Automatic landing through the turbulent planetary boundary layer

October, 1971.

TUN",sutE HOGESCHOOL

Otl. ~1GIOUWIWN'DE

IUOlllEEK

QUANTITATIVE LASER SCHLIEREN MEASUREMENTS

IN AN EXPANDING HYPERSONIC LAMINAR BOUNDARY LAYER

by W. W. Koziak

I",

QUANTITATIVE LASER SCHLIEREN MEASUREMENTS IN AN EXPANDING HYPERSONIC LAMINAR

BOUNDARY LAYER

by

W. Wo Koziak

Submitted October, 1971.

'.

ACKNOWLEDGEMENT

The author wishes to express his thanks to the Director, Dr. Go No

Patterson, and faculty of UTIAS for having made possible the opportunity to

conduct this investigafion.

He is most indebted to his project supervisor, Dr. P.

A.

SUllivan,

who made the original suggestion for the present experiment al study and has

given continued advice and guidance throughout the course of his work.

The financial assistance received from the National Research Council of Canada is gratefully acknowledged.

The generous assistance given by B. To Whitten and Wo O. Graf, two of his fellow students, in proof reading and computer program development is also gratefully acknowledged.

Finally the author wishes to express his special thanks to his wife, Rose, for her confidence, patience, understanding and forebearance during the

SUMMARY

This thesis describes ~he development and application of a quantitative

space and time resolved laser schlieren system to measure density gradients in a laminar hypersonic boundary layer expanding from Mach

6.5

over a

5

degree expan -sion corner.

A review of previous work shows that the problem of calculating the flow

of a hypersonic boundary layer over an expansion corner has not been satisfactorily

solved. These analyses have invariably used simplifying assumptions which have

resulted in omission of such basic physical aspects of the problem as upstream

influence and centrifugal effects, transverse pressure gradients in the boundary

layer and boundary layer-expansion wa.ve interaction. The present experiment has

been undertaken to test the validity of recently developed theoretical calcula

-tions which do not omit the above effects.

The basic features of the present schlieren system consist of a helium -neon laser which acts as a narrow beam light seurce. The laser beam is scanned across the test section of the flow facility by a rotating mirror assembly followed by a system of lenses which focusses it to a diameter of 0.6 mm and amplifies

its refractien caused by density gradients in the test section. Finally a photo

-multiplier tube-oscilloscope assembly records the resulting deflection of the beam relative to a knife edge. The facility used for the experiment is the U.T.I.A.S • .

11 inch combustion driven hypersonic shock tunnel and the test model consists of a 10 degree wedge followed by a

5

degree expansion corner.

The major contribution to error in the experimental data by the optical system is a re sult of atmospheric disturbances in the neighbourhoed ef the test

section and laser source. In ad~ition, the instrumentation sensitivity is such

that it detects in detail the irregularities characteristic of shock tunnel flows leading to considerable scatter in the raw data. However, suitable statistical tests give reasonable confidence in the conclusions.

t~ ~he schlieren system developed for this experiment has been shown

to be capable of generating quantitative data successfully in the study of

hyper-sonic flow. The experimental results agree at least qualitatively with up-to

-date theories. They show clearly the strong interaction between the downstream bound.ary layer flow and the expansion wave. More important they indicate that the expected centrifugal effects influence the boundary layer flow considerably and that they extend well outside of the immediate vicinity of the corner. In add

i-tion, the detailed experimental density data obtained upstream of the expansion corner reveal a discrepancy with classical zero pressure gradient boundary layer theories and has been shown to be a likely result of leading edge shock wave

-boundary layer interaction. Numerical analysis applied to an existing theory for this type of interaction indicates that the entropy layer generated in the leading edge region where the shock curvature is large appears to remain a signi

-ficant portion of the boundary layer flow even in such a weak interaction regime as :. the present case.

I. 11. 111. IV.

V.

VI. VII. VIII. TABLE OF CONTENTS INTRODU.,cTION

REVIEW -OF PREVIOUS WORK BASIC EXPERIMENT

THE SCANNING LASER SCHLIEREN SYSTEM Physical Description

Calibration of the Schlieren System IV.l

IV.2

IV.3 Discussion of the Quantitative Schlieren System THE CORNER EXPANSION FLOW TEST PROGRAM

V.l Shock Tunnel Naminal Operating Conditions V.2 Correction of Reflected Shock Zone Temperature

for Thermal Losses

V.3 The Shock Tunnel - Schlieren System Interface Triggering and Data Recording Arrangement

v.4

Test Model Configuration and Installation V.5 Correction of Data for Model Edge Effects

v.6

Shock Layer State Properties

V.7 Validityof the Cold Wall Assumption EXPERIMENTAL RESULTS

Density Gradient Flow Field

VLl

VL2

VI. 3

Boundary Layer Growth and Density Distributions Pressure Distributions

DISCUSSION OF EXPERIMENTAL ERRORS CONCLUSIONS

REFERENCES

APPENDIX A: THE UTIAS HYPERSONIC SHOCK TUNNEL APPENDIX B: FLOW SEPARATION PROBLEMS

APPENDIX C: WALL DENSITY CORRECTION

APPENDIX D: THE FLAT PLATE BOUNDARY LAYER - THEORY AND EXPERIMENT FIGURES 1 1

4

5

5

6

6

8

8

9

9

9

10 11 12 12 12

13

14

14

16

18

C f 2 G I

K

M Mst P Pr P

₄

R Rb Re T U W We x, y y s z

a

a

_w ~ ~ ~ _B.L.

Y

5 5* NOTATION

Chapman - Rubesin Cons~ant

Focal Length of Lens L 2

Gaussian Function,

G(x,Y)=(1/(2~)~~)exp(-(x2+ y2)/2~2)

Total Radiation Intensity Gladstone-Dale Constant Mach Number

Tailored Shock Mach Number Pressure

Prandtl Number

Combustion Driver Pressure Molecular Gas Constant Model Corner Radius Reynold's Number Temperature

Velocity in the x ~direction

Physical Model Width

Effective Two Dimensional Model 'Width

Coordinate Reference System

Leading Edge Shock Wave y - coordinate

- -2

Dimensionless x-coordinate, z = X Accommodation Coefficient

Corner Expansion Angle Model Wedge Angle

Boundary Layer Wedge Angle Contribution, ~B.L. ~ 5*/x

Ratio of Specific Heats Boundary Layer Thickness

5(y) 8 p

x

w SUBSCRIPrS e s w o 1 5 00

Laser Beam Def1ection in the y-direction at the Sch1ieren System Knife Edge

Leading Edge Shock Wave Ang1e

Wavelength of ~ight; Molecular Mean Free Path

. -1

Mach Ang1e, ~ = Sln (l/M)

Density

Sta~dard Deviation

Viscous Interaction Parameter, X

=

M

3

(C/Re)!

