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The performance of a turbocharged spark-ignition engine fuelled with natural gas and gasoline Jones, Alan Llewellyn 1985

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THE PERFORMANCE OF A TURBOCHARGED S P A R K - I G N I T I O N ENGINE F U E L L E D WITH NATURAL GAS AND GASOLINE by ALAN LLEWELLYN JONES B S c , U n i v e r s i t y C o l l e g e C a r d i f f , 1980 A T H E S I S SUBMITTED IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D S C I E N C E i n THE F A C U L T Y OF GRADUATE STUDIES D e p a r t m e n t Of M e c h a n i c a l E n g i n e e r i n g We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE U N I V E R S I T Y OF B R I T I S H COLUMBIA A p r i l 1985 © A l a n L l e w e l l y n J o n e s , 1985 22 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a 2324 M a i n M a l l V a n c o u v e r , C a n a d a V 6 T 1W5 D a t e : A p r i l 2 , 1985 i i A b s t r a c t T h i s t h e s i s p r e s e n t s an i n v e s t i g a t i o n o f t h e i n f l u e n c e o f t u r b o c h a r g i n g on t h e p e r f o r m a n c e a n d c o m b u s t i o n b e h a v i o u r o f a d u a l f u e l l e d , s p a r k - i g n i t i o n e n g i n e f u e l l e d w i t h n a t u r a l g a s a n d g a s o l i n e . T h e i n v e s t i g a t i o n was c a r r i e d o u t u s i n g a c o m b i n a t i o n o f e x p e r i m e n t a l a n d a n a l y t i c a l m e t h o d s . T h e e x p e r i m e n t a l d a t a was o b t a i n e d f r o m an i n s t r u m e n t e d , f o u r c y l i n d e r , T o y o t a e n g i n e m o u n t e d i n a t e s t c e l l . An e l e c t r i c a l l y d r i v e n R o o t s b l o w e r was u s e d t o p r o v i d e c o m p r e s s e d a i r t o t h e e n g i n e , a n d a r e s t r i c t i o n was p l a c e d i n t h e e x h a u s t p i p e t o s i m u l a t e t h e e f f e c t s o f an e x h a u s t - d r i v e n t u r b i n e . C y l i n d e r p r e s s u r e d a t a were r e c o r d e d a n d a n a l y s e d u s i n g a c o m p u t e r r o u t i n e i n o r d e r t o p r o v i d e i n f o r m a t i o n on mass b u r n i n g r a t e s a n d b u r n i n g v e l o c i t i e s . C o m p u t e r r o u t i n e s were a l s o d e v e l o p e d t o s i m u l a t e t h e c o m p r e s s i o n , c o m b u s t i o n a n d e x p a n s i o n p r o c e s s e s i n t h e e n g i n e . I t was f o u n d t h a t t h e l a m i n a r b u r n i n g v e l o c i t y o f n a t u r a l g a s i s 50% t o 60% l o w e r t h a n g a s o l i n e , u n d e r e n g i n e - l i k e c o n d i t i o n s o f t e m p e r a t u r e a n d p r e s s u r e . M a s s - b u r n i n g r a t e a n a l y s e s o f m e a s u r e d c y l i n d e r p r e s s u r e d a t a showed t h a t t h e l o w e r b u r n i n g v e l o c i t y o f n a t u r a l g a s h a s i t s g r e a t e s t i n f l u e n c e d u r i n g t h e i g n i t i o n d e l a y p e r i o d (up t o 1% mass b u r n e d ) a n d t h a t i t c a n c a u s e i n c r e a s e s i n i g n i t i o n d e l a y o f b e t w e e n 50% a n d 100% r e l a t i v e t o g a s o l i n e . I t was o b s e r v e d t h a t t h e low b u r n i n g v e l o c i t y o f n a t u r a l g a s a l s o a f f e c t s t h e m a i n c o m b u s t i o n p e r i o d , b u t t o a much l e s s e r e x t e n t , i n c r e a s i n g i t by up t o 10% r e l a t i v e t o g a s o l i n e . I t was c o n c l u d e d t h a t t h e m a i n c o m b u s t i o n p e r i o d i s d o m i n a t e d by t u r b u l e n c e e f f e c t s a n d " t h a t i t i s r e l a t i v e l y u n a f f e c t e d by v a r i a t i o n s i n f u e l t y p e , a i r / f u e l r a t i o o r b o o s t p r e s s u r e . R e s u l t s f r o m t h e e n g i n e t e s t s a n d s i m u l a t i o n p r o g r a m i n d i c a t e d t h a t i t i s p o s s i b l e t o r e c o v e r t h e power l o s s e x p e r i e n c e d by an e n g i n e r u n n i n g on n a t u r a l g a s by b o o s t i n g t h e i n t a k e p r e s s u r e t o 3 p s i g (20 kPa) a b o v e t h a t p r o v i d e d when t h e e n g i n e i s r u n n i n g on g a s o l i n e . T h i s i n c r e a s e i n b o o s t p r e s s u r e d o e s n o t s i g n i f i c a n t l y r e d u c e t h e e f f i c i e n c y o r r a i s e t h e s p e c i f i c f u e l c o n s u m p t i o n . I t was f o u n d , h o w e v e r , t h a t t h e p e a k c y l i n d e r p r e s s u r e s a t t a i n e d c a n be a s much a s 20% h i g h e r on n a t u r a l g a s t h a n on g a s o l i n e a t t h e same power l e v e l . i v T a b l e o f C o n t e n t s A b s t r a c t i i L i s t o f T a b l e s v i L i s t o f F i g u r e s v i i A c k n o w l e d g e m e n t x N o m e n c l a t u r e x i C h a p t e r I INTRODUCTION 1 C h a p t e r II L I T E R A T U R E REVIEW 5 2.1 I n t r o d u c t i o n 5 2 . 2 N a t u r a l l y A s p i r a t e d E n g i n e P e r f o r m a n c e 5 2 . 3 S u p e r / T u r b o c h a r g e d E n g i n e P e r f o r m a n c e 7 2 . 4 L a m i n a r B u r n i n g V e l o c i t y Of N a t u r a l G a s 9 C h a p t e r I I I EXPERIMENTAL APPARATUS AND PROCEDURE 14 3.1 I n t r o d u c t i o n 14 3 .2 A p p a r a t u s 14 3 . 2 . 1 E n g i n e And Dynamometer 15 3 . 2 . 2 A i r S u p p l y 15 3 . 2 . 3 G a s S u p p l y 16 3 . 2 . 4 G a s M i x e r 16 3 . 2 . 5 B a c k P r e s s u r e 17 3 . 2 . 6 C o o l i n g S y s t e m 17 3 . 2 . 7 I g n i t i o n S y s t e m 17 3 . 3 I n s t r u m e n t a t o n 18 3 . 3 . 1 T o r q u e And S p e e d 18 3 . 3 . 2 A i r F l o w r a t e 18 3 . 3 . 3 G a s F l o w r a t e 18 3 . 3 . 4 T e m p e r a t u r e M e a s u r e m e n t 19 3 . 3 . 5 P r e s s u r e M e a s u r e m e n t 19 3 . 3 . 6 A i r / f u e l R a t i o 19 3 . 3 . 7 In C y l i n d e r P r e s s u r e M e a s u r e m e n t 20 3 . 4 T e s t P r o c e d u r e 21 3 . 4 . 1 U n s u p e r c h a r g e d E n g i n e T e s t s 21 3 . 4 . 2 S u p e r c h a r g e d E n g i n e T e s t s 22 C h a p t e r IV ENGINE PERFORMANCE MODELLING 23 4.1 I n t r o d u c t i o n 23 4 . 2 O t t o C y c l e S i m u l a t i o n P r o g r a m (COMB) 24 4 . 3 C o n s t a n t V o l u m e Bomb S i m u l a t i o n P r o g r a m (BOMB) 26 4 . 4 E n g i n e S i m u l a t i o n P r o g r a m (SIM) 28 4 . 5 P r e s s u r e T r a c e A n a l y s i s P r o g r a m (MB) 32 C h a p t e r V D ISCUSSION OF RESULTS 33 5.1 I n t r o d u c t i o n 33 5 . 2 O t t o C y c l e S i m u l a t i o n R e s u l t s 33 V 5 . 3 E n g i n e T e s t R e s u l t s 35 5 .4 M a s s B u r n i n g R a t e A n a l y s i s R e s u l t s 38 5 . 5 E n g i n e S i m u l a t i o n R e s u l t s 41 C h a p t e r VI CONCLUSIONS 45 BIBLIOGRAPHY 48 APPENDIX A - ENGINE DATA A C Q U I S I T I O N AND A N A L Y S I S 87 a . E n g i n e T e s t D a t a A n a l y s i s 87 b . C a l c u l a t i o n Of E x h a u s t B a c k - P r e s s u r e 88 c . C y l i n d e r P r e s u r e M e a s u r e m e n t 89 APPENDIX B - ENGINE PERFORMANCE DATA 93 APPENDIX C - PROPERTIES OF B . C . NATURAL GAS 99 APPENDIX D - OTTO C Y C L E SIMULATION PROGRAM (COMB) 102 a . I n i t i a l M i x t u r e C o m p o s i t i o n And E n e r g y 102 b . A d i a b a t i c C o m p r e s s i o n Of M i x t u r e 104 c . C o n s t a n t V o l u m e C o m b u s t i o n 105 d . A d i a b a t i c E x p a n s i o n Of P r o d u c t s 108 e . C a l c u l a t i o n Of E f f i c i e n c y And MEP 109 APPENDIX E - CONSTANT VOLUME BOMB SIMULATION PROGRAM (BOMB) 128 a . S u b r o u t i n e ENUFLS 128 b . S u b r o u t i n e TEMP 129 c . S u b r o u t i n e C A L F L S 130 APPENDIX F - ENGINE SIMULATION PROGRAM (SIM) 155 a . I n i t i a l M i x t u r e C o m p o s i t i o n And E n e r g y 155 b . C o m p r e s s i o n Of M i x t u r e 155 c . P r o g r e s s i v e B u r n i n g 156 d . E x p a n s i o n Of P r o d u c t s 158 e . C a l c u l a t i o n Of E f f i c i e n c y A n d M . E . P 158 APPENDIX G - BURNING RATE A N A L Y S I S PROGRAM (MB) 192 APPENDIX H - D E F I N I T I O N OF PROGRAM SYMBOLS 226 v i L i s t o f T a b l e s E n g i n e S p e c i f i c a t i o n s v i i L i s t o f F i g u r e s 1. I g n i t i o n a n d k n o c k l i m i t s f o r m e t h a n e - a i r a n d p r o p a n e -a i r m i x t u r e s v s . c o m p r e s s i o n r a t i o , drawn f r o m [12 ] . . 51 2 . C o m p a r i s o n o f p u b l i s h e d e q u a t i o n s f o r l a m i n a r b u r n i n g v e l o c i t i e s o f n a t u r a l g a s a n d m e t h a n e , c a l c u l a t e d a l o n g an u n b u r n e d g a s i s e n t r o p e 52 3 . C o m p a r i s o n o f p u b l i s h e d e q u a t i o n s f o r l a m i n a r b u r n i n g v e l o c i t i e s o f n a t u r a l g a s , p r o p a n e , o c t a n e a n d i n d o l i n e , c a l c u l a t e d a l o n g an u n b u r n e d g a s i s e n t r o p e . 53 4 . E x p e r i m e n t a l l a y o u t o f e n g i n e , dynamometer a n d a i r c o m p r e s s o r 54 5 . T o y o t a e n g i n e m o u n t e d i n t e s t c e l l 55 6 . W a t e r b r a k e d y n a m o m e t e r 56 7 . W a t e r c o o l i n g t o w e r a n d dynamometer w a t e r s u p p l y 57 8 . R o o t s b l o w e r and f l o w c o n t r o l v a l v e 58 9 . E n g i n e a i r s u p p l y 59 10 . G a s M i x e r a n d t h r o t t l e 60 1 1 . P r i n c i p l e o f o p e r a t i o n o f n a t u r a l g a s m i x e r 61 12 . O p t i c a l p i c k u p a s s e m b l y 62 1 3 . E n g i n e I n s t r u m e n t a t i o n L a y o u t 63 14 . P r e s s u r e t r a n s d u c e r l o c a t i o n i n c y l i n d e r h e a d 64 1 5 . D a t a a c q u i s i t i o n s y s t e m . . . . . . . . . 6 5 16 . M e t h a n e a n d o c t a n e f u e l p e r f o r m a n c e v s . a i r / f u e l r a t i o , a s c a l c u l a t e d by t h e O t t o c y c l e s i m u l a t i o n p r o g r a m (COMB) 66 17 . M e t h a n e a n d o c t a n e f u e l p e r f o r m a n c e v s . r e s i d u a l g a s f r a c t i o n , a s c a l c u l a t e d by t h e O t t o c y c l e s i m u l a t i o n p r o g r a m (COMB) 67 18 . M e t h a n e a n d o c t a n e f u e l p e r f o r m a n c e v s . b o o s t p r e s s u r e , a s c a l c u l a t e d by t h e O t t o c y c l e s i m u l a t i o n p r o g r a m (COMB) 68 v i i i 19. C o m p a r i s o n o f T o y o t a e n g i n e p e r f o r m a n c e on n a t u r a l g a s a n d g a s o l i n e , f r o m 1500 t o 5000 rpm 69 20. V a r i a t i o n o f T o y o t a e n g i n e p e r f o r m a n c e w i t h s p a r k a d v a n c e f o r n a t u r a l g a s a n d g a s o l i n e a t 1500 a n d 3500 rpm 70 21. V a r i a t i o n o f T o y o t a e n g i n e p e r f o r m a n c e w i t h a i r / f u e l r a t i o f o r n a t u r a l g a s , MBT t i m i n g , 2000 rpm 71 22. V a r i a t i o n o f T o y o t a e n g i n e p e r f o r m a n c e w i t h b o o s t p r e s s u r e f o r n a t u r a l g a s , A= 1, MBT t i m i n g , 3000 r p m . 72 23. P e r f o r m a n c e o f T o y o t a e n g i n e w i t h n a t u r a l g a s , t u r b o c h a r g e d , a n d w i t h g a s o l i n e , n a t u r a l l y a s p i r a t e d , v s . e n g i n e s p e e d 7 3 24. V a r i a t i o n o f T o y o t a e n g i n e p e r f o r m a n c e w i t h s p a r k a d v a n c e f o r n a t u r a l g a s u n d e r t u r b o c h a r g e d c o n d i t i o n s , X = 1 , 1 750 rpm 74 25. C o m p a r i s o n o f c y l i n d e r p r e s s u r e , p e r c e n t a g e mass b u r n e d a n d b u r n i n g v e l o c i t y c u r v e s f o r n a t u r a l g a s , A = 1, MBT t i m i n g , 1500, 2000 & 3000 rpm 75 26. C o m p a r i s o n o f c y l i n d e r p r e s s u r e , p e r c e n t a g e mass b u r n e d a n d b u r n i n g v e l o c i t y c u r v e s f o r n a t u r a l g a s , A = 1, 1500 r p m , s p k . a d v . = 15°, 27°, 38° 76 27. Number o f c r a n k a n g l e d e g r e e s a f t e r s p a r k t o v a r i o u s mass b u r n e d f r a c t i o n s v s . s p a r k a d v a n c e f o r n a t u r a l g a s,A= 1 , 1 500 r p m . 77 28. C o m p a r i s o n o f c y l i n d e r p r e s s u r e , p e r c e n t a g e mass b u r n e d a n d b u r n i n g v e l o c i t y c u r v e s f o r n a t . g a s a n d g a s o l i n e , A = 1, MBT t i m i n g , 3000 rpm 78 29. P e r c e n t a g e mass b u r n e d v s . c r a n k a n g l e d e g r e e s a f t e r s p a r k f o n a t u r a l g a s a n d g a s o l i n e , A = 1, MBT t i m i n g , 3000 rpm 79 30. T u r b u l e n t b u r n i n g v e l o c i t y v s . mass f r a c t i o n b u r n e d f o r n a t u r a l g a s a n d g a s o l i n e a t A = 1 , 1500 a n d 3000 rpm 80 31. L a m i n a r b u r n i n g v e l o c i t y a n d ( t u r b u l e n t - l a m i n a r ) b u r n i n g v e l o c i t y v s . mass f r a c t i o n b u r n e d f o r n a t . g a s a n d g a s o l i n e , A = 1, MBT t i m i n g , 3000 rpm 81 32. C o m p a r i s o n o f s i m u l a t i o n p r o g r a m r e s u l t s w i t h mass b u r n r a t e p r o g r a m r e s u l t s f o r o c t a n e a t A= 1, 3000 rpm 82 i x 3 3 . C o m p a r i s o n o f s i m u l a t i o n p r o g r a m r e s u l t s w i t h mass b u r n r a t e p r o g r a m r e s u l t s f o r me thane a t A = 1, 3000 rpm 83 3 4 . S i m u l a t i o n p r o g r a m r e s u l t s f o r methane a t 0 p s i , 3 p s i a n d 6 p s i b o o s t p r e s s u r e s , 1 , 3000 rpm 84 3 5 . C o m p a r i s o n o f p r e s s u r e t r a c e s , mass b u r n i n g r a t e s a n d b u r n i n g v e l o c i t i e s f o r me thane a t 3 p s i b o o s t a n d o c t a n e a t 0 p s i b o o s t , X = 1 , 3000rpm 85 3 6 . C o m p a r i s o n o f p r e s s u r e t r a c e s , mass b u r n i n g r a t e s a n d b u r n i n g v e l o c i t i e s f o r me thane a t 6 p s i b o o s t a n d o c t a n e a t 3 p s i b o o s t , X= 1 , 3000rpm 86 X A c k n o w l e d g e m e n t I w o u l d l i k e t o e x p r e s s my s i n c e r e t h a n k s t o my s u p e r v i s o r D r . R. L . E v a n s f o r h i s h e l p a n d e n c o u r a g e m e n t t h r o u g h o u t t h e c o u r s e o f t h i s t h e s i s . I w o u l d a l s o l i k e t o t h a n k F r e d G o h a r i a n , J o h n R i c h a r d s , P h i l H u r r e n a n d J o h n H o a r f o r t h e i r h e l p i n t h e c o n s t r u c t i o n a n d r e p a i r o f t h e e x p e r i m e n t a l e q u i p m e n t a n d S e a h o S o n g f o r h i s work on t h e d a t a a c q u i s i t i o n p r o g r a m . F i n a l l y I w o u l d l i k e t o t h a n k my w i f e , C l a r e , f o r h e r a s s i s t a n c e d u r i n g t h e e x p e r i m e n t s a n d f o r t y p i n g t h e t h e s i s . x i N o m e n c l a t u r e A w s u r f a c e a r e a e x p o s e d t o h e a t t r a n s f e r , m 1 a m u l t i p l y i n g c o n s t a n t f o r h e a t t r a n s f e r b r e y n o l d s number i n d e x D e n g i n e b o r e , m E e n e r g y o f c y l i n d e r c o n t e n t s , k J e s p e c i f i c e n e r g y , k J / k g h/ 0 e n t h a l p y o f f o r m a t i o n , k J / k m o l h s p e c i f i c e n t h a l p y , k J / k m o l k t h e r m a l c o n d u c t i v i t y , kW/mK M m o l e c u l a r w e i g h t , k g / k m o l m m a s s , kg N number o f m o l e s P p r e s s u r e , kPa Q h e a t l o s t f r o m c o m b u s t i o n c h a m b e r , k J R u n i v e r s a l g a s c o n s t a n t , k J / k m o l . K Re R e y n o l d s number r r a d i u s o f f l a m e , m Si l a m i n a r b u r n i n g v e l o c i t y , m / s S T t u r b u l e n t b u r n i n g v e l o c i t y , m / s T t e m p e r a t u r e , K U r t u r b u l e n c e i n t e n s i t y m / s V v o l u m e o f c o m b u s t i o n c h a m b e r , m* v s p e c i f i c v o l u m e , m ' / k g x mass f r a c t i o n b u r n e d X n o r m a l i s e d a i r / f u e l r a t i o 0 e q u i v a l e n c e r a t i o x i i Subscripts tot total cylinder contents u unburned gas b burned gas i unburned gas constituent j burned gas constituent g gas w wall f flame 1 previous calculation step 2 current calculation step 1 I. INTRODUCTION A number o f c o u n t r i e s t h r o u g h o u t t h e w o r l d h a v e l a r g e r e s e r v e s o f e n e r g y i n t h e f o r m o f n a t u r a l g a s . One way o f u t i l i z i n g t h i s e n e r g y i s t o p r o v i d e a u t o m o b i l e s w i t h t h e a b i l i t y t o r u n on n a t u r a l g a s a s w e l l a s g a s o l i n e , t h e r e b y r e d u c i n g e x p e n s i v e g a s o l i n e i m p o r t s . N a t u r a l g a s h a s a number o f a d v a n t a g e s o v e r g a s o l i n e a s an e n g i n e f u e l . In p a r t i c u l a r , i t h a s a h i g h o c t a n e number o f a p p r o x i m a t e l y 130 RON c o m p a r e d w i t h 9 2 - 9 5 f o r r e g u l a r g a s o l i n e . I t a l s o p r o d u c e s l o w e r e x h a u s t e m i s s i o n s , t o l e r a t e s l e a n e r a i r / f u e l r a t i o s w i t h o u t m i s f i r i n g , a n d p r o v i d e s e a s i e r s