On the existence of cross flows in separated supersonic streams

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VUEGTUIGSOUWKUNDIi

TRAINING CENTER FOR EXPERIMENTAL AERODYNAMICS'

TECHNICAL NOTE 6

ON THE EXISTENCE OF CROSS FLOWS

IN SEPARATED SUPERSONIC STREAMS

BY

J.J.GINOUX

RHODE-SAINT-GENESE, BELGIUM FEBRUARY 1962

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VTl

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MONITORING AGENCY DOCUMENT NR ASTIA DOCUMENT NR

TCEA TN 6

ON THE EXISTENCE OF CROSS FLOWS IN SEPARATED SUPERSONIC STREAMS

b y

Jean J. Ginoux

Brussels University and TCEA

CONTRACT NR AF 61(052)-350

LAMINAR SEPARATION IN SUPERSONIC FLOW TECHNICAL NOTE NR 2

February 1962

The research reported in this document has been sponsored by the Air Force Office of Sçientific Research, through the European Office, Aerospace Research, United States Air Force.

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1.

NOTATION

'X distanee along the centre-line of the model froIJl the step base; X>O downstream of the step

~ span-wise axis, positive as indicated in figure 2 2.

àF

distanee between the flow fenees

L

length of the flat plate ahead of the step ~ height of the baekward facing step

S

span of the model

~

boundary-layer thiekness just before separation

e

momentum thickness just before separation

~ statie pressure on the model surface b free-stream statie pressure

plO

.M.

_{oo free-stream Maeh number}

*

SUMMARY

An experimental investigation was made on laminar separated supersonie streams using two-dimepsional qaekward-facing step models. It was shown that a cross-flow existed in the separated region of the flow whieh

is associated with the side wall boundary~layers. lts effeet is to deerease the base pressure and increase the pressure gradient at reattaehment even for large values of the model-span to step-height ratio. It is shown that the eommonly accepted assumption that a two-dimensional flow exists when there is no measurable spanwise pressure variation is a neeessary but not suffieient eondition.

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2.

In the turbulent case, it is gene'rally found that the measured base pressure is lower than is theoretically predicted. This is explained by the existence of a cross-flow (suction) produced by strong vertical vortices near the side walls.

*

INTRODUCTION

In the course of an experimental investigation, made on two-dimensional backward-facing step models, to study the effect of gas injec-tion on laminar separated supersonic flows (ref. 1), some doubt arose as to the possibility of obtainirtg a strictly two-dimensional flow even for a ratio of model-span to step-height as large as forty.

Although no spanwise statie pressure variation could be deteeted in the central portion of the model, the introduction of longitu-dinal fences in the region of separation had foreffect to increase the base pressure and decrease the pressure gradient at reattachment by a few percent.

It was then decided to investigate this effect more systemat-ically by using ~ step model fitted with fenees of various shapes and locations.

The results obtained for the laminar case were extended to turbulent separated flows by using available data from other sources in

order to explain the fact that measured values f b _{o a s e pressure are}_gener~lly ,lower than those predicted by theory.

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3.

DESCRIPTION OF TEE EQUIPMENT

Wind Tunnel

The tests were made in the TCEA 40 cm x 40 cm (16" x 16") continuous supersonic wind tunnel S-l at a Mach number of 2.21 and a

stagnation pressure of 150 millimetres of mercury absolute (5.9 inches Hg). A description of the tunnel is given in reference 2.

Model Confisuration

The tests were made on backward facing step mode1s that com-p1ete1y spanned the working section of the tunnel. Two mode1s were used, having the same step height (10 mm., i.e. about 0.4 inch). The ratio of model-span to step-height was therefore equa1 to forty. The two mode1s differed by the 1ength (L) of the flat p1ate ahead of the step (figure 1).

MODEL 5-3 MODEL S-'-\ Pressure measurements L". 2.2.\ m'\1l. L :: -115

mm.

Figure 1

The statie pressure was measured a10ng the centre-1ine of both models, by the pressure holes indicated in figure 1. The pressure recorded by pressure ho1é n° 1, located 22 mm upstream of the step, was equa1 to the

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free-stream statie pressure (PO' )9 while the pressure measured at orifiee n° 2 was lower than p~ by about 5%. This was most probably due to the upstream influenee of the expansion wave formed at the edge of the step.

