Chemical Kinetic Factors in Gaseous Detonations - ACS Publications

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Chemical Kinetic Factors in Gaseous Detonations CHARLES K. WESTBROOK University of California, Lawrence Livermore National Laboratory, Livermore, CA 94550

Computer modeling techniques have been applied to the study of hydrogen and hydrocarbon oxidation in gaseous detonation waves. Characteristic reaction times and lengths are computed which correlate well with observed detonation parameters, including c r i t i c a l tube diameters for transition to spherical detonation, detonation cell sizes, c r i t i c a l i n i t i a tion energies, and lean and rich limits for detona tion in a linear tube. Inhibition or extinction of a detonation is shown to occur from increases in the ignition delay time, and increased detonability or kinetic sensitization results from decreased ignition delay times. Detonation waves a r e an important c l a s s o f combustion phenomena, due both t o the p o t e n t i a l s a f e t y hazards which they represent and t o t h e i n s i g h t s i n t o fundamental combustion processes which they provide. Gaseous detonations have been examined f o r many years, i n both experimental and t h e o r e t i c a l s t u d i e s . More r e c e n t l y , computer modeling s t u d i e s o f detonation waves have begun t o appear. The chemical k i n e t i c s submodels have been considered t o be the weakest p a r t o f e x i s t i n g detonation models. However, recent development o f comprehensive k i n e t i c r e a c t i o n mechanisms f o r the o x i d a t i o n o f many p r a c t i c a l f u e l s ( 1 , 2 ) has changed t h i s situation significantly. The present paper r e p o r t s progress t h a t has been made on chemical k i n e t i c s i n detonations and how w e l l k i n e t i c p r e d i c t i o n s c o r r e l a t e w i t h a v a i l a b l e experimental data. The success o f t h i s approach i n reproducing experimental data i l l u s t r a t e s the c e n t r a l r o l e o f k i n e t i c s i n detonations, and i t suggests s t r o n g l y t h a t t h i s technique provides a r e l i a b l e b a s i s f o r pred i c t i n g detonation p r o p e r t i e s f o r c o n d i t i o n s which have not y e t been explored e x p e r i m e n t a l l y . For example, very few e x p e r i mental data a r e a v a i l a b l e f o r detonation p r o p e r t i e s a t i n i t i a l 0097-6156/ 84/ 0249-0175$06.00/ 0 © 1984 American Chemical Society In The Chemistry of Combustion Processes; Sloane, T.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

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p r e s s u r e s above 1 atm, a t i n i t i a l t e m p e r a t u r e s d i f f e r e n t f r o m n o r m a l room t e m p e r a t u r e , o r f o r m i x t u r e s i n w h i c h t h e o x i d i z e r i s a i r r a t h e r than oxygen. A l l t h e s e can b e o f extreme p r a c t i c a l i n t e r e s t t o t h e i n d u s t r i a l community i n h e l p i n g t o u n d e r stand the hazards îsociated w i t h e x p l o s i v e m i x t u r e s and t o know how a c c i d e n t a l d i s a s t e r s c a n b e p r e v e n t e d . A s a f u r t h e r e x t e n s i o n o f t h i s type o f approach, t h i s type o f modeling can suggest k i n e t i c means o f m o d i f y i n g t h e d e t o n a t i o n p a r a m e t e r s o f a g i v e n f u e l - o x i d i z e r mixture, e i t h e r enhancing o r i n h i b i t i n g detonab i l i t y through the use o f a p p r o p r i a t e c h e m i c a l a d d i t i v e s . Chemical K i n e t i c s At t h e p r e s e n t t i m e , t h e f u e l s w h i c h c a n b e d e s c r i b e d b y t h i s m o d e l i n g a p p r o a c h i n c l u d e h y d r o g e n , c a r b o n monoxide, methane, methanol, ethane, e t h y l e n e , a c e t y l e n e , propane, and p r o p y l e n e . The r e a c t i o n mechanism u s e d t o d e s c r i b e t h e o x i d a t i o n o f t h e s e f u e l s h a s been d e v e l o p e d a n d v a l i d a t e d i n a s e r i e s o f p a p e r s (3-7). T h e e l e m e n t a r y r e a c t i o n s and t h e i r r a t e e x p r e s s i o n s a r e summarized i n R e f e r e n c e (_7) a n d a r e n o t r e p r o d u c e d h e r e d u e t o s p a c e l i m i t a t i o n s . R e v e r s e r e a c t i o n r a t e s a r e computed f r o m t h e f o r w a r d r a t e s and t h e a p p r o p r i a t e thermodynamic d a t a (J3). T h i s mechanism h a s been shown t o d e s c r i b e t h e o x i d a t i o n o f methane (3,A), m e t h a n o l (_5), e t h y l e n e (6), and p r o p a n e and p r o p y l e n e (7) o v e r w i d e r a n g e s o f e x p e r i m e n t a l c o n d i t i o n s . I t h a s a l s o been u s e d t o d e s c r i b e t h e s h o c k t u b e o x i d a t i o n o f e t h a n e (4,9), a n d a c e t y l e n e (10). The p a r a m e t e r r e g i m e s i n a d e t o n a t i o n a r e s i m i l a r t o t h o s e i n s h o c k t u b e s , s o t h e most i m p o r t a n t t e s t o f t h i s t y p e o f mecha n i s m i s i t s a b i l i t y t o r e p r o d u c e s h o c k t u b e i g n i t i o n d a t a . One example o f t h i s v a l i d a t i o n p r o c e s s compared computed i g n i t i o n d e l a y t i m e s Ç7) w i t h e x p e r i m e n t a l r e s u l t s o f B u r c a t e t a l . (11). I n t h e e x p e r i m e n t s , m i x t u r e s o f p r o p a n e , oxygen, a n d a r g o n were s t u d i e d i n r e f l e c t e d s h o c k waves a t i n i t i a l t e m p e r a t u r e s f r o m 1250 t o 1700 K, p r e s s u r e s from 2 t o 15 a t m o s p h e r e s , and e q u i v a l e n c e r a t i o s f r o m 0.5 t o 2.0. From t h e e x p e r i m e n t a l r e s u l t s , i t was f o u n d t h a t t h e i g n i t i o n d e l a y t i m e τ c o u l d b e approximated i n terms o f the i n i t i a l temperature T a n d r e a c t a n t c o n c e n t r a t i o n s ( i n moles/cm^) b y 0

