ignite. Since the reaction involves a third body, increasing the pressure will increase the probability for collisions and hence lower the critical temperature. Westbrook [16] states that the dominating factor for autoignition is the time at which the mixture reaches the critical temperature and anything that affects this time also affects when autoignition occurs. Low temperature heat release, also called cool flames or Negative Temperature Coefficient behavior (NTC), has strong influence on the time to reach the critical temperature. It is clear from the reasoning in the above paragraphs that the pressure and temperature history of the mixture influences the instantaneous ignition delay time for a given air/fuel mixture.

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NTC behavior and also low temperature heat release is more pronounced for long unbranched paraffinic hydrocarbon chains such as n-Heptane. Risberg [17] summarizes the principal reaction in the low temperature chemistry of some different hydrocarbons. Iso-octane, or 2,2,4-tri-methyl-pentane, is more branched and displays less low temperature heat release and less pronounced NTC behavior which is also evident from Fieweger et. al. [18] where the ignition delay is measured in a shock tube for different PRF mixtures, see Figure 2.1. An increase in temperature increases the ignition delay time in a certain temperature range in the figure. Commercial multi component fuels contain aromatics, olefins and perhaps also oxygenates and their autoignition chemistry is different from that of paraffins [19].

Figure 2.1 Measured ignition delay times in n-Heptane iso-octane mixtures with stronger NTC behavior for higher fractions of n-heptane. Figure 17 in [18].

A fuel’s resistance to autoignition is usually described by the two octane numbers Research Octane number (RON) and Motor Octane number (MON). Practical fuels are rated by comparing their behavior to a primary reference fuel (PRF) in the RON and MON tests. A primary reference fuel is a mixture of iso-octane and n-heptane and the volume percent of iso-octane is the octane number. The RON and MON tests are carried out in a single cylinder CFR engine and the standardized procedures define engine speed, intake air temperature, ignition angle and compression ratio for the two tests. See for example Swarts et. al. [20] for further

10


11

information on the octane rating of fuels in the CFR engine. However, the RON and MON values alone are not sufficient to describe autoignition quality of a fuel. The engine operating conditions, which influence the temperature and pressure history experienced by the fuel, has to be accounted as well. This can be done by using the Octane Index as described in [17][21][22].

2.3.2 Modes of autoignition Pan and Sheppard [23] distinguishes three distinct combustion modes following end gas autoignition; deflagration, developing detonation and thermal explosion. These three basic modes of combustion are discussed in Glassman [9]. The temperature gradient and inhomogeneity in the vicinity of the autoignition center determines which mode is most likely to occur:

• In the case of highly inhomogeneous end gas, autoignition might simply result in a second flame front propagating from the autoignition center, i.e. deflagration.

• Completely homogeneous end gas should result in a thermal explosion, since all unburned charge would ignite at the same time.

• With small end gas temperature gradients and small mixture inhomogeneities, autoignition might result in a developing detonation. In this autoignition mode the reaction front accelerates. Given sufficient time its speed can reach the local speed of sound and there will be a detonation. In engines there is never enough space and time for this to happen. Hence the term “developing” detonation. Nevertheless in this mode very high pressures can be generated.

The pressure wave from an initial deflagrative autoignition center might trigger autoignition elsewhere in the end gas leading to secondary autoignition.

As described above, low temperature chemistry preceding ignition has been shown to have a great influence on autoignition. Higher end gas temperatures promote the low temperature chemistry which increases the probability of initial deflagrative autoignition transforming into developing detonation. Simulations by Pan and Sheppard [23] indicate that an initial deflagrative autoignition at conditions with high mean end gas temperature is likely to result in secondary autoignition centers developing into detonation even under highly inhomogeneous conditions. This is explained by the low temperature chemistry preceding autoignition.

A developing detonation is potentially much more harmful to the engine than deflagration or thermal explosion. The pressure wave amplitudes associated with a developing detonation are high. Conditions in practical SI engines are always


inhomogeneous. The charge is cooled close to the wall or heated by hot spots, e.g. soot particles.

2.3.3 Combustion chamber oscillation modes Knock oscillation frequencies have been shown to correspond to the natural frequencies of the combustion chamber, for example in Brunt et. al. [24] and Bengisu [25]. The engines used in the present work were equipped with a pentroof shaped combustion chamber which can be approximated by a cylinder in an attempt to calculate the natural frequencies of the cylinder. The solution to the wave equation:

⎪⎪⎩

⎪⎪⎨

⎧

=∂∂

=∆−∂∂

boundary on the 0

022

2

nu

uctu

(2.6)

in a cylindrical model of the combustion chamber with cylindrical coordinates (r, θ, z) has the eigenfunctions (possible vibration modes):

( ) ( ) ( )tfhzkm

BrJtzru knmnmmknm ,,,,, 2sincoscos2

,,, ππθαθ ⋅⎟⎠⎞

⎜⎝⎛⋅⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛= (2.7)

for the vibrational modes m, k = 0, 1, … and n = 1, 2, … where m is the circumferential mode number, n is the radial mode number and k is the longitudinal mode number. Jm denotes the Bessel function of the first kind, αm,n are the zeros of the first derivative of Jm to satisfy the boundary conditions, B is the bore, h is the instantaneous model cylinder height and fm,n,k are the natural frequencies:

22

,,, 22

⎟⎠⎞

⎜⎝⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

hk

Bcf nm

knmπα

π (2.8)

The longitudinal modes are often not considered since the natural frequencies of these modes are high close to top dead center, where knock usually occurs. Equation (2.8) then reduces to:

nmnm Bcf ,, α

π= (2.9)

For m > 0, the eigenvalues are double with cos(mθ) replaced by sin(mθ) in the corresponding eigenfunctions.

12


The speed of sound (transverse propagating wave) in an ideal gas is:

MRTc γ

= (2.10)

where γ is the ratio of specific heats, R is the universal gas constant, T is temperature and M is molar mass. Since the speed of sound is proportional to the square root of absolute temperature, the natural frequencies of the combustion chamber will decrease during the expansion stroke when temperature decreases.

Table 2.2 gives natural frequencies and shows eigenfunctions for the six modes with lowest natural frequency for the engines used in this work with a bore of 86 mm. Speed of sound was estimated to 950 m/s which correspond to a temperature of approximately 2500 K. It should be observed that all modes except the first radial mode have a nodal line in the combustion chamber center. This is important when choosing cylinder pressure transducer position for the purpose of knock detection and analysis.

Table 2.2 Predicted vibration modes with natural frequencies below 20 kHz for a cylinder with 86 mm diameter and speed of sound c = 950 m/s.

Vibration

mode

1st circumferential

m = 1, n = 0 2nd circumferential

m = 2, n = 0 1st radial

m = 0, n = 1

α m,n 1,84 3,05 3,83

f m,n [kHz] 6,47 10,7 13,5 um,n

Vibration

mode

3rd circumferential

m = 3, n = 0 4th circumferential

m = 4, n = 0 1st combined

m = 1, n = 1

α m,n 4,20 5,32 5,33

f m,n [kHz] 14,8 18,7 18,75 um,n

13


14

This approximation of the acoustic vibration in the combustion chamber has been shown to give accurate predictions of natural frequencies of pentroof shaped combustion chambers. The first circumferential mode was in good agreement with measured data and the second and third circumferential mode predictions were 10 % higher than measurements in Brunt [24]. Bengisu [25] used a FEM model of a pentroof combustion chamber to predict the natural frequencies and shows that the nodal lines of the circumferential modes are aligned to or perpendicular to the pentroof symmetry axis.

2.3.4 Measures of knock Several definition exist for knock intensity based on either measured cylinder pressure or calculated heat release. Worret et. al. [26] has explored different techniques for detection of knock onset and knock intensity. They conclude that knock intensity should be based on signal energy of the high pass filtered pressure signal or heat release signal. A measure of the signal energy is obtained by integrating the squared high pass filtered signal over a short interval after knock onset. They also conclude that knock onset determined as the point where the signal exceeds a threshold value generally gives too late identified knock onset. A new knock detection algorithm based on high pass filtered heat release is described.

Knock onset determined from the cylinder pressure signal can not be more accurate than the propagation time of a pressure wave from the knock center to the pressure transducer. Assuming that the knock center is at a distance of half the bore from the pressure transducer and that the speed of sound is 950 m/s this propagation time can be calculated. With 86 mm bore, the maximum propagation time from the knock center to a centrally located pressure transducer is 0,5 CA at 1000 rpm and 2,7 CA at 5000 rpm.

2.4 COMBUSTION SIMULATION Several approaches to combustion simulations are used in one dimensional simulation software. The simulation software GT-Power provides three predefined ways of modeling SI engine combustion. First of all, a measured combustion profile can be imposed. This is useful when measured data exists. The second approach is to define the combustion profile by the Wiebe function, which will be described in more detail below. The third approach is a turbulent flame model which also uses a model for in cylinder turbulence to estimate flame propagation. Furthermore, a user defined combustion model can be implemented or the one dimensional simulation can be coupled to three dimensional simulation software. The turbulent flame model has the


15

highest degree of physicality among the three predefined SI combustion models but requires measured or estimated swirl and tumble coefficients and has several multipliers for calibrating the simulated combustion to measured data. The simpler approaches, measured combustion profile and Wiebe function, rely on measured data but can be very useful in the absence of a physical model.

Three dimensional calculation of in cylinder flow and chemical reactions is not practical today, in part because of computer execution time and because of the complex flow field and complex chemical kinetics in the cylinder. State of the art chemical kinetics codes can predict the oxidation of single component fuels, but the research has not yet reached full insight when it comes to practical fuels.

It is important to note how the combustion profile, taken from measured data or calculated by the Wiebe function, is handled in GT-Power. The combustion profile in GT-Power defines the rate at which the charge enters a set of chemical equilibrium equations. The equilibrium composition changes with temperature and mixture strength, which causes the heat release rate to lag the burn rate in a GT-Power simulation [4]. A simple example is shown in Figure 2.2 below. Wiebe parameters fitted to experimental data were used as input to a GT-Power simulation. The GT-Power burn rate in the figure is identical to the input Wiebe function, except for the scaling which is due to a combustion efficiency set below 1 in the simulation. Comparison of the 50 % heat released point and 10-90 % combustion duration of the input and output heat release is given in Table 2.3. As seen in the table it is necessary to adjust the Wiebe parameters to some extent before simulation since the Wiebe parameters are interpreted as burn rate in GT-Power.


-15 0 15 30 45 60

0.0

0.2

0.4

0.6

0.8

1.0

spark timing

Measured heat release Fitted Wiebe GT-Power burn rate GT-Power heat release

Nor

mal

ized

hea

t re

leas

e an

d bu

rn ra

te

Crank angle [aTDC]

Figure 2.2 Measured heat release and Wiebe function fitted to measured data used as input to GT-Power together with GT-Power cumulative burn rate and heat release.

Table 2.3 Wiebe combustion parameters for measured simulation model input heat release and simulation model output heat release from GT-Power. The difference is due to the interpretation of input combustion profile as burn rate as described above.

50 % heat released [aTDC]

10-90 % combustion duration

[CA]

Wiebe parameter m

Input/measured heat release 22,8 22,2 3,97

Simulation model output heat release 24,8 23,9 3,64

Difference 2,0 1,7 -0,33

16


2.4.1 The Wiebe function One way of specifying the combustion rate in a two-zone combustion model is the Wiebe function [27]. The Wiebe function is commonly used in SI engine simulation. The functional form:

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

∆−

−−=+1

0exp1m

b axθθθ

θ (2.11)

is used to describe the fraction of fuel burnt xb based on considerations of chain reactions in general. θ is the crank angle, θ0 is the start of combustion and ∆θ is the total combustion duration. The parameter m is called the combustion mode parameter and defines the shape of the combustion profile. m was introduced by Wiebe to describe the time dependence of concentration of reaction centers by the function:

(2.12) mkt=ρwhere k is a constant. In a spherically expanding flame with constant flame speed one would expect m to be 3. Accelerating flame speed should give higher values and vice versa. Wiebe found m to be in the range 2-4 for SI engines. The value of the constant a in Equation 5 follows from the chosen definition of end of combustion. With the mass fraction burned xb,EOC = 99,9% at the end of combustion, a has the value:

( ) 90,6001,0ln1ln , =−=−−= EOCbxa (2.13)

2.4.2 Knock simulation The knock simulation method used in this work and in Paper II is based on the Livengood-Wu knock integral [28]:

∫=kt dt

0

1τ

(2.14)

where τ is the ignition delay time as a function of temperature and pressure and tk is the time of autoignition. The basic idea behind the Livengood-Wu knock integral is best explained by considering a very simple system with constant autoignition delay time τc at a given pressure and temperature. If the system is exposed to this pressure and temperature for the time τc, it is expected to ignite. The value of the integral in Equation (2.14) at the autoignition instant would be unity. It is assumed that this reasoning holds also for a more complex system where pressure, temperature, composition and ignition delay time vary with time. The ignition delay time in this

17


case is an aggregate ignition delay time for completion of the entire autoignition mechanism as described previously. The instantaneous value of the integral is a measure of the fraction of pre-autoignition reactions that have been completed. It is a way of accounting for the pressure and temperature history of the unburned charge.

It is clear from the description of autoignition chemistry above that the pressure and temperature history of the charge determines the current state of the charge and influences the instantaneous ignition delay time for a given mixture. Pressure and temperature history determines to what extent the low temperature chemistry has been completed and also the concentration of the critical H2O2 species. Nevertheless, an ignition delay time with only temperature and pressure dependence has been used in Equation (2.10) by several authors, e.g. Douaud and Eyzat [29]. The functional form used for this aggregate ignition delay time is:

⎟⎠⎞

⎜⎝⎛= −

TBAp n expτ (2.15)

The functional form is similar to the Arrhenius expression for chemical reaction rate with a pressure dependence added. The constants in Equation (2.15) have been fitted to several fuels from rapid compression machine test data as well as from engine test data. Values of the constants from several references are summarized in Table 2.4.

Table 2.4 Reported values for the constants in Equation (2.15) from several authors for temperature in K and pressure in bar. The value of the constant A has been recalculated to metric units in some cases.

Fuel A

[s.barn]n B

[K] Reference

PRF 95 1.62e-2 1,7 3800 Douaud, Eyzat [29]

PRF 100 1,87e-2 1,7 3800 Douaud, Eyzat [29]

Commercial RON 93, MON 82 1.02e-4 1,01 6220 Douaud, Eyzat [29]

PRF100 (isooctane) 1.68e-2 1,49 7457 By et.al. [30]

Gasoline/Ethanol, RON95 7.59e-3 1.325 3296 Current study

Measured ignition delay times for the reference gasoline RD387 and a surrogate mixture with similar ignition delay behavior as gasoline from Gauthier et. al. [31] are shown in Figure 2.3. The pressure exponential n was found to be 1,64 for n-Heptane and 1,01 for the reference gasoline. The solid markers are ignition delay without residual gases at λ = 1. Other markers are at various lean, stoichiometric and rich mixtures with or without EGR. λ and EGR seem to affect ignition delay time.

18


Gauthier et. al. [31] concludes that richer mixture gives shorter ignition delay at higher pressures and lean mixture gives longer ignition delay. Increased EGR content increases ignition delay. The test data in Gauthier et. al. [31] does not include the region where NTC behavior is expected, compare with Figure 2.1, but it is clear that temperature dependence decreases at lower temperature.

0.8 0.9 1.0 1.1 1.20.01

0.1

1

1250 1111 1000 909 833

λ = 0,5 to 2, 0 to 30% EGR

λ = 1, no EGR

Douaud, Eyzat (1978)gasoline RON 92/MON 83

Douaud, Eyzat (1978) PRF 87

current study

Temperature [K]

Igni

tion

dela

y at

5 M

Pa

[ms]

1000/T [K-1]

Gasoline Surrogate A

Figure 2.3 Measured ignition delay time from shock tube experiments for a reference gasoline RD387 with (RON + MON)/2 = 87 and a surrogate mixture as reported in Gauthier et. al. [31]. Solid markers are λ = 1 aEGR. The lines are estimated aggregate ignition delay time according to

nd no

Equation (2.12) calibrated by engine tests with constants reported in Table 2.4.

emperatures but can not be expected to predict ignition delay at higher temperatures.

Ignition delay time in Equation (2.15) is an attempt to fit a linear curve to represent the data in Figure 2.3 in the region where the engine operates, i.e. at the temperatures and pressures of the end gas at knocking conditions. Figure 2.4 shows the temperature and pressure history from spark timing to detected knock from tests used to calibrate the constants of Equation (2.15) in this work. This data is in the region where the fuel is expected to have low or negative temperature dependence. The estimated ignition delay time at 5 MPa from the calibration in this work as well as from Douaud and Eyzat [29] is also shown as lines in Figure 2.3. The estimate from this work fits the shock tube test data well in the relevant region at low t

19


It is also noticeable from the pressure and temperature data in Figure 2.5 that knock occurs at temperatures slightly above 900 K which is a critical temperature for the decomposition of H2O2 as described earlier. Also drawn in Figure 2.5 is an isentropic compression line leading to one of the knocking cycles calculated with γ = 1,25 which shows that the operating conditions for these knocking cycles were quite similar, i.e. they are close to the same isentrop.

1.1 1.2 1.3 1.4 1.5 1.6

2

4

6

8

10

909 833 769 714 667 625

Unburned zone temperature [K]C

ylin

der p

ress

ure

[MP

a]

1000/T [K-1] Figure 2.4 Pressure and temperature history for several knocking cycles at different operating conditions from approximately 30 bTDC to knock onset.

20


890 900 910 920 930 9407.5

8.0

8.5

9.0

9.5

10.0

10.5

Cyl

inde

r pre

ssur

e at

kno

ck [M

Pa]

Unburned zone temperature at knock [K]

Figure 2.5 Unburned zone temperature and pressure at knock for several knocking cycles at different operating conditions. The dash-dotted line is an isentrop drawn from one of the knocking cycles calculated with γ = 1,25.

In a recent work by Yates et. al. [32] an attempt has been made to model the different regions of the ignition delay times by one Arrhenius type expression according to Equation 2.15 for each of the three regions: low temperature region, NTC-region and high temperature region. The total ignition delay time is formed by the expression:

( )[ ] 113

121

−−− ++= ττττ (2.16)

with values for the constants for a model gasoline found in Table 2.5. The resulting ignition delay surface is shown in Figure 2.6 with ignition delay histories for three knocking cycles. It is evident from the figure that the knocking cycles just barely enter the high temperature region for this test data, which explains why the single stage ignition delay model shown in Figure 2.3 works well. Yates et. al. [32] also show that fuel/air ratio can be modeled by the relationship:

( ) βλ λτλτ 1== (2.17)

where β ≈ 0,67, identified from Figure A.1 in Yates et. al. [32].

21


Table 2.5 Constants for a model gasoline in three part ignition delay model from Yates et. al. [32].

22

ln(A) n B

τ1, low temperature -19,7 -0,101 16196

τ2, NTC-region 11,33 -1,623 -3136

τ3, high temperature -11,02 -0,949 15250

Figure 2.6 Ignition delay surface from three part ignition delay model from Yates et. al. [32] for a model gasoline with ignition delay trajectories for 3 knocking cycles.

23

Chapter 3

EXPERIMENTAL METHOD

This chapter contains a summary of the measurement system used in the experimental part of this work along with estimated errors in the measurements in order to give a general idea of the measurement accuracy. A few paragraphs are devoted to signal processing, which plays a key role in obtaining high quality measurement data. Finally, the engines used in the experiments are described, including a brief overview of the Divided Exhuast Period system.

3.1 MEASUREMENTS

The measurements conducted within this project had several key purposes. One of the purposes was to be able to calibrate a simulation model of the Divided Exhaust Period engine. The second purpose was to gain further understanding of how the Divided Exhaust Period engine responds to different changes in operating conditions and exhaust system geometries. Furthermore, measurements were used as a tool to create and calibrate empirical models for knock and combustion in SI engines, as described in Paper II and Paper III.

3.1.1 Measurement system

The test bed control and measurement system used was Cell4, developed by Professor Hans-Erik Ångström. The system is very flexible and accepts analogue and digital input signals which can be measured either as high frequency crank angle resolved data or low frequency time resolved data. Slow measurements are accomplished mainly through Nudam data acquisition modules [33] which accept voltage or


24

thermocouple input depending on model. A sampling frequency of approximately 1 Hz was possible for these measurement channels. Crank angle resolved measurements were accomplished by a 12-bit PowerDAQ A/D card [34] with 1 MHz total sampling frequency divided over a maximum of 16 input channels in the current setup. PIC microcontrollers measured digital input, such as crank angle encoder pulses and turbo speed signal, and produced control signals for test bed and engine control. The PIC:s additionally produced single engine revolution averages for analogue inputs, accomplished by buffering transducer input from external 12-bit A/D converters at 10 kHz and averaging the buffered data once every engine revolutions. Several custom built signal amplifying units were used to drive transducers in the system and condition transducer output signals.

3.1.2 Pressure measurement

Pressure was measured at several positions on the engine for the purpose of calibrating the simulation model. On the intake side of the engine, pressures were measured upstream and downstream of each major component, such as compressor, charge air cooler and throttle. Flush mounted GEMS steel diaphragm gauge pressure transducers [35] with 4 bar range were used for these measurements. In cylinder pressures were measured in all four cylinders with near flush mounted AVL GM12D uncooled miniature piezo-elecric transducers [36] and Kistler 5011 charge amplifiers [37]. The transducers have M5 dimensions, which was the largest that could be fitted in the Divided Exhaust Period cylinder head. Kistler 4045A10 piezoresistive pressure transducers [37] were used in the exhaust manifold before and after the turbine, primarily due to the availability of suitable cooling adapters, less thermal sensitivity and higher natural frequency. GEMS transducers with cooling adapters were used at several other positions in the exhaust manifolds.

Static calibration of the low pressure transducers, strain gauge and piezo-electric, was accomplished by a traceably calibrated Druck DPI 705 pressure indicator with a hand pump [38]. The entire measurement chain was calibrated at several occasions and the resulting error ranged from ±0,5 - 1 % FS for the 4 bar GEMS transducers and below ±0,08 % FS for the 10 bar Kistler transducers which translates to absolute uncertainty in static measurements of ±2 - 4 kPa for the GEMS transducers and 0,8 kPa for the Kistler transducers.

A dead weight tester, Ametek Hydralite [39], was used for cylinder pressure transducer calibration in the range 0 - 10 MPa. Including the uncertainty for the dead weight tester and A/D conversions, the linearity error for the measurement chain was found to be below ±0,4 % FS or 40 kPa. The cyclic temperature shift according to the

Chapter 3 – Experimental method

25

transducer manufacturer is < ±60 kPa for the GM12D cylinder pressure transducers. Cyclic temperature shift, i.e. thermal shock, typically leads to too low measured pressure during combustion and during the following expansion stroke [40]. Lee et. al. [41] have quantified the effects of thermal shock in an uncooled transducer with similar properties as the ones used in this work and found that thermal shock persisted through the exhaust stroke, ultimately affecting measured IMEP with up to -4 %. One drawback with using the dead weight pressure tester at ambient temperature, which was the case here, is that the sensitivity of the uncooled GM12D transducers at ambient temperature might be different from the sensitivity at operating temperatures in the engine cylinders. The manufacturer states the thermal sensitivity shift to ±2 % in the temperature range 20 - 400° C. Both cyclic temperature shift and thermal sensitivity shift can be kept lower for cooled transducers.

3.1.3 Temperature measurement

Shielded 3 mm type K thermocouples were used for most temperature measurements. Cold junction correction was accomplished in the Nudam 6018 data acquisition modules. Thermocouples measure the temperature of the probe tip, which is not necessarily equal to the temperature of the surrounding gas or liquid. Heat transfer along the stem of the thermometer and radiation to pipe walls decreases the measured temperature in the case of hot fluid in a cooler pipe, which is typically the case in an engine exhaust manifold. The fluid flow rate also affects the heat transfer to the thermocouple. Long insertion lengths were used to minimize errors from conductive heat transfer. [42][43]

The response time for a 3 mm thermocouples is several seconds. Hence, the thermocouple signal is some kind of average temperature in typical engine conditions with highly pulsating temperature. According to an investigation comparing measurements and 1-D simulation of the gas temperature in the exhaust manifold of a turbocharged engine in Westin [5], a 3 mm thermocouple with 100 mm insertion length measures a temperature close to the mass averaged temperature of the gas.

The accuracy of class 1 type K thermocouples is the larger of 1.5° and 0,004 times the measured temperature. When testing the linearity of some thermocouples in a IsoTech HTQuickCal block calibrator [44], the errors for the measurement chain were found to be within the stated accuracy of the thermocouples.

