AIAA-84-1262 Velocity Coupling Experiments of Solid Propellant Acoustic Oscillating Combustion Lu Zhen-Zhong, Beijing Institute of Aeronautics and Astronautics, Beijing, The People’s Republic of China

AIAA/SAE/ASME 20th Joint Propulsion Conference

June 11-13, 1984/Cincinnati, Ohio

For permission to copy or republish, contact the Arnericar: Institute of Aeronautics and Astronautics 1633 Broadway, New York, NY 10019

'4

VELOCITY COUPLING EXPBRINENTS OF SOLID PTiOPEILANT ACOUSTIC OSCILLATING COMMJSTION

Lu Zhen-Zhong*

R e i j i n g I n s t i t u t e of Aeronaut ics and As t ronau t i c s B e i j i n g , The Peop le ' s Republ ic of China

Abstract

The s t a b l e f l o w d i r e c t i o n and ve lcc i ty i n d u a l channels of t u b u l a r g r a i n m o t o r du- r i n g i t s burn ing have been i n v e s t i g a t e d . They a r e t h e basis f o r ana lyz ing a c o u s t i c e r o s i v e burning. The a c o u s t i c S tanding wave p r o f i l e s have been obta ined by i n t e r - r u p t i n g burn ing technique . They provided a powerful evidence of t h e a c o u s t i c e ros ive burning. Author has a l s o designed and tes t - ed t h e "L-Shape Burner" , which i s a u s e f u l appa ra tus f o r t e s t i n g u n s t a b l e oombution of t h e i n t e r n a l p e r f o r a t i o n burning g ra in . A v e l o c i t y coup l ing model has been b u i l t on t h e b a s i s of t h e t es t s and a n a l y s i s , which have no t been performed by o t h e r i n v e s t i g a t o r s .

a

AP A t 0

D

d

d C

k U

L1

f

L

Nomenclature

c o e f f i c i e n t of burn ing rate l a w p o r t area nozzle t h r o a t a r e a sound v e l o c i t y o r i g i n a l e x t e r n a l d iameter o f tubu- l a r g r a i n o r i g i n a l i n t e r n a l diametcr of t u b u l a r g r a i n chamber i n t e r n a l diameter o s c i l l a t i o n frequency e r o s i v e c o e f f i c i e n t grain l e n g t h dis tance from f low s e p a r a t e p o i n t t o forc-end of g r a i n

L e c t u r e r

J

n

P P

PI PAJU R r

r0 r S

T

-

TO

T i t U

U - U1

U t X

W

WX

6

E

n

h P

P t (u

exponent of burn ing rate law p r e s s u r e o s c i l l a t i o n component of p r e s s u r e p r e s s u r e a t p o r t foreend pressure-ampl i tude c o e f f i c i e n t gas c o n s t a n t burn ing r a t e burn ing rate wi thout e r o s i v e o s c i l l a t i o n component of burn ing rate burn ing surface area pe r iod of o s c i l l a t i o n combustion tempera ture a t cons t an t p r e s s u r e i n i t i a l tempera ture of p r o p e l l a n t time a x i a l v e l o c i t y o s c i l l a t i o n component of gas v e l o c i t y r e v e r s a l v e l o c i t y a t p o r t fore-end t h r e s h o l d v e l o c i t y o f e r o s i v e burning d i s t a n c e from fore-endof g r a i n p o r t bu rn t d i s t a n c e ( w i d t h ) bu rn t w i d t h p r o f i l e w i t h x sound phase ang le

e r o s i v e f u n c t i o n

r a t i o of burn ing area t o p o r t a r e a

wave l e n g t h d e n s i t y o f combustion gas d e n s i t y of p r o p e l l a n t c i r c l e f requency

I. I n t r o d u c t i o n

The s t a b l e s t and ing waves of a c o u s t i c e r o s i v e burning i n g r a i n p o r t s have been formed by c o n t r o l l i n g t h e s t a b l e f low d i -

r e c t i o n and v e l o c i t y . The p r o f i l e s of bu- r n t width caused by t h e s e s t a n d i n g waves have been obta ined . I n t h i s way, we can

1

unders tand t h e c h a r a c t e r i s t i c s of t h e o::ci-- l l a t i o n . T h i s exper imenta l method is c l o s e r t o t h e r e a l motor than "T-Burner".

