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EXPERIMENTAL AND ANALYTICAL
INVESTIGATIONS OF THERMAL BLOOMING IN AXIAL PIPE FLOW
P.I-Wu Shen, P. Iyer, D. Regan
To cite this version:
P.I-Wu Shen, P. Iyer, D. Regan. EXPERIMENTAL AND ANALYTICAL INVESTIGATIONS OF
THERMAL BLOOMING IN AXIAL PIPE FLOW. Journal de Physique Colloques, 1980, 41 (C9),
pp.C9-137-C9-147. �10.1051/jphyscol:1980919�. �jpa-00220573�
JOURNAL DE PHYSIQUE CoZloque C9, suppZ6ment au nolZ, Tome 41, novembre 1980, page C9-137
EXPERIMENTAL A N D ANALYTICAL INVESTIGATIONS O F T H E R M A L BLOOMING I N A X I A L P I P E FLOW
P.1-WU Shen, P.A. I y e r and D.R. ~ e ~ a n *
Electro-Optical Engineering Division, Hughes A i r c r a f t Company, Culver c i t y , California 90230, U. S.A.
A b s t r a c t . - An e x p e r i m e n t a l and t h e o r e t i c a l s t u d y of t h e r m a l blooming phenomena i n a h i g h e n e r g y l a - s e r beam p r o p a g a t i n g i n a n a x i a l t u r b u l e n t p i p e flow i s p r e s e n t e d . The e x p e r i m e n t s were conducted by u s i n g a 250 w a t t CW C02 l a s e r a s t h e h e a t s o u r c e and a m i x t u r e of C02 and N 2 a s t h e a b s o r b i n g medium. The o p t i c a l p a t h d i f f e r e n c e (OPD) caused by t h e h e a t i n g of t h e g a s by t h e beam were measu- red by h o l o g r a p h i c i n t e r f e r o m e t r y , u s i n g a k r y p t o n l a s e r a t 0.5208 pm. The t h e o r y was developed by modifying a n e x i s t i n g n u m e r i c a l code i n o r d e r t o i n c l u d e t h e v o l u m e t r i c h e a t i n g due t o a b s o r p t i o n of t h e l a s e r r a d i a t i o n by t h e f l o w i n g g a s . The t h e o r e t i c a l OPD's were c a l c u l a t e d d i r e c t l y from t h e t e m p e r a t u r e p r o f i l e s , and comparison w i t h t h e e x p e r i m e n t a l v a l u e s showed good agreement.
1 . 0 I n t r o d u c t i o n
Thermal blooming, r e c o g n i z e d a s a major s o u r c e of o p t i c a l d e g r a d a t i o n i n high-energy s y s t e m s , i s caused by t h e f i n i t e a b s o r t i o n o f l a s e r beam energy i n t h e gas medium. Gas f l o w , e i t h e r a l o n g o r a c r o s s t h e l a s e r beam p a t h , i s g e n e r a l l y used t o a l l e v i a t e t h e r m a l blooming e f f e c t s . T h i s p a p e r p r e s e n t s t h e r e s u l t s of a n e x p e r i m e n t a l and a n a l y t i c a l i n v e s t i g a t i o n of t h e r m a l blooming i n a l a s e r beam t u b e c o n d i t i o n e d by a t u r b u l e n t a x i a l p i p e flow.
