Laminar separation in supersonic flow woth emphasis on three-dimensional pertubations at reattachment

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TRAINING CENTER FOR EXPERIMENT AL AERODYNAN

TECHNICAL NOTE 3

LAMINAR SEPARATION IN SUPERSONIC FLOW WITH EMPHASIS ON

THREE-DIMENSIONAL PERTURBATIONS AT REATTACHMENT

By JeanJ.Ginoux .

Rhode-Saint-

Genèse,

Belgium . February 1960

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MONITORING AGENCY DOCUMENT NR. ASTIA DOCUMENT NR. TCEA TN 3 ~/z

/:td

~

F~--f

~~

/~

~

'l'r.

'

~

~)

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LR

la -st'!

LAMINAR SEPARATION IN SUPERSONIC FLOW WITH oEMPHASIS ON

THREE-DlMENSIONAL PERTURBATIONS AT REATTACHMENT

by

Jean J. Ginoux

Brussels University, TCEA and CNERA

CONTRACT NR. AF 61 (514)-993 FINAL REPORT February 1960.

Bibliotheek TU Delft

Faculteit L & R c2297706 " " " " ""

I

The research reported in this document has been sponsored by the Air Force Office of Scientific Research of the Air Research and Development Command, United States Air Force,

through its European Office.

This report includes or references all work accomplished under contract AF 61 (514)-993. A further extension of this research is being conducted under contract AF 61 (052)-350.

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FOREWORD

The author would like to thank the European Office of ARDC for the sponsorship of this work and also to record his thanks to CNERA, without whose support this programme of research would not have been started and from which the author has received every possible help and encouragement.

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TABLE OF CONTENTS

Page

ABSTRACT 1

INTRODUCTION 2

DESCRIPTION OF THE EQUIPMENT 2

EFFECT OF MODEL SPAN 4

EFFECT OF LEADING-EDGE THICKNESS

5

EFFECT OF STEP HEIGHT AND BOUNDARY-LAYER THICKNESS

6

EFFECT OF STREAMLINE CURVATURE 11

RESULTS ON VARIOUS TYPES OF SEPARATED AND

UNSEPARATED FLOWS 13

CONCLUSIONS 14

REFERENCES 15

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TCEA TN

3

LAMINAR SEPARATION IN SUPERSONIC FLOW

WITH EMPHASIS ON

THREE-DIMENSIONAL PERTURBATIONS AT REATTACHMENT

by

Jean J. Ginoux

ABSTRACT

1

It was shown that regular and repeatable span-wise flow perturbations existed in the reattachment region of a laminar supersonic boundary-layer on a two-dimensional back-ward-facing step model. It was found that the model span and leading-edge thickness, when below 0.1 mm, had no effect on the wave -length of the flow perturbations.

On backward facing-steps, at a Mach number of 2.16, the ratio of wave-length of the flow perturbations to boundary-layer thickness was a function of the ratio of step-height to boundary-layer thickness.

Similar perturbations were found at the reattachment region of a laminar boundary-layer on forward-facing steps, on compression-corners, on rectangular cavities and in the case of interaction between a shock-wave and the .boundary-layer. They were also detected in unseparated boundary-layeri.

The presence of three-dimensional perturbations seems to be related to the general question of boundary-layer stability.

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2 TCEA TN

3

INTRODUCTION

In the course of a research programme undertaken at TCEA on laminar separated supersonic flow, the author found

that three-dimensional perturbations existed in the

reattach-ment region of the flow around a backward-facing step model

that completely spanned the tunnel. It was shown that

possi-ble irregularities in the air-flow upstream of the model or in the model itself could not explain the existence of strong, regular and repeatable span-wise perturbations in the boundary-layer (3).

In a continuation of the work, a detailed investiga-tion was made on backward-facing steps; the 1nfluence of step-he1ght and boundary-layer thickness on the wave-length of the

flow perturbations was examined. Other types of supersonic

separated flows were al so investigated with emphasis on the presence of span-wise flow per turbations.

DE8CRIPTION OF THE EQUIPMENT

Wind-tunnels

The bulk of the work was made in the TCEA 40 x 40 cm2 (16" x 16") supersonic wind-tunnel (tunnel 8-1) at a Mach

number of 2016

(3).

Measurements were also made for comparison

in a 15 x 15 mm2 (006" x 006") supersonic wind-tunnel at the

same Mach number. Tunnel 8-2 was continuously operated with

dry-air using the vacuum pump of tunnel 8-1 and its auxiliary dr yero The nozzle was asymetric; only one block was contoured,

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TCEA TN

3

the otherone belng flat. The stagnatlon pressure was slightly below the atmospheric pressure.

