Influence of cross flow on two dimensional separation

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van

KARMAN

INSTITUTE

F

O R

P

L U I D DYNAMICS

GRANT AF EOOAR 68-0026 Final Scientitic Report 1 May 1968 - 30 April 1970

INFLUENCE OF CROSS FLOW ON TWO DIMENSIONALSEPARATION by Roger LEBLANC and Jean J. GINOUX VKI TH 62 RHODE-SAINT-GENESE, BELGIUM MAY 1970

von KARMAN INSTITUTE FOR FLUID DYNAMICS TECHNICAL NOTE 62

INFLUENCE OF CROSS FLOW ON TWO DIMENSIONAL SEPARATION

by t Roger LEBLANC and JeanJ. GINOUX MAY 1970

This research has been sponsored in part by the Aerospace Researêh Laboratories through the European Office of

Aerospace Research, OAR, U.S. Air Force, under Grant AF EOOAR 68-0026.

t This work was conducted by Roger Leb1anc, Research Assistant at VKI, under the direct ion of Prbfessor Ginbux, and wi11 con-stitute a part of his doctora1 thesis.

ACKNOWLEDGEMENTS

\

.

The authors gratefully acknowledge the collabprat10n of Dr Horton. who developed the theoretical work used herein.

Much credit is also due to Ro Conniasselle. Tunnel

Engineer. and to the technicians of the supersonic tunnel. who helped in the experi~ental tests.

TABLE OF CONTENTS

SUMMARY _{• • •} 0 • • 0 • • • • • • •

•

• iii

LIST OF FIGURES

_{• •}

_{• • • • • • • •}

_•

_• iv

1. INTRODUCTION.

_•

_{• •}

_{• •}

_{• • •}

_{• • • •}

₁

2. THEORY OF LEES-REEVES-KLINEBERG

-HORTON'S EXTENSION TO THE AXISYMMETRIC

CASE _{• • •}

_•

_{• • • •}

_•

0

•

•

• •

3

2.1 Lees and Reeves _{Klineberg's method 3}

2.2 Horton's extension to the

axisymmetric case _{• • • •}

_•

_•

_{• •}

_•

4

·3 . EXPERIMENTAL TECHNIQUES _•

_•

_•

_{• • •}

_{• •} 6

3.1 Wind tunnel _•

_•

_•

_•

_{• • •}

_•

_•

_•

_•

_•

_•

6

3.2 Model _•

_{• •}

_•

_{• •}

_•

_•

_{• • • •}

_•

_{• •}

_• 6

3.3 Techniques of pressure measurements

_•

₉

4. RESULTS AND DISCUSSION _{• • • •}

_•

_{• • •} 12

4.1 Basic pressure distribution _•

_•

_{• • •} 12

4.2 Comparison between two dimensional

and axisymmetric flows

_{• •}

0 •

•

13

4.3 _{Nature of the boundary layer •}

_•

₁₃

4.4 _{Measurements without cross flow}

-Comparison with theory

_•

_•

_•

_•

_{• •}

_•

14

4.5 Effect of cross flow 0 •

•

•

•

•

•

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15

5. CONCLUSIONS _{• • • • •}

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_{• •}

_{• • •}

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_{• 17}

REFERENCES 0

•

• • • • • • _• 18

SUMMARY

A test technique using an axisymmetric model was suc-cessfully developed in order to study the effect of a small amount of cross flow on two dimensional laminar shock wave boundary layer interactions at a Mach number of 2.25.

In the absence of cross,flow ,the experim~ntal results were in excellent agreement with Horton's theory developed for axisymmetric bodies.

The effect of cross flow was to reduce the statie pressures throughout the complete interaction region. It was also shown that two dimensional models with an aspect ratio of 2.5 could be used free of side effects to study the influence of a small amount of cross flow.

LIST OF FIGURES

1. Uniformity of the free stream of S-l at x

=

0 2. Rotating model and support

3. Example o~ balancing results

4

.

Effect of transducer reference pressur~

5

.

General view of the ~acility

6.

Centrifugal effect on rotating columns of air

7.

