during combustion, which is determined by the pro- ceses of chemical kinetic s, cannot yet be determined theoretically for hydrocarbon fuels and must be found.
COMBUSTION, EXPLOSION, AND SHOCK WAVES
391
TOTAL COMBUSTION KINETICS OF HYDROCARBON F U E L S V. L. Zimont and Yu. M. T r u s h i n F i z i k a G o r e n i y a i Vzryva, Vol. 5, No. 4, pp. 567-573, 1969 UDC 536.46 To c a l c u l a t e the g a s d y n a m i c p r o c e s s e s taking p l a c e in fuel gas m i x t u r e s , it is n e c e s s a r y to know the r a t e of heat r e l e a s e in the c o m b u s t i o n zone as a function of the s t at e of the gas m i x t u r e . The r a t e of heat r e l e a s e during combustion, which is d e t e r m i n e d by the p r o c e s e s of c h e m i c a l kinetic s, cannot yet be d e t e r m i n e d t h e o r e t i c a l l y f o r h y d r o c a r b o n fuels and m u s t be found experimentally. The d i r e c t e x p e r i m e n t a l d e t e r m i n a t i o n of the heat r e l e a s e r a t e s in the combustion zone p r e s e n t s g r e a t : d i f f i c u l t i e s , owing to the high t e m p e r a t u r e s and s h o r t r e a c t i o n t i m e s . E s s e n t i a l l y , only two m e th o d s of d e t e r m i n i n g the absolute value of the heat r e l e a s e r a t e have been d e s c r i b e d : by using a m a s s s p e c t r o g r a p h to m e a s u r e the c o n c e n t r a t i o n s of the components along the c o m b u s t i o n zone in a plane l a m i n a r f l a m e obtained at red u ced p r e s s u r e s on a porous b u r n e r ; and by inv e s t i g a t i n g the conditions of c o l l a p s e of combustion in a homogeneous r e a c t o r . The c o n c e n t r a t i o n and flow v e l o c i t y p r o f i l e s found e x p e r i m e n t a l l y in a m e t h a n e - o x y g e n f l a m e have m a d e it p o s s i b l e to find the d i s t r i b u t i o n s of the absolute r e action r a t e s of the components along the r e a c t i o n zone f o r known values of the diffusion c o e f f i c i e n t s [1]. By using the e x p e r i m e n t a l values of the p a r a m e t e r s at which the c o m b u s t i o n of an i s o o c t a n e - a i r m i x t u r e in a r e a c t o r c o l l a p s e s , it has been found p o s s i b l e to s e l e c t c o e f f i c i e n t s in the e x p r e s s i o n for the o v e r - a l l r e a c t i o n r a t e ( r e a c t i o n constants, activation en er g y , o r d e r of r e a c t i o n ) that c o r r e c t l y d e s c r i b e the r e s u l t s of e x p e r i m e n t s o v e r a broad r a n g e of m i x t u r e p a r a m e t e r s [2]. This a r t i c l e p r e s e n t s the r e s u l t s of an e x p e r i m e n t a l i n v e s t i g a t i o n of the combustion p r o c e s s obtained by -P
3
m e a s u r i n g the oxygen c o n c e n t r a t i o n a c r o s s the r e a c t i o n zone of a f l a m e f r o n t e s t a b l i s h e d in a channel in the p r e s e n c e of a h i g h - v e l o c i t y ( a p p r o x i m a t e l y 50 m / s e c ) k e r o s e n e - a i r flow. The data on the total c o m b u s t i o n k i n e t i c s of :hydrocarbons obtained by d i f f e r e n t m e t h o d s a r e c o m p a r e d with the p u r p o se of r e c o m m e n d i n g k i n e t i c r e l a t i o n s that will allow the b e s t p o s s i b l e d e s c r i p t i o n of the absolute heat r e l e a s e r a t e s f o r h y d r o c a r b o n fuels. INVESTIGATION OF THE COMBUSTION PROCESS IN A HIGH-VELOCITY FLOW The working p a r t of the ap p ar at u s is shown in Fig. 1. Vaporized k e r o s e n e was i n t r o d u c e d into a flow of heated a i r in a c y l i n d r i c a l c o m p a r t m e n t 100 m m in d i a m e t e r through a manifold. The manifold c o n s i s t e d of a s y s t em of p l a n e - p a r a l l e l tubes a