Surface temperature of the aluminium inlet manifold was measured for simulation model calibration with a Testo Quicktemp 860-T3 infrared pyrometer [45]. A pyrometer measures the radiation from an object which depends heavily on the


26

emissivity of the material. The emissivity is a measure of how close to a black body radiator the material is and is a number between zero and unity. Many metals and aluminium in particular has low emissivity. Aluminium has emissivity in the range of about 0,05 to 0,2 depending on oxidation and alloy [46]. A small absolute error in estimated emissivity will give large errors in measured temperature with this low emissivity. Therefore, a small area on the manifold was painted with matte black paint which should have an emissivity around 0,9.


3.1.4 Other measurements

Turbo speed was measured with a Micro-Epsilon eddy current probe [47] mounted in the compressor housing. The probe senses the blade passages of the impeller and the accompanying signal processing unit converts the signal to one digital pulse per completed turbo revolution, which can be up to some 20 crank angles apart depending on engine and turbo speed. The time between pulses is converted to turbo speed and the timestamp of each pulse gives the corresponding crank angle. Any disturbances on the transducer signal might be identified as a blade passage. When this happens, the data analysis system will identify a too high turbo speed. The digital measurement data evaluation algorithms currently used does not handle these errors which, after interpolation to the crank angle basis of the other measurements, gives quite bad results as seen in Figure 3.1.

-180 -90 0 90 180 270 360 450 540

85

86

87

88

89

90

91

average

single cycle(+1000 rpm)

measured data points interpolated data

error in average

correctedaverage

Turb

o sp

eed

[100

0 x

rpm

]

Crank angle [aTDC] Figure 3.1 Error in measured turbo speed from disturbance detected as impeller blade passage make large difference in the averaged data. Single cycle data (top) has been shifted up 1000 rpm.

27


Lambda was measured with an ECM AFRecorder 2000A with the stated accuray ±0.008 for 0,8 < λ < 1,2 [48]. Fuel mass flow was measured by weighing the fuel in a small reservoir with approximately 2,5 dm3 volume. Calibration of the ASE scales was performed by applying known weights to the scales. A measurements accuracy of < ±0,1 % FS was obtained in static calibration, but the measured fuel flow varied significantly over an emptying cycle of the reservoir with the engine running in steady state. Typically, the measured fuel mass flow would decrease during each emptying cycle as in the example in Figure 3.2. This highlights the difference between static and dynamic calibration. The fuel flow measuring system behaved perfectly in static condition, but quite poorly in dynamic conditions. Dynamic calibration has not been performed for any of the measuring systems involved in this work.

0 20 40 60 806.1

6.2

6.3

6.4

6.5

6.6

1150

1250

1350

1450

1550

1650

mass flow

mass

Fuel

mas

s flo

w [g

/s]

Time [s]Fu

el m

ass

[g]

Figure 3.2 Measured fuel flow and the fuel mass in the scales during steady state engine operation.

28


3.2 DATA ACQUISITION

As already mentioned, a 12-bit A/D converter was used for crank angle resolved measurements in the Cell4 measurement system. The input range for the A/D converter was -10 V to +10 V, which was also the output range of the charge amplifiers. The charge amplifiers was set to the physical range 1 V/MPa to be able to measure 10 MPa peak pressure in this set-up. This leads to a quite coarse resolution in the measured cylinder pressure during the gas exchange process, as shown in Figure 3.3. One A/D bit corresponds to 4,88 kPa with these cylinder pressure measurement settings, or 0,049 % FS. The measuring uncertainty introduced by the A/D conversion is small compared to the other error sources described above.

360 405 450 495 540

100

120

140

160

180

Cyl

inde

r pre

ssur

e [k

Pa]

Crank angle [aTDC]

Figure 3.3 Cylinder pressure from a single cycle during intake stroke sampled with 12-bit A/D converter. A 1,5 kHz FIR low pass filter has been applied to the data. (3000 rpm, 1,49 MPa imep)

29


3.2.1 Signal conditioning

Signal filtering is important to obtain high quality measurements. Anti-aliasing low pass filters should be applied to the analog measurement signal before sampling. The cut-off frequency has to be below the Nyquist frequency, i.e. half the sampling frequency. Transducer natural frequency should also be considered in the choice of cut-off frequency for the anti-aliasing filter. The data displayed in Figure 3.3 was sampled at 45 kHz and the built in 30 kHz filter in the charge amplifier was used to limit aliasing. This means that frequencies between 15 and 22,5 kHz in the sampled signal also contain aliased signals from the 22,5 to 30 kHz range in the real signal.

A more detailed study was made of the frequency content of the cylinder pressure signals from one of the engines used in this work. The frequency content was examined over the engine speed range with non-knocking combustion at high load. A discrete Fourier transform of the measured signal from many consecutive cycles shows peaks at every half engine revolution frequency, as should be expected from a four stroke engine with combustion every second revolution. The frequency content along with the envelope of the peak amplitudes is shown in Figure 3.4.

0 2 4 6 8 10

1

10

100

1000Peak amplitude

envelope

Cyl

inde

r pre

ssur

e [k

Pa]

Frequency [1/revolution]

Figure 3.4 Frequency content for several consecutive cycles at 1000 rpm and the peak amplitude envelope.

30


The amplitudes of the peaks decrease at higher frequencies. Figure 3.5 shows the peak frequency envelope for several engine speeds. The peak amplitudes on a per engine revolution basis look very similar for all engine speeds and the peaks become buried in noise above 30 times the engine revolution frequency, which leads to the recommendation to low-pass filter the data with the cut-off frequency:

260

30 NNfLP =⋅= [Hz] (3.1)

with the engine speed N given in rpm.

0 5 10 15 20 25 30 35 400.1

1

10

100

1000

suggested cut-offfrequency

1000 rpm 2000 rpm 3000 rpm 4000 rpm 5000 rpm

Cyl

inde

r pre

ssur

e [k

Pa]

Frequency [1/revolution] Figure 3.5 Cylinder pressure frequency envelope per engine revolution at operating conditions from 1000 rpm to 5000 rpm at high load. Several consecutive cycles at steady state operation was used in the analysis.

Figure 3.6 shows the cylinder pressure frequency content again, with the useful frequency range according to Equation (3.1) marked. It is noticeable from Figure 3.6 that the natural frequencies of the combustion chamber, see Chapter 2.3.3, show up at high engine speed, although there was very few knocking cycles in the data set. Low amplitude combustion chamber pressure oscillations seem to be the result of the rapid pressure rise with respect to time during combustion at high engine speed.

31


0 5 10 15 20

0.01

1

100 2.25 kHz4500 rpm

Pre

ssur

e [k

Pa]

Frequency [kHz]

0 5 10 15 200.01

1

100 1,5 kHz3000 rpm

Pre

ssur

e [k

Pa]

0 2 4 6 8 10

0.01

1

100 Cutoff frequency0,75 kHz

1500 rpm

Pre

ssur

e [k

Pa]

Figure 3.6 Cylinder pressure frequency content analyzed from several consecutive cycles at steady state operation and suggested cut-off frequencies at 30 times the engine rotational frequency.

3.2.2 FIR low pass filter

A Finite Impulse Response (FIR) filter was implemented to filter the sampled pressure data. The filter consists of a windowed sinc function, Equation 3.5, which is convoluted with the data. The idea behind using convolution with the sinc function is that multiplication with a transfer function in the frequency domain corresponds to convolution with the impulse response in the time domain. In the frequency domain, an ideal low pass filter transfer function has zero amplitude for all frequencies above the cut-off frequency fLP and amplitude one with zero phase shift for frequencies below the cut-off frequency. The impulse response of this step-like function in terms of the normalized frequency q0

s

LP

ff

q =0 (3.2)

is its inverse Fourier transform:

32


( ) ( ) ( )[ ]

( ) ∞−∞===

=>==

∫

∫

−

−

.. ,2sin121

,2221

02

0

5,0

5,0

2

0

0

kkqk

dqe

qqqHdqeqHkh

q

q

qki

qki

πππ

πππ

π

π

(3.3)

which is an infinite sequence. The impulse response of the ideal low pass filter is usually truncated with some kind of window function to make computation possible and to limit the computation time. The Hanning window was chosen in this work. A Hanning window with width 2M + 1 centered around k = 0 is given by:

( ) MMkMMkkw .. ,cos5,05,0 −=⎟

⎠⎞

⎜⎝⎛ −

⋅−= π (3.4)

By introducing the sinc function:

( )( )

⎪⎩

⎪⎨⎧

=

≠=0 , 1

0 ,sinsinc

k

kkk

k ππ

(3.5)

Equation 3.3 can be simplified and the final normalized filter kernel is:

( ) ( ) ( )( )

( ) MMkkg

MMkkqq

kwkhkg .. , cos5,05,02sinc2 00

−=⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

⋅−⋅⋅=⋅=

∑

π

(3.6) The filter length determines the steepness of the filter. The length of the filter

was chosen to get a filter kernel with Kf periods of the sinc function by setting the half filter length M according to:

0

0 22qK

MKMq ff =⇒= ππ (3.7)

Kf = 3 was used for most of the filtering in this work. A higher Kf, i.e. a longer filter kernel, gives steeper filter characteristics at the cut-off frequency but also more pronounced non-causal behaviour which shows up as ringing in the filtered signal prior to steep changes in the raw signal. This can be undesired in for example band pass filtering for knock onset detection, as described further below. Kf can be explained as the number of oscillation periods in the filtered signal before and after a step in the input signal.

Figure 3.7 shows an example of cylinder pressure data filtered with the described windowed sinc filter. The suggested cut-off frequency from section 3.2.1 is

33


1,5 kHz, which seems to preserve the characteristics of the data. A lower cut-off frequency removes significant frequency components and produces lower pressure rise rates and lower peak pressure, as seen in the figure. A higher cut-off frequency will attenuate less noise.

25 30 35

4.6

4.8

5.0

5.2A/D reading1,5 kHz filter

1,0 kHz filter

Cyl

inde

r pre

ssur

e [M

Pa]

Crank angle [aTDC]

Figure 3.7 Cylinder pressure filtered with zero phase shift FIR-filter with 1,0 kHz and 1,5 kHz cut-off frequency. (3000 rpm, 1,49 MPa imep)

Convolution of a data sequence of length n with a filter kernel of length 2M + 1 results in a filtered sequence of length n + 2M. 2M points at each end of the data sequence contain data where the original data and the filter do not overlap completely in the convolution. This causes transients in the filtered data sequence. The original data sequence was extended at each end with data from the other end of the sequence to avoid transients. Since the engine pressure data is of periodic nature and all measurements were made at steady state this should be an adequate method of extending the data sequence. A more elaborate method is to mirror, inverse and shift the data set in the end points according to Equation (3.8), which eliminates possible discontinuities due to non-steady state data or transducer drift.

( )( ) ( )

( )( ) ( )⎪

⎩

⎪⎨

⎧

−+≤≤−−−−≤≤

−≤≤−−−=

1 , 212 10 ,

1 , 02

Mnknknpnpnkkp

kMkppkpextended (3.8)

This extended data sequence can be convoluted with the filter kernel and the 2M points at each end can be discarded.

34


3.2.3 FIR band pass filter

The frequency content in the cylinder pressure signal changes significantly during knocking combustion. As described above, autoignition of the end gas induces pressure oscillations in the combustion chamber with frequencies corresponding to the natural frequencies of the combustion chamber. Knock amplitude and knock onset had to be determined in the work with the knock model in Paper II. For this purpose, the acquired cylinder pressure data was band pass filtered with the pass band located around the lowest natural frequency of the combustion chamber. A FIR bandpass filter can be designed as the difference between a high pass filter and a low pass filter as described in the previous section. The resulting windowed filter kernel with passband between q0 and q1 is:

( )( ) ( )( )

( ) MMkkg

MMkkqqkqq

kgBP

BP .. , cos5,05,02sinc2sinc2 0011

−=⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

⋅−⋅⋅−⋅⋅=

∑

π

(3.9) One major drawback with using this type of filter is the non-causal properties

of the filter. This will introduce ripple in the signal prior to the actual knock onset. Using a short filter decrease the ripple but the filter steepness also decreases. A FIR filter according to Equation (3.9) is good for evaluating knock level, but not for detection of knock onset.

3.2.4 IIR filtering for detection of knock onset

A causal filter will not give any output before the actual knock onset, which should be suitable for knock onset detection. Many different recursive filter structures exist of which many are digital representations of common analogue filter structures such as Bessel or Butterworth. These filters are referred to as infinite impulse respone filters (IIR) since they have an infinitely long impulse response in the time domain. IIR filter have phase distortion as opposed to the FIR filter described above with zero phase distortion. The short filter lengths of recursive IIR filters make them very computationally efficient compared to FIR-filters. With IIR forward and backward filtering the phase distortion can be avoided [49]. No evaluation of the most appropriate IIR-filter for detection of knock onset has been made in this work. A low order filter should be preferable to a higher order filter to minimize phase distortion.

35


3.3 HEAT RELEASE CALCULATION

Heat release was calculated from measures cylinder pressure data based on the first law of thermodynamics with a single temperature zone as described in for example Heywood [8]. Heat transfer to the combustion chamber walls were calculated according to Woschni’s correlations also summarized in Heywood [8]. Crevice effects were not accounted for. The resulting equation for calculating rate of heat release is:

( )wcch TTAh

ddpV

ddVp

ddQ

−+−

+−

=θγθγ

γθ 1

11

(3.10)

where Qch is the chemical energy released from the fuel. Calculation of the mixture and temperature dependent ratio of specific heats in the mixture is described in detail in section 3.3.1 below. T and Tw is the gas and wall temperatures and hc is the heat transfer coefficient given by:

(3.11) 8,055,08,02,026,3 wTpBhc−−⋅=

where B is the bore, p is cylinder pressure, T is average gas temperature and w is the average gas velocity in the cylinder, approximated by:

( )mrefref

refdp pp

VpTV

CSCw −+= 21 (3.12)

The first term in Equation (1.12) describes the gas velocity from the piston motion and swirl and the second term describes the rise in average gas velocity due to combustion. pm is the motored pressure.

The charge temperature and hence the trapped mass was determined at inlet valve closing (IVC) as the weighted average of intake temperature and exhaust temperature at inlet conditions:

(3.13) *)1( exhrinletrIVC TxTxT ⋅+⋅−=

Residual gas content xr was obtained from simulations. T*exh was calculated by assuming isentropic expansion or compression from exhaust pressure and temperature to inlet pressure:

exh

exh

inlet

exhexhexh p

pTT

γγ 1

*

−

⎟⎟⎠

⎞⎜⎜⎝

⎛= (3.14)

with the average ratio of specific heats of the exhaust gases evaluated at inlet and exhaust temperatures.

36


Charge temperature was calculated from measured pressure and cylinder volume with the ideal gas law:

( ) IVCIVCIVCIVC TVppV

mRpVT

⋅== (3.15)

Motored pressure pm was calculated from inlet valve closing to exhaust valve opening by assuming isentropic compression and expansion of the charge, with ratio of specific heats evaluated for unburned mixture at each time step. Motored pressure was used in the calculation of heat transfer and the calculation of pressure ratio as described below.

3.3.1 Thermodynamic properties of mixture

One key parameter for accurate estimation of heat release from pressure data is the ratio of specific heats [50][51], which is the heat capacity at constant pressure divided by the heat capacity at constant volume, γ = cp/cv,. Thermodynamic theory state that γ is constant for a ideal monoatomic gas whereas γ is a function of temperature only for a semi-perfect gas. The charge in the combustion chamber is a mixture of several components, each of which can be considered as a semi-perfect gas. Several approaches of modeling the thermodynamic properties of the cylinder charge have been tested with the heat release calculation algorithm described above.

First of all the basic relationship between heat capacities is needed. Molar heat capacity at constant volume and constant pressure are related by:

K][J/mol ⋅−= RCC pV (3.16)

where R is the gas constant with appropriate unit. Specific heat capacity is related to molar heat capacity by the molecular mass M:

K][J/kg ⋅=MC

c pp (3.17)

CV of an ideal gas can be predicted by kinetic theory as:

RdfCV 2= (3.18)

where df are the degrees of freedom of motion of the molecules in the gas. For monoatomic molecules only translation energy contributes to the internal energy which gives three degrees of freedom. For diatomic gases two rotational degrees of freedom are added and at high temperatures also vibration energy. For more complex molecules such as the hydrocarbons in gasoline the vibration energy becomes more

37


important which gives an even higher CV. A high value of CV gives a low γ. This can help in understanding the general trends γ of in the combustion chamber. During the compression stroke in a PFI engine, the cylinder charge consists of air and fuel. Air consists mainly of diatomic molecules with 5/2 degrees of freedom giving γ = 7/2 = 1,4 at low temperature. The fuel has very high CV and γ close to 1, which means that overall γ is dependent on air/fuel ratio. Residual gases contain carbon dioxide and water, which are triatomic, giving a slightly lower γ than that of pure air. Temperature rise during combustion decrease γ since vibrational energy becomes important. Figure 3.8 shows CV/R for some of the gas molecules found in the combustion chamber over the temperature range relevant to SI engines. Iso-octane is included in the figure as an indication of the heat capacity of a hydrocarbon fuel.

500 1000 1500 2000 2500 3000

1/2

3/2

5/2

7/2

9/2

11/2

Temperature [K]

CV /

R

20

40

60

80

CV /

R (i

so-o

ctan

e)

iso-octane

CO2

H2 H

H2O O2

N2

Figure 3.8 CV/R for some molecules from JANAF tables [54].

The first investigated approach of estimating γ in the combustion chamber was to consider the trapped charge as pure air, with a temperature dependent γ. A second degree polynomial for the temperature dependence of γ in air is found in Kanury [52]:

(3.19) [g/mol] 96.28

K][J/kg 10105,32402,04.917 25,

=

⋅⋅⋅+⋅+= −

air

airp

M

TTc

The second investigated approach is the AVL model for γ [53], which has linear temperature dependence:

38


( )( ) ( ) 310155,07,0

12888,0

−⋅+⋅+=

+=

iV

V

ATTc

Tcγ

(3.20)

with the constant Ai = 0,1 for SI engines.

The third investigated approach was to calculate frozen mixture equilibrium composition and use NASA polynomials [54] to calculate temperature dependent Cp for air, fuel and residual gases as described in Chapter 4 of Heywood [8].

(3.21) ( ) ∑−=

=4

2i

iip TaTC

Residual gas content was obtained from simulations. The pressure ratio:

( ) ( )( ) 1−=θ

θθmppPR (3.22)

was used to capture the transition from unburned gases to burned gases during combustion. The normalized pressure ratio weighted average of unburned gas γu and burned gas γb was used in the heat release calculations:

( ) ( ) ( )TPRTPR bnormunorm γγγ ⋅+⋅−= 1 (3.23)

39


Ratio of specific heats and calculated heat release with the different models are shown in Figure 3.9. As seen in the figure, the fuel vapor and residual gases has a major impact on the ratio of specific heats compared to pure air. The AVL model estimate of γ is inbetween the frozen mixture model and the pure air model. Ratio of specific heats from the simulation software GTPower is also included in the figure, which is an average of the burned and unburned zone γ. GTPower predicts higher γ during combustion since dissociation at high temperatures is included in the γ-model. Dissociation introduces smaller molecules with less degrees of freedom of motion and hence higher γ. One conclusion from the tests with different γ-models is that the simple linear and quadratic models fail to capture the high temperature behavior of the charge.

-135 -90 -45 TDC 45 90 135

1.20

1.25

1.30

1.35

1.40

0.00

0.25

0.50

0.75

1.00

GTPowersimulated

temperaturedependent air

AVL model

frozen mixturemodelγ =

cp/c

v

Crank angle [aTDC]Fu

el n

orm

aliz

ed

heat

rele

ase

Figure 3.9 Comparison of different models for the ratio of specific heats γ in the mixture and the resulting calculated heat release. Gas composition: λ = 0,9, gasoline/ethanol fuel and 3 % residual gas content.

40


Figure 3.10 Shows the calculated motored pressure compared to measured cylinder pressure for the different γ-models. The frozen mixture model predicts motored pressure close to the measure pressure. Motored pressure was calculated without accounting for heat transfer to the cylinder walls, which explains why the calculated motored pressure is higher than measured pressure around top dead center.

-90 -60 -30 TDC 30 60 90

1

2

3

temperature onlyfrozen mixture

model

measuredpressure

AVL modelC

ylin

der p

ress

ure

[MP

a]

Crank angle [aTDC]

Figure 3.10 Calculated motored pressure with different models for the ratio of specific heats compared to the measured cylinder pressure.

41


3.4 EXPERIMENT ENGINES

The experimental results reported in this thesis were acquired from a modified two liters turbocharged engine. Some key properties of the engine are summarized below.

3.4.1 Divided Exhaust Period

One key target for this research project was to evaluate the Divided Exhaust Period (DEP) system on a modern four cylinder turbocharged engine, see Paper I. The main principle behind the DEP system is to divide the exhaust flow from each cylinder into two different exhaust manifolds with different valve lifts for the two exhaust valves in each cylinder. Figure 3.11 shows a schematic view of the DEP engine.

C T

Inter- cooler

Catalyst

Exhaust scavenging

system

Exhaust blow-down

system

Charge air system

Trapping valve

Figure 3.11 Schematic view of the Divided Exhaust Period engine.

The reason for dividing the exhaust flow into two different manifolds is to decrease exhaust back pressure during the exhaust displacement phase and to prevent interfering pulses between cylinders in four cylinder turbocharged engines. Using DEP results in decreased residual gas content which should improve knock resistance and increase volumetric efficiency. The pumping losses are also decreased. Figure 3.12 shows a comparison between mass flow over the exhaust valves in a standard turbocharged engine and a DEP engine at 5500 rpm full load operation. The energy rich blow-down pulse is fed to the turbine through the exhaust blow-down system and the remaining exhaust is evacuated through the scavenging system, with a much lower exhaust back pressure.

42


90 135 180 225 270 315 360 405

0.0

0.1

0.2

0.3

scavengingvalve

blow-downvalve

DEPscavenging

system

DEPblow-down

system

standard t/c

Mas

s flo

w ra

te [k

g/s]

Crank angle [aTDC]

Val

ve li

ft

Figure 3.12 Mass flow and valve lift in the DEP engine compared to a standard turbocharged engine at 5500 rpm.

3.4.2 Engine specifications

The DEP engine was based on a standard 2 dm3 turbocharged engine with specification according to Table 3.1. The head was modified with separated exhaust runners. The short valve lift durations in the DEP engine puts special demands on the exhaust valves. Exhaust valve diameter was increased from 28 mm to 32 mm to reduce choking in the exhaust ports. Lightweight sodium cooled exhaust valves were used to maximize possible valve lift. Several exhaust and intake camshafts were used in the investigations. Continuously variable camshaft phasing with an adjustment range of 50 CA was used on both intake and exhaust camshafts.

A standard head and standard exhaust manifold was also used on the engine in the knock tests reported in Paper I.

43


44

Table 3.1 Specifications of the test engines. Bore 86 mm Stroke 86 mm Compression ratio 9.5 No. of cylinders 4 Total displacement 2.0 dm3

Inlet valve diameter 32 mm Exhaust valve diameter, DEP head

32 mm

Exhaust valve diameter, standard head

28 mm

Cylinder head 4-valve pentroof with central spark plug Fuel system port fuel injection Fuel 95 RON, up to 5% ethanol

Cooled EGR The DEP engine was equipped with a cooled EGR system with a Valeo water/air EGR cooler. The EGR was extracted in the exhaust blow-down system, before the turbine inlet. EGR was inserted upstream of the throttle to assure good mixing with inlet air and mixing balance between cylinders. A butterfly valve was used to control cooled EGR rate.

45

Chapter 4

KNOCK MODELING

Paper II contains results from calibration and validation of a knock model based on the Livengood-Wu knock integral as described in Chapter 2.4.2. Some additional information about the experiments and calibration of the knock model is found below together with a new calibration for the ignition delay constants.

4.1 EXPERIMENTS

A limited series of experiments were carried out on the standard turbocharged engine, see Chapter 3.4.2 for engine details. The purpose of the tests was to calibrate and validate the knock model at a number of different operating conditions as described in Paper II. The experiment matrix is repeated below for reference.

Table 4.1 Operating conditions in the knock model calibration and validation test series.

Engine speed 2500, 3000, 3500 rpm

λ @ 2500 rpm 0,92

λ @ 3000 rpm 0,86; 0,99; 1,10

λ @ 3500 rpm 0,84

Fuel 95 RON gasoline w. <5% ethanol Coolant temperature 90 °C

During the engine tests, the level of knock was judged from a band pass filtered audio signal recorded by a microphone mounted close to the engine block.