Effect of the position of the pressure taps (Pt ~ 80 mm Hg)

8. Effect of the incidence on the axisymmetric separation

9. Comparison between planar and axisymmetric flows 10. Criterion ~or detecting the presence o~ transition ll.a Shadowgraph of the ~low over the

705°

~lare cylinder

model (L 60 mm)

l l.b Shadowgraph of the ~low over th e 10° flare cylinder model (L

=

60 mm)

l l.c Shadowgraph of the ~low over the

15°

flare cylinder model (L

=

60 mm)

Comparison t h e o r y- e x p e ri me nt

Effect o~ the flare location (th e o r y)

Influence of cross flow due to the rotation (L 60 mm) Influence o~ cross flow due to the rotation (L 80 mm) 12.

13.

14

.

15

.

16. Influence o~ cross flow due to yaw

170

The effect of sweep on the statie pres~ure distribution (t wo dimen s io nal model )

1. INTRODUCTION

There has been considerable interest in the past in the problem of boundary layer shock wave interactions because of its wide practical app~ication to high speed flight and in particular, in laminar interactions related to hypersonic

vehicles. As a result of this past.research, the main features of these interactions are presently well understood and it is possible to evaluate with a reasonable accuracy pressure dis-tributions for the case of two dimensional fully laminar flows

(1,2,3)

.

More recently, attention has been given to interactions between laminar boundary layers and swept shock waves, as they occur for instance in hypersonic inlets or on fins on hypersonic wings, or more generally, to three dimensional interaction

problems which are still far from being solved. As a basic ap-proach, one can study the effect of superposing a uniform cross flow upon a two dimensional shock wave boundary layer interac-tion. For instance, one can consider the flow over simple body configurations such as flat surfaces with deflected flaps which have infinite span and swept back leading edges o

However, it is experimentally difficult to simulate swept back wings of i n f i n i t e span. especially in the presence of flow separation, because of possible side effec ts . With a view to avoiding such difficulties, Ginoux has proposed to study and test axisymmetric bodies which are rotati ng around their axis of symmetry at zero incidence.

In the first part of the st udy (r e f. 5), it was con-cluded that it should be possible. both experimentally and ana-lytically, to use a hollow cylinder flare model with a diameter of 200 mm, spinning at 5,000 rpmo A method was developed to

determine the type of interaction, i .e. , l a mi n a r or transitional, which showed that the flare angle should be l imited to small

The present report covers the experimental aspect of this research program. It discusses the technological problems associated with the design of spinning.models and their use for measuring the effects of cross flowo

In parallel. an extension has been made by Horton of Klineberg's method to axisymmetric flows . This theorYi which in

its present state assumes no cross flow. is presented in ref~

9.

It is only briefly summarized in the present report (Section 2) and used to compare with the experimental data obtained on the non sp inning model (Section

4)

0

2. THEaRY OF LEESREEVESKLINEBERG

-HaRTaN'S EXTENSIaN Ta THE AXISYMMETRIC CASE

As a result .of important past research on two dimen-sional laminar boundary layer i n t e r a c t i o n s , several methods of calculation have been develope~ during the last few decades. It is not the subject of this report to compile them, a complete survey made by Ginoux can be found in ref.

6

.

Lees and Reeves

(1) and more recently Klineberg (2) proposed an interesting type of treatment which enables the computation, with a good accuracy, of pressure distributions for the two dimensional supersonic in-teractions. This method has recently been successfully extended by Horton

(9

)

to the case ofaxisymmetric bodies.

2. 1 Lees and Reeves - Klineberg's method

Lees and Reeves - Kl ineberg's method (LRK method) which is briefly described below has been programmen on the VKI IBM 1130 computer by Gautier

(7)

and Rei thm u l ler and Ginoux

(8)

and com-pared with experiment al re s ult s obtained by Ginoux (5) for two dimensional adiabatic models.

LKR theory is moment integra l method using profile para-meters obtained from solutions of the Falkn r-Skan equation for

similar flows, including the Stewartson reversed flow profiles.