Model configurations

3

The geometry, dimensions and designations of the various models that were used in tunnel 8~l are given in figure 1. Most of the models were formed by assembling together a certain number of interchangeable pieces 0 The leading-edge thickness was equal to 0.1 mm (0.004 inch) with ~ exception of model S-6 which was 0.02 mm thick. Models

completely spanned the 40 ems test section, except CC-1, CC-2, S-6 and S-7 models having a 150 mm span and

s-8

model having a 250 mm span. The models were mounted on a double support

allowing for the adjustment of the angle of attack. Figure 2a shows model S-1 in the test section of tunnel S-l.

In tunnel 8-2, backward-facing steps were directly machined in the flat wallof the nozzle as shown in figure 2b.

Test techniques

Transition from laminar to turbulent flow was detected on shadowgraphs and schlieren pictures, taken with a convention-nal optical system, using pàrabolic mirrors and a spark light souree.

The flow on the surface of the models was qualitati-vely observed by the use of a sub1imation technique. The

indicator was chosen as azobenzene

(3),

which had a slow

response, to allow for rather long starting and stopping times of the wind-tunnel. An indlcation of the surface-flow patternwas

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4 TCEA TN 3

generally obtained (depending upon the thickness of the

azo-benzene layer) af ter 3 to 9-hours running time of the tunnel.

Detailed surveys were made with a total-head probe

using the device described in reference 3. A good agreement

was found (3) between the results of the sublimation and the

surveying techniques. In the early tests, the probe was

manually operated. Later, the probe was moved at a constant

and low speed using an electric motor while the pressure was

measured on a Brown recorder. The repeatability of the

measurements was good as shown in figure 5 for model CC-l at

«

=

0 and Xc

=

20 rnm; two successive surveys were made for the

same stagnation conditions (po

=

200 mm Hg abs.) and two

others at Po

=

146 and 116 mrn Hg.

EFFECT OF MODEL 8PAN

Tests were made on three models (8-5, 8-8 and 8-7)

having the same cross-section (h 4 mrn and L

=

56 rnrn) and

a span respectively equal to 400 mm, 250 mm and 150 mmo There

were no end-plates at the models. The leading-edge thickness

was equal to

t

=

0.1 + 0.02 mmo

The sublirnation technique was used to get the

surface-flow pattern; this is shownin figures 3i, 3q and 3u. Figure 8

shows the results of total-head transverse surveys made

down-stream of reattachrnent. ~p is the difference (in mm of water)

in the readings of the fixed and the moving probes. The

wave-length (À) is the d1stance between successive pressure peaks;

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TCEA TN

3

in figure

8.

Also shown is a mean wave-length defined as the ratio of a certain distance

(6.})

by the number of pressure peaks measured along

A't.

Figure

8

shows that, within the accuracy of measurement, there was no span effect on the wave-length of the flow

perturbations in the region of the model axis.

EFFECT OF LEADING-EDGE THICKNE88

The effect of the leading-edge thickness on the. flow

perturbations was examined by comparing the results of

trans-verse surveys made on models 8-6 and 8-7. Both models had a

150 mm span.

Figures 3g and 3u show the surface-flow patterns that

weregiven by the sublimation technique.

5

The results of total-head surveys made on these models are compared in figure

9. À

was found to be within 2 to

4

mm on model 8-6 having a 0.02 mm leading-edge thickness and within 2.5 to

4

on model 8-7 having a 0.1 mm leading-edge thickness.

The step-height was not the same for both models (h =

3

mm

on 8-6 and h

=

4

mm on 8-7); however, as shown below, this difference could not appr~ciably affect the wave-length of the flow perturbations.

It was concluded that À was not affected when the leading-edge thickness was reduced from 0.1 mm to 0.02 mmo

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6

TCEA TN

3

Figure 10 gives the results of total-head surveys made on model 8-1 when the leading-edge thickness was increa-sed from 0.1 mm to 0.3 mmo It shows that the mean wave-length increased from

6

mm to 12 mm~ probably due to a thickening of

the boundary-layer (see the effect of boundary-layer thickness in the following section).

EFFECT OF STEP HEIGHT AND BOUNDARY-LAYER THICKNE88

The effect of step-height (h) and boundary-layer

thickness

(S)

on the wave-length

(~)

of the flow perturbations has been investigated in tunnel 8-1. The models are shown in figure 1.

b

and

~

were varied wi thin the following ranges

mm mm

where

~

is the boundary-layer thickness at separation; it was computed assuming an adiabatic flat plate with zero leading-e dgleading-e thicknleading-ess.

~

was varied by using different lengths (L)

for the flat plate and by changing the tunnel stagnation

pressure. The leading-edge angle of the models was kept

below 10 degrees; in these circumstances~ it was found

diffi-cult to get separation of very thin boundary-layers and still

have an acceptable range of step-heightso The difficulty was

overcome by using cornpression-corners located at a small distance behind the leading-edge of a flat plate; the models

(CC-models) are shown in figure 1. By varying the angle of the compression-corner and its position on the flat plate, separatlon could be obtained very close to the leading-edge~

thus. glving small values of

~

; an exarnple is given by a

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TCEA TN 3

Po

=

115 mm Hg). CC-models had a 150 mm span and were not fitted with end-plates.