I n t h e one dimensional g r a i n p o r t , t h e p r c f i l e of t h e bu rn t width is

w(x)=j t r ( x , t ) d t ( 1 ) 0

where r = r ( x , t ) i s c o r r e l a t e d wi th x and t by p r e s s u r e p and v e l o c i t y u.

If t h e r e is no e r o s i v e , t hen ro=apn The e r o s i v e f u n c t i o n can be w r i t t e n as

1 +ku( u-ut) , when u > u t

ro r { 1 when u < u t e=-= ( 3 )

A, p r e s s u r e p i n c r e a s e s , t h e c o e f f i c i - e n t ku becomes large and th re sho ld u t becomes small.

We can write

!.I) iC - b q ' ! ' ~ : a t = - b,

"negat ive e r o s i v e burn ing e f f e c t s " . ( 1 )

m P 2

u- , I

T h i s s tudy has no t took acount of

E . Analyses of Quas i -S tab le Plow i n t h e MotorCmtaining Tubular Gra in

The motor con ta in ing t u b u l a r g r a i n -

wi th i n s i d e and o u t s i d e burn ing s u r f a c e s h a s both i n t e r n a l and e x t e r n a l p o r t s . liet-

ween t h e two p o r t s , combustion gases can exchange through t h e fore-end of g r a i n . Let

p o r t area ( 5 ) S burning area

)( =-= *P

( 6 ) 1.4 Only e x t e r n a l p o r t N C X = -

E.

-I L

f ig .1 . f lows i n c a s e n i n > n ex

Whenui,>n then t h e p a r t i a l combu- s t i o n gas i n t h e i n t e r n a l p o r t goes i n t o t h e e x t e r n a l p o r t through t h e fore-end of g r a i n . l'he p l ace of t h e f low s e p a r a t e p o i n t can be found (see f i g . 1 . )

il

and r e v e r s a l d i r e c t i o n v e l o c i t y is P p . a . R T , 21,,

u, = (T) !ill) p, 1-n

=, The f igure ? shows t h e r e l a t i o n o f - L

and u1 with bu rn t width w.

L 3 9 . 5 , d=8.0 d c = l a . O 0.75

p1 =85kg/cm2

0.301 , , 1 0 f ia .2 . seuarate u o i n t and v e l o c i t y

0 2.0 4.0 6 .0 8.0 mm ..

i n - i n t e r n a l p o r t When N e x > W i n , t hen t h e f low separate

p o i n t i s i n e x t e r n a l p o r t . 'The l o c a t i o n o f t h e p o i n t i s

and i t s r e v o r s a l d i r e c t i o n v e l o c i t y i s

au

I n o r d e r t o combine these t w o k inds of P l o w s e p a r a t e p o i n t w i th in i n t e r n a l and e x t e r n a l p o r t s , L e t Li=-L1 and u;=-u1. We

can draw t h e c u r v e s of and u1 wi th w

( see f igure 3. ) . I'rom f i g u r e 3, we can see t h a t i f t ho f l o w s e p a r a t e p o i n t p r i m a r i l y is i n e x t e r n a l p o r t , t h e n t h i s s e p a r a t e po-

1,

i n t w i l l move i n t o the i n t e r n a l p o r t w i th -I

2

W

0.20

0.10

0 ,' 2.0 4.0 6.0 mm

-0.10 ' propul l n t A

-0.20 d=l 0.0.LL39.5 ,dc=42. 5 -0.30 ~8=90kg/cm

I f i g . ? . s e p a r a t e p o i n t moving f r o m

e x t o r n a l p o r t t o i n c r n a l p o r t

=O then the p rogres s of burn ing . L e t - I,, I.