t a r t i n g u n d e r c o l d c o n d i t i o n s . T h e r e a r e , h o w e v e r , two m a j o r d i s i n c e n t i v e s t o c o n v e r t i n g a c a r t o d u a l f u e l o p e r a t i o n . One o f t h e s e i s t h e n e e d t o c a r r y l a r g e , h e a v y , c o m p r e s s e d g a s s t o r a g e t a n k s , and t h e o t h e r i s t h e r e d u c t i o n i n power w h i c h i s e x p e r i e n c e d when s w i t c h i n g f r o m g a s o l i n e t o n a t u r a l g a s . The m a i n r e a s o n s f o r t h i s power l o s s a r e : -a ) t h e d i s p l a c e m e n t o f a i r by t h e g a s e o u s f u e l a n d , b) t h e l o w e r b u r n i n g v e l o c i t y o f n a t u r a l g a s c o m p a r e d t o g a s o l i n e . One p o s s i b l e m e t h o d o f r e g a i n i n g t h i s l o s t power i s t h e u s e o f t u r b o c h a r g i n g , w h i c h i n c r e a s e s t h e d e n s i t y , a n d h e n c e t h e e n e r g y c o n t e n t o f t h e a i r / f u e l m i x t u r e s u p p l i e d t o t h e e n g i n e . T u r b o c h a r g i n g c o u l d t a k e a d v a n t a g e o f t h e h i g h o c t a n e r a t i n g o f n a t u r a l g a s , a l l o w i n g r e a s o n a b l y h i g h b o o s t p r e s s u r e s w i t h o u t t h e n e e d t o r e d u c e c o m p r e s s i o n r a t i o . A 2 t u r b o c h a r g e d d u a l f u e l engine c o u l d t h e r e f o r e be run a t h i g h boost p r e s s u r e when o p e r a t i n g on n a t u r a l gas, and a lower boost p r e s s u r e when o p e r a t i n g on g a s o l i n e , t o a v o i d k n o c k i n g . An exhaust wastegate w i t h two a l t e r n a t i v e s e t t i n g s c o u l d be used t o o b t a i n t h e s e h i g h and low boost p r e s s u r e s . An a d d i t i o n a l b e n e f i t of t u r b o c h a r g i n g r e s u l t s from the f a c t t h a t a t u r b o c h a r g e d g a s o l i n e engine d e l i v e r s up t o 30% more power than i t s n a t u r a l l y a s p i r a t e d e q u i v a l e n t . T h i s c o u l d a l l o w the s i z e of engine i n s t a l l e d i n a v e h i c l e t o be reduced w h i l e m a i n t a i n i n g the same power o u t p u t . The weight saved by u s i n g a s m a l l e r engine would then p a r t i a l l y o f f s e t the e x t r a weight of the n a t u r a l gas s t o r a g e t a n k s . A t u r b o c h a r g e d d u a l f u e l system c o u l d be p a r t i c u l a r l y u s e f u l f o r f l e e t o p e r a t o r s where the l a r g e d i s t a n c e s c o v e r e d by the v e h i c l e s would a l l o w the c o s t b e n e f i t s of r u n n i n g on n a t u r a l gas, t o o f f s e t the i n i t i a l expense of f i t t i n g t u r b o c h a r g e r s . A l t e r n a t i v e l y , advantage c o u l d be taken of the i n c r e a s i n g number of p r o d u c t i o n c a r s which a r e b e i n g i n t r o d u c e d , t h a t a r e a l r e a d y equipped w i t h t u r b o c h a r g e d e n g i n e s . These c o u l d r e a d i l y be c o n v e r t e d t o n a t u r a l gas o p e r a t i o n and f i t t e d w i t h a d u a l s e t t i n g exhaust waste g a t e . W i t h c o r r e c t adjustment i t s h o u l d be p o s s i b l e t o produce a t u r b o c h a r g e d , d u a l f u e l e n g i ne c a p a b l e of p r o v i d i n g the same performance on both n a t u r a l gas and g a s o l i n e . Such a system, however, i n t r o d u c e s a number of q u e s t i o n s r e g a r d i n g the r e l a t i v e boost l e v e l s r e q u i r e d f o r e q u a l power, and c o n c e r n i n g the e f f e c t s on performance of engine o p e r a t i n g 3 p a r a m e t e r s s u c h a s s p a r k t i m i n g a n d a i r / f u e l r a t i o . I t a l s o r a i s e s q u e s t i o n s a b o u t t h e i n c r e a s e i n p e a k e n g i n e p r e s s u r e r e s u l t i n g f r o m t u r b o c h a r g i n g , a n d a b o u t t h e e f f e c t s t h a t v a r i o u s l e v e l s o f b o o s t p r e s s u r e a n d e x h a u s t b a c k p r e s s u r e h a v e on m a s s b u r n i n g r a t e s a n d f l a m e s p e e d s , p a r t i c u l a r l y ' i n t h e c a s e o f n a t u r a l g a s . A l a r g e amoun t o f l i t e r a t u r e i s a v a i l a b l e on t h e p e r f o r m a n c e o f t u r b o c h a r g e d g a s o l i n e e n g i n e s . A s shown i n C h a p t e r 2, h o w e v e r , v e r y l i t t l e i s a v a i l a b l e c o n c e r n i n g t h e p e r f o r m a n c e o f t u r b o c h a r g e d o r s u p e r c h a r g e d , n a t u r a l g a s f u e l l e d e n g i n e s . The o b j e c t i v e o f t h i s t h e s i s i s t h e r e f o r e t o i n v e s t i g a t e t h e e f f e c t s o f t u r b o c h a r g i n g on t h e c o m b u s t i o n o f n a t u r a l g a s i n a s p a r k i g n i t i o n e n g i n e , a n d t o d e t e r m i n e t h e i n f l u e n c e o f v a r i o u s o p e r a t i n g p a r a m e t e r s on e n g i n e p e r f o r m a n c e , u n d e r b o o s t e d c o n d i t i o n s . The i n v e s t i g a t i o n was c a r r i e d o u t u s i n g a c o m b i n a t i o n o f e x p e r i m e n t a l a n d a n a l y t i c a l m e t h o d s . The e x p e r i m e n t a l d a t a w e r e o b t a i n e d by i n s t r u m e n t i n g a f o u r c y l i n d e r T o y o t a e n g i n e m o u n t e d i n a t e s t c e l l . I n i t i a l e x p e r i m e n t s w e r e c o n d u c t e d on g a s o l i n e a n d n a t u r a l g a s , i n o r d e r t o d e t e r m i n e t h e r e l a t i v e p e r f o r m a n c e o f t h e two f u e l s u n d e r n a t u r a l l y a s p i r a t e d c o n d i t i o n s . An e x t e r n a l l y d r i v e n s u p e r c h a r g e r was t h e n c o n n e c t e d t o t h e e n g i n e , a n d a v a l v e p l a c e d i n t h e e x h a u s t s y s t e m t o v a r y t h e b a c k p r e s s u r e . T h i s s y s t e m a l l o w e d more f l e x i b i l i t y i n t h e e x p e r i m e n t s t h a n a t u r b o c h a r g e r s i n c e i t a l l o w e d t h e b o o s t 4 and back p r e s s u r e s t o be v a r i e d i n d e p e n d a n t l y , and made i t p o s s i b l e t o run the engine under both supercharged and s i m u l a t e d t u r b o c h a r g e d c o n d i t i o n s . A p r e s s u r e t r a n s d u c e r was mounted i n the c y l i n d e r head i n o r d e r t o o b t a i n c y l i n d e r p r e s s u r e diagrams, and t h e s e were a n a l y z e d u s i n g computer r o u t i n e s i n o r d e r t o d e t e r m i n e mass b u r n i n g r a t e s and b u r n i n g v e l o c i t i e s . A number of computer programs were a l s o w r i t t e n i n o r d e r t o s i m u l a t e v a r i o u s a s p e c t s of the combustion p r o c e s s , and t h e s e i n c l u d e d a comprehensive engine s i m u l a t i o n program. 5 I I . L I T E R A T U R E REVIEW 2.1 I n t r o d u c t i o n T h i s c h a p t e r r e v i e w s t h e a v a i l a b l e l i t e r a t u r e on t h r e e a s p e c t s o f n a t u r a l g a s f u e l l i n g i n s p a r k i g n i t i o n e n g i n e s . T h e f i r s t s e c t i o n c o n s i d e r s t h e r e l a t i v e p e r f o r m a n c e s o f n a t u r a l - g a s a n d g a s o l i n e - f u e l l e d e n g i n e s o p e r a t i n g u n d e r n a t u r a l l y a s p i r a t e d c o n d i t i o n s . T h e s e c o n d s e c t i o n c o n s i d e r s t h e e f f e c t s o f t u r b o c h a r g i n g a n d s u p e r c h a r g i n g , a n d t h e t h i r d s e c t i o n c o n s i d e r s t h e p r o p e r t i e s o f n a t u r a l g a s a s an e n g i n e f u e l , p a r t i c u l a r l y i t s low l a m i n a r b u r n i n g v e l o c i t y c o m p a r e d w i t h g a s o l i n e . 2 . 2 N a t u r a l l y A s p i r a t e d E n g i n e P e r f o r m a n c e . A number o f a u t h o r s h a v e made c o m p a r a t i v e s t u d i e s o f t h e p e r f o r m a n c e o f s p a r k i g n i t i o n e n g i n e s r u n n i n g on g a s o l i n e a n d n a t u r a l g a s u n d e r n a t u r a l l y a s p i r a t e d c o n d i t i o n s . T h e s e s t u d i e s h a v e p r o v i d e d i n f o r m a t i o n a b o u t t h e r e l a t i v e power l e v e l s , e f f i c i e n c i e s a n d e x h a u s t e m i s s i o n s p r o d u c e d by t h e two f u e l s . S i n g l e c y l i n d e r e n g i n e t e s t s c o n d u c t e d by P e a r c e [ 1 ] , M o o r e [2 ] , B a e t s [3 ] a n d P e r r y e t a l [ 4 ] , a n d m u l t i c y l i n d e r t e s t s by P e a r c e [ 1 ] , G e n s l a k [ 5 ] , a n d E v a n s e t a l [ 6 ] , h a v e shown t h a t be tween 11% a n d 20% o f t h e e n g i n e power i s l o s t when s w i t c h i n g f r o m g a s o l i n e t o n a t u r a l g a s f u e l . T h e a v e r a g e l o s s e x p e r i e n c e d i s a p p r o x i m a t e l y 15%. P e a r c e [1 ] a n d E v a n s e t a l [6 ] a l s o showed t h a t t h e e f f i c i e n c y o f an e n g i n e r u n n i n g on n a t u r a l g a s c a n be a s much a s 5% l e s s t h a n t h e same e n g i n e r u n n i n g on g a s o l i n e . M o s t o f t h e power l o s s (10 o f t h e 15 p e r c e n t a g e p o i n t s ) 6 o c c u r s a s a r e s u l t o f t h e g a s e o u s f u e l o c c u p y i n g 10% o f t h e i n t a k e c h a r g e v o l u m e . The r e s t o f t h e power l o s s , and p e r h a p s most o f t h e e f f i c i e n c y l o s s r e s u l t s f r o m t h e low b u r n i n g v e l o c i t y o f n a t u r a l g a s c o m p a r e d w i t h g a s o l i n e . E v a n s e t a l [6 ] a l s o s h o w e d , h o w e v e r , t h a t t h e b r a k e s p e c i f i c f u e l c o n s u m p t i o n o f an e n g i n e r u n n i n g on n a t u r a l g a s c a n be a s much a s 10% l o w e r t h a n t h e same e n g i n e r u n n i n g on g a s o l i n e . T h i s i s due t o t h e h i g h L o w e r H e a t i n g V a l u e ( L . H . V . ) o f n a t u r a l g a s ( a p p r o x . 4 8 6 0 0 k J / k g ) w h i c h c a u s e s an e n g i n e t o u s e r e l a t i v e l y f e w e r grammes o f f u e l p e r kWh o f e n e r g y o u t p u t t h a n f o r g a s o l i n e w h i c h h a s a c o n s i d e r a b l y l o w e r L . H . V . ( a p p r o x . 4 4 0 0 0 k J / k g ) . E n g i n e s f u e l l e d w i t h n a t u r a l g a s r e q u i r e c o n s i d e r a b l y more s p a r k a d v a n c e t h a n t h o s e f u e l l e d w i t h g a s o l i n e . T h e e x t r a a d v a n c e r e q u i r e d t o o b t a i n MBT (minimum s p a r k a d v a n c e f o r b e s t t o r q u e ) i s t y p i c a l l y 10 d e g r e e s a t w i d e - o p e n -t h r o t t l e , i n c r e a s i n g t o o v e r 20 d e g r e e s more t h a n g a s o l i n e a t p a r t t h r o t t l e . T h i s i n c r e a s e i s r e q u i r e d t o o v e r c o m e t h e s l o w e r b u r n i n g v e l o c i t y o f n a t u r a l g a s . N a t u r a l g a s i s , h o w e v e r l e s s s e n s i t i v e t o c h a n g e s i n i g n i t i o n t i m i n g t h a n g a s o l i n e a n d c a n t o l e r a t e c h a n g e s o f up t o 4 d e g r e e s i n s p a r k a d v a n c e w i t h o u t n o t i c e a b l e c h a n g e s i n p e r f o r m a n c e . (Wong [8 ] a n d E v a n s e t a l [ 6 ] ) . F l e m i n g a n d A l l s u p [7 ] a n d R a s h i d i & M a s s o n d i [9 ] showed t h a t e x h a u s t e m i s s i o n s a r e r e d u c e d when b u r n i n g n a t u r a l g a s i n s t e a d o f g a s o l i n e . T h e l a r g e s t r e d u c t i o n o c c u r s f o r h y d r o c a r b o n s ( a p p r o x i m a t e l y 50% l e s s ) a n d n i t r o u s o x i d e s 7 ( a p p r o x i m a t e l y 20% l e s s ) , w h i l e c a r b o n m o n o x i d e e m i s s i o n s a r e a b o u t t h e same f o r b o t h f u e l s . 2 . 3 S u p e r / T u r b o c h a r q e d E n g i n e P e r f o r m a n c e A l t h o u g h t h e p e r f o r m a n c e o f n a t u r a l - g a s - f u e l l e d e n g i n e s o p e r a t i n g u n d e r n a t u r a l l y a s p i r a t e d c o n d i t i o n s h a s b e e n q u i t e w e l l d o c u m e n t e d i n t h e l i t e r a t u r e , t h e s u p e r c h a r g e d o r t u r b o c h a r g e d n a t u r a l g a s e n g i n e h a s r e c e i v e d v e r y l i t t l e a t t e n t i o n . N a t u r a l g a s h a s a much h i g h e r k n o c k l i m i t (RON=130) t h a n g a s o l i n e (RON=95) a n d a number o f a u t h o r s ( P e a r c e [ 1 ] , E n g l e r [ l 0 ] , A f f l e c k , H a r r o w & M i l l s [ 1 1 ] ) h a v e shown t h a t i n c r e a s e d c o m p r e s s i o n r a t i o c a n be u s e d t o r a i s e t h e power o f an e n g i n e f u e l l e d by n a t u r a l g a s a b o v e t h e power o f t h e same e n g i n e r u n n i n g a t t h e k n o c k l i m i t on g a s o l i n e . F i g u r e 1 c o m b i n e s two o f t h e f i g u r e s g i v e n by K a r i m [12 ] a n d shows t h e d r a m a t i c i n c r e a s e i n c o m p r e s s i o n r a t i o p o s s i b l e on n a t u r a l g a s c o m p a r e d w i t h p r o p a n e b e f o r e t h e o n s e t o f k n o c k i n g . ( P r o p a n e h a s a s i m i l a r k n o c k r a t i n g t o h i g h o c t a n e g a s o l i n e , RON=100 ) . F i g u r e 1 a l s o shows t h a t m e t h a n e h a s a g r e a t e r t e n d e n c y t o k n o c k a t s t o i c h i o m e t r i c c o n d i t i o n s t h a n a t i n c e a s i n g l y r i c h o r l e a n m i x t u r e s , w h e r e a s p r o p a n e h a s a g r e a t e r t e n d e n c y t o k n o c x a t r i c h a i r / f u e l r a t i o s . T h e p a p e r by A n n a n d & S u l a i m a n [ 1 3 ] , h o w e v e r , i s t h e o n l y one w h i c h c o n s i d e r s t h e i n f l u e n c e o f t u r b o c h a r g i n g on t h e p e r f o r m a n c e o f a n a t u r a l - g a s - f u e l l e d e n g i n e . T h e s e a u t h o r s i n v e s t i g a t e d t h e p e r f o r m a n c e a n d k n o c k l i m i t s o f me thane i n a s i n g l e c y l i n d e r t e s t e n g i n e w h i c h was s u p p l i e d w i t h c o m p r e s s e d 8 a i r from an e x t e r n a l s o u r c e t o s i m u l a t e t u r b o c h a r g i n g . A r e s t r i c t i o n i n the exhaust was used t o s i m u l a t e the back p r e s s u r e of a t u r b i n e . E x p e r i m e n t s were conducted a t compression r a t i o s of 7.7/1 and 9.5/1 and a t boost p r e s s u r e s of 3, 6 and 9 p s i g (20, 40 & 60 kPa r e s p e c t i v e l y ) and t i m i n g was a d j u s t e d t o knock l i m i t e d spark advance (K.L.S.A.). Engine speed was 920 r e v s / m i n . T e s t s were run by the a u t h o r s a t 7.7/1 compression r a t i o and 6 p s i g boost on methane and propane and i t was found t h a t the mean e f f e c t i v e p r e s s u r e s d e v e l o p e d were 152 p s i g BMEP and 168 p s i g BMEP r e s p e c t i v e l y . T h i s c o r r e s p o n d s t o a d i f f e r e n c e i n power between the two f u e l s of 9.5%, a p p r o x i m a t e l y the same d i f f e r e n c e as would be e x p e c t e d under n a t u r a l l y a s p i r a t e d c o n d i t i o n s . The much h i g h e r knock r e s i s t a n c e of methane, however would a l l o w a boost of 11 p s i g a t 7.7/1 compression r a t i o and under t h e s e c o n d i t i o n s i t was d e t e r m i n e d t h a t the output would be 204 p s i g on methane. I n c r e a s i n g the boost p r e s s u r e on methane t o the knock l i m i t , t h e r e f o r e , a l l o w s an i n c r e a s e i n mean e f f e c t i v e p r e s s u r e over propane of a p p r o x i m a t e l y 20%. At a more r e a l i s t i c c ompression r a t i o of 9.5/1, Annand & Sulaiman found the k n o c k - l i m i t e d boost f o r methane t o be 6 p s i g (40 kPa) a t s t o i c h i o m e t r i c m i x t u r e . As found by Kar i m [ 1 2 ] , maximum knock s e n s i t i v i t y was seen t o occur a t s t o i c h i o m e t r i c c o n d i t i o n s , h i g h e r l e v e l s of boost b e i n g p o s s i b l e w i t h p r o g r e s s i v e l y l e a n or r i c h m i x t u r e s . I t seems p o s s i b l e , t h e r e f o r e , t o r e g a i n the power l o s t when s w i t c h i n g from g a s o l i n e t o n a t u r a l gas by i n c r e a s i n g t h e 9 boost l e v e l i n a t u r b o c h a r g e d engine by a r e l a t i v e l y s m a l l amount, and t h a t f u r t h e r i n c r e a s e s i n boost a r e p o s s i b l e on n a t u r a l gas b e f o r e k n o c k i n g i s en c o u n t e r e d . 