7

A few tests were made for comparison at the same Mach number in tunnel 8-2. Backward-facing steps were located in the flat nozzle-wall. The boundary-layer was laminar and its thickness at separation was.equal to 0.6 mm; this value was measured by surveying the boundary-layer with a small circular total-head probe. An example of the surface flow

pattern is given in figure )v.

Shadowgraphs and schlieren pictures were taken of each flow to locate the position of transition; examples are shown in figure 4. The sublimation technique was used to obtain a qualitative picture of the flow on the surface of the various models; examples are given in figure ).

For quantitative information, detailed surveys were made using a total-head probe which was moved accross the model at a constant distance (x) from the ~ep-base. Except in a few cases, a survey was made on each model for only one value of Xj because it was found (see figure

6

related to

model 8-1) that

À

was the same as measured for various values of x. The same cylindrical pro be was used for all the various flow conditions and models. It had an external diameter of 1 mm and an internal diameter of 0.5 mm; the probe was always moved in contact with the model surface.

The results of such surveys are given in figure 11, where ~p is the difference (in millimetre of water) in the readings of the moving probeand of an identical fixed probe, located at the same distance (x) from the st ep-base.

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8

TCEA TN 3

Figure 11 shows that span-wise variations of

llr

existed in the region of reattachment where the pressure peaks

and valleys were almost precisely equally spaeed. The wave

-length of the flow perturbations was measured on these

diagrams. Not much attention was given on the recorded

amplitudes of the pressure peaks because of their irregular form and because the same probe diameter was used, although

~

was different in each case. The strongest peaks were

found to exist on compression-corners (CC-models); (~p)s of

about 300 mm of water were measured.

On the other hand, for small values of (h) on step

models (h

=

0.8 and 0.3 mm), the total-head probe gave no

indication of pressure variations (within the accuracy of

measurement,i.e. a few mm of water) although a striation

pattern was clearly indicated by the azobenzene (see for

example figures 31 and 3n). In these cases, quantitative

information, sueh as the wave-length of the perturbations, was taken directly from the pictures of the surface flow.

In all cases, the striation pattern existed up to

the point where transition occurred (as determined from the

shadowgraphs), with the exception of models 8-18 and 8-19

where the :Ilo \'1 perturbations seemed .to vanish well upstream of

transitionj this is shQwn in figures 3h and 3j, and in figures

4j and 4k. ~he sublimation technique gave no lndication of a

striation pattern in the turbulent region of the flow.

However , surveys made with the probe in that region did show

pressure variations over a certain distance downstream of

transition. The results are shown in figure

6

for model 8-1,

the striation pattern being also indicated. Figure 4f gives

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TCEA TN 3 9

Table 1 summarizes the results obtained on the various types of models. The distance between successive pressure

peaks ("wave-length") was not exactly constant on .each model, but varied within the range indicated. Values of

(b)

were computed from the distance L (figure 1) and from the tunnel stagnation pressure given in table 1 (po in mm of mercury).

Except for compression-corner models (CC-models) for which (h) could not be accurately defined, non-dimensional quantities such as À/~ and h/~ were introduced and plotted in a diagram as shown in figure 7. A mean wave-length defined as the ratio of a certain basic span-wise length divided by the number of pressure peaks recorded along that l~ngth is also indicated in the graph.

Figure 7 shows that a good correlation was obtained betweenthe experimental results by using these non-dimensiona1 quantities.

~/~

increased when hlS was increased from zero to about 3; then stayed constant for

hlb

up to

8

and then increa-sed again for higher values of

h/~.

Correspondingly, transi-tion moved upstream when h/h was increasedj i t reached the point of reattachment for hlb between 8 and 13.

À;è

did not tend towards zero as

h/~

approached zero. This result was confirmed as a striation pattern was observed

incidentally on the flat surface of model S-17 upstream of the step; the phenomenon is shown in figures 3c and 3d. There was no indication of a boundary-layer separation in that region of the flow; weak perturbatlons were present in the wind-tunnel, one being created by a rubber joint which was not correctly fastened to the model-side.

~/b

was found to be within 1.2 to 1.4 in that case; these values are plotted on the vertical axis of figure 7. Furthermore, three-dimensional

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10

TAB L E I TCEA TN 3

Model

S'MIm,

Range of À Po

(computed) (measured) mm Hg abs

from L

&

Po mm S-l 2008 3.5-6 220 S-2 1.5 3-5 220 S-3 2.47 4-7 181 s-4 1.49 3-5 223 S-5 1.04 2-3.5 213 S-6 1.10 2-4 195 S-7 1.07 2.5-4 212 s-8 1005 2-3.5 211.4 8-11 2019 4-9.3 193.3 8-12 1058 .

