(IASA-Ch-152703) BOUNDABY F77-23060 ISOLATED BOA’TPlIT. U ...

(IASA-Ch-152703) BOUNDABY L&YXt3! SSPAaATI3r0 F77-23060 011 ISOLATED BOA’TPlIT. YOZZLBS U.S. T h m i s (George Yashiagtoa univ,) 75 p HC & O i ) / H u ac 1 CSCL O l A U n c l a s

1;3/02 29470

Boundary Layer Separation on Isolated Boattail Nozzles

fw Willlor k l l y Abeyods

B. S. Nay 1973, brth Carolina State university

A Thesis submitted to

The Faculty of

The School of BPgheering and Applied Science

of Phe George Washington University I n partial sat isfact ion

of the requirersents for the degree of Master of Science

Hay 8, 1977

Thesis directed by

Dr. Richard W. Barnwell

Associate Professorial Lecturer i n hgineering

Ail invest igat ion has been conducted i n the Langley 16-foot

transonic tunnel a t free-stream Mach numbers from 0.40 to 0.95 a t 0'

angle of a t tack to study the phclpacnon of separated flaw on a series

of circular-arc afterbodies.

cylinders with a d ia re t e r equal to the nozzle exit diameter were used to

simulate jet exhausts.

separation locxioas was obtained using oil-flow techniques.

Both high-pressure air and s o l i d c i r cu la r

A deta i led da ta base of bouudary layer

The results of t h i s invest igat ion indicate tha t boundary layer

separation I s most extensive on s teep boa t t a i l s at high Mach nrrmbers.

Changes in the jet total-pressure r a t i o (jet total t o free-stream

static) a f f e c t the extent of separ- t ion very l i t t l e ; however,

entrainment associated with the presence of a je t has a s ign i f i can t

e f f e c t when compared to so l id s h l a t o r data.

c r i t e r i a were evaluated using experipental data.

general accurately predicted the separation locations for the solid

simulator cases. The bes t r e s u l t s vere obtained by curve-f i t t ing a

modified Reshotko-Tucker c r i t e r ion v i t h experimental data.

Several separat ion

No c r i t e r ion in

ii

I would like to thank all of those uho gave e assistance in the

preparation of this paper.

and Space Administration for giving e the opportunity to pursue

graduate study and for providing the tire and facilities necessary

for this investigation.

I am indebted to the National Aeronautics

I would especially like to acknowledge the contributions of

Dr. Richard W. Barnwell, ny advisor, whose advice was greatly

appreciated. I would like to thank %. Dorothy P. Wright and

Ys. Debbie L. Griffith for typing this paper. Also, I would like

to thank Ms. Kathryn H. Peddrew and rcS. Margaret L; Hurt for their

help in preparing the figures. In addition, I would like to thank

Mr. L. E. Putnam for his advice and his adaptation of the boundary-

layer computer program used herein.

p a g e

T I T L E . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

ABsTRAm . . . . . . . . . . . . . . . . . . . . . . . . . . ii

AOXWLEIE- . . . . . . . . . . . . . . . . . . . . iii

TABLEOF-S ..................... iv

L I S T O P S P W O L S . . . . . . . . . . . . . . . . . . . . . . . V

L I S T O F F I C U B E S . . . . . . . . . . . . . . . . . . . . . viii

Chapter

I. ~ o W m I ~ . . . . . . . . . . . . . r . . . . . . 11. EXPERMENTAL APPARATUS MIDpBocEMlRE . . :* . . . .

WIND TUNNEL DESCRIPTION . . . . . . . . . . . . MODEL AND SUPPORT SYSTD4 DESCRIPTION . . . . . . AF'TERBODY~DELDESCBIPTIOK . . . . . . . . . . ILSTRUjlENTATION AND TEST PWOCEDIJRE . . . . . . . DATAREDUCTION. 0 . . 0 .

111. RESULTS AND DISCUSSION . . . . . . . . . . . . . . . EXPERXMENTAL RESULTS . . . . . . . . . . . . . . TEEORETICAL RESULTS . . . . . . . . . . . . . .

Iv. ~ ~ c L u I ) I ~ ~ b 0 0 . . 0

REPERFNCES . . . . . . . . . . . . . . b . . . . . . . . .

1

3

3

3

1c

10

15

16

16

29

61

62

l v

2 cross-sectional area, m

cf

C P

in te rcept of linear Xcast-squares curve

slope of l i nea r least-squares cume

constant in Stra t ford c r i t e r i o n

loca l skin f r i c t i o n coef f ic ien t , w T

91.

pressure coeff ic ient based on free-stream conditions,

pe - p,

cP

- C

P

d

E

F

G

pressure coef f ic ien t based on conditions a t t he m i n i r r

s t a t i c pressure on the boa t t a i l , - ‘0

qo

modified pressure coef f ic ien t i n S t ra t ford c r i te r ion ,

--_ . diameter, m

standard e r ro r of estimate, 1 I [yi - (a + bzi)l 2

n-2

r a t i o of boundary-layer thickness a t the miniarm s t a t i c

pressure t o tha t at separation defined in equation 4 6 6

in Presz c r i t e r lon , o

SeP

r a t i o of boundary-layer thickness a t the minimum s t a t i c

pressure t o tha t at separation defined in equation 5 6 in Prese c r i t e r ion , o

6sep

V

v i

I

I

i

n

P

r

S

S

- S

T

t

U

X

X

V

Z

B

*C

Y

Ax

-mentum of entrained mass flow i n Presz c r i t e r ion , N

length of boa t t a i l , m

entrained mass flow In Presz c r i t e r ion , !%- see

Reynolds number, ",d, vm

n d e r of points in l i n e a r least-squares curve

2 pressure, N/m

dynadc pressure, N/m 2

b o a t t a i l circular-arc radius, m

r a d i a l dis tance from center l i n e of model, m

nozzle convergence length, m

axial coordinate i n nozzle convergence section, m

streamwise dis tance along body, m

e f fec t ive streaewfse dis tance along body in Stra t ford

c r i te r ion , m

temperature, K

nozzle throat length, m

veloci ty component in s direct ion, m/sec

a x i a l distance a f t from model nose, m

axial distance a f t from start of boa t t a l l , m

dependent var iable i n l i nea r least-squares curve

Independent var iable in l i nea r least-squares curve

terminal b o a t t a i l angle, deg

b o a t t a i l chord angle, deg

spec i f i c heat ra t io

a x i a l distance from the minimv- s t a t i c pressure 05 the

b o a t t a i l t o boundary layer separation, x - xOs m SeP

d

0

V

P

=w

Subscripts

b

9P

e

fs

j

a

m

0

P

PS

S

SeP

t

1

OD

boundary-layer thickness, m

boundary-hyer displace-t thickness, m

boundary-layer Promenturn thickness, rn

kinematic viscosi ty , m /sec 2

3 density, kg/m

w a l l shear stress, N/m 2

base

drwpo i n t

exit

f i c t i c ious stagnation point

jet

l o c a l

IIkaXimUm

b o a t t a i l minimum stat ic pressure point

predicted

preseparation

plume simulator

separation point

stagnation

boundary layer edge, top edge of control volume i n Presz

c r i t e r i o n

f ree--8 tream

LIST OF FIGURES

Figure

1.