τ = 4.4 χ Ι Ο " * exp(21240/T ) 1

o

[C H ]0.57[o ]-1.22 3

8

2

s

e

c

.

In e a c h c o m p u t a t i o n τ was d e f i n e d a s t h e t i m e c o r r e s p o n d i n g t o t h e maximum r a t e o f r e a c t i o n between CO a n d 0 atoms. Other r e a l i s t i c d e f i n i t i o n s o f τ , s u c h a s t h e t i m e o f maximum r a t e of p r e s s u r e o r temperature r i s e , gave n e a r l y i d e n t i c a l r e s u l t s . From t h e computed i g n i t i o n d e l a y t i m e s a n d i n i t i a l r e a c t a n t c o n c e n t r a t i o n s , model v a l u e s o f t h e c o r r e l a t i o n f u n c t i o n 3 1

β = τ [023 ·

2 2

[C3H ]-0.57 8

u s

(mole/cm3)0.65

In The Chemistry of Combustion Processes; Sloane, T.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.


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were c a l c u l a t e d , and t h e r e s u l t s a r e summarized i n Figure 1. The s o l i d l i n e represents t h e o v e r a l l experimental c o r r e l a t i o n f u n c t i o n o f Burcat e t a l . , while t h e i n d i v i d u a l symbols r e p r e sent computed values o f 3 . The s p e c i f i c c o n d i t i o n s f o r each Mixture i d e n t i f i e d i n Figure 1 can be found i n Reference (11). The general agreement between computed and experimental data i s very good, i n d i c a t i n g t h a t t h e r e a c t i o n mechanism i s p r o p e r l y reproducing t h e shock tube i g n i t i o n behavior f o r t h i s f u e l . S i m i l a r d e t a i l e d comparisons have been c a r r i e d out i n previous modeling s t u d i e s with b a s i c a l l y t h e same r e a c t i o n mechanism f o r ethylene ( 6 ) , methane and ethane (A), and methanol ( 5 ) . The H2 o x i d a t i o n submechanism has been e x t e n s i v e l y v a l i d a t e d , with nearly a l l o f the elementary r e a c t i o n r a t e s being w e l l known. In the past, detonation models have used g l o b a l r a t e expres s i o n s t o compute chemical i n d u c t i o n times f o r f u e l - o x i d i z e r mix t u r e s , but such expressions a r e o f t e n not s a t i s f a c t o r y , even when they have been based on shock tube data. Most shock tube experiments a r e c a r r i e d out with high d i l u t i o n by Ar, He, o r N2, so that f u e l and oxygen concentrations a r e u s u a l l y q u i t e low. However, o v e r a l l r e a c t i o n order and a c t i v a t i o n energy i n g l o b a l i n d u c t i o n time c o r r e l a t i o n s o f t e n change with the amount o f d i l u t i o n . G l o b a l r a t e parameters can a l s o change with equiv alence r a t i o , pressure and temperature. As a r e s u l t , i n d u c t i o n times computed from g l o b a l expressions can be s e r i o u s l y i n e r r o r when a p p l i e d t o u n d i l u t e d f u e l - o x i d i z e r mixtures, making a de t a i l e d k i n e t i c mechanism an e s s e n t i a l part o f the present deto n a t i o n model. The k i n e t i c submechanism f o r the i n h i b i t i o n s t u d i e s was a l s o developed by a s e q u e n t i a l process, beginning w i t h HBr (12) and the other halogen a c i d s HC1 and HI, followed by r e a c t i o n s i n v o l v i n g methyl, v i n y l , and e t h y l h a l i d e s (13) and CF3Br (14). The i n h i b i t i o n mechanism and r e a c t i o n r a t e s a r e given i n Reference (13). Detonation Model The model used here i s t h e Zeldovich-von Neumann-Doring (ZND) model i n which, l o c a l l y , a detonation c o n s i s t s o f a shock wave t r a v e l i n g a t t h e Chapman-Jouguet (CJ) v e l o c i t y , followed by a r e a c t i o n zone. The shock wave compresses and heats t h e f u e l o x i d i z e r mixture which then begins t o r e a c t . I n most mixtures the f u e l o x i d a t i o n c o n s i s t s o f a r e l a t i v e l y long i n d u c t i o n p e r i o d during which t h e temperature and pressure remain n e a r l y constant, followed by a r a p i d r e l e a s e o f chemical energy and temperature i n c r e a s e . F o r each f u e l - o x i d i z e r mixture, a c a l c u l a t i o n i s f i r s t made o f t h e relevant CJ c o n d i t i o n s . From t h e detonation v e l o c i t y D Q J , t h e c o n d i t i o n s i n t h e von Neumann spike, including t h e temperature Τχ, pressure P i , and p a r t i c l e v e l o c i t y u i o f the post-shock unreacted gases can be computed and then used as i n i t i a l c o n d i t i o n s f o r t h e chemical



