EXPERIMENTAL INVESTIGATION OF SHOCK WAVE AND B O W A R Y LAYER INERACTION NEAR

CONVEX CORNERS IN HYFERSONIC FLOW

Sohail Mohammed

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Aerospace Studies

University of Toronto

O Copyright by Sohail Mohammed, 1997

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EXPERIMENTAL INVESTIGATION OF SHOCK WAVE AND BOUNDARY LAYER iNTERACTION NEAR

COMEX CORNERS IN HYPERSONIC FLOW

Sohail Mohammed, 1997 Master of Applied Science

f n s t i ~ e for Aerospace Studies University of Toronto

ABSTRACT

The hypersonic impulse gun tunnel at the UTIAS was i lsed io expriment &Y

investigate the interaction between an oblique shock wave and boundary layer near convex

corners in hypersonic flow. Experiments were conducted in two phases. The first phase

involved tunnel test operathg conditions that presurnabiy developed Mly turbulent

boundary layer on the model surface in Mach 7.2 flow. Schlieren photographs indicated

that it was not possible to conclude that the boundary layer developed was, in fact,

turbulent. The second phase o f the program included preliminary investigation of shock-

laminar boundary layer interaction near rounded convex comers. As a £irst sep,

experiments were repeated to validate previously documentai resutts achieved at the

current facüity. Surface static pressure measurements and Schlieren photographs were

taken to investigate interaction near a 5 degrees convex corner. Results obtained in this

phase supportai the repeatable characteristics of the facility.

Guidance provided by my research supervisor, Prof. P. A. Sullivan , throughout the

program is highiy appreciated. Instructions provided by Richard Stockmans and Doug

Challenger to operate the gun tunnel were professional and I am than)ôul to them. It was

great to share the experimental facility with William 'Ba' O'Gorman. Thanks to Giovanni

'John' Fusina, who violated aU the t r a c laws and &ove me to Branson Hospital after 1

injured myself in the tunnel. 1 am departing fiom another segment of life with good

memories and, 1 thank dl the staff and students for making it happen.

i i i

TABLE OF CONTENTS

Contents Pane No.

Abstract

Acknowledgement s

Table of Contents

List of Figures

List of Tables

Nomenclature

1 . Introduction

2. Literature Review

2.1 General Comments on S hock Layer Interaction

2.2 Differences Between Laminar and Turbulent Boundary Layers

2.3 Previous S tudies of Shock-Boundary Layer

Interaction Near Convex Corners

2.3.1 ExperimentaI Work Done By Chung and Lu

2.3.2 Experimental Work Done By White and Ault

2.3.3 Summary of Hawboldt's Investigation at the Facility

3. The Current Experirnental Program

3.1 Description of the Experimentai Facility

3.1 .1 Hypemonic Impulse Gun Tunnel

3.1.2 Data Acquisition System

3.1.3 Schlieren Photography System

3.1 -4 Pressure Transducers

3.2 Description of the Experimentai Mode1

11

iii

iv

vi

vi

vii

1

4

4

5

6

6

7

7

11

11

11

14

15

16

16

Contents

4. Expetirnental Results and Discussion

4.1 Exploration of Possible Turbulent Boundary Layer

Development on the Experimental Mode1 22

4.2 Preliminary Investigation of Shock Wave and Laminar Boundary

Layer Interaction Near Rounded Convex Corners 26

4.2.1 Repeatability Test for Corrvex Corner Results

Without Incident Shock 27

4.2.2 Repeatability Test for Shock-Layer Interaction Results 29

5 . Conclusion and Recommendation

Page No.

22

References

LIST OF F I G W S

Figure No. and Title Paae No.

Typical Iniet for a Scrarnjet Engine

Schematic Diagram of the Hypersonic Gun Tunnel

Wave Digram of the Gun Tunnel

Operating hinciple of the Optical System

Expenmental Model for the Current Shidy

Model Set-Up in the Test Section

Cross-Section of Instmented Plate with Transducers

Photograph of Transducers Mounted Inside the Model

Shock Layer Interaction : 0, = 9.9 deg., 0. = 10 deg.

Correlation of Lamlliar, Transitional and Turbulent Incipient Separation

on the Wedge Compression Corner

Pressure Distribution over a 5 deg. Expansion Corner

Pressure Distribution of Shock-Layer Interaction (e8= 5.1 deg., O,= 5.0 deg, = 6.5 mm)

Pressure Distribution of Shock-Layer interaction (0,=5.1 deg., 0.=5.0 deg, xi=-9.0 mm)

LIST OF TABLES

TabIe No. and Title

3.1 Sample Operathg Condition of the Gun Tunnel

4.1 Operating Conditions for the Turbulent Case

4.2 Operating Conditions for the Laminar Case

Page No.