2.

3.

4.

5 .

6.

7.

8.

9.

10.

11.

12.

13.

14.

Sketch of air-powered cone-cylinder model with a typ ica l circular-arc convergent nozzle ins ta l led . . . . . Air-powered model with configuration 8 attached, i n s t a l l ed in the Langley 16-foot transonic tunnel. . . . Sketch of cone-cylinder nacel le model showing in t e rna l s t i ng arrangeme3t f o r support of simulators. . . . . . . . . . . . . . . . . . . . . . . Nacelle model i n s t a l l ed i n the Langley 16-foot transonic tunnel with typ ica l circular-arc afterbody and ds/de = 1.00 simulator attached. . . . . Sketch of model and support system with corresponding cross-sectional area d is t r ibu t ions . . . . . . . . . . . . . Detailed sketch of typ ica l configuration with tab les of geometric parameters and in t e rna l coordinates. . . . . Band of the f ree-stream parameters encountered during the investigatinn. . . . . . . . . . . . . . . . . . . . Example of two-cell vortex separation. . . . . . . . . . Oil-flow photographs showing the e f f ec t of Mach number on separation location. . . . . . . . . . . . . . . . . . Oil-flow photographs showing the e f f e c t of j e t to t a l - pressure r a t i o on separation location. . . . . . . . . . Separation locat ions f o r configurations using a so l id cylinder to simulate j e t exhausts. . . . . . . . . . . . Separation locations fo r configurations using high- pressure a i r t o simulate jet exhausts. . . . . . . . . . Comparison of separation locat ions obtained through the use of so l id simulators with those obtained from j e t operation a t ~ , , ~ / p , . = 2.

Comparison of the var ia t ion of separation locat ion predicted by various methods with Mach number f o r configurations with so l id plunre simulators. Experimental pressure d is t r ibu t ions used i n predicting Separation locations. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . .

Page

4

6

7

8

9

11

14

1 7

18

19

2 1

22

28

35

v i i i

i x

Figure Page

15.

16.

17.

18.

19.

Comparison of the variation of separation locatim predicted by various methods with Mach number f o r configurations with s o l i d plume simulators. Theoretical inviscid pressure d is t r ibu t ions used I n predicting separat ion locat ions . . . . . . . . . . . . Evaluation of predicted separation locations with oil-flow data f o r configurations with s o l i d p l a n e simulators. Experimental pressure d is t r ibu t ions used i n predicting separation locations . . . . . . . . Evaluation of predicted separat ion locat ions with oil-flow data f o r configurations with s o l i d plume simulators. m e o r e t i c a l inv isc id pressure d is t r ibu t ions used i n predict ing separation locat ions . . . . . . . . . . . . . . . . . . . . . . . Comparison of oil-flow data and predicted separation locations made using least squares curve f i t applied t o Reshotko-Tucker c r i t e r ion . . . . . . . . . . . . . . Comparison of experimental and predicted pressure- coeff ic ient d i s t r ibu t ions on a circular-arc b o a t t a i l nozzle using a s o l i d cone t o represent the separated region . . . . . . . . . . . . . . . . . . . . . . . .

39

44

50

58

60

W T E R I

INTRODUCTION

The nacelle afterbody is a critical ares as f a r as a i r c r a f t

performance is concerned.

complex, and therefore hard t o predict .

The flow i n t h i s region can be extremely

The external flow goes

through an expansion and then a compression (ref. I); it a lso i n t e r a c t s

with the j e t plume. This phenomenon causes the afterbody boundary

layer to thicken, and i n many cases separate. In cases i n which

boundary layer separation does occur, the pressure d i s t r ibu t ion and

drag on the afterbody great ly d i f f e r from those of unseparated cases

(ref . 1). t

This f a c t has led t o much experimental work i n the area

(refs . I t o 9 ) ; however, l i t t l e de ta i led separation data is avai lable

from 2, hich improved ana ly t i ca l techniques can he developed.

Presently there are many theore t ica l methods f o r predicting

afterbody flows (refs . 9 t o 33). Most of these employ a poten t ia l flow

calculat ion coupled with a boundary layer calculation. Some of the

boundary-layer methods are designed to predict and ca lcu la te separated

flows implici t ly .

separation locat ion using simpler, semiempirical techniques

(refs . 34 t o 52) and modeling the separated region as a so l id cone

Others approach the problem by predict ing the

frustum ( re f . 37).

unseparated b o a t t e i l flows ( r e f , 1). For separated flow casee,

howevei, the d i f f i c u l t y in correct ly modeling the complex flow near

Good r e su l t s have been obtained fo r cases with

afterbodies has caused the theore t ica l r e s u l t s obtained up t o now t o be

inaccurate .

1

2

I n order t o b e t t e r understand b o a t t a i l flow separation and t o

determine what c r i t e r i a can bes t p red ic t i t f o r use i n patched

i n v i s c i d h i s c i d so lu t ions , an oil-flow study was conducted i n the

Langley 16-foot transonic tunnel using a series of circular-arc

af terbodies ( re f . 1). The inves t iga t ion was conducted a t free-stream

Mach numbers from 0.40 t o 0.94 a t 0' angle of a t tack.

simulate j e t exhausts with j e t total-pressure r a t i o s ( j e t t o t a l t o

free-srream stat ic) varying from jet-off up t o about 9 , depending upon

the configuration and the free-stiram Mach number.

were a l so used t o simulate the j e t s a t the on-design condition. (The

f l w conditions f o r which pressure da ta w a s ava i lab le i n references 1

t o 3 were repeated as closely as possible during the oil-flow tests.)