The spanwise statie pressure distribution was measured in the

separated reg ion of the flow by seventeen orifiees loeated 30 mm downstream of the step~base.

The pressures were measured by a differentia1 pressure trans-dueer and indieated on a strip chart recorder. Rotary valves» .1oeated in-side the tunnel» were used to conneet all the pressure orifiees to the same transducer whieh was calibrated to within one percent accuraey.

Flow Fences

y

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s.

Fenc8s were used to isolate the central portion of the

separ-ated flow from the side regions, as shown in figure 2, where (R) is the

reattachment line of the supersonic flow. The thickness of the fences was 0.4 mm (0.016 inch). Various shapes (either triangular or rectangular

fences) were used, which gave essentially the same results.

The fences were located at various distances (zf) from the

centre-line of the model. In each case, they were glued to the model along

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6.

LAMINAR BOUNDARY LAYERS

The statie pressure measured at (z

=

0, x

=

30 mm) was refer~ red to the free-stream statie pressure (Pao) and plotted versus the distance

(zf) of the fences from the centre~line of the model. This is shown in figure 3 by curve (a) for model S-3 and by eurve (b) for model 8-4. The

.70 pIp 00 .65

o

--..:---.-.60

o

.55

o

50 100 150 200 Figure 3

stagnation pressure was equa1 to 150 mmHg absolute and the stagnation temper -ature was about 2930 _K. _{The po}_i_n_t _s _l_ab_ell_{ed (0) o}_n _t_{he r}_i_{ght of figure 3}

eorrespond to the base pressure levels for tha models in the absence of fences. Curve (a) shows that the base pressure inereased by 6% by instal

-ling the fences in positions 19 11» 111 and IV. For position V, this increase was equal to 7%, while it was of on1y 5% for position VI (no explanation was found for these differenees which ware also observed on model 8-4, as shown by curve (b».

The effect of the fences on the statie pressure distribution, measured along the centre-line of the model (z

=

0) is given in figures 4. It shows that the maximum pressure gradient decreased by 14% on model S~3

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1.0t---r---~~~~=_~----~7

pip 0'0 .90 .80 .70 .60 1.0 pip Gc.:l .90 .80 .70 .6 a) Model 8-3 [] without fences () fences in position IV

f

0 10 x/h 1 !\ b) Model 8-4

[J

without fences

o

fences in, position IV

I

O)---5t---ï.O~----~x~---J

Figure 4

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MODEL S - 4 MODEL S - 3

::~:B:~

::

~

.

=

~

-1.0 -.S 0 .S' ".0 -.0

,

-.5""

· 5 · 0 ~~5 2z/. . Figure 5 /s . ,

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9.

and 11% on model S-4, when the fences were introduced.

The spanwise pressure distributions are given in figure 5 for

various positions of the fences. They show a reduction of the base pressure

in the side-re~ions as compared with the pressure measured without the fences.

It is also seen that the side pressure is 10wer than the pressure measured between the fences (by 17% on model S-3 and by 19% on model S-4 for position IV of the fences). The latter is found to be constant a10ng the span, at least within the accuracy of themeasurements. Without the fences, it is near1y constant except near the sides where it is 10wer by 3 to 4 percent.

The fact that the flow was different between the fences than

in the side~regions is i11ustrated on the schlieren pictures of figure 6, by

the existence of double shock-waves and expansion-waves. Without fences on1y

one shock and one expansion wave are observed. ( see pa~e 11 )

*

At a stagnation pressure of 150 mmHg, a laminar boundary-layer

existed p~ mode1s S~3 and S-4, transition being 10cated downstream of the

reattachm~nt zone of the flow. However, because of the turbulent

boundary-layers that existed on tbe side wa11s_of the test section, a lateral turbulent

contamination of the 1aminar boundary-layer was present. This was observed,

. ,

spreading at an ang1e of about 6 degrees, b~ using a sublimation technique

to visua1ize the flow on the surface of the model; the resu1ts are schematic-a11y shown in figure 7 for both mode Is.