2.4 Laminar B u r n i n g V e l o c i t y Of N a t u r a l Gas I t was s t a t e d i n s e c t i o n 2.2 t h a t a p p r o x i m a t e l y 10% of the power l o s s e x p e r i e n c e d by an engine when s w i t c h i n g from g a s o l i n e t o n a t u r a l gas f u e l was a r e s u l t of a i r d i s p l a c e m e n t by t h e gaseous f u e l . The r e m a i n i n g 5 or more p e r c e n t a g e p o i n t s of power l o s s p r o b a b l y o c c u r as a r e s u l t of the low l a m i n a r b u r n i n g v e l o c i t y of n a t u r a l gas, or r a t h e r i t s main c o n s t i t u e n t , methane . T h i s s e c t i o n p r o v i d e s a comparison of the l a m i n a r b u r n i n g v e l o c i t i e s of n a t u r a l gas, methane, propane, octane and i n d o l e n e under e n g i n e - l i k e c o n d i t i o n s of tem p e r a t u r e and p r e s s u r e . The l a m i n a r b u r n i n g v e l o c i t i e s of n a t u r a l gas and methane (the n a t u r a l gas used i n t h i s s tudy c o n s i s t e d of 94% methane) have been measured by a number of i n v e s t i g a t o r s , t h r e e of whom have d e r i v e d e m p i r i c a l f o r m u l a e f o r t h e v a r i a t i o n of l a m i n a r b u r n i n g v e l o c i t y as a f u n c t i o n of unburned gas p r e s s u r e and t e m p e r a t u r e . The most quoted work i s t h a t of Andrews & B r a d l e y [14] who proposed s e p a r a t e f o r m u l a e f o r the dependence of methane l a m i n a r b u r n i n g v e l o c i t y on unburned gas p r e s s u r e ( P a ) and te m p e r a t u r e ( T M ) -0.5 Sj = 43 P u (at T = 298K ) (1 ) 10 S, = ( 10 + 0 .000371 T u 2 ) ( a t c o n s t a n t P M ) (2) where S, , T M a n d PM h a v e u n i t s o f c m / s , K a n d b a r r e s p e c t i v e l y . In o r d e r t o a p p l y t h e s e f o r m u l a e t o e n g i n e l i k e c o n d i t i o n s where b o t h t h e p r e s s u r e a n d t h e t e m p e r a t u r e a r e v a r y i n g s i m u l t a n e o u s l y , t h e y h a v e b e e n c o m b i n e d t o o b t a i n S, = (10 + 0 .000371 T M 2 ) Pu~°'5 (3) C o m b i n i n g t h e e q u a t i o n s i n t h i s way i s j u s t i f i e d by a g r a p h shown by S h a r m a , A g r a w a l & G u p t a [15 ] w h i c h i n d i c a t e s t h a t t h e r a t e o f i n c r e a s e o f b u r n i n g v e l o c i t y w i t h t e m p e r a t u r e d o e s n o t v a r y w i t h i n c r e a s i n g p r e s s u r e . R y a n & L e s t z [ 16 ] a l s o o b t a i n e d a f o r m u l a f o r t h e v a r i a t i o n o f me thane l a m i n a r b u r n i n g v e l o c i t y w i t h p r e s s u r e a n d t e m p e r a t u r e u s i n g t h e c o n s t a n t v o l u m e bomb m e t h o d t o o b t a i n -0.6Z3 Sj = 9656 P M e x p ( - 2 1 4 5 / T u ) (4) o v e r t h e r a n g e T u = 4 5 0 - 6 0 0 K , P u = 4 - 1 8 b a r . T h e o n l y p a p e r f o u n d w h i c h d e a l s w i t h t h e l a m i n a r b u r n i n g v e l o c i t y o f n a t u r a l ~ g a s was t h a t o f S h a r m a , A g r a w a l & G u p t a [15 ] who o b t a i n e d t h e f o l l o w i n g f o r m u l a e I.68/J& Sj = C^. ( T M / 300 ) f o r 0 < 1.0 (5a) 11 a n d Sj = ( T M / 300 ) f o r 0 > 1.0 (5b) where C*.= - 4 1 8 + 1287 /0 - 1196/0*+ 3 6 O / 0 3 - 15 0 ( l o g P M ) V a l u e s o f l a m i n a r b u r n i n g v e l o c i t y o b t a i n e d f r o m e q u a t i o n s 3 , 4 & 5 a r e p l o t t e d i n f i g u r e 2 v e r s u s u n b u r n e d g a s t e m p e r a t u r e . The p r e s s u r e a t e a c h t e m p e r a t u r e was c a l c u l a t e d by a s s u m i n g i s e n t r o p i c c o m p r e s s i o n f r o m t h e i n i t i a l c o n d i t i o n s o f 1 a t m o s p h e r e a n d 2 9 8 K . I t c a n be s e e n t h a t t h e c u r v e o b t a i n e d u s i n g Ryan & L e s t z ' s e q u a t i o n i s much s t e e p e r t h a n t h e o t h e r t w o , a n d c u r v e s drawn f r o m Ryan & L e s t z ' s r e s u l t s f o r o t h e r f u e l s 1 a l s o show t h i s s t e e p r i s e f r o m a low i n i t i a l v a l u e , v a r y i n g c o n s i d e r a b l y f r o m t h e v e l o c i t i e s p u b l i s h e d by o t h e r a u t h o r s . T h e c u r v e o b t a i n e d f r o m A n d r e w s & B r a d l e y ' s r e s u l t s i n d i c a t e s t h a t t h e . i n c r e a s e i n l a m i n a r b u r n i n g v e l o c i t y w i t h t e m p e r a t u r e i s s t r o n g l y o f f s e t by t h e l a r g e n e g a t i v e p r e s s u r e c o e f f i c i e n t , r e s u l t i n g i n a s l i g h t d e c r e a s e i n l a m i n a r b u r n i n g v e l o c i t y w i t h t h e i n c r e a s i n g p r e s s u r e s a n d t e m p e r a t u r e s r e s u l t i n g f r o m i s e n t r o p i c c o m p r e s s i o n . T h e c u r v e drawn f r o m S h a r m a , A g r a w a l & G u p t a ' s e q u a t i o n s 5a a n d 5b f o r n a t u r a l g a s shows a s l i g h t i n c r e a s e i n l a m i n a r b u r n i n g v e l o c i t y when t e m p e r a t u r e a n d p r e s s u r e a r e i n c r e a s e d a c c o r d i n g t o i s e n t r o p i c c o m p r e s s i o n . B e y o n d 450K ( a p p r o x . 5 b a r ) t h e v e l o c i t y o f n a t u r a l g a s i s i n d i c a t e d t o be g r e a t e r t h a n methane w h i c h c o u l d be a r e s u l t o f t h e a d d i t i o n a l c o m p o n e n t s o f t h e n a t u r a l g a s m i x t u r e c a u s i n g a f a s t e r r e a c t i o n r a t e . 12 A s a r e s u l t o f t h e g e n e r a l a g r e e m e n t b e t w e e n e q u a t i o n s 3 a n d 5 , a n d t h e f a c t t h a t e q u a t i o n s 5 r e p r e s e n t n a t u r a l g a s r a t h e r t h a n m e t h a n e , i t was d e c i d e d t o u s e t h e s e e q u a t i o n s o f S h a r m a , A q r a w a l & G u p t a i n t h i s s t u d y . F i g u r e 3 shows a c o m p a r i s o n o f t h e l a m i n a r b u r n i n g v e l o c i t i e s o f p r o p a n e , o c t a n e a n d i n d o l e n e w i t h n a t u r a l g a s , a g a i n p l o t t e d a l o n g i s e n t r o p e s o f u n b u r n e d g a s t e m p e r a t u r e s a n d p r e s s u r e s . The v a l u e s f o r p r o p a n e , o c t a n e a n d i n d o l e n e were o b t a i n e d u s i n g M e t g h a l c h i & K e e k ' s [17 ] e q u a t i o n s o f t h e f o r m S, » Sj. ( T M / T 0 j"" ( P M / P„ f (6) where s u b s c r i p t 0 r e p r e s e n t s v a l u e s a t 298K a n d 1 a t m . F i g u r e 3 c l e a r l y shows t h a t p r o p a n e , o c t a n e a n d i n d o l e n e h a v e v e r y s i m i l a r v a l u e s o f l a m i n a r b u r n i n g v e l o c i t y u n d e r e n g i n e l i k e c o n d i t i o n s a n d t h a t a l l t h r e e r i s e t o much h i g h e r v a l u e s t h a n n a t u r a l g a s w i t h i n c r e a s i n g t e m p e r a t u r e a n d p r e s s u r e . F o r t h i s work i t was a s s u m e d t h a t t h e e q u a t i o n f o r i n d o l e n e p r o v i d e s t h e b e s t a p p r o x i m a t i o n f o r t h e l a m i n a r b u r n i n g v e l o c i t y o f t h e g a s o l i n e u s e d i n t h e e n g i n e e x p e r i m e n t s , s i n c e i n d o l e n e c o n s i s t s o f a m e a s u r e d b l e n d o f f u e l s r e p r e s e n t a t i v e o f t h e c o n s t i t u e n t s o f g a s o l i n e . F o r i n d o l e n e S / c = 2 5 . 2 c m / s , © C = 2 . 1 9 a n d / 3 = - 0 . 1 3 i n e q u a t i o n 6 . I t c a n be s e e n t h a t t h e t e m p e r a t u r e e x p o n e n t i s g r e a t e r t h a n t h a t f o r n a t u r a l g a s o r m e t h a n e a n d t h a t t h e p r e s s u r e e x p o n e n t h a s a much s m a l l e r n e g a t i v e v a l u e . 13 I t i s c o n c l u d e d f r o m t h e s e c o m p a r i s o n s t h a t t h e l a m i n a r b u r n i n g v e l o c i t y o f n a t u r a l g a s c a n be l e s s t h a n h a l f t h a t o f g a s o l i n e u n d e r s i m i l a r e n g i n e l i k e c o n d i t i o n s . 14 I I I . EXPERIMENTAL APPARATUS AND PROCEDURE 3.1 I n t r o d u c t i o n The aim of the e x p e r i m e n t s was t o p r o v i d e performance d a t a on a n a t u r a l - g a s - f u e l l e d engine o p e r a t i n g under s u p e r c h a r g e d and t u r b o c h a r g e d c o n d i t i o n s . The e n g i n e used was a 4 - c y l i n d e r model 3TC Toyota mounted on a dynamometer s t a n d i n a t e s t c e l l . The s p e c i f i c a t i o n s of the engine a r e g i v e n i n T a b l e 1. The exhaust gas r e c i r c u l a t i o n and e m i s s i o n s c o n t r o l systems were removed f o r the d u r a t i o n of the t e s t s , and the s t a n d a r d g a s o l i n e c a r b u r e t t o r was removed when r u n n i n g supercharged on n a t u r a l gas. I n t a k e a i r boost p r e s s u r e was p r o v i d e d by an e l e c t r i c a l l y d r i v e n Roots b l o w e r , and a b u t t e r f l y v a l v e was i n s t a l l e d i n the exhaust system t o a l l o w the back p r e s s u r e t o be i n c r e a s e d i n o r d e r t o s i m u l a t e the e f f e c t of an exhaust d r i v e n t u r b o c h a r g e r . T h i s system gave g r e a t e r e x p e r i m e n t a l f l e x i b i l i t y than a t u r b o c h a r g e r s i n c e i t a l l o w e d the i n t a k e and exhaust p r e s s u r e s t o be v a r i e d i n d e p e n d e n t l y . I t a l s o a l l o w e d measurements t o be taken under su p e r c h a r g e d as w e l l as t u r b o c h a r g e d c o n d i t i o n s . 3.2 A p p a r a t u s The e x p e r i m e n t a l a p p a r a t u s i s shown s c h e m a t i c a l l y i n f i g u r e 4 and a view of the engine mounted i n the t e s t c e l l i s shown i n f i g u r e 5. 15 3 . 2 . 1 E n g i n e And Dynamometer The T o y o t a e n g i n e was m o u n t e d on a t e s t s t a n d and c o u p l e d t o a M o d e l DA316D Go Power w a t e r - b r a k e d y n a m o m e t e r ( f i g u r e 6 ) . In t h i s t y p e o f i n s t a l l a t i o n t h e power o f t h e e n g i n e i s a b s o r b e d by r o t a t i n g v a n e s p a s s i n g t h r o u g h w a t e r , w h i c h t r a n s m i t s t h e t o r q u e t o s t a t i o n a r y v a n e s i n s i d e t h e dynamometer h o u s i n g . T h e h o u s i n g i s p r e v e n t e d f r o m r o t a t i n g by a s t r a i n g a u g e l o a d c e l l a s s e m b l y w h i c h m e a s u r e s t h e t o r q u e . T h e l o a d a p p l i e d t o t h e e n g i n e i s a f u n c t i o n o f t h e w a t e r l e v e l i n t h e dynamometer a n d t h i s was c o n t r o l l e d by an e l e c t r o - p n e u m a t i c a l l y o p e r a t e d i n t a k e v a l v e l i n k e d t o a l o a d s e t t i n g d i a l i n t h e c o n t r o l r o o m . T o p r o v i d e a s t e a d y w a t e r s u p p l y p r e s s u r e a c o n s t a n t h e a d t a n k a n d e l e c t r i c pump were i n s t a l l e d a s shown i n f i g u r e 7 . 3 . 2 . 2 A i r S u p p l y The i n t a k e a i r f o r t h e e n g i n e was f i r s t d rawn t h r o u g h a f i l t e r a n d l a m i n a r f l o w e l e m e n t i n t o a p u l s e d a m p i n g d r u m , a n d t h e n t o t h e i n t a k e o f t h e r o o t s b l o w e r ( S c h w i t z e r , m o d e l 4504) a s shown i n f i g u r e s 8 a n d 9 . T h e c o m p r e s s e d a i r t h e n f l o w e d i n t o a g a s m i x e r b e f o r e p a s s i n g t h r o u g h t h e t h r o t t l e a n d i n t o t h e e n g i n e . T h e c o m p r e s s o r was d r i v e n a t c o n s t a n t s p e e d by an e l e c t r i c m o t o r , a n d t h e b o o s t p r e s s u r e was c o n t r o l l e d by means o f a b l o w o f f v a l v e w h i c h r e c i r c u l a t e d e x c e s s a i r b a c k t o t h e i n t a k e o f t h e c o m p r e s s o r . When t h e e n g i n e was o p e r a t e d u n d e r n a t u r a l l y a s p i r a t e d c o n d i t i o n s , t h e b l o w o f f v a l v e was o p e n e d w i d e t o a l l o w t h e a i r t o b y p a s s t h e c o m p r e s s o r . 1 6 3 . 2 . 3 G a s S u p p l y The n a t u r a l g a s f o r t h e e n g i n e was drawn f r o m t h e m a i n s s u p p l y a t a p r e s s u r e o f 5 p s i g . I t was t h e n p a s s e d t h r o u g h a l a m i n a r f l o w e l e m e n t b e f o r e e n t e r i n g t h e p r e s s u r e r e g u l a t o r w h i c h r e d u c e d i t t o a p r e s s u r e s l i g h t l y h i g h e r t h a n t h a t o f t h e i n t a k e a i r . A f t e r t h e r e g u l a t o r t h e g a s p a s s e d t h r o u g h a f l o w c o n t r o l v a l v e w h i c h was u s e d t o v a r y t h e a i r / f u e l r a t i o , a n d t h e n t h r o u g h 1 i n c h t u b i n g t o t h e g a s m i x e r . 3 . 2 . 4 G a s M i x e r The m i x e r u s e d was a M o d e l 200 I m p c o , p o s i t i v e -d i s p l a c e m e n t g a s m i x e r ( f i g u r e 1 0 ) . The p r i n c i p l e o f o p e r a t i o n o f t h i s m i x e r i s i l l u s t r a t e d i n f i g . 1 1 drawn f r o m t h e Impco s e r v i c e m a n u a l . A s a i r f l o w i n c r e a s e s , t h e p r e s s u r e t r a n s m i t t e d t o t h e t o p o f t h e d i a p h r a g m i s r e d u c e d w h i c h c a u s e s i t t o r i s e a g a i n s t t h e s p r i n g , t h e r e b y o p e n i n g t h e g a s v a l v e . The s c r e w on t h e s i d e o f t h e b o d y c o n t r o l s i d l e m i x t u r e . T h e s t a g n a t i o n p r e s s u r e o f t h e i n t a k e a i r was s e n s e d by a p r e s s u r e p o r t f a c i n g i n t o t h e f l o w , a n d t h i s was f e d , v i a a b a l a n c e l i n e , t o t h e v e n t o f t h e p r e s s u r e r e g u l a t o r ( s e e f i g u r e 4 ) . T h i s e n s u r e d t h a t t h e g a s p r e s s u r e was k e p t c o n s t a n t r e l a t i v e t o t h e i n t a k e a i r p r e s s u r e . F o r t h e p r e l i m i n a r y t e s t s w h i c h were r u n on n a t u r a l g a s a n d g a s o l i n e u n d e r n a t u r a l l y a s p i r a t e d c o n d i t i o n s , t h e s t a n d a r d g a s o l i n e c a r b u r e t t o r was l e f t i n p l a c e a n d an Impco M o d e l 300 d u a l f u e l m i x e r u s e d t o s u p p l y t h e n a t u r a l g a s . T h i s m i x e r h a s an i n t e r n a l v a l v e w h i c h , when o p e n e d , a l l o w s i n t a k e a i r t o p a s s f r e e l y t h r o u g h t o t h e c a r b u r e t t o r f o r 17 g a s o l i n e o p e r a t i o n . F o r n a t u r a l g a s o p e r a t i o n t h e v a l v e was c l o s e d a n d t h e m i x e r f u n c t i o n e d i n t h e same manner a s t h e M o d e l 200 d e s c r i b e d a b o v e . 3 . 2 . 5 B a c k P r e s s u r e In o r d e r t o i m p o s e a b a c k p r e s s u r e on t h e e n g i n e , a b u t t e r f l y v a l v e was i n s t a l l e d i n t h e e x h a u s t s y s t e m . T h i s a l l o w e d t h e b a c k p r e s s u r e t o be r a i s e d t o a maximum o f 4 p s i g . 3 . 2 . 6 C o o l i n g S y s t e m E n g i n e c o o l i n g was p r o v i d e d by_ t h e c o l u m n shown i n f i g u r e 7 w h i c h m i x e d c o l d , f r e s h w a t e r w i t h t h e w a t e r c i r c u l a t i n g t h r o u g h t h e e n g i n e when t h e t e m p e r a t u r e r o s e a b o v e a g i v e n p r e s e t v a l u e . ( 8 0 ° C f o r a l l e n g i n e t e s t s ) . E n g i n e a n d e x h a u s t c o o l i n g were a l s o a s s i s t e d by t h e u s e o f a f a n m o u n t e d i n t h e t e s t c e l l . 3 . 2 . 7 I g n i t i o n S y s t e m T h e s t a n d a r d e l e c t r o n i c i g n i t i o n f i t t e d t o t h e e n g i n e was a u g m e n t e d by e x t e r n a l c i r c u i t s w h i c h a l l o w e d t h e s p a r k t i m i n g t o be a d j u s t e d r e m o t e l y f r o m t h e c o n t r o l room w h i l e t h e e n g i n e was r u n n i n g . A p a i r o f o p t i c a l s e n s o r s a n d a t o o t h e d w h e e l m o u n t e d on t h e e n g i n e c r a n k s h a f t were u s e d t o g e n e r a t e e l e c t r i c a l p u l s e s e v e r y 2 d e g r e e s o f c r a n k - s h a f t r e v o l u t i o n , t o g e t h e r w i t h t o p a n d b o t t o m d e a d c e n t r e p u l s e s ( s e e f i g u r e 12) . T h e s e p u l s e s were f e d t o e l e c t r o n i c c i r c u i t s , a l o n g w i t h t h e d e s i r e d s p a r k a d v a n c e w h i c h was d i a l e d i n a t t h e c o n t r o l p a n e l . The c i r c u i t s t h e n s e n t a p p r o p r i a t e s i g n a l s t o t h e i g n i t i o n s y s t e m , t o o b t a i n t h e c o r r e c t s p a r k a d v a n c e . 18 3 . 3 I n s t r u m e n t a t o n The i n s t r u m e n t i o n l a y o u t i s shown s c h e m a t i c a l l y i n f i g . 1 3 . 3 . 3 . 1 T o r q u e And S p e e d The e n g i n e t o r q u e was m e a s u r e d u s i n g a s t r a i n gauge l o a d c e l l m o u n t e d on t h e d y n a m o m e t e r h o u s i n g . The s i g n a l s f r o m t h e t r a n s d u c e r were s e n t t o c i r c u i t s i n t h e c o n t r o l room where t h e t o r q u e was p r e s e n t e d on a d i g i t a l d i s p l a y i n u n i t s o f f t . l b s . E n g i n e s p e e d was m e a s u r e d by a s p e e d s e n s o r a t t a c h e d t o t h e m a i n s h a f t o f t h e d y n a m o m e t e r . The s e n s o r c o n s i s t e d o f a 60 t o o t h g e a r a n d m a g n e t i c p i c k u p , d e v e l o p i n g a s i g n a l whose f r e q u e n c y was d i r e c t l y p r o p o r t i o n a l t o e n g i n e s p e e d . T h e s p e e d was d i s p l a y e d on a d i g i t a l m e t e r i n t h e c o n t r o l r o o m . 