The h e a t s o u r c e i n t h e s e e x p e r i m e n t s was a 250 w a t t , c o n t i n u o u s wave (CW), CO l a s e r beam a t 10.6 um,
2
p r o p a g a t i n g a l o n g t h e c e n t e r o f t h e p i p e . A g a s m i x t u r e o f CO and N w i t h t h e CO c o n c e n t r a t i o n o f
2 2 2
9 p e r c e n t was s e l e c t e d t o o b t a i n measurable t h e r m a l blooming w i t h o u t l o s i n g t o o much l a s e r beam i n t e n - s i t y due t o a b s o r p t i o n . The l a s e r beam h e a t e d up t h e g s s a r d caused d e n s i t y changes which were meas- u r e d by h o l o g r a p h i c i n t e r f e r o m e t r y , u s i n g a k r y p t o n l a s e r a t 0.5208 vm. F r i n g e p a t t e r n s o b t a i n e d from t h e i n t e r f e r o m e t r y were a n a l y z e d i n o r d e r t o d e t e r - mine t h e o p t i c a l p a t h d i f f e r e n c e s (OPDs) a s a func- t i o n o f r a d i a l p o s i t i o n i n t h e p i p e . The v a r i o u s
* p r e s e n t l y w i t h Poseidon Research Los Angeles, C a l i f o r n i a 90049
p a r a m e t e r s c o n s i d e r e d i n t h e e x p e r i m e n t s were:
( a ) flow v e l o c i t y , ( b ) p i p e w a l l - i n l e t g a s tempera- t u r e mismatch, ( c ) w a l l roughness, ( d ) L/D r a t i o , ( e ) t y p e o f i n l e t t o p i p e - s t r a i g h t , curved elbow and m i t e r bend, ( f ) beam d i a m e t e r and, (g) s w i r l v e l o c i t y a t t h e e n t r a n c e t o t h e p i p e . Of t h e s e v e r a l p a r a m e t e r s mentioned above, o n l y t h e r e s u l t s
o b t a i n e d f o r t h e c a s e of a s t r a i g h t i n l e t w i t h v a r i a b l e flow v e l o c i t i e s and p i p e w a l l t e m p e r a t u r e s , a r e p r e s e n t e d i n t h i s p a p e r .
2.0 E x p e r i m e n t a l Apparatus
The t e s t a p p a r a t u s i s shown i n F i g u r e 1. The t e s t s e c t i o n c o n s i s t s o f modular t u b e s mounted between f l a n g e s . The maximum t u b e l e n g t h , which can be accommodated by t h e a p p a r a t u s i s 6 m e t e r s . The t u b e i n s i d e d i a m e t e r was chosen t o b e 5.08 cm
(2 i n c h e s ) . A blow-down flow system was used f o r t h e f l o w s o u r c e . The flow v e l o c i t y can be v a r i e d from 5 m/sec t o 20 m/sec i n t h e t e s t s e c t i o n . The i n l e t gas t e m p e r a t u r e u n i f o r m i t y can b e m a i n t a i n e d a t c 0 . 1 ~ ~ . A l a r g e r a d i a l flow i n l e t plenum was used t o e n s u r e good e n t r a n c e flow i n t o t h e t e s t s e c t i o n w i t h low f r e e s t r e a m t u r b u l e n c e and minimum s e c o n d a r y flow. Flow i s i n t r o d u c e d i n t o t h e i n l e t
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980919
C9-138 JOURNAL DE PHYSIQUE
plenum t h r o u g h a 4 i n c h d i a m e t e r i n l e t t u b e or, t h e s i d e w a l l , and t h e chamber i s d e s i g n e d t o have s u f f i c i e n t l y l a r g e volume f o r p r o p e r flow d i s t r i b u - t i o n and mixing. The flow p a s s e s through two l a y - e r s o f porous p l a t e s o f 2.2 p e r c e n t p o r o s i t y b e f o r e e n t e r i n g t h e r a d i a l flow i n l e t . ' h e l v e i n l e t v a n e s were i n s t a l l e d i n t h e r a d i a l f l o w i n l e t s e c t i o n t o e n s u r e t h e b e s t flow p o s s i b l e w i t h minimum secon- d a r y flow. The v a n e s c a n b e r o t a t e d t o p r o v i d e v a r i o u s v o r t e x f l o w s . Five l a y e r s of s c r e e n a r e p l a c e d downstream of t h e v a n e s f o r f i n a l f l o w smoothing and may b e r e p l a c e d by s c r e e n s o f v a r y i n g c o a r s e n e s s t o o b t a i n d i f f e r e n t i n l e t t u r b u l e n c e l e v e l s . The e x h a u s t plenum i s i d e n t i c a l t o t h e flow s u p p l y plenum e x c e p t t h a t t h e porous p l a t e s have l a r g e r p o r o s i t y t o minimize p r e s s u r e i n t h e
test s e c t i o n . The w a l l r o u g h n e s s can b e s i m u l a t e d by v a r i o u s i n n e r l i n i n g s . The t e s t s e c t i o n i s mounted on a 1 4 i n c h I beam and s u p p o r t e d a t two
f o o t i n t e r v a l s t o a s s u r e r i g i d i t y and t o minimize t u b e d e f l e c t i o n .