178


F i g u r e 1. C o r r e l a t i o n f u n c t i o n s f o r shock tube i g n i t i o n o f propane. S o l i d l i n e i s o v e r a l l c o r r e l a t i o n from Burcat et a l . ( i l ) ; symbols are computed values.



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k i n e t i c s m o d e l . The s h o c k v e l o c i t y v a r i e s w i t h i n a s i n g l e d e t o n a t i o n c e l l from an i n i t i a l v a l u e o f a b o u t 1.6 D ç j t o a m i n i mum o f a b o u t 0.6 D Q J , so t h e C J c o n d i t i o n s u s e d h e r e r e p r e s e n t a v e r a g e v a l u e s , and computed i n d u c t i o n t i m e s w i l l a l s o b e averages. The r e a c t i v e m i x t u r e i s assumed t o r e m a i n a t a c o n s t a n t volume o v e r i t s r e a c t i o n t i m e , and t h e i n d u c t i o n t i m e i s d e f i n e d i n terms o f i t s temperature h i s t o r y . Most o f t h e mixtures underwent a l a r g e t e m p e r a t u r e i n c r e a s e o f more t h a n 1000 K, and t h e i n d u c t i o n t i m e i s d e f i n e d as t h e t i m e o f maximum r a t e o f temperature increase. I n most c a s e s , t h i s c o i n c i d e s a p p r o x i m a t e l y w i t h t h e t i m e a t w h i c h t h e t e m p e r a t u r e has c o m p l e t e d about h a l f o f i t s t o t a l i n c r e a s e . T h i s i s not, s t r i c t l y speaking, a t r u e i n d u c t i o n p e r i o d , o f t e n d e f i n e d as the time r e q u i r e d f o r a s m a l l ( i . e . 1-5%) t e m p e r a t u r e o r p r e s s u r e i n c r e a s e , b u t i t r e p r e s e n t s a t i m e s c a l e f o r t h e r e l e a s e o f a s i g n i f i c a n t amount o f energy. In a d d i t i o n to the i n d u c t i o n time τ, i t i s u s e f u l t o d e f i n e the i n d u c t i o n length Δ Ξ T ( D C J - U I ) , which r e p r e sents a c h a r a c t e r i s t i c length s c a l e i n the post-shock unreacted gas m i x t u r e . As a r e s u l t o f t h e s e s i m p l i f i c a t i o n s , t h e computed i n d u c t i o n t i m e s and l e n g t h s d e f i n e c h a r a c t e r i s t i c t i m e and l e n g t h s c a l e s r a t h e r t h a n t h e p r e c i s e h i s t o r y o f a gas e l e m e n t t h r o u g h t h e d e t o n a t i o n f r o n t . The e v o l u t i o n o f t h e r e a c t e d gas s u b s e q u e n t t o the i n d u c t i o n p e r i o d considered here i s dominated by the f l u i d mechanics o f the p o s t - i n d u c t i o n expansion o f the r e a c t i o n products. T h i s e x p a n s i o n r e d u c e s t h e p r e s s u r e and d e n s i t y o f t h e s e p r o d u c t s and a l t e r s t h e k i n e t i c e q u i l i b r i u m , l e a d i n g eventually to the C J s t a t e . Since v i r t u a l l y a l l of the react a n t s h a v e been consumed b y t h i s t i m e , t h e k i n e t i c s o f t h i s f i n a l e x p a n s i o n p h a s e a r e c o n t r o l l e d by r e l a t i v e l y s l o w r a d i c a l recombination processes. The p r e s e n t model d o e s n o t a t t e m p t t o f o l l o w t h a t e n t i r e r e l a x a t i o n p h a s e , c o n c e n t r a t i n g o n t h e de t a i l s o f t h e i n d u c t i o n k i n e t i c s i n t h e von Neumann s p i k e . T h i s model o f t h e d e t o n a t i o n n e g l e c t s some p o t e n t i a l l y s i g n i f i c a n t e f f e c t s a r i s i n g from h y d r o d y n a m i c - k i n e t i c interac tions. Variations o f density, temperature, and particle v e l o c i t y i n the post-shock unreacted mixture are not c o n s i d ered. M u l t i p l e s h o c k wave r e f l e c t i o n s , r a r e f a c t i o n s , i n t e r a c t i o n s w i t h c o n f i n i n g w a l l s , c e l l u l a r s t r u c t u r e , and r e l a t e d e f f e c t s a r e a l s o n o t t r e a t e d d i r e c t l y by t h e p r e s e n t s i m p l i f i e d m o d e l . A r e a l l y c o m p r e h e n s i v e d e t o n a t i o n s i m u l a t i o n model w i l l h a v e t o i n c l u d e s u c h i n t e r a c t i o n s and a t l e a s t two and p r o b a b l y even t h r e e space dimensions, but such a treatment i s beyond the scope o f the present formulation. I n c a s e s where s u c h i n t e r a c t i o n s a r e i m p o r t a n t , t h i s a p p r o a c h may n o t be a d e q u a t e . Results Many C J and i n d u c t i o n d e l a y t i m e c a l c u l a t i o n s h a v e been c a r r i e d



