29 The Detailed Modelling of Premixed, Laminar,
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Steady-State Flames. Results for Ozone JOSEPH M. HEIMERL and T. P. COFFEE Ballistic Research Laboratory, ARRADCOM, Aberdeen Proving Ground, MD 21005
The overall objective of these studies is to deli neate and validate the elementary gas phase kinetic mechanisms involved in the combustion of the cyclic nitramines, HMX and RDX. The modeling of premixed, laminar, steady state flames is the approach taken. First, because the governing equations are simple relative to other combustion processes one can focus upon the kinetics. Second, because laser-based diagnostics enable species and temperature profiles to be probed experimentally and one can validate the model. Detailed comparisons of predicted and mea sured profiles of temperature and of species (particularly radi cals) serve either to validate the model or to indicate refine ments. Given the pausity of reliable temperature dependent rate coefficient data, the latter situation is anticipated. Such dis crepancies can be exploited by using them to direct experiments on or theoretical calculations of elementary rate coefficients. This sequence of comparison and direction can be iterated. The ideal end product is a validated network of elementary reactions that can then be used with some confidence in more complex simulations. A sequence of flame studies is planned; from the test case, ozone, through the recognized intermediates, formaldehyde/oxides of nitrogen, to the gas phase elementary networks that describe the HMX and RDX flames. This paper discusses some of the ozone model ing results. A more complete description of the background, moti vation and other details is available (1). E q u a t i o n s and S o l u t i o n s . The g o v e r n i n g e q u a t i o n s t h a t d e s c r i b e a one d i m e n s i o n a l , p r e m i x e d , l a m i n a r , unbounded f l a m e f o r a m u l t i component i d e a l g a s m i x t u r e a r e ( 2 , _3, 4_) :
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This chapter not subject to U . S . copyright. Published 1980 A m e r i c a n Chemical Society
Crosley; Laser Probes for Combustion Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
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366
LASER PROBES FOR COMBUSTION CHEMISTRY
For the k t h s p e c i e s and a r e t h e mass and mole f r a c t i o n s , r e s p e c t i v e l y , Rfc i s t h e n e t r a t e o f t h e p r o d u c t i o n due t o c h e m i s t r y a n d Mj< i s t h e m o l e c u l a r w e i g h t . In a d d i t i o n the d i f f u s i o n velocity i s g i v e n by the Stefan-Maxwell r e l a t i o n
and t h e o t h e r s y m b o l s have t h e i r u s u a l m e a n i n g . The p r e s s u r e t h r o u g h t h e f l a m e i s one a t m o s p h e r e a n d c o n s t a n t (£, 5). We n e g l e c t e f f e c t s o f v i s c o s i t y , t h e r m a l d i f f u s i o n , body f o r c e s and r a d i a t i o n . To o b t a i n a s o l u t i o n , we employ a r e l a x a t i o n t e c h n i q u e a n d u s e t h e PDECOL p a c k a g e ( 6 ) . PDECOL i s b a s e d on a f i n i t e e l e m e n t c o l l o c a t i o n method e m p l o y i n g B - s p l i n e s . F o r c o m p u t i n g e f f i c i e n c y we have d e v e l o p e d a method o f c o n c e n t r a t i n g o u r b r e a k - p o i n t s i n t h e s t e e p f l a m e f r o n t where a c c u r a c y i s n e c e s s a r y ( 7 ) . K i n e t i c , t r a n s p o r t and t h e r m o d y n a m i c c o e f f i c i e n t s a r e r e q u i r e d a s i n p u t t o t h e m o d e l . The k i n e t i c mechanism i s : 0 „ + M - < - > 0 + CL + M
(1) (2) (3)
E x p r e s s i o n s f o r the r a t e c o e f f i c i e n t s are t a k e n from the l i t e r a t u r e (8^ 9_, 10) a n d a r e shown i n T a b l e I . E x p r e s s i o n s f o r t h e t r a n s p o r t c o e f f i c i e n t s ( 1 , .Π, 12^ 13) a r e shown i n T a b l e I I a n d t h e s p e c i f i c e n t h a l p y , h ^ , a n d s p e c i f i c h e a t c a p a c i t y , Cp^, a r e o b t a i n e d f r o m G o r d o n and M c B r i d e ( 1 4 ) . E a c h e x p r e s s i o n t o r t h e i n p u t c o e f f i c i e n t s i s b a s e d o n s e p a r a t e , i n d e p e n d e n t measurements and t h e m e t h o d o l o g y f o r o b t a i n i n g them h a s been d i s c u s s e d (1_) . R e s u l t s a n d D i s c u s s i o n . F i g u r e 1 shows t h e 0, O2, O3 a n d temp e r a t u r e p r o f i l e s computed f o r a n i n i t i a l o z o n e m o l e f r a c t i o n of unity. No e x p e r i m e n t a l p r o f i l e s a r e known f o r c o m p a r i s o n and s o b y o u r own d e f i n i t i o n t h e o z o n e f l a m e r e m a i n s u n v a l i d a t e d . We c a n however compare b u r n i n g v e l o c i t i e s . As c a n be s e e n i n F i g u r e 2 o u r computed b u r n i n g v e l o c i t i e s compare f a v o r a b l y w i t h b o t h t h e e x p e r i m e n t a l r e s u l t s o f S t r e n g a n d G r o s s e (15) a n d t h e modeling r e s u l t s o f Warnatz (16). (Warnatz h a s d e v e l o p e d a f i n i t e d i f f e r e n c e model t h a t a l s o r e q u i r e s s p e c i e s d e p e n d e n t input coefficients.) The s o l i d l i n e i n t h e f i g u r e i s S t r e n g and G r o s s e s f i t t o t h e i r d a t a . O v e r t h e r a n g e o f 0.25 t o 1.0 i n i t i a l o z o n e m o l e f r a c t i o n s o u r r e s u l t s a r e n o more t h a n 3 0 % g r e a t e r t h a n S t r e n g and G r o s s e s . Over t h e e n t i r e r a n g e shown o u r r e s u l t s a g r e e w i t h W a r n a t z s w i t h i n _+ 12%. T h i s agreement does n o t i m p l y t h a t t h e s e t s o f i n p u t c o e f f i c i e n t u s e d i n t h e r e s p e c t i v e models a r e e q u i v a l e n t . F i g u r e 3 shows t h e r a t i o o f t h e v a l u e s o f W a r n a t z i n p u t c o e f f i c i e n t s t o o u r c o r r e s p o n d i n g v a l u e s . T h i s f i g u r e shows t h a t a t t h e h i g h e r t e m p e r a t u r e s ( i . e . , a t t h e l a r g e r i n i t i a l o z o n e mole f r a c t i o n s ) , t h e v a l u e s f o r k^ a n d k2 d i f f e r m a r k e d l y . The f a c t 1
1
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Crosley; Laser Probes for Combustion Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
Crosley; Laser Probes for Combustion Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
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COEFFICIENT
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REFERENCES
TABLE I . KINETIC COEFFICIENTS
3
1000K < Τ < 800K, M=0
2
1000K
