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7/25/2019 A Theoretical and Experimental Study of a Small-scale Steam Jet Refrigerator
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UTTE RWQRTH
I N E M N N
h z t J R ~ f r i g Vo] . 18 , No . 6 , pp . 378 386 , 1995
E l s e v i er S c ie n c e L t d a n d l l R
P r i n t e d i n G r e a t B r i t a i n . A l l r i g h t s r e s e r v e d
0 1 4 0 - 7 0 0 7 / 9 5 / 1 0 . 0 0 + 0 . 0 0
A t h e o r e t ic a l a n d e x p e r i m e n t a l s t u d y o f a s m a l l- s c a le s t e a m j e t
re fr igerator
I . W . E a m e s , S . A p h o r n r a t a n a a n d H . H a i d e r
D e p a r t m e n t o f M e c h a n i c a l a n d P r o c e s s E n g i n e e r i n g , U n i v e r s i t y o f S h ef fi el d, M a p p i n
S t r e e t , S h e f f i e ld S 1 3 J D , U K
R e c e i v e d 2 6 M a y 1 9 9 4 ; r e vi s e d 1 2 A p r i l 1 9 9 5
The pap er provides the results o f a theoretical and experimental study of a steam jet refrigerator. A small-
capacity steam jet refrigerator has been tested with boiler temp eratures in the range 120-140C. The
experimental data were fou nd to be within 85 of the theoretical values. The experiments showed that
choking o f the secondary flow in the mixing chamb er of the ejector plays an im porta nt role in the system
performance. M axim um CO P was ob tained when the ejector was operated a t i ts critical flow condition. Off-
design perform ance characteristics of the system are provided.
K e y w o r d s : r e f r i g e r a t io n ; e j e c t o r ; j e t p u m p ; c y c l e ; e x p e r i m e n t a l ; t h e o r e t i c a l ; s tu d y )
E t u d e t h 6 o r i q u e e t e x p 6 r i m e n t a l e d u n r 6 fr ig 6 r a te u r d e p e t it e
ta i l le 5. j e t de va pe ur
On prOsente les rdsul tats d un e Otude th~orique et ex p~rim entale d un rdfr ig~rateur de pet i te s dime nsions h je t de
vapeur . On a essayd eelui-ci dans une gam me de temp dratures de gOndrateur al lant de 120 h 140C. Le s donnOes
expOrimentales ont correspon du aux valeurs th~oriques . L es expd rienees ont montr~ que l ~ tranglem ent de
l ~coulement s econdaire dans la cais son de mdlange de l ~ j ec teur oue un r6 le imp or tant dans la per forma nce du
sys t kme. On a obtenu l e C OP l e p lus d l evd lor squ on a fa i t f on ct ionne r l Oject eur dans d es condit ions
d ~couleme nt cr it ique. On indique de s caractdris tiques de per fo rma nce n on prOvues dans son projet .
(M ot cl6s: froid; 6jecteur; pom pe ~ jet; cycle; 6tude exp6rimentale; 6tude th6orique)
A s t e a m j e t r e f r i g e r a t o r w a s f i rs t d e v e l o p e d b y L e B l a n c
a nd Pa r son a s e a r ly a s 19011 . I t s f i rs t w a ve o f popu la r i t y
c a m e i n t h e e a r l y 1 9 3 0s f o r a i r c o n d i t i o n i n g o f l a r ge
b u i l d i n g s 2 . H o w e v e r , s t e a m j e t r e f r i g e r a to r s h a v e b e e n
s u p p l a n t e d g e n e r a l l y b y s y s t e m s u s i n g m e c h a n i c a l
c o m p r e s s o r s . T h e l a t t e r t y p e w e r e s u p e r i o r i n t h e i r
c o e f fi c ie n t o f p e r f o r m a n c e ( C O P ) , f l ex i b i li t y a n d c o m -
p a c t ne s s i n m a n u f a c t u r e a n d o p e r a t i o n . T o d a y , h o w e v e r ,
w i t h e v e r - i n c r e a s i n g a w a r e n e s s a n d p r e s s u r e s f o r p r o -
t e c t i n g t h e e n v i r o n m e n t , r e f r i g e r a n t s u s e d i n c o n v e n -
t i o n a l v a p o u r c o m p r e s s i o n s y s t e m s h a v e c o m e u n d e r
a t t a c k , a n d m a n y a l t e r n a t i v e s h a v e b e e n a n d a r e s t i l l
b e i n g d e v e l o p e d . L e a v i n g t h e u s u a l p e r f o r m a n c e m e a -
s u r e s a si d e f o r t h e m o m e n t , i t is w o r t h n o t i n g t h a t s t e a m
w o u l d f a l l o n t h e o t h e r e x t r e m e r e g a r d i n g t h e e n v i r o n -
m e n t a l c r i t e r i a : i t i s t h e m o s t e c o n o m i c a l a n d e n v i r o n -
m e n t - f r i e n d l y fl u i d m e d i u m f o r r e f r i g e r a ti o n .
S t e a m j e t r e f r i g e ra t o r s , l i k e a b s o r p t i o n - b a s e d s y s t e m s ,
a r e p o w e r e d b y h e a t , w h i c h i s a v e r y l o w - g r a d e e n e r g y
a nd he nc e i s s ign i f i c a n t ly c he a p e r t h a n e l e c t r i c i t y o r
m e c h a n i c a l ( w o r k ) r e l a t e d p o w e r . A n o t h e r o f t e n u n d e r -
s t a t e d a d v a n t a g e o f h e a t - p o w e r e d r e f r i g e r a t i o n s y s te m s
i s th e i r u n i q u e p h a s a l r e l a t i o n s h i p w i t h t h e a v a i l a b i l i t y o f
* T o w h o m a ll c o r r e s p o n d e n c e s h o u l d b e a d d r e s s e d
t h e p o w e r s o u r c e t o d r i v e t h e m . T h i s i s v e r y o b v i o u s
w h e n s u c h s y s t e m s h a r n e s s s o l a r e n e r g y , f o r e x a m p l e .
W h e n m o r e r e f r i g e r a t i o n i s r e q u i r e d ( e . g . w h e n t h e
a m b i e n t w e a t h e r i s h o t ) t h e r e i n h e r e n t l y is m o r e a n d
h o t t e r s u n s h i n e t o d r i v e t h e r e f r i g e r a t o r o r a i r - c o n d i -
t i o n e r . P e r h a p s l e s s o b v i o u s b u t e q u a l l y i m p o r t a n t i s
t h e i r p o t e n t i a l i n c o m b i n e d h e a t a n d p o w e r s y s t e m s
r u n n i n g o n g a s o r f o s s i l f u e l . S u c h s y s t e m s r u n o n
m i n i m a l c a p a c i t y i n t h e s u m m e r ( o r h o t s e a s o n ) t o
p r o v i d e d i r e c t h o t w a t e r a n d / o r s i m p l y k e e p t h e p i p e
n e t w o r k s c l e a n a n d c i r c u la t i n g . R u n n i n g s t e a m j e t
r e f r i g e r a t o r b a s e d s y s t e m s c a n e x p l o i t t h i s u n u t i l i z e d
c a pa c i ty a t e xa c t ly t he t ime w he n i t i s su rp lu s .
T h e a b o v e a d v a n t a g e s w a r r a n t a s e r i o us r e - vi s it t o t h e
t e c h n o l o g y , e s p e c i a l l y t o r e - e v a l u a t e t h e p o t e n t i a l a n d
f e a s ib i l it y o f d e v e l o p i n g p r a c t i c a l s m a l l - c a p a c i t y s t e a m
j e t r e f r i g e r a t o r s y s t e m s . A f t e r a v e r y b r i e f d e s c r i p ti o n o f
t h e p r i n c ip l e o f o p e r a t i o n , t h e p a p e r w i ll e la b o r a t e o n
t h e p r o c e s se s i n v o l v e d i n t h e t e c h n o l o g y , f r o m b o t h t h e
the o re t i c a l a nd p ra c t i c a l pe r spe c t ive s .
