analysis of stirling engine performance
TRANSCRIPT
899155ANALYSIS OF STIRLING ENGINE PERFORMANCEKazuhiko Kawajiri
,
Michio F u j i w a r a
,
and Takuya Suganami
C e n t r a l Research L a b o r a t o r y , M i t s h u b i s h i E l e c t r i c C o r p o r a t i o n Amagasaki , Hyogo , J a p a n ABSTRACT I n t h e S t i r l i n g engine design ,it i s i m p o r t a n t t o p r e d i c t t h e e n g i n e p e r f o r m a n c e , i.e. , s h a f t power , f u e l i n p u t , n e t t h e r m a l e f f i c i e n c y , etc. u n d e r c o n d i t i o n s d e s c r i b e d by m a i n o p e r a t i n g p a r a m e t e r s s u c h a s mean g a s p r e s s u r e , h e a t e r t u b e t e m p e r a t u r e , e n g i n e speed , etc. I n o r d e r t o c a r r y o u t such engine performance prediction , t h e S t i r l i n g e n g i n e p e r f o r m a n c e s i m u l a t i o n which t a k e s account o f p e r f o r m a n c e o f a b u r n e r , a h e a t exchanger and a d r i v e mechanism i s t o b e developed. This paper presents such engine performance s i m u l a t i o n . I n t h e s i m u l a t i o n , a r e v i s e d 2nd o r d e r a n a l y s i s i s a d o p t e d t o p r e d i c t themodynamic c y c l e by t a k i n g a c c o u n t o f s e v e r a l t h e r m a l l o s s e s . The b u r n e r p e r f o r m a n c e s i m u l a t i o n and t h e m e c h a n i c a l l o s s c a l c u l a t i o n are combined w i t h t h e c y c l e a n a l y s i s . E x p e r i m e n t a l r e s u l t s are a l s o p r e s e n t e d t o c o n f i r m i t s v a l i d i t y . The e x p e r i m e n t a l t e s t s were c a r r i e d o u t t o e x a m i n e t h e d e p e n d e n c y o f t h e e n g i n e p e r f o r m a n c e on s e v e r a l o p e r a t i n g p a r a m e t e r s by 3kW class S t i r l i n g engine. A good a g r e e m e n t was found between t h e s i m u l a t i o n r e s u l t s and t h e e x p e r i m e n t a l ones. ENGINE PERFORMANCE SIMULATION Thermodynamic C y c l e S i m u l a t i o n The thermodynamic c y c l e s i m u l a t i o n model o f t h e d i s p l a c e r t y p e S t i r l i n g e n g i n e i s shown i n Fig.1. T h i s m o d e l i s t h e r e v i s e d o n e o f t h e q u a s i s t e a d y f l o w m o d e l by U r i e l i , e t a l . [ l ] t o t a k e a c c o u n t of t h e s e v e r a l t h e r m a l l o s s e s s u c h as h e a t c o n d u c t i o n l o s s , s h u t t l e l o s s and pumping l o s s and e f f e c t of h e a t t r a n s f e r i n a n e x p a n s i o n s p a c e and a c o m p r e s s i o n one on t h e e n g i n e performance. T h e a s s u m p t i o n s made i n t h e a n a l y s i s a r e a s follows: uniform (1) The i n s t a n t a n e o u s p r e s s u r e i s t h r o u g h o u t t h e s y s t e m and t h e p r e s s u r e d r o p i n t h e h e a t exchanger i s evaluated s e p a r a t e l y from t h e thermodynamic c y c l e s i m u l a t i o n . ( 2 ) The w o r k i n g g a s t e m p e r a t u r e i n t h e e a c h s p a c e e x c e p t t h e r e g e n e r a t o r are uniform and t h e w a l l temperature is constant. (3) The t e m p e r a t u r e d i s t r i b u t i o n s o f t h e w o r k i n g g a s and t h e m a t r i x i n t h e r e g e n e r a t o r are l i n e a r . ( 4 ) The h e a t t r a n s f e r and t h e f l o w f r i c t i o n i n t h e h e a t e r , t h e c o o l e r and t h e r e g e n e r a t o r are e v a l u a t e d by t h e e m p i r i c a l e q u a t i o n s u n d e r t h e steady flow condition. (5) The working g a s s a t i s f i e s t h e p e r f e c t g a s l a w . (6) No l e a k a g e i s a l l o w e d .
