Effect of mach number om streamwise vortices in laminar reattaching flows

<:

x

H

BIBLIOTHEEK

von

KAR MAN

INSTITUTE

FOR FLUID DYNAMICS

TECHNICAL NOTE 26

-EFFECT OF MACH NUMBER ON STREAMWISE VORTICES IN LAMINAR REATTACHING FLOWS

by

Je an J. GINOUX

RHODE-SAINT-GENESE, BELGIUM

TECHNICAL NOTE 26

EFFECT OF MACH NUMBER ON STREAMWISE VORTICES IN LAMINAR REATTACHING FLOWS

BY

Jean J. GINOUX

Brussels University and V.K. I.

CONTRACT NR AF EOAR

65-11

TECHNICAL REPORT NR 1 July

1965

Bibliotheek TU Delft

Faculteit L & R c3027507

111111111111

TABLE OF CONTENTS page ABSTRACT 0 0 0 Q 0 0 0 0 0 0 0 0 • i i NOTATlONS 0 0 0 0 0 0

..

0 0 • 0 0 0 :î.ii LIST OF FIGURES

..

_• 0 0 0 0 0

..

iv INTRODUCTION 0 0

•

0 0 0 0 0 0 0 0 1 WIND TUNNELS AND MODELS 0 0 0 e 0 3 TEST TECHNIQUES 0 0 0 • 0 " 0 • 0 7 RESULTS 0 0 0 0 0 0 0 • • • 0 8 M

=

2.21 _• 0

..

0 0 0 0 • • 0 8 M

=

105 and 2 .15 0 0 • 0

•

0 0 9 M

₌

2.67 0 0 • 0 0 0 • 10 M

₌

503 ; 6.0 and

7

00 " 0

•

0 11 DISCUSSION OF THE RESULTS 0 0 0 0 13 CONCLUSIONS 0 0 0 0 • 0 • 0 • 15

ABSTRACT

An exp~rimenta1 investigation has been made in various supersonic and hypersonic wind tunnels at VKI to determine the effect of Mach number on the existence of streamwise vortices in the reattachment region of the flow over two-dimensional backward faci ng stepso It was found that the phenomenon

previ-ously observed at M

=

2021 remained unchanged over a Mach number range of 105 to 7000 The ratio of the wave length of the vortices

to the boundary layer thickness at separation varied slightly with free stream Mach number~ with a maximum at about M

=

30

SOMMAIRE

Une étude expérimentale a été effectuée dans plusieurs souffleries supersoniques et hypersoniques de l Vlnstitut von

Karman. pour déterminer l'effet du nombre de Mach sur l 'existence de tourbillons 10ngitudinaux dans la zone de recol lement d'

écou-lements plans autour de marches descendanteso On a trouvé que

le phénomène observé antérieurement à M = 2,21 se reproduisait sur une gamme de nombre de Mach s ' étendant de la5 à

7

_aOo Le rapport entre 1a longueur dionde du phénomène et liépaisseur de

la couche limite au décollement variait peu avec le nombre de

h L M Re ö À m NOTATlONS

step height in millimeters

length of flat plate upstream of the step, in milli

-meters

free stream Mach number

free stream Reynolds number. based on a length of

one inch

boundary layer thickness at separation

wave length or spacing of the flow perturbations e

It is the distance between successive pitot pressure

peaks or st ri ations in the sublimation picturese

is a mean value of Ào It is the ratio of a certain basic

spanwise l ength di vided by the number of pressure

LIST OF FIGURES

1 - Tunnel S-l 2 - Tunnel S-2 3 - Tunnel S-3 4 - Tunnel H-l

Test section and step modelo

M

=

105 nozzle with backward facing step.

with step model.

with wedge t i l t nozzle and step modelo

5 - Summary of previous results at M

=

2021.