F i g u r e 1 s h o w s a s c h e m a t i c d i a g r a m o f a je t r e f r i g e ra -
t i on c yc l e . A s he a t i s a dde d to t he bo i l e r , t he h igh -
p r e s s u r e a n d t e m p e r a t u r e r e f r i g e r a n t v a p o u r , k n o w n a s
p r i m a r y o r m o t i v e f l u i d , i s e v o l v e d . T h i s e n t e r s t h e
p r i m a r y n o z z l e o f t h e e je c t o r, w h e r e i t e x p a n d s t o
7 8
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7/25/2019 A Theoretical and Experimental Study of a Small-scale Steam Jet Refrigerator
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A s m a l l s c a l e s t e a m j e t re f r i g e r a t o r 79
omenclature
A A re a (m 2 )
C O P C o e f fi e nt o f p e r f o r m a n c e
h Spe c i fi c e n th a lpy (k J kg J )
I E le c t r ic c u r re n t (A )
k Spe c i fi c he a t r a t i o
m M a ss f l ow (kg s I )
M M a c h n u m b e r
N X P N oz z le e x i t pos i t i on ( se e Figure 7
P Pre ssu re (ba r )
R rn E n t r a i n m e n t r a t i o
T T e m p e r a t u r e ( K , C )
V V o l t a ge
Greek l e t t e r s
'qd Diffus er e ff ic iency
% Pr im a ry noz z l e e f f i c ie nc y
qm M i x i n g c h a m b e r e f fi c ie n c y
t ) D e ns i ty
1- f / f p
S u b scr ip t s
1 Pr im a ry noz z l e e x i t p l a ne ( see
Figure 2
2 U p s t r e a m o f t h e m i x i n g c h a m b e r t h r o a t ( se e
Figure 2
3 U p s t r e a m o f t h e n o r m a l s h o c k w a v e ( se e
Figure 2
4 D o w n s t r e a m o f t h e n o r m a l s h o c k w a v e ( se e
~ u r e 2 )
boi le r Boi le r
c o n C o n d e n s e r
e Exi t
e v a p E v a p o r a t o r
f Sa tu ra t e d l i qu id
i In le t
o S t a g n a t i o n s t a t e
p P r im a ry f lu id
s S e c o n d a r y f l u id
t P r i m a r y n o z z l e t h r o a t
v S a t u r a t e d v a p o u r
S u p erscr ip t s
' P r im a ry f lu id
S e c o n d a r y f l u id
F i g u r e I
F i g u r e 1
o i l e ~
condenser
t r
~ e v a p o ra to r [
S c h e m a t i c r e p r e s e n t a t i o n o f a j e t r e f r i g e r a t o r c y c le
Diagramm e sch& natique d'un cycle JHgorifique ~ et de vape ur
c o n s t a n t a r e a
m i x i n g s e c t i o n
p r i m a r y P lZ - ~ ~ c o m b i n e d f l o w
f l o w t ~ _ _j J ~
C O l l s t a n l p i P s s u r t
secondary flow mi xin~ sectio n
subson ic d i f fu se r
F i g u r e
F i g u r e 2
r=
7.
P
I ) I S I ~ \ I : ~ I ,O N ; X X I S
S c h e m a t i c r e p r e s e n t a t io n o f a n e j e c t o r
Sch& na d 'un ~ jecteur ,~upervoniquc lvpique
p r o d u c e a s u p e r s o n i c f l o w w i t h i n a l o w - p r e s s u r e r e g i o n.
T h e p a r t i a l v a c u u m c r e a t e d b y t h e s u p e r s o n i c p r i m a r y
f l o w is f e d b y a s e c o n d a r y f l o w c o n s is t i n g o f e n t r a i n e d
r e f r i g e r a n t v a p o u r c o m i n g f r o m t h e e v a p o r a t o r . T h e
p r i m a r y a n d s e c o n d a r y f l u i d s c o m b i n e i n t h e m i x i n g
c h a m b e r o f th e e j e c to r a n d d i s c h a r g e t h r o u g h a d i f f u s e r
t o t h e c o n d e n s e r , w h e r e t h e r e f r i g e r a n t v a p o u r c a n b e
l i q u ef i ed a t a m b i e n t t e m p e r a t u r e . T h e l i q u id r e f r i g e r a n t
i s r e tu rne d to t he bo i l e r v i a a f e e d -pump w h i l e t he
r e m a i n d e r i s e x p a n d e d t h r o u g h t h e t h r o t t l i n g o r e x p a n -
s i o n v a l v e to t h e e v a p o r a t o r t o c o m p l e t e t h e c y c l e.
S m a l l - c a p a c i t y j e t r e f r i g e ra t o r s u s i n g R 1 1 , R I 2 a n d
R 13 a s t he w ork i ng f lu id s ha ve be e n re po r t e d 3 5
H o w e v e r , t h e a u t h o r s a r e n o t a w a r e o f a n y sm a l l -
c a p a c i t y s y s t e m s o p e r a t e d w i t h l o w - p r e s s u r e s t e a m .
N o r m a l l y , s t e a m e j e c t o r s a r e o p e r a t e d u s i n g s t e a m
supp l i e d f rom indus t r i a l - sc a l e bo i l e r s w i th sa tu ra t ion
p re ssu re s i n the r a nge 5 20 ba r .
In t he se c t ions b e low , t he spe c if i c a im i s t o p ro v ide the
b a s ic b a c k g r o u n d i n th e o r y a n d o p e r a t i o n o f a s te a m je t
r e f r i g e r a t o r . T h e t h e o r e t i c a l a n d e x p e r i m e n t a l s t u d y
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7/25/2019 A Theoretical and Experimental Study of a Small-scale Steam Jet Refrigerator
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3 8 0 I W E a m e s e t a l
f o c u s e d o n a s t e a m je t r e f r i g e r a t o r w i t h a f ix e d g e o m e t r y
e j e c t o r , d e s ig n e d t o o p e r a t e w i t h r e l a t iv e l y lo w b o i l e r
t e m p e r a t u r e s ( 1 2 0 - 1 4 0 C ) o r 2 - 3 . 6 b a r p r e s s u re s .
jector theory
T h e e j e c t o r is a c ri t ic a l c o m p o n e n t o f th e j e t r e f r ig e r a t i o n
c y c l e. T h e c o n c e p t o f a n e j e c t o r is n o t n e w . S t e a m - d r i v e n
e j e c t o r s h a v e b e e n u s e d e x t e n s i v e l y i n p o w e r g e n e r a t i o n ,
c h e m i c a l p r o c e s s i n g a n d t h e n u c l e a r i n d u s t r y f o r m a n y
y e a r s . T h e m o s t n o t a b l e u s e s h a v e b e e n t o p r o d u c e o r
m a i n t a i n a p r a c t i c a l v a c u u m i n g a s - f il l e d v e s s e ls 6 . Th e
m a i n a d v a n t a g e o f e je c t o rs o v e r c o n v e n t i o n a l c o m p r e s -
s o r s o r p u m p s is th a t t h e y h a v e n o m o v i n g p a r t s a n d t h u s
r e q u i r e l i t tl e m a i n t e n a n c e .
A t y p i c a l s u p e r s o n i c e j e c t o r is s h o w n s c h e m a t i c a l l y in
Figure 2.
H i g h - p r e s s u r e p r i m a r y f l u i d ( P ) e n t e r s t h e
p r i m a r y ( s u p e rs o n i c ) n o zz l e , th r o u g h w h i c h i t e x p a n d s t o
p r o d u c e a l o w p r e s s u r e a t t h e e x i t p l a n e ( 1 ) . T h e h i g h -
v e l o c it y p r i m a r y s t r e a m d r a w s a n d e n t r a in s t h e s e c o n d -
a r y f l u i d ( S ) i n t o t h e m i x i n g c h a m b e r . T h e c o m b i n e d
s t r e a m s a r e a s s u m e d t o b e c o m p l e t e l y m i x e d a t t h e e n d o f
t h e m i x i n g c h a m b e r ( 3 ) a n d t h e f l o w s p e e d i s s u p e r s o n i c .
A n o r m a l s h o c k w a v e i s t h e n p r o d u c e d w i t h i n t h e
c o n s t a n t - a r e a s e c t i o n , c r e a t i n g a c o m p r e s s i o n e f f e c t, a n d
t h e f l o w s p e e d i s r e d u c e d t o s u b s o n i c v a l u e . F u r t h e r
c o m p r e s s i o n o f t h e fl u id is a c h i e v e d a s th e c o m b i n e d
s t r e a m s f l o w t h r o u g h t h e s u b s o n i c d i f f u s e r s e c t i o n .
