AI AA-86-0534 Experimental Analysis of Unstable Combustion in Double Base Solid Propellant Rocket Motors Lu Zhen-Zhong, Beijing Institute of Aeronautics and Astronautics, China

AIM 24th Aerospace Sciences Meeting January 6-9, 1986/Reno, Nevada

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EXPERIMENTAL ANAIYSIS OF UNSTABLii COKEUSTION I N DOUBLE BASE SOLID PROPiLLANT ROCZL~'~' MOTORS

Lu Zhen-Zhong*

403 Teaching Group, Je t Propuls ion Department B e i j i n g I n s t i t u t e of Aeronaut ics and Ast ronaut ics The Pople ' s Republic of China

ABSTMCT L g r a i n l e n g t h Lc chamber l e n g t h

c o n s t a n t mena have been descr ibed by f i r i n g t h e m2 c o n s t a n t expermental r o c k e t motors with t u b u l a r n exponent of burning ra te law g r a i n . Some of these phenomena are d i f f e r e n t P mean p r e s s u r e from t r a d i t i o n a l view p o i n t s about uns tab le Pi combustion. I t v a s found t h a t i n the combus- Peq c a l c u l a t e d e q u i l i b r i u m P r e s s u r e

The v a r i o u s u n s t a b l e combustion pheno-.

mean p r e s s u r e a t p o r t fore-end

t i o n process , t h e main frequency o f t h e spectrum exchanges .from high o r d x harmonic t o low one. Tho experiments have proved t h a t t h e main frequency of a x i a l o s c i l l a - t i o n can be as h igh as above IOKHZ. The experiments have expressed t h a t when secondary pressure s p i k e appeears , t h e high frequency o s c i l l a t i o n s a r e stopped. The spectrum before t h e secondary sp ike has been checked. .?her2 i s no more s t r o n g high frequency o s c i l l a t i o n . The r e s u l t s of experiments about low frequency i n s t a b i l i t y d iverge f r o m the "L*-'l!heory". The experi- ments have a l s o proved t h a t i n t e r m i t t e n t Vfree combustion not only i s caused by low pressu- wx r e but i s a l s o c l o s e l y r e l a t e d t o t h e c o n d i t i o n s of mean flows. i n a l y s i n g t h e e f f e c t o i t h e nega t ive erosive c h a r a c t e r on e x t i n c t i o n of combustion, au thor b e l i e v e s t h a t t h e o ld " f i r i n g is blown out" hypo-

T i U h U

u t h

U t r

X E

PP n

h P P r - Pressure ampli tude o f s t a n d i n g wave

average p r e s s u r e over burning time burning ra te burning ra te without e r o s i v e time i n i t i a l temperature of p r o p e l l a n t a x i a l mean v e l o c i t y

U = U t h , &=I) t r a n s i t i o n Doint of e r o s i o n (when u = u t r , =minimum) chamber f r e e volume burn t w i d t h with x d i s t a n c e f rom foro-end of' grain p o r t e r o s i v e f u n c t i o n d e n s i t y of p r o p e l l a n t burning per imeter

t h e s i s is reasonable . I . I n t r o d u c t i o n

Nomenclature

a c o e f f i c i e n t of burning ra te law Ab burning surface a r e a AT) D o r t area

hozzle t h r o a t area c o n s t a n t

A; bi

c o n s t a n t C c h a r a c t e r i s t i c v e l o c i t y D o r i g i n a l e x t e r n a l diameter of

t ubul ?r g r a i n d o r i g i n a l i n t e r n a l diameter of

t u b u l a r g r a i n dc chamber i n t e r n a l diameter ac nozzle t h r o a t diameter f" frequency G mass f l u x ( a x i a l )

Ab K=- r a t i o of burning area t o p o r t area

ka e r o s i v e c o e f f i c i e n t kb nega t ive e r o s i v e c o e f f i c i e n t L* c h a r a c t e r i s t i c length

.* Lecturer

A t

GPYd8hl @ Amrd- Imltllut. of AemnsuUo and AStmn.oUw, lw., 1986. All rights mewed.

The combustion i n s t a b i l i t y happening i n t h e real s o l i d p r o p e l l a n t rocke t motors i s a complex. l i v e l y and e x c i t i n g s u b j e c t . However,-i t i s d i f i ' i c u l t t o understand i t s mechanism"). Kany i n v e s t i g a t o r s t r i e d t o uncover t h e mystery by v a r i o u s methods. The T-Burner t e s t s seem t o have soloved some problems about mechanism of combustion i n s t a b i l i t y and Some models about combustion i n s t a b i l i t y had been formulated on t h e basis

I -. o f T-Burner"'.

F u r t h e r a n a l y s i n g the d i f f e r e n c e bet- ween '?-Burner and^ real r o c k e t motors, w e found t h a t many i n s t a b i l i t y phenomena t a k i n g p l a c e i n real m o t o r s do not happen i n t h e T-Burner and t h a t t h e p r e d i c t i o n of i n s t a - b i l i t y i n t h e rea l motor by t h e d a t e obta- i n e d from T.-Burner i s hard ly successful.

Now. t h e imDortant t h i n n s are t o review more Lhe'phenorneha of combustion i n s m b i l i t y i n the so!id p r o p e l l a n t motors and t o reveal t h e essence of i n s t a b i l i t y accord ing t o these phenomena.