46

This method of judging knock level is common, but not entirely repeatable and somewhat subjective. Unfortunately the inexperienced operators, the author being one of them, were frightened by the aggressive knocking noise, and very few cycles were found to be knocking in the test series. An engine failure due to valve-piston interaction made further tests impossible at the time. However, the low number of knocking cycles in the test data assured that the engine was operating close to normal operating conditions. It is the borderline knock operation that is relevant for simulation purposes. Operation with large fraction of knocking cycles will affect wall temperature and hence unburned charge temperature which in turn might give a calibration of the knock model to the wrong temperature range. As described in Chapter 2.4.2 the autoignition delay time used in this work is an attempt to linearize the autoignition delay time of a fuel in a temperature range relevant to the normal operation of an engine. Actual autoignition delay time of a hydrocarbon fuel is nonlinear due to the presence of cool flames and negative temperature coefficient regions.

4.2 DATA EVALUATION

As described in Paper II, the data was band pass filtered and knocking cycles were detected by examining the maximum value of the absolute band pass filtered signal. The filter pass-band was set from 3,5 kHz to 10 kHz. Cycles with maximum amplitude above 1 bar were defined as knocking. Knock onset was determined for the knocking cycles as the first time the absolute band pass filtered signal exceeded a threshold value. The threshold value was selected as a compromise between sensitive detection (lower required threshold) and the risk of faulty detection due to noise (higher required threshold). A threshold value of 0,9 bar was found to be good for cycles with high knock intensity, while lower knock intensity cycles needed a lower threshold. A compromise was to use 0,7 times the knock intensity as threshold for low knock intensity cycles.

An finite impulse response filter, FIR, as described in Chapter 3.2.3 was used to band pass filter the data. As already mentioned, this type of filter is non-causal. The result is very obvious in Figure 4.1. The band pass filtered signal starts to oscillate well before the cylinder pressure shows any trace of knock. As a consequence, the detected knock onset was always too early. There was no time to correct this in Paper II. Since there was only a small number of cycles to investigate, knock onset was determined by visual inspection of the signals. A low order recursive filter and zero crossing search as described in Chapter 3.2.4 should have been used instead.

Chapter 4 – Knock modeling

0 5 10 15 20 25 300

20

40

60

80

100

-4

-2

0

2

4

6

detectedknock onset

Cyl

inde

r pre

ssur

e [b

ar]

Crank angle [aTDC]

Band

pas

s fil

tere

d pr

essu

re [b

ar]

Figure 4.1 Cylinder pressure and FIR band pass filtered cylinder pressure for a knocking cycle.

4.3 KNOCK MODEL CALIBRATION

In Paper II, only the constant A was optimized in the Ahrrenius type expression for ignition delay:

⎟⎠⎞

⎜⎝⎛= −

TBAp n expτ (4.1)

The reason for this approach is obvious from the shape of the least squares optimization target function:

( ) ( )

∑ ∫⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

−i

KO

IVC

i

ni

dt

TBAp

SS

2

1exp

1

θθ

(4.2)

shown in Figure 4.2. The data does not contain enough information to uniquely determine the three parameters of the ignition delay correlation. The pressure and temperature data used is also shown in Figure 2.4. Figure 4.2 also shows how the ignition delay constants from other works, see Table 2.4, perform for our data set.

47


Figure 4.2 The shape of the knock model optimization target function with varying A and pressure exponent -n. and fixed temperature coefficient at 2396 K. The results from some previous studies [29][30] are also shown in the figure.

The optimization routine did however converge to a value comparable to other works, despite the low quality for ignition delay parameter optimization in the data set. These optimized parameters, see Table 4.2, are not presented in Paper II since the work was carried out after submission of the paper.

Table 4.2 New optimization of ignition delay function constants. A

[s.barn]n B

[K]

7.59e-3 1.325 3296

The three part ignition delay model with λ dependence from Yates [32] described in Chapter 2.4.2 predicts too late knock onset by 6 to 12 CA for the test data set used in this work. With a scaling factor of 0,60 for the three part ignition delay correlation in Equation (2.16), the model fits the test data with similar errors as the calibrated single part ignition delay model.

48

Chapter 4 – Knock modeling

49

4.4 DISCUSSION

Douaud and Eyzat [29] found the pressure exponent n in Equation 4.1 to be 1,7 for primary reference fuels and close to 1 for a commercial gasoline fuel, see table 2.4. Bradley et. al. [55] refers to an investigation by Hirst and Kirsch where a toluene reference fuel had a value of n of about 1,3. Toluene reference fuels is a mixture of toluene and n-heptane which behaves more like typical gasoline fuels in terms of autoignition in the RON and MON tests [17]. The value of n found in this investigation is close to 1,3 which gives some confidence to the optimized values. As for the temperature coefficient B, the optimum value will depend on the operating region of the engine, i.e. where in respect to the negative temperature coefficient region in the ignition delay surface of Figure 2.6 the engine primarily operates when knocking is observed. As shown in the comparison to shock tube ignition delay data in Figure 2.3 the actual ignition delay time is nonlinear. If the unburned zone temperature reaches high values before knock occurs, a higher temperature coefficient will probably be required. The approach described in Paper II, to optimize the constant A only, seems to be a good approach considering the discussion above.

The unburned zone temperature as shown in Figure 2.4 is usually calculated by assuming isentropic compression of the end gas. If low temperature heat release occurs in the end gas, the temperature will be higher than the isentropically calculated temperature. This is a key difference that should be kept in mind when comparing the autoignition correlations from SI engine tests to for example shock tube autoignition data or HCCI combustion data.


50

51

Chapter 5

COMBUSTION MODELING USING THE WIEBE

FUNCTION

Paper III contains results from adapting and calibrating a combustion model based on the Wiebe function and laminar burning velocity correlations to experimental data. The Wiebe function was described in detail in Chapter 2.4.1 and the laminar burning velocity correlations used are summarized in Chapter 2.2.1. This chapter has some additional background and information about the measurements and calibration procedure for the combustion model, which is not covered in the paper. Results from two similar correlations that served as a base for the current investigation are shown first. The contribution of this work is to include laminar burning velocity correlations in the Wiebe combustion model to account for variations in cylinder gas properties. It is suggested that Paper III is read before reading this chapter.

5.1 EXISTING WIEBE MODELS

The approach of correlating measured Wiebe function parameters to engine operating parameters has been used by several authors. Two of these works by Csallner [56] and Witt [57] are summarized below starting with the model structure, which is the same for both models. The Wiebe function is repeated here for reference:


( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

∆−

−−=+1

0exp1m

b axθθθ

θ (5.1)

where xb mass fraction burned

θ crank angle

θ0 start of combustion

∆θ total combustion duration, θEOC - θ0

m combustion mode parameter

a scaling factor, a = -ln(1-xb,EOC)

5.1.1 Structure of existing models

Both Csallner [56] and Witt [57] correlated engine operating parameters such as spark timing and air/fuel ratio to the Wiebe parameters total combustion duration and combustion mode parameter. An additional set of correlations are presented for the period from spark timing to detectable pressure rise due to combustion in the cylinder, denoted ignition delay, ∆θd. Each correlation was made in the form of relative changes from a base operating condition denoted by subscript zero henceforth. The basic set of functions describing the correlation is:

∏

∏

∏

⋅=

⋅∆=∆

⋅∆=∆

ii

ii

iidd

hmm

g

f

0

0

0,

ˆ

ˆ

ˆ

θθ

θθ

(5.2)

where f, g and h are the functions for relative influence of each operating parameter i. The functions for relative influence were identified by normalizing experimental data with the base operating condition. To make the identified functions valid for base operating other than that used during identification, each function for relative influence is normalized by the current base operating condition, i.e.:

0,i

ii G

Gg = (5.3)

where Gi is the function found during the identification procedure with an arbitrary base operating condition. The model structure is very flexible since only the relative influence of each operating parameter is used.

52

Chapter 5 – Combustion modeling using the Wiebe function

53

5.1.2 Model identification procedure

Provided that there are no interaction effects between operating factors, the model calibration can be performed directly from engine tests where one parameter is varied at a time. In cases where more than one parameter has been varied in each test, an iterative identification procedure has to be adopted. The test data has to be normalized not only by the base operating condition but also by the influencing functions for operating parameters other than the operating parameter in the current correlation. The other correlations then have to be corrected with the new identified relative influence function.

The functional form for each influencing function is chosen to best fit the test data.

5.1.3 Csallner

Csallner [56] correlated Wiebe combustion parameters to spark timing, air/fuel ratio, engine speed. Load influence was modeled by in cylinder pressure and temperature during the compression stroke at 60 bTDC, referred to as p300 and T300, and residual gas fraction. Two naturally aspirated engines were used during in the work: a single cylinder MTU MB 331 engine with 3,3 dm3 displacement converted to gas operation and a four cylinder BMW engine with 0,5 dm3 displacement and two valves per cylinder. The correlations are summarized for the BMW engine in Table 5.1. The correlations for temperature and residual gas content do not have the form of Equation 5.3. Data from a total of 31 operating conditions are shown in the work.


Table 5.1 The Wiebe combustion parameter correlations from Csallner [56] for the BMW 2 dm3 four cylinder two valve engine. Spark timing, temperature and pressure relative to gas exchange TDC.

Ignition delay

∆θd

Total combustion

duration, ∆θCombustion mode

parameter, m

Fi Gi Hi

Spark timing θspark

sparkθ−430 1 1

Air/fuel ratio 95,0≤λ 54,274,3

2,2 2

+−λ

λ92,452,9

6,5 2

+−λ

λ 375,0 644,0+λ

Air/fuel ratio same as above same as above 27,2+33,1−

95,0>λλ

Compression temperature T300 [K]

16,116,2300

0,300 −TT

33,033,1300

0,300 −TT

1

Compressions pressure, p300

47,0300

−p 28,0300

−p 1

Residual gas content, xrg

912,0088,0 0, +rg

rg

xx

763,0237,0 0, +rg

rg

xx

1

Engine speed N [rpm] 2

51084001NN

−⋅−+ 625,0750

+N

N

66033,1 −

As can be seen in Table 5.1, only air/fuel ratio and engine speed was found to

influence the combustion mode parameter in Csallner’s correlations. This is in part due to the method used for fitting Wiebe functions to test data. First of all, the 50 % burned point was used as anchor angle in the identification. The total combustion duration was adjusted so that the mass fraction burned in an 8 CA interval beginning at the 50 % burnt point was equal in the test and the Wiebe function. The combustion mode parameter was then chosen arbitrarily to match measured data. This rather strange identification procedure was chosen to get correct mass burn rate when the burn rate is high and also because start of combustion could not be identified.

54


5.1.4 Witt

Witt [57] made two sets of Wiebe parameters correlations to compare throttled and throttleless operation in the simulation and testing of a modern BMW four valve naturally aspirated engine running on part load. Similarly to Csallner, the Wiebe parameter identification method used by Witt focused on getting the 50 % burn point correct in the identified Wiebe function. A very large number of tests were used to identify the combustion model parameters: 221 operating points in throttleless operation and 193 operating points in throttled operation. The parameters investigated were spark timing, residual gas content, indicated work and engine speed. Results from throttled operation are shown in Table 5.2. All identified equations have the form of Equation 5.3, i.e. normalized functions for relative influence.

Table 5.2 Wiebe combustion parameter correlations from Witt [57] for throttled operation in a BMW 4-valve engine. Ignition delay,

∆θd

Total combustion

duration, ∆θCombustion mode

parameter, m

Fi Gi Hi

Spark advance θspark [bTDC] 2410383,2

678,0

sparkθ−⋅

+ 5,0

48,2596,0sparkθ

+ 2

56,75

sparkθ+964,0

Residual gas content, xrg [%] 2410648,3

879,0

rgx−⋅

+2410534,2

076,1

rgx−⋅

− 2031,0429,0 rgx+

Indicated work wi [kJ/dm3]

5,1545,0112,1 iw− iw346,0115,1 − iwln004,0+007,1

Engine speed N [rpm] 2

510246,1992,0N

⋅−

N49,18355,1 −

5,1710075,4

046,1

N−⋅

−

5.2 EXPERIMENTS

As described in Paper III, a few engine operating parameters were singled out as candidates that were likely to have an influence on the combustion. The first group of operating parameters are those related state of the combustible mixture of air and fuel, namely air/fuel ratio, intake pressure and temperature and residual gas content. Engine speed and spark timing make up the other group of parameters which are related to the turbulence which the flame encounters as it traverses the combustion chamber. Spark timing actually related to both groups, since the temperature and

55


56

pressure during the early part of combustion is highly dependent on the spark timing. Coolant temperature was also varied in the tests.

The experimental procedure chosen for the combustion model investigation was to vary one parameter at the time while trying to keep other influencing factors constant. As all engine experimentalists know it is not straightforward to change only one parameter in an engine test, since many factors are affected when one control parameter is changed. Retarding the spark timing in a turbocharged engine will for example increase exhaust temperature which leads to increased turbine power producing a change in intake pressure and temperature which in turn affects combustion. The waste gate and throttle were used to control the intake conditions. Some care was also taken to tune the charge air cooler controller. This means that the engine torque was varying quite significantly between the tests. Figure 5.1 shows some test data from a spark timing variation test just to see the large variation in for example turbine inlet temperature and torque. The figure also shows that spark timing were chosen close to MBT timing and later. The pressure after the compressor varies more than the intake pressure since the throttle was used to control intake pressure.


1 2 3 4 5 6 7

1.0

1.1

1.2

1.3

10

20

30

40

Lam

bda

Inta

ke p

ress

ure

[bar

]P

ress

ure

afte

r com

pres

or [b

ar]

Test no.

Pressure after compr.

Intake pressure

Lambda

Spark timing

50 % burnt

Intake temp.

Inta

ke te

mpe

ratu

re [°

C]

Spa

rk ti

min

g [b

TDC

]50

% b

urnt

[aTD

C]

1 2 3 4 5 6 7

820

840

860

880

900

920

940

960

200

210

220

230

240

250

Turb

o sp

eed

/ 100

[rpm

]Tu

rbin

e in

let t

emp.

[°C

]

Test no.

Turbo speed

Turbine inlet temp.

Torque

Engine speed

Torq

ue [N

m]

Eng

ine

spee

d / 1

0 [rp

m]

Figure 5.1 Test data from spark timing variation with constant intake manifold pressure and temperature. Other measured parameters vary quite significantly. Waste gate and throttle was varied along with charge air cooling.

Two sets of tests were performed with varying engine speed. One test was made with constant spark timing and one test with constant angle for 1 % mass fraction burned. Figure 5.2 shows the measured data from these two tests. The tests with constant 1 % burnt point were made to remove the influence of varying flame development period in terms of crank angles at different engine speeds.

57


1500 2000 2500 3000 1500 2000 2500 3000-2

-1

0

1

2

3

10

15

20

25

30

35

1 % burnt

Lambda

Intake pressure

50 % burnt

Intake temp.

Spark timing

Lam

bda

1 %

bur

nt [a

TDC

]In

take

pre

ssur

e [b

ar]

Engine speed [rpm]

Inta

ke te

mpe

ratu

re [°

C]

Spa

rk ti

min

g [b

TDC

]50

% b

urnt

[aTD

C]

Figure 5.2 Test data for speed variation tests with constant spark timing (left) and constant 1 % burnt (right).

Interaction effects between parameters might be left out when using a one parameter at the time approach [58]. A second set of experiments was carried out to check for interactions, and also to have a data set for validation of the model. A reduced order two level factorial design with center points, augmented with a so called star composite design, was used. Figure 5.3 shows the basic structure of the design. The factors in the test were air/fuel ratio, spark timing, residual gas content and intake temperature. Engine speed was constant at 3000 rpm and the intake pressure was 125 kPa. The experimental matrix is shown in Table 5.3. The goal with the design of experiments approach was not to fit a response surface to the data but to get a validation data set which spans the experimental range. If there are significant interaction effects between any of the variables, the fit of the identified model in the validation data set will be poor. A total of 30 tests were performed for the validation data set.

58


Table 5.3 Operating points for the factorial experimental design at 3000 rpm and 125 kPa intake pressure.

Normalized level

Air/fuel ratio

Spark timing[bTDC]

Intake temperature [°C]

EGR fraction

+1 1,00 18,0 45,0 2,4% -1 0,80 13,0 35,0 0,4% 0 0,90 15,5 40,0 1,4%

+1,41 1,04 19,0 47,1 not possible -1,41 0,76 12,0 32,9 0,0%

-1 0 1

-1

0

1

R = 20,5

Central points

Extra points

Base points

Nor

mal

ized

leve

l, fa

ctor

2

Normalized level, factor 1

Figure 5.3 Basic structure of central composite two level factorial design augmented with a star complement design.

5.3 DATA EVALUATION

200 engine cycles were recorded for each of the four cylinders and each operating condition. Heat release was calculated for each cycle with the algorithm described in Chapter 3.3. Wiebe parameters were identified for each individual cycle, described in more detail below. The average of the identified Wiebe parameters for each operating condition was then used to identify the combustion model parameters.

59


5.3.1 Wiebe parameter identification

As mentioned above in the summary of the works of Csallner [56] and Witt [57], different methods were used for identifying the Wiebe parameters from calculated heat release. Both Csallner and Witt also identified the flame development period for each operating point. Some different methods for identifying the Wiebe function parameters were tested in this work. It was found that the double logarithm method suggested in Wiebe [27] gave quite accurate results when the spark timing was used as start of combustion. After transforming the calculated mass fraction burned and the crank angle by two logarithms:

( )

( )

( ) ( ) ( ) ( )( )θθθ

θθθ

θθθ

θ

∆−−⋅+=⎟⎠

⎞⎜⎝

⎛−−

⎟⎠

⎞⎜⎝

⎛∆−

⋅−=−

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛∆−

−−=

+

+

lnln11ln

ln :logarithm 2

1ln :logarithm 1

exp1

0nd

10st

10

max

ax

ax

b

m

b

m

b

(5.4)

it is straightforward to fit a straight line to the data and solve for the interesting parameters ∆θ and m.

The results are fully comparable to a nonlinear least squares fit of a Wiebe function to measured data as shown in Figure 5.4, but the computational burned for the Wiebe method is only a small fraction of a nonlinear least squares fit. As an example, the time to fit Wiebe parameters for 200 engine cycles with the Wiebe method took about half a second, while a nonlinear least squares solver needed one minute to perform the same task. The crank angle transformation of the data, ln(θ - θ0), is nonlinear which gives an overweight for the later part of combustion in the estimation of Wiebe parameters. The same results could have bee accomplished with a weighted least squares estimate.

60


-15 0 15 30 45 60

0.0

0.2

0.4

0.6

0.8

1.0

-2 %

-1 %

0 %

1 %

2 %

3 %

Mas

s fra

ctio

n bu

rned

, xb

Crank angle [aTDC]

Measured Double logarithm Nonlin. least squares

Err

or

Figure 5.4 Comparison of nonlinear least squares and double logarithm method of fitting a Wiebe function to measured data.

One concern for selecting more complicated methods of fitting Wiebe functions mentioned in both Csallner [56] and Witt [57] was to get correct 50 % burn point in the fitted Wiebe function. Another concern was to get correct mass fraction burned in a crank angle interval around the 50% burnt point, which I translate to correct 10-90 % burn duration. Figure 5.5 shows how the Wiebe double logarithm method with spark timing as start of combustion performs in estimating several mass fraction burn points for 89 operating conditions from the combustion model data sets. The standard deviation of the estimated burn points are also shown in the figure. The weighting introduced by the logarithm transformation is evident, since the 50 % burnt point and the 90 % burnt point has the best fit.

61


1% 5% 10% 50% 90% 10-90 %-1

0

1

2

3

-0,68

2,66

1,931,26

0,58

-0,21

Standarddeviation

Meanerror

Err

or [C

A]

Sta

ndar

d de

viat

ion

[CA

]

Mass fraction burned Figure 5.5 Mean error in mass fraction burned points of fitted Wiebe function compared to measured data. Ensemble averaged data from 89 operating conditions.

5.4 COMBUSTION MODEL CALIBRATION

The presented combustion model differs from the existing models described above in two respects: the use of laminar burning velocity and the Wiebe parameters identification method. The identification method with spark timing taken as start of combustion removes the need for separate correlations for the flame development period. Only spark timing and engine speed remains as influencing parameters after the laminar burning velocity influencing function has been removed. For the combustion mode parameter, influencing functions were determined for engine speed and total combustion duration. Equation 5.2 simplifies to:

∏

∏⋅⋅=⋅=

⋅⋅⋅∆=⋅∆=∆

∆i

speedi

ispeedsparkSLi

hhmhmm

gggg

θ

θθθ

ˆ00

00

ˆ

ˆ

(5.5)

The first influencing function for total burn duration, gSL, accounts for the laminar burning velocity influence. Paper III shows the good results when using inverse laminar burning velocity as influencing function. In order to identify the remaining influencing functions for total combustion duration, data was normalized with the laminar burning velocity influencing function. The spark timing influencing

62


function, gspark, is also described in Paper III. Below I will describe the process of identifying the engine speed influencing function, gspeed, in more detail, which for some cases requires normalizing with both laminar burning velocity and spark timing influencing function.

5.4.1 Modeling speed influence

Two different test series were made for identifying the speed influence function, one with constant spark timing and one with constant 1 % mass fraction burnt, as shown in Figure 5.2. The structure of the model for total combustion duration directly gives the influencing function:

sparkSLspeed

speedsparkSL

ggg

ggg

⋅⋅∆∆

=⇒

⋅⋅⋅∆=∆

0

0

θθ

θθ

(5.6)

The first step is to normalize the data with a base operating condition, as shown in the top left figure in Figure 5.6. The figure also contains the final identified speed influencing function to see what each step in the normalization does to the data. Since the gas conditions at spark timing for the speed test data varied, the data then had to be normalized by the laminar burning velocity influencing function, shown in the top right figure. Finally, after normalizing with the spark timing influencing function, bottom left, the test data collapses around the identified influencing function. The bottom right figure shows the measured and predicted total burn duration for the speed modeling data. The bottom left figure is identical to Figure 11 in Paper III.

63


1500 2000 2500 3000 3500 4000

0.7

0.8

0.9

1.0

1.1

1.2

1.3 Constant spark timing Constant 1 % burnt Points from other tests

Engine speed [rpm]

∆θ

∆θ

0

1500 2000 2500 3000 3500 4000

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Engine speed [rpm]

∆θ

∆θ

0 x g

(SL)

1500 2000 2500 3000 3500 4000

0.7

0.8

0.9

1.0

1.1

1.2

1.3 alt. G(N) = 0.0102 x0.584

G(N) = 2,13 - 55,5 x N-0,5

∆θ

∆θ0 x

g(S

L) x

g(θ

ign)

Engine speed [rpm]1500 2000 2500 3000 3500 4000

40

45

50

55

60

65

70

measured modelM

easu

red

and

estim

ated

∆θ

Engine speed [rpm] Figure 5.6 Illustration of the steps of fitting an total combustion duration influence function for the speed influence. Top left shows test data normalized with the base operating condition only. Top right data is also normalized by laminar burning velocity influence. Bottom left is additionally normalized by spark timing influence. All normalized data is plotted together with the identified influencing function for comparison. Bottom right shows the prediction of total combustion duration for the model identification data.

The functional form for the speed influencing function was chosen from Wittt [57]. Several other functional forms were tested for the speed influencing function. One of them, a power function, is shown in the bottom left figure of Figure 5.6. The behavior outside of the identification data range has to be considered when choosing the functional form.

5.5 RESULTS

The results from calibrating the combustion model along with some validation are summarized in Paper III. All identified influencing functions are summarized in an appendix to the paper.

64

65

Chapter 6

CONCLUSIONS

Combustion simulation in one dimensional software has to be a very simplified description of the actual process, if the software is to maintain reasonably fast execution time. Complete three dimensional simulations of the real physics and chemistry of combustion is not practically possible today. Simulation of in cylinder turbulence requires sub models for turbulence structures smaller than the calculation mesh or an extremely dense mesh which renders the calculation near unfeasible. Chemical kinetic models exist for simple model fuels but are yet to be developed for practical automotive fuels. When three dimensional simulation of SI engine combustion becomes a practical alternative, which I’m sure will happen some time in the future, cycle to cycle variations is the next problem to tackle.

Simplified empirical approaches for combustion and knock modeling have been described in this thesis. The combustion model only uses one key property of the flame, the laminar burning velocity, which makes it easy to use and interpret. However the combustion model will not react to changes in turbulence which is the major drawback of this approach. The knock model has been used by many others and this work simply adds to the understanding of the calibration and use of the model.