The t e m p e r a t u r e mismatch between t h e f l o w i n g gas and t h e t u b e w a l l was o b t a i n e d through t h e u s e o f h e a t i n g t a p e s wrapped around t h e t u b e o u t e r diam-
e t e r . I n o r d e r t o m o n i t o r t h e t e m p e r a t u r e d i f f e r - e n c e , a d i f f e r e n t i a l thermocouple c i r c u i t was used, c o n s i s t i n g o f two chromeconstantan thermocouples.
The o u t p u t o f t h e s e r i e s connected d i f f e r e n t i a l thermocouples c i r c u i t was a m p l i f i e d by a high- impedance D.C. a m p l i f i e r and f e d i n t o a c h a r t r e c o r d e r f o r m o n i t o r i n g p u r p o s e s . The r e s o l . u t i o n o f t h e d i f f e r e n t i a l thermocouple c i r c u i t i s s u c h t h a t f o r a t e m p e r a t u r e d i f f e r e n c e AT = 0 . 2 O ~ , t h e measurement e r r o r i s a p p r o x i m a t e l y 1 0 p e r c e n t . The
The mean and t u r b u l e n t p i p e flow c h a r a c t e r i s t i c s were d e t e r m i n e d u s i n g l i n e a r i z e d TSI-1050 h o t - f i l m anemometers. S i n g l e s e n s o r TSI-1276Y h o t - f i l m anemometer probes h a v i n g a r a t i o o f p i p e t o p r o b e s t e m d i a m e t e r of 57 were used t o measure t h e mean and t u r b u l e n t f l u c t u a t i o n v e l o c i t i e s a t s e v e r a l a x i a l p o s i t i o n s a l o n g t h e p i p e . A c a l i b r a t e d p i t o t - s t a t i c probe mounted on t h e a x i a l flow beam t u b e and a TSI-1125 flow c a l i b r a t o r were u s e d t o c a l i b r a t e t h e h o t - f i l m anemometer probes. The h o t - f i l m anemometers were p o s i t i o n e d i n s i d e t h e p i p e w i t h motor d r i v e n probe t r a v e r s i n g mechanisms t h a t pro- v i d e a D.C. s i g n a l v o l t a g e p r o p o r t i o n a l t o t h e r a d i a l probe p o s i t i o n . The l i n e a r i z e d anemometer o u t p u t s and t h e probe p o s i t i o n v o l t a g e s were f e d i n t o X-Y p l o t t e r s t o a u t o m a t i c a l l y r e c o r d t h e r a d i a l mean v e l o c i t y and r m s t u r b u l e n c e i n t e n s i t y p r o f i l e s . A TSI-1076 t r u e r m s v o l t m e t e r was used t o d e t e r m i n e t h e r m s t u r b u l e n c e f l u c t u a t i o n v e l o c i t i e s .
The s t a t i c p r e s s u r e drop a l o n g t h e a x i a l beam t u b e was measured w i t h a Validyne DP-103, 20.05 p s i d v a r i b l e r e l u c t a n c e d i f f e r e n t i a l p r e s s u r e manometer.
The d i f f e r e n t i a l p r e s s u r e manometer was c a l i b r a t e d u s i n g b o t h v e r t i c a l and i n c l i n e d w a t e r manometers.
A Validyne DP-103, k0.01 p s i d d i f f e r e n t i a l manometer was used t o d e t e r m i n e t h e dynamic p r e s s u r e measured by t h e United Sensor p i t o t - s t a t i c probe p o s i t i o n e d i n s i d e t h e a x i a l beam t u b e d u r i n g t h e anemometer probe c a l i b r a t i o n sequence.