In the adiabat i c ca s e t h e t h r e e required equations are the integral conservat ion equa t ion s fo r mas s and momentum, and additionally, the moment of momentum equat ion. This enables the introduction of a vel ocit y pro f i le parameter a(x) independent of the external pressu re grad i ento This can be transformed into three differential equations in t he Stewa rt s on plane with four dependent variables;

M~

,Ö~'

Han d a(x ). x bei ng the ind e p end e n t variable. Here ö~ is the displa cement thickn es s i n the

trans-1

formed plane and H the i n cli n atio n t o the sur face of t h e stream-line at the edge of the boundary l a y er. The l a t t e r can be re-lated to the external Mach number, Me, by the Prandtl-Meyer function.

A Runge-Kutta integration procedure of this system of ordinary differential equations is then used to calculate the properties of the interaction and the static pressure distribu-tion.

The systemof equations is unstablë in the adiabatic

case, and interact~ons are generated by applying an appropriate

perturbation to the solution for self-induced flat plate flows.

The position and strength of the applied,perturbation must be

iterated to satisfy the downstream böundary- conditions, but an

interpolation procedure is used behind re-attachment which

reduces the number of iterations requiredo'

2.2 Horton's extension to the axisymmetric case

Klineberg's method has been ext~nded by Horton

(9)

for calculating adiabatic laminar shock wave boundary layer

in-teractions on flared axisymmetric bodies wi t hout rotation. This

work will later be extended to the case óf bodies with spin.

The existing two dimens ional comp u t e r program of

Riethmuller

(8)

has been used as a basis for the axisymmetric

program. the following modificat ions being necessary o

Firstly. the Prandtl-Meyer relat ion us e d in the two

dimensional case in order to relate the i ncli n a t i on to the sur-face of the inviscid external flow t o the local Mach number must be replaced by an appropriate inviscid sol u t ion of the axisymmetric external flowo More exact meth od s su c h as the

method of characteristics . which was appl ied by Leblanc to the

inviscid flow calculation on the fl a re a were found impracticable

because the large number of inte gration ste ps and i t e r a t i o n s required in the ~iscous intera c t i on calcul ationo Therefore.

a second order approximate method_a due to Syverts on and Dennis

Secondly. some additional streamline divergence terms

appear in the continuity. momentum and moment o~ momentum

inte-gral equations. Important simpli~ications result when the boun-dary layer may be considered thin compared with the body radius. The addition o~ transverse curvature terms showed that this thin boundary layer assumption is valid in the present case.

Thirdly. some modi~ications o~ the test and

inter-polation procedu~es are also necessary downstream o~ reattach-ment because the inviscid Mach number does not remain constant as in the two dimensional case. but instead rises. leading to a peak in the viscous pressure distribution. Special tests on the type o~ solution are required to pass over this peak.

Experimental data have been compared with success to the results obtained with this theoryo As indicated in

30

EXPERIMENTAL TECHNIQUES

3.~ Wind tunnel

The tests we re made in the VKI l6"x16" continuous supersonic wind tunnel at a Mach number of 2.25. The stagnation pressure is adjustable in the range of 70 mm Hg (~.3 psi) to

~80 mm Hg (30 2 psi) abso~ute which corresponds to free-stream

unit Reyno~ds numbers of 1.lxl06 and 207xl06 _{per meter}

respecti-velyo

The stagnation temperature i s between 15° C to 40° C (59°F to 104°F) depending upon the stagnation pressure o

The tunnel is equipped with shadow and sing~e pass schlieren systems with parabolic mirrors o Photographs are taken with a spark ~ight source of a few microseconds duration time.

The uniformity of the flow is ~ ~% in Mach number as indicated in fig. 1 obtained in the exit section of the nozzle with a pitot rake. In this figure the Mach number is plotted -a g a i n s t the transverse coordinate z for different values of

the vertica~ coordinate y; .Pt is the stagnation pressure. Similar results were obtained at va~ues of x from -8 cm to +16 cm.