The primary goal of the test was t o e s t a b l i s h a systematic data base

from which the dependency of flow separation on such f ac to r s a s t he

free-streem Mach number, the longitudinal surface curvature, and the

j e t total-pressure r a t i o could be determined. (Since e s ing le m . l e l

was used f o r the test , and the tunnel i s an atmospheric tunnel, i t was

possible only t o test over a limited Reynolds number range. For t h i s

reason, the e f f e c t of Reynolds number was not included i n the data base.)

The experimental r e s u l t s w i l l be reported in t h i s paper.

evaluation of severa l of the semiempirical techniques f o r predicting

flow separation w i l l also be presenced.

A i r was used to

Sol id cylindeTs

An

CHAPTER I1

EXPERIMENTAL APPARATUS AND PRCICFJNRE

Wind Tunnel Description

This flow separation study was conducted in the Langley l6-foot

transonic tunnel. The tunnel is a single-return, continuous,

atmospheric tunnel.

with s l o t s a t each of the e ight corners.

is contixuously var iable from 0.20 to 1.30.

description of the Langley l6-foot tunnel can be found i n references

53 t@ 55.

Its test sect ion has octagonal cross sect ions

The free-stream Mach number

A more de ta i led

Model and Support System Description

The model used i n t h i s invest igat ion was an isolated, single-

engine nacel le model, t o which various circular-arc b o a t t a i l nozzles

could be attached.

pressure a i r was used to simulate the j e t exhaust, is shown i n f igure 1.

The nacel le model had a rounded shoulder a t the junction of the conical

nose and the cy l indr ica l section.

s t a t i o n 111.76 cm.

a t s t a t ion 121.92 cm.

simulation had a stagnation temperature of about 274 K.

throtigh a s t ing-strut , which supported the model, i n t o the high-

pzeseure plenum.

t o the model axis) i n to the l w p r a e s u r e plenum through e ight multi-

holed sonic nozzles.

circumference of the high-pressure plenum.

A sketch of a typ ica l configuration, i n which high-

The nozzles were attached a t

Nozzle b o a t t a i l s fo r a l l configurations s t a r t ed

The dry, high-pressure air used fo r j e t

It was p iped

The air then flowed r ad ia l ly outward (perpendicular

The nozzles were equally spaced around the

The flow then accelerated

3

4

0 0 ln s;

5

rearward, passing through flovcsroothing screens in the model

ta i lp ipe . These screens, supported by four vanes, consisted of a

0.635-an mesh forwed using 0,0635-cm w i r e .

of the air-powered model ins t a l l ed i n the langley 16-foot transonic

tunnel.

Figure 2 is a photograph

Solid cylinders were also used to simulate jet exhausts.

Figure 3 i l l u s t r a t e s 9 configuration typ ica l of those tested.

i n t e rna l s t i n g w a s ins ta l led in the single-engine nacel le d e l t o

s u p p o r t the solid simulators. Figure 4 shows one of these

configurations ins ta l led i n the Langley 16-foot transonic tunnel.

simulators with a di2ateter equal to the nozzle e x i t diameter

(ds/d, = 1.0) were tested.

f e l t t h i s w a s long enovgh so t h a t base e f f e c t s of the simulator woldd

be negl igible on the boa t ta i l s .

An

Only

All simulators were 27.94 cm long. It was

The model was .nounted i n the tunnel on a s t ing-s t ru t support

system. As shown i n f igures 1 to 5, the nose of the model w a s

attached t o the s t r u t blade.

percent thick with a 50.8-cm chord.

i n cross sect ion, with t h e top d bottom capped With half-cylinders of

2.54-cm radius.

below tSe wind-tucnel center line.

the runnel center l i n e and the nose of the model a t tunnel s t a t i o n

39.93 meters. Cross-sectional area d ie t r ibu t lons of the model and

support system are shown in f igure 5.

percent of the cross-sectional area of t he test sect ion; the maximum

blockage of the model and support system was 0.148 percent.

The blade w a s s-ept 45* and was 5

The s t i n g was 5.08 c m by 10.16 cm

The center line of the s t i n g w a s located 55.88 cm

This placed the a d s of the model on

The model blockage vas 0.099

9

Tunnel 6- - -- ~- *- -

I

55.88 cm !

I

I 1-L Tunnel station 39.93 meters

X, cm

Figure 5.- Sketch of model and support system with corresponding cross-sectional area distributions.

lo

Afterbocq Model Description

A family of e ight circulaparc af terbodies w a s ava i lab le f o r

kigcre 6 shaws sketches and correuponding table8 of tes t ing .

dimamions f o r these nozzle afterbodies. The i n t e r n a l contour of

each nozzle vas bas ica l ly an ASME long-throat nozzle (ref. 56). Sore

mdl f i ca t ions were necessary because the external contour8 set lidts

within which the in t e rna l contours had t o contract from a f ixed

i n t e r n a l diameter t o the required exit diameter.

be a l l o t t e d f o r tube routing.

c i r cu la r cross sections.

Also, space had to

A l l of the nozzles had throa ts with

Instrtmrentation and T e s t Procedure

The e ight afterbody m d e l s and t h e i r so l id simulators w e r e

equipped with static-pressure orif ices.

s ta t ic-pressure data used in t h i s paper were presented i n reference 1.

For the cases i n which air w a s used t o simulate jet exhauets, j e t

total-pressure measurements were obtained by using an internal ly-

mrmted total-pressme rake (fig. 6). The j e t t o t a l pressures were

measured using e l e c t r i c a l strain gage pressure transducers ca l ibra ted

t o an accuracy of 9 . 5 percent of the gage capacity

(6.89 x lo5 N/m2)*

The o r i f i c e locat ions and

A l l t e s t i n g was conducted i n the Langley 16-foot transonic tunnel

a t free-stream Mach numbers ranging from 0.40 t o 0.94 and at an angle

of a t tack of 0’. The model a t t i t u d e was not changed during the t e s t .

The tunnel upflow (on the order of 0.1 degree throughout the free-stream

Mach number range) and s t i n g def lect ion (known t o be extremely small)

were not taken i n t o account. Boundary layer t r ans i t i on waa fixed

11

i(l 1 i

ORIGINAL PAGE IS OF POOR QUAL1TY

12

0

5

0 5

l o D l '

00

0 4J

U W

d U Q &I 1 M d Ccl C 0 u n P W

13

by a 0.254-cm s t r i p of No. 100 g r i t located 2.54 cm from the t i p of

the nose, using the techniques described in references 57 and 58.

High-pressure air w a s used t o simulate je t exhausts with jet

total-pressure r a t i o s varying from jet-off up t o 9, depending upon the

configuration and f ree-stream conditions.

ussd t o simulate the on-design condition.

range covers t ha t typ ica l ly used i n subsonic f l i g h t by t ransports and

f +.ghters.