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wind

<l

side wall 60 side wall 60

---

----___ tàà

220 115 111 (!I

I

0 w ~ UI _Lamina ~ Laminar I.!I I-~ :2 C!l <:) Q V) Q .::t < IlJ Turbulent ..J Turbul

--:-;

-

---0 Side wall MODE\... ;:'-3 .MODEL S-~

Top view of the Models

Figure 7

Because of separation and reattachment, a further lateral

spreading of turbulence was noted as shown in the figure by the displacement fiz. Therefore, the laminar flow did not cover the full span of the modelsp but only 85% of the span on model S-3 and 92% on model S-4.

By installing the fencesp the laminar separated flow is isolated from the two side-flows which are partly turbulent. As aresult, the base~

pressure is lower in the side-regions~an~ in the central portion of the flow.

By removing the fences, there is a tendency for these pressures to equalize

and therefore a cross-wind is established in the separated region of the flow,

from the centre-line towards the sides of the model.

Such a cross flow produces the same effe~~ as a suction of air

from the centre portion of the flow. It is known that only a small amount of suction has a large effect in decreasing the base pressure and increasing the

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\.J'ITHOUT

FENCES

Position II

Position IIl

Position V

FIGURE 6 - Schlieren pictures of the flow around model S-4

---

,

1-' I-'

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pressure gradient of reattachment. For example, it can be seen from the

results of reference 1, that the 6% variation of the base pressure which was observed on model 8-3 by removing the fences, could be obtained by sucking,

from the central portion of the flow, only 2.5% of the total mass flow in the boundary-layer computed at separation; quantity which is indeed very small.

It is commonly assumed that a two-dimensional separated flow

is obtained on a two-dimensional model when there is no spanwise variation of the static pressure or when a straight reattachment line is observed near the centre-line of the model. The present study showed that this condition,

although necessaryp is NOT SUFFICIENT for the existence of a TRUE two=dimen-sional flow. Even when this condition is satisfied (within reasonable limits

of measurement), the base pressure can differ significantly from its true two-dimensional value. The difference increases by increasing the length of

the flat plate upstream of separation and it is expected that it will increase

considerably by reducing the ratio of model-span to step height.

TURBULENT BOUNDARY LAYERS

A comparison is made in figure 8 between experimental and

theoretical values of base pressures in the case of turbulent boundary-layers

flowing over two=dimensional backward facing steps. Theoretical values

(reference 3) are based on the assumption that a fully developped velocity profile exists in the jet mixing reg ion, which is the case for a thin

approach-ing boundary-layer (upstream of separation). In this case, the lowest value of the base pressure is obtained, as the theory predicts an increase of base

pressure when the mix~pg profile is non-fully developpedp i.e. when the

approaching boundary-layer is thick.

Asp in most of the practical cases, the approaching

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which is higher than theoretically predicted. This does not seem to be true

as figure 8 shows that experimental values either fall on the theoretical

curve Or lie below.

*

* *

An asymptotic value of the base pressure was recently measured by Sirieix (reference 4) at a Mach number of 2.025. By increasing the step-height from 10 to 25 mm, for a given approaching turbulent boundary-layer,

he found that the base pressure ratio (pIpa:> ) decreased fr om 0.375 to 0.325;

that is, from a value which was 7% higher than Korstls value (0.350) to a

value 7% lower. By extrapolating the results.towards an infinite step height,

be found an asymptotic value of 0.30 wbieh is 14% lower than theoretieally

predieted (figure 8).

However, by inereasing tbe step height, Sirieix deereased the

ratio of model-span to step-height from 8.0 to a value as low as 3.5. He

earefully investigated tbe effect of sueh a small ratio, by insta1ling fences in tbe separated region of the flow and a1so by measuring tbe statie pressure distributions on and off the eentre-1ine of bis model. He concluded

that there was no important span effect.

Also shown in.figure 8, is a value of the base pressure measured by Maddox (reference 5) at a Mach number of 2.66 which is 18%

lower than tbe theoretical va1ue, altbough the approaching boundary layer

was thick (approximately one third of tbe step-height). In these tests,

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15 0.7

p/p~

_KEY

0

CHAPMAN 0.6

•

_EGGINK

6

oNERA 1. Sfb

=

8.0 0.5 2. 5.3 3. 3.5 4. Asympt.