The o p t i c a l arrangement, shown s c h e m a t i c a l l y i n F i g u r e 2, is composed of t h r e e b a s i c o p t i c a l sys- tems: CO l a s e r h e a t s o u r c e a t 10.6 pm, a krypton
2
i o n l a s e r f o r h o l o g r a p h i c i n t e r f e r o m e t r y a t a b s o l u t e t e m p e r a t u r e o f t h e t u b e w a l l was d e t e r - 0.5208 pm and a HeNe l a s e r a t 63288 f o r j i t t e r mined u s i n g a n o t h e r d i f f e r e n t i a l thermocouple c i r - measurements ( j i t t e r d a t a a r e n o t p r e s e n t e d i n t h i s c u i t whose r e f e r e n c e j u n c t i o n i s p l a c e d i n a n i c e p a p e r ) . The g e n e r a l s e t u p i s s u c h a s t o p r o v i d e
b a t h a t O'C. s i m u l t a n e o u s o p e r a t i o n o f t h e t h r e e b a s i c
measurements. The 1 0 . 6 um power s o u r c e i s a f o c a l l e n g t h l e n s , t h e f o c u s e d s p o t s i z e i s Coherent R a d i a t i o n model 41 CO l a s e r w i t h a con-
2 e x p e c t e d t o b e on t h e o r d e r o f 3 mm and a d e q u a t e t i n u o u s o u t p u t o f 250W, TEMoo, and a beam d i a m e t e r r e s o l u t i o n s h o u l d b e o b t a i n e d w i t h t h e 0.25 mm o f 8 mm l / e 2 power p o i n t . ZnSg o p t i c s were s e l e c t e d d i a m e t e r p i n h o l e .
i n o r d e r t o accommodate t h e h i g h l a s e r f l u x
H o l o g r a p h i c i n t e r f e r o m e t r y was performed w i t h a d e n s i t y . ZnSe i s s e m i t r a n s p a r e n t t o v i s i b l e l i g h t
k r y p t o n l a s e r ( S p e c t r a P h y s i c s Model 171) c a p a b l e o f above a b o u t 4 9 0 0 i and i s a c c e p t a b l e f o r t r a n s m i s *
0 . 7 w a t t s a t 5 2 0 8 i . Output from t h e l a s e r i s s p l i t s i o n o f t h e v i s i b l e w a v e l e n g t h s under c o n s i d e r a t i o n .
i n t o two beams, one p a s s i n g t h r o u g h t h e medium o f A t a 45' a n g l e of i n c i d e n c e , t y p i c a l c o a t i n g s a r e
i n t e r e s t and t h e o t h e r t h r o u g h a i r a s a r e f e r e n c e . c a p a b l e o f 99 p e r c e n t r e f l e c t i o n a t 1 0 . 6 um and
The beam which p a s s e s t h r o u g h t h e t e s t medium a l s o 50 p e r c e n t t r a n s m i s s i o n a t b o t h 5208k and 6328A.
p a s s e s t h r o u g h low p a s s o p t i c a l f i l t e r s . The o p t i - The h i g h power C02 beam i s expanded t o 2 cm by a c a l f i l t e r s a r e r e q u i r e d f o r i n s e r t i o n and e x t r a c - beam expander and i s d i r e c t e d i n t o t h e t e s t chamber t i o n of t h e HeNe 6328k l i g h t . Both beams a r e recom- by a ZnSe f l a t m i r r o r , d i e l e c t r i c c o a t e d f o r a b i n e d on a p h o t o g r a p h i c p l a t e t h a t was f i r s t exposed
r e f l e c t i v i t y o f 99 p e r c e n t . The beam t h e n p a s s e s t o b o t h beams i n a s t a t i c c o n d i t i o n w i t h no flow i n t h r o u g h a ZnSe window, AR c o a t e d a t 10.6 um, propa- t h e t u b e i n o r d e r t o p r o v i d e a r e f e r e n c e p a t t e r n . g a t e s down t h e e x p e r i m e n t a l s e c t i o n and e x i t s The p l a t e was t h e n developed and p l a c e d a c c u r a t e l y t h r o u g h a n i d e n t i c a l ZnSe window a t t h e o p p o s i t e i n i t s o r i g i n a l p o s i t i o n u s i n g a k i n e t i c mount.