The combustion model does not take cycle to cycle variations into account. The knock model on the other hand is a single cycle model. When using the knock model together with any ensemble average combustion model, it is quite hard to distinguish the meaning of the results. Some arbitrary limits for knock have to be set in order to get any useful results. In Paper II we used 30 crank angles after top dead


66

center and approximately 90 percent mass fraction burned as limits. If knock was predicted within/below these limits, the combustion was phased later until either of the boundaries were reached at simulated knock onset. This is not to be confused with the severity of knock or any other measure of knock. It is just a way to get useful output from the simulations.

The use of one dimensional simulation tools in engine development has put new demands on engine measurement technique. Both cycle or time averaged measurements and crank angle resolved measurements fill an important role in simulation model calibration and validation. This thesis has put special focus on measurement data conditioning with some suggestions on filtering of noisy data and filtering for knock detection. These two filtering tasks have separate demands on the filters. Another area of interest is the calculation of heat release from cylinder pressure data. If the data is to be used for calibration or validation of combustion in a simulation model, it is essential to use the same assumptions and models as the simulation software when calculating heat release from measured data. The model for ratio of specific heats described in this thesis is an attempt to get closer to the simulation software in estimating in cylinder gas properties during combustion. The Woschni model for heat transfer is common between the simulations and measured data analysis. The largest discrepancy between measured data analysis and the simulation software is found in the single zone calculation of heat release for the measured data. A two zone model was used in the simulation software in order to be able to draw conclusions regarding knock.

6.1 FUTURE WORK

The three dimensional calculated ignition delay surface for a model gasoline fuel developed by Yates and co-workers seems to be a reasonable next step in refining the knock model described in this work. For future development of the presented combustion model, it would be interesting to try to correlate combustion duration to for example swirl- or tumble numbers. This would enable appropriate scaling of the combustion duration when changing for example cylinder head and combustion chamber geometry or, the other way around, to suggest an appropriate turbulence level of a new engine design to avoid for example knock. Additional refinement of the model would be to look into part load and camshaft phasing or fully variable valve trains. Cycle to cycle variations could be incorporated by means of some statistical distribution of the Wiebe parameters, correlated to engine operating conditions in a similar way as the Wiebe parameters themselves. For knock simulation, the most likely knocking cycle could be found from the statistical distribution. After finding the

Chapter 6 – Conclusions

67

knock limited combustion phasing for the most likely knocking cycle, the ensemble average cycle could be simulated to give an accurate prediction of engine output at the knock limit.

69

REFERENCES

[1] www.acea.be (May 2005); Monitoring of ACEA’s Commitment on CO2 Emission Reductions from Passenger Cars (2002); Joint Report of the European Automobile Manufacturers Association and the Commission Services, Final Report, 2003.

[2] Mitchell, Bill; Advanced fuel cell development for automotive operation; Oral presentation at the SAE Fuels & Lubricants Meeting and Exhibition, Rio de Janeiro, May 12, 2005.

[3] Blair, Gordon P.; Design and Simulation of Four-Stroke Engines; Society of Automotive Engineers, 1999.

[4] GT-Power User Manual, Version 6.1; Gamma Technologies, August 2004. [5] Westin, Fredrik; Simulation of turbocharged SI-engines – with focus on the

turbine; Doctoral Thesis in Machine Design, KTH, Stockholm, 2005, ISSN 1400-1179.

[6] Watson, N., Janota, M. S.; Turbocharging the Internal Combustion Engine; The Macmillan Press Ltd, London, 1982.

[7] Söderberg, Fredrik, Johansson, Bengt; Fluid Flow, Combustoin and Efficiency with Early or Late Inlet Valve Closing; SAE Technical Paper 972937.

[8] Heywood, John B.; Internal Combustion Engine Fundamentals; MCGraw-Hill 1988.

[9] Glassman, Irvin; Combustion, third edition; Academic Press, 1996. [10] Kalghatgi, Gautam T.; Early Flame Development in a Spark-Ignition Engine;

Combustion and flame 60 (1985) 299-308. [11] Tagalian, Joel, Heywood, John B.; Flame Initiation in a Spark-Ignition Engine;

Combustion and Flame 64: 243-246 (1986). [12] Metghalchi, Mohamad, Keck, James C.; Burning Velocities of Mixtures with

Methanol, Isooctane and Indolene at High Pressure and Temperature; Combustion and Flame 48 (1982) 191-210.

[13] Metghalchi, Mohamad, Keck, James C.; Laminar Burning Velocity of Propane-Air Mixtures at High Temperature and Pressure; Combustion and Flame 38 (1980) 143-154.

[14] Johansson, Bengt; On Cycle to Cycle Variations in Spark Ignition Engines; Doctoral thesis, Division of Combustion Engines, Department of Heat and Power Engineering, Lund Institute of Technology, 1995.

[15] Grandin, Börje; Knock in Gasoline Engines – the effect of mixture composition on knock onset and heat transfer; Doctoral thesis, Department of Thermo and Fluid Dynamics, Chalmers University of Technology, Gothenburg, 2001.


70

[16] Westbrook, Charles K.; Chemical Kinetics of Hydrocarbon Ignition in Practical Combustion Systems; Proceedings of the Combustion Institute, vol. 28, 2000, 1563-1577.

[17] Risberg, Per; A Method of Defining the Auto-Ignition Quality of Gasoline-Like Fuels in HCCI Engines; Licentiate Thesis in Machine Design, KTH, Stockholm, 2005.

[18] Fieweger, K., Blumenthal, R., Adomeit, G.; Self-Ignition of S.I. Engine Model Fuels: A Shock Tube Investigation at High Pressure; Combustion and Flame 109 (1997) 599-619.

[19] Viljoen, Carl L., Yates, Andy D. B., Swarts, André, Balfour, Gillian, Möller Klaus; An Investigation of the Ignition Delay Character of Different Fuel Components and an Assessment of Various Autoignition Modelling Approaches; SAE Technical Paper 2005-01-2084.

[20] Swarts, André, Yates, Andy D. B., Viljoen, Carl L., Coetzer, Roelof; A Further Study of Inconsistency between Autoignition and Knock Intensity in the CFR Octane Rating Engine; SAE Technical Paper 2005-01-2081.

[21] Kalghatgi, Gautam T.; Fuel anti-knock quality – Part I. Engine studies.; SAE Technical Paper 2001-01-3584.

[22] Kalghatgi, Gautam T.; Fuel anti-knock quality – Part II. Vehicle studies – how relevant is Motor Octane Number (MON) in modern engines?; SAE Technical Papers 2004-01-3585.

[23] Pan, J., Sheppard, C. G. W.; A Theoretical and Experimental Study of the Modes of End Gas Autoignition Leading to Knock in S.I. Engines; SAE Technical Paper 942060.

[24] Brunt, Michael F. J., Pond, Christopher R. and Biundo, John; Gasoline Engine Knock Analysis using Cylinder Pressure Data; SAE Technical Paper 980896.

[25] Bengisu, Turgay; Computing the Optimum Knock Sensor Locations; SAE Technical Paper 2002-01-1187.

[26] Worret, R., Bernhardt, S., Schwartz, F., Spicher, U.; Application of Different Cylinder Pressure Based Knock Detection Methods in Spark Ignition Engines; SAE Technical Paper 2002-01-1668.

[27] Wiebe, I. I.; The Combustion Speed in Internal Combustion Piston-Engines – fuel combustion rate equation combining an empirical and a theoretical approach; Collected works of piston engine research, Laboratory of Engines, Academy of Science, USSR, Moscow 1956. (Translated from the Russian text by Marek Kiisa, KTH, Stockholm 1993)

[28] Livengood, J. C., Wu, P. C.; Correlation of Autoignition Phenomena in Internal Combustion Engines and Rapid Compression Machines; Fifth Symposium (International) on Combustion, 347-356, 1955.

[29] Douaud, A. M., Eyzat, P.; Four-Octane-Number Method for Predicting the Anti-Knock Behaviour of Fuels and Engines; SAE Technical Paper 780080.

References

71

[30] By, A., Kempinski, B., Rife, J. M.; Knock in Spark Ignition Engines; SAE Technical Paper 810147.

[31] Gautier, B. M., Davidsson, D. F., Hanson, R. K.; Shock tube determination of ignition delay times in full-blend and surrogate fuel mixtures; Combustion and Flame 139 (2004) 300-311.

[32] Yates, Andy D. B., Swarts, André, Viljoen, Carl L.; Correlating Auto-Ignition Delay And Knock-Limited Spark-Advance Data For Different Types Of Fuel; SAE Technical Paper 2005-01-2083.

[33] www.adlinktech.com (May 2005) [34] www.ueidaq.com (May 2005) [35] www.gemssensors.com (May 2005) [36] www.avl.com (May 2005) [37] www.kistler.com (May 2005) [38] www.druck.com (May 2005) [39] www.ametekcalibration.com (May 2005) [40] Pischinger, Rudolf; Engine Indicating – User Handbook; AVL List Gmbh,

Austia, 2002. [41] Lee, S., Bae, C., Prucka, R., Fernandez, G., Filipi, Z. S., Assanis, D. N.;

Quantification of Thermal Shock in a Piezoelectric Pressure Transducer; SAE Technical Paper 2005-01-2092.

[42] Odendall, B.; A Discussion of Errors in the Measurement of Gas Temperature; MTZ 3/2003 pp. 196-199.

[43] www.pentronic.se; StoPextra 6/98 [44] www.isotech.co.uk (May 2005) [45] www.testo.com (May 2005) [46] www.monarchinstrument.com [47] www.micro-epsilon.de (May 2005) [48] www.ecm-co.com (May 2005) [49] Smith, Steven W.; The Scientist and Engineer’s Guide to Digital Signal

Processing, second edition; California Technical Publishing, San Diego, California 1999; http://www.dspguide.com

[50] Brunt, Michael F. J., Rai, Harjit, Emtage, Andrew L.; The Calculation of Heat Release from Engine Cylinder Pressure Data; SAE Technical Paper 981052.

[51] Klein, Marcus, Eriksson, Lars; A Specific Heat Ratio Model for Single-Zone Heat Release Models; SAE Technical Paper 2004-01-1464.

[52] Kanury, A. Murty; Introduction to combustion phenomena; Table A.3; New York cop. 1975.

[53] AVL List GMBH; Operating Instruction AVL Concerto Software Version 3.0; AVL List GMBH, Graz 1999.


72

[54] www.galcit.caltech.edu/EDL/public/thermo/thermo.inp; NASA tables of species thermodynamic properties; January 2005.

[55] Bradley, D, Morley, C and Walmsley, H.L.; Relevance of Research and Motor Octane Numbers to the Prediction of Engine Autoignition; SAE Technical Paper 2004-01-1970.

[56] Csallner, Peter; Eine Methode zur Vorausberechnung der Ändrung des Brennverlaufes von Ottomotoren bei Geänderten Betriebsbedingungen; München Techn. Univ., Diss., 1981.

[57] Witt, Andreas; Analyse der thermodynamischen Verluste eines Ottomotors unter den Randbedingungen variabler Steuerzeiten; Graz, Tech. Univ., Diss., 1999.

[58] Box, George E. P., Hunter, Willam G., Hunter, J. Stuart; Statistics for experimenter; John Wiley & Sons, Inc. 1978.

PAPER I

1

2005-01-1150

Divided Exhaust Period – a gas exchange system for turbocharged SI engines

Christel Elmqvist Möller, Pontus Johansson, Börje Grandin Fiat-GM Powertrain - Sweden

Fredrik Lindström Royal Institute of Technology

Copyright © 2004 SAE International

ABSTRACT

The necessity to limit the boost pressure in turbocharged gasoline engines results in higher exhaust pressure than inlet pressure at engine speeds when the wastegate is opened. This imbalance has a negative influence on the exhaust scavenging of the engine and results in high levels of residual gas and consequently the engine is more prone to knock.

This paper presents a study of a gas-exchange system for turbocharged SI engines. The concept aims at improving the performance and emissions of a turbocharged SI engine by dividing the exhaust flow from the two exhaust valves into two different exhaust manifolds, one connected to the turbocharger and one connected to a close coupled catalyst. By separating the valve opening period of the two valves and keeping the duration of both valve opening events shorter than 180 crank angle degrees, the disturbance of the exhaust blowdown pressure pulse during valve overlap in a four cylinder engine can be completely eliminated.

The study was carried out both experimentally on a four cylinder turbocharged SI engine and with extensive 1-D simulation of the system. A positive pressure difference over the engine could be realized over the entire speed range by using the concept system. Simulations show up to 60 % reduction of residual gas content compared to a standard turbocharged engine. The study also showed that the time to catalyst light off could be reduced with over 35% compared to a standard turbocharged engine with a conventional exhaust system.

INTRODUCTION

It is a well-known fact that the emission levels from the transport sector needs to be decreased. At the same time customer request is for more powerful engines with less fuel consumption. These different requirements can

be hard to meet at the same time and is a major challenge for engine manufactures and researchers.

Using turbochargers can be a viable solution to this challenge. The major advantage of the turbocharged engine is achieving the same power output with a smaller displaced volume, thereby decreasing the fuel consumption. However, turbocharged engines have some drawbacks. The turbine increases the pressure in the exhaust manifold, thereby increasing the amount of residual gas trapped in the cylinder. This decreases the knock resistance of the engine [1] and also reduces the volumetric efficiency [2]. In a four stroke turbocharged engines with four cylinders and a single turbine, the blowdown pulse from one cylinder can interfere with the previous cylinder in firing order during exhaust-intake overlap. This further impairs the scavenging of the combustion chamber and as a consequence increases the charge temperature and reduces volumetric efficiency and knock resistance. Other drawbacks are the relatively high pumping losses compared to a naturally aspirated engine and delayed catalyst light off due to the turbine acting as a heat sink in the exhaust system. Finding ways to avoid these shortcomings would of course improve the performance of the turbocharged engine.

One way mentioned as early as 1924 in a British patent [3] has been further investigated on a modern four-cylinder turbocharged engine. In this paper the potential of this concept, which will be called DEP (Divided Exhaust Period), will be examined. The concept has been investigated by means of 1-D simulation as well as by tests on a prototype engine. This paper will deal with the theories behind the concept, the development of a 1-D simulation model and experience gained from a prototype engine. In particular cold start catalyst light-off time and full load performance of the DEP engine with varying exhaust valve lift profiles have been studied. High full power potential of a new engine concept is important to enable a high degree of downsizing.

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Figure 1 Schematic view of the of the exhaust systems configuration in the DEP engine.

TECHNICAL CONCEPT

The Divided Exhaust Period (DEP) concept is an alternative way of accomplishing the gas exchange in a turbocharged engine. The aim is to improve the performance of a turbocharged engine, regarding low-end torque, peak power and emissions. In the DEP engine the two exhaust ports from each cylinder have been separated. The blowdown pulse is evacuated through the blowdown valve, which leads to the turbocharger. As the pressure in the exhaust is decreased and the piston displacement phase commence, the scavenging valve open and lead the remaining exhaust gas directly to a close-coupled catalyst (CCC). By bypassing the turbine the high pressure in the manifold connected to the blowdown valve is avoided and the gas exchange is improved. The engine is schematically shown in Figure 1. Figure 2 show the valve lifts for the blowdown valve leading towards the turbine and the scavenging valve connected to the close-coupled catalyst.

Important parameters for turbine performance are the mass flow, the pressure difference and temperature difference over the turbine, since these are related to the enthalpy. Ideally the high enthalpy blowdown pulse is located around BDC and a positive pressure difference exists between cylinder and exhaust manifold. When the pressure in the cylinder decreases, the positive pressure difference decrease. By opening the cylinder to the scavenging manifold, which has a lower pressure compared to the blowdown manifold, positive pressure difference can be achieved over the engine during the exhaust/intake overlap higher up in the speed range of the engine.

The majority of exhaust gases are evacuated during the blowdown pulse. The crank angle duration and mass fraction evacuated during the blowdown phase depend on engine speed. With increased engine speed the pressure difference between the cylinder and the exhaust manifold decreases and as a consequence the mass fraction evacuated during the displacement phase increases. Choking of the exhaust valves influences the

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duration of the blowdown phase. Figure 3 shows simulated mass flow in both of the DEP engine exhaust systems compared to a standard turbocharged engine at 5500 rpm. Over 60% of the mass flow and the highest enthalpy levels are found in the blow-down pulse at 5500 rpm in the standard turbocharged engine. The remainder of the mass flow is generated by the piston displacement, which can be seen in the figure as a second peak in the mass flow.

In previous sections five main difficulties with a 4-cylinder conventional turbocharged engine were described: • Cylinder evacuation • Negative PMEP • Pulse interaction between cylinders • Knock sensitivity • Cold start The same reasoning as for a conventional turbocharged engine holds true for the DEP concept when it comes to choosing between a small or large turbine. The main driving force behind the DEP concept is to avoid or decrease the negative effects coupled to a small turbine. The turbine is restricted in mass flow so that a wastegate needs to be used at high load. Using a

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Figure 3 Simulated mass flows in the DEP engine exhaust systems compared to a standard turbo charged engine at 5500 rpm.

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wastegate is a loss of potential work. With the DEP concept the mass flow is divided already in the cylinder, which has the same effect as a wastegate at high load, i.e. bypassing the turbine.

Dividing the mass flow already in the cylinder, as with the DEP concept, has other advantages compared to a wastegate. Cylinder evacuation was mentioned as an important factor for engine performance. By opening up the cylinder to a low pressure exhaust manifold, which in a sense is connected to the atmosphere, the high pressure created by the turbine can be avoided. This enables a better evacuation of the cylinder.

By making the duration of the exhaust blowdown valve only slightly longer than 180° CA, the pulse interference between cylinders at blowdown can be eliminated. By eliminating the pulse into the cylinder the DEP engine should be able to decrease the amount of hot residual gases in the engine and decrease the gas exchange pumping losses, thus enabling better volumetric efficiency, knock resistance and overall engine efficiency.

Catalyst light-off time has a great influence on cold start emissions. Hence, it is important to keep as much heat in the exhaust as possible in order to quickly reach catalyst light-off. Therefore placement of the catalyst close to the exhaust ports is important. By implementing valve de-activation for the blowdown valve, all of the exhaust gas is lead directly to the close-coupled catalyst mounted in the scavenging exhaust system. Consequently the emissions in terms of catalyst light-off time can be improved. The turbine is in this configuration effectively bypassed and the turbine will not act as a heat sink during cold start.

From the discussion presented above it is clear that valve phasing and duration will have a great influence on the results. In order to investigate and evaluate the DEP concept even further a number of cam profiles were designed. The aim was to minimize the number of cams and to have a clear strategy when evaluating the gas exchange process for the DEP concept. The tests with different camshafts aimed at determining the influence on pumping losses, engine output and cylinder scavenging. Four key factors were identified and are described in Table 1.

Table 1 Identified key factors for cam timing and duration evaluation.

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Case Parameter Objective

1 Duration blowdown valve

Investigate influence of cylinder emptying towards turbine

2 Duration scavenging valve

Investigate required energy to drive the turbine

3 Overlap scavenging valve – intake valve

Investigation of overlap influence between exhaust and intake valve

4 Intake valve closing Investigate intake valve closing influence with constant TDC overlap

EXPERIMENTAL SET-UP

SIMULATION MODEL - In order to investigate the DEP concept more thoroughly an engine model was developed in the 1-D software GT-Power [4]. The aim was to gain a more in-depth understanding of the gas exchange process and to optimize the engine design with respect to valve timing and pipe design. 1-D simulation is based on the solution of the governing equations; momentum-, energy- and mass- conservation, in 1-D. However, in order to transform a 3-D problem to 1-D some additional information is needed. Figure 4 give some example of areas dependent on input data.

3-D phenomena• Combustion • Pipes • Valves • Turbocharger • Intercooler • …

1-D modelRepresentation of 3-D phenomena in 1-D

⇒ Dependence on quality of input data

Additional information • Measurement data • Coefficients • Advanced sub-models

Figure 4 Schematic image of the transformation from a 3-D heat transfer, flow and chemical kinetics problem to 1-D.

The engine model was built by transferring the geometrical dimensions of the engine into the model. Since the governing equations are only solved in 1-D, in the direction of the flow, 3-D effects must be taken into account in some other manner. Flow loss coefficients are used in order to find the right pressure loss occurring from pipe bends, materials etc. These coefficients are pre-defined in the software and usually not in need of much adjustment. The flow through the intake and exhaust valves was modeled by discharge coefficients as a function of lift height, which was measured in a flow bench [5]. Simulating the combustion is more complicated. Due to the combination of 3-D flow and chemical kinetics it is necessary to use special combustion models or measurement data. In this project the combustion has been simulated with the Wiebe function [4], which can be described as a curve fit to measured heat release. The main drawback with using such a combustion model is its dependence on measured combustion data, i.e. at what crank angle 50 % of the fuel is burnt and the duration of the combustion. Hence, simulating unknown engine concepts relies on the quality of the assumptions made for these combustion parameters.

The turbocharger is another complicated area. Turbocharger modeling is based on performance maps for the compressor and turbine. These performance maps are based on flow bench measurements with

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stationary flow [6]. The experimental data is then inter- and extrapolated to obtain the full-range maps. The maps relate speed and efficiency to the pressure ratio and mass flow over the turbine and compressor. Since the turbocharger models are based on stationary measurements in a limited range, these models can require an extensive amount of tuning [7]. In order to simplify the turbocharger simulation it is important to measure pressure, mass flow and turbocharger speed. The turbocharger simulation is difficult to perform when no knowledge of the actual engine performance is available.

MEASUREMENT SET-UP - Since little knowledge was available of how the combustion would change with the DEP concept and how the turbine would react to the change in mass flow when the exhaust pulse was divided, a prototype engine was built to run parallel to the simulations. A number of experiments have also been made to determine the potential of the DEP concept. The engine tests were performed at KTH and Fiat-GM Powertrain in-house facilities.

Cylinder pressures have been measured with AVL GM12D piezoelectric pressure transducers at a sample rate of 0.1 to 0.4 crank angles. 200 or more cycles have been recorded for each operating condition as a base for cycle resolved indicated statistics. [8][9] Crank angle resolved pressures in the intake and exhaust system have been measured at several positions with piezoresistive and steel diaphragm strain gauge pressure transducers. These pressure transducers were calibrated in a static test rig, obtaining a total static measurement uncertainty of the measuring chain in the range ± 3 - 8 kPa. Analogue anti aliasing filters and digital zero phase shift low pass filtering was applied to the pressure signals prior to further analysis. Temperatures have been measured time resolved with type K thermocouples, with a typical response time in the order of one second. Emissions have been measured time resolved at different positions in the exhaust systems. A two-channel fast flame ionization detector was used for crank angle resolved hydrocarbon measurements in the cold start tests. Other measurements include fuel mass flow rate, broadband lambda, turbine speed and torque. Air mass flow was estimated from measurements of lambda and fuel mass flow.

Limiting factors during the maximum torque tests has been 980°C maximum turbine inlet temperature measured with a 6 mm thermocouple, minimum overall relative air/fuel ratio of 0.77, 100 kPa maximum boost pressure and maximum coefficient of variance of IMEP (COV) 5 %. Ignition was advanced towards the knock limit.

HARDWARE MODIFICATIONS – The DEP engine was based on a standard 2 dm3 turbocharged port fuel injected engine. The standard cylinder head with 4 valves per cylinder had 32 mm inlet valve diameter and

28 mm exhaust valve diameter. The cylinder head was modified to house 32 mm exhaust valves with separated exhaust runners to the exhaust pipe flange. The coolant channels were also modified to ensure sufficient cooling of the exhaust ports. Specifications of the DEP engine are found in Table 2.

Table 2 DEP engine specifications.

Bore 86 mm Stroke 86 mm Compression ratio 9.5 Combustion chamber Pentroof Inlet valve diameter 32 mm Exhaust valve diameter 32 mm

The valve durations are quite short compared to an ordinary turbocharged engine, especially the scavenging valve. In order to handle the dynamics of the valve and yet obtaining maximum valve lift, lightweight materials had to be used for the exhaust valves. TI-Al exhaust valves were originally chosen to maximize possible valve lift area. These valves were replaced with sodium cooled steel exhaust valves due to high thermal load on the blowdown valve. Lightweight conical valve springs and valve spring retainers were also used along with the standard roller rocker arms and hydraulic lifters.