A t t h i s time, t h e r e i s no exchange o f co- mbustion gases between i n t e r n a l and e x t e r n a l p o r t s .

ID. The S t a b l e S tanding Waves i n t h e I n t e r n a l Po r t of Tubular Grain

The experiments have demonstrated:when f l o w s e p a r a t e p o i n t i s i n t h e i n t e r n a l p o r t of the t u b u l a r g r a i n , by means of i n t e r r u - p t i n g t echn ique , bu rn t wid th p r o f i l e s r e p r - e s e n t i n g t h e s table s t and ing wave can be found (see figure 4 ) . But when t h e f l o w s e p a r a t e p o i n t i n t h e e x t e r n a l p o r t such r e s u l t s c a n ' t be always found.

s t r a t e d i n f igure 4 . W e can see t h a t bu rn t i n t e r n a l p o r t appears as a wave shape. Each peak of wx-x curve cor responds t o an an t ino - de of v e l o c i t y . The a c o u s t i c e r o s i v e w r i n k l - es can be seen on the b u r n t s u r f a c e c o r r e s - ponding t o t h e s e an t inodes . T h i s is t h e obvious evidence of t h e a c o u s t i c e r o s i v e burnipg.

shown i n f i g u r e 4c. I t cor responds t o t h e t h i r d o rde r hamouic of gaseous column i n a tube w i t h t w o opening ends.

W

The 3 motor f i r i n g experiments are illu-

The s t a n d i n g wavc of main frequency i s

The results i n f i g u r e 4 show: 1 . T h i s kind of a c o u s t i c e r o s i v e bur-

n i n g is one dimensional and a x i a l . The main frequency of o s c i l l a t i o n is much b igge r t han 1000H~.

s imple harmonic s t a n d i n g wavc i s u , < u t . A t .d 2 . The s table f l o w c o n d i t i o n formingthe

t h i s time, most of i n t e r n a l p o r t p l a c e s i n the l a y e r f low w i t h o w t s t a b l e e r o s i v i t y . I n t h i s Slow f i e l d the a c o u s t i c e r o s i v e burn ing w i t h s i n g l e f requncy can be c x c i t e d .

u2 > u t . There i s a s t a b l e e r o s i v e t r a n s i t i o n p o i n t i n rear p a r t of t h e p o r t . The a c o u s t i c wave w i l l . p a r t l y re f lec t a t t h i s p o i n t . I t w i l l suit wi th t h e r e f l e c t i o n s between both ends. 'This i s one r eason t h a t h igh o r d e r harmonic becomes main frequency.

e x i t s of both ends. When e x i t area i s abru-

3 ; I n t h e s e experiments t h e r e i s a l s o

4 . There are s t r o n g mean f lows a t t h e

P t l y en la rged , t h i s flow w i l l create a s t r o n g j e t no i se . It p rov ides an e n e r a sou- rce f o r t h e a c o u s t i c o s c i l l a t i o n . The v i b r a - t i n g source is s o s t r o n g t h a t t h e o s c i l l a - t i o n becomes "overblown" e a s i l y ( ? ) T h i s i s ano the r reason t h a t why h igh o r d e r harmonic becomes main f requency .

harmonic. The v i b r a t i n g p r e s s u r e and the v i b r a t i n g v e l o c i t y of the s t a n d i n g wave

Supposing t h e o s c i l l a t i o n is a s imple

must have f o l l o w i n g r e l a t i o n s : (3) - wx p ( x , t ) = ~ ~ ~ s i ~ ( - ) s i ~ ( w t + 6 ) @g

C

- p w i l l cause the a l t e r n a t i n g burning

- u w i l l cause the a l t e r n a t i n g burn ing rate

Because n o n l i n e a r i t y bctween r and u (nearby t h e 9 ) i s much b i g g e r than t h a t between r and p, the a c o u s t i c s e l f c x c i t i o n i s mainly caused by the e f f e c t s of u on r.