Solid cylinders were a l so

This jet t o t a l pressure

Since the Langley 16-foot t ransonic tunnel is an atmospheric

tunnel, the tunnel free-stream conditions vary with the ambient

conditions.

of the free-stream Mach number i n f igure 7.

consisted of several runs.

tested.

For configurations which used high-pressure a i r t o simulate j e t exhausts,

a sweep of nozzle total-pressure r a t io s was conducted a t each Mach

number.

var ia t ion, data w a s generally taken a t the highest Mach number f i r s t ,

and then a t progressively lower Mach numbers.

(i.e. each Mach number and/or nozzle total-pressure r a t i o s e t t i n g a t

which data was recorded) , tunnel conditions were allowed to s t a b i l i z e ,

a t which time 10 frames of data were taken over a 10 second period.

The 16-foot tunnel has a small cyc l ic var ia t ion i n the flow with a

period of about 10 seconds.

therefore used f o r each point t o minimize e r ro r s i n the measured

quant i t ies resul t ing from t h i s cy l l c var ia t ion.

The range of free-strean? conditions is s.. own as a function

The oil-flow study

In each run, a pa r t i cu la r configuration w a s

Each run consisted of a sweep of free-stream Mach .lumbers.

In an e f f o r t t o minimize t h e tunnel t o t a l temperature

A t each da ta point

The average of t he 10 frames of data was

14

Q)

5 M C

-0 PI l.4 aJ U c 1 0 r)

E

c; Q PI l.4 c) v) I 0) PI l.4 w

w 0

To obtain oil-flow data, the a f t portion of the model w a s

painted with 100-weight o i l before each run, and repainted as often a s

w a s necessary t o insure good oil-flow qual i ty . Photographs were taken

using a camera mounted on the top f l a t of the test section.

t o make the o i l f luoresce, the photographs were taken under u l t r av io l e t

l igh t . To check fo r hysterecis , some conditions were repeated during a

run, going up and coming down in Mach number.

In order

Data Reduction

Separation locations were obtained from the oil-flow photographs.

X photograph of a gr id held next t o the -del before a run w a s used to

sca le distances. Separation distances were measured a t the top of the

b o a t t a i l because of the poss ib i l i t y of support-strut interference.

References 2 and 3 and some unpublished data ind ica te tha t the top can

be assumed t o be interference free.

see i f there w a s too much o i l on the model.

Photographs were a lso checked t o

CHAPTER I11

RESULTS AND DISCUSSION

Experimental Results

Typical photographs obta-iaed during this oil-flow investigation

are presented as figures 8 , 9, and 10. They illustrate some of the

problems encountered while making oil-flow tests. One problem is

getting the proper amount of oil on the model.

oil of a high enough viscosity to remain on the model the length of

There must be enough

time needed for the tunnel to reach the test conditions. Conversely,

the oil must have a low enough viscosity to react to changes in flow

conditions within a reasonable length of time, and be present in a

layer thin enough t o not greatly alter the effective body shape.

Another problem is measuring the separation locations since the

separation line is usually not straight. Generally the line is

curved, conforming to a series of vortlces spaced around the body in

the separated region. This pheilomenon, similar t o Taylor arid Goertler

vortices (ref. 59), is characteristic of turbulent flow, and perhaps

is triggered by small asymmetries in the flow. Figure 8 also shuws a

line in the separated region near the nozzle exit.

that a two-cell vortex pattern may exist in the separated region, at

This indicates

least at high jet total-pressure ratios.

Some factors influencing the location of the separation point are

the free-stream Mach number, the longitudinal curvature of the model,

and the jet plume entrainment and blockage. The Reynolds number also

affects the separation location; however, it was not possible t o test

16

20

over a wide Reynolds number range since the tunnel is an atmospheric

tunnel and only one model was used in the test. For subsonic flow,

the separation point moved forward on a given configuration as the

free-stream Mach number increased. (See figures 9 and 11.) For

transonlc flows (free-stream Nach numbers above about 0 . 8 , depending

upon the configuration), pressure distributions indicate that A shock

probablv existed on the boactail when the flow decelerated from

supersonic to subsonic speeds (ref. 1). When this happened, the

boundary layer separation probably became shock induced. The

separation point moved forward on the boattail to a point in the

vicinity of the shock. It is speculated that the shock-induced

separated region combined with the previously described separated

region to cause this movement. This may explain the large shifts in

the separation location at transonic speeds which occarred for two of

the configurations.

The lnagitudinal curvature of the boattail also greatly affc+.ted

tile separat ion lacation. As expected, for a given iree-stream Nach

number, the most forward separation location occurred cn the zteepest

boattail configuration. As the longitudinal curvature progressivel)

decreased from configuration to configuration, the separation

location moved rearward. Only on the four steepest boattai!

configurations was any separation ever found over the free-stream

Mach number range tested.

The entrainment and blockage of the jet plume are functions of

the jet total-pressure ratio. It i s seen in figures 10 and 12 that

the separation location changed little over the jtrc total-pressure

i m u n 0 . 4 . 5 .6 .7 I .9 1.0

0

Figure 11.- Separation locations for configurations using a s o l i d cylinder to simulate jet exhausts.

22

8 5 8 S 8 % 8 . I . . . a oooada

n 0 v\

0

u

‘0 \

‘0

6

al

0

u

23

c I

0

0

P 0 \ 0

. 0 d

n 8 a >

B x- P \

. ,c al 1 G 4 U C 0 V

c I

N N rl

al d w 0 1 a M bd 4 3 CI M d u-c

U

h

v n

24

n 0 9

P) P

V.l C 0 U

n 0 W

25

0

I \ 0

0

n

2

n w W

r a t i o range teated. (The level of some of the da t a curves may be i n

e r r o r because of an excesi of o i l on the modal.

are at the free-stream Mach number of 0.84 f o r configuration 1, 0.85

and 0.40 f o r configuration 2, and 0.94 f o r configurations 4 and 6.)

The data i n question

The f l a tnes s of the curves probably indicates t h a t the changes i n

entrainment and blockage e f f e c t s induced by varying the je t to t a l -

pressure r a t i o were nearly equal in magnitude and opposite i n e f f ec t .

The jet entrahment tends to mve the separation location

rearward on the b o a t t a i l by en t ra in ing mass from the separated region

rearward i n t o the jet. The magnitude of entrainment is a function of

both the velocity difference and "surface" area between flows.