end. The beam i s t h e n t o t a l l y r e f l e c t e d o f f Then, w i t h f l o w i n t h e t u b e , b o t h beams were a l l o w e d a n o t h e r ZnSe f l a t a t a n a c u t e a n g l e and p a s s e s t o f a l l on t h e p l a t e a g a i n and t h e r e s u l t i n g i n t e r - t h r o u g h a 1 . 0 p e r c e n t e l e m e n t b e f o r e a b s o r t i o n by f e r e n c e f r i n g e s were photographed w i t h a p o l a r i o d
a power m e t e r . camera.
The r e f l e c t e d beam i s t r a n s p o r t e d t o a n o p t i c a l 3.0 Theory s e t u p f o r n e a r and f a r f i e l d i n t e n s i t y p r o f i l e
measurements. The measurement of beam i n t e n s i t y p r o f i l e was performed by s c a n n i n g t h e beam, a r o t a t i n g m i r r o r a c r o s s a l i q u i d n i t r o g e n c o o l e d Ge:Au d e t e c t o r a p e r t u r e d by a p i n h o l e . I n t h e c a s e o f n e a r f i e l d measurements, t h e beam i s scanned a s above w i t h o u t any f o u s i n g . T y p i c a l p i n h o l e diam- e t e r s a r e 0.25 mm. For a m i r r o r r o t a t i n g a t 1000 rpm and a m i r r o r t o d e t e c t d i s t a n c e o f 1 m, t h e s c a n t i m e a c r o s s a 4 cm beam i s a b o u t 200
u s ,
w e l l w i t h i n a n y c h a r a c t e r i s t i c f l o w t i m e s . F o r f a r f i e l d measurements, a CdTe l e n s was used t o f o c u s t h e beam a t t h e d e t e c t o r and t h e same r o t a t i n g m i r r o r i s u s e d t o s c a n t h e f o c u s e d p a t t e r n . For a 5 mThe t h e o r e t i c a l a n a l y s i s c o n s i s t e d o f s o l v i n g t h e boundary l a y e r e q u a t i o n s of mass, momentum and e n e r g y u s i n g a n e x p l i c i t f i n i t e d i f f e r e n c e scheme developed by Nelson and P l e t c h e r (Ref. 1 ) . The e q u a t i o n s which were s o l v e d a r e :
Mass C o n s e r v a t i o n
Momentum C o n s e r v a t i o n
-
C9-140 JOURNAL DE PHYSIQUE
Energy C o n s e r v a t i o n where 6 i s t h e boundary l a y e r t h i c k n e s s , A+ i s a
+ .