A number of exhaust and inlet camshafts were manufactured in order to evaluate different valve overlaps; between the exhaust scavenging valve and the inlet valves as well as the overlap between the blowdown valve and the scavenging valve in the exhaust stroke. The choice of valve lift profiles is described in detail in Table 3. Continuously variable camshaft phasing, with an adjustment range of 50 CAD, was installed on both the exhaust and the intake camshaft. The lift profiles of the different camshafts were measured when mounted on the engine to ensure proper valve lift curves as well as proper positioning relative to the crankshaft.

EXPERIMENTS - Several operating modes has been identified and tested on the DEP engine. These include:

1. Low speed, where the scavenging exhaust system is shut off with the trapping valve, see Figure 1, to get sufficient mass flow over the turbine and prevent blow through.

2. High speed, where both exhaust systems are open and assist in emptying the cylinders.

3. Cold start, where the blowdown exhaust system, leading to the turbine, is shut off.

Table 3 Valve opening and closing events for the reference camshaft.

Valve Duration Opening Closing [CAD] [aTDC] [aTDC] Exhaust blow-down 200 120 320 Exhaust scavenging 159 220 379 Intake 239 341 580

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Figure 5 Valve lift profile combinations that have been tested in the Divided Exhaust Period Engine.

Full load performance – A number of camshafts were manufactured and tested on the engine to evaluate the performance of the DEP engine concept at full load. A reference set of camshafts with valve lift events according to Table 3 was selected. The tests with different camshafts aimed at determining the influence of divided exhaust period valve timing on pumping work, engine output and cylinder scavenging. Continuously variable camshaft phasing further increased the possibility to vary the valve timing. Camshaft combinations that have been tested are shown in Figure 5. Results from tests with varying exhaust scavenging valve opening are reported in this paper.

Cold start catalyst light-off – In order to meet future stringent legislation regarding emissions it is imperative to achieve a fast light-off of the catalyst system. It is important to heat up the catalyst substrate as fast as possible to achieve a fast light-off. This is achieved by running the engine with very late ignition timing [10] and sometimes with secondary air injection to produce a secondary reaction in the exhaust manifold [11]. Ideally all of the heat that is generated in this manner should be transferred to the catalyst substrate. A major cause of heat losses for turbocharged engines is the turbocharger. With the DEP system, the turbocharger is excluded during the cold start and a significant improvement in cold start emissions was anticipated.

Two separate tests were performed to evaluate the cold start performance of the DEP engine with active catalysts installed in the exhaust scavenging system. The first tests were focused on the gas exchange

process and power potential during cold start with only the exhaust scavenging valve active. The second set of tests focused on optimizing the valve timing for the cold start. The second set of tests were performed in a cold start rig without cylinder pressure measurements and dynamometer, otherwise with a similar set-up as in the other cold start tests. A comparative test with a standard turbocharged engine was also performed. In the tests with the DEP engine, the roller finger follower was removed from the blowdown valve in order to run the engine with only the scavenging valve active.

Two different catalyst systems were evaluated in the cold start rig. One of the systems was a 400 cells per square inch (cpsi) system that was designed for a close-coupled installation behind the turbocharger in the standard engine. The second system had two catalysts, a 900 cpsi close coupled pre-converter and a 400 cpsi main catalyst. This is a system that could be similar to a production DEP system with the pre-converter placed in the exhaust scavenging system and the main catalyst after the junction of the two exhaust systems.

RESULTS

In this project initial testing was performed in order to calibrate the simulation model so that it could be used in further studies. Testing and simulation was then performed in parallel. Tests were used for simulation model validation and simulations helped in interpretation of test data. Simulation model data will be presented together with test engine performance for a number of key parameters below. Both cycle average and crank angle resolved results are shown.

SIMULATION MODEL CORRELATION - One of the key parameters when simulating an engine model is the volumetric efficiency. Air mass flow was obtained from measured fuel mass flow and measured lambda. Since the DEP engine has two separate exhaust manifolds several possibilities for measuring lambda exist. The lambda value used for calculating mass flow was an

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average from measured values in both the blowdown system and the scavenging system. For some cam settings a significant amount of blow through was obtained, this will inevitably influence the measured lambda value in the scavenging system. Hence the lambda measurement does not necessarily represent the combusted mixture. This will effect the calculation of mass flow. Figure 6 show a comparison between measured and simulated values of air mass flow and volumetric efficiency. The model does not show particularly good accuracy over the speed range, which is surprising since most other engine calibration parameters show good agreement with measurement. This discrepancy might be due to the previously mentioned difficulty in mass flow calculations from measured lambda. Another explanation to the discrepancy in volumetric efficiency is related to the modeling of residual gas. The DEP concept has asymmetrical scavenging of the cylinder since only one exhaust valve is open during the scavenging phase. This will affect the residual gas content. If the residual gas content is not modeled correctly, this will affect the simulated volumetric efficiency. However, 3-D simulation was not available at this stage and 0-D simulation data was considered sufficient.

MEAN EFFECTIVE PRESSURES – Simulated BMEP and IMEP, shown in Figure 7, correlate well with measurements. The engine model targets a specified BMEP by adjusting the wastegate diameter. IMEP does not correlate exactly due to uncertainty of simulated FMEP values.

Looking at BMEP obtained in engine tests with different camshafts in Figure 8, reveals that the DEP reached slightly higher power than the standard engine in the tests. However, low speed BMEP was in fact below the standard engine when the trapping valve, see Figure 1, was open. The reason for the low BMEP can be found in

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Figure 7 IMEP and BMEP comparison between test and simulation. Values for BMEP are on the same curve since the engine model targets BMEP.

the DEP concept. At low engine speeds all of the energy in the exhaust has to be transferred via the turbine to the compressor in order to reach the boost pressure target. However, with the DEP concept a part of the exhaust is bypassed the turbine and as a consequence it is difficult to reach the boost target. With the DEP engine concept it would be possible to use a smaller turbine without suffering from increased residuals, as the amount of residual gas is not directly related to the exhaust pressure before the turbine. Even with a considerably smaller turbine it would be very difficult to reach the target with some of the exhaust energy lost through the scavenging system. A thorough matching of the turbocharger was not carried out and the tests were performed with a standard turbocharger with a smaller inlet area.

In order to increase the boost pressure at low speed the trapping valve has to be closed, which forces all of the exhaust past the turbine. Thereby the required boost pressure can be obtained. With the trapping valve closed it is beneficial to have a very early scavenging exhaust valve opening, denoted early scavenging 2 in Figure 8, thereby obtaining large overlap between the blow down valve and the scavenging valve. (See Figure 8, compare early scavenging 1 and 2 at 1500 rpm.) A large overlap is necessary in order to have mass transfer from the scavenging system into the blowdown system and subsequently through the turbine. The exhaust scavenging system is emptied into the exhaust blowdown system via the following cylinder in firing order during exhaust blowdown/scavenging overlap. The power delivered to the compressor is increased with an increased mass flow over the turbine. By charging the exhaust scavenging system with intake pressure the mass flow across the turbine can be increased further, hence the boost pressure can be increased as well. Camshaft phasing tests with closed trapping valve

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Figure 8 Obtained brake mean effective pressure with different exhaust valve lift curves compared to the standard engine. The solid markers indicate closed trapping valve in the scavenging exhaust system.

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Figure 9 Comparison of pumping mean effective pressure at full load with different divided exhaust period valve lift profiles and standard t/c operation.

showed that increased overlap between the scavenging exhaust valve and intake valves boosted the engine output significantly. A 20 % increase in available torque was observed at 1500 and 2000 rpm when the overlap between exhaust scavenging valve and intake valves was increased by 40 CAD.

The DEP engine exhibits positive PMEP over an extended speed range compared to a standard turbocharged engine, i.e. work is added to the crankshaft during the gas exchange. In addition, high speed negative PMEP is reduced compared to the standard t/c engine. Figure 9 shows PMEP over the engine speed range with three different camshaft combinations, varying the opening of the scavenging exhaust valve and blowdown/scavenging valve overlap, see Figure 5 top graph. Advancing the scavenging exhaust valve opening 15 CAD, denoted early scavenging 1 in Figure 9, extends the range of positive pumping work and decreases high speed pumping losses even further compared to the DEP reference camshaft. A very early scavenging exhaust valve

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Figure 10 Comparison of simulated values of residual gas content in the cylinder for the DEP engine vs. the standard turbocharged engine.

opening, denoted early scavenging 2 in Figure 9, results in pumping work similar to the standard turbocharged engine at low speed. However at high engine speeds the pumping losses are significantly reduced. The power improvement from the reduced pumping losses in the DEP engine is up to 10 kW at 5000 rpm, which is about 6 % of the engine rated power.

RESIDUAL GAS CONTENT - One of the reasons for designing the DEP engine was to decrease residual gas content in the cylinder at full load in order to improve knock resistance and volumetric efficiency. The simulation model proved to be helpful in estimating the residual gas content. Figure 10 illustrate the difference in residual gas content between the DEP engine and a standard turbocharged engine, showing a difference over the entire speed range. At 5500 rpm the residual gas content is decreased with 14 %. However in the lower speed range the decrease is over 60 %.

Residual gas content was not measured in the engine tests. However, the pressure difference from intake system to exhaust system at the gas exchange TDC gives a hint to how well the exhaust gases are scavenged from the cylinders. Figure 11 shows this pressure drop obtained from engine tests with reference camshaft and with early exhaust scavenging valve opening. The standard turbocharged engine barely reaches a positive pressure difference in the mid speed range whereas the DEP engine has a large positive pressure difference at all speeds up to 4500 rpm for the reference camshaft. Increasing the scavenging exhaust valve duration by early opening, denoted early scavenging 1 in Figure 11, gives more time and valve area for evacuating the exhaust and also a higher pressure difference at higher speeds. A very long exhaust scavenging valve duration, denoted early scavenging 2 in Figure 11, gives a lower pressure difference at lower speeds, primarily due to loss of available energy in the exhaust blowdown system and

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Figure 11 Pressure drop over cylinders (from intake runner to exhaust runner in the scavenging exhaust system) at 360 aTDC for several tested divided exhaust period exhaust valve lift profiles.

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subsequent loss of boost pressure. Tuning of the scavenging exhaust system also has an effect on the pressure difference. When the exhaust scavenging valve duration is increased the optimum pulse reflection behavior shifts towards higher speeds.

GAS EXCHANGE IN THE DEP ENGINE – Ideally, the exhaust scavenging system and the cylinder pressure has reached atmospheric pressure when the intake valve opens. However, a very large pressure difference also produces large amounts of blow-through, i.e. fresh charge goes straight through the engine. Excessive blow-through gives poor trapping ratio, especially at low engine speed when valve overlap time is long. Blow-through can however also be of benefit to increase possible boost pressure when the compressor operates close to the surge limit. To increase the trapping ratio, the trapping valve in the exhaust scavenging system has been introduced after the close-coupled catalyst, see Figure 1. By increasing the pressure in the exhaust scavenging system at low engine speed, the blow-through can be limited.

Figure 12 shows an example of the cylinder pressure and both exhaust system pressures together with intake pressure in the DEP engine during gas exchange at 2000 rpm with open and closed trapping valve in the exhaust scavenging system. The initial behavior of the blowdown pulse is similar in both cases. The top figure, where the trapping valve is completely open, shows a

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Figure 12 Pressure in cylinder, exhaust blowdown system, exhaust scavenging system and intake as a function of crank angle after combustion TDC during gas exchange at 2000 rpm with open (top) and closed (middle) trapping valve in the scavenging exhaust system. Valve lift curves are shown in the bottom.

significant pressure drop in the cylinder when the exhaust scavenging valve opens at 230° aTDC. At the same time, the pressure in the exhaust scavenging system rises to the pressure in the cylinder. The cylinder pressure has reached atmospheric pressure a little after 270° aTDC, i.e. after half the exhaust stroke. During overlap between intake and exhaust scavenging valves, there is a 30 kPa pressure drop over the engine, causing large amounts blow-through and poor trapping ratio. There is no evidence of pulse interference between cylinders at blowdown with the 200 CAD duration of the exhaust blowdown valve. However, only moderate 34 kPa boost pressure is produced with open trapping valve.

With closed trapping valve, the boost pressure reaches 57 kPa, an increase of 23 kPa compared to open trapping valve. All of the exhaust is forced through the turbine causing a higher pressure in the exhaust blowdown system in the second half of the exhaust stroke. The exhaust scavenging system acts as a buffer, filling at the end of the exhaust stroke and during exhaust scavenging/intake valve overlap and emptying its contents into the cylinder during exhaust blowdown/scavenging valve overlap of the following cylinder in firing order. This can be seen in Figure 12 where the pressure in the exhaust scavenging system is higher than the blowdown system pressure shortly after the exhaust scavenging valve has opened. The measured hydrocarbon content in the blowdown system at 2000 rpm with closed trapping valve is 6500 ppm CH4 equivalent, supporting the theory that fresh charge is transported to the exhaust blowdown system via the exhaust scavenging system. By closing the trapping valve, BMEP increases from 1,60 MPa to 1,71 MPa and brake specific fuel consumption decreases 16 %, suggesting better trapping ratio.

LIMITING FACTORS – Two key limitations have been identified in the DEP engine; the engine exhibits high turbine inlet temperatures and exhaust valves are choked during the exhaust stroke.

Exhaust temperature - As mentioned previously, simulation of the turbocharger is based on performance maps. By comparing measured turbine speed to simulated, the performance of the simulation can be checked. Figure 13 show comparison of turbine inlet temperature and turbine speed between simulation and measurement. As can be seen in the figure the turbine speed correlate well.

The exhaust gas temperature limit in the engine test was set to 1253 K due to material constraints. For the DEP engine this temperature was reached already at 2250 rpm both in the tests and in the simulation, which can be seen in Figure 13. This is a very low speed compared to a standard turbocharged engine. The most likely explanation to the comparatively high temperature before the turbine can be found in the temperature and

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mass flow across the turbine for the DEP engine. The gas in the blowdown phase has the highest temperature due to low expansion of the gas. As the pressure decreases, the temperature of the gas also decreases and by the end of the displacement phase the lowest temperature is reached. Due to the fact that the turbine is fed only by the blowdown phase, the comparatively low temperature exhaust gas does not cool down the turbine.

Comparing simulation results for a standard turbocharged engine with the DEP concept at 2500 rpm supports this reasoning. In Figure 14 the temperature and mass flow across the turbine is shown. The load in these simulations is around 1.8 MPa BMEP for both engines. There is a slight difference in the position of 50% mass fraction burnt, 31 and 26 CAD aTDC for the standard and DEP engine respectively. Due to the later phasing of combustion the standard engine has a slightly higher peak temperature in the blow down phase. However in the displacement phase the temperatures are comparable. Hence, the problem with the high temperature can be explained by the fact that the mass flow over the turbine for the DEP concept is considerably smaller than for the standard engine during the displacement phase. As a consequence this phase has a much smaller effect in lowering the mass averaged temperature for the DEP concept.

Flow over exhaust valves - The engine works as intended at low engine speeds with a significant pressure drop in the cylinder when the exhaust scavenging valve opens. This can be seen in Figure 15 that show measured cylinder pressures at several engine speeds. At speeds over 3000 rpm the piston displacement phase of the exhaust stroke starts to show in the cylinder pressure. This is due to choked flow over the exhaust valves. Figure 16 show Mach number across the exhaust valve at 5500 rpm. The DEP engine shows a substantially longer period of choked flow during the blowdown phase compared to the standard turbocharged engine, shown by the arrow in Figure 16. It

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g/s]

Figure 14 Temperature and mass flow in the turbine inlet in the DEP engine compared to a standard turbocharged engine at 2500 rpm.

is also apparent that the scavenging valve is choked during almost the entire displacement phase. The DEP concept would benefit from increased flow area of both exhaust valves; the increase in exhaust valve diameter from 28 mm to 32 mm was not enough to compensate the decrease in total valve lift area. Increased choked period was also seen for the blowdown valve at lower engine speeds however less pronounced. The choking of the scavenging valve is in part explained by the lower temperature in the scavenging system port compared to a standard engine, leading to lower speed of sound and more choking.

180 270 360 450 540 63050

100

150

200

250

3000 rpm

4000 rpm

5000 rpm

2000 rpm

1000 rpm

Cyl

inde

r pre

ssur

e [k

Pa]

Crank angle [ATDCf] V

alve

lift

Figure 15 Cylinder pressure during the gas exchange for increasing engine speeds in the DEP engine at full load with early scavenging exhaust valve opening. Valve lift curves for blow-down and scavenging exhaust valve and the inlet valves are also shown.

9

90 180 270 360

0.00

0.25

0.50

0.75

1.00

standardt/c

blow-downvalve

Stan

dard

eng

ine

Crank angle [aTDC]

0.00

0.25

0.50

0.75

1.00 scavengingvalve

DEP

eng

ine

Mac

h nu

mbe

r

Figure 16 Comparison of simulated Mach number across exhaust valve between DEP engine and standard turbocharged engine at 5500 rpm.

COLD START – The power potential during cold start with only the scavenging valve active had to be investigated, since the engine has to run with the turbocharger inactive until both catalysts have reached light-off. The exhaust scavenging valve duration was 174 CAD compared to 240 CAD for the standard turbocharged engine. The most likely scenario during the first 20-30 seconds is low speed driving, similar to the speeds and loads found in for example the EC2005 emission cycle. These loads are typically below 10kW. Therefore the power demand on the engine is rather low. In spite of the extremely short duration of the exhaust period, the engine was capable of producing torque in the same range as a naturally aspirated 1.6 liters engine as seen in Figure 17. Even with a low gearing this torque is sufficient to handle a 1700 kg vehicle.

800 1200 1600 2000 2400130

135

140

145

150

155

160

740

780

820

860

Torq

ue [N

m]

Engine speed [rpm]

Various cam settings

BM

EP

[kP

a]

Figure 17 Torque with only a 174 CAD scavenging valve activated.

-90 0 90 180 270 3600.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

(4)

(3)(2)

DEP Standard t/c

Pre

ssur

e [M

Pa]

Crank Angle [aTDC]

Heat release rate

(1)

Figure 18 Cylinder pressure traces from cold start tests with a standard gas exchange system and the DEP system.

The gas exchange was significantly changed during cold start in the DEP engine compared to a standard turbocharged engine. The combustion phasing is very late in order to heat the catalyst. This, in combination with the short valve duration of the scavenging valve, leads to a rather peculiar cylinder pressure trace as shown in Figure 18. Four observations can be seen (numbered in the figure):

1. The exhaust emptying period is very short for the DEP concept.

2. The cylinder content is recompressed before the scavenging valve opens.

3. The blow down interference from the following cylinder in firing order is eliminated.

4. The combustion is much faster with the DEP-concept.

The short exhaust emptying period is naturally due to the shorter cam duration, which also causes the recompression of the cylinder content. The latter lead to an increased pumping work, which in turn lead to an increased inlet pressure requirement in order to maintain the engine speed. The increased inlet pressure during cold start of the DEP engine, combined with the elimination of the interfering exhaust pressure pulse during the valve overlap lead to decreased residual gas content and increased combustion rate. The combustion phasing is therefore slightly earlier in the DEP engine than for the standard engine with the same ignition timing. The ignition timing that was used during the tests was the same as the calibration for the standard engine. Therefore the temperature in the exhaust manifold was slightly lower for the DEP engine than with the standard engine.

10

300°C after cat

<50 ppmHC

300°C before cat

Std t/c 1 cat Std t/c 2 cat DEP 1 cat DEP 2 cat

Tim

e [s

]

~38%

Figure 19: Emissions cold start, 2 cat denotes close-coupled pre-catalyst 900 cpsi before a main catalyst 400 cpsi. 1 cat denotes close-coupled main catalyst 400 cpsi.

In spite of the lower exhaust temperature, the time to 300° C in front of the catalyst was reduced with 50% compared to the standard engine. The cold start tests also demonstrated the ability to reduce emissions with the DEP system. In comparison to the standard turbocharged engine the light off time, measured as the time to achieve less than 50 ppm HC downstream the catalyst, was reduced with 38% as shown in Figure 19. This result was achieved solely by optimizing the exhaust scavenging/intake valve overlap. With additional calibration of lambda strategy, ignition timing and injection timing the results should be improved.

DISCUSSION

High power-density engines are all limited by engine knock. By completely emptying the combustion chamber from exhaust gas, engine knock can be significantly reduced. This is accomplished by creating a higher pressure in the intake than in the exhaust system during exhaust/intake valve overlap, thereby flushing out the exhaust gas. However, with a PFI engine this usually leads to high engine out HC emissions since the fuel in the port is also blown out into the exhaust. By using direct fuel injection this problem can be overcome. A system such as the DEP system, which can create a positive pressure difference over the engine and has large blow-through, would naturally also benefit greatly from DI.

The temperature in the exhaust blowdown system proved to be high in the DEP engine, making some kind of measure to reduce turbine inlet temperature necessary. The high temperature arises since only the hottest of the exhaust gasses are fed through the turbine, whilst the relatively colder exhaust gas in the late part of the exhaust stroke are completely bypassed the turbine. This puts high demands on the materials

and cooling system in the exhaust blowdown system, from exhaust blowdown valve to the turbine. Since the cold start catalyst light-off is handled by the close coupled catalyst in the scavenging system, aggressive measures can be taken to lower the exhaust gas temperature in the blowdown system without affecting catalyst light off time and cold start emissions. Furthermore, the aging problem of the catalyst, due to high exhaust temperatures, is also of less concern. The close-coupled catalyst is placed in the scavenging system where the exhaust temperature is low and the main catalyst can be placed under the floor of the vehicle where it can be cooled by the airflow underneath the vehicle. This in turn allows a higher temperature out from the turbocharger.

It appears that the scavenging exhaust system plays a major role in the gas exchange even when the trapping valve in the scavenging exhaust system is closed. By varying the trapping valve opening, the exhaust backpressure during the displacement part of the exhaust stroke and during exhaust scavenging/intake valve overlap can be adjusted. This can be used to control the pressure difference over the engine and limit blow-through. Partially closing of the trapping valve can also provide the turbine with increased mass flow and higher enthalpy by increasing the cylinder pressure during exhaust blow-down/scavenging valve overlap.

Variation of exhaust valve sizes might prove valuable to decrease the choking of the exhaust systems at high speeds seen in Figure 15 and Figure 16. Also, CFD computation of the in cylinder flow would give valuable information about how the spatial asymmetry in the cylinder introduced by only having one of two exhaust valves open during exhaust scavenging/intake valve overlap affects the scavenging process. Introducing temporal asymmetry in the intake valve opening could perhaps improve the scavenging further.

The demands on valve lift profiles vary a lot in terms of both valve lift duration and overlaps over the engine operating range. The DEP concept would benefit from fully variable valve mechanisms.

Tuning of the exhaust system is usually not considered in the design of modern turbocharged engines. Exhaust pipe tuning usually requires long pipe lengths due to the high temperature and high speed of sound in the exhaust gases. Compact exhaust manifolds are used in turbocharged engines to minimize heat losses prior to the turbine to preserve exhaust energy and also to decrease catalyst light-off time. Another reason for choosing compact manifolds is to improve transient response of the engine. Introduction of the exhaust scavenging system opens new possibilities for pipe tuning without affecting the turbine. The lower temperature in the exhaust scavenging system combined with the short scavenging valve duration enables short pipes to be used in a tuned scavenging system, facilitating vehicle packing of the engine.

11

12

The DEP concept is not necessarily limited to turbocharged SI engines. Any turbocharged engine could benefit from the reduced exhaust backpressure and pumping losses in the DEP concept, especially when wastegate controlled turbochargers are used. The DEP scavenging system can be considered as a more efficient wastegate.

CONCLUSION

In the section on Technical concept some difficulties with a conventional 4-cylinder turbocharged engine were identified. The objective with the DEP concept was to improve the performance within these areas. Some conclusions could be made from simulations and experiments:

• The DEP concept succeeds in decreasing the amount of residual gases in the engine by increased pressure difference over the engine during overlap between exhaust and intake valve opening.

• The pumping loss is decreased compared to a standard turbocharged engine. The decrease is around 100 kPa.

• Pulse interaction can be avoided by dividing the exhaust flow.

• A significant contribution to improve knock resistance for the engine is indicated by a decrease in residuals gas content.

The catalyst light-off time can be reduced with the DEP system compared to a standard turbocharger system. It was shown that the time to reach a level below 50 ppm HC after the catalyst could be reduced with 38% with a minor effort.

The concept also has some drawbacks. The possible power output of the DEP engine is limited due to high exhaust temperatures. Choked flow in the exhaust valves also gives an extended blowdown pulse and increasingly negative pumping work at high engine speed.

The concept will require several valves and actuators to control the exhaust flow path making it costly to implement in series production. Direct fuel injection and a variable valve mechanism would be desirable to exploit the full benefit of the divided exhaust period concept.