T h e p e r f o r m a n c e o f a n e j e c t o r c a n b e d e f i n e d in t e r m s
o f t h e
entrainment ratio
o r
mass .flow ratio,
wh i c h i s t h e
r a t i o b e t w e e n t h e s e c o n d a r y a n d t h e p r i m a r y f l u i d m a s s
f l o wr a t e s :
Rm = --m~ ( 1
m p
T h e p e r f o r m a n c e o f e je c t o rs c a n b e p r e d i c t e d u s in g o n e -
d i m e n s i o n a l c o m p r e s s i b l e f l o w t h e o r y . T h e f i r s t m o d e l s
w e r e p r e s e n t e d b y K e e n a n a n d N e u m a n n 7 t o a n a l y s e ai r
e j e c t o rs . T h e i r f ir s t w a s a o n e - d i m e n s i o n a l m o d e l b a s e d
o n i d e a l g a s d y n a m i c s i n c o n j u n c t i o n w i t h t h e p r i n c i p l e s
o f c o n s e r v a t i o n o f m a s s , m o m e n t u m a n d e n e r g y . H e a t
a n d f r i c t i o n l o s s e s w e r e i g n o r e d . T h e i r a p p r o a c h
p r o v i d e d s o l u t i o n s f o r e j e c t o r s w i t h c o n s t a n t - a r e a
m i x i n g c h a m b e r s , a n d e x c l u d e d t h e d i f f u s e r s e c t i o n .
L a t e r t h e y e x t e n d e d t h e t h e o r y t o i n c l u d e a c o n s t a n t -
p r e s s u r e m i x i n g c h a m b e r a n d a d i f f u s e r 8 . H o w e v e r , t h i s
l a t e r m o d e l s t i l l d i d n o t i n c l u d e f r i c t i o n o r h e a t l o s s . I n
t h i s c u r r e n t p a p e r , t h e a u t h o r s h a v e m o d i f i e d K e e n a n ' s
m o d e l t o i n c l u d e i r r e v e r s i b i l i t i e s a s s o c i a t e d w i t h t h e
p r i m a r y n o z z l e , m i x i n g c h a m b e r a n d d i f f u s e r . T h e
a n a l y s i s i s b a s e d o n t h e w e l l - k n o w n s t e a d y - s t a t e a n d
s t e ad y - f lo w e q u a t i o n s o f en e r g y , m o m e n t u m , a n d c o n -
t i n u i t y a s f o l l o ws :
E n e r g y e q u a t i o n f o r a n a d i a b a t i c p r o c e s s :
Z m i ( h i +
I/ 2/2) = Z me(he + V ~/2)
M o m e n t u m e q u a t i o n :
Pi Ai Z mi Vi = Pe Ae Z me Ve
C o n t i n u i t y e q u a t i o n :
Z p i V iA i = Z p e V eA e
2 )
3 )
(4)
A l o n g w i t h t h e s e g o v e r n i n g e q u a t i o n s , t h e f o l l o w i n g
s i m p l i f y i n g a s s u m p t i o n s w e r e m a d e :
1 . F r i c t i o n l o ss e s w e r e i n t r o d u c e d b y a p p l y i n g i se n -
t r o p i c e f f ic i e n c i es t o t h e p r i m a r y n o z z l e , d i f f u s e r a n d
m i x i n g c h a m b e r .
2 . T h e p r i m a r y a n d s e c o n d a r y f lu i d s w e r e s u p p l i e d a t
z e r o v e l o c i t y a t P a n d S re s p e c t i v e l y .
3 . A t t h e p r i m a r y n o z z l e p l a n e ( 1 ) w h e r e t h e t w o
s t r e a m s f i r st m e e t , t h e s t a ti c p r e s s u r e w a s a s s u m e d t o b e
u n i f o r m .
4 . M i x i n g o f t h e t w o s t r e a m s w a s c o m p l e t e b e f o r e a
n o r m a l s h o c k w a v e o c c u r r e d a t t h e e n d o f t h e m i x in g
c h a m b e r ( 3 ) .
Ma ch number of the pr imary f luid at the nozz le exi t plane
H i g h - p r e s s u r e p r i m a r y f l u i d a t P e x p a n d s t h r o u g h a
c o n v e r g i n g - d i v e r g i n g n o z z l e a n d l e a v e s t h e n o z z l e a t 1 '
w i t h s u p e r s o n i c s p e e d . A p p l y i n g t h e e n e r g y e q u a t i o n
b e t we e n P a n d 1 ' , i t c a n b e s i m p l i f i e d t o :
V~, = 2% (hp - h, ,) (5)
w h e r e % i s a n i s e n t r o p i c e f fi c ie n c y o f t h e p r i m a r y n o z z l e .
T h e r e l a t i o n b e t w e e n t h e p r e s s u r e r a t i o a c r o s s t h e
n o z z l e a n d M a c h n u m b e r a t t h e e x it o f t h e n o z z l e is g i v e n
a s
[ 2 p i I
Mach number of the secondary f luid at the nozz le exi t
plane
A s t h e l o w p r e s s u r e i s f o r m e d a t t h e p r i m a r y e x i t p l a n e ,
t h e s e c o n d a r y f l u i d a t S e x p a n d s t o 1 . S i m i l a r l y t o t h e
p r i m a r y n o z z le , t h e M a c h n u m b e r o f th e s e c o n d a r y f l u id
a t t h e n o z z l e e x i t p l a n e i s g i v e n a s
= - 1 7 )
The mixing process
A p p l y i n g t h e m o m e n t u m e q u a t i o n w i t h i d e a l l o s s l e s s
m i x i n g b e t w e e n 1 a n d 3 :
P I Al + m p V 1, -4- m s Vv, = P3 A3 + (mp + ms) V3
T h e m i x i n g p r o c e s s b e t w e e n p r i m a r y a n d s e c o n d a r y
f l ui d s is a s s u m e d a l l t o o c c u r b e t w e e n 1 a n d 3 a t c o n s t a n t
s t a t i c p r e s s u r e ( P I = P 3 ) a n d w h e r e t h e c r o s s - s e c t i o n a l
a r e a s a t t h e i n l e t a n d e x i t o f th e m i x i n g c h a m b e r a r e
ass um ed to be e qu a l (A i ---- A3) .
T h e r e f o r e
m p V + m s VI , , = ( m p - { - m s ) V3
Th i s r e l a t i o n d e s c r i b e s f u l l y i d e a l i z e d m i x i n g ; i t c a n b e
m a d e m o r e r e a l i s ti c b y i n c l u d i n g T/m a s a n e f f i c ie n c y f o r
t h e w h o l e m i x i n g c h a m b e r :
~ ]m ( mp V I + m s V I, ,) = ( m p + m s ) V 3 ( 8 )
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7/25/2019 A Theoretical and Experimental Study of a Small-scale Steam Jet Refrigerator
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A s m a l l s c a l e s t e a m e t r e f r i g e r a t o r
3 8 1
T h u s t h e v e l o c i t y o f t h e m i x e d f lu i d a t 3 c a n b e e x p l i c it l y
e x p r e s s e d a s
V 3 = r / m [ m p V I + m s V ,,,] 9 )
- mp
n s
Equ a t ion 9 ) c an be wr i t t en in t e rm s o f t h e M a c h
n u m b e r :
, v t = +
m
1 0 )
x/ 1 + R~) 1 + R m T ~ / T p )
w h e r e t h e r e la t i o n b e t w e e n M a n d M * i s g i v e n a s
/ k + 1 )M 2/2
M *
1 + k - 1 )M 2/2 11)
P r e s s u r e r a t i o a c r o s s a n o r m a l s h o c k w a v e
A t s o m e s e c t i o n w i t h i n th e c o n s t a n t - a r e a m i x i n g
c h a m b e r , a n o r m a l s h o c k w a v e o c c u r s if t h e v e lo c i t y o f
t h e m i x e d f l u i d e n t e r i n g t h e c o n s t a n t - a r e a s e c t i o n i s
s u p e r s o n i c . A s h o c k w a v e i s a p r o c es s w h e r e a s u d d e n
c h a n g e i n f l u i d v e l o c i t y a n d p r e s s u r e t a k e s p l a c e i n
s u p e r s o n i c f l o w a n d w o u l d h a v e i n f i n i t e s i m a l t h i c k n e s s .