DEFINITTON

Dimensiodess Plateau Length

Mach Number

Static Pressure

Unit Reynolds Number

Stagnation Temperature

Initiai Driver Pressure

Initiai Barre1 Pressure

Test Section Pressure

Shock Impingement Location

Shock Generator Angle

Convex Corner Angie

Inclination angle of instnunented plme

Wedge angle for incipient seaparation

Specinc Heat Ratio

Shear Stress at Wall

Coefficient of Viscosity

Air Density

vii

Space Shuttle, a vehicle that takes off to Space as a rocket and re-enters the

Earth's atmosphere as an aircraft, is the most convenient means of transportation between

Earth and Space. It is reliable and efficient, but expensive. Implernentation of a different

propulsion system may reduce this unwanted cost. Theoretical investigation shows that

supersonic combustion rarnjet, or scramjet engines are efficient for hypersonic vehicles

such as the Space Shuttle.

A critical component of the scramjet engine is the inlet. To maximîze inlet

efficiency the losses due to shock waves, viscous eEects of the boundary layer and shock-

induced boundary layer separation need to be minirnized as much as possible. For many

proposed inlet geometries, compression is accomplished in two stages: fira on a ramped

extemal forebody and then by a cowl-generated oblique shock wave that t m s the flow

into the engine '. A sketch of a typicai idet is shown in Figure 1.1. Ideaîiy, the oblique

COMPRESSION HAVE \

OBL t QUE

="OcK 7

BOUNDARY LAYER

INTERACTION RE CI ON-^

Figure 1.1. Typical Inlet for SCRAMJET Engine

shock impinges on the convex comer of the same tuming angle so that its reflection is

thereby cancelled. However, the development of a boundary layer on the inlet forebody

prevents perfect cancellation so that a complex interaction occurs with possible flow

separation.

Hawboldt et al6 completed their investigation, at UTIAS, conceming the

interaction between oblique shock wave and 'laminar' boundary layer in Mach 8.3 airfiow.

The current experimental program, an extension of work cornpleted by Hawboldt,

had its origin in the fotiowing objectives;

to explore the interaction between oblique shock wave and possible 'turbulent'

boundary layer near a 'sharp' convex comer and

to investigate shock-boundaiy layer interaction near other corner geometnes.

The fist phase of the investigation involved high Reynolds number, Rw (85.6 X

106 /m) and lower stagnation temperature, TS (705 K) in the facility test section. These

critical operating conditions presumably produced boundary layer near the convex comer

that is turbulentLs. This paper documents the investigation conducted to comprehend the

boundary layer type that developed near the convex corner after each experiment. Ody

Schlieren photographs were used, at that stage, to idente the boundary layer type.

The second phase of the program involved lower Rw (4.95 X 106 /m), higher

stagnation temperature, TS (934 K) and test conditions identicai to ~awboldt's' with an

attempt to study rounded convex corner geometry. This variation in test operating

conditions was necessary in order to determine repeatability of data previously attained in

the current experimentd facility. Schlieren photographs and surface static pressure

measurements were used to compare and document results. Some data have been

presented here that are in close proximity with the data previously attained. Due to time

constraints, shock-layer interaction near rounded convex corners could not be explored in

the current investigation. However, possible experimentd mode1 modifications necessary

to explore such an investigation in the future have been suggested.

2. LITERATURE REVIEW

Several reports and text books have documented the theoretical and experimental

aspects of the fùndamentals of hypersonic aerodynamics. After reviewing severai

documents, information pertinent to the current study included oblique shock wave

phenornena, nature of boundary layer, shock-boundary layer interaction and shock induced

boudas , layer separation. ~tockrnans~' have reported on the operating conditions of the

current experimeat al facility . Del ery and ~ a r v i n ~ have document ed a compre hensive

report on shock-boundary layer interaction. schlichtingI3 and Anderson'" have written text

books that contain fundamental infonnation useful for the current experimental program.