According t o our experience, t h e unstable combustion phenomena can be divided

1

i n t o t h r e e types: ( 1 ) High frequency u n s t a b l e comhustion: The wavelength of i t s o s c i l l a t i o n i s

on t h e same order of t h e s i z e s of g r a i n o r chamber. We take wavelength t o c o m a r e with t h e the s i z e s of g r a i n o r chamber..

( 2 ) Low frequency u n s t a b l e combustion: The wavelength of i t s o s c i l l a t i o n i s

much longer than t h e s i z e s of g r a i n o r chamber. This kind of i n s t a b i l i t v a l s o involves the irregular changes o? pressure h i s t o r y . and o f f .

( 3 ) I n t e r m i t t e n t combustion: The f i r i n g of motor i s a l t e r n a t i v e l y on

I n - t h e s o l i d p r o p e l l a n t rocke t m o t o r s where g r a i n burns on s i d e surfaces, t h e appearence of unstable combustion i s related t o t h e c h a r a c t e r of e r o s i v e burninE. -

If a p r o p e l l a n t i s fas t burning o r a p r o p e l l a n t burns a t l o w p r e s s u r e , i t a:Lways shows some n e g a t i v e e r o s i v e proper ty . F o r a p r o p e l l a n t with nega t ive e r o s i o n , t h e e r o s i v e burning c h a r a c t e r can be exprc:,sed as fo l lows

1-kbu2 , when u < u t r 2 ( 1 )

l-kbUtr+ka(U-Utr), when U>utr

where u t r and ka are r e l a t e d t o pressure . With the decrease of p r e s s u r e , utr

becomes l a r g e r and k, becomes smaller. It - can be w r i t t e n t h a t

( 2 ) m l

ka=bl P utr=h2pm2 ( 3 )

kb does not change wi th pressure . The above e r o s i v e f u n c t i o n i s b a s i c a l l v

i d e n t i f i e d wi th some i n v e s t i g a t o r s t e s t i n g results ( 3 ) ( 4 )

We mainly used t h e motor with t u b u l a r g r a i n i n t h e experiments. The v a r i o u s unstable combustion phenomena have been obtained by means o f a d j u s t i n g t h e i n i t i a l parameters of grain and motor.

IC. Experimental devices

We u t i l i z e d three kinds of rocke t motors t o observe t h e combustion i n s t a b i l - i t v . - ~” -

( 1 ) The t u b u l a r g r a i n motors w i t h narrow i n t e r n a l p o r t (see figure 3 ) . ‘The c o n d i t i o n s of t h e g r a i n and combustion chamber were satisfied as fo l lows

( 4 ) (5)

( 6 ) 3 L A-L 4 c

If t h e expression (4) i s satisfied, a p a r t of t h e combustion 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 head-end of t h e gain(5) . whereas the expressionS(5) and (6 ) are s a t i s f i e d , the h igh frequency o s c i l l a t i o n can go through wi th in t h e whole burning time.

The p r o p e l l a n t used i n t h e motor i s

s e n s i t i v e t o e r o s i v e burning. We used t h i s kind of motors t o ana lyse the high frequency and l o w frequency o s c i l l a t i n a conmbustion - i n t h e t e s t i n g motors.

( 2 ) ‘The t u b u l a r g r a i n motor w i t h t h e wide i n t e r n a l p o r t ( s e e f i g u r e 9 ( b ) ) . The c o n d i t i o n s of t h e g r a i n and combustion chamber were sat isf ied as fol lows v

d z < ( D + d ) D ( 7 )

If t h e express ions ( 7 ) and (8) a r e sat isf ied, w e can observe the e f fec t of the flow s i t u a t i o n on t h e c r i t i c a l p r e s s u r e which i s the minimum p r e s s u r e t o keep t h e combustion i n motor cont inuous.

motors is a l s o s e n s i t i v e t o t h e e r o s i v e burning.

The p r o p e l l a n t used i n t h i s kind of

( 3 ) r -shape B u r n e r ( 5 ) ( I t s o r i g i n a l name i s L-shape Burner and now we c a l l i t as J?-shape Burner i n order t o d i s t i n g u i s h i t w i t h L*-Burner(6)!.

The t e s t i n g g r a i n was p e r f o r a t i o n t u b u l a r g r a i n . The e x t e r n a l - sur face was i n h i b i t e d and t h e burning takes n lace i n

I

t h e i n t e r n a l p o r t only.

p r o p e l l a n t having weak e r o s i v e c h a r a c t e r . The t e s t i n g g r a i n was made of t h e

m. High Frequency O s c i l l a t i n g Combustion ~~~~ ~

The h igh frequency combustion i n s t a - b i l i t y encountered i n t h e t e s t i n g motors mostly i s of a x i a l mode. The a x i a l mode of V o s c l . l l a t i o n can be determined according t o the burn t width p r o f i l btained by i n t e r r u p t i n g techniqueT57. I n t h e very rare c a s e , t h e a c o u s t i c e r o s i v e wrinkle p r o f i l e a l o n g t h e circumference w a s found. ‘Phis was caused by i n c l i n i n g i n s t a l l a t i o n of the grai.n i n t h e combustion chamber but was n o t caused by t h e t a n g e n t i a l mode o s c i l l a t i o n .