c o n s t a n t e q u a l t o 26.0, and y 1s d e f i n e d by
where 'U i s t h e s t a n d a r d f r i c t i o n v e l o c i t y . The n e c e s s a r y boundary c o n d i t i o n f o r v e l o c i t i e s a r e
( 4 ) The e f f e c t i v e v i s c o s i t y
,
peff and e f f e c t i v e conduc- t i v i t y , K e f f , i n t h e f u l l y developed r e g i o n were ( 5 ) c a l c u l a t e d a s f o l l o w s :and t h e boundary c o n d i t i o n s f o r t e m p e r a t u r e a r e
"eff =
"
+ " t l (16) T (X,?.) =Tw ( 6 )
and
The i n l e t c o n d i t i o n s a t X = 0 a r e
U ( o , r ) = Uo
where
( 8 ) p t l =
ut
f o r y+ < 30P ( o , r ) = Po (10)
and The e f f e c t i v e v i s c o s i t y , p e f f , and e f f e c t i v e con-
d u c t i v i t y ,
afj,
i n t h e e n t r a n c e r e g i o n a r e g i v e n by K t ' = t f o r Y' < 30=--
",:
'(2-;) [I+
2 (I-;)~] f o r yi > 30 whereK e f f = K R + K = t
where t h e s u b s c r i p t s "9." and "t" d e n o t e l a m i n a r
and turbulent, r e s p e c t j v e l y , and prt is t h e turbu- Figure the e f f e c t i v e cOnduc- l e n t P r a n d t l number t a k e n t o b e e q u a l t o 0.9. t i v i t y a s a f u n c t i o n of X / D . It c a n b e s e e n t h a t L e t t i n g y be t h e d i s t a n c e measured from t h e w a l l , i n t h e e n t r a n c e r e g i o n (X/D
;
24.5), t h e h e a t was t h c e x p r e s s i o n f o r mixing l e n g t h , R , f o r t h e assumed t o b e t r a n s p o r t e d by m o l e c u l a r c o n d u c t i o n e n t r a n c e r e g i o n of a smooth t u b e i s g i v e n by o n l y i n t h e c e n t e r o f t h e p i p e .The l a s e r beam was assumed t o h a v e a Gaussian f o r R ( 0 . 0 8 9 6 (13)
p r o f i l e , w i t h a n e x p o n e n t i a l decay of i n t e n s i t y
= 0.089 6 f o r a l l o t h e r y (14) w i t h x ,
where Qin i s t h e measured i n p u t power,
Q l o s t i s t h e power l o s t i n b o t h t h e s o l i d windows, and R i s t h e o u t e r r a d i u s of t h e C02 l a s e r beam. The v a l u e o f t h e a b s o r p t i o n c o e f f i c i e n t a f o r a 9 p e r c e n t CO
2 9 1 p e r c e n t N2 g a s m i x t u r e was c a l c u l a t e d t o be 1.648 x 1 0 - ~ / c m from t h e r e l a t i o n
where
?
i s t h e t e m p e r a t u r e o f t h e g a s r e l a t i v e t o 2 7 3 O ~ and x i s t h e mole f r a c t i o n of CO2'
h. e x i s t i n g code developed by Nelson and P l e t c h e r was m o d i f i e d t o i n c l u d e t h e h e a t s o u r c e Q i n t h e e n e r g y e q u a t i o n i n o r d e r t o r e p r e s e n t t h e p r e s e n c e of t h e l a s e r beam i n t h e p r e s e n t a n a l y s i s .
4.0 R e s u l t s and D i s c u s s i o n
The t e s t a p p a r a t u s was i n i t i a l l y checked o u t by measuring t h e f l u i d dynamic c h a r a c t e r i s t i c s of t h e p i p e flow. V e l o c i t y p r o f i l e s were measured by u s i n g t h e h o t f i l m anemometer a t X/D = 1 0 . 5 and a t X/D = 80.5. The measured v e l o c i t y p r o f i l e s a r e compared w i t h p r e d i c t i o n s c a l c u l a t e d by t h e t h e o r y i n F i g u r e s 4 and 5. I n a d d i t i o n , s t a t i c p r e s s u r e s were measured a t s e v e r a l a x i a l l o c a t i o n s a l o n g t h e p i p e . F i g u r e 6 shows a comparison between t h e a n a l y t i c a l and t h e e x p e r i m e r t a l r e s u l t s on s t a t i c p r e s s u r e d i s t r i b u t i o n f o r a smooth w a l l p i p e . It c a n b e s e e n t h a t e x c e l l e n t agreement h a s been o b t a i n e d between t h e o r y and e x p e r i m e n t , t h e r e b y v a l i d a t i n g b o t h t h e e x p e r i m e n t a l t e c h n i q u e and t h e
t h e o r e t i c a l appr0ac.h a s f a r a s t h e flow i s concerned.
