MEASUREMENT AND COMPUTATION OF FLAME STRUCTURE

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MEASUREMENT AND COMPUTATION OF FLAME STRUCTURE

G. Dixon-Lewis

To cite this version:

G. Dixon-Lewis. MEASUREMENT AND COMPUTATION OF FLAME STRUCTURE. Journal de

Physique Colloques, 1971, 32 (C5), pp.C5b-9-C5b-11. �10.1051/jphyscol:1971557�. �jpa-00214776�

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MEASUREMENT AND COMPUTATION OF FLAME STRUCTURE.

6 . Dixon-Lewis,

Houldsworth School of A p p l i e d S c i e n c e , U n i v e r s i t y of L e e d s , A n g l e t e r r e .

Rbsum6.

-

On d i s c u t e l e s m6thodes p e r m e t t a n t une Btude d 6 t a i l l d e d e l a s t r u c t u r e , d e s p r o p r i d t 6 s e t du m6canisme d e q u e l q u e s t y p e s d e flanrme. T o u t e s l e s f l a m e s i m p l i q u e n t une i n t e r a c t i o n e n t r e 11a6rodynamique e t l a c h i m i e ; pour l e s f l a m e s l a m i n a i r e s c e s o n t n o s c o n n a i s s a n c e s chimiques q u i s o n t l e s moins s a t i s f a i s a n t e s . Avant d ' a b o r d e r c e domaine, il f a u t t o u t e f o i s r e p r 6 s e n t e r d e f a c o n s a t i s f a i s a n t e l e s ph6nomSnes p h y s i q u e s .

A b s t r a c t .

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Methods f o r d e t a i l e d i n v e s t i g a t i o n of t h e s t r u c t u r e , p r o p e r t i e s and mechanism o f some s i m p l e f l a m e s y s t e m s a r e d i s c u s s e d . A l l f l a m e system. i n v o l v e i n t e r a c t i o n between aerodynamics on t h e one hand and c h e m i s t r y on t h e o t h e r , and i n t h e c a s e o f lamin'ar f l a m e s i t i s i n t h e chemical f i e l d t h a t o u r knowledge i s l e a s t s a t i s f a c t o r y . However, b e f o r e one can i n v e s t i g a t e t h e c h e m i s t r y , i t i s n e c e s s a r y t o r e p r e s e n t t h e p h y s i c s o f t h e s i t u a t i o n r e a l i s t i c a l l y .

With t h e p r o v i s o t h a t o n e ' s chemical r e a c t i o n t r a t i o n [ 3 ]

.

Because of d i f f i c u l t i e s o f measure- mechanism i s a b l e t o c o v e r t h e whole c o m p o s i t i o n ment caused b y t h e v e r y low c o n c e n t r a t i o n s o f t h e r a n g e e n c o u n t e r e d , t h e b a s t i c c h e m i c a l r e a c t i o n s i n o t h e r i n t e r m e d i a t e s (OH, 0 , and HO 2 ) i n t h e p a r t i - a f l a m e a r e q u i t e i n d e p e n d e n t o f t h e c o m p l e x i t y o f c u l a r flame s t u d i e d e x p e r i m e n t a l l y , t h i s was t h e t h e aerodynamics. F o r s t u d y i n g t h e c h e m i s t r y t h e r e - o n l y r a d i c a l d e t e r m i n a t i o n which c o u l d b e made.

f o r e , t h e s i m p l e s t p o s s i b l e aerodynamic s y s t e m , t h e Using t h e c o n t i n u i t y e q u a t i o n s f o r t h e s t e a d y one-dimensional premixed f l a m e i s u s e d i n t h i s s t a t e f l a m e , i t i s p o s s i b l e t o deduce r e a c t i o n work, which r e l a t e s s p e c i f i c a l l y t o f u e l

-

r i c h r a t e s from t h e measured p r o f i l e s e . 8 . r 4 ]

,

b u t i t f l a m e s s u p p o r t e d by t h e hydrogen

-

oxygen r e a c t i o n . i s d i f f i c u l t by t h i s approach t o deduce r e a c t i o n E x p e r i m e n t a l l y , s l o w b u r n i n g f l a m e s i n r i c h hydro- mechanism. To do t h i s , i t i s much more s a t i s f a c t o r y gen

-

oxygen

-

n i t r o g e n m i x t u r e s a r e b u r n t on an t o compute t h e flame p r o p e r t i e s e x p e c t e d f r o m pos- E g e r t o n