Stream Functio~

Viscosity Power Law Index

Boundary Layer Edge

Leading Edge Shook Jump Condition

Model Wall

Tota1 Conditions Inviscid Shock Layer

Reflected Shock Zo~e

I. INTRODUCTION

The objective of the present work consists of two main parts. The first is the development of a quantitative space and time resolved schlieren system. The second is the application of this technique to measure flow proper-ties in the region of interaction of a hypersonic laminar boundary layer with a corner expansion wave and to compare these measurements with up-to-date theo-retical results.

Experimental diagnostic techniques as applied to low density hypersonic flows to date, have consisted mostly of surface pressure and heat transfer measure-ments. These, by their nature, are of limited value in describing entire flow fields. This is also the case for pitot pressure measurements which require the use of a flow disturbing probe~ and prior knowledge of local streamline inclina-tion, a flow property which in many cases is difficult to estimat)e accurately. Optical methods avoid the basic difficulty of flow disturbance due to the presence of a probe, and of these, interferometric techniques have been used successfully to provide good quantitative data in shock tube experiments (Ref.

1).

However, their range of applicability falls short of the generally low density conditions in hypersonic flows. Electron beam probes which can be used to measure gas den-sity and temperature are limited, on the other hand, to very low densities where free molecule, transition or at best slip flow regimes must be considered. Al-though the conventional schlieren system appears to be a suitable device to cover the range of flow conditions that occur in a typical hypersonic gas dynamics test facility, it is used in general to give only a qualitative picture of such flows since extraction of quantitative data from a schlieren photograph has been found to be impractical. Some special quantitativeschlieren systems have been developed by Hannah and Dale (Ref. 2) among others, for use in continuous flow facilities, and by Resler and Scheibe (Ref. 3) and Kiefer and Lutz (Ref. 4) for measurements in unsteady one dimensional shock tube flows. The present work includes the de-velopment of a narrow beam system which is essentially an extension of the one used by Kiefer and Lutz (Ref.

4)

modified so as to resolve two dimensional steady or moderately unsteady flows generated in a hypersonic shock tunnel.

A subject of currently renewed interest, the development of winged atmospheric entry vehicles having extensive cross range capabilities emphasizes the need to understand thoroughly hypersonic flow interaction phenomena such as the one investigated in the present thesis. Ih spite of many published attempts, the problem of calculating the flow of a supersonic or hypersonic boundaFY layer over an expansion corner has not really been satisfactorily solved. These analyses have invariably used simplifying assumptions which have resulted in omission of important physical parts of the problem. The full problem is complex as it in-cludes upstream influence and centrifugal effects, transverse pressure gradients in the boundary layer and boundary layer-expansion wave interaction (See Fig.

1).

The present experimental work on ~his subject confirms qualitatively some of the earlier results obtained from measurements of wall and pitot pressures, and it includes the first flow field measurements indicating the presence of significant transverse pressure gradients in the downstream boundary layer.

H. REVIEW OF PREVIOUS WORK

Interest in this type of problem extends as far back as

1953

when Lighthill published a pioneering paper on upstream influence in boundary layers

(Ref.

5).

However, one of the earliest analyses directly applicable to the present work was presented by Zakkay and Tani (Ref. 6) and Zakkay, Toba and Kuo

(Ref.

7).

In their model, viscous flow in the boundary layer is expanded around the corner inviscidly. Downstream the boundary layer is analYr,ed in two parts.

A sublayer starting at the corner is analyzed by utilizing a GJrtler series ex-pansion for non-similar solutions. A viscous shear layer at the outer edge uses the same type of series solutions and has the inviscid profiles immediately

down-stream of the corner as initial conditions. Upstream influence, centrifugal effects and transverse pressure gradients in the boundary layer in the

neighbour-hood of the corner were omitted completely. Also no consideration was given to possible effects of the interaction of the boundary layer downstream of the corner

with the external flow, so that their method is limited to estimation of heat transfer rates.

Curle's method (Ref. 8) of treating this problem consists basically of

two equations; the first relates deflections in the external streamlines to pressure changes by assuming linearized inviscid flow and the second relates

pressure changes to thickening or thinning of the boundary layer by assuming that

the classic Prandtl boundary layer equations can be used. Centrifugal effects are

omitted completelyon the grounds that they should be small for small turning

angles and moderately supersonic flows; but in contrast to the previous work up-stream influence effects and the downstream interaction are modelled. Subsequently

Oosthuizen (Ref. 9) extended Curle's analysis to a wider range of conditions by using the exact Prandtl-Meyer relations to describe the external flow and the full von Karman momentum integral equations for the boundary layer thus avoiding Curle's assumption of constant momentum thickness. This analysis did show the anticipated peak in skin friction and heat transfer at the corner, but as a cusp so that the

magnitude of the peak is not predicted.

Weinbaum (Ref. 10) considered the expansion of a supersonic shear flow,

such as produced by a boundary layer, through a centered expansion fan by making

use of an inviscid rotational characteristic method of solution. The subsonic portion of a supersonic boundary layer was not taken into consideration in this

work. Weinbaum's analysis suggested that for small turning angles and large

ex-ternal flow Mach numbers, the flow immediately downstream of the corner could be

highly underexpanded so that an extensive downstream interaction would be required

to complete the turning process of the external flow. Also the results indicated

the possibility of the formation of a weak shock wave downstream of the corner.

This arises because the outgoing expansion waves reflect off the entropy lines as

compressions in the low supersonic portion of the boundary layer and these in turn

a,re reflected off the wall as compressions. It was not clear from Weinbaum' s

analysis if the outgoing compression waves so formed could focus before being

washed out by the dominant expansion effect. Oosthuizen (Ref. 9) also applied

Weinbaum's method to examine the turbulent boundary layer problem in contrast to

the earlier approach for laminar boundary layers on the grounds that typical up-stream turbulent profiles should lead to very thin subsonic sublayers. Ris

re-sults did show focussing of the weak compressions leading to formation of an iI overexpansion shock".

Brailovskaia (Ref. 11) applied a modified set of Navier-Stokes equations,

where terms of order higher than O(E2 )

=

0 (l/Re) were neglected, to the flow

region adjacent to the corner. No formal derivation of these equations was given

in the publication; however, they included the transverse momentum equation. The boundary conditions were given by the solution of the usual flat plate boundary

layer equations for the upstream flow, the usual wall properties and the inviscid irrotational expansion flow outside of the boundary layer. The downstream

condi-tions were not specified; however, the extent of the region of analysis was adjusted

- - - -, .