Some general comments on shock-layer interaction and findamentai differences between

laminar and turbulent boundary layers are as follows;

2.1 General Comments on Shock-Layer Interaction

A boundary layer is a thin layer across which the flow velocity decreases nom the

high externai value to zero at the wall where the no-slip condition must be satisfied. Shce

the static pressure is ~anmersaiiy constant across it, the bouodary layer can be viewed as a

quasi-parallei flow with variable entropy f?om one streamhe to the other. When a shock

wave propagates through a boundq layer, it 'sees' an upstrearn flow of lower and lower

Mach number as it approaches the w d . The shock must adapt itseifto this situation so

that it becomes vanishingly weak when it reaches the region where the Mach number is

sonic. Moreover, the pressure signal camed by the shock is transmitted in the upstream

direction through the subsonic h e r part of the boundary layer. Thus the pressure rise

caused by the shock is fer upstrearn of the point where the shock would meet the surface

in the perfect fluid model, i.e., a flow without boundary layer. Conversely, the thickenhg

of the boundary layer subsonic channei, resuiting fkom a rise in pressure, generates

compression waves in the adjacent supersonic layer. These waves, in tum, weakens the

strong shock wave.

Thus the interaction involves a very complex mechanism where there is a

reciprocal influence between the shock wave and the boundary layer.

2.2 Differences Between Laminar and Turbulent Bouudary Layers

Due to the large scale tufbulent motion, energy is transrnitted more readiiy in

turbulent boundary layers than in laminar. This is the reason for the m e r velocity profiies

through a turbulent boundary layer, and hence the larger velocity gradients at the surface.

In tuni, the skin fiction and heat trmsfer are larger, sometimes markedly larger, for

turbulent in cornparison to laminar". The fundamental ciifferences between laminar and

turbulent boundary layers are rdected in their interactions with shock waves. For a

turbulent boundaq layer, the sonic line is much closer to the wall so that the shock

penetrates deeper into the boundary layer than its Iaminar equivaient. Turbulent boundary

iayers can sustain much higher adverse pressure gradients without separating, separation

lengths are much shorter, pressure gradients through separation and reattachrnent regions

are larger, and there is a greater possibiüty of substantiai normal pressure gradients 2. An

oblique shock wave which impinges on a larninar boundary layer fkom the outside

becornes reflected from it in the fom of a fan of expansion waves. However, when

turbulent, the reflection appears in the form of a more concentrateci expansion wave.

2.3 Previous Studies of Shock-Boundary Layer Interaction Near Convex Corners

Experimental investigation regarding hypersonic shock wave and boundary layer

interaction near convex corners have not been explored until very recently. Results

pertinent to the current program have been documented by White & Ault ', Chung & Lu ', Hawboldt ' and Hawboldt, Sullivan & Goniieb . A bnef discussion of their study is as

follows;

2.3.1 Exoerimentd work done bv ch un^ and Lu: In 1994, Chung, L M .

and Lu, F. K. at The University of Texas at Arlington made an attempt to evaluate the

effects of an expansion corner on shock wave and turbulent boundary layer interactions in

hypersonic flow. Their experiments involveci shock generator angles, 8,= 2 and 4 degrees

with expansion corner angles, 8, = 2.5 and 4.25 degrees. The facility test section Mach

number, M was 8.0 and Reynolds number, Rm =10.2 X 106 /m. They investigated shock-

layer interaction within one boundary layer thickness, 60, upstream and downstream of the

convex corner. Although the results documentai in their report were rather informative,

the limited range of theu experiments was insufficient to make any observations on the

relationship between the interaction length scales, the location of shock impingement with

respect to the corner, and the overail pressure rise across the interaction.

2.3.2 Emerimcntnl work dont bv White and Ault: White and Ault 4,

in 1994, investigated shock wave and turbulent boundary layer interaction near comer

angles, 0,- 10, 12 and IS degrees in Mach 11.5 airflow. Shock generator angles for their

expenments were identical to the expansion comer angles. In addition to surface static

pressure distribution and Schlieren photography, they characterized the interaction region

with heat transfer rate meanirements that provided a more sensitive indication of flow

separation than pressure measurernents. Similar to Chung and Lu, their range of

acperiments was limited and does not provide any relationship between the interaction

length scales, the shock impingement location and the overaii pressure rise.

2.3.3 Surnmarv of Hawboldt's Investination at the Current Facilitv

In 1992, Hawboldt ' cumpleted his experimeutal investigation of shock- laminar

boundary Iayer interaction near convex corners in Mach 8.3 flow. His final experimental

program inchideci surface static pressure measurements of flat plate, shockwave/tlat plate

boundary layer interactions, S0 and 1 0" convex corner plates without shock generator and

finally, shock wave/boundary layer interactions near those convex comers. In all cases,

Schlieren photographs were used to support the results.