-

Powling t y p e o f f l a t f l a m e b u r n e r [ I ]

,

g i v i n g an e s s e n t i a l l y one d i m e n s i o n a l flow. Slow f l a w s a r e n e c e s s a r y f o r e x p e r i m e n t a l s t r u c t u r e s t u d i e s a t a t m o s p h e r i c p r e s s u r e i n o r d e r t o o b t a i n a d e q u a t e s p a t i a l r e s o l u t i o n . The measurements t o be made a r e : (a) f l o w v e l o c i t y ( 2 1

,

(b) t e m p e r a t u r e p r o f i l e [ 2 , 3 3

,

( c ) c o m p o s i t i o n p r o f i l e s f o r s t a b l e s p e c i e s [ 3

1

and (d) such c o m p o s i t i o n p r o f i l e s f o r u n s t a b l e f r e e r a d i c a l i n t e r m e d i a t e s e . g . H atoms, OH, a s can b e measured. I n t h e low t e m p e r a t u r e f l a m e s s t u d i e d , t h e decay of i n t e n s i t y of sodium D

-

l i n e chemiluminescence w h e n t r a c e s of sodium s a l t s were added t o t h e g a s e s e n t e r i n g t h e flame was u s e d a s a measure of r e l a t i v e H atom concen-

t u l a t e d r e a c t i o n mechanisms, and t o compare t h e s e w i t h e x p e r i m e n t . Such c a l c u l a t i o n s s t a r t f r o m t h e

c o n t i n u i t y e q u a t i o n s . C o n t i n u i t y E q u a t i o n s .

F o r a non-stationary,one-dimensional f l a m e f r o n t p a r a l l e l w i t h t h e x , z

-

p l a n e , t h e g e n e r a l i - zed c o n t i n u i t y e q u a t i o n may be w r i t t e n a s :-

where W i s t h e c o n c e n t r a t i o n of any q u a n t i t y

i

-

³

-

³

( g . cm f o r s p e c i e s o r J. cm f o r e n e r g y ) a t d i s t a n c e y and time t , F . i s t h e f l u x of t h e quan- t i t y p e r u n i t time and a r e a normal t o t h e d i r e c t i o n

2 1 2 1

of f l o w (g. cm- s- o r J . cm- s-

7,

and q i i s i t s

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971557

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G . DMON-LEWIS

3 7 3 1

rate of formation (g. cm- s- or 3 . cm- s- ) . An equation of type ( 1 ) exists for each species present in the gas, and for the energy. Mathematically, the flame is a system of differential equations.

The concentrations Wi may be expressed in terms of the overall density and the weight fractions wi of each species :

while the fluxes Fi consist of two parts

-

first, a convective term Mwi, where M is the overall mass burning velocity, and second, a transport flux ji due to diffusion (or thermal conduction). Thus:.

Fi ⁼

mi

+ ji (3)

Depending on the assumptions made in calcula- ting the ji, the system of simultaneous differential equations can be solved at various levels of sophistication. Two approaches to the solution have been used:

(a) The diffusional fluxes in the multicomponent system are expressed in the approximate form:

and other slight assumptions are made for the tem- perature dependence of the transport properties

[

5 , 6 1

.

The unsteady state, time

-

^dependent

equations are solved by a finite difference procedure which integrates forward in time from arbitra- rily assumed initial flame profiles into the steady state. The method gives a general indication of the flame properties comparatively rapidly, and allows a preliminary selection of reaction and rate constants by fitting the measured burning velocity and then comparing profiles. Because of the approxi- mations, however, it does not allow a detailed comparison of the latter.

(b) Detailed profiles are calculated 1 6 1 by a Runge

-

Kutta procedure which integrates through

the steady state flame (time derivative vanishes in equation (I

) ,

corresponding with a flame sta- bilized in the co-ordinate system). Detailed multicomponent transport properties are calculated L 7 j using the extension of the Chapman

-

Enskog theory to polyatomic gases by Wang Chang, Uhlenbeck and de Boer

[

⁸

] ,

and its subsequent development by

Monchick, Mason and coworkers [ 9 ]

.

By this means it is possible to calculate also the thermal fluxes, and to include thermal diffusion effects in the overall computation of the composition profiles.

Effects of thermal diffusion on the composition profiles may be important, particularly in the case of light reactive species like H atoms, since the reaction rate depends strongly on the atom concentration. The approximate magnitude of the effect of thermal diffusion on the composition profiles of the stable species in the H2

-

^O2

-

^N₂

flame is shown in reference [7

1 .