The p r e s s u r e r e c o r d i n g of t he t y p i c a l h i g h frequency o s c i l l a t i n g combustion i n our experiments i s shown i n f i g u r e 1 .

‘She o s c i l l a t i n g combustion of t he whole burning process can be d iv ided i n t o two per iods . I n the i n i t i a l s t a g e , t he main frequency is h igher order harmonic. I n t h e l a t e r s t a g e , t h e main frequency becomes lower harmonic. The spectrum of o s c i l l a t i n g p r e s s u r e is shown i n f igure 2.

I n t h e i n i t i a l stage, a l l t h e waveleng- t h s of v a r i o u s harmonic are measured accord- i n g t o the g ra in length . Because t h e o s c i l l a t i o n i n t h e i n t e r n a l p o r t of t h e gra:ln was e x c i t e d by the noise at ends of i n t e r n a l p o r t . Comparing wi th t h e i n t e r n a l diameter of t h e chamber. t h e i n t e r n a l D o r t i s very small, the sound waves are r e f i e c t e d only a t t h e t w o ends of t h e i n t e r n a l p o r t .

I n t h e l a t e r s tage . t h e wavelengths of lower order harmonic are measured acEording t o t h e chamber’s length . Because t h e i n t e r n a l p o r t was enlarged by burning, t h e sound waves reflected a t t h e two ends o f t h e chamber can go i n t o the i n t e r n a l p o r t . L

-

2

"

n.ii

0.011

0.1"

0.01"

0.1"

0.0l"

0.001"

'4

proponant it

9825112 0.9lmu 822510

6.65mv

h

@ t = 0.94 Sec I 975 IlZ

@ t ~ 0.70 Qec

0 1 2 3 4 5 6 7 8 9 KHZ

111.7 p ~ r c r spectrum of o s c i l l n t i n p pressure

Moreover, t h e a c o u s t i c erosive burning i n e a r l y s t a g e make t h e i n t e r p a l p o r t bccome the channel h a v i n g r e g u l a r l y changed t h e s e c t i o n s alone t h e a x i a l , t h e channel wi th changed s e c t i o n s c : ~ n modulate t h e o s c i l l a - t i o n of t h e cas column t o fo rm a ncii kind of o s c i l l a t i o n . Phose t w o k inds of o s c i l l a - t i o n f o r m t h e complex spectrum i n t h e l a t e r b u r n i w s t a g e .

of t h e v e l o c i t y i n i n i t i a l and l a t e r burning s taf ies .

13mn-e 3 ske tches t h e s tanding waves

The erowinp: ra te of t h e o s c i l l a t i o n i s

t i o n grows f a s t . When t h e mean p r e s s u r e i s g e n t l e , t h e o s c i l l a t i o n grows s loi i ly or a l l e v i a t e s . While t h e mean Dressure goes

, , , , , , , \ t o 0.2 0.4 0.6 0 . 8 1.0 5ec

ordinary pmssure h i s tory

, -b t = 0.06 5ec

t 2 4 6 8 10 12 14 mSeC 0

I

'based 01) the length or a b b e r n

3

A "1 2 .~ -~

up, t h e o s o i l l s t i o n abates o r even pauses . F igure 4 shoirs t h e t h r e e f i r i n g s of motors t o i l l u s t r a t e t h e s e phenomena. These phenomena are e s p e c i a l l y s i g n i f i c a n t i n t h e l a t e r s t a g e of t h e f i r i n g . I t can be seen from t h e top figure of t h e f i g u r e 4, t h a t the mean pressure e v i d e n t l y dominates t h e o s c i l l a t i o n i n later stage. The two f i r i n s ( t h e b o t t o m of t h e f i w e 4 ) are obtained by i n t e r r u p t i n g technique. Comparing t h e mean p r e s s u r e w i t h growing r a t e of t h e o s c i l l a t i o n about t w o f i r i n g s , we can a l s o

recognize t h e e f f ec t of t h e mean p r e s s u r e on t h e o s c i l l a t i o n . I n the second f i r i n g , t h e main frequency of t h e a x i a l o s c i l l a t i o n i s UP t o 11IcHZ a t the beginning of t h e

3

f i r i n g .

50

proiiellsnt I 0 , ,~~ +-

0 0.2 0.4 0 . 6 0.a 1.0 1 ., 8°C:

la) pressure histors b w n i n q in low pressure

PrOPcllnnt il (rank c~oiiue)

d = 10.12: I = 420

Ti = 27'c

: 50

130

50

0.20 0.30 0 0.10 la! prczaure h i s t o r y

200.

150.

100 -

50 .