The gun tunnel and mode1 alignment conditions were chosen to be the foilowing;

Initial Driver and Barre1 Pressures : 20.8 MPa and 145 kPa

Test Section Pressure : Below 50 Pa

Expansion Corner Angles (0,) : 5" and 10"

Respective Shock Generator Angles (03 : 5. Io and 9.9'

Inclination of Mode1 Relative to N o d e Axis : 1.3' ( kû.OSO)

Before mouncing the shock generator in its position, static pressure distributions

were recorded on the flat plate, S0 and 10" instnimented convex surfaces. Pressure survey

on the flat plate shows that the expetimental values are in close agreement with Sullivan's

cold wall solution ". As predicted by the cold wall approximate solution, there is a

protracted decay in pressure downsiream of both corners, but there is better qualitative

agreement with the SO corner. Disagreement near the corner was to be expected, because

the boundary layer equations do not apply in the comer region and the approximate

solution does not predict upstream influence.

When the shock generator was instalied above the convex corner, its angie was

adjusteci so that the flow was turned to within 0. Io of the convex corner angle. For the S0

codguration, the himing angie was 5.1" and produced an ided pressure ratio of 2.54

across the interaction. The computed boundacy layer thickness at the corner, 6,, was

estimated to be 0.7 mm. The shock impingement point was moved to eight locations

ranging fiom 13.5 mm (1 96,) upstream to 14mm (206J downstream of the corner. The

shock generator angle wap 9.9' for the 10' combination, resulting in an ideal pressure

ratio of 5 .O6. In this case, ten interactions were considered with the shock impulging fiom

10.5 mm (1 56,) upstream to 30 mm (436,) downstream of the comer.

When the shock impinged weil upstrearn or weU downstream of the comer, the

interaction resembled those observed with the flat plate boundary layer. For interactions

occurring upstream of the corner, the boundary layer separated well upstream of shock

impingement and a pressure plateau was formed. The pressure rose through reattachment

to a maximum at approximately 3.56s upstream of the comer, before undergohg a

fluctuating decay to the ideal downstream value. The fluctuation in pressure just

downstream of the corner was due to the intense interaction of the reattachment

compression and comer expansion wiîh the thin boundary layer in that region. The aatic

pressure distributions near separation, upstream of the comer, were weli predicted by the

fkee interaction concept.

When the entire shock-induced boundary layer separation occurred downstream of

the convex comer, the static pressure increased nom a level observeci for the convex

corner expansion to a plateau followed by a smooth, gradual nse to the ideal downmeam

value. Separation apparently occurred through a free interaction, but correlation to predict

the rise in pressure to the plateau were believed to be inapplicable owing to the distorted

velocity profiles of the accelerating boundaty layer near the corner. As a result of the long

plateau length and gradua1 rise fiom the plateau to the final downaream level, the

interaction became very long.

When the shock Unpinged near the comer, the differences between the results for

the S'and 10' cases were more significant. For the 5" case, separation was nearly

eliminated when the shock irnpinged 2 mm dowostream of the comer. In contrast, for the

10" case, an identifiable separation region existed for al1 shock impuigement pohts 6.

3. THE CURRENT EXPERIMENTAL PROGRAV

The ment experimcntd program was conducteci ushg the UTIAS short duration

hypersonic impulse gun tunnel. The model used for investigation was designed and built at

the Uistitute during Hawboldt's ' experimental research program. A brief description of the

curent experimental fmiiity and the model used for investigation is as follows;

3.1 Description of the Experimenbl Faciüty

3.1.1 Hv~crsonk ïm~ulse Gua Tunnel; Hypersonic flight is simdated by

matching the test section flow conditions with Mach and Reynolds numbers as wel as

other parameters. However, this is a difEcult task and, in reality, oniy partid simulation is

obtained. A short period of quasi-steady flow is achieved by cornpressing and heating the

working fluid, in this case air, by accelerating a piston dong a barre1 under the operation

of a very hi& pressure gas releaseû from a reservoir ''.

Figure 3.1. Schematic Diagram of the Hypenonic Gun Tunnel

Figures 3.1 and 3.2 depict the various components that make up the hypersonic

gun tunnel and explain its principle of operation. High pressure air is stored in a reservoir

calleci the driver (1). The driver is C O M ~ C ~ ~ to the barrel (4) through an isolathg bail

valve (2) and a double diaphragm assembly or breech (3). The barrel is, in tum, comected

T Testing Time

- Shoc k Waves i

.'NA

Diaphmgm Nozzle7 Testsection-

Figure 3.2 Wave Diagram of the Gun Tunnel

by the nozzle breech (5) to a convergent-divergent nozzle (6) which delivers the flow to

an open jet test section (7). The test section is connected by a short receiving duct or

diffuser (8) to the dump tank (9). Table 3.1 summarizes the principle dimensions and a

sample operating condition of the tunnel.