Therefore, for a convergent na t z l e with a given free-stream condition, I

the mass entrained i n t o the jet would tend to increase as t he jet-exit

ve loc i ty increased.

an increase in the nozzle total-pressure rat io .

less than the ex terna l velocity, the ex terna l flow actual ly tends t o

Thls Increase in jet-exit velocity corresponds t o

If the jet velocity is

entrain mass from the jet. Also, some mixing occurs s ince the externa l

flow contacts the j e t flow a t an angle and muat be turned by the j e t

flow. When the on-design Condition l e reached, t h e jet-exit Mach

number equals one, and remains constant f o r hl&er j e t total-pressure

rat ios . Consequently, the jet-exit velocity a l so reaaine constant.

The velocity in the jet plume increases with higher jet total-pressure

r a t io s ; however, s ince the jet-exit velocity is constant, the velocity

increases near t he b o a t t a i l are r e l a t ive ly small. Consequently, the

entralnmcnt tends t o level off.

While entralnment :en& t o move the separation location

27

reaward , blockage e f f e c t s of jete tend to pressurize the b o a t t a i l

and move the separation locat lon foruard.

ratio is Increased up t o the on-design condition, the Separation

locat ion mves rearward.

the plume blockage e f f e c t s increase, ha l t i ng the rearward erovement

of the separation locat ion and eventually causing a s l i g h t forward

mvement.

(p

i n pa r t t o unsteadiness which can occur i n base flaw cases.

(Reference 60 presents a theore t ica l approach t o the base flaw

problem.) Also, a t the higher Mach numbers, the separation locat ion

is more sens i t ive t o small e r r o r s In s e t t i n g the Mach number in the

wind tunnel.

As the jet total-pressure

As higher total-presrurc ratios are reached,

There appears t o be a d i spa r i ty In some of the jet-off

Aside from experieental e r ro r , t h i s may be due /p, = 1.0) data. t , j

Since the separation locat ion remains almost s ta t ionary

throughout the jet total-pressure ratio range, i t seems l ike ly tha t

s o l i d simulator data could be used t o estimate the jet-on separation

locations. Hawever, f igure 13 shows tha t a difference exists i n the

Separation locations obtained f o r on-design conditions between the

s o l i d simulator da ta and the high-pressure air data. The je t to ta l -

pressure ratio a t which the on-desj gn condition occurs var ies

s l i g h t l y f o r d i f f e r ing Mach nunbers and configurations, causing some

of the difference.

l i t t l e throughout the range of j e t total-pressure r a t io s , most

of the difference between s o l i d simulator and high-pressure air

separation da ta m u s t be due t o entrainment. For subsonic cases,

However, s ince the separation locat ion changes

28

-- --I -- e

- Solid simulator - - - - p t , j / b = 2.0

0 Z/dm = 0.80, d,/dm = 0.50

0 Z/dm * 1.00, ddd, = 0.50

0 Z/dm = 1.00, d,/d, = 0.60 A V d = 1.00, ddd, = 0.70 m

0 L . I 1 I I I u 0 * 4 .5 .6 . 7 .8 . 9 1.0

Figure 13. - Comparfson of separation locations obtained throug’ the use of solid simulators with those obtained from j e t operaticin < i t

P,,j/P, = 2.

29

t h i s difference i n Separation locat ions obtained using the tvo j e t

simulation techniques appears t o be mainly a function of the

"surface" area of the separated region washed by the jet ( the region

between the jet exit and the reattachment point on the plume). This

tends t o d i r ec t ly correspond t o the extent of separat ion on the

boa t t a i l . For t ransonic cases, shock-Induced separat ion probably

occurs. Within experimental accuracy, the d i f ference i n the data

curves reduces t o almost zero. This ind ica tes t ha t the shock

locat ion is probably not great ly a f fec ted by entrainment.

Theoretical Results

Using t h i s newly acquired da ta base, severa l flow separation

cr i ter ia were evaluated.

empirical methods. A patched inviscid/viscid in te rac t ion computer

program consis t ing of a poten t ia l flow calculat ion (ref . 11) and a

momentum-integral boundary layer calculat ion (ref . 12) was used

t o compute the needed boundary layer and inviscid flow parameters.

The c r i t e r i i were applied using both the experimental and theore t ica l

inviscid pressure d is t r ibu t ions as input t o the boundary-layer

program.

d is t r ibu t ions .

the scatter inherent i n experimrntal data, and they are easily

calculated. This experimental scatter (especial ly i n the minimum

pressure) can cause large deviations i n the separat ion predictiona of

some criteria. Also a c r i t e r ion based on the inv isc id pressure

d i s t r ibu t ion could provide a simpler, noninteractive, and cheaper

Most of these criteria were simple, semi-

There were severa l advantages i n using the inviscid pressure

The inv isc id pressure d is t r ibu t ions do not contain

30

solution. By contrast , a c r i t e r i o n based on expe r iwn ta l data might

be more useful i n an i n t e rac t ive scheme t o solve a f l a t f i e l d .

One of the criteria teated was a modified form of the Reshotko-

Tucker c r i t e r ion (ref. 4 9 ) :

M - 0.762 MO

which s t a t e s t ha t the ratio of the Mach number a t separat ion t o the

Mach number a t the minimum pressure point is a constant. "his

c r i t e r ion is derived by applying the momentum and momentof momentum

in t eg ra l equations with spec ia l functions of the boundary layer

shape factor . The shear stress tenns are assumed negl igible i n I

comparison t o pressure tenns.

the present invest igat ion t o b e t t e r f i t experimental data by

incorporating the e f f e c t of Reynolds wmber through the skin f r i c t i o n

coef f ic ien t a t t h e minimum pressure point C t o yield:

This c r i t e r ion w a s modified during

f ,o

This modified form w i l l herer f t - r be referred t o simply as the

Reshotko-Tucker c r i te r ion . I

Another c r i t e r ion evaluated was the Page c r i t e r i o n (ref . 34):

31

This simple c r i t e r i o n states tha t separat ion occurs where the pressure

coef f ic ien t based on the minimum stat ic pressure reaches 0.38.

A t h i r d method is the Prese c r i t e r i o n (ref. 37). The separat ion

location is determined by wing the following equations:

sep , M 4 2 + (y - l)k? (1 - 6*/6) F = 'rzp sep SeP

(1 + h l o /& )p 0 0 M 4- (1 - 6*/6)o

(4)

This method uses the control volume approach.

consis ts of a sect ion of the boundary layer with one end a t the

minimum s t a t i c pressure locat ion and t h e other a t ;he separation

location.