0 , Y . , , , , \ , t 0 0.10 0.20 0.70 ,as

1

I n c e r t a i n c i rcumstances, t h e neeative e r o s i o n can a l s o take p a r t in t h e velociLy coupl ing. We i l l u s t r a t e these phenomena wi th bgo examples. See f igure 5 and 6.

obtained with t h e r - s h a p e burner. The p r o p e l l a n t used i n t h e t e s t w a s W e a k e r O S i - v e one. In c e r t a i n range of mean pressure . the burn t ernin no-rt becomes t h e channel

'The experiment shown in figure 5 w::s

~ ------ r - - ~

with regularly changed s e c t i o n s as t h e scheme shown i n f igure 5 ( c ) , the correspon- d i n g burn t width p r o f i l e i s shown i n f igure 5 ( b ) . Comparing 5 ( b ) with 5 ( c ) , i t was found t h n t on the burn ine surface. some -~ ~ ~ ~ .~~ p l a c e s correspondent t o t h e Gurnt width peaks have acoustic e r o s i v e wrinkles and some o t h e r peak p l a c e s do n o t have the wr inkles . F u r t h e r a n a l y s i n g t h e amplitude p r o f i l e of t h e o s o i l l a d n g v e l o c i t y shown i n f igure 5(d) , we recognized t h a t a t t h e peak p l a c e s without t h e wrinkles , t h e ampli tudes of o s c i l l a t i o n v e l o c i t y are smaller than t h e e r o s i v e t h r e s h o l d Of v e l o c i t y , t h e a c o u s t i c nega t ive e ros ion oacurs , s o t h a t above burn t width p r o f i l e and the a c o u s t i c e r o s i v e wr inkles d i s t r i b u - t e d by a l t e r n a t e peaks are formed.

The experimental result shown in figure 6 i s another negative acoustic

o io0 200 300 400 mm

n l u i- Ib) burnt width Pmfi lS

W7.6 b-t width P m f i l a o f external cimle i a caud~d by B o o w t i o n s g e t l w emaiva effect. beoBuBe v e l o a i t g anplltude is -le* than threshold of POBitive *meion.

e r o s i v e phenomenon.Under t h e e x c i t a t i o n of the o s c i l l a t i o n in t h e i n t e r n a l p o r t , t h e weak a c o u s t i c o s c i l l a t i o n t a k e s p l a c e i n

t h e e x t e r n a l por t . Hecause t h e amplitude of t h e o s c i a l l a t i n g v e l o c i t y i s sma!.l.er than e r o s i v e threshold , t h e maximum negacive a c o u s t i c c r o s i o n occurs at the ani inodes 01 the o s c i l l a t i n e : v e l o c i t y . I n t h c T i p r e 6 ( b ) , t h e s o l i d l i n c i s t h o i n t e r n a l burn t width

-and t h e d o t t e d l i n e i s t h e e x t e r n a l burn t width.The vall.cy p o i n t s of t h e s o l i d . l i n e corre.mond t o t h e cme without u o s i t i v e a c o u s t i c e r o s i c n , and t h e peak p o i n t s of t h e d o t t e d l i n e correspond t o the case vibhout nefpt ive a c o u s t i c c ros ion . The vr.11 ey p o i n t s of t he s o l i d l i n e and t h e ueak uoin-Gs of t h e d o t t e d l i n e are b z s i c a l l y i d e n t i c a l .

I V . Low Frequency i n s t a b i l i t y n

h ' e d e v i d c d d t h e l o w frequency insza- b i l i t y i n t o trro c a t e g o r i e s . The f i r s t category i s t h e unoxpected change of t h e mean p r e s s u r e i n v o l v i n g t h e secondary Dressure s v i k c . '?ha second ca tegory Cons is t s bf t h e low- frequency p r e s s u r e c h i l a t i o n .

The low Srequency i n s t a b i l i t y o f t e n occurs i n the circumstances when the predic- t e d equi l ibr ium p r e s s u r e Peq i s r e l e t i v e l y low.

We have found t h a t the seconary pressu- re s p i k e and the 1011 frequecy o s c i l l a t i o n o f p r e s s u r e took p l a c e i n d i f f e r e n i Stages of peq. Generall.y, a t t he same ambient temperature , :I. OI! frequency osc i l l . a t ion occurs a t lovrer peo t h a n secondary p r e s s u r e sp ike does. I n the'ranee neighbouring of the above t w o k inds OP Peg. t h e r e more o f t e n are ord inary unexpected changes of p ressnre .

'L/ Although t h e s e UnexDected changes of pressu- r e are-nei t h e r secoi?aarv Dressure SDike . . . ~~~~

n o r l o w frequency o a o i l i a i i o n , we s t i l l can say t h a t b o t h t h c secondary sp ike o f pressu- re and lovi frer,~ucncy o s c i l l a t i o n of pressure are t h e s p e c i a l cases. lie have mainly s t u d i e d these two s p e c i a l cases.

( 1 ) About t h e secondary pressure sp ike The a u t h o r ' s experiments have proved

t h a t when the secondwy s p i k e occurs , t h e o s c i l l a t i o n s of a c o u s t i c pressure become very weak even pause.

Figure 7 f ' i v ? s t h r e e f i r i n g examples. Two of them were made a t normal ambient temperature , t h e i r secondary s p i k e s appear i n t h e l a t e r stage of t h e f i r i n g - the l o w o rde r hnrmonic s t a g e . The t h i r d f i r i n g was made a t low ambient temperature , i t s secondary sp ike appears i n t h e i n i t i a l stage of f i r i n g - t h e high order harmonic s t a g e .

frequency o s c i l l a t i o n i n t h e per iod before t h e secondary sp ike . I ts spectrum is similar t o t h e spectrum of o t h e r f i r i n g s without secondary spike. There is no very Strong high frequency o s c i l l a t i o n . Therefore t h e au thor bel ieves t h a t t h e assumption t h a t t h e secondary p r e s s u r e sp ike i s caused by s t r o n g high rreqxency o s c i l l a t i o n i s not t r u e .