6 - Schlieren picture of the flow around a 2 mm step at M

=

l Q50 Tunnel S-20

7 - Sublimation picture of the flow around a 2 mm step at M

=

1050 Tunnel S-20

8 - Summary of the results over the range 105 < M < 700, based on the computed bpundary layer thickness o

9 -

Summary of the results over the range 105 < M < 7.0, based on the measured boundary layer thicknesso

10 - Schlieren picture of the flow around model 2 at M = 2 0670

Tunnel S-30

11 - Flow visualization with fluorescent oil M

=

20670 Tunnel S-3g a) Model 5 h

=

1 mm

b) Model 2 h

=

2 mmo

12 - Sublimation picture of the flow over the front portion of model 2; M

=

2.67

Tunnel S-30

13

-

Sublimation picture of the flow around a 2 mm step at M = 503 Tunnel H-la

14

-

Sublimation picture of the flow around a 2 mm step at M

=

7 00

Tunnel H-lo

15

-

Sublimati on picture of the flow around a 4 mm step at ~

=

7 00 Tunnel H-lo

16

-

Sh adowgraph of the flow around a 4 mm step at M

=

503 Tunnel H-lo

INTRODUCTION

Previous studies0 made at VKI at a Mach number of 2021.

have revealed the existence of regular patterns of equidistant counter-rotating streamwise vortices in the laminar boundary layer of several types of reattaching two-dimensional flows

(1.2.3)0 These vortices constitute one step in the process of transition from laminar to turbulent flowo

In a systematic study made downstream of reattachment on backward facing step model s, the spacing of the streamwise vortices was found to be a function of boundary layer thickness at separation and step-hei ght o The presence of the vortices did

not change much the ave rage heat transfer rate over the span of the model, in the reatt achment region. but locally they produced large peaks in the heat rate~ l arger than the values previously known for turbulent flowso

The phenomenon is of practical interest, for instanee

in the case of control surfaces on high speed bodies0 especially at hypersonic velocities where extensive laminar boundary layers exist. The effect of these vortices on heat tr.ansfer was recently qualitatively reconfirmed by Mi ller et alG at Boeing Company

(4)

who observed regular striation patterns scorched into the stain-less steel surface of their flap models during hot shot wind tunnel tests at high Mach numberso Simi lar patterns were also noticed at the surface of a nozzle under similar conditions by Little at Lockheed Georgi a Companyo

The purpose of the present study was to find out if the streamwise vortices. initi ally detected at M

=

2021. existed

over a wider range of Mach number and in particular to deter-mine the effect of Mach number on their spacingo Some of the

resu1ts presented here were obtained in the course of research projects undertaken by VKI students (5~6.7.8)o

The research waS sponsored by the Air Force Office of Scientific Research~ OoAoRo through the European Office

WIND TUNNELS AND MODELS

The tests were made at the von Karman Institute for

Fluid Dynamics o Four different supersonic and hypersonic wind

tunnels were used to cover the Mach number range 105 to 700,

as indicated ~n table I. where stagnation conditions and free

stream Reynolds numbers are also showno

S-l is a continuous closed circuit wind tunnel which

has a test section of

40

x 40 cm 2 (16" x 16") 0 It is operated

at stagnation pressures lower than the atmospheric pressure.

The stagnation temperature is approximately the room temperature ~

TABLE I

Wind tunnel M Stagnopresso Stagn 0 temp 0 Re

psi OK per inch

S-l 2a21 2 to 4 288 5.0 104 S-2 105 14 288 387 105 2015 14 288 ' ,,3 105 S-3 2067 56 288 905 105 I H-l 5.3 450 373 1.,4 106 6.0 450 450 8.0 105 7.0 450 623 3.2 105

The designation and main dimensions of the models are given in table 11, where (h) is the step height and (L) the

length of the flat plate upstream of the stepo Models completely spanned the 16" test seetion except 8-6 and 8-7 having a 150 mm span and S-8 with a span of 250 mmo A typical model in the test seetion is shown in figure 10