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out, examining t h e e f f e c t s o f v a r i a t i o n s i n many p h y s i c a l and chemical parameters. F o r fuel-02 and f u e l - a i r mixtures, t h e equivalence r a t i o can be v a r i e d over the complete range from pure o x i d i z e r t o pure f u e l . For s t o i c h i o m e t r i c fuel-02 mix t u r e s t h e amount o f d i l u t i o n by N2 can be v a r i e d between β = 0 (β i s t h e i n i t i a l r a t i o o f N2 t o O2, so β = 0 c o r r e sponds t o a fuel-02 mixture) and β = 3.76 ( i . e . f u e l - a i r ) . Other d i l u e n t s such as CO2, H2O, and Ar have been used. The i n i t i a l pressure has been v a r i e d between 0.01 and 10.0 atmo spheres, and the i n i t i a l temperature between 200 Κ and 500 Κ i n s t o i c h i o m e t r i c f u e l - C ^ and f u e l - a i r . F i n a l l y , s m a l l amounts o f s e l e c t e d halogenated s p e c i e s have been i n c l u d e d i n f u e l - a i r mixtures i n i t i a l l y a t atmospheric temperature and pressure. As an example, computed values o f t h e i n d u c t i o n l e n g t h Δ are summarized i n F i g u r e 2, showing the e f f e c t s o f v a r i a t i o n s i n the f u e l - o x i d i z e r equivalence r a t i o φ. The dashed curves represent f u e l - a i r and t h e s o l i d curves fuel-02 mixtures. R e s u l t s f o r propane (not shown) a r e very s i m i l a r t o those f o r ethane. A l l o f these r e s u l t s assume t h a t t h e i n i t i a l pressure i s atmospheric and the i n i t i a l temperature i s 300 K. There i s a s i g n i f i c a n t d i f f e r e n c e between the hydrocarbon r e s u l t s and those f o r hydrogen. F o r each hydrocarbon, values o f Δ f o r fuel-02 are lower than those f o r f u e l - a i r by a f a c t o r o f about 100, and the minimum value o f Δ f a l l s on t h e r i c h s i d e o f s t o i c h i o m e t r i c . However, f o r H2-O2 mixtures, values o f Δ a r e only a f a c t o r o f 10 lower than those f o r H2-air (15), and the m i n i mum value o f Δ occurs on t h e lean s i d e o f s t o i c h i o m e t r i c . I n d u c t i o n lengths have been computed f o r a wide v a r i e t y o f other i n i t i a l c o n d i t i o n s as w e l l , and the remaining s e c t i o n s o f t h i s paper w i l l show how these i n d u c t i o n lengths can be r e l a t e d t o s p e c i f i c detonation p r o p e r t i e s . Detonation l i m i t s . The most important r e s u l t o f t h e k i n e t i c modeling work has been the observation t h a t the i n d u c t i o n l e n g t h Δ i s approximately p r o p o r t i o n a l t o t h e c h a r a c t e r i s t i c detona t i o n c e l l width a. For s t o i c h i o m e t r i c f u e l - a i r and fuel-oxygen mixtures i n i t i a l l y a t atmospheric temperature and pressure, t h e r a t i o a/Δ i s approximately 20 and 35 r e s p e c t i v e l y , based on observed c e l l s i z e s from experimental s t u d i e s (16-18). Similar agreement i s obtained between computed i n d u c t i o n lengths and experimental c e l l s i z e data a t i n i t i a l pressures t h a t a r e d i f ferent from atmospheric (19,20). C o r r e l a t i o n s with c e l l s i z e data o f Manzhalei e t aTT ll9) f o r CH4-O2, C2H2-O2, and H2-O2 mixtures a r e shown i n F i g u r e 3. Here i n i t i a l p r e s sures are v a r i e d between 0.01 and 10 atmospheres, and the agree ment w i t h computed r e s u l t s i s good when a/Δ = 29, c o n s i s t e n t with t h e p r o p o r t i o n a l i t y obtained above a t atmospheric pres sure. The computed r e s u l t s reproduce even the s l i g h t curvature i n t h e H2-O2 measurements. This p r o p o r t i o n a l i t y can then be used t o p r e d i c t the l e a n and r i c h l i m i t s o f detonation i n l i n e a r



F i g u r e 2. Computed i n d u c t i o n lengths f o r f u e l - o x i d i z e r mixtures. Dashed curves are f o r f u e l - a i r mixtures ; s o l i d curves f o r f u e l - O ^ mixtures.