From second and t h i r d p i c t u r e of f i g u r e 7, we can see t h a t a f t e r t h e second- a r y s p i k e , t n e h i s h frequency o s c i l l a t i o n - grows again. This f a c t mani fes t s t h a t t h e

We have s t u d i e d t h e spectrum of high

g r a i n was s t i l l keeping i n an i n t e g r a t e t u b u l a r shape and was n o t broken p a s t t h e secondary p r e s s u r e spkie . Some i n v e s t i g a t o r s had conjec tured t h a t the secondary sp ike might be caused by t h e g r a i n beak. T h i s c o n j e c t u r e a l s o proves not t u r e by above mentioned f a c t .

A t t h e per iod near by t h e secondary s p i k e , t h e mean p r e s s u r e d i f f e r e n c e between the head-end and rear-end of t h e grain goes up, i t may be i n f e r e d t h a t t h e r e probably is h igher mean v e l o c i t y and s t r o n g t r a n s i e n t e r o s i v e burning occurs i n t h e rear p a r t of t h e g r a i n p o r t .

reason caus ing t h e secondary m i k e i s a According t o t h e a u t h o r ' s a n a l y s i s , t h e

sudden t r a n s i t i o r . with ereit p o s i t i v e feadback from negazive erosive burning t o p o s i t i v e e r o s i v e burning i n t h e s u i t a b l e range cf mean pressure .

( 2 ) Low PrGquency o s c i l l a t i o n A l l tha low frequency prossure csc l l la -

t i o n encountered i n o u r experiments i s of sma:.l amplitude. T h e region of peq i n which t h e low frequecy o s c i l l a t i o n appears is lower than t h e region o f peq i n which t h e socon3ary s p i k e appears . F igure 8 shows

f o u r f i r i n g h i s t o r i e s of The mean 0rc:i:;ure enca o s c i l l a t i o n i s stron;rR-? than n t h , ? v r e p r e s e n t i n g t h 3 10%: f requency p res su rc o s c i l l a t i o n .

Prom t h e p i c t u r e s shown i n Ii:<ure 8 , w e can see fo l lowinn f a c t s .

. , ~ ~ . orde r h:irmonics. I n t h e l a t e stage of t h e f i r j n c , t h e r e i s a l s o t h i s kind of modula- t i o n , but i t is d i f f i c u l t t o i d e n t i f y bec'iii:;e of t h e multi-harmonic of t h e hiph fre,ru-:!cv o s c i l l a t i o n .

v I n "the p a s t , onc? spoking of t h e low frs!ui?!icy o s c i l l a t i o n , PeOpls o f t e n quotod

I < \

t:ie L*- '?heory~ ' ) . The I,*-Theory be l i eves t h a t i 'or a given p rope l l an t and (T,),,, a lOf;--?o;{ p l o t of L* V S P,, should be a striii.':lit l i n e with s l o p e equal t o -2n, and t h a t t h e freiiuencv c P t h e oscillation . ~ ~ ~~ . becom?s small w i t ; tho i n c r e a s e of J:*.

ment.:il~ r e s u l t s of low frequency i n s t a b i l i t y f o r I'ollowina reasons . 'She first reason i s

'The L*-Theory d i s a g r z e s wi th our e x p e n -

thcii. the c lear low frequency o s c i l l a t i o n 0ccur:i i n t h e end-sta>ye of t h e f i r i n g but t h e x i s no low frequzncy o s c i l l a t i o n i n the middle stage of t h e f i r i n g . I n our exper i - men1.s. t h e r e i s t h a t

+ l . j ( L * ) . (L*)end s t a g e middl- stage .4ccording t o t h e L*-Theory, t h e i n s t a b i l i t y mom: probably occurs i n t h e middl? stne;e of the i i r i n g . The second reason is t h a t t h e i'rc.!rrcncy of t h e o s c i l l a t i o n i n o u r cxper i - men!.s v a r i e s w i t h t h e o s c i l l a t i n n :mnli tude

experiinents

( L* ) l a t e s t age& '( L*)ear ly stage

According t o t h e L*-'Theory, the f requ- 50 D =39.91: d ~ 6 . 6 1 : I=410; dc=48.0; dt=14.i

T1-20' C i ~,~=G2.88kd/cm'i propallant A ency i n t h e e a r l y s t a g e shou1.d be h ighe r b' t h a n t h n t i n t h e l a t e stace.

0 0.2 0.4 0.6 0.8 i .0 1.2 SeC ']'he au tho r b e l i e v e s t h a t t h e reason fiR.8 pre39urB history In low froquency matable combuotlnn

A . The main frequency o f t h e low freilu- encv o s c i l l a t i o n changes with i t s owl

I

ampl i tude , t h e g r e a t e r t h e ampli tude, t h e lower t h e main Prequency.