I n t h e t e s t i n g , t h e frequency of the a c o u s t i c p r e s s u r e has been measured. The BPR-3 p r e s s u r e t r a n s d u c e r is se t on t h e fore-end o f t h e chamber. The s i g n a l was recorded on t h e t ape . The spectrum h a s been ana lysed by means of CF-500 F.P.'l'. Analyzer a f t e r the t e s t .

F igu re 5. shows t h e power spectrum of

3

m

2.20

1 .eo

1.40

1 .00

a c o u s t i c p r e s s u r e signal, t h e bottom figure p r e s e n t s t h e t r a n s i e n t r e c o r d i n g of t h e acou- s t i c p r e s s u r e . The p r a c t i c a l l y measured fr::quency of a c o u s t i c p r e s s u r e i s f=3925W,. J The frequency p r e d i c t e d by i n t e r r d p t i n g method i s f4877117,.

::ometimes s t i l l hither o r d e r harmonic becomes the main f requency of t h e o s c i l l a - t i o n i n i n t e r n a l D a r t e€ t h e t u b u l a r r r a i n . I..- X .,

0 100 X K ) 300 4co rnm An cxperirnent shown i n f i g u r e 6 is t h i s kind o f ex:implc. 'She g r a i n O P motor i s t h e sarmc as t h a t i n f i g u r e 4 . But i t s i n t e r n a l d i : i ne to r of t h e chamber i s s m a l l e r t h a n t h a t u s i n g i n t h c t e s t of f igure 4. The fl.cw s e p a r a t e p o i n t p r e d i c t e d from t h e pa- ramcts'rs of f i g u r e 6 is nearar t o t h e fo re - end than t h a t of f i g u r e 4 . I t c a u s e s t h a t t h e t h r e s h o l d p o i n t of t h e s t a b l e era.,'. -1 on i n t!ic rear p a r t o f t h e p o r t moves forwurd. 'Thn o:;r:illation wi th t h e h i g h e r harmonic j.s

1orn:cd by forward moving t h e p a r t l y r e f l e c - t i n $ ? p o i n t . The b u r n t width p r o f i l e i n f i t y r e 6 i s caused by bo th a c t i o n s of t h e

4a. b u r n t width p r o f i l e s

4b. a c o u s t i c e r o s i v e w r i n k l e s

4c. F v e l o c i t y s t a n d i n g wave

A/2=13Omm (f'3873HZ)

50 @q / .

0 stable and t h e a c o u s t i c e r o s i v e burnin(:. 'Phc x i i n frequency of o s c i l l a t i o n i s t h e f o u r t h harmonic. I t s p r a c t i c a l l y measured fre,!iicncy is f=5175H% ( s e e f.i,wre 6 ) .

0 0.10 0.20 sec 4d. mean pressure- t ime c u r v e s

i n t e r n a l p o r t of g r a i n L/ fig.4. S t a b l e s t a n d i n g waves i n

As t h e d e c r e a s e o r t h e d i ame te r of i n t c r n a l p o r t , s t i l l h i g h e r nrdw harmonic a130 t a k e s p l a c e i n t h e beginning of t h e

0.1v

0.01

0.001

I I

-++ 0.05sec fig.5. power spectrum and t r a n s i e n t r e c o r d i n g of a l t e r n a t i n g

I I I I

p r e s s u r e s i g n a l

4

'd

p r o p e l l a n t A , T . 4 F 4.40 {D=39.5,d-S,

dcz43.5

h=195 , fL5.16KHz 3.20 X

0 100 200 300 400 mm burn t width p r o f i l e

0 0 0.10 0.20 0.50 0.40 sec

mean p r e s s u r e

; . , ,

W 0.01v

0.001

f 0 z

power spectrum of o s c i l l a t i n g p r e s s u r e f i g . 6 . f o u r t h harmonic becoming main