The control volume

Quantit ies with a eubsci ipt of 1 are conditions a t t h e

32

outer edge of t h e control volume.

f o r the r a t i o of t h e boundary-layer thickness a t the minimum s t a t i c

Equations 4 and 5 are equations

pressure location t o t h a t a t the separation locat ion. Equation 4

is an integrated form of the continuity equation, while equation 5

is an integrated form of the momentum equation. Flow separation

occurs when

F = G ( 9 )

The St ra t fo rd c r i t e r i o n is a well-known method fo r determining

the separation loca t ion (refs . 36 and 38). Several similar ex is t ing

methods were combined t o form t h i s c r i te r ion . Laht i ' s version of Lis

c r i t e r i o n was used i n t h i s evaluation:

I

sep

The e f f e c t of the forebody pressure dis t r ibr l t ion and the

actual boundary l aye r traneltlon locat ion on the boundary layer

flow over the b o a t t a i l is handled by computing the dis tance t o

a f i c t i t i o w stagnation point sfS ( the e f fec t ive dis tance f o r

a f la t -p la te turbulent boundary layer t o develop the momentum thickness

at Go). Separation l e indicated when the value of C is between 0.5 and

0.6. The Separation locat ion corresponds t o the mr.ximum value of C i n

33

this interval.

consis ts of two d i f f e ren t layers.

This criterion ass- that the boundary layer

The Inner one is

independmt of upstreao conditions, and the outer layer is assumed

to be affected by only t h e Initial ve loc i ty proffle aad the

downstram pressure gradient.

The Tawnshend

(refs . 39 and 52) :

r

c r i t e r i o n is given by the equation

It is derived with the assumption t h a t the separation is dependent

upon the pressure gradient.

by the presence of the pressure gradient upstream of separation.

This is incorporated i n t o the c r i t e r i o n

The Angle method is givc.. by t h e following equation:

M s i n 8 -0.247 SeP seP

It assumes t h a t the separation location t s a function of the loca l

b o a t t a i l angle 6 and Mach number. It was derived by f i t t i n g a

curve to t h i s set of experimental data.

The Goldsdiaied c r i t e r i o n Is another well-known simple method

(refs. 40 and 41):

n

It assumes t h a t the boundary layer cons is t s of two layers. It a l s o

a s s e s t ha t a line of constant total pressure exists p a r a l l e l to

the surface.

of the adverse pressure gradient. Separation is assumed t o occur

when the laminar sublayer thickens enough t o in t e r sec t t he l i n e of

constant t o t a l pressure. Th3s viscons phenomenon is correlated

through the use of the skin f r i c t i o n coef f ic ien t a t the start of the

adverse pressure gradient.

This line intersects the inner layer a t the beginning

The Wu c r i t e r ion is another simple equation ( re f . 51):

p,,p - 0.565 Mo = 0.795 Po

It is based on experimentid data, and assumes t h a t separation is a

function of two parameters.

start of the adverse pressure gradient.

the separation s t a t i c pressure t o the mini- static pressure.

One of these is the Mach number a t the

The other is the r a t i o of

These eight criteria were tes ted by comparing the i r separation

predictions with experimental data.

were the conditions f o r whicli separation was observed on the

configurations with so l id sfmulators. Figures 14 and 15 show the

var ia t ion of separation locat ion with Mach number f o r the various

The cases used in the evaluction

35

t 1

0 Townsend

I 2 -

0 Solid simulator 0 Reshotko-Tucker A Page h Angle c\ Presz 0 Stratford

L O 0

I I 1 I I I! . 4 . 5 .6 . 7 . a . 9 1.0

(a) Configuration 1 (t/d, = 0.80, d,/d, = 0.50)

Figure 14.- Comparison of the variation of Separation location predicted by various methods with Mach number for configurations with so! id plume simulators. Experimental pressure distrikutions used in predicting separation locations.

36

1.0

.9

. 8

.7

- 6

'sep/%

.5

. 4

. 3 . 2 I 0 L

0

Q \ \

0 Solid simulator 0 Reshotko-Tucker A page b Angle b Presz 0 Stratford o Townsend

J I I I 1 I I . 4 .5 .6 . 7 .a . 9 1.0

Mal

(b) Configuration 2 (t/d, = 1.0, de/dm = 0.50)

Figure 14. - Continued.

37

I . 8 C

i

i - 7 t-

i

I .6 + i

Solid simulator Reshotko-Tucker Goidschmied

Angle Presz Stratford Townsend

page

i - 3 !-

I i I

- 2 -

Ll'A-- . 4 . 5 .6 . 7 . 8 .9 1.0

L O 0

Moo

(4 Configuration 4 (!/dm = 1.0. d,/dm - 0.60)

Figure 14. - Continued.

38

. 7

0 Solid simulator

0 Goldschmied A Page b Presz 0 Stratford 0 Tavnsend

.6 0 Reshotko-Tucker :~ I XSep/d"

_J .9 1.0

0 L l i 0 . 4 . 5 . 6 . 7 . 8

(a) Configuration 6 (\/dm - 1.0, de/d, = 0.70)

Figure 14. - Concluded.

39

1.0 - i

‘sep/% . 5

I . 4 t-

I i

I . 3 -

I . 2 -

0

Solid simulator 0 Reshotko-Tucker 0 Goldschmied A Page b Angle b Presz 0 Stratford 0 Townsend 0 wu

L

t 1 I I I 1 _. 1 0 0 . 4 . 5 . 6 . 7 . a .9 1.0

(a) Configuration 1 (\/dm * 0.80, de/d, = 0.50)

Figure 15.- Comparison of the variation of separation location p r e d i c t e d by various methods with Mach number for ccnfigurations with s o l i d plume simulators. Theoretical inviscid pressure distributions used i n predicting separation locations.

1.0 r

40

Solid simulator 0 Reshotko-Tucker 0 Coldschmied A page b Angle [5 Presz 0 Stratford 0 Townsend 0 WU

0 L 0 . 4 . 5 .6 . 7 . 8 . 9 1.0

Mal

(b) Configuration 2 (\/dm = 1.0, de/dm = 0.50)

Figure 15. - Continued.

41

. 7 -

.6 - 0 0

- 0 A b [5

- n 0 0

Solid simulator Reshotko-Tucker Coldschmied

Angle P resf Stratford Town send wu

Page

1 1 1 I 1 1 1 . 4 . 5 . 6 . 7 . 8 . 9 1.0

0 L 0

(c) Configuration 4 (t/dm = 1.0, d,/d, = 0.60)

Figure 15. -Continued.