F i g u r e s 7a and 7b show t y p i c a l i n t e r f e r o g r a m s w i t h and w i t h o u t t h e r m a l blooming r e s p e c t i v e l y . I n t h e r e f e r e n c e i n t e r f e r o g r a m , F i g u r e 7b, t h e c i r c u l a r f r i n g e s were produced by h e a t i n g of t h e ZnSe win- dows b y t h e C02 l a s e r beam. I n t h i s c a s e , n i t r o g e n g a s flowed t h r o u g h t h e test s e c t i o n and a b s o r p t i o n o f t h e l a s e r e n e r g y by t h e g a s was found t o b e n e g l i g i b l e . I n F i g u r e 7a t h e n i t r o g e n g a s was r e p l a c e d by a CO and N g a s m i x t u r e f l o w i n g a t t h e
2 2
same a x i a l v e l o c i t y o f 1 0 m/sec. The r a d i a l d i s t r i - b u t i o n of OPD was t h e n o b t a i n e d by s u b t r a c t i n g t h e r a d i a l d i s t r i b u t i o n o f f r i n g e s i n F i g u r e 7b from t h a t i n F i g u r e 7a.
F i g u r e s 8 t h r u 1 3 show comparison between t h e o r y and e x p e r i m e n t f o r t h e c a s e of a 6 m l o n g p i p e w i t h s t r a i g h t i n l e t and a smooth w a l l . The a x i a l f l o w v e l o c i t i e s a r e 10 m / s and 1 5 m / s , r e s p e c t i v e l y . The w a l l - g a s t e m p e r a t u r e mismatches a r e 0 . 5 ' ~ , 3.0°c, and 5.0°c. S i n c e t h e l a s e r beam d i a m e t e r was 2 cm p r o p a g a t i n g i n a p i p e of 5 . 0 8 cm d i a m e t e r t h e beam e x t e n d e d up t o r / R = 0.4 from t h e c e n t e r - l i n e . I n t h i s r e g i o n t h e comparison i s s e e n t o b e q u i t e good, i n g e n e r a l .
Using t h e r e s u l t s p r e s e n t e d i n F i g u r e s 8 t h r u 1 3 , t h e e f f e c t o f flow v e l o c i t y and w a l l - g a s tempera- t u r e mismatch on (OPD/ACO2) a t t h e edge of beam ( r / R = 0 . 4 ) was e x t r a c t e d and i s p r e s e n t e d i n F i g u r e 14.
I t c a n b e s e e n t h a t i n c r e a s i n g t h e f l o w v e l o c i t y and w a l l - g a s t e m p e r a t u r e mismatch r e d u c e s t h e OPD/
Aco2,
due t o f l a t t e n i n g of t h e r a d i a l t e m p e r a t u r e p r o f i l e i n t h e r e g i o n where t h e beam i s l o c a t e d( r / ~ ( 0 . 4 ) . 5.0 C o n c l u s i o n s
I n c o n c l u s i o n , t h i s p a p e r p r e s e n t s s i g n i f i c a n t r e s u l t s i n t h e a r e a of t h e r m a l blooming phenomena
C9-142 JOURNAL DE PHYSIQUE
f o r t h e c a s e o f a x i a l t u r b u l e n t p i p e flow. It i s R e f e r e n c e s
found t h a t t h e r m a l blooming can indeed d i s t o r t a 1. R.M. Nelson and R.H. P l e t c h e r , "An E x p l i c i t h i g h e n e r g y l a s e r beam i n an a x i a l f l o w beam t u b e Scheme f o r t h e C a l c u l a t i o n o f Confined T u r b u l e n t w i t h o u t p r o p e r c o n d i t i o n i n g e f f o r t s . The main Flows w i t h Heat T r a n s f e r " , Proc. 1974 Heat Trans- mechanism t o a l l e v i a t e t h e r m a l blooming i n a n a x i a l f e r and F l u i d Mechanics I n s t i t u t e , pp. 154-170.
t u r b u l e n t p i p e f l o w i s a n i n c r e a s e i n t h e eddy S t a n f o r d : S t a n f o r d U n i v e r s i t y P r e s s , 1974 d i f f u s i v i t y . P a r a m e t e r s t h a t a f f e c t t h e eddy d i f - Acknowledgement
f u s i v i t y and t h e r e b y OPD, s u c h as t h e flow v e l o c i t y , T h i s work was performed u n d e r USAF C o n t r a c t F-29601- have been i n v e s t i g a t e d e x p e r i m e n t a l l y and we f i n d 77-C-0087, K i r t l a n d AFB, Albaquerque, New Mexico.