3 . 3 . 2 A i r F l o w r a t e The a i r f l o w r a t e was m e a s u r e d w i t h a M e r i a m L a m i n a r F l o w I n s t r u m e n t , M o d e l 5 0 M C 2 - 4 F , m o u n t e d on t o p o f t h e p u l s e d a m p i n g drum ( f i g u r e 9 ) . T h e p r e s s u r e d r o p a c r o s s t h e e l e m e n t was r e a d i n i n c h e s o f w a t e r gauge on an i n c l i n e d manometer s i t u a t e d i n t h e c o n t r o l r o o m , a n d t r a n l a t e d t o v o l u m e f l o w r a t e u s i n g t h e c a l i b r a t i o n c h a r t p r o v i d e d . 3 . 3 . 3 G a s F l o w r a t e T h e n a t u r a l g a s f l o w was a l s o m e a s u r e d w i t h a M e r i a m L a m i n a r F l o w E l e m e n t , M o d e l 5 0 M W - 1 . 5 , s i t u a t e d i n t h e g a s l i n e . The p r e s s u r e d r o p , i n i n c h e s o f w a t e r g a u g e , was m e a s u r e d u s i n g a s e c o n d i n c l i n e d manometer i n t h e c o n t r o l r o o m . T h e e l e m e n t was s u p p l i e d w i t h a c a l i b r a t i o n c h a r t f o r a i r a t a t m o s p h e r i c p r e s s u r e , s o c o r r e c t i o n s were made f o r t h e 19 d i f f e r e n t v i s c o s i t y o f n a t u r a l g a s ( s e e A p p e n d i x C) a n d f o r t h e i n c r e a s e d o p e r a t i n g p r e s s u r e o f 5 p s i g . 3 . 3 . 4 T e m p e r a t u r e M e a s u r e m e n t T h e r m o c o u p l e t e m p e r a t u r e s e n s o r s were s i t u a t e d a t t h e f o l l o w i n g l o c a t i o n s : A i r l a m i n a r f l o w e l e m e n t G a s m i x e r E x h a u s t p i p e N a t u r a l g a s l i n e The t e m p e r a t u r e s were r e a d o u t on a d i g i t a l d i s p l a y i n t h e c o n t r o l room i n d e g r e e s F a h r e n h e i t . 3 . 3 . 5 P r e s s u r e M e a s u r e m e n t M e r c u r y m a n o m e t e r s were u s e d t o m e a s u r e t h e f o l l o w i n g p r e s s u r e s : I n t a k e a i r s t a g n a t i o n p r e s s u r e ( b o o s t p r e s s u r e ) I n l e t m a n i f o l d p r e s s u r e E x h a u s t b a c k p r e s s u r e The o v e r p r e s s u r e o f t h e n a t u r a l g a s c o m p a r e d t o t h e i n t a k e a i r was a l s o m o n i t o r e d u s i n g a w a t e r m a n o m e t e r . 3 . 3 . 6 A i r / f u e l R a t i o C o n t r o l o f t h e a i r / f u e l r a t i o was a s s i s t e d by t h e u s e o f a z i r c o n i u m d i o x i d e o x y g e n s e n s o r i n t h e e x h a u s t p i p e . The o u t p u t , o f t h e s e n s o r was f e d t o a d i g i t a l v o l t m e t e r t o i n d i c a t e w h e t h e r t h e e n g i n e was r u n n i n g r i c h ( a p p r o x . 0 . 8 V o l t s ) , s t o i c h i m e t r i c (0 .1 t o 0 . 5 V o l t s ) , o r l e a n ( l e s s t h a n 0.1 V o l t s ) . 20 3.3.7 In C y l i n d e r Pressure Measurement In order to h e l p gain i n f o r m a t i o n about the combustion processes i n the engine, the no. 1 c y l i n d e r was instrumented with a pressure t r a n s d u c e r . The type used was an AVL 8QP500C, water-cooled, p i e z o - e l e c t r i c t r ansducer mounted i n a s t e e l s l e e v e p a s s i n g through the c y l i n d e r - h e a d water j a c k e t (see f i g u r e 14) . The t r a n s d u c e r was recessed one passage diameter as recommended by Benson & Pick [18] to e l i m i n a t e the e f f e c t s of thermal shock. The s i g n a l from the transducer was t r a n s m i t t e d by low noise cable to a K i s t l e r , Model 504, charge a m p l i f i e r and then to a data a c q u i s i t i o n system. T h i s system c o n s i s t e d of a NEFF System 620, a n a l o g u e - t o - d i g i t a l c o n v e r t e r which was connected to a PDP 11/34 mini-computer ( f i g u r e 15). A program was w r i t t e n (see Appendix A) to sample the presure s i g n a l at i n t e r v a l s of one degree crank angle, along with a bottom dead c e n t r e s i g n a l , drawn from one of the o p t i c a l sensors mounted on the toothed wheel at the f r o n t of the engine. The p r e s s u r e s i g n a l was ensemble-averaged by the program over a number of c y c l e s to reduce the e f f e c t s of c y c l e - t o -c y c l e v a r i a t i o n . The averaged p r e s s u r e v a l u e s were then s t o r e d , and l a t e r sent to the main u n i v e r s i t y computer system f o r f u r t h e r a n a l y s i s . 21 3 . 4 T e s t P r o c e d u r e The e x p e r i m e n t s were d i v i d e d i n t o two m a i n s e c t i o n s . F i r s t l y , t h o s e r u n on n a t u r a l g a s a n d g a s o l i n e u n d e r n a t u r a l l y a s p i r a t e d c o n d i t o n s , a n d s e c o n d l y , t h o s e r u n on n a t u r a l g a s u n d e r s u p e r c h a r g e d c o n d i t i o n s . 3 . 4 . 1 U n s u p e r c h a r g e d E n g i n e T e s t s T h e s e t e s t s were c a r r i e d o u t i n o r d e r t o o b t a i n t h e p e r f o r m a n c e c h a r a c t e r i s t i c s o f t h e u n s u p e r c h a r g e d e n g i n e r u n n i n g on g a s o l i n e a n d n a t u r a l g a s . The c o n t r o l a n d m e a s u r e m e n t v a r i a b l e s w e r e : C o n t r o l V a r i a b l e s M e a s u r e m e n t V a r i a b l e s F u e l t y p e T o r q u e E n g i n e S p e e d Power A i r / F u e l r a t i o B . S . F . C . S p a r k t i m i n g B . M . E . P . E f f i c i e n c y A l l t h e t e s t s were r u n a t w i d e o p e n t h r o t t l e u s i n g t h e s t a n d a r d g a s o l i n e c a r b u r e t t o r w i t h a d u a l f u e l g a s m i x e r m o u n t e d on t o p . T h e d a t a r e c o r d e d i n t h e s e t e s t s was p r o c e s s e d u s i n g t h e p r o g r a m D L I S T a s d e s c r i b e d i n A p p e n d i x A , a n d t h e r e s u l t s a r e t a b u l a t e d i n A p p e n d i x B . C y l i n d e r p r e s s u r e r e c o r d s were t a k e n d u r i n g some o f t h e s e e x p e r i m e n t s . 22 3 . 4 . 2 S u p e r c h a r g e d E n g i n e T e s t s T h e s e t e s t s were c o n d u c t e d i n o r d e r t o o b t a i n d a t a on t h e n a t u r a l - g a s - f u e l l e d e n g i n e o p e r a t i n g u n d e r s i m u l a t e d t u r b o c h a r g e d a n d s u p e r c h a r g e d c o n d i t o n s . The c o n t r o l a n d m e a s u r e m e n t v a r i a b l e s i n t h i s s e c o n d s e t o f t e s t s w e r e : C o n t r o l V a r i a b l e s M e a s u r e m e n t V a r i a b l e s E n g i n e s p e e d T o r q u e A i r / f u e l r a t i o Power S p a r k t i m i n g B . S . F . C . B o o s t P r e s s u r e B . M . E . P . B a c k P r e s s u r e I . M . E . P . T h e s e t e s t s were r u n a t w i d e o p e n t h r o t t l e , w i t h t h e g a s o l i n e c a r b u r e t t o r r e m o v e d , a n d t h e d a t a o b t a i n e d was a g a i n p r o c e s s e d u s i n g t h e p r o g r a m D L I S T . T h e p e r f o r m a n c e o f t h e e n g i n e u n d e r s u p e r c h a r g e d c o n d i t i o n s was c o r r e c t e d by s u b t r a c t i n g t h e power w h i c h w o u l d h a v e b e e n a b s o r b e d by t h e b l o w e r , i f i t h a d b e e n d r i v e n d i r e c t l y o f f t h e e n g i n e . T h e p e r f o r m a n c e o f t h e e n g i n e u n d e r s i m u l a t e d t u r b o c h a r g e d c o n d i t i o n s was n o t c o r r e c t e d s i n c e t h e b a c k p r e s s u r e v a l v e a l l o w e d t h e e n g i n e t o s e e t h e same e x h a u s t p r e s s u r e t h a t a t u r b i n e w o u l d h a v e p r o d u c e d . 23 IV. ENGINE PERFORMANCE MODELLING 4.1 I n t r o d u c t i o n T h i s chapter d e s c r i b e s the computer programs which were w r i t t e n i n order to simulate the performance of a turbocharged d u a l - f u e l engine. A program f o r d e r i v i n g mass burning r a t e s and burning v e l o c i t i e s from measured c y l i n d e r pressure data i s a l s o d e s c r i b e d . Four main programs were developed; a) An Otto c y c l e s i m u l a t i o n , which was used to i n v e s t i g a t e d u a l - f u e l o p e r a t i o n without i n t r o d u c i n g the e f f e c t s of d i f f e r e n t burning v e l o c i t i e s (COMB). b) A constant-volume combustion bomb s i m u l a t i o n which allowed the comparison of f u e l s with d i f f e r e n t burning v e l o c i t i e s i n the absence of p i s t o n motion (BOMB). c) A comprehensive spark i g n i t i o n engine s i m u l a t i o n program which combined the previous two programs i n order to simultaneously model most of the f a c t o r s which i n f l u e n c e combustion i n a turbocharged d u a l f u e l engine (SIM). d) A c y l i n d e r p r essure t r a c e a n a l y s i s program, d e r i v e d from the s i m u l a t i o n program, which was used to o b t a i n mass burning r a t e s and burning v e l o c i t i e s from measured pressure curves (MB). Each of these programs are c o n s i d e r e d under separate headings below. 24 4 . 2 O t t o C y c l e S i m u l a t i o n P r o g r a m (COMB) T h i s p r o g r a m was w r i t t e n a s a s t e p t o w a r d s t h e more c o m p r e h e n s i v e e n g i n e m o d e l , a n d p r o v i d e d a m e t h o d f o r c o m p a r i n g t h e p e r f o r m a n c e o f n a t u r a l g a s a n d g a s o l i n e a t v a r i o u s i n t a k e m a n i f o l d p r e s s u r e s a n d a i r / f u e l r a t i o s w i t h o u t i n t r o d u c i n g t h e e f f e c t s o f d i f f e r e n t b u r n i n g v e l o c i t i e s . T h e p r o g r a m i s s t r u c t u r e d i n a s i m i l a r f a s h i o n t o t h a t d e s c r i b e d by B e n s o n & W h i t e h o u s e [19] e x c e p t f o r t h e d i s s o c i a t i o n c a l c u l a t i o n s w h i c h a r e c a r r i e d o u t i n a d i f f e r e n t manner a n d i n c l u d e more r e a c t i o n s . The p r o g r a m a l s o a l l o w s f o r a r e s i d u a l f r a c t i o n t o be i n c l u d e d i n t h e m i x t u r e c o m p o s i t i o n . T h e m a j o r e l e m e n t s o f t h e p r o g r a m a r e a s f o l l o w s : a ) C a l c u l a t i o n o f i n i t i a l m i x t u r e c o m p o s t i o n a n d e n e r g y , g i v e n t h e i n l e t c o n d i t i o n s . b) A d i a b a t i c c o m p r e s s i o n o f t h e m i x t u r e t o T . D . C . c ) C o n s t a n t - v o l u m e a d i a b a t i c c o m b u s t i o n a t T . D . C . i n c l u d i n g up t o s i x d i s s o c i a t i o n r e a c t i o n s . d ) A d i a b a t i c e x p a n s i o n t o B . D . C . e ) C a l c u l a t i o n o f M . E . P . a n d e f f i c i e n c y . T h e p r o g r a m i n p u t s a l l o w f o r v a r i o u s c o m b i n a t i o n s o f f u e l t y p e , i n i t i a l p r e s s u r e a n d t e m p e r a t u r e , c o m p r e s s i o n r a t i o , a i r / f u e l r a t i o , a n d e x h a u s t g a s r e s i d u a l f r a c t i o n . T h e p r o g r a m c a n a l s o be r u n i n two a l t e r n a t i v e m o d e s . T h e f i r s t o f t h e s e a l l o w s t h e c o n s t a n t - v o l u m e a d i a b a t i c c o m b u s t i o n s e c t i o n t o be r u n w i t h o u t c o m p r e s s i o n o r e x p a n s i o n s t r o k e s . T h i s a l l o w s t h e 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 t i n g f r o m 25 c o n s t a n t - v o l u m e c o m b u s t i o n t o be o b t a i n e d f o r a g i v e n s e t o f i n i t i a l c o n d i t i o n s . T h e s e c o n d a l t e r n a t i v e mode a l l o w s f o r t h e c a l c u l a t i o n o f t h e a d i a b a t i c f l a m e t e m p e r a t u r e r e s u l t i n g f r o m c o n s t a n t p r e s s u r e c o m b u s t i o n s t a r t i n g a t s p e c i f i e d i n t i a l c o n d i t i o n s . T h i s was u s e d t o v e r i f y t h e f i n a l p r e s s u r e s o b t a i n e d f r o m t h e BOMB s i m u l a t i o n p r o g r a m d e s c r i b e d b e l o w . A d e t a i l e d d e s c r i p t i o n o f t h e p r o g r a m t o g e t h e r w i t h a f l o w c h a r t a n d l i s t i n g a r e g i v e n i n A p p e n d i x D. T h e p r o g r a m was r u n i n t h e c o n s t a n t - p r e s s u r e c o m b u s t i o n mode t o p r o v i d e v a l u e s o f a d i a b a t i c f l a m e t e m p e r a t u r e f o r c o m p a r i s o n w i t h p u b l i s h e d v a l u e s . T h i s was done i n o r d e r t o c h e c k t h e a c c u r a c y o f t h e d i s s o c i a t i o n s u b r o u t i n e a n d e n e r g y c a l c u l a t i o n s . F l a m e t e m p e r a t u r e a n d s p e c i e s c o n c e n t r a t i o n s were f o u n d t o a g r e e t o w i t h i n 0.5% when c o m p a r e d w i t h v a l u e s f r o m G r a y e t a l [20 ] f o r methane a t s t o i c h i o m e t r i c c o n d i t i o n s . Good a g r e e m e n t was a l s o o b t a i n e d f o r l e a n m i x t u r e s o f m e t h a n e when c o m p a r e d w i t h t h e a d i a b a t i c f l a m e t e m p e r a t u r e v a l u e s g i v e n by K a r i m [ 2 1 ] . T h e p r o g r a m was a l s o c h e c k e d f o r a c c u r a c y i n i t s c o m p l e t e f o r m a g a i n s t t h e r e s u l t s g i v e n by T a y l o r [22 ] f o r o c t e n e a t two d i f f e r e n t c o m p r e s s i o n r a t i o s . T h e v a l u e s o b t a i n e d f o r p e a k p r e s s u r e , peak t e m p e r a t u r e , power a n d e f f i c i e n c y a g r e e d t o w i t h i n one p e r c e n t w i t h t h o s e g i v e n by T a y l o r . 26 4 . 3 C o n s t a n t V o l u m e Bomb S i m u l a t i o n P r o g r a m T h i s p r o g r a m s i m u l a t e s p r o g r e s s i v e b u r n i n g i n e i t h e r a s p h e r i c a l c o m b u s t i o n bomb, o r i n a c h a m b e r h a v i n g t h e same g e o m e t r y a s t h e T o y o t a e n g i n e w i t h f i x e d p i s t o n p o s i t i o n . T h e p r o g r a m was w r i t t e n a s a s t e p t o w a r d t h e c o m p r e h e n s i v e e n g i n e s i m u l a t i o n p r o g r a m , a n d p r o v i d e d a m e t h o d f o r c o m p a r i n g t h e e f f e c t s o f d i f f e r e n t f u e l b u r n i n g v e l o c i t i e s on f l a m e s p e e d a n d c o m b u s t i o n d u r a t i o n i n t h e a b s e n c e o f p i s t o n m o t i o n . T h e p r o g r a m a l s o a l l o w e d t h e a c c u r a c y o f t h e p r o g r e s s i v e b u r n i n g s e c t i o n o f t h e e n g i n e s i m u l a t i o n p r o g r a m t o be c h e c k e d a g a i n s t p u b l i s h e d d a t a f o r s p h e r i c a l b o m b s . T h e m a i n a s s u m p t i o n s made f o r t h e c o m b u s t i o n a r e t h o s e made by M e t g h a l c h i a n d K e c k [ 2 3 ] , n a m e l y , 1. t h e t h i c k n e s s o f t h e f l a m e f r o n t i s n e g l i g i b l e a n d s e p a r a t e s t h e b u r n e d g a s f r a c t i o n , x , a t t h e r m o -d y n a m i c e q u i l i b r i u m , f r o m t h e u n b u r n e d g a s f r a c t i o n ( 1 - x ) . 2 . t h e p r e s s u r e i s u n i f o r m t h r o u g h o u t t h e bomb. 3 . t h e f l a m e f r o n t i s s m o o t h a n d e x p a n d s r a d i a l l y f r o m t h e s p a r k p l u g . 4 . t h e u n b u r n e d g a s i s i s e n t r o p i c a l l y c o m p r e s s e d . 5 . t h e h e a t l o s s i s n e g l i g i b l e . T h e s i m u l a t i o n p r o c e e d s by c o n s i d e r i n g s m a l l t i m e s t e p s , i n c r e m e n t i n g t h e p r e s s u r e a t e a c h t i m e s t e p u n t i l t h e f o l l o w i n g s e t o f e q u a t i o n s i s s a t i s i f i e d : F r o m t h e a s s u m p t i o n o f i s e n t r o p i c c o m p r e s s i o n o f t h e u n b u r n e d g a s 27 P l v u l = P 2 v u 2 . . . . ( 7 ) A s s u m i n g i d e a l g a s b e h a v i o u r P v u = M U R T u (8) and P v b = M b R T h (9) From t h e c o n s e r v a t i o n o f mass a n d e n e r g y E t o t / m t o t = x e b + ( 1 - x ) e u (10) v t o t / m t o t = x v b + ( 1 - x ) v u (11) A l s o , f r o m e = h - P v , a s d e r i v e d i n Van Wy len & S o n n t a g [24 ] e u = IN^HH + ( h T u i - h T o i ) - RT) / m u . . . . ( 1 2 ) e b = E N j C h f j + ( h T b j - h T o j ) - RT) / m b . . . . ( 1 3 ) In a d d i t i o n t o t h e s e t h e r m o d y n a m i c r e l a t i o n s h i p s , t h e l a m i n a r b u r n i n g v e l o c i t y i s g i v e n by s c a l c = "tot • x / { / V V { 1 4 ) and t h e bomb p r e s s u r e i s i n c r e m e n t e d u n t i l t h i s c a l c u l a t e d b u r n i n g v e l o c i t y ( S c a - | c ) , e q u a l s t h e ' t r u e ' l a m i n a r b u r n i n g v e l o c i t y ( s t r u e ^ ' o b t a i n e d u s i n g t h e e x p r e s s i o n s g i v e n by M e t g h a l c h i a n d Keck [17 ] f o r p r o p a n e , o c t a n e , a n d i n d o l e n e , and by S h a r m a , A g r a w a l a n d G u p t a [15 ] f o r n a t u r a l g a s . F u l l d e t a i l s o f t h e c a l c u l a t i o n p r o c e d u r e u s e d , t o g e t h e r w i t h a f l o w c h a r t a n d p r o g r a m l i s t i n g a r e g i v e n i n A p p e n d i x E . T h e a c c u r a c y o f t h e p r o g r a m was c h e c k e d by r u n n i n g i t on p r o p a n e u n d e r t h e same i n i t i a l c o n d i t i o n s a s t h o s e g i v e n by M e t g h a l c h i a n d Keck [ 2 3 ] . ' F o r an i n i t i a l p r e s s u r e o f 101 .3 kPa a n d an i n i t i a l t e m p e r a t u r e o f 298K a t s t o i c h i o m e t r i c a i r / f u e l r a t i o , t h e peak p r e s s u r e s a n d t i m e s t o p e a k p r e s s u r e w e r e : -28 M e t g h a l c h i & K e c k ( E x p e r i m e n t a l ) BOMB S i m u l a t i o n P r o g r a m Peak P r e s s u r e 9 . 