Summarizing, the DEP concept clearly has some positive aspects, such as decreased PMEP, residual gas content and catalyst light-off time. However, the simulations and experiments have also pointed out some weaknesses, like high temperature before the turbine and choking of the exhaust valves. The parallel work with simulations and experiments has proven very valuable both for the understanding of the concept and for the validation and refining of the simulation models.

ACKNOWLEDGMENTS

The authors would like to thank Eric Olofsson, Emil Åberg and Adam Rundqvist for their invaluable help and guidance during the project.

The authors wish to thank the Green Car project funded by the Swedish National Energy Administration for financing parts of this investigation.

REFERENCES

[1] Westin, Grandin, Ångström; The Influence of Residual Gases on Knock in Turbocharged SI-Engines; SAE 2000-01-2840

[2] Grandin B; Full load performance of a turbo charged SI engine in the presence of EGR, ISSN 1400-1179, 1999:17

[3] British patent No. 12,227/22 [4] Gamma Technologies, http://www.gtisoft.com/ [5] Heywood, J. B.; Internal Combustion Engine

Fundamentals; McGraw-Hill Series in Mechanical Engineering, McGraw-Hill 1988

[6] Watson, Janota; Turbocharging the Internal Combustion Engine, MacMillan Press 1982 ISBN 0 333 24290 4

[7] Westin F; Accuracy of turbocharged SI-engine simulations, ISSN 1400-1179, 2002:18

[8] Brunt, M. F. J., Lucas, G.; The Effect of Crank Angle Resolution on Cylinder Pressure Analysis; SAE 910041

[9] Brunt, M. F. J., Emtage, A. L.; Evaluation of IMEP Routines and Analysis Errors; SAE 960609

[10] Chan, S. H.,Zhu, J.; The Significance of High Value of Ignition Retard Control on the Catalyst Lightoff; SAE 962077

[11] Kochs, M. W., Kloda, M., van de Venne, G., Golden, J. E.; Innovative Secondary Air Injection Systems; SAE 2001-01-0658

CONTACT

Christel Elmqvist Möller, M.Sc. Mail: Fiat GM Powertrain, Box 636, SE-151 27 Södertälje. E-mail: [email protected] Phone: +46 77 506 77 414 Fredrik Lindström, M.Sc. Mail: KTH Machine Design, Brinellvägen 83, SE-10044 Stockholm. E-mail: [email protected] Phone: +46 8 790 7867

13

DEFINITIONS, ACRONYMS, ABBREVIATIONS

DEP: Divided Exhaust Period

TDC: Top Dead Center

BDC: Bottom Dead Center

CAD: Crank angle degrees

IVC: Inlet Valve Closing

BMEP: Brake Mean Effective Pressure

IMEP: Indicated Mean Effective Pressure

PMEP: Pump Mean Effective Pressure

MBT: Maximum brake torque spark timing

t/c: turbocharged

SI: Spark Ignited

DI: Direct Injection

PFI: Port Fuel Injection

CCC: Close Coupled Catalyst

cpsi: cells per square inch

PAPER II

2003-01-3123

Optimizing Engine Concepts by Using a Simple Model for Knock Prediction

Christel Elmqvist Fiat-GM Powertrain/ Royal Institute of Technology

Fredrik Lindström and Hans-Erik Ångström Royal Institute of Technology

Börje Grandin Fiat-GM Powertrain

Gautam Kalghatgi Shell Global Solutions


ABSTRACT

The objective of this paper is to present a simulation model for controlling combustion phasing in order to avoid knock in turbocharged SI engines. An empirically based knock model was integrated in a one-dimensional simulation tool. The empirical knock model was optimized and validated against engine tests for a variety of speeds and λ. This model can be used to optimize control strategies as well as design of new engine concepts.

The model is able to predict knock onset with an accuracy of a few crank angle degrees. The phasing of the combustion provides information about optimal engine operating conditions.

INTRODUCTION

One way of decreasing the CO2 contribution from the automotive sector is to increase the fuel efficiency. Down-sizing, the use of supercharging, has proven to be an effective way of increasing the fuel efficiency in spark ignition (SI) engines. Unfortunately down-sized SI engines are highly limited by knock.

Knock in SI engines has been the focus of extensive research ever since the first engine was manufactured more than a century ago. It is widely accepted that knock is an acoustic phenomenon produced by the autoignition of the unburned gas in front of the flame front [1,2]. Due to the potential for engine damage it is very important to avoid knock but at the same time, due to efficiency reasons, be as close to knocking combustion as possible. Although our knowledge of the phenomena that cause knock has increased

significantly, it is still not possible to accurately model autoignition of the unburned gas and the phenomena that subsequently lead to engine knock, to such an extent that such a model can be used as a predictive tool. The goal of such simulation work could be to aid and guide in the product development phase.

Simulations can be performed with different levels of accuracy, where the knock prediction codes including detailed chemical kinetics have the largest level of physicality. These codes are based on the chemical reactions and rate coefficients for combustion and are very complex. A different approach is using empirical relationships based on the Arrhenius function. The physicality decreases but on the other hand the potential for studying realistic problems increase and the computational time decrease drastically. In the absence of knock models a common way is to look at the simulated temperature in the unburned zone and change the phasing of combustion when the temperature increases above a certain value. The change in phasing of the combustion in the simulation is seen as analogue to retarding the spark timing on a real engine.

This paper will show the use of a zero-dimensional model integrated in a one-dimensional simulation tool, which is capable of calculating the onset of knock for a defined combustion with a reasonable accuracy as well as controlling the combustion phasing, analogue to retarding the spark-timing. This tool is very important for optimizing turbocharged SI engine concepts and to make a first calibration effort.

BACKGROUND

The term knock originates from the noise created by pressure oscillations originating from spontaneous ignition of the unburned mixture, the so called “end-gas”, ahead of the advancing flame front [3].

n and the

occurring when the pressure oscillations exceed a pre-defined threshold value.

Knock also depends critically on the autoignition quality of the fuel, which is usually determined by the octane number. However, in this work, we consider the engine running on a single fuel and consider the effects of changed operating conditions on knock.

Autoignition centre

A common approach for modeling knock is to look at the temperature in the end-gas. This can give a very rough idea of knock onset, but for turbocharged engines this method is especially inappropriate. Knock is highly pressure dependent, as well as temperature, and since turbocharged engines generally have higher cylinder pressure than naturally aspirated engines it is a non-negligible effect.

End gas

* Burnt gas

Flame front

As the end-gas is compressed by the pisto

Figure 1 Autoignition centres in the combustionchamber.

propagating flame front, its temperature increases, which can lead to autoignition centered around one or more points (see Figure 1). The location of these autoignition centers depends on local inhomogeneities in composition and temperature [4]. Autoignition can lead to a drastic increase in heat release, which in turn could cause pressure oscillations in the combustion chamber. Under some circumstances the heat release rate is too small to sustain these pressure oscillations, hence autoignition does not necessarily lead to knock [2]. On the other hand, the pressure oscillations could be severe enough to cause engine failure. Pressure development following autoignition depends on the mean temperature and the temperature gradient in the end-gas. Three different modes have been identified for the progress of combustion following autoignition: deflagration, thermal explosion and developing detonation [5,6]. The last of these modes can cause very high amplitude pressure fluctuations, which could cause engine damage. While engine damage from knock is an important issue, usually the main practical problem is low intensity knock, which is easily perceptible through its characteristic noise. So in this work, as in most other studies associated with knock, the events leading up to autoignition and autoignition itself are the primary concern. The occurrence of these different autoignition modes complicates the detection of knocking combustion. An effective way of detecting knock is to measure the cylinder pressure. Depending on the sensor position the detected pressure oscillations will vary due to the occurrence of the knock modes [7]. For practical reasons it is common practice to mount the pressure sensors in some channel connected to the cylinder. However, when studying knock it is preferable that the pressure sensor is flush mounted since otherwise oscillations stemming from the channel might interfere with the oscillations originating from autoignition. Since knock intensity is usually defined by the amplitude of the pressure oscillations, it is important to eliminate spurious oscillations. Common practice is to consider knock as

EXPERIMENTAL SETUP

The experiments were performed on a standard 2.0-liter, 4-cylinder turbocharged SI engine. In Table 1 engine specifications can be found.

Table 1 Engine specification

Bore 86 mm Stroke 86 mm Compression ratio 9.5 Combustion chamber hemisphere with central

spark plug

The experiments were aimed at running the engine with knocking combustion for different operating modes, the conditions can be found in Table 2. When running into knocking combustion the spark was advanced from the standard map until knock was audible.

Table 2 Experimental conditions

Engine speed 2500, 3000, 3500 rpm λ @ 2500 rpm 0.92 λ @ 3000 rpm 0.86, 0.99, 1.1 λ @ 3500 rpm 0.84 Fuel 95 RON Coolant temperature 90°C

Cylinder pressure measurements were performed with one AVL GM12D pressure transducer per cylinder. The natural frequency of these transducers is 130 kHz. The transducers were nearly flush mounted in order to be able to detect knock with as little disturbance as possible. They were positioned 12 mm off the radial cylinder center in order to avoid the nodes of the pure circumferential pressure oscillation modes. The signals were sampled with an AVL Indimaster 670 with a resolution of 0.1 crank angles (CA) in the interval -30 to 60 CA around combustion top dead center (CTDC), corresponding to 150 kHz at 2500 rpm. In the remainder

of the cycle the resolution was 1 CA. For each operating condition and cylinder at least 500 cycles were recorded.

KNOCK DETECTION

To find the knock onset from the measured data, the cylinder pressure was digitally band pass filtered. The band pass window of the filter is centered on the 1st circumferential mode of the knock induced pressure oscillations, which normally has the highest energetic content [8]. The width of the window is chosen to get small phase distortion at the frequency of the first circumferential mode. The cut-off frequencies 3.5 and 10 kHz were chosen. The reason for band-pass filtering instead of high-pass filtering is to avoid high frequency measurement noise and disturbances.

The analytical solutions of the general wave equation [10] in a closed cylinder with flat ends, which is a rough model of the combustion chamber, gives a good starting point for the selection of cut-off frequencies for the filter. The solutions and, hence, the natural frequencies of the combustion chamber model are [8, 9]:

Bcf nm

nm πα ,

, ⋅= Equation 1

where m is the circumferential mode number, n the radial mode number, αm,n the vibration mode factor determined by means of Bessel’s equations, cf. Table 3, B the bore and c the speed of sound estimated to 950 m/s. Table 3 contains estimated natural frequencies of the combustion chamber model.

Table 3 Acoustic modes of a closed cylinder model of the combustion chamber with c = 950 m/s

(m,n) (1,0) (2,0) (0,1) (3,0) (1,1) description 1st

circ. 2nd circ.

1st radial

3rd circ.

1st combined

αm,n 1.841 3.054 3.832 4.201 5.332 fm,n [kHz] 6.5 10.7 13.5 14.8 18.7

Fast Fourier Transform (FFT) of the measured knock cycles confirms the calculated frequency of the 1st circumferential mode at approximately 6.5 kHz. Figure 2 is an example of the frequency content in a knocking cycle. The peaks at the frequencies of the cylinder oscillation modes from Figure 2 are clearly seen. Another observation is that the transducer position, 12 mm off the cylinder center, suppresses the circumferential oscillation modes while the radial modes at approximately 14 and 19 kHz are more prominent.

0 5 10 15 20101

102

103

104

FFT

of c

ylin

der p

ress

ure

[bar

]

Frequency [kHz]

Figure 2 Fast Fourier transform of a knocking cycle with frequency peaks at the oscillation modes of the cylinder.

Knocking cycles were identified by the peak value of the band-pass filtered cylinder pressure signals. The threshold for defining a cycle as knocking was set to 1 bar. The peak amplitude of the band pass filtered cylinder pressure was used as individual cycle knock index (KI). A threshold of was used for determination of knock onset (KO), which proved to give accurate results of KO. The value 0.7KI is chosen as a compromise between the risk of erroneous detection of KO due to signal noise and the accuracy of the KO detection. More elaborate methods for determination of KO has been suggested in [11] which also includes the search of a zero crossing ahead of the threshold in the filtered pressure signal. Figure 3 shows pressure and band-pass filtered pressure of a knocking cycle and the detected KO.

{ 9.0 ;KI7.0min ⋅ }

Since information of the knock location is not available, the measured KO is only accurate to within approximately 1-2 CA, depending on engine speed. The distance between the pressure transducer and the autoignition center together with the local speed of sound determines the delay between real KO and measured KO [12].

-20 0 KO 20 40 60

0

20

40

60

80100

Cyl

inde

r pre

ssur

e [b

ar]

CA-20 0 KO 20 40 60

-2

0

2

Filte

red

cylin

der

pres

sure

[bar

] KI

Figure 3 Cylinder pressure for a knocking cycle from lean combustion at 3000 rpm and filtered cylinder pressure of the cycle. KO = 14.1 CA, KI = 2.57.

SIMULATION MODEL

The aim with the simulation model is to integrate a knock model into an existing one-dimensional model of the engine. The one-dimensional model is based on thermodynamic laws for calculation of the pressure and temperature in the engine. The assumption of one-dimensional simulation is that three-dimensional phenomena can be simulated with one-dimensional tools sufficiently if the output data from the one-dimensional simulations agree with measurements of the physical phenomena.

COMBUSTION

An SI-engine always suffers from cycle to cycle variations. These variations depend on in-cylinder flow variations due to the stochastic nature of turbulent flow, local variations in the fuel/air mixture in the cylinder etc. These phenomena can currently not be practically simulated by any simulation code. In one-dimensional codes the combustion is often specified in either of two ways: By a Wiebe function or by estimating the laminar and turbulent flame velocity. The Wiebe function is commonly presented as [3]:

∆−

−−=+1

0exp1m

b axθθθ

Equation 2

where θ is the crank angle, θ0 the start of combustion, ∆θ the combustion duration, a and m are adjusted to the measured curve. The Wiebe function can be described as a curve fit to the accumulated heat release, which is based on measured cylinder pressure. Hence, a Wiebe based model can never be predictive. On the other hand, the Wiebe method of describing combustion is very robust and can accurately describe the engine operating conditions for which it has been tuned. The model can even be used for semi-predictive modeling, if care is taken when analyzing the results. Common parameters when describing the combustion are: The CA for 50% burnt and the duration between 10% and 90% burnt. By defining these parameters the combustion event is defined through the Wiebe function.

As mentioned previously, knock is caused by autoignition of the unburned gas ahead of the flame front, leading to pressure oscillations in the combustion chamber. Hence, in order to model the thermodynamic state of the unburned zone a two-zone combustion model is used. The pressure in the combustion chamber is assumed to be uniform in the unburned and burned zone. The unburned zone temperature can be calculated by assuming adiabatic compression, neglecting the heat transfer between the burned and unburned zone.

KNOCK MODEL THEORY

Knock occurrence has a clear relationship to the phasing of the combustion. In Figure 4 CA for 50% burnt are

plotted for several knocking cycles and showed in relation to the average, minimum and maximum value for the entire test run.

Figure 4 50% burn point for knocking cycles and minimum, maximum and average 50% burn point for all cycles at 2500 rpm and λ=0.92.

02468

1012141618

0 10 20 3

Cycle number

CA

for 5

0% b

urnt

[CA

] Maximum CA for 50% burnt

Average CA for 50% burnt

Minimum CA for 50% burnt

0

As can be seen in Figure 4 the knocking cycles have a faster than average combustion event, where the CA for 50% burnt is seen as a measure of the combustion speed. The flame development speed also influences the knock intensity. For a given operating condition, the faster the flame development, the higher the knock intensity [12,13]. In the evaluation process of an engine the average values are commonly used, this then give a rough idea of the engine performance. When studying knock the perspective is moved from the average values to the faster than average, since these are the knocking cycles. The faster cycles will be limiting for engine performance and decisive for permitted boost pressure, the choice of fuel octane requirement and compression ratio.

Since knock is dependent on the flow characteristics, fuel distribution etc, a thorough simulation of the knock phenomena would require a three-dimensional simulation with chemical kinetic calculations. This approach is very time consuming and also dependent on local details in the turbulent flow field and rate coefficients for the chemical reactions, which are not available for practical fuels. For quicker and more practical calculations of the knock onset an empirical model is used. The knock model is integrated in a one-dimensional simulation code and based on an empirical relationship for calculation of the ignition delay and the theory developed by Livengood and Wu [14]. Livengood and Wu proposed that autoignition occurs when:

11

0

=∫=

dtknockt

t τ Equation 3

where τ represents the ignition delay time and t is the elapsed time between start of compression to time of autoignition. The ignition delay time, τ, represents the time it takes to establish the amount of radicals and heat necessary for autoignition to take place for a fixed pressure and temperature. This time is calculated by fitting experimental data to an Arrhenius type function:

= −

u

X

TX

pX 31 exp* 2τ Equation 4

where τ is the ignition delay in ms, X1, X2 and X3 are constants that should be fitted to the experimental data, p is the pressure and Tu the unburned zone temperature. Hence, by substituting Equation 4 into Equation 3 one gets:

1exp*

1

0 31

2

=

∫= −

dt

TX

pX

knockt

t

u

X

Equation 5

Some additional limit is needed to distinguish between knocking and non-knocking cycles. In Figure 5 knock intensity is plotted against mass fraction burned.

Figure 5 KI as a function of mass fraction burnt.

From Figure 5 it can be concluded that no cycles knock after 93% of the fuel is burned. Cowart et. al. [15] propose that unburned mass at knock onset is about 10 to 20%. Hence, it was found appropriate to add the restriction that the integral must become equal to one before 93% of mass is burned for the simulation to be considered operating at the knock limit. COMBUSTION PHASING

Once it has been established that it is possible to calculate the knock onset by these empirical relationships, this can be used in practical engine development. As mentioned earlier, for efficiency reasons it is important to operate an engine as close to knock as possible. Since knock is dependent on the phasing of combustion, common practice when running engines on test beds is to retard the spark timing until knock does not occur. Information about knock onset as well as optimal combustion phasing at different

operating conditions is important information in the calibration process of an engine. Additionally when examining a new engine concept it is important that the simulations are performed as realistically as possible. Producing simulation data that would actually be impossible to obtain in real life due to the occurrence of knock, is of limited value.

A control block was integrated in the one-dimensional simulation code. The aim of the control block is to simulate the retardation of the spark timing, in order to move the simulated operating point to the knock limit. In this way approximate information about engine conditions in the non-knocking regime as well as information of optimal combustion phasing is gained.

Since the model is based on the Wiebe combustion model, the simulation model has no spark timing. Instead a change in the CA for 50% burnt is seen as analogue to a change in spark timing. As the combustion phasing is changed so does the duration of the combustion. A general relationship, for the measured data, between the CA for 50% burnt and the combustion duration can be found by fitting straight lines to measured CA for 50% burnt and combustion duration for different cases. It was found that these lines have similar slopes. The coefficient of determination, R2, is in the range 0.3 – 0.6 for most cases. Figure 6 shows the relationship between duration and the CA for 50% burnt for one test condition.

0 5 10 15 20 2518

20

22

24

26

28

30

32

Com

bust

ion

dura

tion

[CA

]

CA for 50 % burnt [ATDC]

Figure 6 Measured combustion duration as a function of 50% burn point and a straight line fitted to data recorded in cylinder 1 at 3000 rpm and λ = 1.1. The slope is 0.61 and R2 = 0.57.

As an approximate tool for phasing the combustion the duration will be changed with 0.5 CA for each CA increase in CA for 50% burnt. The phasing of CA for 50% burnt is approximated by fixed phasing steps.

50 60 70 80 90 1001

2

3

4

Kno

ck in

dex

[bar

]

Mass fraction burned at knock [%]

3000 fuel-lean3000 stoich.3000 fuel-rich

Figure 7 gives a schematic image of the engine simulation and control blocks.

In short the zero-dimensional combustion model provides the knock model with the cylinder pressure and temperature of unburned zone. The knock model calculates Equation 5 and the value of the integral is used as input to the control block. If the integral value is equal to one, before 93% of the mass is burned, and hence the engine is simulated to be knocking, the control block changes the CA for 50 % burnt and the duration of the combustion. When this information is sent back into the combustion model cylinder pressure etc are recalculated. These calculations are performed until the engine simulation fulfills the pre-defined convergence criteria. Once the model has converged the one-dimensional simulation of the engine will provide us with information about the new operating condition. This goes on until the control block no longer detects any knock, the integral is less than one at 93% burned mass. The simulations will then have resulted in information about the original knock onset as well as one-dimensional information about the engine operating condition.

The combustion phasing can also be used to move the engine from non-knocking, inefficient conditions to its most efficient operating condition. Hence, by using the control block for combustion phasing simulations can be performed at the operating condition most efficient for the specific engine.

Results OPTIMIZATION OF THE KNOCK MODEL

Since the main interest is to find the knock onset rather than knock time in seconds Equation 5 has been modified accordingly. The idea was to minimize the error of the Livengood-Wu integral at measured knock angle by using the least squares method as suggested by Douaud and Eyzat [16]. Equation 6 gives the equation to be minimized.

( )

2

1 140 ,31

1exp

16

1 ,

2∑ ∫= −=

−

−

⋅=

k

i iuX

ii

dTXpNX

SSiknock

φφ

φ

1-D simulation of the engine Equation 6 Integral

value Cylinder pressure Unburned temperature Knock model

0-D simulation of the combustion where k is the number of individual cycles to be studied

and N is the cycle speed in rpm. However, Equation 6 proved to have poor properties for optimization and a unique minimum could not be determined. Figure 8 shows the value of Equation 6 when X1 and X2 are varied.

50 % burn point Control of combustion phasing Duration

Figure 7 Structure of simulation

00.01

0.020.03

00.511.520

2

4

6

X1X2

SS

Douaud and Eyzat

Figure 8 The shape of Equation 6 when X1 and X2 are changed and X3 = 3800 K. The marker shows the values recommended by Douaud and Eyzat [16].

The parameters of Equation 6 are coupled. X2 and X3 control the shape of the Livengood-Wu integral and X1 sets the overall level of the integral. An increase in X1 will decrease the value of the Livengood-Wu integral, which can be compensated by an increase in X2. This makes Equation 6 inadequate for optimization purposes. Suggestions to use mean pressure and temperature between ignition and knock onset for optimization have not been attempted in this paper [10,15]. Instead the values of X2 and X3 were set to 1.7 and 3800 respectively, according to the recommendations of Douad and Eyzat [16]. Equation 6 was minimized by finding the optimal value for X1. The optimization was performed using pressures and knock angles from measurements and simulated temperatures of the unburned gas from the two-zone combustion model. The optimization was performed for several cases with varying speed and lambda. Only a fraction of the measured knock cycles were used for optimization, whilst the rest were used for validation of the identified parameter X1. The optimization resulted in that the following values were used for the constants:

X1 = 0.021, X2 = 1.7, X3 = 3800

Figure 9 shows measured and simulated knock onset for ten cycles with a comparison between the simulated knock onset using the optimized value for X1 and the parameters from Douaud and Eyzat [16].

0 2 4 6 8 10 128

10

12

14

16

18

20

Cycle

Kno

ck o

nset

[CA

ATD

C]

measuredsimulated, Douaud and Eyzatsimulated, optimized X1

Figure 9 Validation of the optimisation of parameter X1 for ten knocking cycles not used in the optimisation.

From Figure 9 it can be concluded that using the optimised value of X1 give a great improvement of the simulated knock onset when comparing to measured data.

KNOCK MODEL

Firstly the convention of studying the unburned zone temperature for knock detection was examined. Figure 9 shows a clear dependence between the temperature and knock onset.

on the operating condition. Hence, there is a need for a method with greater generality in predicting knock onset.

As mentioned previously a small selection of knocking cycles were used to optimize the constants in Equation 4. The model was then used to predict the knock onset for cycles not optimized for. Figure 11 to Figure 13 show simulated knock onset versus measured knock onset for a range of speeds and lambda.

Figure 11 Measured versus simulated knock angle for 2500 rpm and λ= 0.92

Figure 12 Measured versus simulated knock angle for 3000 rpm and λ= 0.99 (Stoich.), λ= 0.86 (rich), λ= 1.1 (lean)

12131415161718

12 13 14 15 16 17 18Measured knock onset [CA ATDC]

Sim

ulat

ed k

nock

ons

et

10

12

14

16

18

20

10 12 14 16 18 20Measured knock onset [CA ATDC]

Sim

ulat

ed k

nock

ons

et

Stoichiometric

rich

lean

880890900910920930940

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Knock onset [ATDC]

Unb

urne

d zo

ne

tem

pera

ture

[K]

2500 rpm

3000 rpm

3500 rpm

6789

1011121314

6 8 10 12 14

Sim

ulat

ed k

nock

ons

et

Figure 10 Unburned zone temperature as a function of knock onset for three different speeds.

