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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
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iv
vi
vi
vii
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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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