r r a n g e d 6 m m apart, in which 400 holes 0.4 m m in d i a m e t e r w e r e f o r m e d in a c h e c k e r b o a r d p a t t e r n at i n t e r v a l s of 6 m m at an angle of 30 ~ to the flow. The c y l i n d r i c a l c o m p a r t m e n t was followed by a conical s e c t i o n 1.5 m longwith a 4 ~ t a p e r , in which the f l a m e f r o n t was e s t a b l i s h e d . The length of the c y l i n d r i c a l c o m p a r t m e n t v a r i e d with the i n i t i al flow t e m p e r a t u r e in a c c o r d a n c e with the change in the induction p e r i o d of the m i x t u r e . (A m o r e detailed d e s c r i p t i o n of the apparatus is given in [3]. ) In the c o u r s e of the e x p e r i m e n t s , we i n v e s t i g a t e d the change of oxygen c o n c e n t r a t i o n in a d i r e c t i o n p e r p e n d i c u l a r to the f l a m e front. The s a m p l e s w e r e taken with a cooled gas s a m p l e r , which was d i s p l a c e d along the axis of the conical s e c t i o n of the c h a m b e r during the e x p e r i m e n t . To r e d u c e the length of the gas s a m pling channel, a s p e c i a l l y t h e r m o s t a t e d gas a n a l y z e r was mounted on the t r a v e r s e c a r r i a g e .
4
5
~7 Io
~ 8
-,r
Fig. 1. Working s e c t i o n of apparatus: 1) t r a v e r s e m e c h a n i s m ; 2) c a r r i a g e ; 3) gas a n a l y z e r ; 4) vacuum pumps; 5) o s c i l l o g r a p h ; 6) E P P - 0 9 ; 7) t h e r m o c o u p l e s ; 8) fuel supply; 9) m a n o m e t e r bank; 1 0 ) w a t e r inlet and outlet.
392
FIZIKA
To measure the o x y g e n concentration, we used a specially designed low-inertia thermomagnetic gas analyzer of the compensation type. This instrument had an improved internal gasdynamic system and employed open tungsten spirals. This made it possible .
.
.
.
o
r
or f ; t z 4
0.50
-- -- -
5
0.01
..
0.009
0.010
0.011~,
sec
to r e d u c e the t i m e c o n s t a n t ( t i m e t a k e n by the i n s t r u m e n t r e a d i n g s to c h a n g e w h e n t h e supply w a s s w i t c h e d r a p i d l y f r o m p u r e n i t r o g e n to p u r e oxygen) to 0.32 s e c , and w i t h a l l o w a n c e for the s a m p l i n g c h a n n e l e m p l o y e d to 0.4 s e c . When the b r i d g e w a s p r o p e r l y b a l a n c e d , t h e c o m p e n s a t i o n c i r c u i t m a d e it p o s s i b l e to o b t a i n r e a d i n g s t h a t w e r e i n d e p e n d e n t of the i n s t r u m e n t o r i e n t a tion in s p a c e , so that it could be e m p l o y e d u n d e r our particular experimental conditions. (Adetailed descript i o n of the i n s t r u m e n t i s g i v e n in [4]. ) ~O
500
| o2
400
/ Z -~200o.~ ~ 9
'
300
o
.~
I VZRYVA
p r e s s u r e a l o n g the c h a n n e l , and t h e t o t a l p r e s s u r e m e a s u r e d with a P i t o t t u b e w h i c h was i n t e g r a l with t h e t r a v e r s e . The s a m p l e was s u c k e d t h r o u g h t h e gas a n a l y z e r by m e a n s of a f o r e p u m p . A n a l y s i s of t h e o s c i l l o g r a m s e n a b l e d us to c o n s t r u c t the d e p e n d e n c e on the l o n g i t u d i n a l c o o r d i n a t e of t h e f r a c t i o n of o x y g e n c o n s u m e d r e f e r r e d to the o x y g e n r e q u i r e m e n t s f o r c o m p l e t e c o m b u s t i o n e. C o n v e r s i o n to the e(~-) c u r v e s w a s a c c o m p l i s h e d by m e a n s of the m e a s u r e d v e l o c i t y c o e f f i c i e n t (with r e s p e c t to P/P0) and t e m p e r a t u r e (with r e s p e c t to e). An a n a l y s i s s h o w e d that the r e s u l t s of the e(T) c o n v e r s i o n a r e s i m i l a r , no m a t t e r w h e t h e r the a c t u a l t o t a l p r e s s u r e p r o f i l e o r its l i n e a r a p p r o x i m a t i o n is u s e d .
