INVESTIGATION

OF

CHARACTERISTICS TURBULENT Yu.

Photometric

CERTAIN OF

AN

COMBUSTION AXISYMMETRIC

FLAME V.

Ignatenko

and

V.

UDC 536.46

F. Sokolenko

Analysis

To a c o n s i d e r a b l e extent the investigation of combustion p r o c e s s e s in turbulent flows r e d u c e s to the calculation of the extent of c o m b u s t i o n along the flame. The d i r e c t r e l a t i o n between the t i m e - a v e r a g e d lum i n o s i t y of the turbulent f l a m e and the physical extent of combustion, e s t a b l i s h e d in [1] for a plane jet, m a k e s it p o s s i b l e to c a l c u l a t e the l a t t e r at any point along the f l a m e and to employ p h o t o m e t r i c techniques to analyze the negatives of a x i s y m m e t r i c f l a m e s . The p h y s i c a l extent of c o m b u s t i o n in any c r o s s section of a p l a n e turbulent f l a m e [1] can be r e p r e s e n t e d in the following f o r m : A

I (x, y) dS = P (x, y),

(1)

w h e r e I(x,y) is the l u m i n o s i t y of the f l a m e at the point x, y; s is the l a t e r a l s u r f a c e of the plane flame; A is a n o r m a l i z a t i o n constant, which is found f r o m the condition that P(x,y) = 1 at the end of the c o m b u s t i o n zone. S i m i l a r l y , the function l~(x,y) for an a x i s y m m e t r i c f l a m e can be r e p r e s e n t e d in the f o r m (2)

A ~ i (x, r) ds = P (x, r), $

w h e r e s is the plane p r o j e c t i o n of the a x i s y m m e t r i c flame. In calculating the extent of combustion in f r o m the r e s u l t s of a p h o t o m e t r i c a n a l y s i s it is each of the s e c t i o n s x k c o n s i d e r e d . In the c a s e r a d i a l l u m i n o s i t y distribution i (r) is r e l a t e d as

different sections along the x axis of a n a x i s y m m e t r i c f l a m e n e c e s s a r y to know the r a d i a l l u m i n o s i t y distribution i(r) in of a t r a n s p a r e n t luminous object with axial s y m m e t r y the follows with the l u m i n o s i t y of its plane i m a g e I(y): R

1(y) = k

O.V~r'-------; '

(3)

Y

an integral equation that c a n be solved for the unknown function i(r) by m e a n s of an Abel t r a n s f o r m [2] l

k'd ~

(4)

I(7).7d7

rh

w h e r e ~k = y / R , Y = r / R , R is the r a d i u s of the turbulent f l a m e in the s e c t i o n x k. Since the e x p e r i m e n t a l function I(~k) is given in t a b u l a r or graphic f o r m , Eq. (4) is solved n u m e r i c a l l y . In [2, 3] n u m e r i c a l methods of solving equations of type (4) a r e d e s c r i b e d in connection with the r e s u l t s of a shadowgraph method of investigating gas flows. By dividing the c r o s s section into N annular zones and specifying the values of I(-f) at the e d g e s and at the c e n t e r s of these zones, we r e d u c e the integration to the solution of a s y s t e m of 2 N - 1 l i n e a r a l g e b r a i c equations i

=

, (7 -0 - ,

,

(5)

N o v o s i b i r s k . T r a n s l a t e d f r o m Fizika Goreniya i Vzryva, No. 4, pp. 585-589, O c t o b e r - D e c e m b e r , 1971" Original a r t i c l e submitted May 19, 1971.

01974 Consultants Bureau, a division of Plenum Publishing Corporation, 227 g'est I7th Street, New York, N. Y. 100t}. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. /t copy of this article is available from the publisher for $15.00.