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Detonations

183


tubes, i f i t i s assumed t h a t single-head s p i n n i n g detonation occurs a t t h e l i m i t s w i t h a t r a n s v e r s e wave spacing t h a t i s twice t h e tube diameter. This has been done (15,21-24), u s i n g experimental data from a v a r i e t y o f sources (25-29). Using t h e computed i n d u c t i o n l e n g t h , the experimental tube diameter can be used t o p r e d i c t t h e l i m i t compositions. Alternatively, the l i m i t composition can be given and t h e model w i l l p r e d i c t t h e tube diameter r e q u i r e d . C r i t i c a l tube diameter. I t has been found (30-32) t h a t , f o r a planar detonation i n a l i n e a r tube o f c i r c u l a r c r o s s s e c t i o n t o i n i t i a t e an unconfined s p h e r i c a l d e t o n a t i o n , t h e tube must have a diameter d l a r g e enough t o accomodate a t l e a s t 13 t r a n s verse waves. Since the k i n e t i c i n d u c t i o n l e n g t h i s p r o p o r t i o n a l to t h e t r a n s v e r s e wave spacing, i t should a l s o be p r o p o r t i o n a l t o t h i s c r i t i c a l tube diameter d . I n F i g u r e 4 we r e l a t e these q u a n t i t i e s , together with experimental data (33-35). I n these experiments, stoichiometric fuel-C^ mixtures were d i l u t e d by s u c c e s s i v e l y l a r g e r amounts o f Ν , u n t i l t h e r a t i o 3 o f N2/O2 i n t h e unreacted mixture was equal t o 3.76, t h e value o f 3 i n normal a i r . I n F i g u r e 4 t h e experimental data are represented by symbols, w i t h χ i n d i c a t i n g C2H^-oxidizer mixtures s t u d i e d by Z e l d o v i c h e t a l . ( 3 5 ) , p l u s i n d i c a t i n g C2H4-oxidizer mixtures s t u d i e d by Moen e t a l . ( 3 4 ) , and a l l other symbols showing data o f Matsui and Lee (33ΤΓ Both con v e n t i o n a l s t o i c h i o m e t r i c mixtures and "CO s t o i c h i o m e t r i c " mix t u r e s are shown. The best agreement between computed and meas ured r e s u l t s i s obtained when d = 380 Δ. Combined with t h e c e l l s i z e p r o p o r t i o n a l i t y from F i g u r e 2 o f a = 29 Δ, these computations p r e d i c t c

c

2

c

d

c

= 13.1 a

(1)

which i s i n e x c e l l e n t agreement w i t h t h e o b s e r v a t i o n s t h a t 13 c e l l diameters a r e r e q u i r e d f o r t h e c r i t i c a l tube diameter. Because t h e o v e r a l l agreement between computed p r e d i c t i o n s o f d and experimental values shown i n F i g u r e 4 i s good f o r a l l o f t h e f u e l s considered (as w e l l as f o r propane and hydrogen, not shown), t h e model can be used t o p r e d i c t values f o r f u e l o x i d i z e r mixtures which have not been s t u d i e d e x p e r i m e n t a l l y . I t i s a l s o important t o note t h a t H2-O2 responds much d i f f e r e n t l y t o d i l u t i o n by ΙΨ? than do t h e hydrocarbon mixtures. Although H2-O2 has a value o f Δ s i m i l a r t o that o f C2H5-O2, t h e computed v a r i a t i o n o f Δ with d i l u t i o n f o r H2 i s much l e s s than f o r t h e hydrocarbons, so t h a t Δ f o r H2-air i s very s i m i l a r t o t h a t o f s t o i c h i o m e t r i c C2H2-air. C r i t i c a l tube diameters have a l s o been measured f o r s t o i c h i o m e t r i c f u e l - o x i d i z e r mixtures a t pressures d i f f e r e n t from atmospheric (33,36-38). Comparisons between experimental values for d and computed values o f Δ a t d i f f e r e n t initial c

c



184


Ο I

υ T3

Air 4

Figure k. V a r i a t i o n of computed i n d u c t i o n l e n g t h and c r i t i c a l tube diameter with degree of n i t r o g e n d i l u t i o n f o r s t o i c h i o m e t r i c f u e l o x i d i z e r mixtures. The symbols are described i n the t e x t .


10.

WESTBROOK


185

pressures are shown i n Figure 5. Again the general agreement i s good when d = 380 Δ. Several other p o i n t s a r e worth not ing. F i r s t , f o r a l l o f the hydrocarbon-02 mixtures, c


P

0

= k i Δ-a

(2)

i s c o n s i s t e n t w i t h experimental observations (33). However, f o r H2-O2 there i s a d e f i n i t e curvature i n the computed r e s u l t s when they a r e p l o t t e d l o g a r i t h m i c a l l y as i n F i g u r e 5, although over the pressure range s t u d i e d e x p e r i m e n t a l l y t h e apparently l i n e a r r e s u l t s are reproduced w e l l by the k i n e t i c model. A l l o f the f u e l - a i r computed r e s u l t s show curvature i n F i g u r e 5. Of p a r t i c u l a r i n t e r e s t i s t h e computed curve f o r H2-air which i s m u l t i p l e - v a l u e d f o r some values o f d o r Δ. S i m i l a r t o ex p l o s i o n l i m i t curves f o r H2-O2 (28), t h i s behavior i s due t o changes with pressure i n the dominant elementary r e a c t i o n chains which occur i n H2 o x i d a t i o n , p a r t i c u l a r l y the competition be tween the r e a c t i o n s c

