38 Droplet-Size Measurements in Reacting Flows
Laser Probes for Combustion Chemistry Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SAN DIEGO on 07/14/16. For personal use only.
by Laser Interferometry UMBERTO GHEZZI Politecnico, p. Leonardo da Vinci, 32-Milano, Italy
ALDO COGHE and FAUSTO GAMMA C.N.P.M., v. F. Baracca, 69-Peschiera Borromeo, Milano The c u r r e n t s t a t u s o f p r e d i c t i o n a n d m o d e l l i n g i n t h e a r e a o f f u e l s p r a y c o m b u s t i o n r e q u i r e s , among o t h e r p a r a m e t e r s , t h e measu rement o f d r o p l e t o r s o l i d , p a r t i c l e s i z e d i s t r i b u t i o n a n d t h e r e l a t i v e v e l o c i t y "between t h e f u e l a n d t h e s u r r o u n d i n g g a s . Many o p t i c a l t e c h n i q u e s , based on l a s e r l i g h t s c a t t e r i n g , have been i n v e s t i g a t e d t o t h i s p u r p o s e (Refs.l,2,2,U,j>,6 a n d 7), b u t t h e o n l y system a b l e t o s i m u l t a n e o u s l y determine t h e s i z e and t h e v e l o c i t y i s t h e d u a l - b e a m l a s e r D o p p l e r v e l o c i m e t e r shown i n F i g u r e 1. I t h a s b e e n d e m o n s t r a t e d ( R e f s . 8 , ^ a n d 10 ) t h a t a p a r t i c l e c r o s s i n g t h e i n t e r s e c t i o n o f t w o l a s e r beams s c a t t e r s a m o d u l a t e d l i g h t s i g n a l c o n t a i n i n g v e l o c i t y a n d s i z e i n f o r m a t i o n . The f i r s t i s r e l a t e d t o t h e modulation frequency, t h e second t o t h e r a t i o o f t h e A.C. t o t h e mean a m p l i t u d e . T h i s r a t i o i s c a l l e d v i s i b i l i t y r -, \
v
_ I
Max m m + I . Max mm
_ Ρ
where I.. , I . , D a n d Ρ a r e d e f i n e d i n F i g u r e 1. Max mm &
It
(2)
i s p o s s i b l e t o express
the v i s i b i l i t y
V = V ( - ^ . m, -J-'-f ' 1
i n a f u n c t i o n a l form
Y ' % )
where d i s t h e d i a m e t e r o f t h e s c a t t e r i n g p a r t i c l e , m i s t h e com plex r e f r a c t i v e index o ft h e p a r t i c l e , ^ i s t h e cross-angle o f the two l a s e r beams, X i s t h e l a s e r w a v e l e n g t h , y a n d ^ a r e a n g l e s d e f i n i n g t h e p o s i t i o n o f t h e a x i s o f t h e c o l l e c t i n g aperture,-/!, i s t h e c o l l e c t i n g s o l i d a n g l e a n d cf = X /(2 s i n ( j 0 / 2 ) ) . The o t h e r p a r a m e t e r s b e i n g f i x e d , t h e r e l a t i o n V ( d ) c a n b e n u m e r i c a l l y evaluated f o l l o w i n g the Mie s c a t t e r i n g theory applied t o i n d i v i d u a l s p h e r i c a l p a r t i c l e s , supposed i n t h e c e n t r a l r e g i o n o f t h e c r o s s o v e r v o l u m e o f t w o c o h e r e n t beams (Ref.10). B e c a u s e o f t h e l a r g e number o f p o s s i b l e a r r a n g e m e n t s o f t h e p a r a m e t e r s a p p e a r i n g i n eq.(2), i t i s i m p o s s i b l e t o g i v e a c o m p l e t e r e p r e s e n t a t i o n of the v i s i b i l i t y behaviour.A parametric a n a l y s i s covering also
0-8412-0570-l/80/47-134-443$05.00/0 ©
1980 A m e r i c a n Chemical Society
LASER PROBES FOR COMBUSTION
Laser Probes for Combustion Chemistry Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SAN DIEGO on 07/14/16. For personal use only.