'

,..

until further increase downstream did not produce significant changes in the flow

properties. Results shown for the ~

=

2,

a

W

=

20

0

, Tw/T

o

=

0.25 case indicate

some upstream influence, large transverse pressure gradients in the immediate

vicinity of the corner and a very small downstream interaction region. Brailovskaia's

results also show the presence of some weak compression just downstream of the

corner.

Sullivan (Ref. 12) pointed out that for sufficiently large M , the boun-e

dary layer would be supercritical in the sense first proposed by Crocco and Lees

(Ref.

13)

for the shock wave-boundary layer interaction problem in contrast to

the subcritical upstream boundary layers used by Curle (Ref. 8) and Oosthuizen

(Ref.

9).

In this case the upstream influence effect in the boundary layer cannot

be modelled by the Prandtl equations since they predict that the boundary layer

would react to the decreasing external pressure by thickening. Sullivan suggested

that this would imply that upstream influence should be small and confined to the

corner region where Prandtl's equations should be inapplicable, and that

conse-quently, the very large drop in pressure through the corner expansion expected for even very small turning angles would have to be accommodated almost entirely in the downstream interaction. He obtained results for this model by using the cold wall similarity theory of Lees to describe the boundary layer and the

hyper-sonic small disturbance equations to describe the external flow. Centrifugal

effects were omitted completely and the analysis could not predict the corner peaks but the results did show the large extent of the interaction and the strong effect of any upstream shock wave-boundary layer interaction as expressed by the value of the viscous interaction parameter

X

at the corner.

Victoria and Kubota (Ref. 14) also calculate the upstream flow for a small value of

X

in order to provide initial conditions for the corner region. The integral moment form of the usual boundary layer equations is used for the

flow around the corner with the external flow represented by the inviscid

ir-rotational Prandtl-Meyer function simplified for large Mach numbers. A singular

perturbation expansion approach for the upstream and corner flows together with

the introduction of the supercritical-subcritical jump condition are used to match

the upstream and corner region solutions and predict upstream influence.

Down-stream of the corner the original boundary layer equations are relaxed to the

Blasius equation through a weak in~eraction process with the external flow.

As part of a theoretical and experimental program on this problem at

the University of Toronto Institute for Aerospace Studies (UTIAS), Lo and

~ullivan (Ref. 15) published an analysis which attempted to give a complete

pic-ture. The calculations~ which used an integral technique, are related to the

classical von Karman-Polhausen method. By using the "viscous-inviscid" equations

throughout the entire regime of interest significant centrifugal effects were

shown to occur in a region which could extend far downstream of the corner. Details

of the skin friction and heat transfer peaks were obtained, and the calculations also indicated the presence of a weak shock wave immediately downstream of the

corner. Figure 2 shows typical calculated values of Pand P non~dimensionalized

w

e

by the value upstream of the corner P

l as a function of the distance x along the

wall non-dimensionalized by the upstream boundary layer thickness 6

1 for an

up-stream Mach number ~ = 6.0, a turning angle

a

w 5.15

0

and a corner radius Rb/61

=

1. Figure 3 shows the same effects for a Mach number ~

=

10.

hypersonic boundary layer and corner expansion flow problem. This is due mainly to the difficulty in obtaining good data, particularly since only flow field information can verify the presence of the more important physical effects pre-dicted by Lo and Sullivan (Ref. 15).

S4ernberg (Ref.

16),

Zakkay and Tani (Ref.

6)

and later Zakkay, Toba and Kuo (Ref. 7) obtained surface temperature, pressure and heat transfer data on axisymmetric expansion models for flow Mach numbers ranging from about 1.5 to

4

and hence at relatively low values of

x.

Their measurements indicate that the wall pressure distribution is close to the one predicted in an inviscid centered expan~ion. Otherwise, the temperature and heat transfer data is in-conclusive as far as the corner flow interaction problem is concerned. Murthy and Hammit (Ref. 17) investigated the interaction of a turbulent boundary layer with a Prandtl-Meyer expansion at M

=

1.88.

They found that the pressure

down-00

stream of the corner was initially appreciably higher than the simple wave theory predicted, but gradually approached the inviscid limit about five boundary layer thicknesses downstream. Surface pressure measurements by Robinson (Ref.

8)

show an almost antisymmetrical distribution about a 150 _{corner at a flow Mach number}

of 2.75. The extent of the corner influence appears to be about

4

boundary layer thicknesses upstream and

6

downstream.

Puhl (Ref.

18

₆

made extensive surface and pit ot pressure measurements in the flow around a 20 included angle cone-cylinder adiabatic wall model at a free stream Mach number of about

7.8.

The flow field is constructed from pitot pressure data assuming constant statie pressure and total temperature across

the boundary layer whose rapid thickening is observed almost immediately downstream of the corner. Surface pressure measurements indicate a weak shock wave-boundary layer interaction together with an upstream influence extending approximately two boundary layer thicknesses. Downstream of the corner the wall pressure appears to approach the inviscid value very slowly, hence illustrating astrong interaction which continues at a diminishing rate to at least 15 boundary layer thicknesses. Similar experimental results were obtained by Victoria and Kubota (Ref. 14) for a

5

0 wedge angle followed by a

5

0 _{expansion corner. two-dimensional model under}

similar test conditions as in the previous case.

Stollery (Ref. 19) reported experimental measurements of surface pres-sure on an

18.5

0

wedge-plate combination in a Mach 14 flow. Although his results agree quite well with the theory of Sullivan (Ref. 12) for the pressure distri-bution on the wedge; the same theory substantially overestimates surface pressure downstream. The resolution of this difficulty is suggested by the results of Lo and Sullivan (Ref. 15) which show that although P decays quite slowly, P decays

e w

rapidly owing to the presence of centrifugal effects.

The remarks in the previous paragraph highlight the need for flow field measurements in order to check both boundary layer growth and the ratio P

lp

w

e

and consequently resolve this problem. The present work has been aimed at achieving this end.

lIIo BASIC EXPERIMENT

The principle of the experiment is as follows. The quantitative laser schlieren system is used to obtain measurements of density change relative to the reference conditions (1) in Fig. 1, which are located just upstream of the ex-pansion corner. The values at the reference conditions are established by

computation from basic tunnel flow parameters. Density changes are measured across the expansion wave to the edge of the boundary layer and across the boundary layer to the wall. Density traverses upstream of the corner have shown that the inviscid flow is isentropic so that pressures at the edge of the layer can be inferred

through the isentrope law pIp!