3e2 Model

Figure 2 shows schematica lly the spinn ing model and its supporting mechanism e It consis ts essentiallY of a hollow cylinder (stove pipe) on which a fla re i s mountede l t s outside diameter is 200 mmo Flare angle s of 705. ~o and 15 degrees at different locations from the le a di n g edge of t h e cyli n d e r have been used. The model was designed to rotate up to 5,000 rpm. An inner conica~ cylindrica~ body su p po r t s the cylinder by means of two sets of vaneso The external diame ter of th e i n n e r body

(a) is 65 mm which was selected to allow supersonic internal

~low and su~~icient space tor the in n e r sha~ts (b) and (c) .

The rear part o~ the sting (including the driving

mechanism. see below) is connected by a swept back:support (a)

to a mechanism located under the wall o~ the test section which

allows ~ine adjustment to obtain zero in c i d e n c e and yaw o~ the

model. This is necessary because ot the presence o~ rubber

shock .a b s o r b e r s used to reduce model vibrations.

The vanes connecting the cylinder to the inner body

were twisted to produce the driving torque (t h e amount ot twist

was determined ~rom pre~iminary tests) . Fine co n t r Ql (within

!

10 rpm) ot the angular velocity was obtained by the use o~

trai-ling edge tlaps (d) tixed to each vane (c).

The system i s shown i n the sketch below . A 24

De

volts

motor was installed in the conical nose of tbe central bQdy to

cylinder

---

---

--

- -

--control. tbrougb a reducing gear~ the rot a t i on of three shatts

(a). Thin steel wires (b) connected to these sbafts permitted

the control of the angular deflection ot three trailing edge

A hydraulic brake Ce) acting on the rear part ot the cylinder vas used to slov dovn the m'odel trom 5,000 rpm to rest in a tev seconds in case ot emergency.

One ot the important technological problems associ ted vith-the design ot the present spinning model vas posed by the e xistence ot vibrations. Bec,ause ot the unusual contiguration ot the model and the trequent moditic tions to the measuring system such as the moditication ot the tlare position, pressure tubing, etc., it vas necessary to develop an in situ method ot dynamically balancing the model.

The principle ot the method is described on the tol-loving sketch. Because ot the shock bsorbers, the model has tvo degrees ot treedom, i.e., along x and y (the existing tree-dom on the directi~n perpendicul r to the plane x,y is v ry

I

sm 11) which are excited by the rotation nd me' sured by tvo

vibration t ransd uc er ~:..:;::;::.:..::==:...:..===:;...::.:;::::==:~

-

_

.

i

+

Y

L

(1)

4!r

.

I

x

(

~

-

!4b

CD

\

)

!

®

contaetless displacement transducers (dx causes a magnetic

~ield variation which itsel~ produces a voltage change at the output o~ the transducer) . These measurements allow the deter-mination of bob weights to be fixed in two planes A and B in order to minimize the vibrations.

These tests were made outside of the test section, so the twisted vanes could not be used to drive the model. Use was made of an air turbine shown on fig. 2. With this turbine the maximum rate of spin of the model was limited to about 3,000 rpm.

An example o~ results is shown in fig. 3. Before balancing the model, the vibrations were so large that it was unsafe to exceed 475 rpm, at which the first resonance frequeney occurred. Af ter two suceessive corrections it was possible

to spin up to 3,000 rpm with an acceptable amplitude of vibra-tions.

3.3 Techniques of pressure measurements

The pressure distribution on the cylinder-fl~rewere measured by a 48 position scanivalve and a Statham pressure

transducer loeated in the nose of the in n e r body, as shown in fig. 2. The pressure tubing connect ing the stati e orifices to the scanivalve ran along the trail ing edge of the radial vanes

supporting the cylinder. The maximum range of the pressure transducer was 2.5 psi with an accuracy o~ + 0075% of its

full scale.