Model 8-1 8-2 8-3 8-4 8-5

s-6

8-7 8-8 8-11 8-12 8-13 8-14 8-15 Table 11 h(mm) 15 15 10 10 4 3 4 4 17 17 19 19 21 L(mm) 225 120 225 120 56 60 56 56 225 120 225 120 225 Model 8-16 8-17 8-18 S-19 DS-l D8-2 D8-3 D8-4 D8-5 D8-6 D8-7 D8-8 D8-9 DS-l0 h(mm) 21 1 0.5 1

4

4

2 2 7 7 00

4

0 08 L(mm) 120 460 12 25 120 225 120 225 120 225 120 120 225 225

S-2 is a very small continuous wind tunnel with a ·test section of 15 mm x 15 mm (i oe. about 1/2" x 1/2") 0 Dry air is sucked in through the nozzle by the vaeuum pump that is used to maintain tunnel 8-1 at its low pressure levelo Tests were made

on baekward faei~g steps maehined ~n the nozzle bloek itself. aS shown in figure 2e Step heights of 00 5 mm and 2 mm at M = 2015

and of 00

7

mm. 104 mm and 2 mm at M

=

105 were usedo

S-3 is a blowdown tunnel ejecting air to the atmospheree

It has a test section of 5 x 6 cm2 (ioe. 2" x 2.5")0 lts running

time is of about two minutes when using its own independent air supply (160 cuft at 560 psi). but can be much longer when con-nected to the air supply of the hypersonic tunnel H-l (2000 cuft

at 560 psi)o Models completely spanned the working section of the tunnel. The designation of the models is shown in table 111

together with the main dimensions. L is the length of the flat plate upstream of the suep and h the step height.

Table 111

Model nr 1 2 3 4 5 6

L mm 20 20 25 20 15 25

h mm

The nozzle walls had to be modified downstream of the test section to avoid tunnel blockage. This is shown in figure 3, which is a picture of the 2.67 Mach number nozzle with a step

model in the test sectiono

H-l is a blowdown tunnel with an effective test

section of 120 mm x 120 mm (i.e o about 5" x 5"). It is equipped

with a contoured rectangular nozzle for M

= 5.3

and wedge t i l t blocks for the Mach number range

6

to

8.

The running time is two minutes at a stagnation pressure of 450 psi. The test section is connected between a 2000 cubic feet reservoir pressuri~ed

at 560 psi and a back pressure lowered to 7 psi absolute by a sUipersonic ejector us'ing the same air supply. A pebble bed

heater is used to preheat the air up to 500 o CoThe model span

was 120 mms the flat plate length ahead of the step 60 mm and

step heights of 2 mm0 4 mm and 6 mm were usedo A photograph

TEST TECHNIQUES

Each tunnel was equipped with its own schlieren and

shadQw system. Flow pictures were taken with spark light sourees

of small duration timeo

Surface flow visualizations were made by a sublimation

technique using azobenzene or acenaphthene as indicators. The

response time varied between a few seconds and several minutes

depending upon the type of indicator. its thickness (of the

order of a few hundredths of a mm) and the flow conditions.

~he fluorescent oil technique was also used.

Vertical and spanwise surveys of the boundary layer

were made with small pitot probes. Statie pressures were

measured at the surface of the mod~ls •

RESULTS

A summary of the results previously obtained (1) at a free stream Mach number of 2021, is shown in figure 5 where (À)

is the wave-length or spacing between two pairs of streamwise vortices, (ó) the boundary layer thickness at separation and

(h) the step heighto

À was determined from the results of spanwise surveys of the boundary layer, downstream of reattachment, with small pitot pro~es or from the sublimation picturese À was taken as the distance between successive pitot pressure peaks or

stria-tions of higher sublimation rates o À was not strictly constant

over the span but varied within the range indicated by ~he bars in figure

50

For each test, a cross indicates the mean wave length (À ,) defined as the ratio of a certain basic spanwise

m

length divided by the number of pressure peaks recorded along that length c

Values of (ó) were computed, for an insulated flat pla te, from the the ory of eh apman an d Rubesin (9) at a di s t an ce