499

where 2N-i p,=k

I(~p) is a function obtained b y making p h o t o m e t r i c m e a s u r e m e n t s on the negatives a c r o s s the x axis in v a r ious s e c t i o n s x k. The coefficients flky a r e a s s u m e d to be known [2, 3], which m a k e s it p o s s i b l e to calculate the i (~) p r o f i l e s on a c o m p u t e r . E x p e r i m e n t s w e r e conducted on an a p p a r a t u s with a c i r c u l a r b u r n e r 30 m m in d i a m e t e r at the mouth. A u n i f o r m velocity p r o f i l e was c r e a t e d at the b u r n e r mouth by m e a n s of a p r o f i l e d nozzle, and i n t e r c h a n g e able turbulence g r i d s m a d e it p o s s i b l e to v a r y the turbulence level in the c o r e of the jet. The d e g r e e of t u r bulence in the cold jet (without combustion) was m e a s u r e d with Disa h o t - w i r e a n e m o m e t e r . The h o m o g e n e ous fuel m i x t u r e was continuously ignited around the p e r i p h e r y of the b u r n e r mouth by a hydrogen jet issuing f r o m a n a r r o w slit orifice. As the fuel we used technical p r o p a n e m i x e d with a i r . The f l a m e was photographed on fiat negative film (film s p e e d 65 standard units) with a 2 - s e c e x p o s u r e . The c h a r a c t e r i s t i c c u r v e (negative density as a function of object luminosity) was obtained b y the method d e s c r i b e d in [1]. By way of illustration Fig. 1 shows the I(y) l u m i n o s i t y p r o f i l e s obtained f r o m a p h o t o m e t r i c a n a l y s i s of the negative c o r r e s p o n d i n g to one of the c o m b u s t i o n r e g i m e s . In Fig. 2 we have plotted the radial d i s tribution of the t i m e - a v e r a g e d l u m i n o s i t y of the a x i s y m m e t r i c f l a m e obtained by p r o c e s s i n g the I(y) p r o files (see Fig. 1) in a c c o r d a n c e with Eq. (5) on an M-220 c o m p u t e r f o r N = 25. In Fig. 3 we have r e p r o d u c e d the v a r i a t i o n of the l u m i n o s i t y i(x) along the flow axis and the c o r r e s p o n d i n g extent of combustion (curve 2) obtained by graphic i n t e g r a t i o n of c u r v e 1. Turbulence

in the

Combustion

Zone

One a s p e c t of the study of the combustion m e c h a n i s m of a turbulent f u e l - a i r flow involves the d e t e r m{nation of the effect of c o m b u s t i o n on the l e v e l of turbulence. F o r this p u r p o s e we m e a s u r e d the velocity fluctuations and the a v e r a g e flow v e l o c i t y in the combustion zone of an a x i s y m m e t r i c turbulent flame. The d e g r e e of turbulence in the i s o t h e r m a l jet and in the p r e s e n c e of c o m b u s t i o n w e r e m e a s u r e d by the e l e c t r o n - o p t i c method d e s c r i b e d in [4]. As the t r a c e r p a r t i c l e s we used aluminum powder, which s a t i s fies the usual c r i t e r i a of r e l a t i v e i n e r t i a l e s s n e s s [5]. The d e g r e e of turbulence e was calculated as the ratio of the r m s value of the fluctuation of the longitudinal v e l o c i t y component to the a v e r a g e velocity m e a s u r e d

I

i L

L_

I# IV%ol GUI \1 I ~/\lU I/I &
L__A ~_LJ~.~o'~L, !1!11 I !

J g, ~oI !~/

!m/V! A

~ltl!

i\lt!i

Z/:: 7L

- ~5 - 2 0 - , * 5 - ; 0

-5

0

5

lO

Fig. i

75

y~ITIITI

i/

i2f

200

I I !i '/: ] i !*

IGOI

i#l ~ It

8O l t t

i

Li

- N -:~0 -r

-10 -5

0

/iJ 5

!0

15

r,.mm

Fig. 2

Fig. 1. L u m i n o s i t y p r o f i l e s of the p r o j e c t i o n of a c i r c u l a r f l a m e in v a r i o u s c r o s s s e c t i o n s x i (2-8 a r e the numt~ers of the c r o s s sections.) Fig. 2. Radial l u m i n o s i t y p r o f i l e s calculated f r o m the I(y) p r o f i l e s (see Fig. 1).

500

e,% w, m/sec

i (m, ojp---

24of

,-

, ~

160.,a

""~ "0,8

'[I',

i '

r ~

!

"'F:'#"ixr,~i

)

w !

