387987.pdf

A

Flexible

Nozzle

for

a

Small

Supersonic

Wind

Tunnel

*

SATISH

DHA\VANt

AND

ANATOL

ROSHKO

t

California

I

n.rlitule

oj

Technology

SUMMARY

The

design

of

a

small

supe

rsonic

wind

-

tunn

el

te

st

sect

ion

(

-1

by

10

in .)

in

co

rporating

a

fl

exjb

le nozzl

e is

outlined

.

The

flexibl

e

nozzle

consists

of

a

high-str

e

ngth

s

tepped

steel

plate.

Two

sc

rew

j

acks

provide

an

easy

means

of

continuously

changing

the

nozzle

's

shape

acco

rding

to

the

aerodynamic

requirements.

The

bound-

ary

-l

a

yer

compensation

can

also

be

va ried

during

oper

at

ion

.

Pr

ess

ure

surveys,

together

with

schlieren

and

interferometric

a

nalysis

of

the

te

st

section,

sh

ow

the

flow

to

be

uniform

ov

er

the

operating

range

(Jl

=

1.1to1.5

) .

blTRODt;CTION

T

HE

DEVELOP)IENT

OF

experimenta

l

research

in

transonic

and

supersonic

flow

has

increasingly

demanded

the

use of

a

wind

tunnel

with

cont

inu

ous

control

ove

r

the

fl

ow

parameters.

Since

the

air

speed

in

a s

up

erson

ic

wind

tunnel

is

determined

comp

l

ete

ly

by

the

geometry

of

the

nozzle,

it

is

necessary

to

pro-

vide

a different

nozzle

shape

for

each

different

req

uir

ed

speed.

The

use

of

a flexible

nozzle

permits

a

continuous

change

in

the

fl.ow

Mach

Number

and

constitutes

a

considerable

advantage

and

improvement

ove

r

the

alternative

of

using

a series

of

fixed

geometry

nozzles.

The

idea

of

u sing

a flexible

nozzle

is

not

new,

and

there

are

in

existence

and

operation

in

this

country

several

supersonic

wind

tunnels

incorporating

th

e

device.

However,

as

far

as

can

be

determined

from

published

descriptions

of

these

wind

tunnels,

the

flexible

nozzle

with

its

shape-changing

mechanism

is

rendered

com-

plex

by

the

range

and

accuracy

requirements.

For

instance,

in

order

to

change

the

nozzle

shape

the

wind

tunnel

h

as

to

be

shut

down

and

the

requ

ired

changes

made

in

small

degrees

of

adjustment

.

During

the

past

yea

r or so

there

h

as

been

in

use

a flexible

nozzle

of

ex-

ceptionally

simple

design

in

the

4-

by

10-in.

Transonic

Tunnel

at

the

California

Institute

of

Technology.

t

The

supersonic

range

of

the

tunnel

is

limit

ed

from

Received

l\I

a

rch

22,

195

0.

*

Th

e a

uthors

wish

to

acknowledge

the

supervision

and

help

of

Dr.

H

ans

Wolfg

a

ng

Liepmann,

und

e r whose

direction

the

de-

sign

was

executed.

Harry

As

hk

e n

as

rendered

valua ble

assist-

a n

ce

in

the

mechanical

design.

t

G u

ggen

h

eim

Aeronautic

al

Laboratory.

t

The

test

section

described

h

ere

is a

modific

at

ion

on

th

e

orig-

inal

test

section

of

the

2-

by

20-in.

high

subso

nic

tunnel

built

in

19-1-1

under

A.A .F .

contract

for

high-

speed

flow

inv

est

ig

a

tions

.

A

study

of

boundary-layer

and

s

hock

-

wave

phenomena

is

at

pres-

ent

in

progress

under

:N.A.C.A.

s

ponsor

s

hip;

the

design

pre-

sented

her

e

was

executed

in

the

co

ur

se

of

this

work.

Re

s

ult

s of

recent

r

esearch

in

the

tunnel

are

being

published

elsew

here

by

the

N.A.CA.

approximately

JI

=

1.1

to

1.5,

and

this

fact

is

fully

exp

l

oited

in

the

int

erests

of

simpl

icity

to

ach

ieve

a

design

that

permits

continuous

shape

changes

in

the

nozzle

during

operation

whi

le

r

etain

ing

accuracy

and

uniformity

of

flow.