L from the leading edge, where the backward facing step was

located~

The results of figure 5 have been envelopped by two curves which will reappear in figure 8 where the results obt,ined. at various Mach numbers are comparedo

M

=

le5 and 2015

Because of the &mall si ze of tunnel S-2, i t was diffi-cult to mount a model in its test secti on and therefore the measurements were made di rectly at the wallof the nozzleso Fi gure 2 shows the M

=

105 nozzle and the backward facing step located in the flat wal1 in the test rhombus where uniform flow was achieved.

The boundary 1ayer velocity profile was measured with a sma1l pitot probe,just upstream of the step, to ensure th at laminar flow exi sted and also t o determine the boundary layer thickness whi ch could not be accurate1y calculated in the present case o ö was found to be 0~73 mm at M

=

105 and 0 .45 mm at 2015, the step being located at a different distance from the throat in each of the two caseso

Step heights were seleeted with a view to havi ng laminar flow reattachments . This was checked by comparing the measured base pressure to Chapman' s theoretical value (10) and from

schlieren pictures. An example is given in figure

6

for h

=

2 mm and M

=

1.50

The wave length À of the vortices was determined. downstream of reattachment, by spanwise surveys of the boundary layer with a ~mall pitot probe and checked with the results given by the sublimation pictures0 An example is given in

figure 7 for h

=

2 mm and M

=

105; t he step is seen as a bright l ine located ha1f-way between the third and fourth statie pres-sure orifice~.starting from the left side of the p~otographo

The results are shown in figure 8. where the ratio

À/ö is plotted versus h/ö and compared with the M

=

2021 dataQ

It is seen that they fall between the two envelopes of the

M

=

2.21 results from figure 50 The latter were referred to the calculated boundary layer thickness. while the S-2 tunnel results were based on the measured ö o Surveys made at M

=

2021 showed that the actual value of ö was about 20% higher than its theo-retical value o If one takes this effect into account~ the

agree-ment between the M

=

105 and 2021 results is slightly betteri

as shown in figure 8. where the measured boundary layer thickness is usedo

Figure 10 is a schlieren picture of the flow around a 2 mm step model at M

=

2067 0 À was det~rmined donwstream of

reattachment from surface flow visualization with fluorescent

oil. examples of which are given in figures lla and llb. for h

=

1 mm and h

=

2mm respectivelyo In one case the test was

repeated with a longer running time with the sublimation tech-nique, it gave essenti ally the same resultso Such a comparison

of the results of both techniques had already been done

success-fully by Hopkins et alo (11)0

The values of À. referred to the computed boundary

layer thickness at separation are shown in figure 8 and compared

with the M

=

2021 resultso It is seen that they are much larger

than those measured at lower free stream Mach numbers o It might have been caused by the fact that the flow was not fully laminar

as in the other tests o Indeed. i t is se en in the sublimation

picture of figure 12 (whic~ shows a top view of the front part of the 2 mm step model) that turbulent wedges existed on the

plate upstream of separation

(*)0

Furthermore. a boundary layer

survey with a small pitot probe gave a thickness of about Oa4mm on model 2 just upstream of the step instead of 0 02 mm calculatedo

Based on this value of ö. the À/ö results at M = 2 067 then lie

closer to the zone covered by the M = 2021 data, though they are

st i 1.1 1 a r ge r 0

M = 5 0 3; 6 0 0 an d 7 0 0

The wave length À was determined from sublimation

pictures at M = 5.3, 6 and 7 and also from spanwise pitot surveys of the boundary layer downstream of reattachment at M = 5e3o

Examples of sublimation pictures are sh'own in figures 13 to 15 f 0 r h = 2 mm at M = 5 0 3 an d 7 0 0 an d f 0 r h

=

4 mm at M = 7 0 0 respectivelyo Transition was located downstream of reattachment aS shown for instance by the shadowgraph of figure 16 for h=2 mm and M = 5030