f i r i n g . The b u r n t width p r o f i l e and o s c i l l a - t i n g p r e s s u r e r eco rd ing shown i n f i g u r e 7 can i l l u s t r a t e t h i s phenomenon. Its burn ing h i s t o r y c o n s i s t s of t h r e e i n t e r v a l s . I n t h e f i r s t i n t e r v a l , the main frequency of o s c i - l l a t i o n i s t h e f o u r t h harmonic i n company wi th s t i l l h ighe r o rde r harmonic. I n t h e second i n t e r v a l , t h e main frequency i s t h e t h i r d harmonic. I n t h e t h i r d i n t e r v a l , b e s i - d e s t h e t h i r d harmonic t h e r e a r e lower order hamonic waves. Its burn t width p r o f i l e i s b a s i c a l l y formed by both a c t i o n s of t h e fo- u r t h and t h e t h i r d harmonic. The exper i - mental result i n f igure 7 shows t h a t t h e . .

more abrup t enlargement of t h e e x i t area

frequency

D=39.3,d=6.Z9L=390

4.ao

__.-- -__- ---_r

X e x c i r c l a 4.00

0 100 200 300 460mm

Lg.*:& &j Mi

o s c i l l a t i n g p r e s s u r e r eco rd ing fig.?. main frequency changing f r o m f o u r t h

t o t h i r d harmonic

of t h e p o r t is , t h e h ighe r o r d e r hamonic of o s c i l l a t i o n occIII's.

1Y. L-Shape Burner and Its Bxperimental R e s u l t s

Applying above p r i n c i p l e Iorming sta- b l e s t and ing wave t o t h e i n n e r p e r f o r a t i n g burning g r a i n , w e have des i sned t h e L-Shape llurner and s a t i s f a c t o r y experime-] ta l r e su - l t s have been ob ta ined .

The L-Shape B u r n e r h a s two E r n i n sec- t i o n s ( s e e f i g u r e 8 ) . The t e s t i n g s e c t i o n is mounted h o r i z o n t a l l y and t h e compensa- t i n g s e c t i o n v e r t i c a l l y . Both are se t up i n I,-shape. :n t h e t e s t i n g s e c t i o n , t h e r e i s a circular i n n e r burn ing g r a i n . The compensa- t i n g g r a i n keeps t h e p r e s s u r e a t t h e f i r s t end of t e s t i n g p o r t cons t an t .

Shape Burner a r e similar t o f i g u r e 4 ( s e e figure 9 ) . The o r i g i n a l parameters of t h e 5 f i r i n g tes ts are a l l t h e same, bu t only i n t e r r u p t i n g p e r i o d s are d i f f e r e n t . From t h e s e r e s u l t s we can see t h e p rocess of t h e a c o u s t i c e r o s i v e from growing t o decay.

Using t h e L-Shape Burner , reducing t h e i n t e r n a l d iameter of t e s t i n g g r a i n w i l l a l s o

The exper imenta l r e s u l t s of t h e L-

cause t h e o s c i l l a t i o n with h ighe r o r d e r harmonic. An exper imenta l result shown i n figure 10 can i l l u s t r a t e t h i s effect.

t e s t i n g s e c t i o n A t 2

p r o p e l l a n t A ,

1 0 1.0 2.0 3.0 m

fig.8. L-shape Burner wi th double nozz le s

rnm Wx p r o p e l l a n t A. Ti=2Ooc

3.80 ~

3 . 4 0 ~

=265mm f=3.8KHZ

X 1 .oo I 0 100 200 300 400 mm

fig.9. exper imenta l r e s u l t s of L-shape

Burner wi th double n o z z l e s The power spctrum of o s c i l l a t i n g p res su re before first nozz le and i t s p a r t i a l t r a n s i - en t r eco rd ing is shown i n f i g u r e 1 1 . I n t h e i n i t i a l stage o f burning, t h e main f"PCiU-

ency of o s c i l l a t i o n is t h e f i f t h harmonic

Table 1 . Experimontal da t a shown i n f i g . 9 .