Over

the

major

portion

of

the

operating

range,

the

only

operation

required

to

change

the

flow

:'.\Iach

~umber 

is

the

turning

of

a single

jack-

screw.

This

paper

briefly

out

lin

es

th

e

interesting

fea-

tures

of

this

tunnel

with

special

attention

to

the

design,

construction,

and

use

of

the

flexible

nozzle.

DESCRIPTION

OF

TEST

SECT

I

OX

The

working

section

of

the

G .

.\.LCIT

4-

by

10-

by

4

-in.

tran

sonic

tunnel

is

sketched

in

Fig.

1 showing

the

essential

features

of

the

design.

The

floor

block

of

the

test

section

carries

the

one-wall

flexible

nozzle

plate,

together

with

the

swiveling

jackscrew

contro

ls.

The

floor

is

hinged

just

downstream

of

the

main

jack,

and

its

downstream

end

can

be

raised

or

lowe

red

by

means

of

a screw

jack.

This

allows

a

lt

erations

in

boundary-

l

ayer

compensation

during

operation.

The

ceil

in

g

block

of

the

tunne

l

suppo

rt

s

the

traversing

mechan

ism

and

contains

a

narrow

slot

for

operation

of

the

tr

ave

rs-

ing

arm.

A

pr

ess

ure

box,

with

access

panels

mounted

on

the

ceiling

block,

encloses

the

traversing

mechanism

and

seals

it

to

the

test

section.

Pressure-sealing

of

the

test

section

is

secured

by

means

of

rubb

er tube-in-

grooYe

seals

betw

een

the

sidewa!Js

and

floor

and

the

cei

lin

g

blocks.

The

sidewalls

are

mad

e in

panels

and

a

ll

ow

the

window

to

be

loc

a

ted

anywhere

in

the

4

-in.

length

of

th

e

test

section.

The

main

flexible

nozzle

consists

of

a

continuous

spring

steel

plate

45

1

/

4

in.

l

ong

of

vary

ing thickness,

of

which

36

in.

forms

the

flexible

nozzle

and

the

remai

nder

is

the

floor

of

the

test

section

(

see

Fig.

1) .

It

is

anchored

in

the

contraction

with

the

downstream

end

also

direction-fixed,

but

it

is

free

to

move

horizontally

on

rollers

when

deflected

by

the

jacks.

A

second

flexible

nozz

le p

l

ate

begins

where

the

primary

no

zzle

ends.

The

flexible

second

throat

acts

as

a

speed

contro

l

during

subsonic

operation

of

the

tunnel

and

may

be used

as

an

adjustab

le

super-

sonic

diffuser

during

supe

rsonic

runs.

DESIGN

CoNSIDERAno:-;rs

(I

)

Aerodynamic

Nozz

le Shapes

The

supersonic

range

of

:'.\Iach

~umbers 

in

the

tunnel

is

from

1

11

=

1.1

to

1.5.

Fig.

2 shows

the

th

eoretical

253

254

J

0

l:

R

::\

A

L

0

F

T H E

A

E

R

0

::\

A

l:

T

I C

A L

S

C

I E

::\

C E

S -

A

P

R I

L,

1 9

5

l

CONTRACTION

CASTING

FLEXIBLE

\

'

0

JACKS

~

PRESSURE

BO

STRUT

/

SECOND

THROAT

CONTROL

SECOND

THROAT

FLEXIBLE

PLATE

BOUNDARY

LAYER

COMPENSATION

CONTROL

Fie

.

l.

Sk

et c h

of

th

e

GALCIT

4-

by

1

0-

by

48-in.

transonic-tunnel

test

sect

ion

.

nozz

le

shapes

cove

ring

this

range.

These

shapes

were

o

btained

graphically

by

the

well-known

method

of

two-

dimensional

char

ac

teristics.