T h e o n e o c c u r r i n g b e t w e e n 3 a n d 4 w o u l d t h e r e f o r e b e a n
i r re v e rs ib l e c o m p r e s s i o n p r o c e s s i n w h i c h t h e M a c h
n u m b e r s u d d e n l y f a l l s t o l e s s t h a n u n i t y . T h e M a c h
n u m b e r o f t h e m i x e d f lu i d a ft e r th e s h o c k w a v e i s
o b t a i n e d f r o m
1 )
= 1
1 2 )
T h e p r e s s u r e l i f t r a t i o a c r o s s t h e s h o c k w a v e i s o b t a i n e d
as f o l l o w s :
P4 1 + k M 4
P3 1
+
k
]l,I~ 13)
t h e f l o w s p e e d i s r e d u c e d t o z e r o a t t h e e n d o f t h e d i f f u s er
b ) . T h e p r e s s u r e l i f t r a t i o a c r o s s t h e d i f f u s e r c a n b e
o b t a i n e d f r o m
Pbp4 r/ d k
_
1) v 11 ~
~ . M,~ + 14)
w h e r e q d i s t he i sen t rop i c e f f i c i e n c y o f t h e d i f f u s e r .
S o h t t i o n q E q u a t i o n s 5 ) - 1 4 )
I t i s a s s u m e d t h a t th e t em p e r a t u r e , p r e s s u r e a n d m a s s
f l owra t e o f t h e p r i m a r y a n d s e c o n d a r y f l u i d s are all
2.8
2.4
2.0
1.6
1.2
0.8
11.4
II.|l
IN
b ~ f i h l I ~ l l t p t l : i t L l r t I ~ * (I o (
( ( ) P
. . . . : ~ 1 c : l i ; l l i o
1 2 . 5 = I , z , ,~ t p ( o ( )
22 26
: q l
.14 3~
I , . , m / o
F i g u r e 4 T h e o r e t i c a l C O P o f j e t r e f r i g e r a t o r s v e r s u s c o n d e n s e r
s a t u r a t i o n t e m p e r a t u r e
F i g u r e 4
R~su ltats d u c alcul de la per/ orm ance de.~ r~ /?ig~;rateurs
jimctionnant h d(ff~;rentes temp~;ratures
P r e s s u r e r i f t r a t i o a c r o s s t h e s u b s o n i c d i f f u s e r
F u r t h e r c o m p r e s s i o n o f t h e m i x e d f lu i d is a c h i e v e d a s i t
p a s s e s t h r o u g h t h e s u b s o n i c d i ff u s e r . I t i s a s s u m e d t h a t
2.11
i . 5
R m 1 . 0
0 . 5
0 . 0
I p / P b
= 60
( ) L , \ l ) , . , r i n l , ., i H a l d : l [ l l ( b c ~ l * , : l l u e ~ )
L , M ~ L . , r im e l v t a l d a t a ( I ) p i e 4 1 ~ ; l l u u ~
i h c o t c l i c : l l , . ; i h i t s
~
4 8 12
16
Pb/Ps
F i g u re 3 C o m p a r n s o n b e t w e e n e x p e r i m e n t a l a n d t h e o r e ti c a l e n tr a i n -
m e n t r a t i o ( p r i m a r y p r e s s u r e r a t i o = 6 0 )
F i g u r e 3
CorrOlation avec donn~es expOrimentales four nies par
/ ' E n g in e e r in g S c i e n c es Da ta U n i t ( E D S U)
1.4
1.2
1 . 1 1
v
I ) . 1 ~
I J . 4
O.2
O.ql
I ~ : q , ~ , l : l t , , I I c I I I p L r : t l u t ~ ~ o (
( ( ) 1
2 ( 1 0 ~
,
[ h . i h r
] ~ 0 o (
IN 22 2~ , ~0 t4 38
I c , H ~ I ( )
F i g u r e 5 T h e o r e t i c a l C O P o f j e t r e f r i g e r a t o r s v e r s u s
c o n d e n s e r
s a t u r a t i o n t e m p e r a t u r e
F i g u r e 5
R~sul ta ts du ca lcu l de la perfbrma nce des r( fHg~;rateurs
fonct ionnant h d (~ren tes temp~;ra tures
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7/25/2019 A Theoretical and Experimental Study of a Small-scale Steam Jet Refrigerator
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3 8 2 I W E a m e s e t a l
F i g u r e 6
F i g u r e 6
s u p e r h e : H e r
~ ~ : :il e . l e c t r I ~ ' o I ' : H o r
s t e a m d r u m [~ ~ i , U , n l , . ~ - ]
b o i l e r ~ ,~-. [ i ;
S c h e m a t i c d i a g r a m o f t h e e x p e r i m e n t a l s t e a m j e t r e fr i g e r a to r
Sehdma de l appareil d essai
t ( , d u a i r : - - - J
4
]
- - - c o o l i n g w a t e r
k n o w n . T h e f o l l o w i n g p r o c e d u r e c a n b e u se d i n o r d e r t o
o b t a i n t h e e j e c t o r e x h a u s t p r e s s u r e .
1 . A s t h e p r e s s u r e a t t h e n o z z l e e x i t p l a n e is n o t k n o w n ,
i t c a n b e d e t e r m i n e d b y a n i t e r a t i o n p r o c e s s . F i r s t , t h e
v a l u e o f P I / P s i s a s s u m e d .
2 . C a l c u l a te t h e M a c h n u m b e r s o f t h e p r i m a r y a n d
s e c o n d a r y f l u i d s a t t h e n o z z l e e x i t p l a n e , M ~ a n d
M~ ,
f r o m E q u a t i o n s 6 ) a n d 7 ) .
3 . C a l c u l a t e t h e M a c h n u m b e r o f t h e m i x e d f l ui d , M 3 ,
f r o m E q u a t i o n 1 0 ), a n d
4 . C a l c u l a te t h e M a c h n u m b e r o f th e m i x e d fl u id a ft e r
t h e s h o c k w a v e , M 4 , f r o m E q u a t i o n 1 2 ).
5 . C a l c u l a t e a p r e s s u r e li ft r a t i o a c r o s s t h e s h o c k w a v e ,
P4/P3,
f r o m E q u a t i o n 1 3 ).
6 . Ca l c u l a t e a p r e s s u r e l i ft r a t i o a c r o s s t h e d if f u s e r ,
P b / P 4 , f r o m E q u a t i o n 1 4 ) .
7 . N o w , t h e e j e c t o r e x h a u s t p r e s s u r e P b c a n b e
c a l c u l a t e d , s i n c e
P4/P3, Pb/P4
a n d P I / P s a r e a ll k n o w n .
8 . R e p e a t st e p 1 ) w i t h a n e w v a l u e o f
Pl/Ps
u n t i l t h e
m a x i m u m P b i s o b t a i n e d .
T h e p r i m a r y n o z z l e , d i f f u s e r , a n d m i x i n g c h a m b e r
e f f ic i e n c i e s o f 0 . 8 5 , 0 . 8 5 , a n d 0 . 9 5 r e s p e c t i v e l y we r e
f o u n d t o p r o v i d e a n a c c e p t a b l e c o r r e l a t i o n w i t h t h e
I b c d
e f i
~ I l i
V J I
0
n o z z l e e x i t l ) o s i l i o n
t ) r i m a r y I~ oz zle t h r o a t d i a m e t e r : 2 r a m
p r i m a r y n o z z l e e x it d i a m e t e r : 8 m m
a : = 4 0 m m d : 2 1 0 m m
b := 1 0 0 m m e = 2 -1 m m d i a m e t e r
c = 4 0 n u n f = 1 8 m m d i a m e t e r
g - - 4 0 m m d i a m e t e r
F i g u r e 7 D i m e n s i o n s o f t h e e x p e r i m e n t a l e j e c to r ( n o t t o s c a l e)
F i g u r e 7 Dimensions de base de l ~jecteur utilis~ pour les essais
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A s m a l l s c a l e s t e a m j e t r e f r i g e r a t o r
8
e xpe r ime n ta l da t a p l rov ide d by the Eng ine e r ing Sc i e nc e s
D a t a U n i t E S D U ) 6 , a s s h o w n b y
Figure 3.