Fig. 2. F r a c t i o n of oxygen consumed e as a function of t i m e T; flow t e m p e r a t u r e 1070 ~ K; oxygen concentration f0 = 0.17; T is reckoned f r o m the moment of injection of the fuel.
1) o~ = 1o0; 2) oz = 0.9; 3) oz = 0.7; 4) oz = 0.6; 5) b u r n u p c u r v e s f o r ~ = 0.6 and ~ = 1.
GORENIYA
/600
s
/800
f900
1950 7 ~ i (
~ -t 0.5
0.7 x, cm
0.5
F i g . 4. E x p e r i m e n t a l r e a c t i o n r a t e s [1]. W i t h the p o s i t i o n of the f l a m e f r o n t s t e a d y , t h e w i d t h of t h e b u r n u p z o n e was of the s a m e o r d e r as the d i s t a n c e f r o m the point of f u e l i n j e c t i o n to the i g n i t i o n r e g i o n d e t e r m i n e d f r o m the o n s e t of s i g n i f i c a n t o x y g e n a b s o r p t i o n (about 1 m). It w a s found that this g r e a t width of the b u r n u p z o n e i s a s s o c i a t e d w i t h the p r e s e n c e Of t e m p e r a t u r e f l u c t u a t i o n s . M e a s u r e m e n t s w i t h a l o w - i n e r t i a r e s i s t a n c e t h e r m o m e t e r showed that the a m p l i t u d e of the f l u c t u a t i o n s r e a c h e s 50 ~. T h i s l e a d s to the i g n i t i o n of m o l e s of gas at d i f f e r e n t t e m p e r a t u r e s 160
A,
0
d
1oo
0
!
2
5
4
5
B
d [ 0 2 ] / d t , m o l e / c m z ' see
F i g . 30 H e a t r e l e a s e r a t e as a f u n c t i o n of the r a t e of o x y g e n c o n s u m p t i o n . 1) p = = 0.05 b a r ; 2) p = 0.1 b a r .