1

The

fundamental

pro

-

cedure

in

this

me

thod

consists

of

as

s

um

ing

an

initi

al

expansion

c

urve

sta

rtin

g

from

zero

inclination

at

the

thr

oa

t

up

to

th

e

n ozz

le

expansion

a ngle

8

(

Fig.

3),

which

must

be less

than,

or a t m

ost

e

qual

to,

half

the

Pran

dtl

-

~

'

I

eye

r

a ngle assoc

i

ated

with

th

e

fina

l

l\Iach

••

..

.

~

..

l

09

w

~

§

••

03

i-

Ol3TANCC

f"AO

M

THROAT

-

IN C HE

S

Fre.

2.

;:

~

'~.

~

>~

--

-

- PAR

- A-

LLE

-

L

l

LT";l

i'O""=

·

"""·

~

.

~.,,....=-

--

-ll

_-_

~

--

~

-

---·

·

~~

w

.

~

I

~

=

NOZZLE

EXPANSION

I

NIT

I

AL

ANGLE

EXPANSION

ZONE

Fie

.

3.

J

umber.

The

initi

a l expansion

curve

is

th

en divided

int

o s

uitabl

e

stra

ig

ht

segments.

The

ex

pansi

on

wave-

l

ets

ge

nerat

ed

by

thi

s convex

initi

al

curve

determine

uniquely

th

e s

ub

seq

u

ent

fo

rm

of

t he nozzle

for

pa

ra llel

fl

ow

at

the

ex

it

.

F or a r

eq

uir

ed

l\fach

Number

in

the

t

es

t section,

there

is

thu

s a

n infinit

y

of

poss

ibl

e initial

curve

and

expansion

an gle

e

comb

in

ations.

Th

eo

r

et

-

i

ca

lly,

th

e sho

rt

est l

engt

h nozz

le

·would

be

obta

i

ned

by

using

th

e

maximum

va

lu

e

of

e

(eq

ual

to

ha lf

the

Prandtl

-1\

I

eyer

ang

le)

an

d

an

initi

a l ex

pa nsion

of

in

-

finit

e c

ur

va

tur

e-

i.e.,

a s

h arp

co

mer

a t

the

throat

.

Ac

tu

a lly,

howeve

r,

th

e

presence

of b

o

und

a ry

l

aye

r

limit

s

the

rate

of expans

ion.

F or des

i

gn

purp

oses,

a

r

ad

ius of

c

ur

va

tur

e

at

the

throat

of

approx

im

ate

ly

two

to

four

times

th

e t est-sect

i

on

heig

ht

may

be

used.

In

choos

ing

the

aerody

n

am

ic

shapes

shown

in

Fig.

2,

the

ini

t ia l

expa

nsi

on

wave

and

th

e nozz

le s

lope

8

were so

adj

u

sted

as

to

give

con

sta

nt

l

engt

h nozzles

(

th

roa

t

to

exit

)

fo

r

the

va

riou s

des

ign

Mach

Kumbers.

This

per-

mitted

th

e use

of

a co

n

sta

nt

len

gt

h

fl

ex

ible p

l

ate

for

the

s

up

ersonic

nozz

le a

nd

si

mp

li

fied

th

e mechanica

l d

es

i

gn

consi

de

ra bly.

(2 ) B

oundary-Layer

Compensa

t

io

n

The

theoretically

obtained

nozzle

sh apes

do

not

t

ake

into

a

ccount

th

e

growth

of

the

bound

a ry l

aye

r on

th

e

walls

of

th

e

t u nne

l.

I n o

rder

to

a llow

for

th

is,

it

is

usua l

to

d isplace

the

phys

ical

wa

ll

s a t

each

po

i

nt

by

th

e

"

displacement

thickness

"

of

the

bo

u

nda

ry

layer

at

th

a t

po

i

nt

.

One

met

h

od

of

obta

in ing

appro

ximate

esti-

mates

of

the

bounda

ry-l

aye

r

growth

is

to

ass

um

e

th

e

pressure

grad

ie

nt

on

the

wa

lls

as

obtained

by

the

in

-

F

L

E

X I

B L

E

K

0

Z

L E

f'

0

R

S

::O.I

A L L

S

t.:

P

E

R

S 0

X

I C

\\

'

I

X

D T

U

X

E

L

viscid

flow

computation

and,

then,

to

use

boundary-

l

aye

r

theory

to

calcu

l

ate

the

displacement

thickness.