However, as can be seen from Figure 10, setting a general temperature threshold for knock onset, valid over a range of speeds, will become inaccurate. If a temperature limit should be used for identifying knocking combustion, this limit will need to be changed depending

Figure 13 Measured versus simulated knock angle for 3500 rpm and λ= 0.84

Measured knock onset [CA ATDC]

From the previous pictures it can be concluded that knock onset can be modelled within an accuracy of approximately two degrees.

The measured and simulated knock onset as well as the average difference has been summarized in Table 4.

Table 4 Knock onset

Case [rpm] 2500 3000, lean

3000, stoich.

3000, rich 3500

Measured average 14.7 13.8 14.8 12.3 8.6

Simulated average 14.5 13.5 17.3 12.2 8.9

Average Difference 0.16 0.28 -2.42 -0.08 -0.32

Table 4 shows very good agreement between measured and simulated knock angle. The stoichiometric case at 3000 rpm shows the largest average inaccuracy between measured and simulated values of 2.4 degrees.

CONCLUSION

The conventional way of studying knock by examining the unburned temperature is found to be inadequate since, as shown in Figure 10, the unburned temperature at knock onset is strongly dependent on engine speed. Instead an empirical knock model was implemented into the one-dimensional model of an engine.

The empirical knock model is able to predict knock onset by approximately two crank angle degrees. Due to the difficulty in measuring knock onset, this is seen as a very good result. Although the model is based on the Wiebe function, it can be used as a first estimate in control and design of new engine concepts. The possibility to change the phasing of the combustion increases the usefulness of the model.

ACKNOWLEDGMENTS

The authors wish to thank Eric Lycke, Henrik Nilsson, Emil Åberg at the Royal Institute of Technology and Pontus Johansson at Fiat-GM Powertrain for their invaluable help.

REFERENCES

[1] By, A., Kempinski, B. and Rife, J.M., “Knock in Spark Ignition Engines”, SAE 810147, 1981.

[2] König, G. and Sheppard, C. G. W., “End Gas Autoignition and Knock in a Spark Ignition Engine“, SAE 902135, 1990.

[3] Heywood, J. B., “Internal Combustion Engine Fundamentals”, McGraw – Hill, inc 1988.

[4] Burgdorf, Klaas, “Engine Knock: Characteristics and Mechanisms”, PhD thesis, Chalmers University of Technology, 1999

[5] König, G., Maly, R. R., Bradley, D., Lau, A. K. C. and Sheppard, C. G. W., “Role of Exothermic Centres on Knock Initiation and Knock Damage”, SAE 902136, 1990.

[6] Pan, J. and Sheppard, C. G. W., “A Theoretical and Experimental Study of the Modes of End Gas Autoignition Leading to Knock in S.I. Engines”, SAE 942060, 1994.

[7] Fischer, M., et.al., “Knock Detection in Spark-Ignition Engines: New Tools and Methods in Production-Vehicle Development“, MTZ Issue 3/2003.

[8] Brunt, F. J., et. al., “Gasoline Engine Knock Analysis using Cylinder Pressure Data”, SAE 980896, 1998.

[9] Millo, F. and Ferraro, C. V., Knock in S.I. Engines: A Comparison between Different Techniques for Detection and Control, SAE 982477

[10] Young, H. D., Freedman, R. A.,University Physics, 9th Ed., Addison-Wesley, 1995

[11] Worret, R. et. al., “Application of Different Cylinder Pressure Based Knock Detection Methods in Spark Ignition Engines”, SAE 2002-01-1668

[12] Chun, K. M. and Heywood, J. B., “Characterization of Knock in a Spark-Ignition Engine”, SAE 890156, 1989.

[13] Kalghatgi, G. T., Snowdon, P. and McDonald, C. R., “Studies of Knock in a Spark Ignition Engine with CARS Temperature Measurements and Using Different Fuels”, SAE 950690, 1995.

[14] Livengood, J. C. and Wu, P. C., “Correlation of Autoignition Phenomenon in Internal Combustion Engines and Rapid Compression Machines”, Fifth Symposium (International) on Combustion, pp. 347-356, 1955.

[15] Cowart, J. S., Haghgooie, C. E., et. al., “The Intensity of Knock in an Internal Combustion Engine: An Experimental and Modeling Study”, SAE 922327, 1992.

[16] Douaud, A. M. and Eyzat, P., “Four-Octane-Number Method for Predicting the Anti-Knock Behaviour of Fuels and Engines”, SAE 780080, 1978.


KO knock onset

KI knock index

FFT fast Fourier transform

CA crank angle

CTDC combustion top dead center

ATDC after top dead center

R2 coefficient of determination in a least squares

curve fit ( )

)(ˆ

1 ,ˆ 2

yVaryyVarRbxay −

−=+=

Tu Unburned zone temperature

PAPER III

1

2005-01-2106

An Empirical SI Combustion Model Using Laminar Burning Velocity Correlations

Fredrik Lindström, Hans-Erik Ångström Royal Institute of Technology (KTH)

Gautam Kalghatgi Shell Global Solutions and KTH

Christel Elmqvist Möller GM Powertrain-Europe


ABSTRACT

Predictive simulation models are needed in order to exploit the full benefits of 1-D engine simulation. Simulation model alterations such as cam phasing affect the gas composition and gas state in the cylinders and have an effect on the combustion. Modelling of these effects is particularly important when the engine is knock limited. A knock model, able to phase the combustion towards the knock limit, was previously developed by the authors. A major challenge in such knock models is to predict the pressure and temperature evolution in the end-gas accurately through an adequate combustion model. The Wiebe function is often used to model the combustion in SI engine simulations, owing to its ease of use and computational efficiency. The Wiebe function simply imposes a curve shape for the fuel burn rate and the parameters are easily determined from calculated heat release. Detailed models of turbulent combustion also exist which require more knowledge or assumptions about combustion chamber turbulence. The combustion model proposed in this paper uses existing correlations of laminar burning velocity to predict the parameters of the Wiebe function relative to a base operating condition. The model aims at predicting combustion at high load operation. Experimental and simulation data from a gasoline fuelled 4-cylinder turbo charged port injected spark ignition engine are used to correlate the Wiebe function parameters dependence on laminar burning velocity.

INTRODUCTION

Engine simulation is becoming an increasingly important engineering tool for time and cost efficiency in the development of internal combustion engines. Many phenomena in engines are three-dimensional in their nature. Three-dimensional CFD simulation requires high

levels of expertise and uses large amounts of computation time. Therefore, simplified one-dimensional simulation is often used. In one-dimensional simulation, equations for conservation of mass, momentum and energy are solved in time and in one space dimension along the main flow direction in the engine pipes. Additional models, correlations or measurements are needed in one-dimensional codes to capture three-dimensional phenomena such as flow over valves and combustion.

Three-dimensional modeling of the combustion in SI engines requires a combination of chemical kinetics and turbulent flow modeling. Simplified models in one-dimensional simulations estimate the turbulent flame propagation in the combustion chamber based on combustion chamber geometry, turbulence intensity and laminar and turbulent burning velocities. Even simpler two-zone combustion models divide the combustion chamber into two sub volumes, the burned zone and the unburned zone, and impose a combustion rate to determine the relative size of each zone. Finally, the measured or estimated cylinder pressure can be used as input to the simulation model to eliminate the need of a combustion model.

The combustion model is used to predict the pressure and temperature development in the cylinder after the combustion has been initiated. Accurate predictions of unburned zone pressure and temperature are particularly important when the modeled engine might be knock limited. Knocking combustion is caused by auto ignition of unburned mixture ahead of the propagating flame and is a strong function of pressure and temperature. The complex models are comprehensive in that they try to address all the relevant physical and chemical phenomena but they may not be more accurate than the simpler models at predicting pressure

and temperature because of the many uncertainties in modeling these complex phenomena. Livengood and Wu [1] suggested that the integral of the inverse of the ignition delay τ :

11

0

=∫=

dtknockt

t τ (1)

can be used to predict when knock occurs. Douaud and Eyzat [2] proposed the Arrhenius type expression for ignition delay time:

⎟⎟⎠

⎞⎜⎜⎝

⎛= −

u

n

TBpA exp*τ (2)

where p is cylinder pressure and Tu is unburned zone temperature. The constants A, n and B are different for different fuels. A value of 1.7 for the pressure exponent, n is suggested by Douaud and Eyzat for primary reference fuels, PRF, [2] whereas Hirst and Kirsch [3] suggest that for toluene / n-heptane mixtures, toluene reference fuels, TRF, n~1.3. A value of 3800 is suggested for B for PRF fuels by Douaud and Eyzat. It is only the latest part of combustion, when temperature is high, that will give significant contribution to the integral in Equation 1. This might have implications on where simulated combustion have to be accurate with a knock model as described above.

The combustion in SI engines has been studied extensively in the past. The first stage of combustion after spark discharge is considered to be a spherical flame growing with a speed close to the laminar burning velocity [4]. Cyclic variations originate during the flame development period due to variations in mixture strength, residual gas content and turbulence close to the spark plug. Turbulent flame propagation onsets once the flame radius reaches the local length scale of turbulence. The turbulence wrinkles the flame. Turbulent burning velocity depends on the laminar burning velocity and the turbulence intensity and length scales.

Several correlations of laminar burning velocity for different fuels are found in the literature. These correlations describe the influence of air-fuel ratio, pressure, temperature and residual gas content onto the laminar burning velocity. The experiments are normally conducted in constant volume combustion vessels at several initial pressures and temperatures. Heywood [5] summarizes the results of several authors in the equations:

( )( )

( )( )2

0,

77,00,

122,016,018,018,2

~06,21013,1298

mmL

rgu

LL

BBS

xpTSS

φφ

φβφα

φ

βα

−+=

−+−=−−=

−⎟⎠

⎞⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=

(3)

and especially for gasoline:

(4) 77,2

51,3

141,0357,0

271,04,2

φβ

φα

+−=

−=

g

g

Bm, and Φm are constants for specific fuels. φB rgx~ is the residual gas mole fraction.

One origin of turbulence is the intake stroke; small scale turbulence is created by the flow over valves and large scale charge motion is created by orientation and symmetry of intake ports. The piston motion also induces turbulence. The turbulence intensity in tumbling engines increases near top dead center due to tumble breakdown. Measurements of local turbulence near the spark plug in a tumbling SI engine by Söderberg [6] show turbulence intensity maximum just before or at TDC and also a transition from larger scale turbulence to smaller scale turbulence around TDC. Turbulence intensity decreases after TDC.

THE WIEBE FUNCTION - One way of specifying the combustion rate in a two-zone combustion model is the Wiebe function [7]. The functional form:

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

∆−

−−=+1

0exp1m

b axθθθ

θ (5)

is used to describe the fraction of fuel burnt xb based on considerations of chain reactions in general and the time dependence of concentration of reaction centers. θ is the crank angle, θ0 is the start of combustion and ∆θ is the total combustion duration. The parameter m is called the combustion mode parameter and defines the shape of the combustion profile. m was introduced by Wiebe to describe the time dependence of concentration of reaction centers by the function:

(6) mkt=ρ

where k is a constant. In a spherically expanding flame with constant flame speed one would expect m to be 3. Accelerating flame speed should give higher values and vice versa. Wiebe found m to be in the range 2-4 for SI engines. The value of the constant a in Equation 5 follows from the chosen definition of end of combustion. With the mass fraction burned xb,EOC = 99,9% at the end of combustion, a has the value:

( ) 90,6001,0ln1ln , =−=−−= EOCbxa (7)

Total combustion duration ∆θ is not to be confused with 10-90% combustion duration, which is often reported from engine tests and used as input to the Wiebe function in the simulation software GTPower. Relationship between ∆θ and 10-90% combustion duration are found in Appendix A.

2

The Wiebe function is commonly used in SI engine simulation. Several correlations of one or several of the Wiebe function parameters to engine operating conditions have been proposed in the literature, see references [8][9][10]. These works provide correlations of the change of Wiebe parameters and ignition delay time ∆θign relative to a base operating condition:

∏

∏

∏

⋅=

⋅∆=∆

⋅∆=∆

ii

ii

iiignign

hmm

g

f

0

0

0,

ˆ

ˆ

ˆ

θθ

θθ

(8)

3

and the functions for relative influence of different operating parameters have the form:

0,i

ii G

Gg = (9)

where Gi are functions describing the influence of operating condition i. The relative influence of operating condition i is found by forming the quota gi. The results from Witt [9] have been used with good results in [11] to predict combustion in simulations. A different approach is found in [12] where functions for relative change similar to Equation 8 are used to correlate changes of 5% burnt, 90% burnt and max burn rate. The obtained changes are used to stretch a predefined Wiebe combustion rate profile to the desired shape. Other functional forms for the combustion rate have also been proposed in [13].

This paper describes a method to use existing correlations of laminar burning velocity as a function of pressure, temperature, air-fuel ratio and residual gas content to predict the relative change in the Wiebe parameters total burn duration ∆θ and combustion mode m. The use of laminar burning velocity in the modeling should increase the generality of the combustion model and reduce the need to calibrate the model for dependencies already captured in the laminar burning velocity correlations. The influence of engine speed and spark timing is modeled as functions for relative change as in [8][9][10]. No correlations for ignition delay time are provided since this is captured in the combustion mode parameter m in the Wiebe function.

EXPERIMENTAL METHOD

Experiments were performed on a modified 4-cylinder turbocharged SI-engine with engine specifications according to Table 1. The engine is described in more detail in [14]. Due to the engine design, very low residual

Table 1 Engine specifications

Bore 86 mm Stroke 86 mm Compression ratio 9,5 Displaced volume 0,5 dm3 per cylinder Cylinder head 4-valve pentroof with

central spark plug Fuel gasoline, 95 RON

gas content could be achieved. The engine was fitted with a cooled EGR system. The engine was mounted in a test bed with capability of precise control of temperatures in engine, charge air cooler and EGR-system.

Measurement setup - Cylinder pressure was measured in all four cylinders with un-cooled AVL GM12D miniature piezoelectric pressure transducers. Cycle individual cylinder pressure referencing was obtained by setting the average cylinder pressure equal to average inlet runner pressure in a crank angle interval during the intake stroke. Inlet and exhaust pressures were measured at several positions in the intake and exhaust system with GEMS 2200-series strain gauge pressure transducers and Kistler 4045 piezoresistive pressure transducers. The signals were sampled with 0.2° or 0.4° crank angle resolution with a 12-bit A/D-converter. Analogue low-pass filters, chosen with regard to sampling frequency and transducer resonance frequencies to avoid aliasing, and digital FIR-filters with zero phase distortion were used to assure undistorted data with low noise. Temperatures were measured with type K thermocouple probes with long insertion lengths parallel to the gas flow to avoid heat transfer losses. CO2 concentration was measured in the intake and exhaust to estimate EGR content in the charge. Air/fuel ratio was measured in the exhaust with an ECM AFRecorder 2000A. Top dead center position relative to the crank angle encoder was determined with high accuracy [16].

The trapped residual gas fraction was obtained from calibrated and validated simulations in GTPower [14]. The simulation data was also used to determine suitable crank angle intervals for cylinder pressure referencing against intake pressure.

CALCULATION OF HEAT RELEASE - A first law single zone thermodynamic analysis [5] was used to calculate heat release from the pressure data. Heat transfer according to Woschni and temperature dependent ratio of specific heats was used in the calculations. The cylinder charge temperature at inlet valve closing was estimated as the mass averaged temperature of the inlet gases and trapped exhaust gases. The trapped exhaust gas temperature at inlet pressure conditions, T*exh, was calculated by assuming an isentropic state change from exhaust pressure and temperature to inlet pressure:

γγ 1

int*

*int)1(

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

⋅+⋅−=

exhexhexh

exhrgrg

ppTT

TxTxT

(10)

where xrg is residual gas mass fraction obtained from simulation.

WIEBE PARAMETER ESTIMATION - Several methods for estimating Wiebe parameters from measured data have been suggested in the literature. Wiebe [7] suggests a transformation by rearranging and taking the natural logarithm of the Wiebe function, Equation 5, twice. This yields:

( )( ) ( ) ( ) (( θθθθ

∆−−⋅+=⎟⎠⎞

⎜⎝⎛ − lnln1

001.0ln1lnln 0mxb ))

(11)

from which the combustion mode parameter m can be determined as the slope and the total burn duration ∆θ as the intersection of the ordinate axis of the transformed normalized accumulated heat release. The crank angle of start of combustion θ0 has to be known to uniquely determine m and ∆θ. To resolve this ambiguity, Csallner [8] compared the calculated cumulative heat release in a crank angle interval with high burn rate with the Wiebe function to get the same fuel mass burned in that interval. m was then adjusted to improve the fit. Witt [9] used existing software to determine total burn duration ∆θ and combustion mode parameter m to minimize the error between identified and calculated heat release. The start of combustion was determined as 2% of the maximum heat release rate in [9].

The Wiebe function fitting method used in this work is the double logarithm method suggested by Wiebe [7]. Figure 1 shows an example of transformed heat release

3.0 3.5 4.0 4.5

-6

-4

-2

0

24.6 17.6 39.1 74.5

0.017

0.119

0.607

0.999

Measured Wiebe estimate 1,000

0,006

0,045

0,291

0,921

Cum

ulat

ive

norm

aliz

edhe

at re

leas

e

Crank angle [aTDC]

Tran

sfor

med

hea

t rel

ease

ln(θ−θ0) [CA]

Figure 1 Example of transformed heat release and fitted straight line. The range used for fitting the straight line is marked.

data, the region used for fitting a straight line and the fitted line. Ordinary least squares fit of the straight line gives extra weight to the late part of combustion, since the transformation of the crank angle is nonlinear. This should be desirable in simulation of knock with the Livengood-Wu integral, Equation 1, since the late part of combustion influences the integral value the most due to very short ignition delay at high temperature.

Figure 2 shows the same data as in Figure 1 as a function of crank angle. The error between experimental and estimated normalized heat release is within 2%, which was found to be a typical value for the data presented in this work.

Start of combustion θ0 was chosen as the spark timing in the transformation Equation 11. By using the spark timing as start of combustion in the Wiebe function, the need for additional correlations of ignition delay is omitted. The ignition delay is well captured in the combustion mode parameter m for the data examined. A longer ignition delay is reflected in a larger identified value of m.

The influence of start and end of transformed heat release data straight line fit was examined in detail. In the crank angle ranges where the burn rate is low, the calculated heat release is more sensitive to disturbances and other errors. Therefore, it should be beneficial to the quality of the heat release regression if only the central part of the heat release is used to fit the Wiebe function. Nonlinear least squares was used to find the optimal limits in terms of cumulative normalized heat release xb, with the target being to minimize the error between the measured and estimated heat release over the entire combustion event. Heat release data from 100 operation conditions with 200 recorded cycles for each of the four cylinders was used. The optimal range was determined individually for each operating condition and each cylinder, as seen in Figure 3. The average optimal range for fitting the straight line was determined as xb = 0,15 to 0,93.

-15 0 15 30 45 60

0.0

0.2

0.4

0.6

0.8

1.0

-3%

-2%

-1%

0%

1%

2%

Spark at-15,5 aTDCC

umul

ativ

e no

rmal

ized

heat

rele

ase

Crank angle [aTDC]

Measured Wiebe estimate

Mod

el e

rror

Figure 2 Example of Wiebe function fitted to experimental data with range used for fitting marked.

4

0.12 0.13 0.14 0.15 0.16 0.170.920

0.925

0.930

0.935

0.940

0.945x b a

t end

of r

egre

ssio

n

xb at start of regression

Figure 3 Optimal range for fitting a straight line to transformed heat release data determined for 100 operating conditions.

EXPERIMENTS - Engine experiments were conducted to determine the influences of various operating conditions on the Wiebe function parameters. The parameters and ranges of variation are shown in Table 2. The operating parameters are grouped according to their expected primary way of influencing the Wiebe parameters. Temperature, pressure, mixture strength and residual gas content have been shown to have an influence on laminar burning velocity. Engine speed influences the level of turbulence. Spark timing will affect the gas properties during combustion and also the turbulent burning velocity since turbulence varies on a crank angle basis. The parameters were varied one at the time to be able to easily distinguish the individual influence of each parameter, as described in Equation 8. The tests were performed with open throttle and low to moderate boost pressure. The ranges for each parameter was chosen to reflect probable ranges of operation of the actual engine at high load. In particular, spark timing was chosen at or later than MBT timing. A total of 40 different operating conditions were tested.

Table 2 Base operating condition and range of variation of engine parameters in tests.

Engine parameter

Base operating condition

Range of

variation Gas properties related parameters λ 1,0 0,85..1,14 EGR [%] 0 0..5,5 Intake air temperature [°C] 34 29..54 Intake pressure [kPa] 128 112..143 Turbulence related parameters Spark advance [bTDC] 15 6..25 Engine speed [rpm] 2500 1500..4000

5

Additionally, a central composite fractional factorial experiment was conducted with the factors λ, spark timing, intake temperature and EGR mole fraction. A total of 30 tests were conducted. The design of experiments methodology is a good help in finding test points that span the entire experimental range. One at a time tests, as the tests described above, might miss interaction effects between operating parameters. However, the aim was not to make a response surface model in several variables, but rather to get a suitable validation data set.

Cylinder pressures were recorded for 200 engine cycles at each operating condition to assure accurate estimates of averages in the presence of cyclic dispersion. Heat release and Wiebe parameters were determined for each cycle individually. The Wiebe estimation could be automated thanks to the choice of parameter estimation method described above.

PARAMETER VARIATION RESULTS

The results from varying the operating parameters one at a time are shown in Figure 4. The operating parameters that have large influence on the Wiebe parameters can be distinguished in the figure. λ, residual gas fraction, spark timing and engine speed influence the combustion duration ∆θ and combustion mode parameter m strongly. Intake air temperature and intake pressure has a small influence in the ranges of variations selected. It is also noticeable that ∆θ and m seem to be negatively correlated – high values of ∆θ are associated with low values of m.

0.8 0.9 1.0 1.1 1.250

60

70

3.6

4.0

4.4

4.2

4.4

4.6

4.8

4.2

4.3

4.10

4.15

3.6

4.2

4.8

3.8

4.0

4.2

∆θ [C

A]

λ [-]0.00 0.02 0.04 0.06

55

60

65

70

∆θ [C

A]

EGR fraction [-]

110 120 130 140

55

56

∆θ [C

A]

Intake pressure [kPa]30 40 50

56

58

60

∆θ [C

A]

Intake temperature [°C]

-25 -20 -15 -10 -5

50

60

70

∆θ [C

A]

Spark timing [aTDC]1500 2500

50

60

70

∆θ [C

A]

Engine speed [rpm]

m m

m m

m m

Figure 4 Identified Wiebe parameters from test with variation of one operating condition at the time.

TOTAL BURN DURATION - As mentioned before, several correlations of burn durations to operating conditions exist. In these correlations the influence of operating conditions are correlated one at a time to measured combustion data. Choices of functional form, i.e. linear fit, polynomial fit etc., are made to best fit the data. The correlations are valid within the range where data was available. It would be desirable to increase the generality of the correlations in some way. One way could be to use existing correlations of laminar burning velocity SL as a function of gas composition and gas properties to describe the variations. The resulting model would have the form:

( ) ( ) ( )speedgsparkgSg L0ˆ θθ ∆=∆ (12)

Laminar burning velocity - Examining total burn duration ∆θ as a function of λ in Figure 4 reveals that rich mixture gives the shortest burn durations. One explanation for this would be that laminar burning velocity of gasoline has its peak value for rich mixtures giving short burn duration. The same reasoning holds for residual gas fraction and temperature influence. Increased residual gas content leads to decreased laminar burning velocity and increased burn duration. Increased intake temperature leads to increased combustion temperature and increased laminar burning velocity. The effect of varying the intake pressure seems to be almost negligible in Figure 4. Total burn duration seems to be proportional to the inverse of laminar burning velocity.

Most of the variation in total burn duration can be explained by using the relative change of inverse laminar burning velocity SL in gasoline from Equations 3 and 4. The describing function G in the expression for relative influence of operating condition on burn duration is found below. The temperature and pressure at spark timing was used to calculate laminar burning velocity for the different operating conditions.

0.85 0.90 0.95 1.00 1.05 1.10

50

55

60

65

70

Base operatingcondition ∆θ

0

Predictedoptimized S

L

Predictedstandard S

L

Measured

∆θ [C

A]

λ Figure 5 Measured and predicted total burn duration as a function of λ. Predictions are based on laminar burning velocity SL at spark crank angle.