~ 4o o 0.5
In t h e e x p e r i m e n t , a c e r t a i n a i r t e m p e r a t u r e and v e l o c i t y w a s a s s i g n e d , a f t e r w h i c h the n e c e s s a r y a m o u n t of v a p o r i z e d f u e l w a s a d m i t t e d to the f l o w t h r o u g h the m a n i f o l d . T h i s led to the f o r m a t i o n of a f l a m e f r o n t in t h e c o n i c a l p a r t of the c h a m b e r . An i n v e s t i g a t i o n of the t r a n s v e r s e t e m p e r a t u r e d i s t r i b u t i o n s h o w e d that t h e s t e a d y f l a m e f r o n t w a s not p l a n e but c o n v e x t o w a r d t h e manifold. As the g a s s a m p l e r w a s d i s p l a c e d , we o b t a i n e d a r e c o r d of the g a s a n a l y z e r r e a d i n g s and the s a m p l e r c o o r d i n a t e on a loop o s c i l l o g r a p h . M o r e o v e r , we r e g i s t e r e d the flow r a t e s of a i r and fuel, the flow t e m p e r a t u r e at v a r i o u s p o i n t s along the c h a n n e l , the t e m p e r a t u r e of the c h a m b e r w a l l s , the f u e l t e m p e r a t u r e , t h e
0.5
0.7 x, cm
F i g . 5. E x p e r i m e n t a l v a l u e s of the h e a t r e lease for a two-dimensionla methane-oxygen f l a m e at p --- 0.05 b a r c o m p a r e d with the r e s u l t s of a c a l c u l a t i o n u s i n g E q s . (1) and (2): 1) c a l c u l a t i o n b a s e d on the d a t a p r e s e n t e d in F i g . 4; 2) and 3) c a l c u l a t i o n b a s e d on E q s . (1) and (2) u s i n g e x p e r i m e n t a l v a l u e s of f C n H m ' f c o and f o ~ and the t e m p e r a t u r e ; 4) total h e a t r e l e a s e c u r v e ; 5) h e a t r e l e a s e a c c o r d i n g to the k i n e t i c f o r m u l a f o r m e t h a n e [7]. at d i f f e r e n t d i s t a n c e s f r o m the f u e l a d m i s s i o n point and to a c o r r e s p o n d i n g i n c r e a s e in the a v e r a g e width of the b u r n u p z o n e m e a s u r e d in the e x p e r i m e n t s .
COMBUSTION,
EXPLOSION,
AND
SHOCK
WAVES
As the d i f f e r e n c e between the flow t e m p e r a t u r e and the wall t e m p e r a t u r e d e c r e a s e s , the t e m p e r a t u r e f l u c tuations in the flow a r e r e d u c e d . T h e r e f o r e , we p e r f o r m e d e x p e r i m e n t s in which the wall was p r e h e a t e d by r a i s i n g the ai r t e m p e r a t u r e by 200-300" in c o m p a r i s o n with the e x p e r i m e n t a l t e m p e r a t u r e ; the burnup c u r v e was m e a s u r e d when the t e m p e r a t u r e s of the walls and the flow w e r e s i m i l a r . It is i n t e r e s t i n g to note that in t h e s e e x p e r i m e n t s the f l a m e f r o n t was convex toward the channel outlet, s i n c e ignition o c c u r r e d at the heated w a l ls e a r l i e r than on the flow axis. In this c a s e , the f l a m e front was not steady and moved slowly in the d i r e c t i o n of the m a n i fold. The r e s u l t s of the e x p e r i m e n t s a r e p r e s e n t e d in Fig. 2 f o r v a r i o u s f u e l - a i r r a t i o s a. In c o n s t r u c t i n g the c u r v e s , the m o m e n t s at which burnup began w e r e combined (in the e x p e r i m e n t s the m o m e n t of ignition v a r i e d by 0.001 s e c owing to i n a c c u r a c y in m a i n t a i n i n g the initial flow t e m p e r a t u r e ) . A c c o r d i n g t o the m e a s u r e m e n t s , the amplitude of the t e m p e r a t u r e fluctuations was not g r e a t e r than about 4 - 5 ~ As follows f r o m Fig. 2, the burnup t i m e is much l e s s than the induction t i m e . It should be noted that the a c c u r a c y of the burnup c u r v e m e a s u r e m e n t s p r e s e n t e d in Fig. 2 is not v e r y high, owing to the n a r r o w n e s s of the burnup zone. Under t h e s e conditions, the e r r o r due to the i n e r t i a o f t h e g a s a n a l y z e r m ay r e a c h 3 0 - 5 0 % .