= constant, and pressure at the wall can be

calcula-ted since the wall temperature of ~he model (cold wall flow case) is known accu-rately.

IV. THE SCANNING LASER SCHLIEREN SYSTEM IV.l Physical Description

The instrumentation system used here was developed for the present experi-ment and has been described by Koziak (Ref. 20). The schlieren system shown

sChematically in Fig. 4 us es a Spectra-Physics model 132 helium-neon laser as the narrow beam source. The laser beam is swept across the flow field by an eight-sided front surface mirror assembly (Fig. 5) which is driven at 3600 rpm by an ac motor. In the case of a steady flow experiment, each one of the eight separate mirrors is inclined with respect to the axis of rotation so that the laser beam sweeps along a maximum of eight separate scan li~es. On the ot her hand, the same mirrors can be adjusted to provide repetitive scanning along the same line for time resolution in an unsteady flow field. Although the repetition rate in the present system, which is set up for a steady flow experiment, is about 480 scans/sec., it can be increased by at least an order of magnitude by increas-ing the number of mirror faces and the speed of rotation of the mirror assembly. The assembly itself is located such that the reflection OCCurS at the focal point of the first lens Ll' This 10 cm diameter, 1 m focal length positive lens serves two main purposes. First, it transforms the rotary motion of the reflected beam into a translational motion perpendicular to the optical axis of the schlieren system. Second, it focuses the laser beam which is initially about 1 mm in_

diameter to a value of 0.6 mm across the test section. The location of this lens with respect to the test section axis and also that of t he laser source with respect to the rotating mirror assembly is optimized by trial and error to achieve the

above minimum average beam diameter. In addition lens Ll also increases the laser beam natural divergence and consequently the beam diameter at the knife edge. This has the effect of extending the linear range of the system response since it is directly proportional to the beam size at that point in the schlieren system. The test section windows are optically flat to À/2 and have been coated with mag-nesium fluoride to minimize interference between the transmitted and internally reflected light. To further reduce the interference problem, the optical axis of the system has been tilted about 3 degrees with respect to the normal direction of the windows. The focal length of the second lens L

2 determines the sensitivity of the schlieren system (Ref. 21) and in the present experiment a 10 cm diameter, 2 m focal length positive lens was chosen, for estimated test conditions to be measured, so as to avoid schlieren system saturation and operation in a non linear range. lts additional function is to reverse the translatory motion of the beam in the test section into a rotary motion centered on its focal point. This is where the schlieren system knife edge is located. A neutral density filter is used to reduce the beam intensity by a factor of 20 and a narrow band pass filter centered on the helium-neon laser wavelength of 6328 ~ excludes extraneous light from ente"ring the photomultiplier tube assembly. The photomultiplier tube is an EMI type 9558C with an S-20 photocathode. It is wired to give a fast response, moderately high output signal which is then displayed on an oscilloscope.

IV.2 Calibration of the Schlieren System

The schlieren system in its scanning mode of operation was calibrated by recording the photomultiplier output for different cut-off positions of the knife edge. The movement of the knife edge, which is controlled with the use of a micrometer assembly, in steps of 0.25 roro is plotted vs photomultiplier out-put on Fig.

6.

The straight line drawn through the experimental points shows that the response of the system is closely linear for knife edge movements as much as 2 roro on either side of the 50% cutoff position. This plot then gives, as a function of photomultiplier output, the lateral deflection of the laser beam with respect to the knife edge. Lateral beam deflection 5(y) at the schlieren system knife edge is related to the density gradient cp/cy measured in an ideal two dimensional flow by the formula for a low density medium (Ref. çl)

5(y)

=

f

2 K( àp/cy) W ( 1)

where f

2 is the focal length of lens 12, K is the Gladstone-Dale constant of the working gas and W is the width of the two dimensional flow region. A quanti-tative check of the system response was made by placing a 4'30" + 5" glass wedge having an index of refraction of 1.5242 + 0.0004

(*)

in the test-section to simulate a representative density gradient in hypersonic flow. The photomulti-plier output was then recorded as the laser beam swept across the glass wedge and this quantity together with the calibration data of Fig.

6

was then used to calculate back the glàss wedge angle. The resulting figure agreed with the manufacturer's specification to within 1.7%. In addition to the above procedure, a similar but simplified calibration was performed iroroediately before each run of the shock tunnel. It consisted of recording the photomultiplier tube output for two different positions of the knife edge within the expected linear range of the system.

IV.3 Discussion of the Quantitative Schlieren System

A number of technical problems were identified in the course of develop-ing the quantitative laser schlieren system. Their possible effects on the present experiment and where important their method of solution are described as follows. Op the time scale of the experiment, temporal variation in the laser beam inten-sity is, according to manufacturer's specifications, less than 1% and · there-fore negligible in comparison to ot her sources of error. This was also verified with the use of the photomultiplier detection system used in the present

experi-men~. Construction of the rotating roirror assembly presented two major

diffi-culties. One was provision for fine control (of the order of minutes of arc) of individual mirror inclination with respect to the axis of rotation. This feature is necessary for setting scan line spacing. The other was distortion of the re-flecting surface, initially a result of the mirror mounting arrangement. Both of these problems were overcome by carefully cementing the 10 x 7 x 1 roro glass

mirrors on similar sized aluroinum pla~es. These, together with a thin sheet of deformable plastic material, were fastened to the shaft assembly by means of fine thread screws. Although a subject of concern initially, spherical abbe-ration of lenses Land 1

2 (this decreases with lens f/number) resulted in a

measured signal moaulation of less than 5%. However, because this is a systematic error, it is eliminated from the test data by simple subtraction ot the no flow signal. One of the more important contributions to error in the experiment al

data is caused by atmospheric disturbances in the neighbourhood of the test section

'"

and . laser source. This error as shown in the scatter of calibration data

on Fig.

6

is estimated to result in a maximum random error of +

5%

in the

subse-quent density gradient measurements

(*).

To reduce this problem for very

sensi-tive systems one should enclose the area in question in a well insulated chamber.

The laser beam diameter in the test section was measured by recording

the photomultiplier output as the beam was swept across ,a razor edge located

in the test section (Fig.

7).