In

the

design

und

er

discussion,

th

e

compensation

for

boundary

l

ayer

was

taken

into

acco

unt

in

a

more

ele

-

mentary

fash

i

on

.

Experience

in

the

sect

i

on

of

the

wind

tunnel

had

shown

that

a line

a r co

r-

r

ection

of

0.021

in.

per

in.

in

the

walls

was

sufficient

to

allow

for

the

boundary-layer

growth.

In

addition,

th

e

present

design

includes

provision

for

a

lt

e

rations

in

the

allowance

with

the

tunnel

in

operation.

Subsequent

resu

lts

justified

the

estimates

used

.

THE

~OZZLE 

PLATE

(I

)

Requirements

(a)

The

no

zzle

plate

sho

uld

be

able

to

reproduc

e,

during

operation,

any

aero

dynamic

nozzle

shape

in

the

r

eq

uir

ed

range.

(b)

The

shape-changing

mechanism

should

be

simple

and

no

zzle

settings

acc

urately

repeatable.

(c)

The

plate

must

be

free

from

l

oca

l

distortion

and

vibrationally

stable

during

operation

of

the

wind

tunn

el.

(2)

Plat

e

Shape

and

Control

Configuration

Study

of

th

e

aerodynamic

shapes

(Fig.

2)

to

be

re-

produced

by

the

nozzle

pl

ate

shows

that,

in

gene

ral,

the

aerodynamic

sh

apes

h

ave

an

initi

al

region

of

rel

a-

ti

ve

ly

high

curvature

fo

ll

owed

by

an

a

lm

ost

straight

portion

containing

an

inflexion

point

(reve1sal

in

si

gn

of

the

curYature

) .

The

terminal

sect

i

on

of

the

shapes

is

seen

to

have

rel

ative

ly

the

lar

gest

l

engt

h

and

a uni-

formly

decreasing

curvature.

Fi

g.

4 shows

the

curva-

tures

of

various

configmations

of

a pl

ate

repres

ented

as

an

elastic

beam

in

rel

at

i

on

to

the

curvatures

of

a r

ep

re-

sentative

ae

r

odynam

ic

shape.

It

is

clear

th

at

a mini-

mum

of

two

contro

ls is

required

to

produce

the

requir

ed

change

in

sign

of

c

ur

vat

ure

in

the

pla

t e.

Fig.

4 a lso

shows

how

the

j

acks

for

changing

the

shape

of

the

no

zzle should

be

l

ocate

d.

Since

the

greatest

curvature

in

the

plate

is

produced

in

the

vicinity

of

the

main

jack,

this

must

be

situated

close

to

th

e

throat

of

the

nozzle.

It

is a lso

evident

that

it

is impos

sib

le

exactly

to

repro-

duce

the

req

uir

ed

curvat

ur

es

with

a

cont

inu

ous

plate

of

co

n

sta

nt

thi

ckness.

Fig.

4d

shows

the

manner

in

which

a

va

riati

on

in

moment

of

inertia

of

the

plate

cross

section

may

be

used

to

advantage

in

br

inging

the

elastic

and

ae

r

odynam

ic

shape

curvatures

closer

to-

gether.

The

second

integrals

of

these

c

ur

Yes

-

i.e.,

the

act

u

al

shapes

-

would

then

be

sti

ll

closer.

In

o

rd

er

to

secure

smoot

h

ent

r

an~e 

and

ex

it

conditions

at

a

ll

:\Iach

Numbers,

it

is

highly

desirable

to

h

ave

the

ends

of

the

nozzle

plate

fixed

in

direction.

A

comparative

study

of

several

configurations

alo

ng

th

e lines

indicat

ed

above

led

to

th

e

adoption

of

the

configuration

schematically

r

epresented

in

Fig.

5.

