Experimental study of supersonic axisymmetric base flow

MECHANICS RESEARCH COb~4UNICATIONS 0093-6413/92 $5.00 + .00

Vol. 19(3), 199-207, 1992 Copyright (e) 1992

Printed in the USA Pergamon Press Ltd.

EXPERIMENTAL STUDY OF SUPERSONICAXISYMMETRIC BASE FLOW •

Gamal H. Moustafa,

••

OIl

D. Bisht, K. S. Murali Rajan and

E. R a t h a k r i s h n a n ' "

(Received 4 September 1991; accepted for print 31 January 1992)

Abstract

Supersonic flow f r o m a c i r c u l a r c o n v e r g e n t / d i v e r g e n t nozzle expanded suddenly into a circular parallel duct has been investigated e x p e r i m e n t a l l y . Attention was focused on the e f f e c t s of nozzle exit Mach n u m b e r , the r a t i o of enlarged duct to nozzle exit a r e a and length to d i a m e t e r r a t i o of the enlarged duet on the base p r e s s u r e and mean wall s t a t i c p r e s s u r e field in the e n l a r g e d duct. The Mach n u m b e r as wall as the area r a t i o have a s i g n i f i c a n t e f f e c t on the base flow. The base p r e s s u r e i n c r e a s e s (the base drag decreases} with i n c r e a s i n g approach Mach number. Also, the base p r e s s u r e i n c r e a s e s with i n c r e a s i n g a r e a r a t i o f o r all Mach n u m b e r s of the p r e s e n t study. It is found t h a t the optimum length of the enlarged duct which gives the maximum base p r e s s u r e a t the tested Mach n u m b e r and a r e a r a t i o is equal to 6.0 times its diameter. The wall s t a t i c p r e s s u r e increases smoothly along the duct length in the case of supersonic flow compared to subsonic flow a t the same g e o m e t r i c a l conditions of the enlarged duct. •

Lecturer, Dept. of Mechanical Power Engg., College of Engg., Menoufia Univ., Egypt.

•,

G r a d u a t e Student, Dept. of Aerospace Engg., Indian I n s t i t u t e of Technology, Kanpur, India.

•..

Associate P r o f e s s o r , Dept. of Aerospace Engg., Indian I n s t i t u t e of Technology, Kanpur, India. 199

200

E. RATHAKRISHNAN,

G. MOUSTAFA,

D. BISHT and K. RAJAN

Nomenclature

AR

: E n l a r g e d duct area to nozzle exit area

Cps : Base p r e s s u r e coefficient CPw : Wall s t a t i c p r e s s u r e coefficient D

: Duct d i a m e t e r

L

: Duct length

M

: Mach n u m b e r

p

: pressure

X

: Distance along the duct length : s p e c i f i c heat r a t i o : Approach condition to enlarged duct

Introduction

Channels fields, and

with

a

including

backstep

are

supersonic

supersonic

widely used

missiles,

combustors.

The

in

hypersonic

gasdynamic

many

industrial

control

surfaces

characteristics

of

channels of t h i s kind in supersonic regime have been studied over a long period of time and the r e s u l t s obtained have been widely used

in

practical

main

parameters

applications.

The

base

pressure

in the study of sudden

is

expansion

one of

the

at supersonic

flow. The aim of most studies in this area is to increase the base pressure

and

thus

decrease

the

base

drag.

A

number

of

investigations for the suddenly expanded flow showed that the base pressure

is strongly

inlet Mach number,

influenced by inflow parameters

the Reynolds number and the channel to nozzle

area ratio. But only limited information effect

of

the

such as the

channel

length

on

the

is available to show base

drag

which

the

is the

objective of the present study. There

are

pressure

several

in two

theories

dimensional

for

the

supersonic

prediction flow.

of

the

base

Perhaps

the

most

important ones are based on the flow model of Chapman where

the basic

predicted

if the

physical pressure

idea is that the base at

the

reattachment

and Korst I

pressure point

can

be

is known.