Analysis of the results shows that the beam diameter

between the e- 2 points is 0.6 mm assuming a Gaussian intensity distribution and

that this diameter varies by +

15%

across the 20 cm wide test section. This

varia-tion appears to be due to either distortion of the mirror faces or more probably

in the present case, the less than ideal quality of ~he reflecting surfaces which

are flat to several wavelengths only. The data reduction procedure, which will be

outlined in detail in a later section, includes the following important point

related to the above discussion. Since the beam intensity distribution is Gaussian

(Ref. 22), its deflection caused by the presence of a density gradient is not

directly proportional to the average density change rate across the beam as would

pe expected for a square distribution, but, it is proportional to a weighted average

as shown by the expres sion below for a two dimensional flow in the x-y plane,

00 00 00 00

5(y)

=

f

2KWJ J

~

(s,t) G(x-S,y-t) dsdt

1

J

G(x-s,y-t) dsdt (2)

-00 -00 -00 -00

where 5(y) is the beam deflection at the knife edge, f

2, K and W are the constants

defined previously, (àp/oy)(s,t) is the density gradient at coordinate position

s,t in the x-y plane, and G(x-s, y-t) is the value of the Gaussian function at

s, t where x, y is the coordinate position of the péak of the Gaussian function~

An analytic expression of (op/oy)( s, t) representati ve of the densi ty gradient

distribution to be expected in a

3

mm thick hypersonic laminar boundary layer

was analyzed numericallyon a computer. ,The results indicate that treating the

experimental data as if the laser beam is infinitessimally narrow rather than

finite (0.6 mm) and having a Gaussian intensity distribution, produces a maximum

error of

.

5%

of the absolute value of op/ày. The above analysis was used also

to check on the effect of changes in the laser beam diameter. The results in this case show that a diameter variation of + 20% produces a signal variation of ~ 0.5% for the same boundary layer profile.

The frequency response of the photomultiplier tube and oscilloscope system was checked by observing the output of a gallium arsenide infrared "eniitter

driven by a square wave power supply. The results of this test indicate th at the

frequency response limitation of 2 MHz of the system is due to the Tektronix

type 3A74 plug-in amplifier but that nevertheless it is well within the range

required for subsequent flow measurements. All of the critical schlieren system

components which include the laser source, rotating mirror assembly, lenses 1

1

and 1 and the knife edge assembly are mounted on platforms having two adjustable

rotatfonal and translational degrees of freedom. These permit ' accurate

align-ment of the scan lines and ~he knife edge with the local ver±i~al and horizontal

directions respectively. The platforms aré in turn fastened to heavy rigid

supports in order to minimize the effects of mechanical vibration on the

measurements.

(*)

note that unless otherwise specified in the present thesis, quoted values of

either scatter or estimated errors are computed on the basis of an assumed normal distribution.

Finally, a point which should be considered carefully in setting up any quantitative schlieren system is that the beam deflection within the test flow must be small in comparison to the physical dimensions of the flow features investigated. In the present experiment this maximum deflection was found to be approximately 0.08 mm and therefore considered adequate in view of the fact that it is much smaller than the laser beam radius, itself a practical measure of the spatial resolution possible. As an aside observation, investigation ofaxi-symmetrie flows appears to be feasible wi th the present diagnostic technique since data in this instanee are reducible with the use of Abel's integral equation

(Ref. 23).

V. THE CORNER EXPANSION FLOW TEST RROGRAM V.l Shock Tunnel Nominal Operating Conditions

The hypersonic shock tunnel was designed and built by the hypersonic gas dynamics group at U.T.I.A.S. in 1968 in order to provide a new, reliable and versatile test facility which could be used for such experiments as the one presented in this thesis. It is described in detail together with some of its developmental problems in appendix A.

The test section flow properties required for the study of the present interaction problem were used to determine the nominal shock tunnel operating conditions, which in addition to those mentioned in appendix A include the following:

1. The tailored incident shock Mach number is 3.2 in nitrogen.

This results in a reflected shock zone temperature of 13500K which is high enough to prevent condensation of the test gas during expansion to high Mach numbers and sufficiently low to avoid significant vibrational excitation of the nitrogen molecules (Ref. 24).

2. The reflected shock zone pressure is 1000 psi. This is a result of the operating conditions specified above and in appendix A.

3. The test section flow Mach number is 10.5 and is considered large enough to satisfy the basic requirement of hypersonic flow and still avoid the inherent difficulties that arise

when the test gas is expanded to higher Mach numbers (Ref. 25). Table I summarizes the above operating conditions together with the im-portant flow properties calculated with the use of standard gas dynamics tables

(Refs. 26, 27).

In developing the above tunnel operating conditions, possible constraints, other than those already implied,were examined carefully. For example, the test section free stream density should be high enough to avoid the slip flow or transi-tion flow regimes. This situatransi-tion, as was shown by simple calculatransi-tions based on information found in Refs.

28

and

29

could arise especially in the high temperature hypersonic boundary layer. Also for similar flow situations, density gradients increase with free stream density, thus making flow features easier to detect with the schlieren system. On the other hand, the flow Reynolds number, which is

- - - -- - - -

--_._----~~-directly proportional to density, must be low enough to ensure a stable laminar boundary layer on the test model.

V.2 Correction of Reflected Shock Zone Temperature for Thermal Losses

In calculating the reflected shock zone temperature, the effects of thermal losses due to radiatJon, conduction and unsteady weak rarefaction waves were estimated by utilizing results of spectroscopie and total intensity measure-ments (Ref, 30) taken at a nominal incident shock Mach number of 4.0. These show that in this case the radiation is predominently of the continuum type and that it is caused by the presence of impurities in the nitrogen test gas. Consequently, the temperature correction procedure makes use of the recorded intensity history during the run and it assumes that the doubly shocked gas radiates as a black body

(i.e., IOCT

4).

Figure

8

is a record of the reflected shock zone pressure and total radiation intensity obtained simultaneously during a run of the shock tunnel. Analysis of these results indicate that the reflected shock zone temperature

de-creases by about 1% per millisecond af ter incident shock reflection in the present experiment. The oscilloscope traces on figure

8

also illustrate the close corres-pondence between identifiable events on the pressure and total radiation intensity histories.

V.3 The Shock Tunnel - Schlieren System Interface Triggering and Data Recording Arrangement

The flow chart on figure

9

shows the triggering and data recording se-quence followed during each run of the test facility, together with typical photo-graphic results. The raw data thus obtaiaed includes:

1. Incident shock speed measurement.

2. Reflected shock pressure history on which are superimposed scan timing marks.

3.

Schlieren system photomultiplier output which consists of eight traces corresponding to eight sequential scans of the flow field of interest.

4.