( )rgsparksparkLSL xpTSG

,,,1

λ= (13)

L

L

SL

SLSL S

SGG 0,

00,

0ˆ ⋅∆=⋅∆=∆ θθθ (14)

Figure 5 to Figure 8 show the predicted total burn duration when using values found in Heywood [5] for the constants in the laminar burning velocity Equations 3 and 4. The laminar burning velocity calculated at the spark crank angle is not automatically representative for the average laminar burning velocity during the entire flame propagation. Nor is it representative for the turbulent burning velocity. It was found that decreased temperature and pressure dependence in the expression for laminar burning velocity decreased the error in predicted total burn duration. The temperature and pressure dependence of laminar burning velocity was changed by optimizing the constant terms in αg and βg in Equation 4 to minimize the prediction error in both the one factor at a time tests and the factorial design tests.

(15) 77,2

,

51,3,

141,015,0

271,03,1

φβ

φα

+−=

−=

optg

optg

Laminar burning velocity with the new constants in temperature and pressure exponents is shown in Appendix B.

Spark timing – The spark timing influence on total burn duration is not captured in the laminar burning velocity correlations. The gas temperature at spark crank angle will be colder for advanced spark position resulting in a lower predicted laminar burning velocity. As mentioned before, the spark timing was chosen later than MBT timing. Advancing the spark in this operating region will generally lead to shorter burn durations due

0% 1% 2% 3% 4% 5% 6%55

60

65

70


0

Measured

Predictedstandard S

L

Predictedoptimized S

L

∆θ

[CA

]

EGR mole fractionFigure 6 Measured and predicted total burn duration as a function of EGR mole fraction. Predictions are based on laminar burning velocity SL at spark crank angle.

6

25 30 35 40 45 50 5550

55

60Base operating

condition ∆θ0

Measured

Predictedoptimized SL

Predictedstandard S

L

∆θ [C

A]

Intake temperature [°C] Figure 7 Measured and predicted total burn duration as a function of intake temperature. Predictions are based on laminar burning velocity SL at spark crank angle.

to faster pressure and temperature rise in the cylinder. The faster pressure rise for advanced sparks is due to higher levels of turbulence and positive feedback from piston movement when combustion occurs closer to top dead center. On the other hand, the ignition delay time increases with advanced spark timing primarily due to lower temperature and laminar burning velocity during the ignition delay time. The overall effect of advancing the spark beyond MBT timing might be increased total burn duration, but no such spark timing have been tested in this work.

The correlation for spark influence on burn duration found in Witt [9] seems to be able to predict the change in total burn duration well. Figure 9 shows measured total burn duration change normalized by the reference condition total burn duration as a function of spark timing and the predicted relative change from the Witt model [9]. Burn duration influence from Witt’s correlations is plotted in Figure 9. The equation for burn duration correction in Witt is:

[ ]( )spark

sparkGϕ

ϕ 480,2596,0 +=bTDC (16)

The validity range for spark advance in this model is 17 to 57 bTDC. The Witt burn duration model predicts the total burn duration well also for spark timing at 9 bTDC. However, the estimates degenerate as spark timing approach top dead center due to the choice of functional form for burn duration influence, inverse of square root spark advance. This highlights the point that great care has to be taken when using correlations outside the validity range.

110 115 120 125 130 135 140 145

51

52

53

54

55

56

57

58


0

Measured

Predictedstandard SL

Predictedoptimized SL

∆θ [C

A]

Intake pressure [kPa] Figure 8 Measured and predicted total burn duration as a function of intake manifold pressure. Predictions are based on laminar burning velocity SL at spark crank angle.

The measured data in Figure 9 is the total burn duration. The ignition delay time correlation in Witt is:

[ ]( ) 2410383.2678,0 sparksparkF ϕϕ −⋅+=bTDC (17)

The sum of ignition delay (17) and rapid burn duration influence (16) would be an estimate of total burn duration according to Witt. This estimate is also plotted in Figure 9 for reference. However, the predictions are worse than the predictions from the rapid burn duration correlation (16) alone. The combined prediction from Witt shows a minimum total burn duration at 32 bTDC.

The correlations of Witt could be used, had it not been for the laminar burning velocity model introduced above. Figure 10 shows the same data as in Figure 9 normalized by combustion duration as predicted by the

-25 -20 -15 -10 -5

1.0

1.2

1.4

Witt ∆θr+∆θignestimate

Witt ∆θrestimate

measured∆θ

∆θ 0

Spark timing [aTDC]Figure 9 Measured burn duration normalized by reference operating condition and estimates from Witt [9].

7

-40 -35 -30 -25 -20 -15 -10 -5

0.8

1.0

1.2

1.4

1.6

Polynomial fitR2 = 0,9996

measured

Witt ∆θr

estimate

Witt ∆θr+∆θ

ignestimate

∆

θ

∆θ 0g

(SL)

Spark timing [aTDC]Figure 10 Relative influence of spark timing on total combustion duration and predictions.

laminar burning velocity model, i.e.:

( )LSg0θθ

∆∆

(18)

The Witt models no longer fit the data well. A second degree polynomial dependence was selected for the data. A second order polynomial was chosen to avoid degeneration for spark timings close to top dead and also to capture the possibility of increasing total burn duration at some point beyond MBT spark timing. The identified polynomial has its minimum at 29 CA bTDC, similar to the combined Witt model.

The identified polynomial for spark influence on total combustion duration is:

[ ]( ) 24101,9053,060,1bTDC sparksparksparkG ϕϕϕ −⋅+⋅−= (19)

Engine speed – Combustion duration variation as a function of engine speed is not captured by the laminar burning velocity correlation. Engine speed affects turbulence in the cylinder during combustion. This calls for a separate engine speed influence correlation, similar to the spark advance correlation described above. The functional form of Witt [9] has been used as a basis for the correlation, but a new set of parameters has been identified. The influencing function for rapid burn duration according to Witt is:

[ ]( )N

NG 49,18355,1rpm −= (20)

where N is the engine speed. Identification of new parameters were performed on data normalized by a reference operating condition, laminar burning velocity

1500 2000 2500 3000 3500 40000.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

new estimate, R2 = 0.982

measured

Csallner ∆θr+∆θignestimate

Witt ∆θr+∆θignestimate

∆θ

∆θ

0g(S

L)g(φ

spar

k)

Engine speed [rpm]Figure 11 Relative influence of engine speed on total combustion duration and predictions.

influence and spark timing influence. The identified model is shown in Figure 11 together with predictions from the Witt correlation and Csallner correlation [8]. The new estimate for model parameters is:

[ ]( )N

NG 5,5513,2rpm −= (21)

COMBUSTION MODE PARAMETER – Closer examination of the correlation between Wiebe function parameters reveal that m seems to be linearly dependent on ∆θ for each engine speed tested. Figure 12 shows straight lines fitted to m(∆θ) at several engine speeds. The slopes of these lines are nearly identical. Plotting the intercept of the straight lines with the abscissa against engine speed, shown in bottom right of Figure 12, indicate that m is also linearly dependent on engine speed N. A least squares regression of m as a function of ∆θ and engine speed N yields the following equation:

( ) 71,51051,30421,0, 4 +⋅⋅+∆⋅−=∆ − NNm θθ (22)

with overall R2 = 0,868. Equation 22 could be used directly as describing function H(∆θ,N) to calculate the relative change h(∆θ,N) from the reference operating condition. Another approach would be to simply look at the changes in ∆θ and N from the reference operating condition and calculate m as:

( ) ( )04

00 1051,3ˆ0421,0ˆ NNmm −⋅+∆−∆−= −θθ (23)

A summary of the correlations for ∆θ and m is found in Appendix C.

8

50 60 70 80

3.6

4.0

4.4

4.82500 rpm

m

∆θ [CA]50 60 70 80

3.6

4.0

4.4

4.83000 rpm

m

∆θ [CA]

50 60 70 80

3.6

4.0

4.4

4.8

1500 rpm 2000 rpm

4000 rpm

m

∆θ [CA]2000 3000 4000

6.0

6.5

7.0

m(∆

θ =

0)

Engine speed [rpm]Figure 12 Straight lines fitted to m as a function of ∆θ at different speeds. Bottom right figure shows estimated intercepts of equal slope m (∆θ) lines as a function of engine speed N. Dash-dotted lines show the model m (∆θ,N) for the different engine speeds.

VALIDATION OF COMBUSTION MODEL

The identified correlations were tested on the validation data set. Temperature, λ, residual gas content and spark timing was varied in the validation tests. Figure 13 show predicted values of total combustion duration plotted as a function of measured values. The predicted total combustion duration is within ±4% of the measured values. The errors are not correlated to any of the investigated operating parameters, suggesting that the model captures the dependencies of the different operating parameters well.

The error in combustion mode parameter m is within ±8% of the measured values, see Figure 14. The prediction error in combustion mode parameter is party due to propagating errors from the prediction of total combustion duration, since m is modeled as a function of predicted total combustion duration. Closer examination of the errors in m reveals that the errors seem to be correlated to λ, as seen in Figure 15. High values of λ give large prediction errors in m. One way of reducing the errors in predicted m would be to develop an additional correlation for λ influence on m. This has not been done.

SIMULATION MODEL SENSITIVITY - A series of simulations were made to investigate the sensitivity of simulation model output to errors in Wiebe function parameters. The correlations described above give a prediction error of ±4 % in ∆θ and ±8 % in m. These error ranges were used as input to the simulation model. The prediction error ranges are well within the ranges for cycle to cycle variations in the engine tested. The Wiebe function parameters that were tested are found in Table 3 below. The sensitivity analysis was performed at 3000 rpm. The sensitivity in IMEP and predicted knock angle was studied in particular. Knock angle was defined

45 50 55 60 65 70 75 8045

50

55

60

65

70

75

80

Pred

icte

d ∆

θ [C

A]

Measured ∆θ [CA] Figure 13 Predicted vs. measured total combustion duration in validation data set. R2 = 0,96.

3.2 3.6 4.0 4.4 4.83.2

3.6

4.0

4.4

4.8

Pred

icte

d m

Measured m Figure 14 Predicted vs. measure combustion mode parameter in validation data set. R2 = 0,72.

0.75 0.80 0.85 0.90 0.95 1.00 1.05

-8%

-6%

-4%

-2%

0%

2%

4%

m p

redi

ctio

n er

ror

λ Figure 15 Error in combustion mode parameter m as a function of λ.

9

Table 3 Wiebe parameters used for analysis of simulation model sensitivity to errors in Wiebe parameters.

Speed [rpm]

Spark timing [bTDC]

∆θ [CA]

m

standard 1500 7,5 50.1 3.73high value 7,5 52.6 4.11low value 7,5 47.6 3.36standard 3000 13,5 58.2 3.68high value 13,5 61.1 4.05low value 13,5 55.3 3.31standard 5500 23,5 59.2 4.02high value 23,5 62.2 4.43low value 23,5 56.3 3.62

10

-15 0 15 30 45

0.00

0.01

0.02

0.03

0.04

0.05

∆θ: +5%m: +10%fitted

∆θ and m

∆θ: -5%m: -10%

measured

Hea

t rel

ease

[CA-1

]

Crank angle [aTDC] Figure 16 Measured, estimated and worst case predicted heat release at 3000 rpm.

0

400

800

1200

600

700

800

900

-15 0 15 30 45 60-0.5

0.0

0.5

1.0

Kno

ck in

tegr

al v

alue

Crank angle [aTDC]

4

6

8

10

∆θ: +5%m: +10%

∆θ: -5%m: -10%

∆θ: +5%m: +10%

∆θ: -5%m: -10%

Cyl

inde

r pre

ssur

e [M

Pa]

1/τ

[ms-1

] U

nbur

ned

zone

tem

pera

ture

[K]

Figure 17 Variations in cylinder pressure and temperature together with resulting inverse ignition delay τ and knock integral from simulations with estimated and worst case predicted heat release.

as the crank angle where the Livengood-Wu integral in Equation 1 equals 1 with ignition delay time according to Equation 2 and calibration of knock model in [15].

Figure 16 Shows the measured heat release at 3000 rpm and Wiebe functions used in simulations. The worst case difference in predicted IMEP is below 0,5 %. The error in change in predicted knock angle is larger, ±3,9 CA. Cylinder pressure and temperature is highly affected by the worst case errors in predicted combustion as seen in Figure 17. The value of the knock integral starts to deviate already in the early stages of combustion.

DISCUSSION

The need for calibration data for the combustion model has been highly reduced by using existing laminar burning velocity correlations to model relative change in Wiebe function parameters. Witt [9] identified a total of 24 parameters from his test data to describe the combustion dependence on spark timing, residual gas content, indicated work and engine speed. Csallner [8] identified 18 parameters to describe the above mentioned dependencies and 6 additional parameters to describe the air/fuel ratio dependence. The number of parameters identified in this paper is 10. Thus, the need for calibration data is reduced. The introduction of laminar burning velocity dependence should also make the correlations valid outside of the identification data set, provided that the laminar burning velocity correlations are valid.

By introducing laminar burning velocity in the correlations for Wiebe function parameters, fuel dependent variation can be captured. It is possible for the simulation engineer to examine the influence of changing fuel on engine output. The extra information that is needed for such investigations would be correlations or models for laminar burning velocity of the new fuel, similar to the correlations found in Heywood [5]. The change in Wiebe function parameters can then be calculated relative to the laminar burning velocity of the fuel with which the simulation model has been calibrated.

The presented correlations are not predictive when it comes to simulation model alterations that might affect turbulence in the combustion chamber. The operating parameter influences that are not captured by laminar burning velocity influence, i.e. engine speed and spark timing, have to be calibrated to a specific engine. When looking at Figure 10 and Figure 11, it is clear that the correlations and constants found in for example Csallner [8] and Witt [9] need to be recalibrated for each new engine.

One operating parameter which has not been investigated in this work is camshaft phasing. Camshaft phasing will affect fundamental properties of the combustible mixture, in particular residual gas content.

This will be captured in the laminar burning velocity dependence. Intake camshaft phasing will however also influence the turbulence in the combustion chamber during combustion [6]. An additional correlation of total burn duration as a function of for example inlet valve closing would improve on the Wiebe function correlation presented here.

As stated in the introduction, one of the main motivations for making a combustion correlation was to be able to model knock more accurately. However, knock is usually not associated with the average combustion event. It is the fastest burning cycles that give highest pressures and temperatures in the cylinder. Figure 18 shows Wiebe parameters for 800 engine cycles at an operating condition with some knocking cycles. The knocking cycles are found among the cycles with low ∆θ and low m. A correlation for cycle to cycle variation in terms of standard deviations in Wiebe parameters could be developed in a similar way as the combustion correlation in this paper. Development of such a correlation could improve the ability to predict knock in 1-d simulations.

35 40 45 50 55 603.2

3.6

4.0

4.4

4.8

5.2

5.6

99%95%

m

∆θ [CA]Figure 18 Wiebe parameters for 800 engine cycles at 1500 rpm with 95% and 99% contours of joint normal distribution. Triangles are knocking cycles sized according to knock intensity.

CONCLUSION

This paper describes a method for predicting Wiebe function parameters based on existing correlations of laminar burning velocity. Relative change in Wiebe function parameters can be predicted by comparison to the relative change of estimated laminar burning velocity at spark timing. Additional correlations that describe turbulence related operating parameters influence on Wiebe function parameters have also been developed and compared to the results from other similar correlations. The introduction of laminar burning velocity reduces the need for calibration data. Only the turbulence related correlations have to be calibrated to the specific engine.

REFERENCES

[1] Livengood, J. C. and Wu, P. C.; Correlation of Autoignition Phenomenon in Internal Combustion Engines and Rapid Compression Machines; Fifth Symposium (International) on Combustion, pp. 347-356, 1955.

[2] Douaud, A. M. and Eyzat, P.; Four-Octane-Number Method for Predicting the Anti-Knock Behaviour of Fuels and Engines; SAE Technical paper series 780080.

[3] Hirst, S. L. and Kirsch, L. J.; The Application of a Hydrocarbon Autoignition Model in Simulating Knock and Other Engine Combustion Phenomena; in Combustion Modeling in Reciprocating Engines, edited by J. N. Mattavi and C. A. Amann, Plenum Publishing, New York, 1980.

[4] Kalghatgi, G.T.; Early Flame Development in a Spark-Ignition Engine; Combustion and Flame 60 (1985) 299-308.

[5] Heywood, J. B.; Internal Combustion Engines Fundamentals; McGraw-Hill Series in Mechanical Engineering, McGraw-Hill 1988.

[6] Söderberg, F., Johansson, B. and Lindoff, B.; Wavelet Analysis of In-Cylinder LDV Measurements and Correlations Against Heat Release; SAE Technical Paper Series 980483.

[7] Wiebe, I.I.; The combustion speed in internal combustion piston engines; Collected works of piston engine research, Laboratory of Engines, Academy of Sciences, USSR, Moscow 1956. (Translated to English by M. Kiisa, KTH 1993)

[8] Csallner, P.; Eine Methode zur Vorausberechnung der Ändrung des Brennverlaufes von Ottomotoren bei geänderten Betriebsbedingungen; München, Techn. Univ., Diss., 1981.

[9] Witt, A.; Analyse der thermodynamischen Verluste eines Ottomotors unter den Randbedingungen variabler Steuerzeiten; Graz, Techn. Univ., Diss., 1999.

[10] Bayraktar, H. and Durgun, O.; Development of an empirical correlation from combustion durations in spark ignition engines; Energy Conversion and Management 45 (2004) 1419-1431.

[11] Scharrer, O., Heinrich, C., Heinrich, M., Gebhard, P. and Pucher, H.; Predictive Engine Part Load Modeling for the Development of a Double Variable Cam Phasing (DVCP) Strategy; SAE Technical paper series 2004-01-0614.

[12] Vávra, J. and Takáts, M.; Heat Release Regression Model for Gas Fuelled SI Engines; SAE Technical paper series 2004-01-1462.

[13] van Nieuwstadt, M. J., Kolmanovsky, I. V., Brehob, D. and Haghgooie, M.; Heat Release Regressions for GDI Engines; SAE technical paper series 2001-01-0956.

[14] Elmqvist Möller, C., Grandin, B., Johansson, P. and Lindström, F.; Divided Exhaust Period - a gas

11

exchange system for turbocharged SI engines; SAE technical paper series 2005-01-1150.

[15] Elmqvist, C., Lindström, F., Ångström, H.-E., Grandin, B. and Kalghatgi, G.T.; Optimizing Engine Concepts by Using a Simple Model for Knock Prediction; SAE Technical paper 2003-01-3123.

[16] Ångström, H.-E.; Cylinder Pressure Indicating with Multiple Transducers, Accurate TDC-Evaluating, Zero Levels and Analyse of Mechanical Vibrations; Conference paper, 3rd International Indicating Symposium, Mainz am Rhein, April 1998.

CONTACT

Fredrik Lindström, M.Sc. Mail: KTH Machine Design, Brinellvägen 83, SE-10044 Stockholm, Sweden. E-mail: [email protected] Phone: +46 8 790 7867


CA: Crank angle

aTDC: Crank angle after combustion top dead center

bTDC: Crank angle before combustion top dead center

xb: Mass fraction burned

xrg: Residual gas mass fraction

rgx~ : Residual gas mole fraction

m: Combustion mode parameter

SL: Laminar burning velocity

λ: Air/fuel ratio

φ: Fuel/air ratio

θ: Crank angle

∆θr: Rapid burn combustion duration

∆θign: Ignition delay time in SI engine

∆θ: Total combustion duration, ∆θr+∆θign

θ0: Start of combustion

ϕspark: Spark timing before top dead center

τ: Ignition delay time

APPENDIX A - WIEBE PARAMETER TRANSFORMATIONS

Wiebe function parameters can easily be transformed to common heat release analysis output, e.g. 50% mass fraction burned and 10-90% burn duration. The mass fraction burned at any crank angle θ is determined by Equation 5 repeated below:

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛∆−

−−=+1

0exp1m

b axθθθ

θ (A.1)

The crank angle of any heat release fraction is found by solving for θ. For example the crank angle of 50% mass fraction burned is:

( )( )

( ) θθθ

θθθθ

∆⎟⎠

⎞⎜⎝

⎛ −+=⇒

⎟⎠⎞

⎜⎝⎛

∆−

⋅=−

+

+

11

050

10

50

001,0ln5,01ln

001,0ln1ln

m

m

bx

(A.2)

Hence, the 10-90% burn duration is:

( ) ( )⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛⎟⎠

⎞⎜⎝

⎛ −−⎟

⎠

⎞⎜⎝

⎛ −∆=

++

−

11

11

9010 001,0ln1,01ln

001,0ln9,01ln mm

DUR θ

(A.3)

Inversely, the Wiebe parameters can be determined from heat release output if the m parameter is known as:

( ) ( )

( ) 11

500

11

11

001,0ln5,01ln

001,0ln1,01ln

001,0ln9,01ln

+

++

⎟⎠

⎞⎜⎝

⎛ −∆−=

⎟⎠

⎞⎜⎝

⎛ −−⎟

⎠

⎞⎜⎝

⎛ −=∆

m

mm

DUR

θθθ

θ

(A.4)

12

mailto:[email protected]

APPENDIX B – LAMINAR BURNING VELOCITY

13

The figures below show the estimated laminar burning velocity with equations and constants according to Equations 3 and 4 compared to the estimated laminar burning velocity according to Equation C.6 and C.7.

0.7 0.8 0.9 1.0 1.116

18

20

22

24

26

28

30

modified

standard

Lam

inar

bur

ning

vel

ocity

[cm

/s]

λFigure 19 Laminar burning velocity as a function of λ at 2 MPa and 600 K for standard correlation (Equations 3 and 4) and modified correlation (Equations C.6 and C.7).

580 600 620 640 660 680 700 72014

16

18

20

22

24

26

28

30

modified

standard

λ = 0,8λ = 0,9

λ = 1,0

λ = 1,1

Lam

inar

bur

ning

vel

ocity

[cm

/s]

Temperature [K]Figure 20 Laminar burning velocity as a function of temperature at 2 MPa for standard correlation (Equations 3 and 4) and modified correlation (Equations C.6 and C.7).

1.6 2.0 2.4 2.818192021222324252627282930 λ = 0,8

λ = 0,9

λ = 1,0

λ = 1,1

standard

modified

Lam

inar

bur

ning

vel

ocity

[cm

/s]

Pressure [MPa]Figure 21 Laminar burning velocity as a function of pressure at 600 K for standard correlation (Equations 3 and 4) and modified correlation (Equations C.6 and C.7).

APPENDIX B - SUMMARY OF CORRELATIONS

Predictions of total combustion duration ∆θ and combustion mode parameter m are made from functions describing changes relative to a base operating condition, ∆θ0 and m0.

(C.1) N

NsparksSL

hmmggg

,ˆ0

,0

ˆ

ˆ

θ

ϕθθ

∆⋅=

⋅⋅⋅∆=∆

The functions for relative influence, gi and hi, are summarized below.

TOTAL COMBUSTION DURATION

0,0,,

,

0,0

,0ˆ

N

N

spark

spark

SL

SL

NsparkSL

GG

GG

GG

ggg

⋅⋅⋅∆=

⋅⋅⋅∆=∆

ϕ

ϕ

ϕ

θ

θθ (C.2)

( )rgsparksparkLSL xpTSG ~,,,

1λ

= (C.3)

24, 101,9053,060,1 sparksparksparkG ϕϕϕ

−⋅+⋅−= (C.4)

N

GN5,5513,2 −= (C.5)

The following expression for laminar burning velocity has been used:

( 77,00,

~06,21013,1298

,,

rgu

LL xpTSSoptgoptg

−⎟⎠

⎞⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=

βα

)

(C.6)

With fuel specific constants for gasoline:

(C.7)

( )

77,2,

51,3,

20,

141,015,0

271,03,1

21,19,545,30

φβ

φα

φ

φφ

φ

φ

+−=

−=

=−==

−+=

optg

optg

mm

mmL

BBBBS

Equations and constants values from [5] except 1,3 and -0,15 in the expressions for temperature and pressure exponents, α and β.

COMBUSTION MODE PARAMETER

0,,

,ˆ

,ˆ0ˆN

NN H

Hhmm

θ

θθ

∆

∆∆

=⋅= (C.8)

71,51051,3ˆ0421,0 4,ˆ +⋅⋅+∆⋅−= −

∆NH N θθ

(C.9)

or

( ) ( )04

00 1051,3ˆ0421,0ˆ NNmm −⋅+∆−∆−= −θθ

(C.10)

14

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Empirical Combustion Modeling in SI Engines