B . The low frecluency o s c i l l a t i o n Lake3 p l a c e i n t h e lowor reg ion of t h e mean p r e s s u r e h i s t o r y . I n t h e experiments shown i n f i g u r e 8, tha low frequency osci1. lnt ions occur both i n t h e e a r l y and l a t e burn ing stages.

The o s c i l l a t i o n i n t h e e a r l y s t w e cor responds t o t h e per iod when lar, m?r area of t h e e x t e r n a l g r a i n p o r t is occupied by nega t ive e r o s i o n caused by mean f low, and t h e l a t e stage o s c i l l a t i o n corresponds t o t h e per iod when t h e larger area o f t h e i n t e r n a l grain p o r t is taken by negat ive e ros ion .

l a t e staae i s easier t o d i s t i n g u i s h than C . The low frequency o s c i l l a i i o n i n t h e

t h a t i n The early stage. D. I n t h e experiments , i t was found

t h a t t h e low frequency p r e s s u r e o s c i l l a t i o n modulates t h e ampli tude of t h e h igh f requ- ency o s c i l l a t i o n , as shown i n t h e second f i r i n g of f igure 8 . T h i s f ac t is more d i s t i n c t i n the e a r l y stage of t h e f i r i n g , because t h e main frequency of h igh frequ-

causin,:: low r'requency o s c i l l a t i o n i s t h a t t h e burning area occuni3d by negsrtive e r o s i - ve l iurning repezitedly ch;inEes wi th t h e way of !p:irLial i n c r e m e and decrease .

motor:: bu rn ing on th.: s i d e su r faces , t h e e i f x t of t h e l e n c t h from t h e grriin b:xk end t o t h e nozz le t h r o a t on t h e low l rcyuency i n s t a b i l i t y (involvin..: t h e low frequency i r r e g u l a r i t y ) is v e r y important . When t h i s lengh dec reases , t h e tendency t o t h e low frertuency i n s t a b i l i t y s i g n i f i c a n t l y inc rea - ses.

Our expcrim?nts expresses t h a t f o r t h e

V. I n t e r m i t t e n t Combustion

,The o rd ina ry i n t e r m i t t e n comlust ion w a s p resented a l o t by o t h e r s t l ) . General ly , i t is be l ieved t h a t t he ra i s an upper l i m i t of mean p r e s s u r e about t h e i n t e r m i t t e n t combustion f o r a o e r t o i n kind of p rope l l an t .

t h i s upper l i m i t of mean p res su re is severe- l y a f f e c t e d by t h e mevl flow f i e l d i n t h e chanber. L ike t h e f low f i e l d of t h e t e s t s

O u r exper imenta l resu l t s i n d i c n t e t h a t

shown i n figure 8 , t h e i n t e r m i t t e n t combus- t i o n does go t occur even as pe i s as low as 60kg/cm ( T i = Z O C ) . However. ?f t h e r e i s h igh ve loc i ty -o f t h e mean flow i n t h e larger burn ing area, t h e i n t z r m i t t e n t combustion can t ake p l a c e a t t h e h igher peq. The 4

6

v

experiments ihow i n f i g u r e 9 i l l u s t r a t e t h i s phenomenon.

pmpcllnnt A

peq= 72.4 h d o r ?

50

0.1 0.2 4 . 6 4.8 5.0 5.2 5.4 QeC

h d c 2 propellant A

D =19.19: d= 17.54: t 400;

50

0.2 0.4 0.6 0.8 980

( c ) tendency t o e x t i n c t i o n i s restminned by ra is in8 the PPBSSUe.

flg.9 effect of combustion ens f lows an Intermit tent eombustlon u I n t h e m o t o r s used i n the experiments

of f i g u r e 9, 'the separa t ion p o i n t o f t h e mean f l o w i s i.n t h e e x t e r n a l p o r t (See f i g u r e 5 ( b ) ) . Because of t h i s mean f l o w f i e l d , the mean r l o w f i e l d makes negat ive e ros ive reg ion cover i n t h e r e l a t i v e l y l a r g e burning area . Aftei- t h e i g n i t i o n of t h e g r a i n , t h e n e m t i v e e r o s i o n l e a d s t o t h e reduct ion of both t h e burning r a t e and t h e mean pressure .

more s e r i o u s negative eros ion , s o t h a t t h e burning a r e a talien by negat ive e ros ion f u r t h e r extends. These a l t e r n a t e a c t i o n s fina1l.y r e s u l t i n t h e e x t i n c t i o n of t h e f i r i n g (see f i22ure 9 ( a ) ) . A f t e r a de lay of time ( 4 . j second) t h e g r a i n re-burns. Because t h e re-burnine pressure i s r e l a t i v e - l y high, t h e nega t ive e r o s i v e area becomes Small enougn. Then t h e g r a i n can cont inuos ly burn t o i t s end.

I n t h e t e s t with t h e flow f i e l d l i k e f i g u r e 9(b), t h e oscssure peq i s r a i s e d till pe -87.41cky/cm-, t h e burning can only be cont4nuous ( s e e f i g u r e g ( c ) ) . However, i t can be seen th:3t t h e r e i s a b i g v a l l e y of p r e s s u r e i n t h e i n i t i a l per iod of t h e f i r i n g . It expresses t h a t t he nega t ive e r o s i v e e f f c t s t i l l e x i s t s . The r e a d e r s yourse lves can review your experimental r e s u l t s of t he ord inary r o c k e t motors( 1 ), - there is a l s o a l i t t l e v a l l e y of pressure

The lowsr ing 0 mean pressure causes

a f t e r t h e i g n i t i o n , bu t i t i s not as b i g as t h e v a l l e y shown i n f igure 9 ( c ) .