3 4 b a r 9 . 6 4 b a r 3 . 0 T i m e t o Peak P r e s s u r e : 3 9 . 0 msec 3 9 . 2 msec 0 . 5 T h e s e r e s u l t s d e m o n s t r a t e d t h e a c c u r a c y o f t h e p r o g r a m , a n d t h e s m a l l d i s c r e p a n c y i n t h e p r e s s u r e v a l u e s m i g h t be due t o t h e f a c t t h a t h e a t t r a n s f e r was n o t a c c o u n t e d f o r i n t h e s i m u l a t i o n p r o g r a m . 4 . 4 E n g i n e S i m u l a t i o n P r o g r a m (SIM) T h i s p r o g r a m s i m u l a t e s c o m b u s t i o n i n one o f t h e c y l i n d e r s o f t h e T o y o t a e n g i n e u s e d f o r t h e e x p e r i m e n t s . I t was w r i t t e n t o i n v e s t i g a t e t h e e f f e c t s o f v a r y i n g e n g i n e o p e r a t i n g p a r a m e t e r s , p a r t i c u l a r l y t h o s e w h i c h c o u l d n o t be r e a d i l y a l t e r e d i n t h e e x p e r i m e n t s . T h i s p r o g r a m t a k e s t h e i n i t i a l m i x t u r e c o m p o s i t i o n a n d e n e r g y c a l c u l a t i o n s , t o g e t h e r w i t h t h e c o m p r e s s i o n a n d e x p a n s i o n s t r o k e c a l c u l a t i o n s d e v e l o p e d f o r t h e O t t o c y c l e s i m u l a t i o n ( C O M B ) , a n d a d d s a p r o g r e s s i v e b u r n i n g s e c t i o n b a s e d on t h e m e t h o d u s e d i n t h e BOMB s i m u l a t i o n p r o g r a m . The m a j o r e l e m e n t s o f t h e p r o g r a m a r e a s f o l l o w s : a ) C a l c u l a t i o n o f i n i t i a l m i x t u r e c o m p o s i t i o n a n d e n e r g y , g i v e n t h e i n l e t c o n d i t i o n s ; b) C o m p r e s s i o n o f t h e m i x t u r e up t o t h e s p a r k a d v a n c e a n g l e ; c ) P r o g r e s s i v e b u r n i n g o f t h e m i x t u r e t h r o u g h 29 T . D . C . t o t h e e n d o f c o m b u s t i o n ; d) E x p a n s i o n o f t h e p r o d u c t s o f c o m b u s t i o n t o B . D . C . ; e ) C a l c u l a t i o n o f mean e f f e c t i v e p r e s s u r e a n d e f f i c i e n c y ( n o t i n c l u d i n g i n t a k e a n d e x h a u s t s t r o k e s ) . T h e p r o g r a m p r o c e e d s t h r o u g h t h e s e s e c t i o n s , c a l c u l a t i n g p r o p e r t i e s a t e v e r y 2 d e g r e e s o f c r a n k a n g l e r e v o l u t i o n . A s i n t h e c a s e o f t h e O t t o c y c l e s i m u l a t i o n , t h e i n p u t s t o t h e p r o g r a m a l l o w f o r d i f f e r e n t c o m b i n a t i o n s o f f u e l t y p e , a i r / f u e l r a t i o , c o m p r e s s i o n r a t i o , a n d e x h a u s t g a s r e s i d u a l f r a c t i o n . . The p r o g r e s s i v e b u r n i n g s e c t i o n o f t h e p r o g r a m i s b a s e d on t h e same a s s u m p t i o n s u s e d i n t h e BOMB s i m u l a t i o n p r o g r a m , e x c e p t t h a t h e a t t r a n s f e r t o t h e c y l i n d e r w a l l s i s now a c c o u n t e d f o r . T h e c o m b u s t i o n c h a m b e r i s a g a i n s e p a r a t e d i n t o b u r n e d a n d u n b u r n e d z o n e s s e p a r a t e d by a s p h e r i c a l l y e x p a n d i n g f l a m e f r o n t . T h i s a s s u m p t i o n i s j u s t i f i e d i n t h e c a s e o f t h e T o y o t a e n g i n e w h i c h h a s a . h e m i s p h e r i c a l c o m b u s t i o n c h a m b e r w i t h no d e l i b e r a t e l y i n d u c e d s q u i s h o r s w i r l . T h e a s s u m p t i o n i s a l s o s u p p o r t e d by K o z u k a e t a l [ 25 ] who show p h o t o g r a p h s o f s p h e r i c a l l y e x p a n d i n g f l a m e f r o n t s , t a k e n i n s i d e a c y l i n d e r h a v i n g a s i m i l a r h e m i s p h e r i c a l h e a d t o t h e T o y o t a e n g i n e . T h e i r p i c t u r e s were g e n e r a t e d u s i n g a m i c r o c o m p u t e r w h i c h a v e r a g e d v i d e o c a m e r a r e c o r d s o v e r a l a r g e number o f c y c l e s . A f t e r e a c h c r a n k a n g l e s t e p , t h e same s e t o f e q u a t i o n s ( 7 - 1 4 ) a s u s e d i n t h e BOMB s i m u l a t i o n p r o g r a m a r e s o l v e d . 3 0 H o w e v e r , s i n c e p i s t o n m o t i o n h a s t o be a c c o u n t e d f o r , t h e t o t a l v o l u m e ( V t o t ) a n d t o t a l e n e r g y ( E t 0 t ) n o w v a r y w i t h c r a n k a n g l e f r o m one t i m e s t e p t o t h e n e x t . T h e v o l u m e c h a n g e i s e a s i l y c a l c u l a t e d f r o m t h e c h a n g e o f p i s t o n p o s i t i o n o v e r t h e c r a n k a n g l e i n c r e m e n t . T h e c h a n g e i n t h e t o t a l e n e r g y o f t h e s y s t e m i s o b t a i n e d by c o n s i d e r i n g t h e 1s t Law f o r a c o n t r o l mass w h i c h i n c l u d e s a l l t h e c y l i n d e r c o n t e n t s E t o t 2 - E t o t l " P dV + dQ . . . . ( 1 5 ) Where P dV r e p r e s e n t s t h e work done a s a r e s u l t o f p i s t o n m o t i o n , a n d dQ r e p r e s e n t s t h e h e a t t r a n s f e r e d t o t h e w a l l s o f t h e c o m b u s t i o n chamber f r o m t h e b u r n t g a s e s , a s c a l c u l a t e d u s i n g t h e h e a t t r a n s f e r e q u a t i o n g i v e n by A n n a n d [26 ] d Q / d t = A „ a ( k / D ) (Re)** ( T t - T^ ) (16) where A ^ = a r e a o f p i s t o n a n d c y l i n d e r e n c l o s i n g b u r n e d m i x t u r e , k = t h e r m a l c o n d u c t i v i t y o f b u r n e d m i x t u r e , D = c y l i n d e r b o r e , Re = R e y n o l d s number = ( mpv . D ) / ( v- . / * ) , a & b = c o n s t a n t s ( 0 . 8 a n d 0 .7 r e s p e c t i v e l y ) , Tj, = b u r n e d g a s t e m p e r a t u r e , T w = w a l l t e m p e r a t u r e ( 450K ) . mpv = mean p i s t o n v e l o c i t y ( m / s ) . H e a t i s o n l y c o n s i d e r e d t o be t r a n s f e r e d f r o m t h e b u r n t g a s r e g i o n s i n c e t h i s i s o f t h e o r d e r o f 10 t o 15 t i m e s t h e amount t r a n s f e r e d f r o m t h e u n b u r n e d g a s e s , and a l l o w s t h e 31 a s s u m p t i o n o f i s e n t r o p i c c o m p r e s s i o n o f t h e u n b u r n e d m i x t u r e t o be m a i n t a i n e d . T h i s t e c h n i q u e was u s e d by P a t t e r s o n & Van W y l e n [27] a n d was j u s t i f i e d by t h e a s s u m p t i o n t h a t t h e h e a t l o s t f r o m t h e u n b u r n e d r e g i o n t o t h e w a l l s i s made up by h e a t t r a n s f e r f r o m t h e b u r n e d g a s r e g i o n t o t h e u n b u r n e d r e g i o n . A l s o e r r o r s r e s u l t i n g f r o m t h i s a s s u m p t i o n a r e s m a l l c o m p a r e d t o t h e e r r o r a s s o c i a t e d w i t h t h e d e t e r m i n a t i o n o f t h e w a l l h e a t t r a n s f e r c o e f f i c i e n t . The l a m i n a r b u r n i n g v e l o c i t y e q u a t i o n s u s e d i n t h e p r o g r a m a r e t h o s e g i v e n by M e t g h a l c h i & K e c k [17 ] f o r o c t a n e , i n d o l i n e a n d p r o p a n e , a n d by Sharma A g r a w a l & G u p t a [15 ] f o r n a t u r a l g a s . V a l u e s f o r t h e t u r b u l e n t b u r n i n g v e l o c i t y were o b t a i n e d by u s i n g t h e r e l a t i o n a s s u m e d by M a t t a v i [ 3 2 ] : Sr = Sj + C U T . . . . ( 1 7 ) where S T = t u r b u l e n t b u r n i n g v e l o c i t y ; Sy = l a m i n a r b u r n i n g v e l o c i t y ; C = g i v e n f u n c t i o n f o r a g i v e n e n g i n e ; u r = t u r b u l e n c e i n t e n s i t y . V a l u e s o f t h e f u n c t i o n Cu a t v a r i o u s e n g i n e s p e e d s were o b t a i n e d f r o m t h e e n g i n e t e s t r e s u l t s p r o c e s s e d by t h e mass b u r n i n g r a t e a n a l y s i s p r o g r a m d e s c r i b e d i n t h e n e x t s e c t i o n . T y p i c a l c u r v e s o f Cu-,- ( = S-r-Sj ) v e r s u s mass f r a c t i o n b u r n e d a r e g i v e n i n f i g u r e 3 1 . D e t a i l s o f t h e c a l c u l a t i o n p r o c e d u r e u s e d a r e g i v e n i n A p p e n d i x F , t o g e t h e r w i t h a f l o w c h a r t a n d p r o g r a m l i s t i n g . 3 2 4 . 5 P r e s s u r e T r a c e A n a l y s i s P r o g r a m (MB) T h i s p r o g r a m was d e v e l o p e d i n o r d e r t o o b t a i n mass b u r n i n g r a t e s , f l a m e s p e e d s , a n d b u r n i n g v e l o c i t i e s f rom t h e m e a s u r e d c y l i n d e r p r e s s u r e r e c o r d s . The p r o g r a m i s i d e n t i c a l t o t h e s i m u l a t i o n p r o g r a m d e s c r i b e d a b o v e , e x c e p t f o r t h e f a c t t h a t i n t h i s c a s e , t h e p r e s s u r e a t e a c h c r a n k a n g l e i n c r e m e n t i s g i v e n i n t h e i n p u t f i l e . T h e c o m p r e s s i o n s t r o k e c a l c u l a t i o n s s i m p l y p r o v i d e t h e e n e r g y and t e m p e r a t u r e o f t h e m i x t u r e r e s u l t i n g f r o m s o l u t i o n o f t h e 1 s t Law a n d I d e a l G a s Law e q u a t i o n s . T h e p r o g r e s s i v e b u r n i n g s e c t i o n o f t h e p r o g r a m f o l l o w s t h e same s e q u e n c e a s t h a t u s e d i n t h e s i m u l a t i o n , i n w h i c h t h e e q u a t i o n s 7 t o 14 a r e s o l v e d a t e a c h c r a n k a n g l e s t e p . T h e d i f f e r e n c e b e i n g t h a t t h e i t e r a t i o n p r o c e d u r e w h i c h makes t h e ' t r u e ' b u r n i n g v e l o c i t y ^ s t r u e ^ e q u a l t o t h e ' c a l c u l a t e d ' b u r n i n g v e l o c i t y ( s c a i c ) i s n o l o n g e r r e q u i r e d , s i n c e t h e p r e v i o u s l y unknown p r e s s u r e i s now g i v e n a s an i n p u t . The p r o g r e s s i v e b u r n i n g r o u t i n e p r o v i d e s v a l u e s a t e a c h c a l c u l a t i o n s t e p o f : mass f r a c t i o n b u r n e d , v o l u m e f r a c t i o n b u r n e d , f l a m e s p e e d , b u r n i n g v e l o c i t y and b u r n e d a n d u n b u r n e d g a s t e m p e r a t u r e s . F u l l d e t a i l s o f t h e a s s u m p t i o n s made i n t h e p r o g r a m a n d t h e c a l c u l a t i o n p r o c e d u r e u s e d a r e g i v e n i n A p e n d i x G t o g e t h e r w i t h a p r o g r a m l i s t i n g a n d f l o w c h a r t . A l i s t c o n t a i n i n g d e f i n i t i o n s o f a l l t h e s y m b o l s u s e d i n t h e a b o v e f o u r p r o g r a m s i s g i v e n i n A p p e n d i x H . 33 V. DISCUSSION OF RESULTS 5.1 I n t r o d u c t i o n T h i s c h a p t e r p r e s e n t s and d i s c u s s e s the r e s u l t s o b t a i n e d from the Toyota engine e x p e r i m e n t s and from the c a l c u l a t i o n p r o c e d u r e s which were d e s c r i b e d i n the p r e v i o u s c h a p t e r . The f i r s t s e c t i o n d i s c u s s e s the r e s u l t s o b t a i n e d from the O t t o c y c l e s i m u l a t i o n program (COMB) run a t a . v a r i e t y of d i f f e r e n t i n l e t c o n d i t i o n s . The second s e c t i o n p r e s e n t s the engine performance t e s t r e s u l t s o b t a i n e d from r u n n i n g the Toyota on n a t u r a l gas and g a s o l i n e under n a t u r a l l y - a s p i r a t e d , and t u r b o c h a r g e d c o n d i t i o n s . The t h i r d s e c t i o n d i s c u s s e s t h e r e s u l t s o b t a i n e d from the mass-burning- r a t e a n a l y s i s program (MB) run w i t h a number of p r e s s u r e t r a c e i n p u t s o b t a i n e d d u r i n g the engine t e s t s . The f o u r t h and l a s t s e c t i o n d i s c u s s e s the r e s u l t s of r u n n i n g t h e engine s i m u l a t i o n program (SIM) a t h i g h i n l e t p r e s s u r e s , c a l i b r a t e d w i t h the r e s u l t s from the mass b u r n i n g r a t e a n a l y s i s program. 5.2 O t t o C y c l e S i m u l a t i o n R e s u l t s T h i s s e c t i o n d e a l s w i t h the c o m p a r a t i v e performance f i g u r e s o b t a i n e d by r u n n i n g t h e O t t o c y c l e s i m u l a t i o n program, COMB, on methane and octane a t v a r i o u s s t a r t i n g c o n d i t i o n s . As d e s c r i b e d i n the p r e v i o u s c h a p t e r the COMB program c a l c u l a t e s the p r e s s u r e s , t e m p e r a t u r e s , IMEP, e f f i c i e n c y and ISFC r e s u l t i n g from i s e n t r o p i c c ompression of a s p e c i f i e d f u e l / a i r m i x t u r e from BDC t o TDC, f o l l o w e d by c o n s t a n t volume 34 c o m b u s t i o n o f t h e m i x t u r e a t T D C , a n d e n d i n g w i t h i s e n t r o p i c e x p a n s i o n b a c k t o B D C . T h i s p r o g r a m a l l o w s t h e c o m p a r i s o n o f d i f f e r e n t f u e l s w i t h o u t i n t r o d u c i n g t h e e f f e c t s o f v a r y i n g b u r n i n g v e l o c i t i e s . A t y p i c a l o u t p u t i s g i v e n i n A p p e n d i x D, a l o n g w i t h a d e t a i l e d d e s c r i p t i o n a n d l i s t i n g . F i g u r e 16 c o m p a r e s t h e O t t o c y c l e p e r f o r m a n c e o f methane a n d o c t a n e f u e l s a t i n c r e a s i n g l y l e a n a i r / f u e l r a t i o s . A t s t o i c h i o m e t r i c c o n d i t i o n s , t h e r e d u c t i o n i n IMEP e x p e r i e n c e d by methane r e l a t i v e t o o c t a n e i s s e e n t o be 10%. T h i s l o s s o f power o c c u r s a s a r e s u l t o f t h e d i s p l a c e m e n t o f a i r by t h e low d e n s i t y m e t h a n e , a n d i s e q u a l t o t h e d i f f e r e n c e i n e n e r g y c o n t e n t p e r u n i t v o l u m e b e t w e e n t h e two f u e l / a i r m i x t u r e s . T h e power l o s s becomes r e l a t i v e l y s m a l l e r w i t h l e a n e r m i x t u r e s , s i n c e t h e d i s p l a c e m e n t o f a i r by t h e low d e n s i t y m e t h a n e becomes l e s s s i g n i f i c a n t . I t c a n a l s o be s e e n i n f i g u r e 16 t h a t t h e e f f i c i e n c i e s o f t h e two f u e l s a r e v e r y s i m i l a r a n d t h a t t h e y b o t h i n c r e a s e w i t h l e a n e r a i r / f u e l r a t i o s due t o t h e c h a n g e s i n t h e s p e c i f i c h e a t r a t i o s o f t h e m i x t u r e s . T h e i n d i c a t e d s p e c i f i c f u e l c o n s u m p t i o n o f m e t h a n e , h o w e v e r , i s a p p r o x i m a t e l y 10% l e s s t h a n o c t a n e a t s t o i c h i o m e t r i c c o n d i t i o n s . T h i s o c c u r s a s a r e s u l t o f t h e h i g h L o w e r H e a t i n g V a l u e o f me thane (50000 k J / k g ) c o m p a r e d w i t h o c t a n e (44788 k J / k g ) . F i g u r e 17 shows t h e e f f e c t s o f i n c r e a s i n g e x h a u s t g a s r e s i d u a l f r a c t i o n on t h e p e r f o r m a n c e s o f m e t h a n e a n d o c t a n e . I t c a n be s e e n t h a t b o t h f u e l s a r e e q u a l l y a f f e c t e d a n d t h a t s u b s t a n t i a l g a i n s i n power c a n be a c h i e v e d by r e d u c i n g t h e 35 r e s i d u a l f r a c t i o n t o a m i n i m u m . The e f f e c t s o f i n c r e a s i n g i n l e t m a n i f o l d p r e s s u r e a n d t e m p e r a t u r e on p e r f o r m a n c e a r e i l l u s t r a t e d i n f i g u r e 18. I t c a n be s e e n t h a t t h e power o u t p u t on b o t h f u e l s r i s e s s h a r p l y w i t h i n c r e a s i n g b o o s t a n d t h a t t h e e f f i c i e n c y a n d f u e l c o n s u m p t i o n c u r v e s r e m a i n a l m o s t c o n s t a n t . I t c a n a l s o be s e e n t h a t t h e i n c r e a s e i n b o o s t p r e s s u r e r e q u i r e d t o o v e r c o m e t h e power l o s s e x p e r i e n c e d by m e t h a n e r e l a t i v e t o o c t a n e i s l e s s t h a n 3 p s i g ( 2 0 k P a ) . F i g u r e 18 d e m o n s t r a t e s t h a t methane r e q u i r e s a p p r o x i m a t e l y t w i c e t h e b o o s t l e v e l o f o c t a n e i n o r d e r t o m a i n t a i n t h e same power o u t p u t i f t h e e f f e c t s o f d i f f e r e n t b u r n i n g v e l o c i t i e s a r e n e g l e c t e d . 5 . 