0

PRINCETON 0.4

'V'

MADDOX

•

TCEA 0.3 0.2 0.1~ ________ ~ ______ ~~ ______ - L ________ - L ______ ~ 1.0 1.5 2.0 2.5 3.0 3.5 H Figure 8

A value of the base pressure was measured by the author at

the Gas Dynamics Laboratory of Princeton University (unpublished) at a

Mach number of 2.31 (figure 8). I~ was 23% lower than theoretica11y pre

-dicted a1though the boundary-1ayer was thick (approximate1y one half the

step height). The ratio of model-span to step-height was equal to 2.6.

The experimenta1 poin~given in figure 8 by Chapman (reference

6) lies on Korst's curve. The boundary 1ayer thickness is not known and the

span ratio was about 80. Va1ues by Eggink (reference 8) are a1so shown

I

a1though his test conditions are not we11 defined.

The base pressure ratio (p/Poo ) from reference 1 is 13% lower

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one"third and the span to step height ratio was equal"to twenty.

*

The above results show that the experimental values of the

base pressure are too low, espeeially when span to step-height ratios are smalle It is possible, based on the results obtained in the laminar ease,

that a span effect exists whieh deereases the base pressure.

Available spanwise pressure distributions are given in figure

9. They show that the statie pressure is lower near the side-walls than

in the central portion of the flow. For example, from the results given

by Sirieix, it is seen that the pressure ratio p/P.,p near tbe sides is 8% lower than the pressure ratio measured on the eentre-line.

0.4r---.---.---~~~--~ O.}~~---~---~---~~---~I _- _.0 _-0.5 ₀ _0.5 _.0 2 z -S

P~INCETON

0.5 2z S SPAM-lISE VARIATION of STATIe PRESSURE

Figure 9

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17

It is therefore expected that a rather strong cross-wind exists

in the separated reg ion of the flow, from the centre-line towards the sides,

responsib1e for a decrease of the base pressure.

Experimenta1 evidence of such cross-flows is shown in figure 10, which gives the streamline pattern visua1ized by an oi1 technique. These

resu1ts were a1ready reported by the author in reference 7 and were more

recent1y confirmed by the investigation made by Sirieix (reference 4).

Figure 10 shows the existence of two strong vortices, with vertica1 axes,

side ,~all

_<J

free stream direction

SLOW

- -.. $ .... ' ...,O'ILL..-.- _ _ _ _

side wall

Figure 10

formed near the side wal1s of the model; which are associated with the low

pressure measured naar the sidas. It is seen that, in the reversed flow,

the streamlines deviate from the centre line direct ion to reach these

vortices. As a result, air is removed (or sucked) from the central portion

of the flow and reinjected in the side regions. It is expected that figure 11

would be representative of the phenomenon. (The three-dimensional periodic

aspect of the f~ow which was observed earl ier (re;erence 7) is not shown in

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18 side wall

,

_,

streamlines in the boundary-layer vortex Reattachment line Figure 11

It was therefore concluded that a cross-flow in the separated re&ion of a turbulent flow is responsible for a decrease in the base pressure.

This effect is opposite to the increase in base pressure caused by the finite

thickness of the approaching boundary-layer and this could explain the reason why experimental values of the base pressure are either equal to or even

lower than the values theoretically predicted for a thin boundary-layer.

Cross-flows are also important to consider when studying the effect of air injection in a separated flow in the case of small span to step-height ratios. Theyare indeed responsible for~ shift of the zero value of the injection coefficient.

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19

REFERENCES

1. Jean J. Ginoux - Gas Injection in Separated Supersonic Flow~ TCEA TN 7, February 1962.

2. Jean J. Ginoux - The TCEA Continuous Supersonic Wind Tunnel S-l~ TCEA TM 7, October 1960.

3. H.H. Korst, R.H. Page and M.E. Chi1ds - A Theory for Base Pressures in

Transonic and Supersonic Flow~ University of Illinois,

TN 392-2, March 1955.

4. M. Sirieix - Pression de cu10t et processus de mé1ange turbulent en écou1ement supersonique plan. La Recherche Aéronautique, ONERA n° 78, 1960.

5. A.R. Maddox - Effect of Air Injection in a Separated Flow of a Super-sonic Turbulent Boundary-Layer. Student Project Thesis, TCEA, June 1961.