No. ,kg/cm2 t e f , s e c bW,,,,,m 1 90.8 0.113 0.198 2 82.5 0.193 3 81.2 0.24 0.54 4 73.8 0.30 0.433 5 82.9 0.413 0.26

0.29 L/

and tho o s c i l l a t i o n is almost pure s i n e wme. I n t h e middle and l a t e r s t a g e of bu- rnj.ng t h e main fryuency of o s c i l l a t i o n becomes t h e t h i r d hamonic. The bu rn t width p r o l i l e i n f igure 10 r e s u l t s from both a c t i o n s of t h e f i f t h and t h e t h i r d hamonic.

The exper imenta l r e s u l t shownin f i g u r e 12 r e p r e s e n t s t h a t t h e main f requncy of o s c i l l a t i o n changes from t h e s i x t h t o t h e t h i r d harmonic.

The L-shape Burner can be cons t ruc t ed as ii rorm wi th a s i n g l e nozz le . That i s A t l = O and A t p A t . I t has a l s o produced t h e a c o u s t i c e r o s i v e s t a n d i n g wave p a t t e r n .

A group of exper imenta l r e s u l t s & t a m b y L-Shape Burner wi th t h e s i n g l e nozz le i s shown i n f i g u r e 13.There i s t h e severe

WX

0 100 & 360 400 mm loa. bu rn t width p r o f i l e

kg/cm2

81 =106.7kg/cm

r i _ t 0 0.1 0.2 0.3 0.4 sec

: ! i. .i. .L-. 1.. .t ..,. 1 ..A ,...... I . _ _ . L. ,, lob. maan p r e s s u r e and a l t e r n a t i n g

p r e s s u r e f ig .10 . experiment with main frequency

bhanging from f i f t h harmonic t o t h i r d harmonic

6

3675H~ 3625H~

'4 o*'vl 1 { 4.89mv \ 4.21 , 7mv

1 ! t 2 d . 1 6 5 s e c

t, =O.o925sec

V

b , : t 8 10 12 114 msec 0 2 4

f ig .11 . time- power spectrum and p a r t i a l t r a n s i e n t r eco rd ing of o s c i l l a t i n g p r e s s u r e

p r o p e l l a n t A,Ti=lO'c

Y=5.0 d&.O,L=420, d 4.40 8, =98.9kg/cm

W

4.001

3.60 0 100 200 300 400 mm

f ig .12 . t e s t c o n t a i n i n g s i x t h and t h i r d hamonic

s t a b l e e r o s i o n at t h e back o f t h e p o r t . The a c o u s t i c e r o s i v e s t and ing wave i s s i g n i f i - c a n t a t t h e i n t e r v a l between t h e fore-cnd and t h e th re sho ld p o i n t s t a b l e e ros ion . I t

rnm Iwx p r o p e l l a n t c , ~ ~ = 2 0 ~ ;

108.7 1.80

1 .00

0.60 I X

0 lob 260 300 400 mm

Burner wi th s i n g l e nozz le f ig .13 . exper imenta l results of L-Shape

exper imenta l r e s u l t s can be found i n o t h e r r e f e r e n c e s .

Conclusions proves t h a t the a c o u s t i c wave i s p a r t l y r e f l e c t e d a t t h e t h r e s h o l d p o i n t of s tab le e ros ion . The a c o u s t i c e r o s i v e obta ined by L-Shspe Burner with t h e s i n e l e n o m l e is much weaker than onc wi th double nozz les .

T h i s paper p re sen ted t h e d i f f e r e n t exper imenta l r e s u l t s Of t h e a c o u s t i c e r o s i v e burn ing and analysed the r e l a t i o n between t h e a c o u s t i c e r o s i v e and mean f low. The fo l lowing conclus ions can be obta ined:

1. T h e a c o u s t i c e r o s i v e burning-

The L-shape Burner wi th t h e s i n g l e nozz le i s v e r y similar t o t h e motor w i th i n n e r p e r f o r a t i n g buru ing g r a i n . The similar

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v e l o c i t y c o u p l i n g i s correlated w i t h t h e s t a b l e f low states i n g r a i n p o r t .