3 E n g i n e T e s t R e s u l t s The f i r s t s e r i e s o f e n g i n e t e s t s were c a r r i e d o u t on g a s o l i n e a n d n a t u r a l g a s u n d e r n a t u r a l l y a s p i r a t e d c o n d i t i o n s . T h e s e p r o v i d e d b a s e l i n e m e a s u r e m e n t s w i t h w h i c h t h e t u r b o c h a r g e d e x p e r i m e n t s c o u l d be c o m p a r e d . A l l o f t h e e x p e r i m e n t s were c o n d u c t e d a t f u l l l o a d w i t h w i d e open t h r o t t l e . F i g u r e 19 shows how t h e p e r f o r m a n c e o f n a t u r a l g a s c o m p a r e s w i t h g a s o l i n e o v e r a r a n g e o f e n g i n e s p e e d s a t X= 1 a n d MBT t i m i n g on n a t u r a l g a s , a n d a t k n o c k - l i m i t e d s p a r k a d v a n c e ( K L S A ) a n d c a r b u r e t t o r - r e g u l a t e d a i r / f u e l r a t i o on g a s o l i n e . T h e BMEP c u r v e s f o r b o t h f u e l s show t h e c h a r a c t e r i s t i c hump i n t h e m i d - s p e e d r a n g e w h i c h i s t h e r e g i o n o f h i g h e s t v o l u m e t r i c e f f i c i e n c y . T h e BMEP d e v e l o p e d by n a t u r a l g a s i s a p p r o x i m a t e l y 14% l e s s t h a n t h a t o f g a s o l i n e 36 c o n f i r m i n g t h e r e s u l t s o f e a r l i e r w o r k e r s a s d i s c u s s e d i n c h a p t e r 2 . T h e e f f i c i e n c y o f n a t u r a l g a s i s s e e n t o be s l i g h t l y l o w e r t h a n g a s o l i n e a b o v e 2500 r . p . m . A t low s p e e d s t h e e f f i c i e n c y o f n a t u r a l g a s i s i n d i c a t e d t o be h i g h e r t h a n g a s o l i n e , h o w e v e r t h i s i s p r o b a b l y a r e s u l t o f t h e r i c h m i x t u r e p r o v i d e d by t h e g a s o l i n e c a r b u r e t t o r a t low s p e e d s . F i g u r e 19 a l s o i n d i c a t e s t h e b r a k e s p e c i f i c f u e l c o n s u m p t i o n o f n a t u r a l g a s t o be l o w e r t h a n g a s o l i n e o v e r most o f t h e s p e e d r a n g e a s was p r e d i c t e d by t h e O t t o C y c l e s i m u l a t i o n r e s u l t s d e s c r i b e d i n t h e l a s t s e c t i o n . The r e d u c t i o n i n BSFC a t 3000 r . p . m . i s a p p r o x i m a t e l y 14%, a n d i s p r i m a r i l y due t o t h e h i g h e r L . H . V . o f n a t u r a l g a s . F i g u r e 20 d e m o n s t r a t e s t h e c h a n g e s i n s p a r k t i m i n g r e q u i r e d t o r u n g a s o l i n e a n d n a t u r a l g a s u n d e r op t imum c o n d i t i o n s . Due t o t h e h i g h o c t a n e r a t i n g o f n a t u r a l g a s , i t was p o s s i b l e t o a d j u s t t h e s p a r k t i m i n g f r e e l y w i t h o u t e n c o u n t e r i n g k n o c k . T h i s a l l o w e d t h e e n g i n e t o be r u n a t min imum a d v a n c e f o r b e s t t o r q u e (MBT) t i m i n g . A t t h e 9:1 c o m p r e s s i o n r a t i o o f t h e T o y o t a e n g i n e , h o w e v e r , t h e g a s o l i n e f u e l u s e d (RON=95) c a u s e d k n o c k i n g when t h e s p a r k was a d v a n c e d t o o f a r . The o p t i m u m t i m i n g f o r g a s o l i n e f u e l was t h e r e f o r e K L S A . A l t h o u g h i t c a n be s e e n t h a t a t h i g h e r s p e e d s , ( a b o v e 3000 r . p . m . ) i t was p o s s i b l e t o a d v a n c e t h e s p a r k q u i t e c l o s e t o MBT t i m i n g . F i g u r e 21 shows t h e c h a n g e i n p e r f o r m a n c e o f n a t u r a l g a s w i t h i n c r e a s i n g l y l e a n a i r - f u e l m i x t u r e s . I t c a n be s e e n t h a t 37 t h e BMEP f a l l s o f f a s t h e m i x t u r e becomes more l e a n , a s e x p e c t e d . T h e r e d u c t i o n i n BMEP f r o m X = 1.0 t o X= 1.3 i s a p p r o x i m a t e l y 13% w h i c h i s s i m i l a r t o t h e v a l u e p r e d i c t e d by t h e O t t o C y c l e s i m u l a t i o n p r o g r a m . A l t h o u g h t h e power i s r e d u c e d , i t c a n be s e e n t h a t t h e e f f i c i e n c y r i s e s by a l m o s t 10% a t X = 1.3 a n d t h a t t h e B S F C i s r e d u c e d by a p p r o x i m a t e l y 13%. F i g u r e 22 shows t h e i n f l u e n c e o f i n c r e a s i n g b o o s t p r e s s u r e on n a t u r a l g a s f u e l l e d e n g i n e p e r f o r m a n c e a t 3000 r . p . m . , X= 1 a n d MBT t i m i n g . T h i s t e s t was r u n w i t h t h e R o o t s b l o w e r p r o v i d i n g v a r i o u s l e v e l s o f b o o s t p r e s s u r e , a n d t h e e x h a u s t v a l v e a d j u s t e d t o p r o v i d e a r e a l i s t i c b a c k p r e s s u r e , a s w o u l d be c a u s e d by t h e t u r b i n e o f a t u r b o c h a r g e r ( s e e c a l c u l a t i o n s i n A p p e n d i x A ) . I t c a n be s e e n t h a t BMEP i n c r e a s e s a l m o s t l i n e a r l y w i t h b o o s t p r e s s u r e , a s p r e d i c t e d by t h e O t t o c y c l e s i m u l a t i o n , r i s i n g by a p p r o x i m a t e l y 18% a t a b o o s t o f 3 p s i g f r o m t h e v a l u e w i t h no b o o s t . O v e r t h e same r a n g e , 0 - 3 p s i g b o o s t , t h e e f f i c i e n c y d r o p s by o n l y 3%, a n d t h e BSFC r i s e s by o n l y 3%. F i g u r e 22 a l s o shows t h e BMEP a c h i e v e d by g a s o l i n e a t 3000 r . p . m . a n d i t c a n be s e e n t h a t t h e BMEP d e v e l o p e d on n a t u r a l g a s a t 3 p s i g b o o s t e q u a l s t h a t o f g a s o l i n e . T h i s r e s u l t i s c o n f i r m e d by f i g u r e 23 w h i c h c o m p a r e s t h e p e r f o r m a n c e o f t h e e n g i n e r u n n i n g on n a t u r a l g a s a t 1.5 a n d 3 p s i g b o o s t , w i t h t h e p e r f o r m a n c e a c h i e v e d on g a s o l i n e o p e r a t i o n , u n d e r n a t u r a l l y a s p i r a t e d c o n d i t i o n s . I t c a n be s e e n t h a t t h e BMEP d e v e l o p e d by n a t u r a l g a s a t 3 p s i g b o o s t i s 38 s l i g h t l y h i g h e r t h a n t h a t d e v e l o p e d by g a s o l i n e , o v e r t h e w h o l e s p e e d r a n g e . I t c a n a l s o be s e e n t h a t t h e c h a n g e s i n e f f i c i e n c y a n d BSFC a r e l e s s t h a n 3%. F i g u r e 24 shows t h e e f f e c t o f s p a r k t i m i n g on t u r b o c h a r g e d e n g i n e p e r f o r m a n c e . I t c a n be s e e n t h a t t h e minimum a d v a n c e f o r b e s t t o r q u e d o e s n o t c h a n g e w i t h i n c r e a s i n g b o o s t p r e s s u r e . 5 .4 M a s s B u r n i n g R a t e A n a l y s i s R e s u l t s T h i s s e c t i o n d i s c u s s e s and c o m p a r e s t h e mass b u r n i n g r a t e a n d b u r n i n g v e l o c i t y c u r v e s o b t a i n e d by a n a l y z i n g m e a s u r e d p r e s s u r e t r a c e s w i t h t h e p r o g r a m MB d e s c r i b e d i n t h e p r e v i o u s c h a p t e r . F i g u r e 25 shows t h e r e s u l t s o b t a i n e d by r u n n i n g t h e b u r n i n g r a t e a n a l y s i s p r o g r a m o n . n a t u r a l g a s p r e s s u r e d a t a a t e n g i n e s p e e d s o f 1500 , 2 0 0 0 , a n d 3000 r p m . The f i n a l mass b u r n e d v a l u e a c h i e v e d i n a l l t h r e e c a s e s i s a b o u t 94%. The f a c t t h a t 100% b u r n i n g i s n o t a t t a i n e d c o u l d be t h e r e s u l t o f a number o f f a c t o r s i n c l u d i n g ; b l o w b y w h i c h was n o t a c c o u n t e d f o r i n t h e c a l c u l a t i o n s ; i n c o m p l e t e c o m b u s t i o n ; u n e q u a l d i s t r i b u t i o n o f t h e f u e l be tween t h e 4 c y l i n d e r s o f t h e e n g i n e ; a n d e r r o r s i n t h e h e a t t r a n s f e r c a l c u l a t i o n s . S i n c e 100% mass b u r n e d was n o t o b t a i n e d i n a n y o f t h e t e s t s , c o m b u s t i o n d u r a t i o n A 0 C i s d e f i n e d t o be t h e t i m e ( i n * c . a . ) b e t w e e n 1% a n d 90% o f t h e c h a r g e b u r n i n g . The t i m e b e t w e e n t h e s p a r k o c c u r r i n g a n d 1% o f t h e c h a r g e mass b e i n g b u r n e d i s d e f i n e d t o be t h e i g n i t i o n d e l a y p e r i o d (A&Jf ) . F i g u r e 25 a l s o shows t h e v a r i a t i o n o f t u r b u l e n t b u r n i n g 3 9 v e l o c i t y w i t h e n g i n e r o t a t i o n f o r t h e t h r e e e n g i n e s p e e d s . T h e a l m o s t s t r a i g h t l i n e b e n e a t h t h e s e c u r v e s i n d i c a t e s t h e l a m i n a r b u r n i n g v e l o c i t y , a n d i t c a n be s e e n t h a t t h e maximum f l a m e s p e e d r a t i o s S ^ / S / a r e 10 , 1 2 . 5 a n d 1 8 . 5 a t 1500 , 2000 a n d 3000 rpm r e s p e c t i v e l y , s c a l i n g l i n e a r l y w i t h e n g i n e s p e e d F i g u r e 26 shows t h e mass b u r n i n g r a t e s a n d b u r n i n g v e l o c i t i e s o f n a t u r a l g a s a t 1500 rpm a n d v a r y i n g s p a r k a d v a n c e . I t c a n be s e e n t h a t t h e s l o p e o f t h e mass b u r n e d c u r v e i s s t e e p e s t a t 2 7 ° w h i c h c o r r e s p o n d s t o MBT t i m i n g . The t u r b u l e n t b u r n i n g v e l o c i t y i s a l s o g r e a t e s t a t MBT t i m i n g . F i g u r e 27 shows t h e r e s u l t s o f f i g u r e 26 r e p l o t t e d i n t e r m s o f d e g r e e s c r a n k a n g l e a f t e r s p a r k t o v a r i o u s mass b u r n e d f r a c t i o n s , a s a f u n c t i o n o f s p a r k a d v a n c e . I t i s a p p a r e n t t h a t t h e t o t a l c o m b u s t i o n d u r a t i o n t o 90% b u r n e d i s a minimum a t MBT t i m i n g , however t h e i n c r e a s i n g d u r a t i o n on e i t h e r s i d e o f MBT i s a r e s u l t o f d i f f e r e n t r e g i o n s o f t h e c o m b u s t i o n b e i n g e x t e n d e d . When t h e s p a r k i s a d v a n c e d b e y o n d MBT, t h e i g n i t i o n d e l a y p e r i o d A © ^ i n c r e a s e s b u t t h e m a i n c o m b u s t i o n p e r i o d A9C r e m a i n s a l m o s t c o n s t a n t . In c o n t r a s t , when t h e s p a r k i s r e t a r d e d c l o s e r t o T D C , A 0 ^ i s r e d u c e d s i g n i f i c a n t l y a n d AQC i s e x t e n d e d . F i g u r e 28 shows a c o m p a r i s o n o f t h e mass b u r n i n g r a t e s a n d b u r n i n g v e l o c i t i e s o f n a t u r a l g a s w i t h g a s o l i n e a t 3000rpm a n d MBT t i m i n g . I t i s c l e a r f r o m t h e p r e s s u r e c u r v e s t h a t a l t h o u g h t h e two f u e l s g i v e a p p r o x i m a t e l y t h e same p e a k p r e s s u r e , t h e n a t u r a l g a s c u r v e i s c l o s e r t o TDC a n d a s i g n i f i c a n t l y g r e a t e r p o r t i o n o f t h e p r e s s u r e r i s e o c c u r s 40 b e f o r e TDC t h a n i n t h e g a s o l i n e c u r v e . The p r e s s u r e r i s e b e f o r e TDC r e s u l t s i n n e g a t i v e work a n d i s p a r t o f t h e c a u s e o f t h e power l o s s e x p e r i e n c e d when s w i t c h i n g f r o m g a s o l i n e t o n a t u r a l g a s . I t c a n be s e e n t h a t t h e t o t a l c o m b u s t i o n d u r a t i o n i s c o n s i d e r a b l y g r e a t e r f o r n a t u r a l g a s t h a n g a s o l i n e s i n c e b o t h e n d t h e i r c o m b u s t i o n a t t h e same t i m e , b u t t h e n a t u r a l g a s i s i g n i t e d 1 4 ° e a r l i e r t h a n g a s o l i n e . T h e mass b u r n r a t e c u r v e s o f f i g u r e 28 h a v e been r e d r a w n i n f i g u r e 29 i n t e r m s o f mass p e r c e n t b u r n e d v e r s u s d e g r e e s c r a n k a n g l e a f t e r s p a r k . I t i s c l e a r t h a t t h e i g n i t i o n d e l a y p e r i o d i s a b o u t 50% g r e a t e r f o r n a t u r a l g a s , (A&jp ( g a s o l i n e ) = 1 2 ° c . a . a n d Z \ 0 ^ ( n a t u r a l g a s ) = I 8 " c . a . ) . T h e i n c r e a s e a t 1500 rpm was f o u n d t o be e v e n g r e a t e r , a p p r o a c h i n g 100%. F i g u r e 29 a l s o shows t h e g a s o l i n e mass b u r n e d c u r v e d i s p l a c e d t o t h e same i g n i t i o n d e l a y a s t h e n a t u r a l g a s c u r v e . A t 90% b u r n e d t h e d i s p l a c e d g a s o l i n e c u r v e i s 6° t o t h e r i g h t o f t h e t r u e g a s o l i n e c u r v e a n d t h e n a t u r a l g a s c u r v e i s a n o t h e r 4° b e y o n d t h i s i n d i c a t i n g t h a t t h e c o m b u s t i o n d u r a t i o n , AOc , i s 4 ° l o n g e r f o r n a t u r a l g a s , an i n c r e a s e o f o n l y a b o u t 10% T h e s e r e s u l t s i n d i c a t e t h a t t h e low l a m i n a r b u r n i n g v e l o c i t y o f n a t u r a l g a s h a s i t s g r e a t e s t i n f l u e n c e d u r i n g t h e e a r l i e s t s t a g e s o f c o m b u s t i o n up t o 1%—10% b u r n e d , a n d t h a t i t p l a y s a l e s s s i g n i f i c a n t r o l e d u r i n g t h e m a i n c o m b u s t i o n p e r i o d , where f l a m e p r o p o g a t i o n i s p r i m a r i l y a f f e c t e d by t u r b u l e n c e . F i g u r e 30 shows t h e b u r n i n g v e l o c i t i e s o f n a t u r a l g a s a n d 41 g a s o l i n e a t 1500 and 3000 rpm r e p l o t t e d a s a f u n c t i o n o f mass f r a c t i o n b u r n e d . I t shows t h a t t h e two f u e l s have v e r y s i m i l a r t u r b u l e n t b u r n i n g v e l o c i t i e s a n d when t h e l a m i n a r b u r n i n g v e l o c i t i e s f o r e a c h f u e l a r e s u b t r a c t e d f r o m t h e m e a s u r e d t u r b u l e n t b u r n i n g v e l o c i t i e s , t h e c u r v e s o f f i g u r e 31 a r e o b t a i n e d f o r n a t u r a l g a s and g a s o l i n e a t 3000 r p m . T h e s e c u r v e s a r e v e r y s i m i l a r a n d seem t o c o n f o r m w i t h t h e e q u a t i o n , S r = Sj + C u-r (18) u s e d by M a t t a v i [32 ] where C i s a g i v e n f u n c t i o n f o r a g i v e n e n g i n e a n d ur i s t h e t u r b u l e n c e i n t e n s i t y w h i c h i n c r e a s e s l i n e a r l y w i t h e n g i n e s p e e d a s shown by a number o f a u t h o r s , e . g . L a n c a s t e r & K r i e g e r [ 3 3 ] . R e a r r a n g i n g e q u a t i o n 18 g i v e s , S r - S, = C u ^ (19) where C u , . i s a g i v e n f u n c t i o n f o r an e n g i n e a t a g i v e n s p e e d , a n d i t c a n be s e e n t h a t f i g u r e 31 c o n f i r m s t h i s r e l a t i o n s h i p . 5 . 5 E n g i n e S i m u l a t i o n R e s u l t s T h i s s e c t i o n d i s c u s s e s t h e r e s u l t s o b t a i n e d by r u n n i n g t h e e n g i n e s i m u l a t i o n p r o g r a m (SIM) a t a number o f d i f f e r e n t b o o s t p r e s s u r e s on methane and o c t a n e , a s an e x t e n s i o n o f t h e e n g i n e t e s t r e s u l t s . T h e s i m u l a t i o n was c a l i b r a t e d w i t h t h e r e s u l t s f r o m t h e mass b u r n r a t e a n a l y s i s p r o g r a m a t 3000 rpm u s i n g an a v e r a g e 42 o f t h e two c u r v e s o f Sr-Si i n f i g u r e 3 1 . T h i s p r o v i d e d a g e n e r a l r e l a t i o n s h i p f o r t h e C u T t e r m i n e q u a t i o n 19 v e r s u s mass f r a c t i o n b u r n e d , w h i c h i s i n d e p e n d a n t o f t h e f u e l t y p e , a i r / f u e l r a t i o a n d b o o s t p r e s s u r e . F i g u r e 32 shows a c o m p a r i s o n o f t h e c y l i n d e r p r e s s u r e t r a c e s , p e r c e n t a g e mass b u r n e d a n d b u r n i n g v e l o c i t i e s f o r g a s o l i n e a t 3000 rpm o b t a i n e d f r o m t h e mass b u r n r a t e a n a l y s i s p r o g r a m (MB) a n d f r o m t h e s i m u l a t i o n p r o g r a m (SIM) r u n on o c t a n e u n d e r t h e same c o n d i t i o n s . F i g u r e 33 shows a s i m i l a r c o m p a r i s o n f o r n a t u r a l g a s a n d m e t h a n e . T h e s e f i g u r e s c o n f i r m t h a t t h e s i m u l a t i o n p r o g r a m c a n r e p r o d u c e t h e e x p e r i m e n t a l c y l i n d e r p r e s s u r e t r a c e s on b o t h f u e l s when i t i s c a l i b r a t e d w i t h a g e n e r a l C u T c u r v e f o r a g i v e n e n g i n e s p e e d . T h e p e r f o r m a n c e f i g u r e s o b t a i n e d f r o m t h e s e c o m p a r i s o n s a l s o d e m o n s t r a t e t h e a c c u r a c y o f t h e s i m u l a t i o n , O c t a n e M e t h a n e (MB) (SIM) (MB) (SIM) IMEP ( b a r ) 11 . 3 11.1 9 . 6 9 . 5 E f f i c i e n c y (%) 3 8 . 5 3 7 . 8 3 7 . 6 3 6 . 5 P e a k P r e s s . ( b a r ) 4 4 . 4 4 3 . 2 4 4 . 0 4 3 . 6 S i m i l a r c o m p a r i s o n s were made o v e r a r a n g e o f a i r / f u e l r a t i o s a n d b o o s t p r e s s u r e s a n d t h e s e a l s o c o n f i r m e d t h e a c c u r a c y o f t h e s i m u l a t i o n p r o g r a m . F i g u r e 34 shows t h e r e s u l t s o f r u n n i n g t h e s i m u l a t i o n p r o g r a m on m e t h a n e a t 3000 r p m , X= 1, w i t h 0 , 3 and 6 p s i g b o o s t p r e s s u r e . T h e f o l l o w i n g v a l u e s o f I M E P , e f f i c i e n c y a n d p e a k p r e s s u r e were o b t a i n e d , 43 B o o s t P r e s s . IMEP E f f i c i e n c y Peak P r e s s . ( k P a X p s i g ) ( b a r ) (%) ( b a r ) 0 (0) 9 . 