Η + 0 Η + 0

2 2

= 0 + OH + Μ = H0 + M 2

No experimental data could be found t o compare w i t h t h i s pre d i c t e d behavior o f H2~air mixtures a t d i f f e r e n t i n i t i a l p r e s s u r e s ; i t would be i n t e r e s t i n g t o see i f the same value o f d would be found a t s e v e r a l d i f f e r e n t i n i t i a l pressures, as t h e k i n e t i c model p r e d i c t s . F u r t h e r , because o f t h e curvature and m u l t i p l e - v a l u e d behavior shown f o r some mixtures i n F i g u r e 5, Equation 2 should not be used f o r e x t r a p o l a t i n g r e s u l t s t o p r e s sures o u t s i d e the range a c t u a l l y s t u d i e d e x p e r i m e n t a l l y . The model has a l s o been used t o p r e d i c t t h e v a r i a t i o n o f i n d u c t i o n length with i n i t i a l gas temperature T (35). At constant i n i t i a l pressure, the i n d u c t i o n length and c r i t i c a l tube diameter were found t o i n c r e a s e s l o w l y with T . The v a r i a t i o n i n i n i t i a l d e n s i t y w i t h T i s t h e r e f o r e more impor t a n t than the s l i g h t increase i n elementary r e a c t i o n r a t e s w i t h T. These r e s u l t s suggest t h a t t h e d e t o n a b i l i t y o f c o l d gas mixtures, such as those which can r e s u l t from s p i l l s o f l i q u e f i e d n a t u r a l gas (LNG) o r other c r y o g e n i c a l l y s t o r e d f u e l s , w i l l be s l i g h t l y g r e a t e r than t h e same mixtures a t normal ambient temperatures. c

0

0

0

0

C r i t i c a l energy o f d i r e c t i n i t i a t i o n . The k i n e t i c s model has been used t o p r e d i c t the amount o f energy necessary t o i n i t i a t e unconfined detonations, using t h e r e l a t i o n o f Z e l d o v i c h e t a l . (35) E

c

α

AJ

where j = 1, 2, o r 3 f o r p l a n a r , c y l i n d r i c a l ,

(3) or spherical



186

configurations, r e s p e c t i v e l y . Comparisons between computed v a l u e s o f A J a n d c r i t i c a l h i g h e x p l o s i v e i n i t i a t o r masses (39-46) show good a g r e e m e n t ( 1 5 , 2 1 - 2 4 ) . F o r example, i n F i g u r e 6 t h e c r i t i c a l mass o f T e t r y l h i g h e x p l o s i v e r e q u i r e d t o i n i t i a t e unconfined s p h e r i c a l d e t o n a t i o n i n C2H£-air (43) i s p l o t t e d a s a f u n c t i o n o f e q u i v a l e n c e r a t i o φ. A l s o shown i s t h e computed c u r v e f o r Δ f o r t h e same m i x t u r e s ( 2 1 ) . T h e shape o f the c u r v e a n d the v a l u e o f φ c o r r e s p o n d i n g t o t h e minimum v a l u e o f E (and maximum d e t o n a b i l i t y ) a r e b o t h r e p r o duced very w e l l by the numerical k i n e t i c model. S i m i l a r agree ment was f o u n d w i t h t h e o t h e r f u e l - a i r m i x t u r e s f o r which d a t a were a v a i l a b l e . F o r i n i t i a t i o n o f s p h e r i c a l d e t o n a t i o n b y means o f a l i n e a r t u b e , Lee e t a l . (33,47) and U r t i e w and T a r v e r (48) r e l a t e d t h e c r i t i c a l i n i t i a t i o n e n e r g y t o t h e work which must b e done t o produce a s u f f i c i e n t l y s t r o n g source i n the unconfined gas. The resulting expression 3


c

g i v e s the c r i t i c a l energy i n terms o f the c r i t i c a l tube diameter d and t h e p r e s s u r e P, p a r t i c l e v e l o c i t y u , and s h o c k v e l o c i t y D o f t h e C J s t a t e . T h i s c a n be combined w i t h t h e r e l a t i o n between d and Δ, g i v i n g c

c

E

c

=

k

o T

3

3

( δ°) Δ

3

^

Computed v a l u e s o f E , b a s e d o n t h e k i n e t i c model ( w i t h ko = 0.1964) a g r e e w e l l (23,24) w i t h v a l u e s d e r i v e d from e x p e r i m e n t a l measurements i n f u e l - 0 2 m i x t u r e s ( 3 3 , 4 9 ) . F o r a l l o f t h e s e c o r r e l a t i o n s , p e r h a p s t h e most s i g n i f i c a n t c o n c l u s i o n i s t h a t t h e computed c u r v e s a g r e e s i m u l t a n e o u s l y w i t h the e x p e r i m e n t a l r e s u l t s f o r a l l o f t h e f u e l s examined. The r a t i o s between t h e e x p e r i m e n t a l a n d p r e d i c t e d v a l u e s o f E a r e e s s e n t i a l l y t h e same i n e a c h c a s e . T h i s means t h a t s i m i l a r p r e d i c t i o n s c a n b e made f o r o t h e r f u e l s f o r which e x p e r i m e n t a l d a t a a r e l a c k i n g b u t f o r which a r e l i a b l e k i n e t i c mechanism e x i s t s . c