I t m u s t b e
r e m e m b e r e d , h o w e v e r , t h a t t h i s m e t h o d c a n b e u s e d o n l y
w h e n a n e j e c t o r is o p e r a t e d a t i t s d e s i g n e d c o n d i t i o n .
T h e o r e t i c a l p e r f o r m a n c e o f a s t e a m j e t r e f r i g e r a t o r
T h e t h e r m o d y n a m i c p e r f o r m a n c e o f a j e t r e f r i g e r a t i o n
c yc le i s u sua l ly e va lua t e d th rough i t s
coef f i c iem of
perJormance
C O P ) , w h i c h i s t h e r a t i o b e t w e e n t h e
e v a p o r a t o r h e a t l o a d a n d t h e e n e r g y i n p u t t o t h e b o i le r .
B e c a u s e t h e p o w e r i n p u t t o t h e f e e d p u m p w a s n e g l i g ib l e ,
i t w a s o m i t t e d f r o m t h e p e r f o r m a n c e c a l c u l a t i o n . I f t h e
e n t r a i n m e n t r a t i o i s k n o w n , t h e C O P c a n b e c a l c u l a t e d
f r o m
C O P -- Rm [ hv.ev~p - hr.co~]
1 5 )
Lhv,boiler -- hf.con/
Figures 4
a n d 5 s h o w t h e r e s u l ts o f t h e c a l c u l a t e d
p e r f o r m a n c e o f s t e a m j e t r e f r i g e ra t o r s o v e r a r a n g e o f
o p e r a t i n g t e m p e r a t u r e s . T h e e j e c t o r p e r f o r m a n c e
( O I
0.5
0.4
0.3
0.2
ILl
0.0
I
c n
(()()
25 28 31 34
37
nozz le x i l m si tion 26.15 i l l e~ap ora lorenlpe ra lure lL0 (
Tboiler= 120.((sa()
' ' ~ Thoi le r 125oCsat)
~ ~ , i ~i ( ' { ' ( ' ( 1 . . . . . . . . .
- - - - m T l m i k . r = 3 ~ ( ( M I I )
- - l h o i l ( r = 1 4 0 , ) ( ( s a t )
|
3il 40 50 60
])~,)n f i l l ) i l l ' )
F i g u r e
8 V a r i a t i on i n meas u red CO P w i t h bo i l e r t empe ra tu re and
c ondens e r p res s u re
F i gu re 8 C o u rb e s d u C OP mesur h di ~rentes temp ratures de
g ndrateur
o b t a i n e d f r o m E q u a t i o n s 5 ) - 1 4 ) w a s th e b es t v a l u e
f o r t h e g iv e n c o n d i t i o n s . T h u s t h e p e r f o r m a n c e s h o w n b y
the so l id - l i ne c u rve s doe s no t r e p re se n t t he va lue o f one
s ing le op t imiz e d sys t e m, s inc e a ny po in t on the so l id l i ne
re qu i re s a pa r t i c u l a r e j e c to r ope ra t e d a t it s de s ign
c o n d i t i o n ) . T h e p e r f o r m a n c e o f ej e c to r s w i t h s i m i l a r a r e a
ra t io
A4/At )
w a s c a l c u l a t e d by sc a l ing ba se d on
c o n t i n u i t y , t h e i d e a l g a s la w a n d a n i s e n t ro p i c c o m p r e s -
s i o n p r o c e s s w i t h c o n d i t i o n s a t a n y s e c t i o n n o r m a l i z e d
by re fe re nc e to t he p r im a ry noz z l e t h roa t . S uc h sc a l ing i s
w e l l de sc r ibe d in s t a nd a rd f lu id me c ha n ic s t e x t s l a nd
p r o d u c e d r e s u l t s s h o w n b y t h e d o t t e d l i n e s i n
Figures 4
a nd 5 .
F r o m t h e pl o ts o f Figures 4 a n d 5, t he fo l low ing w e re
obse rve d :
1 . A c yc l e de s igne d to ope ra t e a t h igh bo i l e r a nd
e v a p o r a t o r t e m p e r a t u re s a n d l o w c o n d e n s e r t e m p e r a tu r e
w o u l d h a v e h i g h e r C O P v a l u e s a n d r e q u i r e a n e j e c t o r
w i th l a rge r a re a r a t i o
A4/At )
t h a n a n o t h e r c y c le .
2 . Fo r one pa r t i c u l a r e j e c to r o r e j e c to r s w i th s imi l a r
a r e a r a t i o
A4/At),
w i t h t h e g i v e n e v a p o r a t o r t e m p e r a -
t u r e , a n y r i s e in t h e b o i l e r t e m p e r a t u r e w o u l d c a u s e t h e
C O P t o f a ll . H o w e v e r , t h e c y c l e c o u l d t h e n b e o p e r a t e d
a t a h i g h e r c o n d e n s e r t e m p e r a t u r e .
3 . Fo r one pa r t i c u l a r e j e c to r o r e j e c to r s w i th s imi l a r
a r e a r a t i o
A4/At),
w i t h a g i v e n b o i l e r t e m p e r a t u r e , a n
i n c r e a s e i n t h e e v a p o r a t o r t e m p e r a t u r e w o u l d c a u s e t h e
C O P to r i se . H e re a l so , t he c yc le c ou ld be op e ra t e d a t a
h i g h e r c o n d e n s e r t e m p e r a t u r e .
E x p e r i m e n t a l t e s t s o n a s t e a m j e t r e f r i g e r a t o r
Experimental set-up
The t e s t se t -up is show n sc he m a t i c a l ly i n
Figure 6.
T h e
b o i l e r d e s i g n w a s b a s e d o n t h e t h e r m o - s y p h o n p r i n c ip l e .
H e a t e n e r g y w a s d i r e c t l y tr a n s f e r r e d t o t h e w a t e r b y t w o
3 .5 k W e l ec t ri c h e at e r s . T h e e v a p o r a t o r d e s i g n w a s b a s e d
on sp r a y a nd fa l l i ng f i lm c o lum n . A s ing le 3.25 kW he a te r
w a s u s e d t o s i m u l a t e t h e e v a p o r a t o r c o o l i n g l o a d . A l l t h e
e l e c t r i c he a t e r s w e re c on t ro l l e d u s ing va r i a b l e t r a ns fo r -
me rs . A she l l a nd c o i l c onde nse r w a s u se d , c oo le d by
w a te r .
0.5
I
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7/25/2019 A Theoretical and Experimental Study of a Small-scale Steam Jet Refrigerator
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3 8 4 I W E a m e s e t a l
T a b l e 1 P e r f o r m a n c e a t o f f - d es i g n o p e r a t i o n , a s s h o w n i n Figures 10 a n d l l
T a b l e a u 1 Per /brma nce lo r s du Jonc t ionn emen t ~t des cond i t i ons non pr~vues dans l e p ro j e t comm e on peu t vo it dans l es F igures 10 e t 11
C o o l i ng T e m p e r a t u r e ( C )
O p e r a t i n g p o i n t c a p a c i t y
o n t h e f i gu r e s C O P ( W ) E v a p o r a t o r B o i l er
P r e s s u re ( m b a r )
c o n d e n s e r
a 0.207 710 7.5 130.0 45.7
b 0.207 7 l0 7 .5 130.0 42.5
d 0.221 710 7 .0 127.2 42.5
e 0.239 752 7.5 126.9 42.5
f 0 .278 936 10.0 130.0 47.6
g 0.197 690 7.5 131.7 47.6
Note: T h e d a t a p r o v i d e d i n t h i s t a b le a r e o b t a i n e d g r a p h i c a ll y f r o m t h e f i g ur e s
l c .n l uC)
22 26 3tl 34 38
1400
T l , , ,i l c r = 1 2 0 , , C 1 2 5 " ( "
~ I O O O 1 3 o . (
.] 135~
= t ~ I I 1 " (
=
600 =5 (
z
i i " l ' e , . . . .