TABLE 3.1 Sample Operatin~ Condition of the Gun Tunnel

Jntcnor Dimensions: 305 mm dia x 5.2 m Charge ntssurc: 20.5 MPa

Bmd Intcrior Dimensions: 76.2 mm dia x 6.1 m Chafgc Prcssurc: 1.45 atm to 8 m

(145-000 kPû)

Nozzle Conioud Throai diamem. Exit plmc diamctcr:

Test Section open* hsh:

1.52 m long 12.7 mm 217mm

D m p Tank 1.22 m dia x 2.44 m

Siagnation (mervou) pressure: 255 MPa Sirputiai t e m m %00.1300K F m sbcam W n m b c r 8.3 F m Stream unit Rcynolds nmbcr (204) x 10% UsaMc tcst timc 8 4 m s

Preparation of the tunnel for finng requires removing barrel debris, installation of

diaphragms, placing a piston in the barrel just downstrearn of the diaphragms, placing two

layers of clear tape (or, a lexan plug) in the nozzie throat and pressunzing the driver and

the barrel to the desired levels. For the current experiments, the driver was pressunzed to

20.5 MPa and 20.8 MPa and the barrel to 400 kPa and 145 kPa respectively, while the test

section pressure was reduced to below 50 Pa. These pressures were regulated through an

independent control panel. The sun is initiated by reducing the pressure stored between the

two steel diaphragrns, which are designed to withstand 10 MPa, but not the full driver

pressure. These diaphragms rupture and the piston accelerates down the barrel,

cornpressing and heating the working fluid. The pressure generated by the piston motion

bums the tape attached to the nozzle throat and the air ahead of the piston accelerates

through the nozzle and enters the test section. A pressure transducer located at the nozzle

end of the barrel is used to detect the arrivai of the fist shock wave generated by the

piston motion, and thus to provide a trigger for the data acquisition system and a Schlieren

flow visualition system light source.

3.1.2 Data Acauisition Svstem: Data is collected digitally through a data

acquisition system. Transient data recorders were used, each capable of taking input

voltages ranging from +10 volts tu -10 volts, sampling with 12 bit resolution to ensure a

high fidelity record of the signal at a maximum rate of 1 MHz, and storing a maximum of

64000 words, which are segmented hto 16 parts. The data retrieval computer has 640 Kb

of intemal memory, a 340 Mb hard drive for storage of data, and a colour rnonitor to

simuitaneously display up to 6 transducer histones. A translation program was used to

convert the data from binary to ASCII to allow M e r analysis of the data with software

packages developed by ~tockmans".

3.1.3 Schlieren Photoen~hv Svstem: To visualize the shock wave,

boundary layer and their interaction, a standard Schlieren system was ernployed. It

consisted of two 229 mm diameter, 1.83 m focal length, front silvered, concave mirrors

F i p n 3.3 Operating Principle of the Opticai System

with a rectangular shaped light source at the focus of the fist mirror and a knife edge at

the focus of the second mirror. The rnirrors were approximately 7 m apart. A standard

10.2 X 12.7 cm view carnera capable of holding sheet film or Polaroid film (No. 53) was

used to record the Schlieren photographs. A standard camera flash (Vivitar) was used to

generate the light source. Figure 3.3 shows a schematic diagram of the optical system

ernployed.

3 . 1 Pressure Transducers: Endevco built 5 psi pressure transducers

were used for al1 experiments. The output signais from Endevco Model 4423 Signal

Conditioners and Model 4225 Power Supplies were fltered at a cutoff frequency of 20

kHz. The barre1 end pressure hiaory was measured with a PCB Model 1 1 3A22

piezoelectric transducer in combination with a PCB Model 494A Voltage Amplifier. A

maximum of 5 pressure transducers were mounted in the model for experimentation.

3.2 Description of the Experimental Model

The model used for the current experimental program was originally

designed for ~awboldt's' experiments. It was designed and constnicted to permit detailed

measurements of the çtrearnwise static pressure distribution through a shock wave and

larninar boundary layer interaction.

The instrumented flat plate was 133 mm wide and 254 mm long, and it was fitted

with 5 1 mm skirts that extended down fiom the model surface. The pressure taps were

0.8 1 mm in diameter and spaced 2.3 8 mai apart on h e s 2.3 8 mm on each side of the

centerline. The strearnwise spacing was 4.76 mm near the leading edge, where space for

transducers was more Limiteci, and also at the downstream end of the mode1 where high

resolution was unnecessary.

The instnunented plate and shock generator were supported by a single sting, as

depicted in Figures 3.4 and 3.5. This aiiowed precise adjustment of one plate with respect

Figure 3.4 Experimentai Mode1 for the Cnmnt Study

Figure 3.5 Mode1 Set-Up in the Test Section

to the other. The sting was connected to the floor of the test section through a base plate

that permitted fine adjustment of mode1 orientation with respect to the 6ree Stream flow.