-

195.3 8-13 2 016 5-up 198.9 s-14 1.6 6-10 193.2 8-15 2.16 8-18 200 8-16 1.57

-

197.7 S-17 3.07

_-

200 . 8-18 0.50 0.5 ... 1 2000) 8-19 0.72 105-2 195.5 DSl 1.48 2-5 225.4 D82 2.23 4-6 185.3 D83 1053 2.5-4 210.7 Ds4 2.07 3-5 213.6 D85 1.53 3-5 209 04 Ds6 2.22 4-6 188 D87 1.58 1 .. 2-2 198 nsB 1.59 1.5-3 195 DS9 2.2 1.7-3.5 206 DS10 2.15 1.2-2.5 199 8R-1 2005 4-7.5 220 8R-2 1.75 3-6 160 SR-3 2.12 2-5 205 SR-4 1050 2.29 206 CC1

~

r:i..

=00 0.4 1-2.5 200 xc==20

ei.

=90 0.4 1.5-3 197 CC1 D( =00 003 1 198 xc=20 C02 0.3 105-4.5 200 xc=20

Dl

=00

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TCEA TN 3 11

perturbations were also observed in the boundary-layer on the

contoured wallof tunnel S-2, this is shown in the last section

of this report. The boundary-layer was unseparated (h 0) and

À

was equal to 1 mm; the boundary-layer thickness was taken approximately as 0.5 mm giving thus

À/~

of about 2.

It w~s found occasionally that very irregular, weak and localised striations existed on the model surface

upstream of the step~ al though these were notclearly indicated. This is shown in ~igure 3 b of reference 3 (model S-l) and is also shown in figure 3ro It might be thus possible that three-dimensional perturbations existed initially in the laminar boundary-layer and as the flow separated and reattached, the perturbations corresponding to a given wave-length were ampli-fied~ the selected wave-length being related t o the bo undary-layer thickness. The perturbations then travel led for a

certain distance, function of the ratio

h/b

before transition appeared.

EFFECT OF STREAMLINE CURVATURE

The effect of the streamline curvature, related to the positive pressure gradient that always existed at reattach-ment, is presently peing investigatedo Only a few tests

have' been made so faro The radius of curvature of the surface

upon which reattachment occu~ was variously chosen as

1000 mm and 250 mm as shown in f igure 1 (SR-models) and by the shadowgraphs given in figures 4b and 4c.

The importance of the streamline curvature has been pointed out by Gortler in a theoretical investigation on

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12 TCEA TN 3

incompressible boundary-layers

(4,5).

However,

three-dimensional perturbations have been detected experimentally at low speeds by Hama et al

(6),

and also by Klebanoff

(7)

that could not be attributed to streamline curvature. Moreover, the tests made on the SR-models showed that the flow pertur-bations still persisted when the boundary-layer was flowing along convex surfaces. The results from total-head surveys are given in figure

7

and examples of striation patterns obtained by the sublimation technique are shown in figures 3k and 3s.

SURVEYS WITH OTHER PROBES

A transverse survey was made in the reattachment region of one model with a total temperature probe which did not show any variation.

A survey was made on model CC-I, using a

directional probe instead of the usual total-head probe. The probe was formed by assembling two cylindral tubes (0.5 mm I.D. and 1 mm O.D.), soldered together; its nose had the shape of 90° wedge. The difference in the readings (~p) of the two pressure holes was recorded as the probe was moved accross the model. The result is shown in figure 12 and compared withthe result given by the total-head probe.

EssentiallY the same pressu're variations were recorded and the wave-length was found to be the same.

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TCEA TN

3

13

RESULTS ON VARIOUS TYPES OF SEPARATED AND UNSEPARATED FLOWS

Various types of sepa~ated flows were examined in

relation to the existence of span-wise perturbations in the

boundary-layer. The tests were made in tunnel S-lo

A separated flow was obtained by interacting a

laminar boundary-layer with two-dimenslonal oblique

shock-waves. The shock strengths were 50 chosen that separation

odcurred with a laminar reattachment as shown in figure 4a. Figure 3b shows that a striation pattern existed downstream

of reattachment.

The flow around an upstream-facing step (model DS-ll)

was also investigated. A 006 mm step height was used.

Figure 4g is a schlieren picture of the flow around model

DS-ll. The result of a test made with the sublimation

technique is given in given in figure 3m; it shows the

existence of span-wise perturbations in the flow downstream

of reattachment.

The reattachment of a laminar boundary-layer behind a rectangular cavity located in a flat plate was observedo The width (B) of the cavity was 20.6 mm and its depth (H)

was 10 mmo The stagnation pressure was equal to 154 mm Hg.