393 In the equation d e s c r i b i n g the total c o m b u s t i o n k i n e t i c s , it is convenient to e x p r e s s the r a t e of oxygen consumption not in t e r m s of the r e l a t i v e v o l u m e but in t e r m s of the r e l a t i v e m a s s c o n c e n t r a t i o n s of fuel and o x i d i z e r . In this case, t h e r e is no need to know the m o l e c u l a r weight of the fuel, the d e t e r m i n a t i o n of which m a y be f u r t h e r c o m p l i c a t e d by t h e r m a l d e c o m position of the fuel in the flow. F u r t h e r m o r e , t h e r e ar e e x p e r i m e n t a l data indicating that, at i d en t i cal f u e l - o x i d i z e r m a s s r a t i o s , the kinetic c h a r a c t e r i s t i c s of the c o m b u s t i o n of d i f f e r e n t hyd r o c a r b o n s a r e s i m i l a r . Data p r e s e n t e d in [6] show that, at identical f u e l - a i r r a t i o s , the p a r a m e t e r s at which the combustion of p r o p a n e - a i r and i s o o c t a n e - a i r m i x t u r e s c o l l a p s e s in a homogeneous r e a c t o r a r e s i m ilar. The kinetic r e l a t i o n s obtained in [2] for i s o o c t a n e can be w r i t t e n in t e r m s of the r e l a t i v e m a s s c o n c e n t r a t i o n s , the o r i g i n a l h y d r o c a r b o n or carbon m o n o x i d e being r e g a r d e d as unburned fuel. (The c a r b o n m o n o x ide a p p e a r s in the zone of i n t e n s e heat r e l e a s e , in the p r e s e n c e of e x c e s s o x i d i z e r . ) 40000
d[02]
--3.3.
10 ~ e
p~
T1.5 f%H fo ~ m o l e / s e c ' c m
F r o m the standpoint of heat r e l e a s e , it is m o r e convenient to e x p r e s s the intensity of the combustion p r o c e s s not in t e r m s of the r a t e of d e c r e a s e of the s t a r t i n g fuel c o n c e n t r a t i o n but in t e r m s of the r a t e of oxygen consumption. This is b e c a u s e the r a t e of heat r e l e a s e is p r o p o r t i o n a l to the r a t e at which oxygen is consumed. The r a t e s of oxygen consumption and the intensity of heat r e l e a s e , c a l c u l a t e d f o r points along the r e a c tion zone f r o m the e x p e r i m e n t a l r e a c t i o n r a t e s of the m i x t u r e components found in [1] f o r a m e t h a n e - o x y g e n f l a m e ( s t a r t i n g c o n c e n t r a t i o n s of m e t h a n e and oxygen 0.078 and 0.919), a r e p r e s e n t e d in Fig. 3. F o r d e t e r m i n i n g the r e l a t i o n between oxygen consumption and heat r e l e a s e , we also found (from the data of a total c h e m i c a l a n a l y s i s of a s a m p l e of h o m o geneous k e r o s e n e - a i r and g a s o l i n e - a i r m i x t u r e s with = 1 - 2 , taken f r o m the c o m b u s t i o n zone behind a point ignition s o u r c e ) a dependence of the extent of c o m b u s t i o n on the f r a c t i o n of oxygen c o n s u m e d that c o n f i r m s the p r o p o r t i o n a l i t y of th e s e quantities. E x p r e s s i n g the k i n e t i c s of the p r o c e s s in t e r m s of the r a t e of fuel c o n s u m p ti o n m a y lead to i n c o r r e c t c o n cl u s i o n s r e g a r d i n g the r a t e of heat r e l e a s e , since, owing to the c o m p l e x c h a r a c t e r of the p r o c e s s , the s t a r t i n g fuel p a s s e s through a s e r i e s of i n t e r m e d i a t e s t a g e s b e f o r e the final c o m b u s t i o n products a r e f o r m e d . In p a r t i c u l a r , in the p r e s e n c e of an e x c e s s of o x i d i z e r , c a r b o n monoxide a c c u m u l a t e s in the c o m b u s t i o n zone and is then oxidized to c a r b o n dioxide and w a t e r [1].