444
CHEMISTRY
many o f f - a x i s l i g h t c o l l e c t i o n d i r e c t i o n s a n d p a r t i c l e d i a m e t e r s up t o 1 0 0 / i m h a s b e e n p e r f o r m e d ( R e f . l l ) . I n t h e r a n g e o f i n t e r e s t o f f u e l sprays i t has been found t h a t i n forward s c a t t e r , w i t h s m a l l cross-beam and c o l l e c t i n g a n g l e s , t h e r e f r a c t i v e index o f t h e p a r t i c l e h a s no s i g n i f i c a n t ' i n f l u e n c e a n d a o n e - t o - o n e c o r r e s p o n dence between v i s i b i l i t y and p a r t i c l e d i a m e t e r c a n b e o b t a i n e d , as shown i n F i g u r e 2. The m a j o r l i m i t t o t h e p r a c t i c a l u s e o f t h e s e r e s u l t s i s t h e maximum p a r t i c l e c o n c e n t r a t i o n , N , t h a t c a n b e a l l o w e d i n o r d e r t o p r e s e r v e t h e s i n g l e s c a t t e r i n g c o n d i t i o n . Roughly, Nmax(m"3)/vVp and t h e p r o b e v o l u m e , V p , i s v a r y i n g a s l / s i n ) ? . W i t h β 1*, t h e maximum c o n c e n t r a t i o n c a n b e a b o u t 10$ m~3. w i t h h i g h e r β , t h e range o f a monotonie r e l a t i o n between v i s i b i l i t y and p a r t i c l e s i z e i s d r a m a t i c a l l y reduced. I t has been found p o s s i b l e , however, t o overcome t h e s e d i f f i c u l t i e s a n d t o m e a s u r e p a r t i c l e s i z e d i s t r i b u t i o n s i n f u e l sprays. P a r t i c l e s i z i n g measurements w e r e p e r f o r m e d i n w a t e r s p r a y s produced b y a p r e s s u r e - j e t n o z z l e and i n an i n d u s t r i a l f u r n a c e . I n t h e f i r s t c a s e ( R e f . 1 2 ) , a 5mW He-Ne l a s e r a n d t h e LDV g e o m e t r y r e l a t i v e t o t h e v i s i b i l i t y c u r v e o f F i g u r e 2 , w i t h β = .5* was u s e d . Because o f t h e h i g h d r o p l e t c o n c e n t r a t i o n and t h e l a r g e probe v o lume d i m e n s i o n s , we u s e d t w o g l a s s p r o b e s c o a x i a l t o t h e LDV o p t i c a l a x i s a n d f a c i n g e a c h o t h e r ( s e e F i g u r e 3 ) . The t w o p r o b e s we r e centered on t h e c e n t r a l r e g i o n o f t h e cross-beam r e g i o n and k e p t 5 mm a p a r t t o r e d u c e t h e e f f e c t i v e c r o s s - s e c t i o n a n d t h u s t h e m e a s u r e d p a r t i c l e r a t e . The a l l o w e d maximum c o n c e n t r a t i o n was a b o u t 1θ9 m~3 a n d h e n c e r e l i a b l e measurements w e r e o b t a i n e d o n l y i n t h e o u t h e r p a r t o f t h e j e t . The p a r t i c l e number c o n c e n t r a t i o n c a n b e determined by t h e r e l a t i o n _1
η = N U S
(3)
- 1
where ή i s t h e p a r t i c l e r a t e ( s ) , S t h e c r o s s - s e c t i o n a l a r e a o f t h e e f f e c t i v e p r o b e v o l u m e , n o r m a l t o t h e m e a s u r e d mean v e l o c i t y component, U. The v i s i b i l i t y o f s e v e r a l h u n d r e d s i n d i v i d u a l s c a t t e r e d s i g r a l s has b e e n m e a s u r e d b y a s t o r a g e o s c i l l o s c o p e a n d s e v e r e v a l i d a t i o n c r i t e r i a were d e f i n e d t o f u l f i l l t h e h y p o t h e s i s o f t h e t h e o r e t i c a l m o d e l . The a c t u a l s i z e d i s t r i b u t i o n f u n c t i o n , f ( d ) , was d i r e c t l y deduced b y t h e measured v i s i b i l i t y d i s t r i b u t i o n , g ( V ) , t h r o u g h t h e V ( d ) r e l a t i o n o f F i g u r e 2. R e s u l t s o f T a b l e 1 d e m o n s t r a t e d t h e c a p a b i l i t y o f t h i s technique t o r e s o l v e d i f f e r e n t i n j e c t i o n pressures. Pressure (atm) 2 10 15
S.M.D.
66 Λ 5^.3 k9.k
X^j-tm)
70.0 58.5 52.5
T a b l e 1: E x p e r i m e n t a l r e s u l t s w i t h a p r e s s u r e - j e t n o z z l e . S.M.D. i s t h e S a u t e r mean d i a m e t e r , X t h e R o s i n - R a m m l e r mean diameter.
Laser Probes for Combustion Chemistry Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SAN DIEGO on 07/14/16. For personal use only.
GHEZZi E T A L .
Figure 1.
Laser
445
lnterjerometry
Geometry of the dual-beam LDV optics with the enlarged probe volume and the shape of a single-particle Doppler signal
1.3