Chow z analyzed the effect of interaction of a supersonic external

SUPERSONIC BASE FLOW

201

s t r e a m w i t h a s o n i c or subsonic j e t issuing out f r o m t h e base of the

model

and

investigated pressure

the

separated

of

flows

on

and

transfer

base

ldcDonald 3

layer

the

flow

pressure

of

pressure,

boundary

Korst

and

downstre~.m

suction

the

initial

Chapman

Heat

mass

effect

effect

using

modifications.

without

their

model

rearward

facing

when

some

in

steps

c o m p a r a b l e to or l a r g e r t h a n

base

with

distribution

a t supersonic conditions,

layer thickness was

on

laminar

with

and

the boundary

the s t e p height

were i n v e s t i g a t e d by Jakubowski and Lewis 4. In

fact,

the

derivatives

Chapman-Korst I

are

able

to

predict

flow

model

steady

base

and

its

subsequent

pressure,

with

good

a p p r o x i m a t i o n , f o r m o d e r a t e supersonic Mach n u m b e r s (M ~ 1.6) and thin

separating

qualitative as

a

turbulent

agreement

function

of

boundary

however,

separating

layer.

They

show

only

in the v a r i a t i o n o f b a s e boundary

layer

thickness.

a

pressure, The

main

problem a p p e a r s t o be the f o r m u l a t i o n of an a d e q u a t e r e a t t a c h m e n t criteria.

Tanner s has

rate

entropy

of

pressure

circumvented

increase

theory,

in

this

the

problem

flow.

In

relating

his

drag

supersonic

to

base

he e q u a t e s r e a l flow with an inviscid f l o w with

same b a s e p r e s s u r e .

Base p r e s s u r e is o b t a i n e d by e q u a t i n g t h e r a t e

of e n t r o p y i n c r e a s e , d i f f e r e n c e in r a t e

due to the r e a t t a c h i n g s h e a r

layer,

w i t h the

o f e n t r o p y i n c r e a s e in t h e w a k e shocks o f the

two f l o w s . T o r e d u c e the base d r a g of s u p e r s o n i c a i r f o i l s , Wilcox 6 investigated mounted

e x p e r i m e n t a l l y the

in a f l a t

investigation

plate

showed

drag

of a r e c t a n g u l a r

box c a v i t y

by using a passive venting

system.

the

closed f l o w

that

d r a g of a c a v i t y w i t h

The

was s u b s t a n t i a l l y h i g h e r t h a n t h a t of a c a v i t y w i t h open f l o w and this

kind

of

passive

flow field at

control

can

be

employed

s u p e r s o n i c speed. This kind o f

to

control

information

cavity will be

valuable f o r an u n d e r s t a n d i n g of the base f l o w b e h a v i o u r since t h e basic mechanism external

or

in t h e b a s e flow

internal.

incidence a n g l e on results

show

Also,

the

effect

t h e base d r a g was

that

the

base

numbers

is g r e a t e r

for

the

without

cavity.

pressure

was

The

is same,

effect

studied

by

whether of

coefficient

cavity base than lipshocks

]dagi

and

flow

cavity

is

with

s t u d i e d by T a n n e r ~. These

pressure

of

base

the

on

Gal.s

for

all

Mach

the

base

the

supersonic

base

For

internal

flow,

that

for

202

E. RATHAKRISHNAN, G. MOUSTAFA, D. BISHT and K. RAJAN

Rathakrishnan the

flow

et.

field

el. q used

of

a

subsonic

passive

sudden

the

c a v i t y aspect

ratio

has

as

well

base

p r e ssu r e.

as

the

control

(cavity)

expansion.

to

handle

They r e p o r t e d

that

a s i g n i f i c a n t e f f e c t on the f l o w f i el d The

structure

of

a

reattaching

s u p e r s o n i c s h e a r layer was studied by Samimy and Abu Hijleh n. The objective content,

of

that

and

study

was

coherency

of

to

explore

l ar g e

scale

the

existence,

structures

frequency

in

the

sh ear

to

investigate

layer. From this

literature

it

is

kind of problem

parameter. duct

for

that

there

is

need

i n c o r p o r a t i n g the e n l a r g e d duct length as a

Therefore,

length

clear

it

is

different

intended

to

investigate

inlet Mach n u m b er s

and

the

effect

of

area

ratios

on

th e mean p r e s s u r e f ie ld as well as on t h e base pressure.