3,
(1)
4~000
d [O2t -- 1.3 9 10TM e COMPARISON OF THE E X P E R I M E N T A L R E S U L T S OBTAINED BY D I F F E R E N T METHODS
~r
dt
R:r
dt p:
/.1.~- ]'co fo0 m o l e / s e c 9 cm a ,
(2)
w h e r e p is the p r e s s u r e in b a r s , and R is the u n i v e r sal g as constant (1.987 g . c a l / g . m o l e . ~ In (1) and (2), the m o l e c u l a r weight of the r e a c t i n g m i x t u r e was taken equal to 28.3. The o v e r - a l l o r d e r of the c o m b u s t i o n r e a c t i o n obtained in [2], n a m e l y 1 . 8 - 2 . 0 , co i n ci d es with the va l ue found in [1] by c o m p a r i n g the t e m p e r a t u r e and c o n c e n t r a t i o n p r o f i l e s in the f l a m e s at p r e s s u r e s of 0.05 and 0.1 arm. It is i n t e r e s t i n g to note that f r o m the t h e r m o c h e m ical p r o p e r t i e s of h y d r o c a r b o n s [5l it follows that, f or all s i m p l e h y d r o c a r b o n s and for c o m p l e x h y d r o c a r b o n fuels (gasoline, k e r o s e n e ) , the c o m b u s t i o n e n e r g y pe r unit m a s s of oxygen consumed i s a p p r o x i m a t e l y the s a m e , namely, c o r r e c t to • 100 000 cal pe r m o l e of Oxygen consumed (apart f r o m c e r t a i n h y d r o c a r b o n s of the benzene group, f o r which the d e v i a t i o n f r o m the above f i g u r e m a y r e a c h 1 0 - 2 0 % ) . This makes it p o s s i b l e to e m p l o y Eqs. (1) and (2) d i r e c t l y to d e t e r m i n e the absolute heat r e l e a s e r a t e s of hydroca~,bon fuels. In F i g s. 4 and 5, the e x p e r i m e n t a l h e a t r e l e a s e r a t e in a t w o - d i m e n s i o n a l m e t h a n e - o x y g e n f l a m e at a p r e s s u r e of 1/20 b ar is c o m p a r e d with the r e s u l t s of a c a l c u lation based on (1) and (2). As follows f r o m t h e s e f i g u r e s , the c o r r e s p o n d e n c e between e x p e r i m e n t and c a l culation in the zone of i n t en se heat r e l e a s e is p e r f e c t l y s a t i s f a c t o r y . The e x a g g e r a t i o n of the c a l c u l a t e d heat r e l e a s e r a t e at the end of the c o m b u s t i o n zone is a t t r i b u t a b l e to the fact that, in the zone of i n t e n s e heat
394 r e l e a s e , t h e r e is a c o n c e n t r a t i o n of hydroxyl OH an o r d e r g r e a t e r than the e q u i l i b r i u m value [1]. T h e r e fo r e, the u s e of the o v e r - a l l kinetic equation, which e x p r e s s e s the r e a c t i o n r a t e in t e r m s of the fuel and o x i d i z e r c o n c e n t r a t i o n s and c o r r e c t l y d e s c r i b e s the heat r e l e a s e in the i n t e n s e combustion zone, e x a g g e r a t e s the r e a c t i o n r a t e at the end of the r e a c t i o n zone, w h e r e the c o n c e n t r a t i o n of a c t i v e p a r t i c l e s is c l o s e to the e q u i l i b r i u m value. Calculation of the heat r e l e a s e f r o m the kinetic f o r m u l a f o r m e t h a n e obtained in [7] and a p p r o x i m a t i n g the e x p e r i m e n t s at the v e r y beginning of the c o m b u s tion zone does not p e r m i t the c o r r e c t c a l c u l a t i o n of the h e a t r e l e a s e in the zone of i n t e n s e c o m b u s t i o n (see Fig. 5, c u r v e 5). In Fig: 2, c u r v e s 5 r e p r e s e n t the c a l c u l a t e d burnup c u r v e s for a = 0.6 and ce = 1 on the a s s u m p t i o n of a s i n g l e - s t