5 0 3 5 . 5 5 4 4 . 9 6 20 (3) 1 0 . 9 6 3 5 . 5 0 5 1 . 4 7 40 (6) 1 2 . 1 6 3 5 . 4 5 5 7 . 9 0 T h e s e f i g u r e s show t h a t t h e power o u t p u t o f a me thane ( o r n a t u r a l g a s ) f u e l l e d e n g i n e c a n be s i g n i f i c a n t l y i n c r e a s e d by m o d e r a t e l e v e l s o f b o o s t p r e s s u r e , t h o u g h i t c a n be s e e n t h a t t h e p e a k c y l i n d e r p r e s s u r e a l s o r i s e s s i g n i f i c a n t l y ( % p e a k p r e s s u r e i n c r e a s e = % power i n c r e a s e ) , a n d t h a t t h e e f f i c i e n c y f a l l s s l i g h t l y . F i g u r e 35 shows t h e c y l i n d e r p r e s s u r e s , p e r c e n t a g e mass b u r n e d a n d b u r n i n g v e l o c i t i e s o b t a i n e d f r o m t h e s i m u l a t i o n p r o g r a m r u n n i n g on o c t a n e u n d e r n a t u r a l l y a s p i r a t e d c o n d i t i o n s a n d on m e t h a n e w i t h 3 p s i g o f b o o s t p r e s s u r e . F i g u r e 36 shows a s i m i l a r c o m p a r i s o n o f o c t a n e a t 3 p s i g b o o s t a n d methane a t 6 p s i g b o o s t . T h e s e c o n d i t i o n s were c h o s e n i n o r d e r t o o b t a i n a p p r o x i m a t e l y t h e same power o u t p u t w i t h b o t h f u e l s . F u e l B o o s t IMEP E f f i c i e n c y Peak P r e s s ( p s i g ) ( b a r ) (%) ( b a r ) O c t a n e 0 11 . 0 5 3 7 . 7 7 4 3 . 1 9 M e t h a n e 3 1 0 . 9 6 3 5 . 7 0 51 .47 O c t a n e 3 12.61 3 7 . 7 0 4 9 . 1 3 M e t h a n e 6 1 2 . 2 6 3 5 . 4 5 5 7 . 9 0 T h e s e r e s u l t s c o n f i r m t h e p r e v i o u s l y d i s c u s s e d O t t o c y c l e s i m u l a t i o n a n d e n g i n e t e s t r e s u l t s by s h o w i n g t h a t an e n g i n e r u n n i n g on m e t h a n e o r n a t u r a l g a s r e q u i r e s a p p r o x i m a t e l y 3 p s i g (20 kPa) more b o o s t p r e s s u r e t h a n t h e same e n g i n e 44 r u n n i n g on o c t a n e o r g a s o l i n e i n o r d e r t o g i v e t h e same power o u t p u t on b o t h f u e l s . T h e l o s s i n e f f i c i e n c y r e s u l t i n g f r o m t h e s e b o o s t l e v e l s i s v e r y s m a l l ( l e s s t h a n 1%), h o w e v e r t h e p e a k c y l i n d e r p r e s s u r e s a t t a i n e d on methane a t t h e h i g h e r b o o s t p r e s s u r e s i s s i g n i f i c a n t l y g r e a t e r (by 18 - 20%) t h a n when t h e e n g i n e i s r u n on o c t a n e a t t h e same power o u t p u t . 45 V I . CONCLUSIONS The o b j e c t i v e o f t h i s p r o j e c t was t o i n v e s t i g a t e t h e i n f l u e n c e o f t u r b o c h a r g i n g on t h e p e r f o r m a n c e a n d c o m b u s t i o n b e h a v i o u r o f a d u a l f u e l l e d , s p a r k - i g n i t i o n e n g i n e o p e r a t i n g on n a t u r a l g a s a n d g a s o l i n e , a n d a number o f c o n c l u s i o n s c a n be d r a w n . I t h a s been c o n f i r m e d t h a t a s p a r k i g n i t i o n e n g i n e o p e r a t i n g on n a t u r a l g a s e x p e r i e n c e s a power l o s s o f a p p r o x i m a t e l y 15% c o m p a r e d w i t h t h e power o b t a i n e d on g a s o l i n e . T e n o f t h e s e p e r c e n t a g e p o i n t s c a n be a c c o u n t e d f o r by t h e d i s p l a c e m e n t o f a i r by t h e g a s e o u s f u e l a n d t h e r e m a i n i n g f i v e p e r c e n t a g e p o i n t s b y t h e low l a m i n a r b u r n i n g v e l o c i t y o f n a t u r a l g a s . A c o m p a r i s o n o f p u b l i s h e d e q u a t i o n s f o r l a m i n a r b u r n i n g v e l o c i t i e s i n d i c a t e s t h a t t h e l a m i n a r b u r n i n g v e l o c i t i e s o f m e t h a n e o r n a t u r a l g a s a r e 50% - 60% l o w e r t h a n g a s o l i n e u n d e r e n g i n e - l i k e c o n d i t i o n s o f t e m p e r a t u r e a n d p r e s s u r e . M a s s b u r n i n g r a t e a n a l y s e s o f e n g i n e c y l i n d e r p r e s s u r e d a t a show t h a t t h e low b u r n i n g v e l o c i t y o f n a t u r a l g a s h a s i t s g r e a t e s t i n f l u e n c e d u r i n g t h e i g n i t i o n d e l a y p e r i o d , up t o 1% mass b u r n e d , a n d i t c a n c a u s e i n c r e a s e s i n i g n i t i o n d e l a y o f b e t w e e n 50% a n d 100% r e l a t i v e t o g a s o l i n e . T h e low b u r n i n g v e l o c i t y o f n a t u r a l g a s a l s o a f f e c t s t h e m a i n c o m b u s t i o n p e r i o d b u t t o a much l e s s e r e x t e n t , i n c r e a s i n g i t by up t o 10% r e l a t i v e , t o g a s o l i n e . T h i s r e d u c e d e f f e c t i s a r e s u l t o f t h e m a i n c o m b u s t i o n p e r i o d b e i n g d o m i n a t e d by t u r b u l e n c e e f f e c t s . I t h a s b e e n c o n f i r m e d t h a t t h e m a i n c o m b u s t i o n p e r i o d c a n be c h a r a c t e r i s e d by t h e e q u a t i o n S ^ S , + C u r a n d t h a t a g e n e r a l 46 form of the Cu,- term can be obtained from analysis of experimental cylinder pressure traces for a given engine which is independent of fuel type, a i r / f u e l r a t i o and boost presure. This general form can then be incorporated in a simulation program to predict engine behaviour under a wide variety of operating conditions. Results from the engine tests and simulation program indicate that i t i s possible to recover the power loss experienced by an engine running on natural gas by boosting the intake pressure to 3 psig (20 kPa) above that provided when the engine is running on gasoline. This increase in boost pressure does not s i g n i f i c a n t l y reduce the e f f i c i e n c y or raise the s p e c i f i c fuel consumption, however, the peak cylinder pressures attained can be as much as 20% higher on natural gas than on gasoline at the same power l e v e l . Recommendations for further work include the extension of t h i s study to investigate a number of d i f f e r e n t engine cylinder geometries, especially those which may enhance the burning v e l o c i t y during the early stages of combustion. It i s also recommended that the simulation program be extended to include calculations of the intake and exhaust stroke to allow a more complete investigation of the e f f e c t s of adding a turbocharger or supercharger. 47 E n g i n e M o d e l D i s p l a c e m e n t T o y o t a 3TC-1 (1981) 1772 c c . 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P r e s s . 2 3 . M e t g h a l c h i , M . , K e c k , J . C . , " L a m i n a r B u r n i n g V e l o c i t y o f P r o p a n e A i r M i x t u r e s a t H i g h T e m p e r a t u r e a n d P r e s s u r e " , C o m b u s t i o n a n d F l a m e 3 8 : 1 4 3 - 1 5 4 , 1980 . 2 4 . V a n W y l e n , G . J . , S o n n t a g , R . E . , " F u n d a m e n t a l s o f C l a s s i c a l T h e r m o d y n a m i c s " , J o h n W i l e y & S o n s , 1978 . 2 5 . K o z u k a , K . , S a i t o , A . , O t s u k a , M . , K a w a m u r a , K . , " T e l e v i s i o n S y s t e m f o r V i e w i n g E n g i n e C o m b u s t i o n P r o c e s s e s a n d t h e Image A n a l y s i s " , SAE 8 1 0 7 5 3 . 2 6 . A n n a n d , W . J . D . , " H e a t T r a n s f e r i n t h e C y l i n d e r s o f R e c i p r o c a t i n g I n t e r n a l C o m b u s t i o n E n g i n e s " , P r o c . I. M e c h . E . , V o l 1 7 7 , N o . 3 6 , 1 9 6 3 . 2 7 . P a t t e r s o n , D . 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B . , K e c k , J . C . , " E x p e r i m e n t a l a n d T h e o r e t i c a l S t u d y o f N i t r i c O x i d e F o r m a t i o n i n I n t e r n a l C o m b u s t i o n E n g i n e s " , C o m b u s t i o n , S c i e n c e & T e c h n o l o g y 1, 3 1 3 , 1970 . 3 1 . H i r e s , S . D . , T a b a c z y n s k i , R . J . , N o v a k , J . M . , " T h e P r e d i c t i o n o f I g n i t i o n D e l a y a n d C o m b u s t i o n I n t e r v a l s f o r a H o m p g e n i o u s C h a r g e , S p a r k I g n i t i o n E n g i n e " , SAE 7 8 0 2 3 2 . 3 2 . M a t t a v i , J . N . , G r o f f , E . G . , L i e n e s c h , J . H . , M a t e k u n a s , F . A . , N o y e s , R . N . , " E n g i n e I m p r o v e m e n t s T h r o u g h C o m b u s t i o n M o d e l i n g " , C o m b u s t i o n M o d e l i n g In R e c i p r o c a t i n g E n g i n e s P l e n u m P r e s s , 1980 . 3 3 . L a n c a s t e r , D . R . , K r i e g e r , R . B . , " E f f e c t s o f T u r b u l e n c e on S p a r k I g n i t i o n E n g i n e C o m b u s t i o n " , SAE 7 6 0 1 6 0 . 3 4 . W a t s o n , N . , J a n o t a , M . S . , " T u r b o c h a r g i n g t h e I n t e r n a l C o m b u s t i o n E n g i n e " , M a c m i l l a n P r e s s L t d . , 1982 . 51 F i g u r e 1 p r o p a n e - a i r - I g n i t i o n a n d k n o c k l i m i t s f o r m e t h a n e - a i r m i x t u r e s v s . c o m p r e s s i o n r a t i o , d rawn f r o m a n d [12] 52 100.0 90.0 tn 80.0 s : c_> w 70.0 g 60.0 10.0 0.0 I 1 1 1 r CD NAT.GAS S.R I G A METHANE R I L + METHANE A L B I I Tl - 300K P I = 1 BAR _L 300 400 500 600 UNBURNED GAS TEMP. (K) 700 800 Figure 2 - Comparison of published equations f o r laminar burning v e l o c i t i e s of n a t u r a l gas and methane, c a l c u l a t e d along an unburned gas ise n t r o p e . [ S,A & G = Sharma, Agrawal & Gupta; R & L = Ryan & L e s t z ; A & B = Andrews & Bradley. ] 53 200.0 180.0 -£ 160.0-3: w 140.0h g 120.Oh > or ZD CD cr O NAT.GAS S.P & G A PROPANE M I K + OCTANE M I K X IND0LINE M I K i i r Tl - 300K Pl = 1 BAR 300 400 500 600 UNBURNED GAS TEMP. (K) 700 800 Figure 3 - Comparison of published equations f o r laminar burning v e l o c i t i e s of n a t u r a l gas, propane, octane and i n d o l i n e , c a l c u l a t e d along an unburned gas is e n t r o p e . [ S,A & G = Sharma, Agraual & Gupta; M & K = Metghalchi & Keck. ] PULSE DAMPING DRUM GAS IN GAS LAMINAR FLOW ELEMENT AIR FILTER AIR LAMINAR FLOW ELEMENT RECIRCULATING AIR ELECTRICALLY DRIVEN ROOTS BLOWER GAS PRESSURE REGULATOR BALANCE LINE AIR/FUEL RATIO CONTROL VALVE WATER BRAKE DYNAMOMETER A FLOW CONTROL VALVE - E A T " MIXER EE EXHAUST BACK PRESSURE THROTTLE VALVE TOYOTA ENGINE TOOTHED WHEEL PMfV»- OPTICAL PICKUP DYNO WATER IN F i g u r e 4 - E x p e r i m e n t a l l a y o u t o f e n g i n e , d y n a m o m e t e r a n d a i r c o m p r e s s o r . 55 F i g u r e 5 - Toyota engine mounted i n t e s t c e l l 1 - toothed wheel 2 - o p t i c a l pickup c i r c u i t box 3 - N.G. supply l i n e 4 - gas mixer 5 - A i r Intake from blower 6 - engine water c o o l i n g tower 56 F i g u r e 6 - W a t e r b r a k e dynamometer 1 - s p e e d s e n s o r 2 - l o a d c e l l a s s e m b l y 3 - w a t e r i n t a k e t o dynamometer 4 - w a t e r o u t l e t f r o m dynamometer 5 - w a t e r f l o w c o n t r o l v a l v e 6 - e x h a u s t t e m p e r a t u r e s e n s o r 57 F i g u r e 7 - Water c o o l i n g tower and dynamometer water s u p p l y 1 - C o n s t a n t head water tank 2 - Water Pump 3 - C o o l i n g Tower 4 - Temperature C o n t r o l V a l v e 58 F i g u r e 8 - Roots blower and flow c o n t r o l v a l v e 1 - i n t a k e a i r from drum 2 - compressed a i r from blower 3 - blowoff v a l v e r e c i r c u l a t i n g excess a i r 4 - compressed a i r to engine 5 - p r e s s u r e r e l i e f v a l v e 59 F i g u r e 9 - Engine a i r su p p l y 1 - a i r f i l t e r 2 - a i r l a m i n a r f l o w element 3 - p u l s e clamping drum 4 - i n t a k e a i r t o blower from drum 5 - r o o t s blower motor 6 - compressed a i r t o engine 60 F i g u r e 10 - G a s M i x e r and t h r o t t l e 1 - g a s s u p p l y l i n e 2 - a i r s u p p l y l i n e 3 - i n t a k e a i r t e m p e r a t u r e s e n s o r 4 - i n t a k e a i r p r e s s u r e 61 TO INTAKE MANIFOLD F i g u r e 11 - P r i n c i p l e o f o p e r a t i o n o f n a t u r a l g a s m 62 F i g u r e 12 - O p t i c a l p i c k u p a s s e m b l y 1 - t o o t h e d w h e e l 2 - o p t i c a l s e n s o r c i r c u i t r y 3 - t o p d e a d c e n t r e h o l e 4 - p r e s s u r e t r a n s d u c e r c a b l e GAS TEMP. N.G. DIFF. PRESSURE GAS PRESSURE 5 AIR/FUEL RATIO CONTROL VALVE L.F.E. PULSE DAMPING DRUM BOOST PFESS. MIXER INTAKE TEMP. 4-r »N0.1 CYLINDER PRESSURE EXHAUST TEMP. & PRESSURE 1 r OIL OIL COOLANT PRESS. TEMP. TEMP. F i g u r e 13 - E n g i n e I n s t r u m e n t a t i o n L a y o u t 64 Water Cooling Tubes Pressure Signal to Charge Anpllfler No. 1 Cylinder Head AVL Water Cooled Pressure Transducer F i g u r e 14 - P r e s s u r e t r a n s d u c e r l o c a t i o n i n c y l i n d e r h e a d 65 F i g u r e 15 - Data a c q u i s i t i o n system 1 - NEFF analogue t o d i g i t a l c o n v e r t e r 2 - remote t e r m i n a l f o r PDP11 computer 3 - o s c i l l o s c o p e t o m o n i t o r p r e s s u r e s i g n a l s 4 - p r i n t e r f o r h a r d copy of d a t a 66 Figure 16 - Methane and octane fuel performance vs. a i r / f u e l r a t i o , as calculated by the Otto cycle simulation program (COMB). 67 EFFICIENCY (Z) 42 m 22 20 I.M.E.P. (bar) 18 —x-OCTANE METHANE 0.05 0.10 0.15 RESIDUAL GAS FRACTION (/ ) 0.20 Figure 17 - Methane and octane f u e l performance vs. r e s i d u a l gas f r a c t i o n , as c a l c u l a t e d by the Otto c y c l e s i m u l a t i o n program (COMB). 68 200 50 EFFICIENCY (X) 42 2H 1 1 • 9 12 - OCTANE METHANE 0.0 20.0 40.0 BOOST PRESSURE (kPa) 60.0 F i g u r e 18 - Methane and o c t a n e f u e l performance v s . boost p r e s s u r e , as c a l c u l a t e d by t h e O t t o c y c l e s i m u l a t i o n program (COMB). 69 400 300 BiSaFaCi (p/Wh> 200 Figure 19 - Comparison of Toyota engine performance on n a t u r a l gas and g a s o l i n e , from 1500 t o 5000 rpm. 70 KNOCK LIMIT B.M.E.P. (bar) A tr KNOCK LIMIT - * — N.G.1500rpm -m— N.G.3500rpm — * ~ GASOLINE 1500 GASOLINE 3500 a. 10* 20* 30* SPARK ADVANCE 10" 50* F i g u r e 20 - V a r i a t i o n of Toyota e n g i n e performance w i t h s p a r k advance f o r n a t u r a l gas and g a s o l i n e a t 1500 and 3500 rpm. 71 F i g u r e 21 - V a r i a t i o n of Toyota engine performance w i t h a i r / f u e l r a t i o f o r n a t u r a l gas, MBT t i m i n g , 2000 rpm. 72 400 300 BiSaFaCa <p/kWh) 200 100 35 EFFICIENCY «) Figure 22 - Variation of Toyota engine performance with boost pressure for natural gas, X- 1, MBT timing, 3000 rpm. 73 F i g u r e 23 - Performance of Toyota engine w i t h n a t u r a l gas, t u r b o c h a r g e d , and w i t h g a s o l i n e , n a t u r a l l y a s p i r a t e d , v s . e n g i n e speed. 74 Figure 24 - V a r i a t i o n of Toyota engine performance with spark advance f o r n a t u r a l gas under turbocharged c o n d i t i o n s , X • 1# 1750 rpm. 75 - 4 0 - 2 0 T D C 2 0 4 0 6 0 8 0 - 4 0 - 2 0 TDC 2 0 4 0 6 0 8 0 i o . 0 | , , , 1 1 1 1 1 1 r - 4 0 - 2 0 T D C 2 0 4 0 6 0 8 0 . D E G R E E S C R A N K A N G L E F i g u r e 25 - Comparison of c y l i n d e r p r e s s u r e , percentage mass burned and burning v e l o c i t y curves f o r n a t u r a l gas, X= 1, MBT t i m i n g , 1500, 2000 & 3000 rpm. 76 D E G R E E S C R R N K R N G L E F i g u r e 26 - C o m p a r i s o n o f c y l i n d e r p r e s s u r e , p e r c e n t a g e mass b u r n e d a n d b u r n i n g v e l o c i t y c u r v e s f o r n a t u r a l qas,X= 1, 1500 r p m , s p k . a d v . = 1 5 ° , 2 7 ° , 38" 77 0* -10* -15' -20" -25* -30" -35' -MO" SPARK ADVANCE F i g u r e 27 - Number of c r a n k v a r i o u s mass burned f r a c t i o n s gas, X « 1, 1500 rpm. a n g l e degrees a f t e r spark t o v s . s p a r k advance f o r n a t u r a l 78 50.0 D E G R E E S C R R N K R N G L E F i g u r e 28 - C o m p a r i s o n o f c y l i n d e r p r e s s u r e , p e r c e n t a g e m a s s b u r n e d and b u r n i n g v e l o c i t y c u r v e s f o r n a t . g a s a n d g a s o l i n e , A = 1, MBT t i m i n g , 3000 r p m . 79 F i g u r e 29 - P e r c e n t a g e mass burned v s . crank a n g l e degrees a f t e r spark f o n a t u r a l gas and g a s o l i n e , A = 1, MBT t i m i n g , 3000 rpm. 80 F i g u r e 30 - T u r b u l e n t b u r n i n g v e l o c i t y v s . m a s s f r a c t i o n b u r n e d f o r n a t u r a l g a s a n d g a s o l i n e a t \ = 1, 1500 a n d 3000 r p m . 