The shock generator was supported by a threaded rod to d o w precise adjustment of its

streamwise position while maintainhg a constant angle. The threaded rod was comected

to the shock generator through a speciaiiy constnicted wedge, of the appropriate angle,

and an adjustment mechanism permitted fine adjustment of the shock generator angles and

alignment with the instmmented plate.

The pressure transducers were mounted inside the model near the pressure taps to

ensure adequate dynarnic response. Figure 3.6 is a diagram of the transducer mounting

technique and Figure 3.7 shows an actual photograph taken after the transducers were

mounted in the model.

TOP VIEW OF PRESSURE TAP

r - - - - - -1-

l- . . . . . .

O ! * I L , - - - - -------- ' 1 0

I -1

I Q.

SECTION A - A

Figure 3.6 Cross-Section of Inatnimented Plate with Transducers

The convex corner models were constructed by using parts of the flat plate model

descnbed above. A piece was cut fiom the flat plate and replaced by specidy constructed

convex corners, one of 5" and one of 10°, so that none of the pressure tap locations were

Figure 3.7 Photograph of Tramducen Monnted Inside tàe Mode1

lost and there was one tap precisely at the comer. The location of the corner was 73 mm

from the leading edge. The comection to the sting was designed so that the leading edge

of the flat plate and both convex comer models were located in the same place with

respect to the nozie exit.

The horizontal dignment of the center plate with respect to the upstream and

downstream plate sections posed some difnculty and small steps less than 0.05 mm were

sometirnes present near the edges. However, these steps did not cause any visible shock

structure as can be determined tiom the Schlieren photographs.

The instrumented plate was inclined to the Free stream at 1.3", and, as a result, the

oblique shock wave of the shock generator was refracted by the shock generated fkom the

leading edge of the instrumented plate. For the purposes of the shock wave and boundary

layer interactions, the fiee stream was considered to be the flow inside the shock of the

instrumented plate.

4. EXPERIMENTAL RESULTS AND DISCUSSION

The current experimental program consisted two phases. The first being the

exploration of possible fùiiy 'turbulent' boundary layer development on the instmmented

plate and the next, investigation of shock wave and 'larniaar' boundary layer interaction

near 'rounded' convex corners. Experimental results obtained for both cases have been

described in the foliowing sections;

4.1 Exploration of Possible Turbulent Boundary Layer Developrnent

on the Experimental Mode1

in 1995, ~tockmans'~ completed his experimental research, at UTIAS, aïler

proposing extended operating conditions of the hypersonic gun tunnel. As claimed by

~tockmans'~, this extension of the operating conditions include fully turbulent boundary

layer development in the test section.

In this phase of the program, the possibility of achieving fùily turbulent boundary

layer from the leading to traiiing edge of the instmmented plate of the mode1 has been

explored by using operating conditions as suggested by Stockmans. Following are the

conditions employed for this investigation;

TABLE 4.1 Operatine conditions for the Turbulent Case

Nozzle Throat Diameter 18.16 mm

Free Stream Mach Number : 7.2

Unit Reynolds Number, & : 85.6 X 106 /m

Stagnation Temperature, Ts : 705 K

Initial Driver Pressure, Pdi : 20.5 MPa

Initial Barre1 Pressure, Phi : 400 kPa

Test Section Pressure, Pt, Below 50 Pa

Experiments were conducted with the 10 degrees convex comer mode1 in the test

section including the shock generator mounted with 0, = 9.9 degrees. Three shock

impingement locations (x*) were selected arbitrarily. Schlieren photographs were taken for

flow visuaiization. The flow is fiom lefi to right in al1 photographs. Figures 4. I (a), (b) and

(c) show oblique shock waves impinging forward of the corner, on the comer and aft of

the corner, respectively. Clearly, f?om these figures, it is difficult tu deduce the nature of

the boundary layer accurately.

Needham and ~tol lery~ suggested a method that c m be used to determine a

boundary layer type (laminar, transitional or turbulent) if the incipient separation ângle,ai,

Mach and Reynolds numbers are known. From Figure 4.l(a), the incipient separation

angle is estimated to be approximately 8 degrees. This yields, ai/ = 2.98. With the

Reynolds number of 3 0 X 1 o6 /ft it cm be seen nom Needham and ~ to l e ry 'sa correlation

cuve (see Figure 4.2) that the boundary layer developed in these experimeats are difficult

to comprehend.

Figure 4.1 Shock-Layer Interaction : O r 9.9 deg., 0, = 10 deg

24

O 54.5 " Il

A 14.8 Stollery O 16 Miller et of.