On a spinning body a problem arises in the select ion of a reference pressure for the differential transducer. It is indeed extremely diffieult to obtain a known absolute pressure independent o~ the angular velocity of the model . However, this

results. In the present report. this was done by plotting the difference between alocal value of t h e pressure and the pres-sure meapres-sured at the beginning of the interaction (p_eo). nor-malized by the nominal free stream statie prespure. However. with a view to cross checking the measurements. and in parti-cular the correction for centrifugal effect (s e e below). two reference pressures were used. i oeo. the co n e pressure measured on the nose of the inner bodv and_{. ~} t h e value of p i t s e l f . As_eo shown in figo 4a and 4b for sluwly and fast spinning model. no significant difference was obtained by changing the reference pressure

Electric wires from the t r a n s duc er passes inside the hollow shaft (c) (s e e figo 2) and were connec ted to rotating mercury contacts of a "Vibrometer " t r a n s mit t er and from these to a standard recordero Controls of t h e sc aniv al v e rotation and of the

24

oVo DoC . motor of the dri ving mechan ism were ob-tained by step pulses transmitted from spec ially made carbon contacts and electric wires running inside shaft (c ) .

The angular velocity of the model i s measured by counting the number of pulses given by the "Vibrometer" trans-mittero

Figure 5 shows the model mounted in the tes t section together with the 19" rack contain ing the output recorders and instrumentso

Pressure measurements on the spinni n g model are in-fluenced by centrifugal effects due to th e difference i n the length of the pressure tubings conn e c t e d t o each side of the transducer. This effect whi ch ex~sts wi t h or wi thout flow around the model is illustrated in t h e sk e t chj next page.

One can show that for an external con s tan t pre ssure p ex

B tl

ar e

cylinder ! ~ ! L c o n i c Zl I rio se ~ t r ansd ucer dXiSCw

the difference 6tmeasured

lil2 2

- 2RT

hl 6p

=

Pl-P2

=

_{P e x e}

by the transducer will be given by

:-

~~T h~

- e

~

(1)

where hl and hz are the different l e n g t h s of the pressure tubings and lil the angular velocity.

This equation is represented by the solid line curve

in figo

5

0

As may be seen. it prediets an,error of about 1

0

6%

at 5.000 rpmo This ef~ects was checked experimentally by ro-tating tlie model in .s t i l l air in the test s e ct.i on , At diffe~ent pressure lev~ls Pex between the atmospheric value and approxi-mat ely 100 mm Hg ab sol ut e , As shown iri fig~ ;6a the agreemen t

between t h e o r y and experiments is genèrálly good within thè accuracy of the measurements.

4.

RESULTS AND DISCUSSION

4

01 Basic pressure distribution

In the present studYi the cross flow effect is deter-mined by comparing the pressure dis tr ibutions measured on the fixed and rotating body respectivelyo The accuracy of the method is strongly influenced by the way in which the basic reference.

i. eo• the body f ixed pressure distr ibut ion~ is measuredo

Figure 7 shows t y pi c al statie pressure distributions

measured on the f i xed body at t hr e e az imutal ~o c at i o n s

(12

=

twelve o'clock (o/c) . 40 5

=

40 5 o/ c . 9

=

9 o/c) for a

. 8

I

· ·

P-Peo .

tunnel stagnat10n pressure of 0 mm Hgo n th 1 s f1gure 1S

p=

the difference between t he l oc al stati e pressu~e and the

pres-I su~e at the beginning of the in t e r a c t i o n_e normalized by the free stream static pressure and x i s the str eamwise coordinate along the model surface o

As may be seen. differenc e s of a few percent existed

among th e s e pressure di s tr ibut ions o They ca n be attributed to

non-uniformi~y of·the free stream as shown in fig o 1 and

mis-alignment of the model (b o t h in incid e nc e and yaw )0 Fig ure 8

shows the effect on th~ pressure di s t r ibut i on of a ch a n g e of

incidence of the model from +1 to -1 degree o It shows varia

-tions of as much as 20% at separati on (x

=

38 mm) and rea

ttach-ment (x

=

75

mm) and about

9%

downs treamo

Accordi nglY i the inci d ence and yaw of the model was carefully checked duri ng f inal tes t s and adj usted to zero to within a fraction of one degree o H_{owe v e r i} even in t hi s case

small variations still exi s ted ar o u nd the mode l and i t was then decided to average t h e m by me as u r i n g t he pressure distr ibution .

for each test condi t i on . on a slowly rotati n g body (iO_{e. i} 10

-100 rpm) . A typi cal re sul t is shown in fig.