From a n a l y s i n g t h e e f f e c t of nega t ive e r o s i o n on e x t i n c t i o n of combustion, it is concluded t h a t t h e o ld hypothesis--"the f i r i n g can be blown out" i s reasonable , see f i g u r e I O .

0 u negative emsion (a) area of neeatfve emsm

CM n V t h e r ertend.under 1.2" p183- i t results

cannot further Bxtend, i t reaul ta 10. ~ 1 8 . 1 9 ~ ~ ~ dom

In e l t i n c t l O n easily. Bnd up a l i t t le .

i~~.to w g a t i v e emsive c ~ n blow o u t tho firing.

The s o c a l l e d "blown o u t " hypothes is is tha t if t h e v e l o c i t y of t h e mean f low f i e l d on t h e burning s u r f a c e i s big enough, the f i r i n g of t h e motor can be blown out by i t s own combustion gases. The b i g enough v e l o c i t y means i n excess of t h e e r o s i v e t h r e s h o l d a t a cer ta in pressure . Author believes t h a t i f t h e burning area taken by negat ive e r o s i o n i s b i g enough, i t w i l l r e s u l t i n t h e reduct ion of average burning ra te over t h e chamber. The r e d u c t i o n of t h e average burning rate l e a d s t o t h e r e d u c t i o n of t h e mean pressure . The reduct ion of t h e mean pressure i s the cause t h a t t h e e r o s i v e tlnresold becomes l a r g e and t h e burning area taken by negat ive e r o s i o n f u r t h e r extends. The ex tens ion of t h e burning area taken by negat ive e r o s i o n f u r t h e r leads t o the r e d u c t i o n of the mean pressure . The alterna- t i v e a c t i o n s l i k e t h i s f i n a l l y c a u s e s t h e f i r i n g t o d i e o u t ,

I n another c?ise,if t h e burning area thaken by negat ive e r o s i o n can not f u l l y extend, t h e r e d u c t i o n of mean p r e s s u r e only l e a d s t o nega t ive e r o s i o n a l l e v i a t e d , s o t h a t t h e mean p r e s s u r e goes up again. T h i s mean p r e s s u r e go ing down and up is p r a o t i a a - l l y t h e low frequency o s c i l l a t i o n , s e e f i g u r e 10(b).

VI. Conclusions

Through t h e review of t h e experimental r e s u l t s wi th t h e r o c k e t motors and t h e a n a l y s e s about t h e combustion i n s t a b i l i t y , we recap t h e main conclusions as f o l l w s :

1. By means of c o n t r o l l i n g t h e grain and t h e chamber parameters , t h e a x i a l h igh frequency o s c i l l a t i o n can go through dur ing t h e whole burning time. The whole burning process of t h e h igh frequency o s c i l l a t i o n can be d iv ided i n t o t w o per iods . I n t h e i n i t i a l stage, t h e main frequency of t h e

7

o s c i l l a t i o n i s h igher order harmonic, while i n t h e l a t e s t a g e , t h e main frequency becomes lower order harmonic.

The growing ra te of t h e h igh frequency o s c i l l a t i o n i s r e l a t e d t o t h e change of the mean pressure . When the mean p r e s s u r e f:!lls, the o s c i l l a t i o n g rows fast , while t h e :win p r e s s u r e goes up, t h e o s c i l l a t i o n a b a t e s o r even pauses. T h i s phenomenon is e s p e c i a l l y s i g n i f i c a n t i n t h e la ter s t a g e o f the f i r i n g

2. The a c o u s t i c e r o s i v e burn ine u l a v s .I I

an important r o l e t o t h e high frequency o s c i l l a t i o n . N o t only t h e a c o u s t i c p o s i t i v e e r o s i v e burning can t a k e p a r t i n t h e ve loc i - t y coupl ing, bu t t h e a c o u s t i c nega t ive e r o s i v e burning can a l s o do t h a t .

3 . The secondary s p i k e , t h e low frequ- ency o s c i l l a t i o n and t h c unexpected ch::riges of t h e mean p r e s s u r e a l l belong t o t h c low freauencv i n s t a b i l i t v o f combustion. 'I'ho

burning. The l o w freauencv i n s t a b i l i t v of ten

occurs i n the circumstances when t h e nrcd i - c ted peq i s r e l a t i v e l y low.

low frequency o s c i l l a t i o n i s %we, t h m the I t was found t h a t t h e Pe caus ing tho

caus ing t h e secondarv m i k e . ~ - 3 4. It-was found t h a t &en t h e secondary s p i k e appears , t h e h igh irequency o s c i l l a - t i o n s become very weak o r pause.

t i o n before t h e secondarv m i k e shows t h a t The spectrum OS high frequency o s c i l l a -

t h e r e i s no very s t r o n g high frequency o s c i l l a t i o n . ?he aosumption t h a t t h e secondary sp ike of pressure i s d i r e c t l y caused by very s t r o n g high frequencv n s c i l l n t i o n i s not t r u e . ~~ ~~~~ ~ ~.