----1----7 ~I

t

]

.......

e J

{

{"

'I

l--i--i~l

t

L_Li_j__L 8

1,0

Fig. 3

Fig. 4

Fig. 5

Fig. 3. Axial l u m i n o s i t y distribution [(x,0) and P(x,0) curves obtained from the r e s u l t s of a photom e t r i c analysis. Fig. 4. Degree of turbulence and mean velocity on the jet axis at various distances f r o m the b u r n e r mouth. (TA stands for h o t - w i r e a n e m o m e t e r . ) Fig. 5. Variation of the d e g r e e of turbulence e and the mean velocity along the flame axis. 1, 2) and w for a burning 4% p r o p a n e - a i r mixture; 3, 4) 8 and w for a burning 5% p r o p a n e - a i r m i x ture; 5, 6) e and w for a burning 4% p r o p a n e - a i r mixture; 7) e without combustion; 8, 9) w without combustion. at the s a m e point. The r e s u l t s of the m e a s u r e m e n t s in the i s o t h e r m a l flow were c o m p a r e d with the r e s u l t s of m e a s u r e m e n t s of the s a m e quantity using a Disa h o t - w i r e a n e m o m e t e r (Fig. 4). Clearly, there is s a t i s f a c t o r y a g r e e m e n t between the 8 m e a s u r e m e n t s made by the two different methods. The r e s u l t s of m e a s u r i n g the degree of turbulence along the flame axis of a burning homogeneous p r o p a n e - a i r m i x t u r e a r e shown in Fig. 5. The m a x i m u m values of the additional velocity fluctuations generated by the turbulent flame were calculated from the e x p r e s s i o n U z' =

8T.U--8OLCJO)

where 8 0 and w 0 a r e the d e g r e e of turbulence and the mean velocity in the i s o t h e r m a l jet. The r e s u l t s of the calculations qualitatively confirm the r e s u l t s obtained for a flat b u r n e r [6], the ~ m a x i m u m c o r r e s p o n d i n g to the end of the combustion zone, where the extent of combustion on the axis is equal to 0.7-0.8. At a high mean f u e l - m i x t u r e flow velocity under open flame conditions the combustion zone moved outside the c o r e of the cold jet. In this c a s e it was possible to observe a m a x i m u m value of e that did not exceed the value of ~ in the cold ]et (Fig. 5, curve 5)o While the 8 of the cold jet, having r e a c h e d its m i n i m u m value at a distance of two b u r n e r d i a m e t e r s f r o m the b u r n e r mouth, begins to i n c r e a s e , the e in the f r e s h m i x t u r e inside the flame cone continues slowly to d e c r e a s e . The i n c r e a s e in ~ begins from the m o m e n t when the m i x t u r e s t a r t s to burn on the flow axis, i.e., when the t i m e - a v e r a g e d extent of combustion b e c o m e s nonz e r o . Under these conditions ~ i n c r e a s e s f r o m a much lower level than in s h o r t e r flames. Moreover, as a r e s u l t of intense heat r e l e a s e in the combustion zone, which c a u s e s c o n s i d e r a b l e expansion of the combustion products, the a v e r a g e flow velocity develops a radial component. This, in its turn, leads to a change in the nature of the flow and " d r a g s out" the flow c o r e . Summary 1. F r o m a p h o t o m e t r i c analysis of a x i s y m m e t r i c flames it is possibIe to calculate the variation of the extent of combustion along the entire flame. 2. M e a s u r e m e n t s of the d e g r e e of turbulence in the combustion zone have revealed a considerable inc r e a s e in all c a s e s and qualitatively c o n f i r m the r e s u l t s obtained under other conditions.

LITERATURE Io 2.

CITED

L L. Kuznetsov and Yu. V. IgnaterLko, Fiz. Goreniya i Vzryva, 3, No. 1 (1967). L. V. Vasil'ev, Shadow Techniques [in Russian], Nauka, Moscow (1968).

501

3~

4. 5. 6.

502

V. A. Eme!'yanov and G. P. Zhavrid, Inzh.-Fiz. Zh., 4_, 18 (1962). A. M. Trokhan, I. L. Kuznetsov, et al., Fiz. Goreniya i Vzryva, 2~ No. 1 (1966). V. G. Levich and S. I. Kuchanov, ]gold. Akado Nauk SSSR, 174, No. 4 (1967). Io L. Kuznetsov, G. R. Baranova, et al., Fiz. Goreniya i Vzryva, 2, No. 3 (1966).