Experimental procedure The e x p e r i m e n t a l a p p a r a t u s

used in t h e p r e s e n t study is shown in

Fig.1. Compressed dry a i r f r o m s t o r a g e tank w a s passed t h r o u g h the control

valves

chamber

and

before

restored

to

stagnation

being a c c e l e r a t e d

to

state

a prescribed

in

the

settling

supersonic

t h r o u g h an e n l a r g e d a x i s y m m e t r i c channel. Wire mesh scr een s placed th e

in t h e

s e t t l i n g c h a mb er

n o z z l e exit.

into

the

present

The f l o w f r o m t h e

ambient study

is

to r e d u c e t h e

a tm o s p h e r e. illustrated

in

model

Fig.2.

n o z z l e s of design Mach numbers

flow disturbance

enlarged

The

1.2,

at

duct was d i s c h a r g e d

geometry

Three

2.0,

level were

used

in

the

convergent/divergent

and 2.5 w e r e used.

The

t h r o a t d i a m e t e r was kept as 3 mm, but t h e e x i t d i a m e t e r w as v a r i e d a c c o r d i n g t o the design Mach number. The a r e a r a t i o (the r a t i o of enlarged varied

duct

from

cross 1.5 to

sectional 10.36.

area

For

a

to

fixed

that

of

nozzle

nozzle exit

exit)

diameter,

was the

e n l a r g e d duct d i a m e t e r was v a r i e d in o r d e r to achieve t h e d e s i r e d area

ratio.

For

every

area

ratio,

the

enlarged

duct

length

to

d i a m e t e r (L/D) was v a r i e d f r o m 1.0 to I0.0 and m e a s u r e m e n t s w e r e made

with

L/D

of

I. 0,

2. O,

3.0 . . . . . . . .

,

10.0.

The

c o n f i g u r a t i o n of the p r e s e n t e x p e r i m e n t a l study is given below :

test

SUPERSONIC BASE FLOW

Mach

Duct

n umber

D

diameter D

AR

6.2

For

the

2.6

constant

at

2.95

the

settling for

12.6 1 0.36

15.7

12.6 3.6

atmosphere

10.36

6.6

9.3 I .5

experiments,

9.8

10.0

1.5

AR

4.2

6.2

6.0

D

AR

2.6

4.7

2.5

ratio

D

AR

1.5

2.0

/ area

4.9

3.7

1.2

203

10.36

6.6

chamber all

the

pressure cases

by

was

kept

using

the

p r e s s u r e r e g u l a t i n g valve. The s t a g n a t i o n t e m p e r a t u r e was u n i f o r m a t 29 + 1° while the a m b i e n t p r e s s u r e was uniform at 72.6 ± 0.I cm hg

during

all

the

experimental

runs.

Pressure

taps

with

inner

d i a m e t e r of I mm were used f o r m e a s u r e m e n t s of pressure a t t h e base and the wall s t a t i c p r e s s u r e d i s t r i b u t i o n along the length of the enlarged duct. The base p r e s s u r e was measured with a single p r e s s u r e tap located a t the midpoint of the base plane. The wall s t a t i c pressure r e a d i n g was

taken from pressure taps d i s t r i b u t i o n

along the duct wall , f o r example, f o r L/D = I0.0 :

1

X/L

I 0.07 I

0.15

0.24

0.34

0.45

0.57

0.78

0.9

'I

f r o m the beginning of the e n l a r g e d duct. This number of p r e s s u r e taps decreased to become one t a p a t X/I. = 0.7 for L/D ffi 1.0. The measured pressures w~re r e p e a t a b l e w i t h i n t 3 Z .