A shadowgraph of the flow is given in figure 4i; i t shows thatfue flow was slightly unsteady as could be expected for

that opening (B/H = 2.06) of the cavity. Figure 3t shows

that a striation pattern existed upstream of transition; the

picture, which was obtained af ter a running time of the tunnel

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14

TCEA TN 3

Finally, separated flow was studied on a body of revolution in which a "backward-facing step" was formed by a sudden decrease in the diameter (figure 1). Figure 3(0)

shows the existence of essentially similar perturbations to

those found in the earlier models.

A test was made in tunn~S-2, using the sublimation technique, to visualize the flow on the surface of the

contoured nozzle-wall in the presence of a laminar

boundary-layer. Figure 3p shows that three-dimensional perturbations

existed in the boundary-~yer upstream of transition. The

wave-length was about 1 mmo The perturbations were located

on the flat portion of the wall (i.e. downstream of its curved portion) ; there was no indication of separation in that region.

These tests seem t o show that the existence of

three-dimensional perturbations in a laminar boundary-layer

is not restricted t o a particular type of flow but is more

f~ndamental.

CONCLUSIONS

1. Regular and repeatable span-wise flow perturba-tions exist in various types of separated and~eparated flows.

2. The presence of three-dimensional perturbations seems to be related to the general question of boundary-layer stablility.

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TCEA TN 3 ₁₅

the ratio of wave-length of the flow perturbations toboundary-layer thickness is a function of the ratio. of step-height to boundary-layer thickness.

*

REFERENCES

1. Dean R. CHAPMAN, Donald M. KUEHN and Howard K. LARSON Investigation of Separated Flows in Supersonic and Subsonic stream with emphasis on the Effect of Transition. NACA TN 3869, March 1957.

2. Dean R. CHAPMAN

A Theoretica1 Ana1ysis of Heat Transfer in Regions of Separated Flow NACA TN 3792, October 1956.

3. Jean J. GINOUX

Experimenta1 Evidence of Three-dimensiona1 Perturba-tions in the Reattachment of a Two-dimensiona1 Laminar Boundary-layer at M

=

2.05. TCEA TN 1, November 1958. 4. H. GOERTLER

Dreidimensionale Instabi1ität der Ebenen Staupunkt-stromung gegenüber Wirbelartigen Storungen. 50 Jahre Grenzschichtforschung. Friedr., Vieweg

& Sohn, 1955;

pp. 304-314.

5. H. GOERTLERand H. WITTING

Theorie der Sek undären· Insta b.i1i tät der Laminaren Grenzschichten. Boundary-láyer research, Proc. Int. Uni on and Appl. Mech., H. Gortler, ed. Springer Verlag

(Berlin) 1958, pp. 110-126.

6. F.R. HAMA, J.D. LONG and J.C. HEGARTY

On Tran~ion from Laminar to Turbulent Flow. Jour.

Appl. Phys., vol. 28, n° 4, Apr. 19577 pp 388-394. 7. P.S. KLEBANOFF and K.D. TIDSTROM

Evolution of Amplified Waves Leading to Transition in Boundary-Layer with Zero Gradient. NASA TN D-195, September 1959.

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I-

L

"I

.ct

I I

L

Single step (S -) modeis. Double sle p (05- )models.

Model _{h mm} _Lmm Model _hmm _Lmm S - 1 15 225 OS - 1

"

120 S - 2 15 120 OS - 2 4 225 S - 3 10 225 OS - 3 2 120 S - 4 10 120 OS - 4 2 225 S - 5 4 56 OS - 5 7 120 S - 6 3 59,6 OS - 6 7 225 S - 7 4 56 OS - 7 0,41 120 S - 8 4 56 OS - 8 0,82 120 S - 11 17 225 OS - 9 0,3 225 S - 12 17 120 OS -10 0,82 225 S - 13 19 225 S - 14 19 120 S - 15 21 225 S - 16 21 120 S - 17 1 460 _. -S - 18 0,5 12 5 - 19 1 25 L

.c.

I

1---T

---

I

~

SR-models, CC - modeis. Model _hmm _Lmm _Rmm Model SR - 1 10 225 1000 CC - 1 14" SR - 2 10 120 1000 CC - 2 25" SR - 3 4 225 250 SR - 4 4 120 250 Cone - cylinder

l'

90

j'

130

t;:j

Nl

-_.

Figure 1_ Model configurations and designalions,

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(27)

-a) Tunnel 5-1

b) Tunnel 5-2

(28)

(29)

a) Model S-I ; Po = 220 b) Shock-wave B. L. in ceraccion Po 126

The widch of each whice band of che scale is 5 mm

c) Model S-17 Po 200 d) Model S-17 - Details

(30)

(31)

e) Model CC-I- ex.

=

0 Xc

=

10 f) Model CC-2 - ex.