After t h e secondary sp ike , t h e hich frequency o s c i l l a t i o n g-rows aga in . ?h i s i l l u s t r a t e s t h a t the assumption of t h e g r a i n break a l so i s not t r u e .

5 . The main freauencv of t he low freou- _. ~

ency o s c i l l a t i o n cha iges wi th i t s own ampli tude, t h e b igger the ampli tude, tho lower the main frenuency.

happening corresponds t o the time when the l a r g e r p a r t of burning area is occupied by negat ive e ros ion caused by mean flow.

o s c i l l a t i o n modulates t h e amnlitude of the

The per iod of l o w frequency o s c i l l < , t i o n

It was found t h a t t h e low frequency

high frequency o s c i l l a t i o n .

frequency o s c i l l a t i o n disagrees w i t h t h e 6. Our experimental r e s u l t s about low

L*-Theory.

t h e upper l i m i t of mean p r e s s u r e ahout i n t e r m i t t e n t combustion is s e r i o u s l y affected by mean flow f i e l d i n the chamber.

Seen from t h e viewpoint of a l t e r n a t i v e a c t i o n s between t h e nega t ive e ros ion and mean p r e s s u r e , t h e old hypothes is "the f i r i n g can be blown out" is reasonable .

p r o p e l l a n t is very important f o r t h e cornbus- t i o n i n s t a b i l i t y . B e s i d e s t h e nega t ive ero- s i o n can take p a r t i n the h i g h frequency o s c i l l a t i o n , i t can a l s o cause t h e secondary pressure s p i k e , t h e low frequenouy o s c i l l a - t i o n and t h e i n t e r m i t t e n t combustion i n d i f f e r e n t cases r e s p e c t i v e l y .

7. For a c e r t a i n kind o f propellanL,

8 . The negat ive e r o s i v e c h a r a c t e r of a

V I 1 . Acknowledgements

The a u t h c r wishes t o extend s p e c i a l acknowledgement t o professor k'eng wen-Lan, who g i v e s t h i s research many guides. He shou?d been one of au thors , but he prefern bc inf : a guide.

The experiments were c a r r i e d out with the a s s i s t a n c e of GUO Xi : io , Zhu Zhen-XonE and Yuan Shi-Hane, whom are a l s o g r a t e f u l l y achncwledged.

R:W:IRi<AC ::

( 1 ) P r i c e , :2 . \ i . , "Bxporimcntal S o l i d Rocket Combustion I n s t a b i l i t y " , Tenth Symposium ( 1 n t e r n a t i o n a l ) o n CornbZ€Eh, P1067-1082, The Combusticri I n s t i t u t e 1965. __I--.- - .-

( 2 ) Culick. F . Z - C . . " S t a b i l i t v of . , I - - I Y~

Lonei tudinal O s c i l l a t i o n s wiiih Prcssurc m d Veloci ty Coupling i n a Sol id P r o p e l l e n t Rocket", Combustion Science ._ and 'rcchnology, V o l . 2 , No.2, 1970.

( 3 ) Zucroc, ?C.J., Osborn, J.K. and Murphy, J.M., "An Experir!entsl I n v e s t i g a t i o n of t h e Erosive Burninrr C h a r a c t e r i s t i c s of a Non-Eomogeneous Sol id ' Propel lan t , - A I A A P r e p r i n t 64-107.

( 4 ) Kamath, H . , Aro ra R. , and Kuo, k.k. "Erosive Burning Neasurcments and Predic t - i o n s f o r a Highly Aluminized Composite Propel lan t" , AIAA-S2-1111. -

( 5 ) Lu, Zhen-Zhog, "Veloci ty Couplint; Sxperiments of S o l i d P r o p e l l a n t Acoustic O s i c i l l a t i n g Combustion", AIM-84-1 262.

of Low-Frequency Combustion I n s t a b i l i t y i p . So l id Rocke t ?:otors", A I A A Journa l , Vo1.2, No.4, 1964.

( 6 ) SehEal, R. and Srand, L., "A Theory

W

W

8

RXP13RIPP>NTAL ANALYSIS OP UNSTABLE COKBUSTION I N DOUJ3LE RASE SOLID PROPELLANT ROCKET MOTORS

Lu Zhen-Zhong

403 ?ea.ching Grcup, Jet Propuls ion Department I3eijing I n s t i t u t e of Aeronautics and As t ronau t i c s The Pople's Republic of ch ina

ENCY OSCILLATING PRESSURE

Fig.l(b) t y p i c a l t r a n s i e n t r eco rd ing of h igh frequenoy o s c i l l a t i n g p res su re

v

Fig.4 e f f e c t of change i n mean p res su re on growing r a t e of o s c i l l a t i n g p res su re

.,. . . .

Fig.7 when t h e secondary p r e s s u r e s p i k e t a k e s p l a c e , t he high frequency o s c i l l a t i o n is i n t e r r u p t e d

F ig .8 h igh frequency o s c i l l a t i n g p res su re happening a t the motor f i r i n g con ta in - i n g low frequency o s c i l l a t i o n

9