Results and Discussion

The

results

are

presented

in t e r m s

of

the

base p r e s s u r e

and

wall s t a t i c pressure c o e f f i c i e n t s . Fig.3 shows the v a r i a t i o n of base p r e s s u r e coefficient with t h e approach Mach number. This' t r e n d is in good agreement with t h a t r e p o r t e d by Korst*. The base p r e s s u r e coefficient corresponding t o

204

E. RATHAKRISHNAN,

G. MOUSTAFA,

D. BISHT and K. RAJAN

the measured pB/poo is calculated from

CPS

2 ~" M2

--

( ps/pw

1 )

(I)

~o

One

can

see

that

the

CpB values increase (the p r e s s u r e drag decreases) with i n c r e a s e in the approach Mach number M . In fact, this is in a c c o r d a n c e with the expanded flow behaviour a t a convex corner. At the a b r u p t expansion, there has to be an oblique shock (overexpanded nozzle

case)

exit

requires

to

few

to

the

take

the

pressure

diameter

of

low pressure

value

in

enlarged

the

at

the

enlarged

duct

supersonic duct.

before

the

with

area

This

pressure

equilibrium can occur. The

variation

shown

in

increase

of

Fig. 4. of

base The

area

pressure

base

ratio.

coefficient

pressure

Also,

the

coefficient

present

ratio

increases

results

are

in

is

with quite

good a g r e e m e n t with t h a t of Ref.3, which shows the same t r e n d for the

base

pressure

coefficient

at

different

L/D

ratios.

The

comparison is not shown in the figure because both the cases are at d i f f e r e n t conditions. Fig.5

shows

coefficient. decreases value

the

It

effect

is

seen

L/D

that

ratio

the

on

base

the

base

pressure

pressure coefficient

with i n c r e a s i n g L/D ratio up to L/D = 6.0,

the

effect

of

L/D

insignificant. Therefore, the

of

optimum

length

on

from

in case

the this

of

base

pressure

results

it

after

this

coefficient

can

be

seen

is

that,

supersonic a x i s y m m e t r i c e n l a r g e d

flow is equal to 6.0 t i m e s the duct diameter. Fig.6

indicates

the

variation

of

wall

static

pressure

coefficient C a t d i f f e r e n t Mach numbers along the duct length. pw C is c a l c u l a t e d f r o m equation (I) by replacing the base p r e s s u r e

pw

by the wall s t a t i c p r e s s u r e . For all tested Mach numbers, t h e wall static

pressure

length

and

coefficient

there

subsonic flow I°.

is This

no

increases oscillatory

also

passive c o n t r o l s (cavities)

agreed

flow

develops

nature

well

with

along

as

the

that

that

of

shown flow

duct by with

in case of a x i s y m m e t r i c subsonic flow,

Ref.9. It can be s u m m a r i z e d that, the

smoothly

smoothly

to

in supersonic sudden e x p a n s i o n s

ambient

atmosphere

without

oscillations as t h a t of subsonic flows with passive controls.

any

SUPERSONIC BASE FLOW

205

Conclusions From t h e above r e s u l t s it is c l e a r l y seen t h a t the approach Mach number has s i g n i f i c a n t e f f e c t on the b a s e flow. The base p r e s s u r e coefficient

increases

Mach number.

(the

Also,

increasing area

the

base base

drag

decreases)

pressure

r a t i o f o r all t e s t e d

with

coefficient

increasing

increases

Mach n u m b e r s

with

and this is in

good a g r e e m e n t w i t h the l i t e r a t u r e data. The L / D r a t i o has s t r o n g e f f e c t on t h e b a s e flow and it is found t h a t t h e optimum value of LID

is

equal

coefficient pressure

to

6.0.

along level

the

to

The

variation

enlarged

almost

close

of

duct to

goes

ambient

wall

static

smoothly

pressure

from

atmospheric

base

pressure

level. This may be considered as the main a d v a n t a g e of o p e r a t i n g with s u p e r s o n i c j e t s compared to subsonic ones w h e r e the duct wall static

pressure

is

oscillatory

along

the

duct

length

especially

n e a r t h e b a s e region.

References

l.Korst,

H.

H.

transonic

;

III,

U.;

1955:

A theory

for

base

pressure

in

Mechanics

23,

L. ; 1959: On the base pressure resulting from

the

and

supersonic

flow,

J. of

Applied

593 -600. 2.Chow,

W.

interaction of

a

supersonic external

stream

with

a sonic or

subsonic jet, J. of Aero/space Sciences 26, 176-180. 3.McDonald,

H.