2 0 0 , i , I ,
25 35 4'~ 55 65
Pcon (m ba r)
F i g u r e 11 M e a s u r e d c o o l i n g c a p a c i t y c h a r a c t e r i s t i c s o f t h e e x p e r i -
m e n t a l r e f r i g e r a t o r
Figu re 11 Courbes de per fo rmance ca l cu lOes h par t i r des donnOes
observOes l o r s du fone t ion nem en t h l a p res s ion cr i t ique du condenseur
F i g u r e 7
i s a s k e t c h s h o w i n g t h e e s s e n ti a l d i m e n s i o n s o f
t h e e j e c t o r u s e d i n t h e t e s ts . T h e c r o s s - s e c t i o n a l a r e a w a s
o b t a i n e d f r o m t h e s c a l i n g c o n s i d e r a t i o n s d e s c r i b e d
e a r l i e r . O t h e r g e o m e t r i c a l d e s i g n p a r a m e t e r s w e r e
b a s e d o n t h e s t a n d a r d r e c o m m e n d a t i o n b y E S D U 6.
P e r f o r m a n c e c h a r a c t e r is t i cs o f a s t e a m j e t r e f r ig e r a t i o n
u n i t
T e s t s o n t h e s t e a m j e t r e f r i g e r a t o r w e r e c a r r i e d o u t o v e r a
r a n g e o f b o i le r , c o n d e n s e r a n d e v a p o r a t o r c o n d i t i o n s . I n
e a c h s i t u a t i o n , t h e s y s t e m w a s s e t a n d l e f t t o r e a c h
e q u i l i b r i u m w i t h r e s p e c t t o a l l t e m p e r a t u r e s , a n d t h e r e -
f o r e a l l h e a t / e n e r g y i n p u t s a n d o u t p u t s w e r e s t e a d y . T h e
e l e c tr i c p o w e r i n p u t s t o t h e b o i l e r a n d t o t h e e v a p o r a t o r
w e r e m e a s u r e d i n r e a l t i m e w i t h a c o m p u t e r d a t a -
a c q u i s i t i o n s y s te m . S a m p l i n g o f t h e v o l ta g e V ) a c r o s s ,
t h e e l e c tr i c c u r r e n t I ) t h r o u g h e a c h h e a t e r , a n d l o g g i n g
t h e i r r e a l - ti m e p r o d u c t V x I ) g a v e a n i n d i c a t i o n o f t h e
i n s t a n t a n e o u s h e a t p o w e r a d d e d i n e a c h c as e . T h e s e d a t a
l o gs p r o v i d e d v e r y a c c u r a t e m e a s u r e m e n t s o f t h e a c tu a l
h e a t i n p u t t o t h e b o i l e r a n d t h e e l e c tr i c a ll y i m p o s e d l o a d
o n t h e e v a p o r a t o r .
T h e C O P o f t h e w h o l e s y s t e m in t h is e q u i l i b r i u m s t a t e
c o u l d b e e s t i m a t e d a c c o r d i n g t o t h e f o l l o w i n g :
C O P e l e c _ ( V x I ) e v a p ( 1 6 )
( V X / ) b o i l e r
B a s e d o n t h e e l e c tr i c p o w e r i n p u t t o t h e b o i le r , a n d l o a d
o n t h e e v a p o r a t o r , t h is C O P e s t im a t e w a s t h e r e f o r e th e
o v e r a l l w o r s t - c a s e p e r f o r m a n c e , a s i t i n c l u d e d a l l t h e
u n w a n t e d h e a t l o s se s a n d g a i n s t o t h e s y s te m d u e t o
i m p e r f e c t i o n s i n t h e i n s u l a t io n .
F i g u r e s 8
a n d 9 s h o w p l o ts o f th e C O P m e a s u r e d a t
d i f f e r e n t b o i l e r t e m p e r a t u r e s , f r o m w h i c h i t w a s p o s s i b le
t o o b s e r v e t h e f o l l o w i n g :
1. T h e C O P w a s in d e p e n d e n t o f t h e c o n d e n s e r p re s s u re
u n t i l a n u p p e r l i m i t o f t h e l a t t e r w a s r e a c h e d , w h e r e t h e
C O P f e ll r a p i d l y t o z e r o . T h e c o n d e n s e r p r e s s u r e a t
w h i c h t h e C O P s t a r t e d d r o p p i n g i s t e r m e d t h e c r i t i c a l
c o n d e n s e r p r e s s u r e 5
2 . F o r a g i v en c o n s t a n t e v a p o r a t o r t e m p e r a t u r e l o a d
s e t p o i n t ) , i n c r e a s in g t h e b o i l e r p r e s s u r e a n d t e m p e r a -
t u r e ) r e s u l te d i n w o r s e C O P , b u t t h e c y c l e c o u l d b e
o p e r a t e d a t h i g h e r c r i ti c a l c o n d e n s e r p r e s s u r e a n d w o u l d
t h e r e f o r e b e le s s s u s c e p t ib l e to c h a n g i n g c o n d e n s e r o r
a m b i e n t ) c o n d i t i o n s i n r e a l a p p l i c a t i o n s .
3 . W i t h a c o n s t a n t b o i l e r p r e s s u r e a n d t e m p e r a t u r e ) , a
h i g h e r C O P w a s a c h i e v a b le i f t h e e v a p o r a t o r t e m p e r a -
t u r e s s e t - p o i n t s ) we r e a l l o w e d t o r i se , a n d t h i s f u r t h e r
a l l o w e d t h e c y c l e t o b e o p e r a t e d a t h i g h e r c r i t i c a l
c o n d e n s e r p r e s s u r e s .
W h e n t h e c y cl e w a s o p e r a t e d a t a c o n d e n s e r p r e s s u r e
b e l o w t h e c r i t i c a l v a l u e , t h e C O P w a s c o n s t a n t a s t h e
e j e c t o r e n t r a i n e d t h e s a m e a m o u n t o f s e c o n d a r y f l ui d .
A c c o r d i ng t o H u a n g e t a l 5 a n d M u n d a y a n d B a g s t e r 9 ,
t h is p h e n o m e n o n m a y h a v e b e e n c a u s e d b y c h o k i n g o f
t h e s e c o n d a r y f lo w w i t h in t h e m i x i n g c h a m b e r . T h e y
e x p l a in e d t h a t , a f t e r e x p a n d i n g t h r o u g h t h e p r i m a r y
n o z z l e , t h e p r i m a r y f l u i d f a n s o u t w i t h o u t m i x i n g w i t h
t h e s e c o n d a r y f u i d . T h i s r e s u l t s i n a n e f f e c t i v e l y
c o n v e r g i n g d u c t f o r t h e s e c o n d a r y f l u i d , t h r o u g h w h i c h
i t i s e n t r a i n e d a n d a c c e l e r a t e d t o s o n i c v e l o c i t y a t s o m e
c r o s s - s e c t io n d e f i n e d a s
a n e f f e c t i v e a r e a
M i x i n g o f t h e
t w o s t r e a m s is t h o u g h t t o b e g i n a f t e r th e s e c o n d a r y f l o w
c h o k e s 9 . W h e n t h e e j e c t o r is o p e r a t e d w i t h s e c o n d a r y
c h o k i n g o r c o n d e n s e r p r e s s u r e b e l o w t h e c r i ti c a l v a l u e , a
t r a n s v e r s e s h o c k t h a t c r e a t e s t h e m a j o r c o m p r e s s i o n
e f f e c t w i ll a p p e a r i n t h e c o n s t a n t - a r e a m i x i n g s e c t i o n .
W h e n t h e c o n d e n s e r p r e s s u r e i s h i g h e r t h a n c r i t i c a l , t h e
t r a n s v e r s e s h o c k t e n d s t o m o v e b a c k o p p o s i t e to th e
d i r e c t i o n o f fl o w ) , a n d t h e s e c o n d a r y f l ui d f lo w r a t e s t a r t s
t o f a l l r a p i d l y t o z e r o .