Basic e q u a t i o n s a r e d e s c r i b e d under t h e a s s u m p t i o n s . The e n e r g y e q u a t i o n s o f t h e g a s i n a l l t h e c e l l s i n Fig.1 are a s f o l l o w s
rz
ZL
z / d t + d QI o - t A t H v (T, D -T I )+dQ e Cvd(M .T,)/d t=CpT p . p t A .H. (T, -T. ) i -PdV,/dttdQI.,,l/dt__-------_------________________
s
, 3
/dt
(1)
The e q u a t i o n s of c o n t i n u i t y are dMe/dt = dMh/dt = dMrl/dt= dMrz/dt=- i e hi e h i h r l
- i h r l - i r i T z - i r z t -
---------_--____
(2)
i r i r z
dMp/dtdM,/dt
= =
irzp
itc
in.
The e n e r g y e q u a t i o n s o f t h e r e g e n e r a t o r m a t r i x e s a r e g i v e n by
CmM,r idT,r i/dt=A, I H T I (TT1-T, CmM. r z dT, r z /dt=A T z H r z (T r z-T,
r
1)
-------
(3)
r 2)
I n t h e e q u a t i o n s ( 1 ) , t h e terms dQp.,,/dt r e p r e s e n t t h e h e a t losses and t h e y a r e g i v e n byQ e O , , i = Q c n d
(d)
~ ~ , , , ~ = ~ , ,( c e y ) t Q . b t Q p u d
-------------
(4)
Qt
o s ,
3=Qc n d
( C
h d ) tQc
D
d (mx)
where Qp.,.1 is t h e h e a t conduction l o s s a t t h e displacer piston from the expansion space t o t h e c o m p r e s s i o n one , Qt,,,z is t h e h e a t l o s s f r o m t h e e x p a n s i o n a p a c e t o t h e c o o l e r which c o n s i s t s of t h e heat conduction loss a t t h e cylinder l i n e a r , t h e s h u t t l e l o s s and t h e pumping l o s s , Q e o , s 3 is t h e h e a t l o s s from t h e h e a t e r t o t h e c o o l e r which c o n s i s t s of t h e h e a t c o n d u c t i o n l o s s e s a t t h e r e g e n e r a t o r h a u s i n g and t h e m a t r i x . The s h u t t l e l o s s a n d t h e p u m p i n g l o s s a r e e v a l u a t e d by t h e equations a f t e r Martini[2]. The h e a t t r a n s f e r i n t h e h e a t e r and t h e c o o l e r i s e v a l u a t e d by e m p i r i c a l e q u a t i o n s u n d e r t h e s t e a d y f l o w [ 3 ] and t h e h e a t t r a n s f e r i n t h e
2341CH2781-3/89/0000-2341$1.00 1989 IEEE.~
v
-
i
-
HeaterI
Regenerator
Cooler
Fig.2
Temperature d i s t r i b u t i o n i n r e g e n e r a t o r
T h e r e f o r e , i n d i c a t e d works , h e a t f l o w s and i n d i c a t e d e f f i c i e n c y are d e s c r i b e d by t h e f o l l w i n g e q u a t i o n s w h i c h t a k e a c c o u n t of t h e e f f e c t o f t h e p r e s s u r e d r o p on t h e e n g i n e performance. Fig.1 Thermodynamic c y c l e s i m u l a t i o n modelWe =
W, W,Qh
==
$PedVe 9PcdV,
we
t
w,f
r e g e n e r a t o r i s e v a l u a t e d by M i y a b e ' s e q u a t i o n [ 41. Woschni's e q u a t i o n [ 5 ] is a p p l i e d t o t h e h e a t t r a n s f e r i n t h e e x p a n s i o n s p a c e and t h e compression one and i s g i v e n by
= =
$dQb
$APdve/2
----------------
(10)
QE
Nu=0.035Re0. 8
_____----____---__-_______
() 5
The t e m p e r a t u r e s a t i n t e r f a c e s a r e g i v e n by t h e a d j e c e n t u p s t r e a m o n e s and a r e d e f i n e d as follows.Teh
$dQp f $APdVc/2 Q, = $dQe Qc = $dQ, Q,,= W , f Q t 1 , = W,/Q,. Burner Performance S i m u l a t i o n The b u r n e r c o n s i s t s o f a combustor i n which f u e l ( n a t u r a l g a s ) and air are burned on s w i r l s t a b i l i z e d d i f f u s i o n f l a m e and a a i r p r e h e a t e r i n which waste h e a t i s r e c o v e r e d from e x h a u s t g a s t o t h e a i r f o r combustion. The energy f l o w i s shown i n Fig.3. I n t h e b u r n e r p e r f o r m a n c e s i m u l a t i o n i t i s assumed t h a t combustion i s completed i n t h e combustor. The h e a t t r a n s f e r a t t h e h e a t e r i s g i v e n by
=
Te ThT h
(he
b
LO)
(ieb/(VrltVrz)T r z c = Trz-(T,I-Trz)Vrz/(VrifVrz)
(irzt2O)( i r z e