The boundary layer thickness ö was computed from the theory of Chapman and Rubesin_a assuming an insulated flat plateQ In fact, due to the small running times of tunn~l H-l. the

models never reached complete equilibrium SD th~t the actual wall temperat ure varied during the tests with time and with

distance from the leading edge, being always lower than the

recovery temperatureo Some of the tests were rep~ated wi th

different stagnation temperatures of the tunnel, even lower than necessary to avoid liquefaction; they did not show any

(*)

Previous studies showed that the transition Reynolds number in tunnel S-3 is fai ly low e

change in ~ within the usual scatter of the datao

The ratio ~/ö is p10tted versus h/ ö in figure

8,

~for

the three Mach numberso These resu1ts fa11 approximately within

the en~opes of the M

=

2021 datao However, when using the measured value of ö, which was aboUt twice aS large as the computed value for M

=

503 and 700, the corresponding ratios

~/ö become Smaller than the M

=

2021 val ues. as shown in figure

90

DISCUSSION OF THE RESULTS

Three dimensional perturbati ons appeared systematically

at reattachment over the whole Mach number range; 105 < M <

7

000

They were detected by the existence of rather regular spanwise

pitot pressure variations in the boundary layer downstream of

reattachment and/or by the presence of regular striation patterns

shown by the sublimation technique o As these pressure variations

and striations were shown to be caused by counter-rotati~g

streamwise vortices in the previous studies made at M

=

2021 (3),

i t can be concluded that these streamwise vortices existed over

the whole Mach number range covered in the present studyo It is

interesting to note that the tests were made in four different

wind tunnels and that in one case (at M

=

1 0

5)

the model had no

leading edge_i the step being located in the wallof the nozzle o

Moreover, aS a similar phenomenon was systematically observed

in various types of laminar separated flows,at M

=

2021 (ioe e

over cavities, forward facing steps and ramps on a flat plate

and also in shock wave boundary layer interactions), there is

no reason to believe af ter the present investigation that they

do not also e,xist at other Mach nU'Inberso The phenomenon is

therefo.re of a wide interest o

Figure 9 shows that the mean spac~ng of the flow

per-turb(1tions,; i . e o',,' the '

a,ve:f~g~

'

distance .between successive pairs

~ . ' . ~ .

o'f cQunter rot,Br't.ipg vQrti'ces. referred to the measured boundary

l,a,yer thickness. vari'es '

o~

'i

y

slightly with Mach number as compared

to the scatter of the datao It va~ies between say 105 and 300

with a maximum of 30 0 at' a Mach number of 205 to 30 00 It is

possible that this is relatedto the existence of a minimum

transition Reynolds nu~ber which was found over a flat plate

undoubtly related to the transition process o Further tests at

Mach numbers of' 300 to 305 should be made .to conf'irm the

exis-tence of this maximum value of À/ö ~ they were not available in

the course of' the present study.

It is also seen f'rom figures 8 and 9. that the plateau value of' À/ö~ detected earlier at M

=

2021 over the range 3 < h/ö < 7. was not but little indicated at other Mach numberso However. a range of' step heights larger than used here

CONCLUSIONS

It is conc1uded from the present investigation that regu1ar patterns of streamwise vortices, previous1y observed in 1aminar two-dimensiona1 reattaching f10ws at M

=

2Q21, as

as result of boundary 1ayer instability, exist at least over the Mach number range 105 < M < 7~O~

The ratio of the wave length of the vortices to the measured boundary layer thickness at separation varied slight1y with the free stream Mach number, with a maximum at about M

=

30

REFERENCES

10 GlNOUX; JoJo g The existence of three dimensiona1 perturbations

in the reattachment of a two-dimen~ional supersonic

boundary layer af ter separationo

AGARD Report 272; April 1960 0

20 GINOUX_a JoJo g Leading edge effect on separated supersonic flows o

proceedings of the lCAS, Third Congress. Stockholm 1962.