6. Dean R. Chapman, D. Kuehn and H. Larson - Investigation of Separated Flows in Supersonic and Subsonic Streams with Emphasis

on the Effect of Transition. NACA TN 3869, March 1957. 7. Jean J. Ginoux - Experimenta1 Evidence of Three-Dimensiona1 Perturhations

in the Reattachment Region of a Two-Dimensiona1 Laminar

Boundary-Layer at M

=

2.05. TCEA, November 1958. 9. H. Eggink - The Improvement in Pressure Recovery in Supersonic Wind

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TCEA TN 6

Training Center for Expertmental Aerodynamics

ON mE EXISTENCE OF CROSS FImS IN SEPARATED SUPERSONIC STREAMS

February 1962 Jean J.Ginoux

An experimental inveetigation was made on laminar separated auperaonic

streama using two-dimensional back-ward facing step modeis. It was ahown

that a croas-flow existed in the

separated region of the flow which is aS80ciated with the side wall boundary layers. lts effect is to

TCM TN 6

Training Center for Experimental

A er odynami cs

ON THE EXISTENCE OF CROSS FLGlS IN

SEPARATED SUPERSONIC STREAMS

An experimental investigatian was made on laminar separated superaonic

streama using two-d1mensional back-ward facing step modeis. It was

shown that a cross-flow existed in

the separated regi~ of the flow which is associated with the aide wal boundary layers. Ita effect is to

I. Ginoux, Jean

Il. TCFA TN 6

I. Ginoux,Jean

Il. TeM TN 6

decr . . ae the base presaure and incr . . ae the pre •• ure

gradient at reattachment even for large va lues of the model-span to step-height ratio. It is ahown that the commonly accepted aasumption that a two-dimen.ional flow

exists when there is no meaeurable ap&nwi.e pressure

variation is a necesaary but not 8ufficient condition.

In the turbulent case it is generally found that the meaaured base pre8sure is lower than is theoretically

predicted. Thia is explained by the existence of a cro.s

-flow (euction) produced by strong vertical vortices

near the side walis.

(copiea avallable at TCEA - Library)

decrease the base preseure and increase the presaure

gradient at reattachment even for large va lues of the

model-span to step-helght ratio. It 1s shown that the

commonly accepted assumption thet a evo-dimen.ional flow

exi.tawhen there i. no maaaurable spaowise pre.aure

variation ia a nece •• ary but not .uffieient eondition.

In the turbulent case it is generally found that the

me&aured base pressure is lower than is theoretieally

predicted. Thie is explained by the exi.tenee of a

crosa-flow (suetion) produced by strong vertical

vortices near the aide walls.

(26)

TCEA TN 6

Training Center for Experimental A er odynamic a

ON TUE EXISTENCE OF CROSS FJmS IN

An experimental inve.tigation waa made

on laminar aeparated .uperaonic streama uaing two-dimenaional back-ward facing atep modeis. It waa sbown

that a cross-flow .xiated in tbe separated region of tbe flow wbich

is aa80ciated witb the aide wall

boundary layers. lts effect ls to

TCEA TH 6

Training Center for Experimental Aerodynamics

ON mE EXISTENCE OF CROSS F~S IN

An exper1mental inve.tigatian waa

made on laminar aeparated supersonic

ctreama using two-dimenaional back-ward facing step models.It was

sbown that a cross-flow existed in the separated regi~ of the flow

whicb is associated with the side wal boundary layers. lts effect is to

I. Ginoux, Jean

11. TCEA TN 6

I. Ginoux,Jean

11. TeM TN 6

ae tbe baae pressure and increa.e the pre •• ure ent at reattachment even for large value. of the -span to atep-height ratio. It ls .bown that the nly accepted aaaumption tbat a two-dimen.ional flow s wh en there is no meaaurable spauwi.. pressure tion is a neees.ary but not suffieient condition.

