High-Frequency Combustion Instability in Solid Propellant Rockets. Part 1

A theory of u n s t a b l e h ighf requency osci l la t ions i n solid p rope l l an t rocke t s is advanced w i t h t h e m e c h a n i s m of self-excitat ion based o n t h e fol lowing simplified m o d e l . Bo th t h e r a t e of p r i m a r y decompos i t i on of solid p r o p e l l a n t e lement a n d t h e r a t e of ac t iva t ion of t h e i n t e r m e d i a t e p roducts d u r i n g t h e t i m e lag a r e a s s u m e d to depend u p o n t h e gas osc i l la t ions . B o t h i n t e r a c t i o n s a re expressed i n t e rms of t h e i n s t a n t a n e o u s p ressu re accord ing to power law wi th exponent n a n d m respect ively. T h e dependence of t h e r a t e of decompos i t i on o n d r i f t ing velocity is s h o w n to be no t of f u n d a m e n t a l i m p o r t a n c e i n d e t e r m i n i n g t h e s t a bili ty of osc i l la t ions i n t h e c o m b u s t i o n c h a m b e r . Analysis shows t h a t a simplified over-al l p re s su re index of i n t e r ac t ion S = m — (n/2) m u s t b e bigger t h a n c e r t a i n m i n i m u m value if u n s t a b l e osc i l l a t ion is t o be possible . U n stable osc i l la t ion f u r t h e r r equ i re s t h e t i m e lag to be in proper r ange . T h e m o s t u n s t a b l e m o d e is s h o w n to be t h e f u n d a m e n t a l sp i ra l m o d e , a n d i t s t a n g e n t i a l c o m p o n e n t w i th exactly t h e acous t i ca l f requency is t h e o n e which is m o s t easily observed a t finite m a g n i t u d e s because of i ts rap id ampl i f ica t ion . Several conf igura t ions of t h e p rope l lan t g ra in w i t h r ad ia l b u r n i n g surfaces have been invest igated. Rod g ra in becomes m o r e s t ab le whi le o t h e r grain shapes b e c o m e less s t ab le in t h e course of firing. Rod gra in is t h e m o s t s t ab le whi le t u b u l a r g r a in is t h e mos t u n s t a b l e conf igura t ion . T h e s tab i l i z ing effect of inse r t ing a n o n b u r n i n g solid rod i n t o t u b u l a r g ra in is verified by t h e t h e o r y . Several o t h e r aspec ts have also been t r e a t ed . Solid rocke t w i t h end b u r n i n g g ra in also becomes less s t ab le i n t h e course of o p e r a t i o n . B o t h t h e spiral a n d t h e l o n g i t u d i n a l m o d e s in rocke t wi th e n d b u r n i n g g ra in a re briefly inves t iga ted .