=

0 Xc

=

20 g) Model 5-6 ; Po = 201

Po = 198 Po = 196

h) Model 5-18 ; Po = 200 i) Model 5-5 ; Po 209 _j) Model 5-19 Po = 195

(32)

(33)

k) Model SR-2 ; Po 162 I) Model DS-9 Po = 206 m) Model DS-II ; Po 198 n) Model DS-8 ; Po = 205

0) Body of revolution Po =210 p) Contoured wal! of tunnel S-2 ; Po = 750

(34)

(35)

q) Model $-8; Po = 209

u) Model $-7; Po = 208

r) Model D$-7; Po = 194 s) Model $R-3; Po = 208 t) Cavity flow; Po

v) Tunnel $-2; h

=

0.6 mm; Po

=

750 Figure 3. Concluded.

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(37)

a) Shock-wave Boundary-Iayer Interaction Po = 126

b) Model SR-4 ; 197

-'L-.~,.---

__

.~---c) Model SR-2 ; Po 134

(38)

(39)

d) Model 0$-1 Po = 213

e) Model 0$-5 Po = 191

f) Model $-1 _Po = 209

g) Model 0$-1 I p., 198 h) Model CC-I, C(.=o, Xc =20 Po = 115

(40)

(41)

i) Flow over a rectangu lar cavity; Po = 154

j) Model 5-18; Po = 200 k) Model 5-19; Po = 195

(42)

(43)

t

oor 06 OZ OT .' _g _• 1 It) ₀ ~ 11 I j ~ _E

~

E 0 :i 0 N "'

~

9 _x11 U 1 ~ OOT 06 OT E > E

!

M 11 _Vl X l Z U U 0 ~ ...J UJ 0 0 ~ 8

t

OOT 06 08 OL OS OT Ll) UJ g a::: ::> (!) 6 LL 9 N l ll'I 01 ... 8 OOT 06 08 OL OS Or. OT .- - --- - - -6 0 Ir 01 0 ₀ 0 0 0 0 0 0 0 0 0 0

g

n

It) U> t'-- Q) ~ -,- I I I

(44)

(45)

...

• ..

_..

• -

0 E E a

• "-1"' .... , ..

_ -

- - - -

- - - -- --

--x.,o

mm 6S 80 100

I i nes shown

b,

the subl i mat ion teohnique

(46)

(47)

~/& 7 6 5 4 3 m en c

o

i

I

· 1

ID 6,.

~

- c;:r 0: en ": en ('of Cl) ;!. c-o. co en &I)

~

a

_•

• I

Cl)

FIGURE

7. A

6 h '4

-Cl) ('of

-en

I

f

wave length B. L. thick ness step height

I

I I I I I I I I I I 5Q en

(48)

(49)

1 _..

ti

..

_..

J

..

_o

I

"

..

<l

j

/)P:I Pr.f _~Pmovi"l_probe

V\

A

,..

f'\

\J

'\

\

MODEL 5-7 I . JI mm

IV

I!\,

_r\

V

I'()I

_~n

1\

MOD EL $-1

v~

V _\JJ v 1.40 mm \J ~

n

f

~

MODEL s-.~

~q

_'\r

_M

11

r,

~

1.35 mm (

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_I1

fV \

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V

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TCEA TN 3

Centre de Formation en Aérodynamique

Expérimentale

PERTURBATIONS TRI-DIMENSIONNELLES AU REC

OLLE-HENT DE COUCHES-LIMITES LAHINAIRES

SUPERSONI-QUES.

Février 1960. Jean J. Ginoux

L'auteur a montré par ailleurs que des

perturbations régulièrement réparties en en-vergure et répétables existaient dans la

ré-gion de recollement d'une couche-limite

la-minaire supersonique dans l'écoulement au tour

d'une marche descendante bi-dimensionnelle. L'étude a été poursuivie en montrant que l'en-vergure du modèle et l'épaisseur de son bord

d'attaque (lorsqu'elle était inférieure à

0,1 mm) n'avaient pas d'influence sur la

lon-gueur d'onde des perturbations. (voir au verso

TCEA TN 3

Training Center for Experimental Aérodynamics

I

WIINAR SEPARATION IN SUPERSONIC FL~ HITH EMPHASIS ON THREE-DIMENSIONAL PERTURBATIONS

AT REATTACHHENT

February 1960. Jean J. Ginoux

It was shown that regular and repeatable

span-wise flow perturbations existed in the reattachment region of a laminar supersonic boundary-layer on a ~.,o-dimensional backward-facing step model. It was found that the model span and leading-edge thickness, when

below 0,1 mm, had no effect on the wave-length

of the flow perturbations.