c

I n h i b i t i o n o f d e t o n a t i o n . Chemical a d d i t i v e s can have a l a r g e e f f e c t on experimentally observed i g n i t i o n delay times. Small amounts o f NO2, N2O, H2, o r h i g h e r a l k a n e s c a n s i g n i f i c a n t l y r e d u c e t h e i n d u c t i o n t i m e i n CH4-O2 a n d C f y - a i r mixtures (4,9,42,46,50-55). Conversely, halogenated species h a v e b e e n shown (56,57) t o i n c r e a s e t h e i n d u c t i o n t i m e i n fuel-02 mixtures. S i n c e t h e i n d u c t i o n time i s a c r i t i c a l factof i n determining the detonability o f fuel-oxidizer m i x t u r e s , h a l o g e n a t e d compounds a n d o t h e r s p e c i e s may h a v e a n important r o l e i n reducing the d e t o n a b i l i t y hazards o f p r a c t i c a l fuels.


10.


WESTBROOK

187

Detonations

d - (meters) c

0.1


0.001

100

1

Induction length Δ (meters) Figure 5 . V a r i a t i o n o f computed i n d u c t i o n l e n g t h and experimental l y measured c r i t i c a l tube diameter with i n i t i a l pressure. Solid curves are computed r e s u l t s f o r fuel-O^ mixtures ; dashed curves f o r f u e l - a i r mixtures ; and dotted l i n e s with symbols represent experimental data from Matsui and Lee ( 3 3 ) .

I

I

I

I

_

I

"

-

10"

DO Deto- / Ί nation /

c 03 c ο

1

10" éDOO#

~

No detonation

10

7

-

C H — Air 2

6

Bull et al (1979) Ο Detonation • No detonation

— I 1

ο

I

2

I

ο 10"

Equivalence ratio φ Figure 6 . Cube o f computed i n d u c t i o n l e n g t h i n ethane-air mixtures, with data from B u l l et a l . ( U 3 ) .




188

Using t h e present model, t h e k i n e t i c response o f h y d r o c a r b o n - a i r m i x t u r e s t o t h e a d d i t i o n o f v a r y i n g amounts o f halogenated s p e c i e s h a s been examined (13). These i n h i b i t o r s i n c l u d e t h e h a l o g e n a c i d s HC1, HBr a n d H I , a s w e l l a s m e t h y l , v i n y l , a n d e t h y l c h l o r i d e s , b r o m i d e s , a n d i o d i d e s . T h e common f l a m e r e t a r d a n t CF3Br was a l s o u s e d . A s a n example o f t h e s e r e s u l t s , computed v a l u e s o f t h e i n d u c t i o n l e n g t h Δ a r e shown i n F i g u r e 7 f o r C2H4-air. From t h i s f i g u r e i t i s c l e a r that, r e l a t i v e t o the case without i n h i b i t o r s , a l l o f the a d d i t i v e s increased the i n d u c t i o n length. This i n c r e a s e i s s m a l l e s t when C I atoms a r e a d d e d , r e g a r d l e s s o f w h e t h e r t h e a d d i t i v e i s HC1, CH3CI, C2H3CI, o r C2H5CI, a n d o n l y the results w i t h 1% HC1 a r e shown i n F i g u r e 7. T h e i o d i d e s were most e f f e c t i v e a s i n h i b i t o r s , a n d t h e b r o m i d e s were n e a r l y a s e f f e c t i v e as t h e i o d i d e s . T h e compound CF3Br was s l i g h t l y more e f f e c t i v e a s a n i n h i b i t o r t h a n CH3Br, s i n c e t h e F atoms remove a d d i t i o n a l H atoms from t h e r e a c t i n g m i x t u r e s , p r o d u c i n g t h e r e l a t i v e l y i n e r t s p e c i e s HF. A l l o f t h e i n h i b i t o r s a c t a s c a t a l y s t s f o r t h e r e c o m b i n a t i o n o f H atoms, l o w e r i n g t h e s i z e o f the r a d i c a l pool and reducing t h e r a t e o f chain branching by means o f t h e r e a c t i o n H + 0

2

= 0 + OH

The r i c h l i m i t f o r d e t o n a t i o n i n a 7 0 mm t u b e , m e a s u r e d b y B o r i s o v a n d Loban ( 2 7 ) , i s R = 2.5. A t t h i s p o i n t Δ = 1.04 χ 1 C T m. B a s e d o n t h e e a r l i e r d i s c u s s i o n , t h e same v a l u e o f Δ w i l l c o r r e s p o n d t o t h e r i c h l i m i t i n t h e same t u b e f o r o t h e r m i x t u r e s a s w e l l . A s i n h i b i t o r s a r e added t o t h e r e a c t i v e f u e l - a i r mixture, t h e value o f equivalence r a t i o c o r r e s p o n d i n g t o Δ = 1.04 χ Ι Ο m i s g r a d u a l l y r e d u c e d . F o r 1% HI t h i s g i v e s a r i c h l i m i t o f 4>R - 2.0, s h o w i n g a s u b s t a n t i a l narrowing o f the detonation l i m i t s . Because the curves i n F i g u r e 7 a r e v e r y s t e e p o n t h e f u e l - l e a n s i d e , most o f t h e reduction i n detonation l i m i t s occurs a t t h e r i c h l i m i t rather than a t t h e l e a n l i m i t . The i n c r e a s e i n i n d u c t i o n l e n g t h with i n h i b i t o r s a l s o r e s u l t s i n an increase i n t h e c r i t i c a l energy f o r i n i t i a t i o n o f d e t o n a t i o n , w h i c h c a n b e s e e n e a s i l y from E q u a t i o n 5. 2