In~e turbulent case it is generally found that the

mea red base preasure is lower than is tbeoretically

pre eted. This is explained by the existenee of a cro ••

-fl (.uction) produeed by strong vertieal vortices near the side wall ••

(copie. avail.ble at TCEA - Library)

deereaae the base pres.ure and inerease the pre.sure gradient at reattacbment even for large va lues of the model-.pan to step-helght ratio. It ls ahovn thAt tbe commonly accepted a •• umption tbat a two-dimen.ional flow exi.tawben there i. no mea.urabla .pauwise pres.ure variation is • neee.sary but not .uffieient condition. In the turbulent caae it ia generally found that tha meaaured base pre.sure i8 lover than is theoretiealiy predieted. Thi. is explained by tbe exi.tenee of a cross-flow (suetion) produeed by strong vertical vortiees near the side walls.

(27)

TeEA TH 6

ON THE EXISTENCE OF CROSS FLOWS IN

An experimenta1 inve.tigation was mad~

on laminar separ.ted luperlonic

streama using two-dimensional back-ward facing step models. It was shown

that a cross-flow exiated in the separated region of the flow which

is associated with the side wall

boundary layers. lts effect is to

TCEA TN 6

Training Center for Experimenta1

A er odynami cs

ON THE EXISTENCE OF CROSS li'LGlS IN

February 1962 Jean J.Ginoux An experimental investigation was made on laminar separated supersonic streams using two-dimensional back-ward facing step models.lt was

shown that a cross-flow existed in

the separated regiOR of the flow which is aS80ciated with the side wal boundary layers. lts effect is to

I. Ginoux, Jean

11. TCEA TN 6

I. Ginoux,Jean

11. TeM TN 6

decreas. the base presaure and increase the pressure

gradient at reattachment even for large values of the

model-span to step-height ratio. It is Ihown that the

commonly accepted assumption that a two-dimenlional flow

exists wh en there is no mea.urable spauwi.e pressure

variation is a necessary but not sufficient condition.

In the turbulent case it is generally found that the

measured base presaure is lower than is theoretically

predicted. This is explained by the existence of a crol

s-flow (suction) produeed by strong vertieal vortie.a near the side wall ••

(eopies available at TCEA - Library)

deereaa. the base presaure and inerease the pre.sure

gradient at reattaehment even for large values of the model-span to atep-helght ratio. It is shown tbAt the

commonly aecepted a.sumption that a two-dimen.ional flow exiltawhen there il no mealurable .pauwise pr.llure

vari.tion is a neee •• ary but not luffieient condition. In the turbulent case it il generally found that the measured base pres.ure is lower than i. theoretieally

predieted. This il explained by the exiltenee of a

crosl-flow (suetion) produeed by strong vertical vortiees near the lide walls.

(28)

TCEA TH 6

An experimental investigation was made

on laminar aeparated supersonic streama uaing éWo-dimensional back-ward facing atep models. It waa sbown

that a crosa-flow existed in tbe aeparated region of the flow which

is asaociated with the side wall

boundary lay.rs. lts effect is to

TCEA TH 6

Training Center for Expertmental Aerodynamies

ON mE EXISTENCE OF CROSS FLGlS IN

An experimental investigation was

made on laadnar separated aupersonic streama using éWo-dimensional back-vard facing step models. ··It vaa

shown tbat a cross-flow existed in

the separated regi~ of the flow

which is associated with the aide wal

boundary layers. lts effect is to

I. Ginoux, Jean

11. TCEA TN 6

I. Ginoux,Jean

11. TCM TH 6

decr . . s. tbe base pressure and incr . . se the pressure gradient at reattachment even for large values of the model-span to step-height ratio. It is shown that the commonly accepted assumption that a éWo-dimensional flow exists when there is no measurable spanwise pressure variation la & necessary but not 8ufficient condition.

In the turbulent case it is generally found that the measured base pressure is lower than is tbeoretically predicted. This is explained by the existence of a cross-flow (suction) produced by strong vertical vortices near the side valls.

(copiea available at TCEA - Library)

decrease the base pressure and increase the pressure gradient at reattachment even for large values of the model-span to atep-helght ratio. It is shown that the commonly aeeepted aasumption that a two-dimenaional flow existavben there ia no meaaurable spauwise presaure variation ia a neceaaary but not sufficient condition.

In the turbulent case it is generally found that the meAsured base preasure is lower than is theoretieally predicted. Tbis is explalned by the exlstenee of a

cross-flow (suction) produced by atrong vertical vortices near the side valls.