I f t h e e j e c to r w a s o p e r a t e d w i t h z e r o e n t r a i n m e n t r a t i o
i .e . n o s e c o n d a r y f lu i d w a s e n t r a i n e d ) a n d t h e c o n d e n s e r
p r e s s u r e w a s f u r t h e r i n c r e a s e d , t h i s w o u l d c a u s e a l l t h e
p r i m a r y f l u i d t o r e v e r s e b a c k i n t o t h e e v a p o r a t o r . T h i s
w o u l d b e m a n i f e s t e d e x p e r i m e n t a l l y b y a s u d d e n i n c r e a s e
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A s m a l l - s c a l e s t e a m j e t r e f ri g e r a t o r 8 5
Tab l e 2 Experimental and theoretical performance of a steam jet refrigerator at critical condenser pressure operation
Tableau 2 P e r f o r m a n c e s e . x p & i m e n t a l e s e t t h ~ o r i q u e s d ' l m r t { l H g & a t e . t ) ,j e t d e r a p e l o I o r s d u , l b n c t i o m l e m e n t t 't l a p r es .~ i on c r i t i q u e d u c o n d e n s e u r
Temp (C) Pressure (mbar)
. . . . Calculated a
Eva p Boiler Con dense r Con dense r CO P~.k,. COP,,,~,~ C()Pth,.. area rati o
5.0 120 26.5 34 0.2386 0.4044 0.5081 1(/2
125 27.8 37 0.1971 0.3442 0.4660 I l l
130 30.8 44 0.1566 0.2756 0.3645 109
135 33.4 51 0.1270 0.2513 0.3161 111
140 34.4 54 0.1019 0.1779 0.2765 122
7.5 120 27.3 36 0.3063 0.5004 0.5966 98
125 29.5 41 0.2504 0.4189 0.5052 99
130 31.5 46 0.2070 0.3553 0.4356 103
135 33.4 51 0.1733 0.2965 0.3786 t08
140 35.3 57 0.1383 0.2334 0.3284 114
10.0 120 28.3 38 0.3693 0.5862 0.6849 94
125 30.0 42 0.3276 (I.5374 0.6074 98
130 31.9 47 0.2884 0.4734 0.5299 101
135 34.0 53 0.2365 0.3892 0.4544 104
140 36.3 60 0.1884 0.3093 0.3822 106
a The experimental ejector has an area ratio o f 90. The calculated area ratio is obtained using the theoretical data
I,.,m (,,()
22 26 31) 34 38
0 . 8
0 . 6
( O l
I , 4
(1.2
0.0
n o z z l e e x i t p o s it i o n = 2 6 . 1 5 m m
~
t ~ experimental COPmass)
. ; - 4 . . ~ . I . . . . . t h e o r e t i c a l C O P m a s s )
7 + . . . . . .:
o 4 / . ~ . . . . . /
1 2 0 o . . . 4 . l e , a p
/....,.,,,, , / ~
1 3 0 o ~ 7 . 5 0 C
1 3 5 ~ ~ 5 o C
1 4 0 o C
25 35 45 55 65
l ) O l l n | | ) [ I F )
igure 12 Compa riso n between theoretical COP predictions and
experimental results
Figure 12 C o m p a r a i s o n s e n t r e l e s p r & i s i o n s d u m o d b t e e t l e s r & u l t a t s
d e I ' e s s a i
in temperature due to the hot stream flowing into the
evaporator.
Operation of the sys tem
The tests showed that, at constant evaporator and
condenser pressures, the maximum performance was
achieved when the cycle was operated with such a boiler
temperature that forced the ejector to run at its critical
pressure condition. The performance contour plots
shown in Figures 10 and 11 were protected from the
data at critical condenser pressure operation. An
example of how these plots, together with
Table 1
may
be used for design and optimization applications is as
follows.
The cycle may normally be designed to operate at
point a' with a critical condenser pressure of, say,
45.7mbar. If the condenser pressure fell to 42.5 mbar
owing to a reduction of cooling water temperature while
the boiler and evaporator temperatures stayed the same,
the cycle operating point would move to 'b' with the
COP and the cooling capacity essentially remaining
constant*. This is due to the choking phenomenon o f the
secondary fluid in the mixing chamber when the ejector
discharge pressure is lower than the critical value, as
explained earlier. In order to improve the cycle
performance with such reduction in condenser pressure
(from 45.7 to 42.5mbar), the ejector must be made to
operate at a new critical condition by one of the
following methods.
Constan t cooling capacity lower evaporator temp erature
higher COP. If a boiler temperature reduction from 130
to 127.2C was to accompany the condenser pressure
drop from 45.7 to 42.5 mbar, the cycle operating point
would move to point 'd' (with the critical condition).
This would produce a constant cooling capacity at the
lower evaporator temperature (approximately 7.0 C).
The COP would also be higher, owing to the reduction
in boiler heat input.
Con stant evaporator temperature higher cooling capacity
higher COP.
If the cycle was already operating at point
d', and the boiler temperature was further reduced
from 127.2 to 126.9C, the evaporator temperature
would return to 7.5 C. The cycle operating point would
move to point 'e' (with the critical condition). The COP
and the cooling capacity would rise.
If the condenser pressure rose higher than the design
point (e.g. on a hot day), the ejector would operate in an
unstable condition (with fixed boiler temperature and
cooling load). The ejector would temporarily fail its
function and the evaporator temperature would rise
rapidly, forcing the ejector to establish a new critical
operating condition at the higher condenser pressure.
However, since the cooling load is fixed, the evaporator
temperature would have now dropped, and again the
* If the boiler and evapo rator temperatures were fixed, for any
condenser pressure lower than 45.7mbar, the COP and the cooling
capacity would remain constant as shown by the horizontal lines a-c
on F i g u r e s 1 0 and//. However, the ejector would no longer be at the
critical condition
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3 8 6 I W E a m e s e t a l
e j e c t o r w o u l d t e m p o r a r i l y l o s e it s f u n c t i o n . P o i n t s ' f ' a n d
' g ' s h o w t w o s u c h p o s s i b le o p e r a t i n g c o n d i t i o n s w h e n t h e
c o n d e n s e r p r e s s u r e i s i n c r e a s e d t o 4 . 6 m b a r . B e i n g h i g h e r
t h a n t h e c r i t i c a l v a l u e , n e w c r i t i c a l o p e r a t i o n c o u l d o n l y
b e e s t a b l i s h e d w i t h h i g h e r b o i l e r o r / a n d e v a p o r a t o r
t e m p e r a t u r e s .
C o m p a r i s o n s b e t w e e n e x p e r i m e n t a l a n d t h e o r e t i ca l r es u l ts
T o m a k e a c o m p a r i s o n b e t w e e n t h e o r e t i c a l p e r f o r m a n c e
p r e d i c t i o n s a n d t h e e x p e r i m e n t a l t e s t s , t h e w a t e r
e v a p o r a t i o n r a t e s f r o m t h e b o i l e r a n d t h e e v a p o r a t o r
w e r e m e a s u r e d w i t h t h e c y c l e o p e r a t i n g i n th e s t e a d y
s ta t e. T h e e r r o r s p r o d u c e d b y u n w a n t e d h e a t g a i n s ( a t
t h e e v a p o r a t o r ) a n d l o s s e s ( a t t h e b o i l e r ) i n t h e s y s t e m
w e r e t h u s a v o i d e d . T h e e v a p o r a t i o n r a t e s w e r e o b t a i n e d
b y m e a s u r i n g t h e d r o p o f li q u id v o l u m e i n t h e b o i l e r
a n d e v a p o r a t o r o v e r a f i n it e t i m e i n t e rv a l . T h e c o e f f i c i e n t
o f p e r f o r m a n c e o f t h e e x p e r i m e n t a l c y c le w a s t h e n
c a l c u l a t e d f r o m E q u a t i o n ( 1 5) . T h e r e s u l ts o f t h e t es t s
i n d i c a t e d t h a t t h e a v e r a g e b o i l e r h e a t lo s s w a s a p p r o x i -
m a t e l y 2 5 % a t a l l t e m p e r a t u r e s , a n d t h e a v e r a g e
e v a p o r a t o r h e a t g a i n s w e r e f o u n d t o b e a p p r o x i m a t e l y
2 2 % , 2 0 % a n d 1 8 % a t e v a p o r a t o r t e m p e r a t u r e s o f 5 , 7 .5
a n d 1 0 C r e s p e c t iv e l y . T h u s t h e C O P b a s e d o n e l e c t r ic
p o w e r i n p u t w a s f o u n d t o b e a p p r o x i m a t e l y 6 0 % o f
t h e C O P b a s e d o n e v a p o r a t i o n r a t e s . T h e l a t t e r w a s
o b v i o u s l y u s e d f o r c o m p a r i s o n i n j u d g i n g t h e t h e o r y .
