a theoretical and experimental study of a small-scale steam jet refrigerator

7/25/2019 A Theoretical and Experimental Study of a Small-scale Steam Jet Refrigerator

1/9

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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2/9

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

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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 )

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c o n s t a n t a r e a

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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 ~

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secondary flow mi xin~ sectio n

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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


3/9

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 )


4/9

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


5/9


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


6/9

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


7/9


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


8/9

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


9/9


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

1 A S H R A ESteam-jet refrigeration equ ipment

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

2 Stoeeker ,W. F. Refrigeration and Air Conditioning McGraw-

Hill, New Y ork (1959)

3 Ha m m e r ,R. M. An investigation of an ejector-compression

refrigeration cycle and its applications to heating, cooling and

energy conservation Ph D thesis The University of Alabama,

Birmingham, USA (1978)

4 Z er en , . Freon-12 vapour compression et pump solar cooling

systems Ph D thesis Texas A&M University, USA (1982)

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-

tional Ltd, London, UK (1985)

7 Ke ena n, . H., Neumann, E. P. A simpleair ejectorA S M E J A p p l

M e c h (1942) (June) A75 A81

8 Ke ena n . H. Neumann E. P. Lustwerk F. An investigation of

ejector design by analysis and experimentA S M E J A p p l M e ch

(1950) (Sept) 299 309

9 M un da y, . T., Bagster, D. F. A new ejector theory applied to

steam jet refrigeration nd Eng Chem Proe Des Dev (1977 ) 164

442-449

10 Massey,B. S.

Mechanics o f Fluids

6th edn,Van Nostrand Rein-

hold (Internation al) (1989)

a theoretical and experimental study of a small-scale steam jet refrigerator

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