2. Thc v e l o c i t y c o u p l i n g o s c i l l a t i n g combustion i n t h e g r a i n p o r t is mainly cau- sed by n o n l i n e a r r e l a t i o n s between v e l o c i t y and e r o s i v e o h a r a t e r s .

3. For t u b u l a r g r a i n wi th i n t e r n a l and e x t e r n a l s u r f a c e burning, when t h c f low s e p a r a t e p o i n t of combustion gases i s i n t h e i n t e r n a l . p o r t , t hen t h e s t a b l e s t a n d i n g waves c a n be ob ta ined e a s i l y . A t t h e vela-. c i t y antinode:; of s t a n d i n g waves, t h e s i E n i - f i c a n t e r o s i v e wr ink le s can be seen. 'Yhi.5 i s t h e powerful evidence of t h e a c o u s t i c e r o s i v e burning-veloci ty coup l ing .

4 . Applying t h e Same p r i n c i p l e s , wc

have designed t h e L-Shape Burner and o h t a i - ned t h e p a t t e r n of t h e a c o u s t i c e r o s i v e s t a n d i n g wave. The L-Shape Burner can be

used t o examine combustion u n s t a b i l i t y of i n t e r n a l p e r f o r a t i o n burn ing p r o p e l l a n t .

5. I n v e s t i g a t i o n of combustion i n s t a - b i l i t y by means of t h e i n t e r r u p t i n g t echn ique i s a s imple and convenient method. I t i s v a l u a b l e t o f u r t h e r r e s e a r c h . The main frequency of t h e a c o u s t i c p r e s s u r e is c o n s i s t e n t w i th t h e frequency ob ta ind from t h e i n t e r r u p t i n g technique.

We have only i n v e s t i g a t e d t h e coup l ing e f fec t between t h e " p o s i t i v e e r o s i v e " and t h e a c o u s t i c o s c i l l a t i o n . I n some cascc. "nega t ive e r o s i v e " t u k e s p a r t i n t h e coupl- i n g . I t w i l l c ause more complex u n s t a b l e combustion phenomena. T h i s cannot be p r e s e n t e d more i n t h i s paper .

Acknowledgments * X .

The a u t h o r wishes t o extend special acknowledgment who g i v e t h i s r e s e a r c h many gu ides .

The perfomance of experiments was c a r r i e d o u t w i th t h e a s s i s t a n o e of Guo Xiao, %hu %hen-Rong and Yuan Shi-Hang, who a r c a l s o g r a t e f u l l y aoknowleged.

t o prof e s so r i'eng Hen-Lan,

Murphy J . K . , An 13xperi mental I n v e s t i g a t i o n of t h e ih-osive Burning C h a r a c t e r i s t i c s of a Non-Homogeneous S o l i d p r o p e l l a n t , AIM

p r e p r i n t 64.107. 4 ( 2 ) Morse, P.M., V i b r a t i o n and Sound,

L'245, NcCraw-Hill Book Company. Inc . New York Toronto London, 1943.

( 3 ) U i l l i a n s , P . A . , Hung, N.C. and B a r r c r e , E . , Fundamental Aspects of S o l i d P r o p e l l a n t Rockets , 1'61 1 , AGADograph, NATO, 196".

(4) Bacchus works, Magana, Utah, Vela- c i t y Coupling Ana lys i s , P14 , Technica l Repor t , NPRRPL-TR-72-12, Janu.iry 1972.

** T h e a u t h e r e x p r e s s e s h e a r t f e l t t h a n k s

t o p r o f e s s o r B. Zinn who suggested a good

proposalwhen he v i s i t e d o u r l a b o r a t o r y i n

May 1983.

U

References

( I ) Zucrow, M.J., Osborn J.R., and

a

VIGOCI'I'Y COUPLING iXPI+RINENTS OF SOLID PROPELLAN'J' ACOUSTIC OSCILLATING COMBUSTION

Lu Zhen-Zhong"

Bci j ine, I n s t i t u t a or Aeronaut ics and A s t r o n a u t i c s B e i j i n g , Thc P e o p l e ' s Republ ic of China

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