As mentioned previously, in addition to the above, no flow and calibration data is obtained just prior to each run. Also, the relationship between the oscilloscope trace horizontal scale (i.e., sweep rate) and the physical distances which it represents is adjusted accurately ( ~ + 1%) to a convenient factor. This is performed by observing the spacing of pulses generated by the schlieren system when the laser beam is scanned across a grid of

~.010 inch wires spaced 1 cm apart placed just outside of the

test section.

v.4

Test Model Configuration and Installation

The double wedge airfoil shape aluminum model is shown installed in the test section on figure 10. The leading edge, the radius of which is approximately

.0015", forms a 10 degree total included angle. The top and bottom expansion corners,

5 degrees and 10 degrees respectÜ!:vely,,' are also sharp (i.e., Rh/Bl

«

1). They are located approximately

8

inches from the leading edge and

5

incfies from the blunt

trailing edge. The model comprises a"

5

inch wide center section and four 1/2 inch wide side pieces which can be removed or added to vary the overall width. The sting type support provides control of roll and pitch settings and translation along the longitudinal axis of the test section to permit proper alignment of the model with respect to the schlieren system optical axis. In preparation for a test run, careful attention is given to aligning the surface of the model with the laser beam. This consists of manually translating the laser beam (in the

y-direction) aciV.OSS the test section with the use of the rotating mirror assembly to within a graEing distance (~

0.5

mm)

of the model surface. The model is then rotated about its roll axis until the laser beam reflection on the surface ap-pears as a band of light of constant width (~ 1

mm).

A very slight deviation

(~ 0.1

mm)

over the span of the model from parallelism between the laser beam and the model surface is readily visible as a non-uniform width of the reflected band. Since only the 5 degree corner expansion flow case is investigated in the present experiment, the upper surface is inclined at a negative angle of attack (i.e., compression angle) ~

= 10

0 _{to ensure attached flow both upstream and downstream}

of the corner. Flow separation problems encountered initially in this test program are described in appendix B.

V.5

Correction of Data for Model Edge Effects

Because both the model span and the test section flow core are finite, an assumption that the flow over the entire model is two dimensional is not valid. Previous experience using surface flow visualization techniques (Ref.

19)

indicates that a two dimensional core should exist in this type of flow situation. In order to relate the measured beam deflection to the local density gradient in this core

(eq.

(1»,

an effective two-dimensional model width must be determined for a given geometry. This is done in the present experiment by measuring the beam de-flection at some selected point in the flow for models having four different widths but otherwise identical in configuration. One point at x

= -3.351

and another at x

=

8.25

1 upstream and downstream of the

5

0

corner respectively were selected for this purpose. The y-coordinate in both cases corresponded to the location in the boundary layer where the magnitude of the density gradient was a maximum (i.e., maximum signal to noise ratio).Figure 11 shows the results of a number of runs in the form of a plot of P.M. tube signal (which is directly proportional to the beam deflection) versus '. ,! test model width. The curve relating these two variables for an ideal two-dimensional flow would be a straight line through the origin, but physical reasoning suggests that in the present case the curve should be S-shaped with zero slope both at

W

=

0

and as

W

becomes large. Also the centre portion should be linear if a two-dimensional core exists. Since the signal is proportional to

J

(~)

dw,

as w

~

0, model edge effects ensure that this integral should behave like Wl+E where E

>

O. On the other hand as W ~oo, the model will protrude through the boundaries of the free jet flow in the test section and this should cause a finite upper limit. Exponential, hyperbolic and cubic curves were fitted to the data by a least squares technique; all gave effective model wid~hs within the error esti-mates attributable to the scatter of data. The

7-a../2"

wide model was used sub-sequently for the corner flow experiment in order to obtain as high a signal to noise ratio as practical in the present facility, and its effective two-dimensional width W was calculated to be

5.32"

and

5.60"

upstream and downstream of the corner respectrvelY. The error in these values based on the absolute scatter of data

(this should be on the pessimistic side) was found to be about + 11%. These values

may be compared with the theoretical inviscid value of

5.0"

at the corner based on the intersection of the tip Mach cones with the model surface. Since some contriC, bution to the measured signal comes from the region outside of the two-dimensional core, the equivalent model width should lie between the "zone of silence width" and the physical width. In the subsequent calculations of density gradients, it is assumed thay W is constant through the relatively small region of immediate interest. The average vaIue used W

=

5.5",

is in this respect consistent with the error

e

estimates. Finally, close examination of the data reduction procedure shows that the dependence of P

lp

on W is such that an error of 10% in W causes a maximum

w e

error of

4%

in P

lp.

Hence the most important results of the experiment are fairly w e

insensit~ve to the uncertainty in the estimation of the effective two-dimensional width of the model.

v.6

.Shock Layer state Properties

The measured density gradient distributions in the interaction region can be integrated to give density distributions from which pressure data can be inferred if the state properties of the gas are known accurately at some reference position in the flow. Measured density gradients in the shock layer toge~ger

with a relatively low computed value of the viscous interaction parameter X ₀₀

=

1.23, indicate a weak leading edge shock wave - boundary layer interaction. Therefore the reference region in question is taken as the shock layer in the vicinity öf the corner where it is assumed that the flow properties are uniform. These are calculated from measureme4ts of the following:

1. The test section free stream Mach number, at the position where the model corner would normally be located, is determined from

p~tot pressure measurements.

2. The model leading surface inclination with respect to the test section center line is measured to the nearest minute of arc with an inclinometer.

3.

The leading edge shock wave inclination to the model surface is obtained from both the quantitative schlieren data and conven-tional schlieren photographs.

4.

The expansion wave head inclination with respect to the model surface is also obtained in this manner.

All of the above mentioned information (i.e., M , ~, 8, ~ see Figure 12) 00

is combined, utilizing perfect gas relations, in such a way as to produce a self consistent set of conditions together with a reasonable estimate of the displace-ment effects due to boundary layer growth upstream of the corner. In fact the contribution of boundary layer growth to the wedge angle is calculated in the above manner to be ~B.L.

=

42'. This conpares well with a value of 52' computed on the basis of measured bouadary layer thickness which should overestimate this effect (i.e.,

5

>

5*).

Given the above flow geometry, which is assumed to be constant within the same run and also from run to run, the instantaneous values of pressure and density in the shock layer are computed from the measured reflected shock zone pressure and its calculated temperature. The appropriate values for the instant of each lase~ beam scan sequence are thus determined taking into account the ~ag between the flow in the test section and the reflected shock region as des-cribed in appendix A.

V.7 Validity of the Cold Wall Assumption

Solution of the heat conduction equation (Ref. 31) for a semi-infinite solid to which a step input of heat transfer is applied, is thought to represent closely the conditions imposed by the flow over the model in the hypersonic shock tunnel.