a g e c o m b u s t i o n r e a c t i o n using equation (1). In the c a l c u l a t i o n s , diffusion and heat conduction along the burnup zone w e r e n e g l e c t e d ; the p r e s s u r e was a s s u m ed constant along the r e a c t i o n zone. The change of t e m p e r a t u r e during the r e a c t i o n was found using e q u i l i b r i u m v a l u e s of the s p e c i f i c heat Cp(T), the f r a c t i o n of heat r e l e a s e d during combustion was a s s u m e d p r o p o r t i o n a l to e, and the e f f e c t i v e v a l u e s of the r e a c t i o n e n e r g y w e r e found f r o m the condition that the t e m p e r a t u r e of the combustion products at e = 1 should coincide with the e q u i l i b r i u m t e m p e r a t u r e (in the g i v e n c a s e , for ce = 0 . 6 a n d c e = l , T =1960 ~ K a n d T = 2340 ~ K, r e s p e c t i v e l y ) . It follows f r o m Fig. 2 that, f o r the k in e t ic c a l c u l a tions, the a g r e e m e n t between c a l c u l a t i o n and e x p e r i m e n t is quite s a t i s f a c t o r y . On the b as i s of this c o m p a r i s o n (Figs. 2, 4, 5), we m a y conclude that r e l a t i o n s (1) and (2) can be r e c o m mended for the p r e l i m i n a r y quantitative e s t i m a t i o n of the o v e r - a l l c o m b u s t i o n r a t e s of h y d r o c a r b o n fuels; in this c a s e , the u s e of r e l a t i o n (1) alone m a k e s it p o s s i b l e to d e s c r i b e the total combustion k i n e t i c s as a s i n g l e - s t a g e p r o c e s s , while the combined u s e of (1)
FIZIKA
GORENIYA
I VZRYVA
and (2) p e r m i t s t h e i r d e s c r i p t i o n as a t w o - s t a g e p r o c e s s in the p r e s e n c e of e x c e s s o x i d i z e r : to c a r b o n monoxide in a c c o r d a n c e with Eq. (1) with subsequent combustion of the carbon monoxide to c a r b o n dioxide in a c c o r d a n c e with Eq. (2). To find the induction t i m e s of h y d r o c a r b o n fuels (in the ab sen ce of w at er v ap o r in the fuel m i x t u r e ) on the t e m p e r a t u r e i n t e r v a l 1000-2500 ~ K, it is p o s s i b l e to r e c o m m e n d the f o r m u l a obtained by analyzing the e x p e r i m e n t a l data on the ignition lags in a flow, in a moving detonation wave, and behind a r e f l e c t e d shock wave [ 3]: 15200
"c = 6 . tO-ZO p - 2 fo['~
r
sec.
(3)
Equation ( 3 ) d i f f e r s s o m e w h a t f r o m that p r e s e n t e d in [3]; this is b e c a u s e Eq. (3) was obtained after c o r r e e t i n g Wagner, s lag data f o r a moving detonation w ave. REFERENCES 1. A. W e s t e n b e r g and M. F r i s t r o m , J. Phys. C h e m . , 65, 591, 1961. 2. I. Longwell and M. W e i s s , Ind. Eng. C h e m . , 47, 1634, 1955. 3. V. L. Zimont and Yu. M. Trushin, FGV [ C o m bustion, Explosion, and Shock Waves], 3, 1, 1967. 4. Yu. M. Trushin, P e r e d o v o i n a u c h n o - t e k h n i c h e s k i i opyt, Set. P r i b o r y dlya i s s l e d o v a n i y a f i z i c h e s k i k h s v o i s t v gazov, zhidkosti i k o n t r o l y a t e p l o e n e r g e t i cheskikh p a r a m e t r o v , GOSINTI, Moscow, 8, 1962. 5. N. F. Dubovkin, Manual of Hydrocarbon F ue l s and T h e i r Combustion P r o d u c t s [in Russian], G o s e n e r goizdat, Moscow, 1962. 6. A. Clarke, A. H a r r i s o n , and J. O d g e r s , Seventh Symposium on Combustion, 1959. 7. G. I. Kozlov, IFZh, 1, 7, 1958.
9 June 1969
Moscow