- 2

Conclusion D e t o n a t i o n s a r e e x t r e m e l y complex phenomena a n d i n v o l v e many competing p h y s i c a l and chemical processes. Complete t h e o r e t i c a l models o f the i n i t i a t i o n , s t a b i l i t y , and s t r u c t u r e o f d e t o n a t i o n waves r e q u i r e a n a c c u r a t e d e s c r i p t i o n o f t h e c h e m i c a l k i n e t i c s o f t h e i n d u c t i o n p h a s e . T h e p r i m a r y g o a l o f t h e p r e s e n t work i s t o d e m o n s t r a t e t h a t k i n e t i c mechanisms a r e now a v a i l a b l e w h i c h are able t o p r e d i c t the i n d u c t i o n delay period f o r a v a r i e t y o f practical fuels.



Figure 7 · Computed i n d u c t i o n lengths f o r e t h y l e n e - a i r mixtures showing the e f f e c t s o f a d d i t i o n of s e l e c t e d i n h i b i t o r s . Also shown i s the p r e d i c t e d r i c h l i m i t f o r the propagation o f detonation i n a l i n e a r tube, based on the data without i n h i b i t o r s present o f Borisov and Loban ( 2 7 ) .



190


I t was o b s e r v e d t h a t computed i n d u c t i o n d e l a y t i m e s a n d induction lengths c o r r e l a t e well with observed experimental det o n a t i o n phenomena, i n d e p e n d e n t o f f u e l t y p e , o x i d i z e r t y p e , nitrogen d i l u t i o n , i n i t i a l pressure, i n i t i a l temperature, and equivalence ratio. T h i s g e n e r a l agreement emphasizes t h e central role that chemical k i n e t i c s plays i n t h e detonation p r o c e s s , d e t e r m i n i n g t h e c h a r a c t e r i s t i c l e n g t h and time s c a l e s . Eventually, complete coupled multidimensional f l u i d mechanics and k i n e t i c s m o d e l s w i l l a p p e a r , b u t t h e p r e s e n t s i m p l i f i e d approach s t i l l provides a great deal o f u s e f u l information. Acknowledgments Many v a l u a b l e d i s c u s s i o n s w i t h D r . P. A. U r t i e w , P r o f e s s o r F . L . D r y e r , a n d P r o f e s s o r J . H. L e e a r e g r a t e f u l l y a c k n o w l e d g e d . T h i s work was p e r f o r m e d u n d e r t h e a u s p i c e s o f t h e U. S. D e p a r t ment o f E n e r g y b y t h e L a w r e n c e L i v e r m o r e N a t i o n a l L a b o r a t o r y u n d e r c o n t r a c t No. W-7405-ENG-48.

J.

Literature Cited 1. Westbrook, C. Κ., and Dryer, F. L., Eighteenth Symposium (International) on Combustion, p. 749, The Combustion Institute, 1981. 2. Westbrook, C. Κ., and Dryer, F. L., "Chemical Kinetics Modeling of Hydrocarbon Combustion", Prog. Energy and Comb. Sci., to appear, 1983. 3. Westbrook, C. K., Creighton, J., Lund, C., and Dryer, F. L., Phys. Chem. 81, 2542 (1977). 4. Westbrook, C. Κ., Comb. Sci. Tech. 20, 5 (1979). 5. Westbrook, C. K., and Dryer, F. L., Comb. Sci. Tech. 20, 125 (1979). 6. Westbrook, C. K., Dryer, F. L., and Schug, K. P., Nineteenth Symposium (International) on Combustion, p. 153, The Combustion Institute, Pittsburgh, 1983. 7. Westbrook, C. K., and Pitz, W. J., "A Comprehensive Chemical Kinetic Reaction Mechanism for the Oxidation and Pyrolysis of Propane and Propene, submitted for publication, 1983. 8. JANAF Thermochemical Tables, U. S. National Bureau of Standards NSRDS-NBS 37 and Supplements. D. R. Stull and H. Prophet, eds., 1971. 9. Westbrook, C. K., and Haselman, L. C., Prog, i n Astr. and Aero. 75, 193 (1981). 10. Jachimowski, C. J., Comb. Flame 29, 55 (1977). 11. Burcat, Α., Lifshitz, Α., Scheller, K., and Skinner, G. Β., Thirteenth Symposium (International) on Combustion, p. 745, The Combustion Institute, Pittsburgh, 1971. 12. Westbrook, C. K., Comb. Sci. and Tech. 23, 191 (1980). 13. Westbrook, C. K., Nineteenth Symposium (International) on Combustion, p. 127, The Combustion Institute, Pittsburgh, 1983. In The Chemistry of Combustion Processes; Sloane, T.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.


10.

14. 15. 16. E., 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.

WESTBROOK


Detonations

191

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Chemical Kinetic Factors in Gaseous Detonations - ACS Publications

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