T h e p r e s s u r e l o s s i n t h e s u c t i o n l in e w a s d e t e r m i n e d b y
m e a s u r i n g t h e p r e s s u r e a t t h e i n l e t o f t h e m i x i n g
c h a m b e r . T h e d i f f e r e n c e b e t w e e n t h i s a n d t h e s a t u r a t e d
p r e s s u re i n th e e v a p o r a t o r w a s f o u n d t o b e b e t w e e n 1
a n d 1 .5 m b a r , w h i c h i s e q u i v a l e n t t o a n a v e r a g e p r e s s u r e
l o ss o f 1 2 % . T h e p r e s s u r e l o s s o f t h e p r i m a r y s t e a m w a s
n o t m e a s u r e d d i r e c t l y , b u t i t w a s e s t i m a t e d t h e o r e t i c a l l y
a s a f r i c t io n a l l o s s in a p i p e a s d e s c r i b e d i n a n y s t a n d a r d
l0
f l u id m e c h a n i c s t e x t . S u c h e s t im a t e s i n a v e r a g e p r e s s u r e
l os s o f t h e p r i m a r y s t e a m a m o u n t e d t o a p p r o x i m a t e l y
5 % . T h e s e p r e s s u re l o s s fa c t o r s w e r e t h e n i n c o r p o r a t e d
i n t h e t h e o r e t i c a l c o m p u t e r m o d e l t o e s t i m a t e t h e c y c l e
p e r f o r m a n c e a t c r i ti c al c o n d e n s e r p r e s su r e o p e r a t i o n .
T a b l e 2 a n d F i g u r e 1 2 s h o w c o m p a r i s o n s b e t w e e n t h e
m o d e l p r e d i c t i o n s a n d t h e t e s t r e s u l t s , T h e m e a s u r e d
C O P w e r e f o u n d t o li e b e t w e e n 7 0 a n d 9 0 % ( a v e ra g e
8 3 % ) o f th e t h e o r e t i c a l v a l u e s . T h e o v e r a l l d i s c r e p a n -
c ie s w e r e t h u s n e v e r a b o v e 3 0 % , w h i c h p r o v e d t h a t t h e
o d e l l i n g te c h n i q u e u s e d p r o v i d e d a u s e f u l d e s ig n t o o l f o r
s u c h s y s t e m s . I t i s i m p o r t a n t t o n o t e t h a t t h e m e a s u r e d
d a t a w e r e a lw a y s l o w e r t h a n w h a t t h e t h e o re t i c a l m o d e l
p r e d i c t e d . T h i s p o i n t s c l e a r l y t o t h e p o s s i b i l i t y t h a t
a r e a s s t i l l e x i s t i n t h e m o d e l l i n g w h e r e t o o m u c h
i d e a l i z a t i o n h a s b e e n a s s u m e d . F u r t h e r t u n i n g o f t h e
m o d e l i s t h u s i n v i t e d , a n d s h o u l d p r o v e a n i n t e r e s t i n g
t a s k f o r a f u t u r e i n v e s t i g a t i o n .
C o n c l u s i o n
B o t h t h e t h e o r e t i c a l a n d e x p e r i m e n t a l s t u d i e s o n t h e
s t e a m j e t r e f r ig e r a t o r , c a r ri e d o u t w i t h b o i l e r t e m p e r a t u r e s
b e t w e en 1 2 0 a n d 1 4 0 C , a n d e v a p o r a t o r t em p e r a t u r es
b e t we e n 5 a n d 1 0 C , p r o d u c e d r e s u l ts in wh i c h t h e e f f e ct s
o f v a r io u s p a r a m e t e r s o n t h e o v e r a l l o p e r a t i o n w e r e
c o h e r e n t l y i l l u s t r a te d . Th e o v e r a l l c o e ff i c ie n t o f p e r f o r -
m a n c e o f t h e c y cl e m e a s u r e d e x p e r i m e n t a l l y w as , o n
a v e r a g e , w i t h i n 1 7 % o f t h e t h e o r e t i c a l p r e d i c t i o n s . Su c h
d i s c r e p a n c y w a s n e v e r w o r s e t h a n 3 0 % , e v e n n e a r t h e
o u t e r b o u n d s o f t h e o p e r a t in g r a n g e .
F o r a f i x e d - g e o m e t r y e j e c t o r, t h e c o o l i n g c a p a c i t y w a s
f o u n d t o b e l i m i t e d b y t h e c o n d e n s e r p r e s s u r e , w h i c h
w o u l d i t s e l f b e g o v e r n e d b y t h e a m b i e n t c o n d i t i o n s i n a n
a p p l i c a t i o n . G i v e n s u c h a c o n s t r a i n t , a n d t h e a v a i la b i l i ty
o f a f i x ed b o i l e r p r e s s u r e i n a n a p p l i c a t i o n , t h e c o o l i n g
c a p a c i t y c o u l d b e i m p r o v e d w i t h a h i g h e r s e t e v a p o r a t o r
t e m p e r a t u r e . O n t h e o t h e r h a n d , w i t h lo w e r c o n d e n s e r
p r e s s u r e s , l a r g e r c o o l i n g c a p a c i t y c o u l d b e a c h i e v e d w i t h
e v e n l o w e r b o i l e r p r e s s u r e s .
T h e r e f o r e s m a l l - c a p a c i t y s t e a m j e t r e f r i g e r a t o r s y s -
t e m s m a y b e p r a c t ic a l l y u s ef u l. T h e y c a n b e o p e r a t e d
w i t h l o w - g r a d e h e a t e n e r g y w i t h t h e m o d e s t t e m p e r a t u r e
r a n g e s ( 1 2 0 - 1 4 0 ~ 'C). Th e s y s t e m s a r e s i m p l e t o o p e r a t e
a n d r e l i a b l e , w i t h t w o m e c h a n i c a l p u m p s b e i n g t h e o n l y
m o v i n g p a r t s . H o w e v e r , t h e s y s t e m f l e x i b il i ty a t o f f -
d e s i g n o p e r a t i o n i s l i m i t e d b y t h e p e r f o r m a n c e c h a r -
a c t e r is t i cs o f a n e j e c to r . I f a n e j e c t o r w a s d e s i g n e d w i t h
v a r i a b l e g e o m e t r y ( e . g . c r o s s - s e c t i o n a r e a s a n d n o z z l e
p o s i t i o n ) , t h e c o o l i n g c a p a c i t y c o u l d b e m a d e i n d e p e n d -
e n t o f t h e o p e r a t i n g t e m p e r a t u r e s i n a g i v e n r a n g e .
F i n a l l y , t h e t e s t r e s u l t s b e i n g a l w a y s l o w e r t h a n t h e
t h e o r y p o i n t e d t o t h e n e e d f o r f u r t h e r n o n - i d e a l
p r o c e s s e s t o b e i d e n t i f i e d a n d c a t e r e d f o r i n t h e
m o d e l l i n g . S u c h r e f i n e m e n t s p r o m i s e m o r e a c c u r a t e
a n d p r e c i s e p r e d i c t i o n s , r e s u l t i n g u l t i m a t e l y i n a v e r y
r o b u s t d e s i g n t o o l , w h i c h w o u l d s e r ve t h e i n d u s t r y w e l l.
R e f e r e n c e s
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A S H R A E G u i d e
a n d D a t a B o o k ASH RA E, USA (1969) Ch. 13
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4 Z er en , . Freon-12 vapour compression et pump solar cooling
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5 Hu a n g ,B. J., Jiang, C. B., Hu, F. L. E jector performancechar-
acteristics and d esign analysis of a jet refrigeration system
A SM E J Eng G as T urb ines Power (1985) 107 (July ) 792 802
6 E S D U jectors and jet pum ps Data item 86030, ESD U Interna-
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M e c h (1942) (June) A75 A81
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ejector design by analysis and experimentA S M E J A p p l M e ch
(1950) (Sept) 299 309
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