42

1.0

.9

.a

. 7

.6

xSep/dlll

. 5

.4

. 3

. 2

0 Solid simulator 0 Reshotko-Tucker 0 Goldschmied fl page b Pres2 n Stratford

I 0 Townsend 0 wu

-

(d) Configuration 6 (\ /dm = 1.0, de/dm 0.70)

Figure 15 . -Concluded.

43

methods. In f igure 14, the experimental pressure d i s t r ibu t ions were

used i n the calculations. I n f igure 15, the theore t ica l inv isc id

pressure d i s t r ibu t ions were used.

data caused much of the scatter i n f igure 14. Also, because of the

pressure plateau i n the separated region, a small e r r o r in the value

of the predicted separation pressure can r e s u l t i n a l a rge e r r o r i n

separation location when using experimental pressures. In f ac t , the

The scatter i n the experimental

Goldschmied c r i t e r i o n predicted separation f o r only four cases, and

the Wu c r i t e d o n f a i l e d t o pred ic t any a t a l l .

the predicted trends using the inviscid pressure d i s t r ibu t ions were

much smoother, although they were of ten very inaccurate. The Wu

c r i t e r i o n was only ab le t o pred ic t separation f o r f i v e cases.

general when the inviscid pressure d i s t r ibu t ion was used, the

Goldschmied c r i t e r i o n predicted the most rearward separation locations.

It was followed i n order by the predictions of Page, Reshotko-Tucker,

Townshend, Presz, and St ra t ford . The bes t overa l l predictions were

made using the Angle c r i t e r i o n based on experimental pressure

d is t r ibu t ions . This was not surpr i s ing s ince the same data were

used t o derive t h i s c r i t e r ion . However, none of the c r i t e r i a appeared

to provide very accurate r e su l t s .

As shown i n f igure 15,

In

This inaccuracy is b e t t e r seen i n f igures 16 and 1 7 . In f igure16 ,

the predicted separation locat ions 9btained using the experimental

pressure d i s t r ibu t ions are p lo t ted versus the experimental Separation

locations. In f igure 17, the predictions obtained using the inv isc id

pressure d i8 t r ibu t ions are p lo t ted . (The l imited r e s u l t s of the Wu

44

0 0 0 A

l/d, = 0.80, d i d , = 0.50

l /d m = 1.00, d d d , = 0.50 l,’lm = 1.00, de/dm = 0.60 Z/d, = 1.00, d i d , = 0.70

A

.l[

0 >---J--J 0 . 2 . 3 . 4 . 5 .6 . 7 . b

(a) Reshotko-Tucker

Figure 16.- Evaluation of predicted separztion locations with oil-flow data for configurations with solid plume simulators. Experimental pressure distributions used in predicting separation locations.

45

1.0

.9

. 8

. 7

. 6

(&/d 1 m P

. s

. 4

. 3

. 2

. 1

- 0 0

[/dm = 0.80, d,/dm = 0.50 I /d m = 1.00, de/dm = 0.50

- 0 Z/d, = 1.00, d i d , = 0.60

Z/d, = 1.00, d i d , - 0.70 A

-

-

0 0 . 2 . 3 . 4 .5 .6 . 7 . 8

Ax/ dm

(b) Page

Figure 16. -Continued.

46

. 1 -

47

O

.9

lsO F I- O

/ -- - 0- . 2 . 3 . 4 . 5 .6 . 7 .a

. 7

-6

‘ V d m ’ p

- 5

. 4

. j

. 2

.1

0 4dm = 0.8). dJdm = 0.50

0 4dm = 1.00. dJdm = 0.50

0 4d rl, 1.00, dJdm = 0.60 A 4dm = 1.00, de/dm = 0.70

(d) Stratford

Figure 16. -Continued.

48

1.0

- 9

.8

- 1

.6

(Ax/dm;p

. 5

. 4

- 3

. 2

. 1

- 9 0

Ud, = 0.81, dJdm = 0.50

Ild, = 1.00, dJdm = 0.50

- 0 4 d m = 1.00, dJd, = 0.60

4 d m = 1.00. dJdq = 0.70 A

-

-

-

-

O O . 2 - 3 . 4 . 5 .6 . 7 . a

yll

(e) Townsend

Figure 16. -Cont hued.

49

.9 -

-

Figure 16. -Concluded.

. 1 -

50

I i

.9 - i

-.' . 5

0 4dm =O.Bo. ddd, = 0.50 0 l/d = 1.00, de/dm = 0.50

0 l /d = l.@C, de/dm = 0.60

A 4dm = 1.00. d-/d-. = 0.70

m

m e

-4t 0 U

0 7 I

0 . 2 . 3 . 4 .5 . 6 . 7 . a

(a) Reshot ko-Tucker

Figure 17. -Evaluation of predicted separation locations with oil-flow data for configurations with solid plume simulators. inviscid pressure distributions used i n predicting sep,?ration locations.

Theoretical

51

1.0

.9

.8

. 7

.6 Ch/d 1

m P

. 5

. 4

. 3

. 2

. l

0

0 [3

0 A

Udm =O-m, d e m /d = O . %

l/d, = 1.00, de/d, = 0.50

4 d , = 1.00, d d d , = 0.60

Udm = 1.00. d d d - = 0.70

0 0

0 0

0

- e m

0 /

Figure 17. -Continued.

52

.4 1

= 0.8). dJd, = 0.50 = 1.00, dkd, * 0.50 = 1.00. dJd, = 0.60

= 1.00, dkd, = 0.70

= 0.8). dJd, = 0.50 = 1.00, dkd, * 0.50 = 1.00. dJd, = 0.60

= 1.00, dkd, = 0.70

0 0 0 0

0 9

O 0

.1

0 '#'I 0 . 2 . 3 . 4 . s I .6 I . 7 I . 8 J

(c) Presz

Figure 17. -Continued.

53

1.0

.9

.8

. 7

.6

( h / d 1 m P

. 5

. 4

. 3

. 2

. 1

0 0 . 2 . 3 . 4 .5 . 6 . 7 . a

(d) Stratford

Figure 1 7 . -Continued.

54

. 8

. 7

- 6

. 4

- 3

. 2

. 1

- 0 0 0 A

l/d, = 0.83, d,/dm = 0.50

l/dm = 1.00, d,/dm = 0.50 Z/d, = 1.00, dddm = 0.60

Z/dm = 1.00, d I d = 0.70 L

e m

-

-

I I 1 I I I . 2 . 3 . 4 . 5 .6 . 7 .8

0 0 C l

(e) Townsend

Figure 17. -Continued.