On backward-facing steps, at a Mach

num-ber of 2.16, the ratio of wave-length of the

flow perturbations to boundary-layer

.. UJ.Y.ell 1. Ecoulement, com-pressible (1.1.2) 2. Ecoulement, vis-queux (1.1.3) 3. Ecoulement, lami-naire (1.1.3.1) 4. Ecoulement, turbu-lent (1.1.3.2) I. GINOUX, Jean J. 11. TCEA TN 3 1. Flow, compressible (1.1.2) 2. Flow, viscous (1.1.3) 3. Flo"l laminar (1.1.3.1) 4. Flow, turbulent (1.1.3.2) I. GINOUX, Jean 11. TCEA TN 3 TCEA TN 3

Expérimentale PERTURBATIONS TRI-DIMENSIONNELLES AU

RECOLLE-HENT DE COUCHES-LIMITES LAHINAIRES

SUPERSONI-QUES.

L'auteur a montré par ailleurs que des perturbations régulièrement réparties en en-vergure et répétables existaient dans la

la-minaire supersonique dans l'écoulement autour d'une marche descendante bi-dimensionnelle. L'étude a été poursuivie en montrant que

l'en-vergure du modèle et l'épaisseur de son bord

lon-gueur d'onde des perturbations. (voir au verso

TCEA TN 3

Training Center for Experimental Aérodynamics WIINAR SEPARATION IN SUPERSONIC FL~ HITH EMPHASIS ON THREE-DIMENSIONAL PERTURBATIONS

AT REATTACHMENT

It was shown that regular and repeatable span-wise flow perturbations existed in the reattachment region of a laminar supersonic boundary-layer on a ~.,o-dimensional backward-facing step model. It was found that the

model span and leading-edge thickness, when below 0,1 mm, had no effect on the wave-length

(ove.!'l. 1. Ecoulement, com-pressible (1.1.2) 2. Ecoulement, v is-queux (1.1.3) 3. Ecoulement, lami-naire (1.1.3.1) 4. Ecoulement, turbu-lent (1.1.3.2) I. GINOUX, Jean J. 11. TCEA TN 3

1. Flow, compressible

(1.1.2) 2. Flow, viscous (1.1.3) 3. Flo"l laminar (1.1.3.1) 4. Flow, turbulent (1.1.3.2) I. GINOUX, Jean 11. TCEA TN 3

(80)

TCEA TN 3

Une étude détai11ée effectuée à M = 2,16 sur modè1es avec

marche a prouvé que 1e rapport de cette 10ngueur d'onde à l'épaisseur

de la couche-limite était fonction du rapport de la hauteur de la

marche à eet te même épaisseur.

Des perturbations analogues ont été mises en évidence dans la

région de recollement d'une couche-limite laminaire dans les

écoule-ments autour d'une marche ascendante, de coins de compression, de

cavités rectangulaires et dans le cas d'interactions onde de choc couche-limite. Elles ont également été détectées en écoulement non séparé.

Ces perturbations semblent être liées au prob1ème de la

sta-bilité des couches-limites.

Copies disponibles au C.F.A.E., Rhode-Saint-Genèse, Belgique. TCEA TN 3

thickness was a function of the ratio of step-height to boundary-layer thickness.

. Similar perturbations were found at the reattachment region

of a 1aminar boundary-layer on forward-facing steps, on

compression-corners, on rectangular cavities and in the case of interaction

between a shock-wave and the boundary-layer. They were also detected

in unseparated boundary-layers.

The presence of three-dimensional perturbations seems to be

re1ated to the general question of boundary-layer stability.

Copies available at T.C.E.A., Rhode-Saint-Genèse, Belgium.

TCEA TN 3

Une étude détaillée effectuée à M = 2,16 sur modèles avec

marche a prouvé que le rapport de cette longueur d'onde à l'épaisseur de la couche-limite était fonction du rapport de la hauteur de la

marche à ~ette même épaisseur.

Des perturbations analogues ont été mises en évidence dans la

région de recollement d'une couche-limite laminaire dans les

écoule-ments au tour d'une marche ascendante, de co ins de compression, de

cavités rectangulaires et dans le cas d'interactions onde de choc couche-limite. Elles ont également été détectées en écoulement non séparé.

Ces perturbations semblent être liées au problème de la

sta-bilité des couches-limites.

Copies disponibles au C.F.A.E., Rhode-Saint-Genèse, Belgique. TeEA TN 3

thickness was a function of the ratio of step-height to boundary-layer thickness .

Similar perturbations were found at the reattachment region

of a laminar boundary-layer on forward-facing steps, on

(81)

TCEA TN 3

Expérimentale

PERTURBATIONS TRI-DIMENSIONNELLES AU

RECOLLE-HENT DE COUCHES-LIMITES LAMINAIRES

SUPERSONI-QUES.

perturbations régulièrernent réparties en

en-vergure et répétables existaient dans la ré-gion de recollernent d'une couche-limite la

-minaire supersonique dans l'écoulement au tour

d'une marche descendante bi-dimensionnelle.