30 GlNOUX, J oJ og Streamwise vortices in laminar reattaching flowso

Recent developments in boundary layer research o

AGARDograph 97, part I - Naples, May

19650

40 MlLLER, DoSo et aliig Mach 8 to 22 studies of flow separations

due to deflected control surfaces.

AlAA Journal, volG 2, n02, Fe~ruary 1964 .

50 REY du BOlSSlEU~ JoL.: Etude du recollement d'une couche

limite laminaire s~personique derrière une marche en

écou1ement bi-dimensionnel.

CFAE PR ~9-9, juil1et 19590

60 ARNOLD, KeOGg Experimental investigation of three dimensional

perturbations in the reattachment of a two-dimensional

boundary layer af ter separation at M = lo~o

TCEA PR 60-24, June 1960.

70 HOLMGREEN. SoAo: Experimental investigation of three dimen~

sional perturbations in the reattachment region of a

two dimensional boundary layer af ter separation at M=2 067

8. ESCH. Ho ~ Investigation of three dimensi ona1 perturbations in 1aminar separated f10ws at hypersonic Mach numbers. VKI 64-103. ~une 1964.

9. CHAPMAN. DoR. & RUBESIN. MoWo: Temperature and velocity pro-files in the compressib1e 1aminar boundary 1ayer with arbitrary distribution of surface temperature o

J.A.S. Sept ember 1949.

10. CHAPMAN, DoR., KUEHN, D.M. & LARSON, H.K.: Investigation of separated f10ws i n supersonic and subsonic stream with emphasis on the effect of transition.

NACA TN 3869, March 1957.

11. HOPKINS. EoJ. , KEATING, S.J. & BANDETTINI, A. : Photographic evidence of streamwi se arrays of vortices in boundary 1ayer flow.

NASA TN D-328 , September 1960.

12. PROBSTEIN, R.F. & LIN. C.C. : A study of the transition to turbu1ence of the 1aminar boundary 1ayer at supersonic speeds.

Paper present ed at the lAS 24th Annua1 Meeting, New York. J anuary 1956.

Figure 2. Tunnel 8-2 - 1&5 Mach numb~r nozzle with backward facing step

5 4 1

o

IJ') o

....

cf)

[~

I

JL~~~---~~--- N cf) ~ wave length Ö B. L. thickness h step height 3 4 5 6 7 8 9 10 11 12 13 14 h/Ö

Figure

7.

8ublimation picture of the flow around a 2 mm step

10

l

Ei 9 8 7 6 5 4 3 2 1

o

o M= 2~5 - M = 2.21(envelopes) tunnel 5 1 T or I M = 2.67 tu nnel 5 3 I

...

....

_: M = 5.3

.

... _T

-I

M=6 :I: _I QI 1 c _I T _M=7 c ::3 I I

.

-J. _{I (")} I I

+

QI ~ 1 '0 ₀ QI _I lD _I ~ '0 _I 0 QI 1 'T ~

~

'0 I I 0 _I T _I ~ I _I I _I T _I I 1 _I I I

*

I _I oL I 1 _I N _I

1

I ClI I I~ ol '0 I 0 I 1..-: ~ _I I 11 IoC I .::. ol J.C' _(, ClI

.

'0

•

.

0

..

~ 2 4 6 8 10 12 14

Figure 8 SUM MARY OF THE RE SUL TS OVER THE RAN GE 1.5<M<7.0 BASED ON THE COMPUTED VALUE OF 5.

9 8 7 6 5

o

I

tunnel 52 o M= 2~5 - M = 2.21 (envelopes) tunnel 51 T : M= 2.67 tunnelS 3

-

,..