7

by t he sol id l ine

curve. This is an example of a basic ref ere nc e ca s e which i s used to determine the effe c t of t h e cross flow.

4.2 Comparison between two dimensional and axisymmetric rlows

Figure

9

compares the statie pressure distribution

measured on the present non spinning 200 mm diameter model with

those obtained in rer. 5 on a similar model with 100 mm diameter

and on a two dimensional model. In eaeh case. the rlap or the

~lare had an angle or 10° and was loeated approximately 60 mm behind the leading edge or the model. The tunnel stagnation pressure was about 80 mm Hg. In this rigure. the loeal pressure

normalized by its value (p ) measured immediately upstream

ot

eo

the interaction region is plotted versus the streamwise aoor-dinate x in millimeters.

As seen the pressure distribution tendedtowards the

two dimensional one when the diameter was increased rrom 100 mm

to 200 mmo Although the ratio or a typical. radial distance 6

(such as the local rlare thickness near peak pressure) to the

c~lindrical radius was about one tenth ror the larger ~odel.

the pressure distribution still dirrered markedly rrom the two

. . . . 6

d~men6~onal results. It thus seems that a rat~o

R

or 0.1. ror

which a two dimensional rlow was obtained in rer. 10 at Mach

number o~

4.

-

is too large at the present Mach number of 2.25.

4.3

Nature or the boundary layer

Emphasis is laid in the present experimental program on who~ly laminar rlow. The nature or the rlow. i .e •• laminar or transitional. was determined by using the criterion developed

in rer.

5

.

It is based on the observation that the trend or

variation or local pressure (5~ch as in the separation region)

with unit Rey.nolds number is reversed when transition moves into the reattachment region or the rlow rrom downstream. Thererore.

t . . Pxn-Peo . .

by plo.t~ng the rat~o p • where Pxn ~s measured ~n the linear portion or the pressure distribution at separation.

versus tunnel stagnation pressure (Pt) one can decide whether

~n fig. 10 for flare angles of 705D la. 15 degrees. a flare location of 60 mm and w = 0 ropomo In the 705 desrees case. the

increase of the pressure ratio with Pt indicates that the flow

was laminar o For the 100 _f1are

i the flow was laminar up to about

Pt 150 mm Hg and became t r a nsi ti o n a l . above that value. Finally -with the 150 _{flare the drop in pressure ratio in d i c a t es a}

transitional type of flowo The shadowgraphs

ot

fig o 11 a-b-c

illustrate typical flows over the t h r e e flareso Similar results were obtained for the 80 mm location of th e flareo It is known that the location of transit ion is sensitive to the leading edge sweep t h e r e f o r e to Wo However ~ it was imp o s s i b l e to verify

this effect because the present t ra ns i tion cr i ter ion involves 1engthy tests which are unsafe wit h spinn ing modelo

In conclusion. it was dec ided t o evaluate the effect of cross flow by using a 7050

flare l o c a t e d at L

=

60 and 80 mm. for which the flow is fully laminar over the whole range of

Reynolds numbero Transitional ty p es of flow wi l l be studied in an extension of the present invest igation.

4

04 Measurements witho ut cross flow -Comparison with theo~

Basic pressure distributions measured in t h e absenc

,

of c~oss-flow were compared with the results of Horton's theory

described in section 2. A typical example is shown in fig. 12 for L 80 mm and Pt a 98 mm Hg. Lik e wi s e in the t wo dimensional case it is seen that theagreement i s excel lent. A more complete comparison between t h e o r y, and experiment can be found in ref.9.

The theoreti cal effe c t of t h e fla re l o c atio n is indi

-cated i~ fi~. 13 in which the orig i n of t h e abs c i ssa is at the nose of the flareo The i n cr e as e i~ L produces t he wel l known effects of an increase in the separ ati o n lengt hi a dec rea se

in the "plateau" pressure and in t h e pressure grad ient at sepa-ration and reattachmento The press ure z eac h es a maximum

down-stream _.ot_. reattachment which decreases with an increasing, .

separation lengtho Thi~ is to be expected because the tinal

pressure must tend towards the inviscid one which decreases

trom the two dimensional wedge value down to the cone pressure.