8 8.2 prernt study

i, 3 Kuehn 6 Sterrett and Emey

Without surface static pressure and, in particular, heat transfer rate measurements,

it is difficult to assess the nature of the boundary layer. Implementation of heat transfer

rate measurements is beyond scope of the current program and is strongly suggested for

future programs.

4.2 Preliminary Investigation of Shock Wave and Laminar Boundary

Layer Interaction Near Rounded Convex Corners

Before attempting to pemanently m o d e the existing 'sharp' convex corner model

it was necessary to conduct a few experiments for the foilowing important reasons;

i ) to validate the repeatability of the experimental faciiity by comparing

present data with previously obtained data, and

ii) to use the present data as a reference when cornparison needs to be made

in the fiiture after any geometric alteration of any part of the model.

The nozzie was replaced at this stage of the experirnental program to yield

operating conditions used by ~awboldt'. Table 4.2 presents these conditions;

TABLE 4.2 Operatine conditions for the Laminar Case

Nozzle Throat Diameter 12.70 mm

Free Stream Mach Number : 8.3

Unit Reynolds Number, Rm : 4.95 X 106 /rn

Stagnation Temperature, Ts : 934 K

Initial Driver Pressure, PJi : 20.8 MPa

Initial Barrel Pressure, Phi : 145 kPa

Test Section Pressure, Pi, Below 50 Pa

4.2.1 Reoeatabilitv Test for Convex Corner Resuits without Incident Shock

The 5 degrees convex corner mode1 was placed in the test section. The a h was to

obtain surface static pressure distribution as was found by ~awboldt'. Pressure

rneasurernents were taken at five pressure tap locations. The first tap measured static

pressure at 1 1.9 mm upstream of the convex corner and the last tap measured 52.36 mm

downstream. The other three tap locations were selected evedy between the above two.

These tap locations were selected so that a single run would yield an overall pressure

profile. Figure 4.3 presents the resuit obtained for this study. The Schlieren photograph,

~uliivan's" cold wall solution and ~awboldt's' renilt have been included in the figure.

0 Hawboldt CurrentStudy Cold Wall Soln.

Longitudinal Position of Instnimented Plate. x (mm)

Figure 4.3 Pressure Distribution over a 5 deg. Expansion Corner

The static pressure values for the current program were normalized with respect to the

static pressure obtained by J3awboldt1 at 73 mm fkom the leading edge of a flat plate.

Figure 4.3 shows that there exists a reasonable agreement between the current and

previous experimental data.

4.2.2 Reoeatabiiitv Test for Shock-Laver Interaction Results

The shock generator was placed in the tunnel test section and adjusted so that, 8,

= 5.1 degrees, 0, = 5.0 degrees and the shock impingement point, XI = 6.5 mm. In this

case, static pressure measurements were made at twenty pressure tap locations. Since the

current faciiity permits a maximum of five pressure readings per run, it was necessary to

conduct four runs to achieve a complete static pressure profile. This implied that the

instmmented plate, attached to the sting ofthe model, needed to be dismounted from the

test section to rearrange the transducer mounting positions for each of these four required

runs. After necessary re-arrangements, a speciaiiy constructed block was used to adjust

the spacing between the instmmented plate and the shock generator. This block became an

important component of the model as an adjustment mechanism.

Figure 4.4 shows the pressure protile for the current study with shock impinging at

the 5 degrees convex corner. Previous data obtained by ~awboldt' for similar test

conditions dong with Schlieren photograph have aiso been included in the figure.

Longitudinal Position of Instnimented Plate, x (mm)

Figure 4.4 Pressure Distribution of Shock-Layer Lnterrction

(Oc 5.1 deg., 8. = 5.0 deg, x 1 = +6.S mm)

As a final test for repeatabiiity, shock generator was moved forward, such that the

shock impinged approlamately 9.0 mm upstream of the 5 degrees convex corner. The

static pressure distribution has k e n presented for this interaction in Figure 4.5.

For the shock impinging at 6.5 mm downstream of the corner, the overali pressure

nse was slightly lower than previously achieved. The static pressure results are extremely

sensitive to the mode1 alignment that may have caused this discrepency. Ais0 noteworthy

is that, there appears to be a slight drop in static pressure near the corner as discovered by

Hawboldt. This was not the case for the m e n t study, where the pressure continued to

gradualiy rise in that region. For the shock impioging 9.0 mm upstream of the corner, the

maximum aatic pressure was found near the comer similar to Hawboldt. The overd

pressure rise in this case reached the approximate solution predicted value of 2.6. A

pressure plateau is dso found in this interaction causai by the precursor shock.