1

M= 5.3

I

M=6

T

M=7 .L I/') CII "0 0 ~ tunn el H 1 N CII "0 0 ~ T I I I I CO) I I

L

I o I

Figure 9. 5UMMARY OF THE RE5ULT5 OVER THE RANGE 1,5< M <7.0 B,A5ED ON THE MEASURED BOUNDARY LAYER THICKNE55.

b) Model 2 - h=2 mm

Figure 14. Sublimation picture of the flow around a 2 mm step

l,j.,

EFFECT OF MACH NUMBER ON STREAMWISE VORTICES

IN LAMINAR REATTACHING FLOWS, by J.J. Ginoux.

An experimental investigation has been made in

various supersonic and hypersonic wind tunnels

at VKI to determine the effect of Mach number

on the existence of streamwise vortices in the

reattachment region of the flow over two-dime

n-sional backward facing steps. It was found that

the phenomenon previously observed at M ~ 2.21

remained unchanged over a Mach number range of

·C

-

W +noq~ +~ wnw~x~w ~ q+~M IJaqwnu qo~W

w~aJ+s aaJJ q+~M Al+q~~ls pa~J~A uOl+~J~das +~

ssau~o~q+ JaA~l AJ~punoq aq+ 0+ sao~+JOA aq+

JO q+~ual aA~M aq+ JO o~+~J aq~

·o·L

0+ Ç·l

1.5

to 7.0. The ratio of the wave length of

the vortices to the boundary layer thickness

at separation varied slightly with free stream

Mach number, with a maximum at about M -

3.

JO a~u~J Jaqwnu qo~W ~ JaAO pa~u~qoun pau~~waJ

l G·G ; W +~ paAJ9sqo Alsno~AaJd uouawouaqd aq+

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aq+ u~ saol+JoA 9S1MW99J+S JO 90ua+slxa aq+ uo

J aq r~ qo~W JO +o_JJa aq+ aUl wJa+ap 0+ I~A +~

sl9uun+ pU~M 0lUOSJ9dAq pu~ OluOSJadns sn01J9A

UI 9~~W uaaq S9q U01+9~1+saAul 1~+uaw~J9dxa uV

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S88I~HOA 8SIMWV8H~S NO H8gWilN H8VW ~O ~88~~8

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EFFECT OF MACH NUMBER ON STREAMWISE VORTICES

IN LAMINAR REATTACHING FLOWS, by J.J. Ginoux.

An experimental investigation has been made in various supersonic and hypersonic wind tunnels

at VKI to determine the effect of Mach number

on the existence of streamwise vortices in the

reattachment region of the flow over two-dimen-sional backward facing steps. It was found that

the phenomenon previously observed at M ~ 2.21

remained unchanged over a Mach number range of

. ( - W ~noq~ ~~ wnwlx~w ~ q~lM 'Jaqwnu qo~W

w~aJ~S aaJJ q~lM Äl~q~11s palJ~A U01~~J~das ~~

ssau~olq~ JaÄ~l ÄJ~punoq aq~ o~ saol~JoA aq~

JO q~~ual aA~M aq~ JO 01~~J aq~

·o·L

o~ Ç·l

1.5 to 7.0. The ratio of the wave length of the vortices to the boundary layer thickness

at separation varied slightly with free stream

Mach number, with a maximum at about M -

3.

JO a~u~J Jaqwnu qo~W ~ JaAO pa~u~qoun paul~waJ

lG·G

=

W ~~ p9AJ9SqO Älsn01AaJd uouawouaqd aq~

~~q~ punoJ S~M ~I ·sda~s ~ulo~J pJ~M~O~q t~uOls

-uawlP-oM~ JeAO MOtJ aq~ JO U01~aJ ~uawqo~~~~aJ

aq~ Ul saOl~JoA aS1Mw~aJ~S JO eoua~slxa aq~ uo

Jaqwnu qo~W JO ~oaJJa aq~ aUlwJa~ap o~ I~A ~~

slauun~ PU1M 01UOSJ9dÄq pu~ 01UOsJadns sn01J~A

Ul ap~w ueaq s~q U01~~~1~saAul 1~~U9wlJedxa uv

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