The value of the heat transfer rate used in the present calculation to estimate the model surface temperature history is taken from Ref. 15, and the transport properties for aluminum out of which the model is made, are taken from standard physical tables. The results of this calculation show that the model surface temperature, in the region upstream of the corner but sufficiently far from the leading edge, should increase by about 20_{K in a time of 20 ms. The model}

surface temperature rise downstream of the corner should be even smaller in the same elapsed time since the surface heat transfer rates in this region are expected to be lower. This indicates clearly that the assumption of a cold constant temp-erature wall (T

= 300

0K = room temperature) through the duration of a test run, which in the pr~sent experiment is approximately 15 ms, should not introduce any significant errors in the boundary layer flow calculations.

VI. EXPERI:MENTAL RESULTS

Vl.l Density Gradient Flow Field

A series of eleven runs of the hypersonic shock tunnel - quantitative schlieren system combination was performed in which the laser beam was scanned four times through the interaction region at each of six stations upstream and sixteen stations downstream of the expansion corner. The photomultiplier tube outputs, which correspond to be~ deflections, were reduced to density gradients in approp-riate units (g-cm-

3

-mm- ) with the use of the pre-run calibration data and equation

(2) which was solved numerically for each case using an iterative technique. The flow chart on Fig. 13 illustrates in detail the full data reduction procedure. Figure 14 is a composite plot of the average density gradient distributions at each

of the scan stations along the model. The more important physical features, such as model surface, leading edge shock wave, boundary layer edge and expansion wave head, are indicated on this figure to faciJitate visualization of the flow field. The position of the leading edge shock wave was determined from data obtained in a preliminary series of runs in which the effective field of view was increased to include that portion of the flow. The leading edge shock wave is indicated on the photomultiplier tube outputs by the presence of a large positive gradient spike. The shock wave angle with respect to the model surface is calculated from this data by joining the experimental points to the model leading edge. The experiment al data, which lies within an estimated 0.3 mm of the model surface (a distance

corres-ponding to the laser beam radius), is corrsidèred unreliable due to effects of laser ~ beam obstruction by the model, and has been discarded. Consequently the probable

model surface is shown shifted from the apparent surface by the said amount. The location of the expansion wave head and the boundary layer edge in the region downstream of the corner is determined af ter consideration of the ex-pected physical effects illustrated qualitatively on Fig. 15. Case I represents the density gradient profile through a centered Prandtl-Meyer expansion fan. Case 11 on the other hand corresponds to the typical cold wall hypersonic boundary layer

(Ref. 32). Superposition of these two distributions, Case 111, resembles closely the experimental results except for that part very close to the wall (discussed previously) and the region of the expansion wave head. The discontinuous behav~our

~~-

---~~~~~~~~~~~~~~~~~----,---of the density gradient predicted fun a centered inviscid expansion is not observed experimentally due to the presence of the boundary layer flow around the sharp cor-ner. This causes 4he wave to be uncentered resulting in a continuous density

gra-dient transition.

The quantitative data on Fig. 14 may be compared·to the upper half of the conventional schlieren photograph on Fig. 16 obtained for identical flow conditions.

The lower half of the photograph shows clearly boundary layer separation well

up-stream of the l~ degree expansion corner on the lower surface of the model.

VI.2 Boundary 1ayer Growth and DeAsity Distributions

The boundary layer growth downstream of the corner is shown on Fig. 17 as a plot of boundary layer thickness 5 versus distance x from the corner, both

nondimensionalized by the boundary layer thickness 5

1 upstream of the corner. The solid curve of yhe form

is fi tted to the experimental data by a least squares technique and i.t is compared

with the theoretical results of 10 and Sullivan (Ref. 15) (dotted line). Although

it is recognized that a bet ter form flor the above expression might include a

functional re~ationship which approaches the flat plate boundary layer growth case (Le., 5oCxl j2) far downstream of the corner, it was chosen for its simplicity and is thought to represent reasonably well the expected physical effects in the

relatively small region of interest.

Given the location of the expansion wave head and the boundary layer

edge, the density distributions a~ong these and along the apparent wall are computed

by integrating the density gradient curves using the calculated instantaneous shock layer properties as reference conditions. Since the acceptable experimental data does not extend completely to the surface of the test model, the true wall density

distribution was estimated by extrapolating the experimental results using the theoretical density profile in 'a compressible zero pressure gradient laminar boun-dary layer under similar flow conditions as a guide. The extrapola~ion procedure and its possible effect on the wall to edge pressure distribution is examined in detail in appendix C.

Asf',me:rmtli:önedt previously in section

v.6,

the flow upstream of the corner is in a weak interaction region and consequently the laminar boundary layer in this case should behave as 4he classical flat plate type for which the theory has been developed extensively (Refs.

32, 33, 34,

35, 36).

Appendix D examines and compares

with theory the experimental density gradient and density profiles for this

flow region.

The distributions of boundary layer edge density Pe and wall density Pw. ~~~~:e~;i~~:l;~;! by 1he _{shock layer density Pl are shown on Fig. 18. The solid}

C exp (-Dx/5

1) - C + 1

(4)

are fitted to the experimental data by a least squares technique where C, D, E and F are the constants found as part of the curve fitting prgcedure. The form of

equation

(4)

is considered to be a reasonable approximation of the expected P~Pl decay in an incomplete corner expansion wave". On the other hand, in view of the fairly large scatter of P~Pl data, fitting a curve to these other than a linear one would be difficult to justify.

VI.3 Pressure Distributions

Lo and Sullivan (Ref. 15) predict th at for cold walls and the values of Mand a used in the present experiment, the pressure decay ahead of the

corn~r (ups~ream influence) is small in extent and amplitude and therefore most

likely indistinguishable from the scatter of experimental data. Consequently, attention to the boundary layer-expansion fan interaction problem is confined to the downstream process. In this region, as outlined in Section 111, the boundary layer edge static pressure is obtained from experimental data (Fig. 18), the cal-culated shock layer properties (Section

v.6)

and the isentrope law p/pl

=

constant. The wall pressures are ~alculated from the experimental data extrapolated to the wall as suggested previously in Section VI.2, the model surface temperature which is assumed to be constant at 3000K (Section V.7), and the ldeal gas law P = pRT. The edge pressure P

IP

l and a measure of the transverse pressure gradient P

lP

e w e

are plotted versus the downstream distance x/5

1 and compared with the theory of Lo and Sullivan (Ref.15) on Fig. 19. The experimental P

lp

distribution is shown

w e

as a cross-hatched band which is a measure of the confidence that can be placed in a least squares curve fit to the individual computed values of P

lp.