; 1966: The

turbulent

supersonic

base

pressure

problem. "a comparison between a theory and some experimental evidence, The Aeronautical Quarterly, 17, 105-126. 4.Jakubowski, A. K. ; Lewis, C. H. ; 1973: Experimental study of supersonic laminar base flow with and without suction, AIAA J. 11, 1670-1676. 5.Tanner,

M.

; 1985: Boundary layer thickness and base pressure,

AIAA J. 23, 1987-1989. 6.Wilcox,

Jr.

F.

J.

; 1988:

Passive venting

system

for

modifying

c a v i t y f l o w f i e l d a t supersonic speeds, AIAA J. 26, 374-376. 7.Tanner,

M.

;

1988:

Base

cavity

at

angle

of

incidence,

AIAA J.

26, 376-377. 8.Magi,

E.

C.

; Gai,

S.

L.

; 1988:

lipshock, AIAA J. 26, 370-373.

Supersonic base pressure

and

206

E,

RATHAKRISHNAN, G. MOUSTAFA, D. BISHT and K. RAJAN

9.Rathakrlshn~m, Influence

E. ; R a m ~ u - a J u ,

O. V. ; Padma~aban,

K. ; 1989:

of cavities on suddenly expanded flow field, Mech. Res.

Communications 16(3), 1:39-146. 10.Rath&kr|shnan, sudden

E. ; Sreekanth,

enl~Lrgement,

A. K. ; 1984: Flow in p|pes with

ProceedLngs

of

the

14

_t_h International

Symposium on Space Technology Lnd Science, tokyo, Japan, 491-496 11.Samtmy, M. ; A b u - H i J l e h , supersonic

K. ; 1990: Structure

of a reattachLng

shear layer, AIAJ~ J. 28, 969-9"/0.

AA

Q ..... ~

i '~

r'"

o_ ~2"_" . . . . . I1

AIR TANK ) I~PtE LinE L GATEVALVE S REGULATINGVALVE i SEtILi~ C ~ l e l l R l SCREEN ~ WINE I TNEIIMONEI I I ! I~ISSU¢~ ~ 10 NOZZLE I1 TXPANSIONTUllE I~ WALLPRESSURE TAPPINC,S 13

A A

.......... ~Se pressure JOpplrl~ I', !9 eKpons)on p~pe

~

U *TUIBE MANOI4[TERS

nOZZIv

woII

FIG.1 EXPERIMENTAL APPARATUS

~11111111111/I re-circulating

( low

•~ 7 / / / L / I / / / ~ /

* Q~ •

/I/II/II//III//III///I/IIIIIII/IIIIII

Fig.2 Supt, rsonic ~low through an l n l a r g ¢ d channel

pressure

tnpp,ng

LO

u

Variation

t4

u

of

CpB

Mach

u with

number

u

u approach

u

o

L/D

u

:6.0

Meoh

P~0 " t 2

u

: 6"01

i

number

u

Fig.4

Variation

area of

CPe

ratio with

area

ratio

OOQL,,,I . . . . I . . . . ~. . . . l . . . . J . . . . I . . . . i . . . . I . . . . J . . . . I . . . . J . . . . I . . . . , . . . . I . . . . K. . . . 0,0 15 10 4+5 tO 1~ 1.0 105 ~0

+

•

O+K--

O~

0,40

0-50

~

Fig.3

to

Mn

M~

li&

1,1

oJ

-

0.1

,-OG

..<1[

,4tm

-O.m

O,OO

104

O00~J...,I

am

UO

~

/

4.0

U

FIg.6

0.1

Cp..

04

FIG.5

U

OJ X/L distribution

o

Effect

L/D

l0

M

U

U

of

~ along

LID

~

on

duct

M

Cp e

lenoth

U

. . . . . . . . . I . . . . , . . . . I . . . . . . . . . I. ~.,L,~,_,J ~,~+L,_,~.+I.. •., •... I . . . . . . . . . l..~:, ....

L?

~

/

/

• 10.36

~lm -I.Z

area rat;o

o

U~

IU

t~ 0

0

L'~

t;U

0 Z

L'~

[/3