L'étude a été poursuivie en montrant que

lon-gueur d'onde des perturbations. (voir au verso TCEA TN 3

Training Center for Experimental Aérodynamics

LANINAR SEPARATION IN SUPERSONIC FLa-J HITH

EMPHASIS ON THREE-DIMENSIONAL PERTURBATIONS

AT REATTACHMENT

span-wise flow perturbations existed in the

reattachment region of a laminar supersonic

boundary-layer on a ~~o-dimensional

backward-facing step model. It was found that the

model span and leading-edge thickness, when

below 0,1 mm, had no effect on the wave-length

num-ber of 2.16, the ratio of wave-length of the flow perturbations to boundary-layer

_(O_'{m 1. Ecoulernent, com-pressible (1.1.2) 2. Ecoulement, vis-queux (1.1.3) 3. Ecoulement, lami-naire (1.1.3.1) 4. Ecoulernent, turbu-lent (1.1.3.2) I. GINOUX, Jean J. Il. TCEA TN 3 1. Flow, compressible (1.1.2) 2. Flow, viscous (1.1.3) 3. Flo~ laminar (1.1.3.1) 4. Flow, turbulent (1.1.3.2) I. GINOUX, Jean Il. TCEA TN 3 TCEA TN 3

Expérimentale PERTURBATIONS TRI-DIMENSIONNELLES AU

RECOLLE-BENT DE COUCHES-LIMITES LAMINAIRES

SUPERSONI-QUES.

perturbations régulièrernent réparties en

en-vergure et répétables existaient dans la

la-minaire supersonique dans l'écoulement au tour

d'une marche descendante bi-dimensionnelle.

L'étude a été poursuivie en montrant que

lon-gueur d'onde des perturbations. (voir au verso TCEA TN 3

Training Center for Experimental Aérodynamics WlINAR SEPARATION IN SUPERSONIC FLa-J HITH EMPHASIS ON THREE-DI}ffiNSIONAL PERTURBATIONS AT REATTACHMENT

span-wise flow perturbations existed in the

reattachment region of a laminar supersonic

boundary-layer on a ~~o-dimensional

backward-facing step model. It was found that the

model span and leading-edge thickness, when below 0,1 mm, had no effect on the wave-length

(over) 1. Ecoulement, com-pressible (1.1.2) 2. Ecoulement, vis-queux (1.1.3) 3. Ecoulement, lami -naire (1.1.3.1) 4. Ecoulernent, turbu-lent (1.1.3.2) I. GINOUX, Jean J. Il. TCEA TN 3 1. Flow, compressible (1.1.2) 2. Flow, viscous (1.1.3) 3. Flo~ laminar (1.1.3.1) 4. Flow, turbulent (1.1.3.2) I. GINOUX, Jean 11. TCEA TN 3

(82)

TCEA TN 3

Une étude détaillée effectuée à M ~ 2,16 sur modèles avec

marche a prouvé que le rapport de cette longueur d'onde à l'épaisseur

de la couche-limite était fonction du rapport de la hauteur de la marche à cette même épaisseur.

Des perturbations analogues ont été mises en évidence dans la région de recollement d'une couche-limite laminaire dans les

écoule-ments autour d'une marche ascendante, de coins de compressio~, de

cavités rectangulaires et dans le cas d'interactions onde de choc

couche-limite. Elles ont également été détectées en écoulement non

séparé.

Ces perturbations semblent être liées au problème de la sta-bilité des couches-1imites.

Co pies disponibles au C.F.A.E., Rhode-Saint-Genèse, Belgique.

TCEA TN 3

thickness was a function of the ratio of step-height to boundary-layer thickness.

. Similar perturbations were found at the reattachment region

of a laminar boundary-layer on forward-facing steps, on compression-corners, on rectangular cavities and in the case of interaction

in unseparated boundary-layer$.

Copies available at T.C.E.A., Rhode-Saint-Genèse, Belgium.

TCEA TN 3

Une étude détaillée effectuée à M = 2,16 sur modè1es avec

marche a prouvé que le rapport de cette longueur d'onde à l'épaisseur

de la couche-limite était fonction du rapport de la hauteur de la

marche à ~ette même épaisseur.

Des perturbations analogues ont été mises en évidence dans la région de recollement d'une couche-limite laminaire dans les écoule-ments autour d'une marche ascendante, de coins de compression, de

cavités rectangulaires et dans le cas d'interactions onde de choc

couche-limite. Elles ont également été détectées en écoulement non

séparé.

Ces perturbations semblent être liées au problème de la sta-bi~ité des couches-limites.

Copies disponibles au C.F.A.E., Rhode-Saint-Genèse, Belgique.

TCEA TN 3

thickness was a function of the ratio of step-height to boundary-1ayer thickness .

Similar perturbations were f~und at the reattachment region

of a laminar boundary-layer on forward-facing steps, on