55

1 . 0

. 9

. 8

. 7

.6

( Y d r n ’ p . 5

. 4

. 3

3 .-

.1

0

- 0 Z/d, = 0.80, d d d , = 0.50

[/dm = 1.00. $/d, = 0.50

l ld , = 1.00, d d d , = 0.60

[Id- = 1.00, d-/d- = 0.70

0

0 A

-

0 0 0 -/ 0

- 0 0

0

f - I I I 1 1 1 1 0 .2 . 3 . 4 . 5 . 6 . 7 . 8

B/dl?l

( f ) Angle

Figure 17. -Continued.

56

.9 - 0 I/d, = 0.80, de/dm = 0. SO

-

(g) Goldschmied

. 1

Figure 17. -Concluded.

-

5 7

c r i t e r i o n and the Goldschmied c r i t e r i o n based on the expeilmental pressure

d i s t r ibu t ions are not presented.) The extent t h a t the predictions

deviate can be seen fo r a l l methods. It should be noted, however,

t h a t some of the scatter seen i n both f igures is due t o the

experimental e r r o r i n the oil-flow data i t s e l f .

standard e r r o r of estimate fo r each c r i t e r i o n ,

By comparing the

i t w a s found tha t the Angle method based on the experimental pressure

d i s t r ibu t ions yielded the bes t results (E = 0.073)! The next bes t

results were obtained by using the Reshotko-Tucker c r i t e r i o n based

on the inv isc id pressure d is t r ibu t ions .

It is a l s o seen i n f igures 16 and 1 7 tha t the results using the

inv isc id pressure d i s t r ibu t ions are more linear. By f i t t i n g a least

squares curve, 1.e. by t r e a t i n g the predictions as a l i n e a r function

of the experimental data , an improved prediction can empirically be

obtained. The standard e r r o r s of estimate of the r e su l t i ng curve

f i t s are as follows:

Reshotko-Tucker - E 0.038, Page - E E 0.041, Presz - E 0.047, StrLt ford - E 0.048, Townshend - E = 0.051, Angle - E 0.058, Goldschmied - E 0.062.

The improved r e s u l t s obtained by applying the curve f i t t o the Reshotko-

Tocker c r i t e r i o n are compared with the oil-flow data i n f igure 18. The

58

. 9 k I

sep /dm X

Experimental Theory

0 l/d, = @. 80, d d d m = 0.50

3 c3 l/d, = 1.00, ddd, = 0.50 l /d, = 1.00, de,'d, = 0.60

[/d, = 1.00, de/d, = 0.70

0 A

U

Figure 18. -Comparison of oi l - f low data and predicted separation l o c a t i o n s made using least squares curve fit applLed to Reshotko-Tucker criterion .

59

least squares equation f o r t h i s c r i t e r i o n is:

X X Xsep = 1.870 - 0.388 + 2

dm m dm

where xo/dm is t h e minimum pressure locat ion.

c r i g i n a l predicted separation locat ion, and x /dm is the

improved prediction. It is seen tha t the accuracy can be

s ign i f i can t ly improved using t h i s technique.

pred ic t s the Separation locat ions of t h i s da ta base w e l l , i t s

predictions f o r other configurations and Reynolds numbers may not be

accurate.

x sep ,pldm is the

SeP

While equation 18

The r e s u l t s of applying t h i s technique t o the pred ic t ion of

pressure d is t r ibu t ions is shown i n f igure 19. Inviscid theory predic t s

a yreater expansion a t the minimum pressure point and places a stagnation

point at the end of t he boa t t a l l .

added, i n which the Presz cone frustum separation model is applied a t the

predicted separation point , the predicted pressure d i s t r ibu t ion more

When a boundary layer calculation is

closely follows the experimental data. There are s t i l l s ign i f i can t

e r ro r s near the dnimum pressure pcint and near the reattachment point

on the so l id simulator.

can be Improved by solving the full po ten t i a l flow equations (ref. 61)

as the inv isc id p a r t of an inviscid lviscid in te rac t ion program.

To improve the prediction near the reattachment point will require a

b e t t e r model of the separated flow t o be developed.

The prediction near the minimum pressure point

1.(

. E

.6

. 4

.2

C

0

-. 2

-. 4

- . 6

- . a

0 Experimental Inviscid theory -- -

._. - .- - Inviscid / viscid theory

I I I 1 I -1.0 - .5 0 . 5 1.0 1 .5 2 0 2 . 5

X/dnl

Figure 19. -Comparison of experimental and predicted pressure-coefficient distributions on a circular-arc boattail nozzle using a s o i i d cone to represent the separated region.

(Mm = 0.8, \/dm - 0.80, de/d, = 0.50)

CHAPTER IV

CONCLUDING

An investigation has been conducted i n the tangley 16-foot

transonic tunnel a t 0. angle of a t tack and free-stream Mach nwnbers

from 0.40 t o 0.95 t o study the phenomenon of separated f l cn on a

series of circular-arc afterbodies.

c i rcu lar cylinders v i t h

exhausts.

Both high-pressure air and s o l i d

ds/de = 1.00 were used t o simulate je t

The r e su l t s of t h i s test indicate four primary conclusions:

1. The separation locat ion moves forward w i t h increasing

longitudinal curvature and free-stream Mach number. A t t ransonic speeds

shock-induced separation p r ~ h b l y occurs, causing the separation

location t o mvz forward t o the v ic in i ty of the shock location.

2. The separation location moves l i t t l e over the j e t to ta l -

pressure r a t i o range from jet-off up t o 9; hwcver, there is a

s ign i f icant va r i Ice a t subsocic Mach nrrmbers with the s o l i d

simulator data because of entrainment.

3. None of the c r i t e r i a tested produced accurate results i n

general,

experimental dat;, results were much be t te r . Using t h i s technique,

HJwevr r when the predicticns were curve-f i t ted with

the Reshotko-Tucker c r i t e r ion gave the bes t r e su l t s (equation 18).

4. Predicted pressure coef f i c i e n t d i s t r ibu t ions are much improved

when the above technique is used t o predict the separation location.

However, much be t t e r agreement with experimental data w i l l be ross ib le

when an improved separated flow ;I- -1 is developed. This improved

model should be able t o handle ne entrainment e f f ec t s of j e t exhausts.

Also, a separated f low model which can vary i n shape may make the

pressure d is t r ibu t ion be less sensit ive t o the predicted Geparation

location.

62

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