The

nozzle

plate

consists

of

a

stepped

beam

l

oaded

at

two

points

by

screw

jacks

(a)

\

/

SIMPLE

BEAM

WITH

\

/

SINGLE

LOAD

\

w

/

\

/

\

/

\

/

\

/

(bl

/

SIMPLE

BEAM

WITH

\

/

\

/

w2

TWO

LOADS

/

\

WI

/

I

\

/

I

\

/

I

\

/

I

\

/

I

\

/

I

/

I

\

I

---

I

/

I

/

I

/

I

/

(c)

I

BEAM

WI

TH

DIRECTION

I

/

FIXED

ENDS

AND

I

/

W2

TWO

LOADS

I

WI

I

/

I

PORTION

CF

BEAM

I

APPROXIMATING

I

HE

AERODYNAMIC

I

NOZZLE

I

(dl

I

"S

TEPPED

"

BEAM

WI

TH

I

W2

DIRECT

ION

flXED

ENDS

I

A

ND

TWO

LOADS

I

FIG.

4.

Curvatur

es

of

e la

tic

and

aerodynam

ic

s h

apes.

and

having

direction-fixed

.ends.

The

l

ocation

of

th

e.

jacks

and

the

step

in

the

plate

was

determined

by

trial

to

give

the

best

overa

ll r

eprod

ucti

on

of

the

aerodynam

ic

shapes

ove

r

the

required

range.

a·

NOZZLE

PLATE

AND

FI TTINGS

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1.4

1.

2

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0 .8

0 .6

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MATCHING

OF

THE

AERODYNAM

IC

I

AND

ELAST

IC

SHAPES

M=

l. 5

J

_J

"

u

~

1

I

4

a

12

16

20

24

28

DISTANC

E

FROM

TH

R

OA

T

INCHES

FIG.

6.

FLE

XI

BLE

NOZZLE

CONTROL

SETT

INGS

I.I

TEST

SECTION

MACH

NUM

BER

FIG.

i .

-1

1.6

(3) D

eterm

inati

on

of

Co

ntr

o l

Settings

The

restriction

on

the

deflection

curve

of

the

pl

ate

when

it

is

r

equi

red

to

reproduce

an

aerodynamic

shape

is

that

it

must

have

a prescribed

maximum

deflect

ion.

This

is given

by

the

un

ique

height

ratio

h

h*

assoc

i

ated

with

a

desired

supe

r

critica

l

fl.ow

in

the

test

section.

Here,

h

is

the

height

of

the

two-dimensional

test

sec-

tion,

and

h*

is

the

height

at

the

throat.

Knowing

the

dimensions,

end

conditions,

and

type

of

l

oading

on

the

p l

ate,

the

elastic

influence

curves

of

the

configuration

can

be

calculated

.

These

permit

a

determination

of

all

the

possible

plate

shapes

(Fig.

6)

with

a

given

maximum

deflection

in

terms

of

the

load

ratio

v

=

H'2

ll'1,

where

Jf'i

=

l

oad

in

pounds

on

the

main

jack-

screw

and

ll'

2

=

load

on

the

second

jackscrew.

:\.

superposition

of

the

required

aet

odynamic

shape

and

the

corresp

;:i

nd

ing

plate

curves

serves

then

to

determine

the

op

t

imum

,·alue

of

v,

and

the

control

settings

are

compu

te

d

fr

om

the

deflection

influence

functions

of

tr.e

pl

at

e.

A

r

epresentative

case

of

matching

of

the

aerodynam

ic

and

el

astic

curves

for

JI

=

1.5

is shown

in

Fig.

6,

the

vertical

scale

being

exaggerated

to

increase

the

accuracy

of

matching.

Fig.

7

shows

the

final

cun-es

from

which

control

settings

for

any

:'.\lach

-um-

ber

within

the

design

range

may

be

obtained.

It

will

be

obse

rved

th

at

ove

r

a lm

ost

th

e

entire

range

of

operation

only

the

main

jack

sett

ing

is

req

uir

ed

to

be

a l

tered.

FABRICATIOX

OF

THE

~OZZLE 

PLATE

The

problem

in

fabr

i

cation

was

to

obtain

a r

elatively

thin,

high-strength

plate

free

from

loca

l

deformation,

particula

rly

loca

l

deformations

near

the

attac

hment

fittings.

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FIG

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Xumber

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ertic

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5

TOP