Longitudinal Position on Instrurnented Plate, x (mm)

Figure 4.5 Pressure Distribution of Shock-Mer Interaction

(Oi= 5.1 deg., 8, = 5.0 deg, XI = - 9.0 mm)

5, CONCLUSION AM) RECOMMENDATION

The experimental study was conducted in two phases. The first phase explored the

possibility of attaining shock-layer interaction measurements with the notion that a fûliy

turbulent boundary layer rnay develop on the model surface by modifjmg the tunnel

operating conditions. The second phase of the study involved preliminary investigation of

shock wave and hypersonic laminar boundary layer interaction near a modified comer

geometry, i.e., rounded convex corner.

Although much effort was made by ~tockmans'~ to provide fully turbulent flow in

the current facility, more explicit experimental validations are required to support his

proposition. Experimentd results for the first phase show that implementation of heat

transfer rate measurement technique may be necessary to iden* the nature of boundary

layer at hypersonic flow speeds.

Repeatabüity tests were conducted in the second phase of the program. Precise

a l i p e n t of the model is crucial for shock-layer interaction study, as was found in this

phase. The results obtained was satisfactory and agreed to the previously documented

results. Wah iimited experimental measurernents, it was difncuit to present a detaiied

description of the shock-layer interaction process. However, the repeatable characteristics

of the facitity used is a motivation to perfom m e r investigations in fields related to the

m e n t &y.

Before making any attempts to investigate shock-layer interaction any further, it is

strongly recornrnended that the screws and threads that hold many parts of the mode1

together are inspected thoroughly. ifappropriate masures are not taken, there is no

parantee that the mode1 will behave as one ngid body.

REFERENCES

Hawboldt, R.J., "Shock Wave-Boundary Layer Interaction at a Convex

Corner", PhD Thesis, December 1992, UTIAS,

Delery, J. and Mamin, J.G., "Shock-Wave Boundary Layer Interactions",

AGARD-AG-280, February 1986.

Kuethe, A.M. and Chow, C.-Y., "Foundation of Aerodynamics", 4th

Edition, John Wiley and Sons, Inc., 1986

White, M.E. and Ault, D. A., "Hypersonic Shock WaveîTurbutent

Boundary Layer Interactions in the Vicinity of an Expansion Corner",

1 994, AIAA Paper No. 95-6 125.

Lu, F.K. and Chung, K.-M, 'Txploratory Study of Shock Reflection Near

an Expansion Corner", 1992, AIAA Paper No. 93-3 132.

Hawboldt, RJ., Sullivan, P. A. and Gottlieb, J.J., 'cExperimentai Study of

Shock Wave and Hypersonic Boundary Layer Interactions Near a Convex

Corner", 1992, üTIAS, AIAA Paper No. 93-2980.

Chew, Y.T. and Squire, L.C., "The Bouodary Layer Development

Downstrearn of a Shock Interaction at an Expansion Corner", Aeronautical

Research Council, R&M No. 3839, 1979

Needham, D.A and StoUeryy J.L., Typersonic Studies of Incipient

Separation and Separated Flows", Aeronauticai Research Council,

ARC 27752, 1966

(9) Chapman, D.R., Kuehn, D.M and Larson, H.K, "Investigation of Separated

Flows in Supersonic and Subsonic Stream with Emphasis on the Effect of

Transition", NACA TN 3869, March 1957.

(10) Green, J.E., "Reflexion of an Oblique Shock Wave by a Turbulent

Boundary Layer", Journal of Fluid Mechaaics, Vd.40, Part 1, 1970.

(1 1) Sullivan, P.A., "On the Interaction of a LaminarHypersonic Boundary

Layer and a Corner Expansion Wave", AIAA Journal, Vol. 8, No.4,

Apnl1970

(12) Sullivan, P.A., Descharnbault, R.L., Hawboldt, RI. and Gordon, K.A.,

"Investigations in the fluid Dynamics of Scrarnjet Inlets", F M Contract

Report for USAF and Johns Hopkins University, Section 2, "Tunnel

Development, Operation and Calibration", July 1992

(13) Schlichting, H.,'Boundary Layer Theory", 7th Edition, 1979, McGraw-HiU

Series in Mec hanical Engineering.

(14) Anderson, J.D., 'Xypersonic and High Temperature Gas DynamicsJ7,

McGraw Hiil Series in Aeronautical and Aerospace Engineering, 1989.

(15) Stockmans, R., ccExtension of the Operathg Conditions of the Hypersonic

Gun Tunnel", M.A.Sc. Thesis, 1995, UTIAS

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