4.5 Ettect ot cross tlow

The typical effect of cross flow as measured on the

cylinder flare model is shown in figs. 14 and 15. By spinning

the model at

4,ooo-4

i300

rpm a cross flow veloeity of about

8%

ot the free stream veloeity was obtained, which ~s

equi-valent to an angle of sweep of 5 degrees on a two dimensional

eonfiguration.

The differenee between the pressures measured locally

(p) and at the beginning of the in t e r a c t i on reg ion (p )

nor-eo

mal ized by the free stream statie pressure (p_m) is plotted

versus the streamwise coordinate x in millimeters. The t~~re

locationwas L = 60 mm and 80 mm in figs. 14 and 15 respeetively.

Results are given at three ditferent wind tunnel stagnation

pressures, i .e o , 100.140 and 180 mm Hgo On eaeh graph, the

pressure distribution with cross flow is compared with the

basic pressure distributionobtained on a slowly rotating model

as de'sêribed previously o Open symbols represent the uncor r e e t e d

measurements while solid ones give t h e results correc ted fo r

centrifugal effect. As expeeted, it i s seen that a small amount

ot cross flow has l ittle effectD t h e t r e n d being t o l owe r the

,

whole pressure di stribution . For in s t a n e ep at reattachment a

decrease ot 1.5

%

is obtainedo

For the sake of comparison another test was made on

the non spinning model with statie pressure taps located in

the 12 o'clock (o/c) positiono Pressure measurements were made

with zero and

5.5

degrees angles of yaw of the model o Under

to be approximately the same as on the spinning model, although

the general flow con~igurationwas certainly much more complex.

The result shown in fig. 16 indicates the same overall trend

aa in figa 0 14 and 15 al though the effect of cross flow seems

to be more pronounced at separation than at reattachmento

A parallel systematic investigation of the influence

of amail.sweep angles on boundary layer separat ions over wedge

modeis with an aspect ratio of 205 was made by Rozendal (ref.ll)

in the same facility under similar test conditionso Typical

reaults obtained with a

7.4

0 _{wedge located at 60 mm behind the}

leading edge of a flat plate, for a tunnel stagnation pressure

of

79

.5

mm Hg are shown in fig, 17.

A

is the angle of sweep of

the ..ID...OJieL As may be seen, the same trend is obtained which

indicates that there 'was but little effect of the finite span

5

.

CONCLUSIONS

A test technique was successfully developed to

accu-rately determine the effect of a small amount of cross flow on a two dimensional laminar shock wave - boundary layer

inter-action. It consists in using cylinder flare models spinning

around thei r axes of symmetry at angular velocities up to

5.000 rpm, equivalent to infinite span wings swept at angles

up to 6 degrees.

As expected, the observed effects of such cross flow were small, the general trend being to lower the whole pressure

distribution measured through the interaction region.

With the present technique, it was possible to verify

that two dimensional models with aspect ratio of 2.5 gave

results on the influence of cross flow which were free of side effects for sweep angles of a few degrees.

The results obtained without cross flow agreed very

well with the theory developed at VKI by Horton (r e f.

9),

who

extended Klineberg's integral method of solving two dimensional shock wave - boundary layer interaction to the axisymmetric

case. The accurate data obtained on spinning models in the

present study will serve to evaluate a future extension of

REFERENCES

l~ LEES. L o

&

REEVES. BoLog Supersonic separated and reattaching flows o 1 0 General theory and application to adiabatic boundary layer/shock wave interactions.

AIAA Jo. vol. 2. nr 111 November 1964~

20 KLINEBERG_e JoM. g Theory of laminar viscous inviscid inter-actions in supersonic flow.

GALClT. PhoD. Thesis. 19680

30 HOLDEN. M.So g Theoretical and experimental studies of the shock wave boundary layer interaction on curved compression surfaceso

Communication presented at the symposium on 'viscous interaction phenomena in supersonic and hypersonic flow ' . Aeronautical Research Laboratories_e May 7-8.