A curve

of the form w e

P

lp

=

1 - J exp (-

Hx/51)

w e (6)

where J and Hare found as part of the curve fitting procedure and the condition P

lp

~ 1 as

x/5

1 ~oo has been imposed, is fitted to fourteen of the total

w

e

fifteen data points. Fifteen such curves are obtained by successively omitting each point in turn. The band, which is the envelope of these curves gives con-siderable confidence that a meaningful distribution can be obtained in spite of the fairly large scatter that is evident in the density ratio P~Pl data on Fig.18. VII. DISCUSSION OF EXPERIMENTAL ERRORS

A number of possible sources of error in the present experiment and their effects on the final experimental results have already been discussed in previous sections. In addition three groups of other possible sources of error, divided on the basis of effective time scale, are examined as follows.

1. The first group consists of errors the effects of which change during

the test run of the tunnel. This includes fluctuation of the reflected shock .~

region conditions. Although an attempt has been made to relate events in this region to each laser beam scan sequence, correction for the expected time depen-dence of the reflected shock zone temperature outlined in Section V.2 is considered to be of limited value in view of the assumptions that have been made. On the ot her hand, the reflected shock region to test section pressure time correlation is probably quite good since the measurement in question is much more direct. Consequently, the estimated error in the instantaneous value of reflected shock zone pressure and temperature is about + 2% and ~ 5% respectively.

This group also includes the effect of atmospheric disturbances, which has already been discussed in Section IV.3.

2. The second group are those sources of error which are expected to remain unchanged during the test run but which may vary from run to run. The only important member of this group is the possible error in the calibration factor which relates photomultiplier output to laser beam lateral deflection at the knife edge. The factor is obtained just prior to every run as described in Section VI.2 and an uncertainty of about +

4%

is a direct result of the atmos-pheric disturbances present during the experiment around the test section and

laser source. This was determined from a routine statistical analysis of a continuous series of calibration runs.

3.

The last group is made up of errors considered as direct results of the basic assumptions which have already been stated or implied in the develop-ment of the present experidevelop-ment. Estimation of the effective two dimensional

model width is probably ~he most important member of this groupo lts effect on the final experimental results has been described in Section V.5. Another possible source of error in ~his group is generally known as conical floweffects

(Refs.

37, 38).

They occur as a re sult of the hypersonic expansion nozzle and test section configuration and are likely to affect the flow geometry and the

gas state properties at any given location in \he flow field. However, because the - region of iIllIjlediate interest in the present experiment is relatively small (approximately

3

x

3

inches campared to a 16 x 16 inches test section), no attempt has been made to estimate quantitatively the possible effects of such a conical flow on the experimental results. Nevertheless, it is highly likely that these effects, in the form of a continuously expanding flow in the test area, cause ~he measured density gradients far downstream of the corner to be under-estimated with respect to the reference density in the shock layer upstream of the corner. This would cause the calculated edge density P~Pl and consequently edge pressure Pe/Pl to approach asymptotically corresponding values that are higher than the expected inviscid limits (see Figs. 18, 19).

In addition to the above, errors in incident shock speed measurements, changes in the speed of rotation of the mirror assembly and time variation of the flow geometry and free stream Mach number either are thöught to be of relatively minor importance or have proved to be so in the course of the experi-ment.

Statistical analysis of the density gradient results in the shock layer excluding the boundary layer, indicates a scatter of + 1.6 x 10-

7

g cm-

3

mm- l

assuming a normal distribution in the experimental data. This results in a possible error of about ~

0.7%

in the shock layer density P

l when integrated over a distance of 1 mmo Similar analysis of free stream (i.e, no model present in the test sec-tion) and no flow density gradient data suggests strongly that the above scatter is caused mainly by the presence of thermal disturbances in the air surrounding the test section and laser source. In the interaction region (i.e., within the expansion wave and boundary layer) the corresponding figure for scatter is +

4.7

x

10-7

g cm-

3

mm- l • Note however that the latter includes effects due to variations in the flow properties (i.e., reflected shock zone temperature and

pressure) which have been accounted for in computing the final density and pressure data.

to contribute to the scatter in the density distribution data P~Pl and P~Pl shown on Fig. 18. However close examination of these reveals the following interesting phenomena.

1. The scatter in the pwlpl data is noticeably larger than in the P~Pl data.

2. The scatter in either PwlPl or P~Pl does not appear to increase significantly with distance from the corner. This would be expected to be the case since integration of density gradient to obtain density involves an inte-gration distance which increases approximately linearly with distance from the corner.

3.

The possible errors discussed so far do not ap~ear to have an effect large enough to account for the scatter of P~Pl data (~

!

27%).

Consideration of the above suggests that one possible explanation for all three points mentioned is a direct result of some flow instability in the boundary layer. In view of the flow separation problems discussed in appendix B, this, at ~he present, seems to be the most plausible one.

VIII. -.cONCLUSIONS

lnitial application of the newly developed laser schlieren system shows that it is capable of generating quantitative data successfully in the study of hypersonic flow under conditions where any such data are at eest difficult to ob-tain. Past experience with shock tunnel measurements in gener al shows that large data scatter is not uncommon (Refs. 37,39,40,41). It should be noted that the sensitivity of the present optical system can probably be increased by at least a factor of

5;

however, as aresult, atmospheric disturbances in the neighbour-hood of the test area and laser source become increasingly significant and special precautions should be taken to eliminate them as suggested previously. Although nót an essential feature for the present experiment, a one order of mag-nitude improvement in the time resolution of the instrument appears to be feasible. This would make it possible to study moderately unsteady flows with characteristic oscillating frequencies of up to 10 KHz. Also a considerable reduction in the scatter of experimental data is thought possible by taking special precautions to ensure a completely stable boundary layer flow over the model, and by increasing the laser beam scan rate so that the measurements can "be taken over a shorter and consequently more quiescent time interval in the operation of the hypersonic shock tunnel.

The experimental results shown on Figs. 17, 18 and 19 agree at least qualitatively with the theories of Sullivan (Ref. 12) and Lo and Sullivan (Ref. 15). They show clearly the strong interaction between the downstream boundary layer flow and the expansio~ wave which manifests itself in a very slowedge pres-sure decay toward a limiting value. Although this value, in the pre sent experi-ment, overestimates the expected inviscid limit probably as a re sult of conical floweffects in the test facility, this does not detract from the basic finding stated above. More important, the rapid growth of the boundary layer immediately downstream of the corner and the behaviour of the wall to edge pressure ratio (a measure of the transverse pressure gradient in the boundary layer) indicate un-mistakably that the expected centrifugal effects influence the boundary layer flow considerably and, as also shown in the theoretical results of Lo and Sullivan