Mechanism of Reaction.

Application of the methods described to a flame A at atmospheric pressure having the initial mole fractions = 0.1883. Xo = 0.0460

2'u

and

S2'U

⁼0.7657, with TU = 336K, and detailed comparison of the results with structure measurements [6

] ,

strongly supports a chemical mechanism consisting of reactions (i) to

(iv),

(vii), (xii) and (xv), with possibly some contributions from reactions (viia)

,

^(xiii)

,

^(xiv)

,

(mi) and (xvii)

.

Subsequent work, as yet unpublished, has confirmed the participation of the additional reactions.

It is possible to establish rate constants for these by comparison of computed and measured burning velocities over a limited range of composition (figure 1

-

measurements by Mr. K. Thompson), and following this we have been able to compute the burning velocities of the whole range of rich

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MEASUREMENT AND COMPUTATION OF FLAME STRUCTURE

F i g . 1 Computed l i n e s and e x p e r i m e n t a l p o i n t s .

hydrogen

-

a i r m i x t u r e s , o b t a i n i n g good agreement w i t h r e c e n t measurements

[

10,11]

.

OH

+

H2

=

H20

+ H

(i

H + 0 2 = O H + 0 ( i i )

OH

H02 'OH

0 H2 H2°

OH 2 H2°

OH

(iii) ( i v ) ( v i i ) ( v i i a ) ( x i i ) ( x i i i ) ( x i v ) ( x v ) ( x v i ) ( x v i i )

F i n a l l y , s i n c e t h e emphasis a t t h i s meeting i s on t h e p h y s i c a l p r o c e s s e s i n v o l v e d , I s h o u l d l i k e t o draw a t t e n t i o n t o t h e magnitudes of t h e v a r i o u s f l u x e s i n t h e r i c h f l a m e s . For t h e flame A t h e computed f l u x e s a r e shown i n r e f e r e n c e

[

6

] .

^For

hydrogen, t h e maximum t h e r m a l d i f f u s i o n a l f l u x i s

o f t h e same magnitude a s t h e maximum d i f f u s i o n a l f l u x due t o t h e c o n c e n t r a Q o n g r a d i e n t s ; b u t f o r t h e o t h e r s p e c i e s t h e r m a l d i f f u s i o n i s r e l a t i v e l y much l e s s i m p o r t a n t . T h i s r e l a t i v e l a c k of impor- t a n c e i n t h e c a s e of hydrogen atoms i s due t o t h e s m a l l c o n c e n t r a t i o n of H atoms i n t h e r e g i o n of s t e e p e s t t e m p e r a t u r e g r a d i e n t . I t i s p a r t i c u l a r l y f o r t u n a t e from t h e p o i n t of view of t h e v a l i d i t y of t h e more approximate c a l c u l a t i o n s which n e g l e c t thermal d i f f u s i o n e f f e c t s . The H atom f l u x e s i n t h e 50

X

hydrogen

-

a i r flame f o l l o w a s i m i l a r g e n e r a l p a t t e r n t o t h o s e i n flame A.

BTBLIOGRAPHIE

[ l ] DIXON-LEWIS, G . e t a l . T r a n s . Faraday Soc.

1957,

2,

193.

[ 2 DIXON-LEWIS, G . e t a l . P r o c . ROY. SOC. A , 1969, 308, 517.

-

13 DIXON-LEWIS, G . e t a l . i b i d . 1970.

317,

227.

[4 DIXON-LEWIS, G. e t a l . Tenth Symp. ( I n t ) on Combustion p. 495. P i t t s b u r g h : Comb. I n s t . 1965.

[5] DIXON-LEWIS, G , Proc. Roy. SOC. A, 1967,

298,

495.

[6] DIXON-LEWIS, G. i b i d . 1970,

317,

235.

[ 7 ] DIXON-LEWIS, G. i b i d . 1969,

307,

1 1 1 .

18) ^WANG^CHANG, C.S. e t a l . Univ. of Michigan Eng.

Research Rept. No. CM-681, 1951.

[9] MONCHICK, L . , MASON, E.A. e t a l . J. Chem. Phys.

1961 onwards.

[lo] EDMONDSON, H. e t a l . C o d . Flame 1971,

16,

161.

[I

I )

GUNTHER, R. and JANISCH. P r i v a t e c o m u n i c a t i o n