196~0

4

0 SYVERTSON1 CoA o• &DENNlSi DoM o : A second order

shock-expan-sion method applicable to bodies of revolution near zero l i f t.

NACA Report 1328i 1957.

5. GlNOUX. J oJ o g Supersonic separated flows over wedges and flares with emphasis on a method of detecting transi-tion.

VKl TN 47. Aug o 1968. also ARL 690009. Jano 19690

6 • GlNOUX. JoJo : Interaction entre ondes de choc et couches

lim~tesQ dans ' Ch o c s et ondes de chocs. Chapitre 4.

Edit~ par A. Jaumotte.

Masson

&

Cie_i to be published.

,

7. GAUTIER. B0 g Calcul de l ' in t e r ac t ion onde de choc - c ouche

1. _ • • • , .,.

11m1te lam1na1re 1n c l u a n t le decollement provoque par une rampe à l'aide des méthodes intégrales de Crocco-Lees _e modifiées par Glick et de Lees-Reeves.

Université Libre de Bruxelles. Institut d'Aéronautique

NT 23A. Bruxelles 1969.

8. RlETHMULLER. MoL . & GINOUX. J oJ o g A param~tric study of adiabatic laminar boundary layer - shock wave inter-actions by the method of Lees-Reeves-Klineberg.

VKl TN 60. May 19700

90 HORTON. HoP. ~ Calculation of adiabat ic laminar bound~ry layer

's h o c k wave interactions in axisymmetric flow. Part I :

The c ase of ,z e r o spin .

10. LEWIS. J oE • • KUBOTA. T ••

&

LEES. Lo : Experimental

investi-gation of supersonic 1aminar. two dimensiona1 boundary layer separation in a compression corner with and

without cooling.

AIAA J •• vol. 6. nr 1. pp 7-14. January 1968.

110 ROZENDAL. D. : The intluence of sma11 sweep ang1es on

boun-dary layer separations over wedges at Mach 2.2 with emphasis on the detection of transition.

Y

=

9 cm .

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1. Originat ing Aellvdy (Corporate author)

von KARMAN INSTITUTE FOR FLUID DYNAMICS

High Speed Laboratory

3.Report Tille

20. Report Seeurity c1assifieat ion

unclassified

2b. Group

INFLUENCE OF CROSS FLOW ON TWO-DIMENSIONAL SEPARATION

4.0eserip t ,ve nore s

Scientific

(type of report and in e l u si v e

Final 1.5.1968

dates)

30.4.1970

5.Author ( s ) (Last name, first name I initicl )

Roger LEBLANC and Jean J. GINOUX

ê.Report date

30.5.1970 7a.Total n! of₄₅ pages 7b. N° of₁₁ refs

Ba. Co n t r a c t or gront n! AF-EOOA R

68 . 0 0 2 6

b. Proje ct and to sk n°

-9a .Orig inator's report number(s)

VKI TN 62

e.O OO element _{61 102 F}

d.oOD subelement 1')81 307

10. Drstribution statement

9b.Othe r report n.2

This document has been approved for public release and sale ; its distribution is unlimited

11 .Supplementor y not e s

Tech, other

13.Abstrae t

12.Spo ns oring military activity

Aer o sp a c e Re se ar ch Lab o r a t o ri e s (ARR) Wrig ht -Pa t t e r s o n AFR,

Ohi o 45433

A test technique using an axisymmetric model was

6UC-cessfully developed in order to study the effect of a small amount of cross flow on two dimensional laminar shock wave boundary layer interactions at a Mach number of 2.25.

In the absence of cross flow the experiment al results were in excellent agreement with Horton's theory developed for axisymmetric bodies.

The effect of cross flow was to reduce the statie pressures throughout the complete interaction region. It was also shown that two dimensional models with an aspect ratio of 2.5 could be used free of side effects to study the influence of a small amount of cross flow.

DO FORM

I JAN.66

1473 Security elassif icat ion

Cross flow Interaction Supersonic speeds Laminar Axi-symmetric Experimental study Pressure measurements

Security Classification