t h a t t h e r e s u l t s compare w e l l w i t h t h e o r e t i c a l pre- The a u t h o r s would l i k e t o thank M r . Roderick E. Bean d i c t i o n s . F i n a l l y , we d e m o n s t r a t e i n b o t h a n a l y s i s f o r h e l p i n performing t h e s e e x p e r i m e n t s . Thanks and e x p e r i m e n t s t h a t a x i a l flow t h e r m a l blooming a r e a l s o d u e t o M r . W i l l i s A. Rosser, Jr., P r o f e s s o r s c a n a l s o b e reduced by i n c r e a s i n g t h e w a l l tempera- Robert E. K e l l y of UCLA and R.H. P l e t c h e r of Iowa t u r e through t h e p r i n c i p l e o f t e m p e r a t u r e S t a t e U n i v e r s i t y f o r many u s e f u l c o n s u l t a t i o n s
compensation. through o u t t h e d u r a t i o n o f this e x p e r i m e n t s .
v b y q
PRESSUREPLOTTER MANOMETER
EXPANDER
F i g u r e 1. Schematic o f T e s t Apparatus
F i g u r e 2. O p t i c a l Arrangement
-
rlR WALL
CO2 LASER
250 W BLOW DOWN
FLOW SYSTEM
F i g u r e 3. E f f e c t i v e C o n d u c t i v i t y a s a F u n c t i o n of X/D and r / R
ZnSe BEAM TUBE
\
\
KRYPTON
REFERENCE
-
+ -CHOPPING ARM WHEELHe-Ne LASER.
JOURNAL DE PHYSIQUE
Figrre 4. Comparison of Velocity Profiles at X/D = 10.5 1.4
1.2
1.0
1 .o
UMAX = 17.6 m/s Re = 48685
x=,,
D
I I I I I I I I I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
WALL Y / R
'x
1
UMAX = 17.6 m/s Re = 48685
-
XID = 10.5-
THEORYFigure 5. Comparison of Velocity Profiles at X/D = 80.5
0.0 I I I I I I I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
WALL
YIR '&
EXPERIMENT
U = 10 mlsec U = 10 mlsec (CO21N2) = (0.0910.91 ) (C021NZ) = (011.0) PIN = 250 watts PIN = 250 watts POUT= 200 watts POUT = 235 watts
a) INTERFEROGRAM WITH bl REFERENCE
THERMAL BLOOMING INTERFEROGRAM
F i g u r e 7. I n t e r f e r o g r a m With and W i t h o u t Thermal Blooming E f f e c t s
0.0
F i g u r e 6. Comparison o f P r e s s u r e Drop f o r a -0.1 Smooth Wall P i p e
-0.2
-0.1 C F
n
8
-0.3-0.2
-0.4 0 N
F - 0 . 3
n
b
-0.5-0.4 0.0 0.2 0.4 0.6 0.8 1 .O
Q r/R WALL
F i g u r e 9 . OPD/XCO2 v s r / ~ f o r Umax = 1 5 m / s ,
-0.5 AT = 0.5Oc
0.0 0.2 0.4 0.6 0.8 1 .O
Q rlR WALL
F i g u r e 8. OPDIhCO2 v s r / R f o r Uma, = 10 m / s , AT = 0.5OC
JOURNAL DE PHYSIQUE
0.0 0.2 0.4 0.6 0.8 1 .O
8
r/R WALLFigure 11. OPD/ACO versus r / ~ f o r Umax =
15 m/g, AT = 3 . 0 ' ~
F i g u r e 12. OPD/XC02 v e r s u s r / R f o r U = 1 0 m / s , F i g u r e 13. OPD/ACO v e r s u s r/R f o r U
-
1 5 m / s ,max AT = 5OC max
AT = 5Oc
VELOCITY m/s
F i g u r e 1 4 . V a r i a t i o n of (OPD/AC02)r/R = 0 . 4 w i t h v e l o c i t y and AT