81 10.0 9.0 8.0 7.0 6.0 VELOCITY (M/S) 5.0 4.0 3.0 2.0 1.0 0.04 0.0 1 Sr-S.. GASOLINE r s s r / / / / It 1 Sr-Si. NAT.GAS J > / // f II ll 1 \ vy \ \ • 11 "• // \ \ \ \ \ \ GASOLU > NAT. GAS I \ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 MASS FRACTION BURNED 0.8 0.9 F i g u r e 31 - Laminar b u r n i n g v e l o c i t y and ( t u r b u l e n t -l a m i n a r ) b u r n i n g v e l o c i t y v s . mass f r a c t i o n burned f o r n a t u r a l gas and g a s o l i n e , X = 1, MBT t i m i n g , 3000 rpm. 82 rr cr m in in UJ tr a. CD in in tn > LD Z z tr CD 60.0 1 —i r | i i i 1 1 1 1 MB - Mass Burn Rate 50.0 1 Program ~~ SIM - Simulation 40.0 I MB ^ Program _ 30.0 / /** SIM — 20.0 10.0 ^ | n n 1 •l 1 | l i 1 1 1 1 1 u. u —i 1.0 40 -20 TDC 20 40 60 80 1 I I I ' ' S I M ' 1 1 i i -40 DEGREES CRRNK ANGLE Figure 32 - Comparison of s i m u l a t i o n program r e s u l t s with mass burn r a t e program r e s u l t s f o r octane at A* 1, 3000 rpm, 8 3 io. o, j 1 1 1 1 1 i i r DEGREES CRANK RNGLE Figure 33 - Comparison of s i m u l a t i o n program r e s u l t s w i t h mass burn r a t e program r e s u l t s f o r methane at X= 1, 3000 rpm. 8 4 Figure 34 - S i m u l a t i o n program r e s u l t s f o r methane at 0 p s i , 3 p s i and 6 p s i boost pressures, X= 1, 3000 rpm. 8 5 Figure 35 - Comparison of pressure t r a c e s , mass burning r a t e s and burning v e l o c i t i e s f o r methane at 3 p s i boost and octane at 0 p s i boost, X * 1, 3000rpm. 86 Figure 36 - Comparison of pressure t r a c e s , mass burning r a t e s and burning v e l o c i t i e s f o r methane at 6 p s i boost and octane at 3 p s i boost, X= 1, 3000rpm. 87 APPENDIX A - ENGINE DATA ACQUIS IT ION AND ANALYSIS T h i s a p p e n d i x c o n s i s t s o f two s e c t i o n s . T h e f i r s t s e c t i o n d e t a i l s t h e c a l c u l a t i o n s w h i c h were c a r r i e d o u t on t h e e n g i n e p e r f o r m a n c e d a t a by t h e p r o g r a m D L I S T , i n o r d e r t o o b t a i n v a l u e s f o r p o w e r , b r a k e mean e f f e c t i v e p r e s s u r e , e f f i c i e n c y a n d b r a k e s p e c i f i c f u e l c o n s u m p t i o n . T h e s e c o n d s e c t i o n shows t h e c a l c u l a t i o n s w h i c h were u s e d t o e s t i m a t e t h e e x h a u s t b a c k - p r e s s u r e t h a t w o u l d h a v e b e e n c a u s e d by an e x h a u s t d r i v e n t u r b i n e a t v a r i o u s b o o s t p r e s s u r e s . T h e t h i r d s e c t i o n d e s c r i b e s t h e m e t h o d u s e d t o o b t a i n e n g i n e c y l i n d e r p r e s s u r e t r a c e s u s i n g a h i g h s p e e d d a t a a c q u i s i t i o n s y s t e m . a . E n g i n e T e s t D a t a A n a l y s i s A l l o f t e s t d a t a w h i c h was a c q u i r e d d u r i n g t h e e n g i n e e x p e r i m e n t s was a n a l y z e d a n d t a b u l a t e d by t h e p r o g r a m D L I S T w h i c h i s l i s t e d a t t h e e n d o f t h i s a p p e n d i x . T w e l v e p a r a m e t e r s were r e c o r d e d a t e a c h t e s t p o i n t , a n d t h e s e i n c l u d e d s p e e d , t o r q u e , a i r f l o w , f u e l f l o w , i n l e t a n d e x h a u s t t e m p e r a t u r e s , b o o s t a n d b a c k p r e s s u r e , s p a r k a d v a n c e a n d a m b i e n t a i r c o n d t i o n s . The d a t a was t y p e d i n t o c o m p u t e r f i l e s w h i c h were r e a d by D L I S T . T h e p r o g r a m f i r s t c a l c u l a t e s t h e a i r a n d f u e l mass f l o w r a t e s f r o m t h e d i f f e r e n t i a l p r e s s u r e s m e a s u r e d a c r o s s t h e l a m i n a r f l o w e l e m e n t s . P o i n t s on t h e c a l i b r a t i o n c u r v e s f o r e a c h e l e m e n t a r e s t o r e d i n t h e p r o g r a m , l i n e a r i n t e r p o l a t i o n b e i n g u s e d t o f i n d t h e f l o w r a t e w h i c h c o r r e s p o n d s t o a m e a s u r e d p r e s s u r e d i f f e r e n t i a l . V o l u m e f l o w r a t e i s c o n v e r t e d i n t o mass f l o w r a t e u s i n g t h e i d e a l g a s r e l a t i o n s h i p where t h e a b s o l u t e p r e s s u r e s a n d t e m p e r a t u r e s o f t h e a i r a n d n a t u r a l g a s a r e m e a s u r e d . An a d d i t i o n a l c o r r e c t i o n f a c t o r i s i n c l u d e d i n t h e n a t u r a l g a s f l o w c a l c u l a t i o n s , t o a c c o u n t f o r t h e f a c t t h a t t h e l a m i n a r f l o w e l e m e n t was c a l i b r a t e d w i t h a i r , w h i c h h a s a d i f f e r e n t v i s c o s i t y t o n a t u r a l g a s . (The p r o p e r t i e s o f t h e n a t u r a l g a s u s e d a r e c a l c u l a t e d i n A p p e n d i x C ) . T h e n e x t s e c t i o n o f t h e p r o g r a m c a l c u l a t e s t h e a i r f u e l r a t i o g i v e n by A i r - F u e l R a t i o = M a i r / M f u e l 0 m where M a i r a n d M f u e l r e p r e s e n t t h e a i r a n d f u e l mass f l o w r a t e s r e s p e c t i v e l y . T h e b r a k e h o r s e p o w e r a n d b r a k e p o w e r i n kW a r e g i v e n by B r a k e H o r s e p o w e r = ( T o r q u e . S p e e d ) / 5 2 5 0 a n d B r a k e Power = ( 0 . 1 4 2 E - 3 . T o r q u e . S p e e d ) 88 where Torque i s measured i n f t . l b s and Speed i n rpm. E f f i c i e n c y on g a s o l i n e i s c a l c u l a t e d u s i n g : E f f i c i e n c y = (0.142 . Torque . S p e e d ) / ( M f u e l . 43.24E4) where M f u e l i s g i v e n i n kg/s and t h i s v a l u e i s m u l t i p l i e d by 0.89048 f o r n a t u r a l gas t o account f o r t h e d i f f e r e n c e i n lower h e a t i n g v a l u e s of the two f u e l s . Brake s p e c i f i c f u e l consumption i s o b t a i n e d u s i n g : BSFC = ( M f u e l . 3.6E9)/(0.142 . Torque . Speed) The v a l u e s c a l c u l a t e d f o r power, t o r q u e and mean e f f e c t i v e p r e s s u r e a r e then c o r r e c t e d t o s t a n d a r d atmosphere c o n d i t i o n s u s i n g the method recommended i n the SAE Handbook. F i n a l l y , the r e s u l t s a r e w r i t t e n i n columns beneath t h e i r r e s p e c t i v e h e a d i n g s . b. C a l c u l a t i o n Of Exhaust B a c k - P r e s s u r e D u r i n g the t u r b o c h a r g e d engine t e s t s t he boost p r e s s u r e was p r o v i d e d by the Roots blower and a v a l v e i n the exhaust p i p e was used t o t h r o t t l e the f l o w i n o r d e r t o s i m u l a t e the e f f e c t s of a t u r b i n e . The b a c k - p r e s s u r e r e q u i r e d a t a g i v e n boost p r e s s u r e was c a l c u l a t e d as f o l l o w s (from Watson & J a n o t a [ 3 4 ] ) . The power r e q u i r e d t o d r i v e a compressor may be e x p r e s s e d a s , Wcomp = Mair.Cpa.Ta. /Pmanifold] - 1 I / ^ comp LvPambient / J and the power de v e l o p e d by a t u r b i n e i s , Wturb = Meng.Cpe.Te. F 1 - / P a m b i e n t \ ^ i ^ 1 . ^ t u r b 1 VPexhausty J The energy b a l a n c e f o r the t u r b o c h a r g e r i s , Wcomp = Wturb . ^ mech L e t >2 t o t = »2comp . *\ t u r b . ^  mech . Meng / M a i r then c o m b i n i n g t h e s e f o u r e q u a t i o n s y i e l d s , [ i - /Pambient^^T 1] = [ /Pmanif old) hrr - 11 • £p_a • Ta . 1 L \Pexhaust/ J [\Pambient / J Cpe Te ^ t o t T h i s e q u a t i o n was s o l v e d f o r each boost p r e s s u r e used. 89 V a l u e s a s s u m e d i n t h e c a l c u l a t i o n s w e r e : P a m b i e n t P m a n i f o l d Ke ( e x h a u s t ) Ka ( a i r ) Cpe ( e x h a u s t ) Cpa ( a i r ) Te ( e x h a u s t ) T a ( a i r ) t o t 1 b a r b o o s t p r e s s u r e 1 . 3 5 1 . 4 0 1.2 k J / k g K 1.0 k J / k g K 900 K 315 K 0 . 5 6 c . C y l i n d e r P r e s u r e M e a s u r e m e n t A s d e s c r i b e d i n C h a p t e r 3 , t h e number one c y l i n d e r o f t h e T o y o t a e n g i n e was i n s t r u m e n t e d w i t h an AVL q u a r t z p r e s s u r e t r a n s d u c e r c o n n e c t e d t o a c h a r g e a m p l i f i e r . T h e o u t p u t o f t h e c h a r g e a m p l i f i e r , t o g e t h e r w i t h t h e b o t t o m d e a d c e n t e r s i g n a l f r o m t h e o p t i c a l p i c k u p m o u n t e d on t h e e n g i n e , was f e d t o a N E F F S y s t e m 620 A n a l o g u e t o D i g i t a l c o n v e r t e r . T h e N E F F s y s t e m , was c o n t r o l l e d by a PDP 1 1 / 3 4 m i n i c o m p u t e r . T h e c o m p u t e r t e r m i n a l a n d N E F F box were b o t h m o u n t e d on a t r o l l e y a s shown i n F i g 1 5 . T h e p r e s s u r e s i g n a l was s a m p l e d a t e v e r y d e g r e e c r a n k a n g l e i n b u r s t s o f 4000 d a t a p o i n t s , a n d was s y n c h r o n i s e d t o t h e e n g i n e r o t a t i o n by t h e b o t t o m d e a d c e n t e r s i g n a l s . The p r o g r a m u s e d t o a c q u i r e t h e d a t a a l l o w e d a l a r g e number o f e n g i n e c y c l e s t o be s t o r e d , a n d t h e n e n s e m b l e a v e r a g e d . T h e a v e r a g e d p r e s s u r e d a t a f i l e s were t r a n s f e r r e d t o t h e m a i n u n i v e r s i t y c o m p u t e r f o r a n a l y s i s by t h e mass b u r n i n g r a t e p r o g r a m (MB) w h i c h i s d e s c r i b e d i n a p p e n d i x G . 90 L i s t i n g of DLIST at 14:33:11 on DEC 10, 1984 f o r CC1d=FHG. Page 1 c 2 C 3 C 4 C 5 c 6 7 8 9 10 11 12 13 14 c 15 c 16 c 17 c 18 19 20 21 22 c 23 c 24 c 26 c 27 28 29 c 30 c 31 c 32 33 34 c 35 36 37 38 39 40 4 1 42 43 44 c 45 46 c 47 c 48 c 49 c 50 c 51 c 52 c 53 54 55 56 c 57 c 58 c 59 c "DLIST" THIS PROGRAM CALCULATES ENGINE PERFORMANCE DATA FROM ======= MEASUREMENT DATA FOR THE TOYOTA ENGINE AND TABULATES THE RESULTS. DIMENSION T0RQ(50),BHP(50).BP(50),BMEP(50). -BSFC(50),EFF(50).DPAIR(50),TAIR(50),DPNG(50),SPAD(50), -VPET(50),TEXH(50),FAIR(50),FFUEL(50),FPET(50), -AFR(50),A(50),BHPC(50).BPC(50),BMEPC(50).TORQC(50), -TALFE(50),PAM(50),TAM(50),AFRR(50),BSFCA(50), -T0R0A(50),T0RQB(5O),BSTP(50),BCKP(50),PNG(50) REAL MF(50),MA(50),MFUEL(50),MAIR(50),K,NN,KK INTEGER V,Y,RPM(50).TNUM(50) DATA POINTS TAKEN FROM L.F.E CALIBRATION CURVES FOR NAT.GAS FLOW (A(1) TO A(10)) AND AIR FLOW (A(11) TO A(20)).... DATA A(1),A(2).A(3),A(4).A(5).A(6),A(7).A(8),A(9),A(10)/2.95,5.86, -8.73. 11.56.14.35.17.08,19.77.22.4,0.0.2.95/ DATA A(11),A(12),A(13).A(14),A(15),A(16),A(17).A(18),A(19).A(20)/ -59.0, 1 17 .72, 175.0,232 .0.289.0.344.5.399.6.453.9,0.0.59.0/ READ TYPE OF FUEL (1=GAS0LINE 2=NAT.GAS); NUMBER OF TEST RUNS TO BE READ IN; STOICHIOMETRIC AIR FUEL RATIO AND NAT. GAS TEMPERATURE... READ(5,11) KFUEL.KRPM.AFSTO,TNG 11 F0RMAT(2I4.2F7.2) WRITE THE INPUT DATA AND THE COLUMN HEADINGS... 95 WRITE(6,100) KFUEL 100 F0RMAT(1H ,'FUEL TYPE (1"GASOLINE.2=NAT. GAS):'.13/) WRITE(6,103) 103 F0RMAT(1H ,'TEST ENGINE BOOST BACK SPARK AMB REL. - AIR FUEL WRITE(6,104) 104 FORMATdH ,'NO. RPM - FLOW FLOW A/F WRITE(6.105) 105 FORMAT(1H ,' - g/s g/s RATIO DO 15 J=1,KRPM TORQUE BRAKE BMEP EFF PRESS. PRESS.ADVANCE TEMP. (N.m) POWER (bar) (%) ( p s i ) ( p s i ) ( btdc) ( C) (KW)'/) INLET EXHAUST BSFC) TEMP. TEMP. (g/KWh)') ( C) ( C) FOR EACH TEST NO READ RPM; BOOST PRESS.; BACK PRESS.; INTAKE AIR TEMP.; EXHAUST TEMP.; TORQUE; DIFF. PRESS. ACROSS AIR LAMINAR FLOW ELEMENT; DIFF. PRESS. ACROSS N.G. LAMINAR FLOW ELEMENT / OR THE VOLTAGE ON THE GASOLINE FLOW VOLTMETER; SPARK ADVANCE; AMBIENT TEMP.; AMBIENT PRESS.; PRESS. IN THE N.G. PIPELINE... READ(5.12) TNUM(J),RPM(J),BSTP(J),BCKP(d),TAIR(J),TEXH(d). -TORQ(J).DPAIR(J).DPNG(d),SPAD(J).TAM(J),PAM( J),PNG( J ) 12 FORMAT(13,I5.2F5.2.F6.1,F7.1,F6.1,F5.2.F5.2,F5.1,2F6.2.F6.3) CALCULATE AIR FLOWRATE FROM DIFF. PRESS. ACROSS L.F.E. BY USING LINEAR INTERPOLATION BETWEEN THE STORED DATA POINTS. THE VALUE OBTAINED IS CORRECTED FOR TEMP. VARIATION FROM THE STANDARD 70F, 91 L i s t i n g of DLIST at 14:33:11 on DEC 10, 1984 f o r CC1d=FHG. Page 2 60 C AND THE MASS FLOW RATE IS ALSO CALCULATED USING AMBIENT PRESS. 61 C & TEMP... 62 C 63 V=INT(DPAIR(J)) 64 S=DPAIR(0)-FLOAT(V) 65 V=V+10 66 IF(DPAIR(d).LT.1.0) V=19 67 Z = A(V) + S*(A(V+1 )-A(V)) 68 P=PAM(J)*3.386 69 K=((TAM(J)-32.0)*0.55556)+273.0 70 CC=(14.92*(K**1.5))/(K+120.54) 71 C=181.87/CC 72 FAIR(J)=Z*C 73 MAIR(d)=(P/(0.287*K))*FAIR(d)*4.7195E-04 74 C 75 C THE NATURAL GAS VOLUME AND MASS FLOWRATES ARE CALCULATED IN THE 76 C SAME MANNER AS THE AIRFLOW CALCULATIONS OF THE PREVIOUS SECTION.. 77 C 78 Y=INT(DPNG(d)) 79 T=DPNG(J)-FLOAT(Y) 80 IF(DPNG(J).LT.1.0) Y=9 81 Z = A(Y)+T*(A(Y+1 )-A(Y)) 82 P=PAM(d)*3.386 83 K=(TNG-32.0)*0.55556+273.0 84 CC=(9.879*(K**1.5))/(K+163.17) 85 C=181.87/CC 86 FFUEL(d)=Z*C*PNG(J) 87 MFUEL(d)=(P/(0.4846*K))*FFUEL(d)*4.7195E-04 88 C 89 C THIS SECTION CALCULATES THE GASOLINE VOLUME AND MASS FLOWRATES 90 C FROM THE VOLTAGE GIVEN BY THE FLOSCAN FUEL FLOWMETER. VOLUME 91 C FLOWRATE IS GIVEN IN L/HR, MASS FLOW IN KG/S.... 92 C 93 IF(KFUEL.EQ.2) GOTO 20 94 FFUEL(d)=(DPNG(d)*7.881) 95 MFUEL(d)=(FFUEL(d)/3600.0)*0.735 96 C 97 C THIS SECTION CALCULATES THE AIR/FUEL RATIO BY MASS. THE BRAKE 98 C HORSEPOWER; BRAKEPOWER IN KW; BRAKE MEAN EFFECTIVE PRESSURE; 99 C EFFICIENCY;BRAKE SPECIFIC FUEL CONSUMPTION;CORRECTED POWERS AND 100 C TORQUE AND AIR/FUEL RATIO RELATIVE TO STOICHIOMETRIC... 101 C 102 20 AFR(d)=MAIR(d)/MFUEL(d) 103 BHP(J)=TORQ(J)*RPM(J)/5250. 104 BP(d)=0.142E-03*TORQ(d)*RPM(d) 105 BMEP(J)=0.0963*TORO(d) 106 EFF(d)=(0.142*TORQ(d)*RPM(d))/(MFUEL(d)*43.24E+04) 107 BSFC(d)=(MFUEL(d)*3.6E+09)/(0.142*T0RQ(d)*RPM(d)) 108 IF(KFUEL.EQ.2) EFF(d)=EFF(d)*0.89048 109 MA(d)=MAIR(d)*1000.0 110 MF(d)=MFUEL(d)*1000.0 110.2 C 110.4 C CALCULATION OF CORRECTION FACTOR FOR CHANGING INLET AIR CONDITIONS. 110.6 C 1 11 XX=16.3761+2.28629*(RPM(d)/10O0.0)+0.297053*((RPM(d)/1000.0) 112 -**2.0) 113 YY=(1.0/100.0)*(5.44659-0.02495*(RPM(d)/1000.0)-0.174376* 114 -((RPM(d)/1000.0)**2.0)) 92 L i s t i n g of OLXST at 14:33:11 on DEC 10. 1984 fo r CC1d=FHG. Page 3 115 NN=100.0/(1.0+(6.89*XX-YY*BMEP(d)*100.0)/(BMEP(d)*100.0)) 1 16 CS=(29.OO/(PAM(J)))*((TAIR(J)+460.0)/(85.0+460.0))* *0.5 117 KK=(100.0/NN)»(CS-1.0)+1.0 117.2 C 117.5 IF(BSTP(d) GT.O.O) KK=1.0 118 BHPC(d)-=BHP(d)*KK 119 BPC(d)=BP(d)*KK 120 BMEPC(d)=BMEP(d)*KK 121 AFRR(d)=AFR(d)/AFSTO 122 TORQB(J) = (TORO(J) )*1.3558 123 TORQC(d)=T0RQB(d)*KK 124 C 125 C THE RESULTS ARE NOW WRITTEN IN COLUMNS BENEATH THE RESPECTIVE 126 C HEADINGS " 127 C 128 WRITE(6,106) TNUM(d),RPM(d),BSTP(d),BCKP(d),SPAD(d),TAM(d), 129 -TAIR(d).TEXH(d),MA(d),MF(d).AFRR(d).TORQC(d).BPC(d),BMEPC(d), 130 -EFF(d),BSFC(d) 131 106 F0RMAT(1H ,13.17,2F7 . 2.3F7. 1 ,F8. 1 ,F8.2,2F7.2.F8. 1.F8.2.F7.2.F8. 1 132 -.F8.1/) 133 C 134 15 CONTINUE 135 STOP 136 END 93 APPENDIX B ~ ENGINE PERFORMANCE DATA * n O) CP to I*- CD 0) 0) O CO Tf t» TT 80 O CO <J SC u s CJ 0) *1 r» CM IB CO CO I- O CM 1- m CO 0) o i» —^ tn a 10 Tt Tf tp tn TT r- tn co IP co tp n CO t- to 10 CD w CX CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM cn r» CX r» CO ^_ O CM to 10 CM CO 0) cn tn CO to u <— co 0) O r- a o O) 80 o r» 0) o CO O) Ul CM CM CO CM CM CO CM CM CO CM CO CO CM CM CO CM CM CM a . L. CO o to CM cn CO cn CO o IP Tf CO u n 0) 0) CO o> CM CM CO CO CM cn CO CO O Z X> CO — CP CP IP CP r- f- IP IP IP f» IP r» r~ r~ ui er Tt IP 9 80 CM 0) 1- o CO Tt CM IP CO to TI Tt o SC ui ~ CO CM O o O IP cn CM t- T r 80 CM TT CO CO « * * a o sc tt) tn tn o CM O 10 to o CM CM co a w CM CM CM CO CO CO r *" CM CM CM CO CO CO Ul 3 — IP CM 80 IP CO "» CO t- CO CO CO m 0> f - cn cn o O E CC • r» 10 Q Q CO CM (p O CO 1 T»— o t- CM CM en o z CD a CD O O Oi O o 0) o en 0) o o 01 o o cn r T»» o CO CO cn to CM <t? at CO IP CO T» CO o CO cn tp _J U K 0) O o O O cn cn OI o en o en en o Ul ^  < a < a o o *~ o o o O o O T»» _ i * IP a u o *> »- O 3 u u CD *~ »-g CM CO IP CM CO CO ao CD CM «- cn in IP to Tf IP CO O o o IP to Tf to CO CM CM CM CM CM CM CM * cr D m _i \ o o CO «p IP IC CM CM CM O o ro o to IP en CM in 0) 0) CM CO CO CO a cn CM CM 10 CO O t -CO CO en to 10 tn cn cn en CO CO en to in in en en en CM CM CM CO CO CO CM CM CM CO CO CO JST O O O O o O O o O o O o o o O o o O cn r- CO 10 CM O cc Tt CN CM m m~ CM en o o o I S O m IP 1 - co CO CM cn Tt CO CO Tf 5 m X U l O O O *• m rt 1 o O o *~ Tt Tt r r ui a ~ z ui o o O o O o o o o o o o o o o o o o CO CO in CO in CO CO Tf CO 10 CO CO CO CO CO CO CM CO CO CO CO CO CO CO CO CO Tt CO to CO in CO in CO . o. — O o o o o o o o O o o o o o o o O o CM CD I CJ Z ui CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM « t- <— r» t> r- t~ t» r» r- t- r» r~ r-in u u « O o o o o o o o O o o o o O o o O o ee < v < > X) CM CM CM IP IP IP o o o 1- in in in • CL O CM CM CM CM CM CM CO CO CO CM CM CM CO co CO CO CO CO »- in < w < z i/i ~ H sc in -CM LIU « O o O o o o o O o o o o o o O O O O • < i t a Ul Z co a. w O o o o o o o O o o o o o o O O o o _> »- in o in m " in O u Cl O CC Q. o o o o o o o O o o o o o o o O o o a * co a w O o o o o o o O o o o o o o o O o o Ul CL >-(9 Z Z a Ul cc 8 8 8 to to to Ul 3 in • Ul o t- z *- CM CO 0) O *" CM CO to IP r- co FUEL TYPE (1=GAS0LINE,2«NAT. GAS): 2 TEST NO. ENGINE RPM BOOST PRESS, (psi ) BACK PRESS (ps i ) SPARK .ADVANCE ( btdc) AMB . TEMP . ( C) INLET TEMP. ( C) EXHAUST TEMP. ( C) AIR FLOW g/s FUEL FLOW g/s REL. A/F RATIO TORQUE (Nm) BRAKE POWER (KW) BMEP (bar) EFF . (%) BSFC (g/KWh) 19 1500 0 .0 0.0 32 .0 72 .0 82 .0 1010 .0 18 .90 i . 18 0 .96 97 .5 15 .32 6 .93 27. 8 267.0 20 1500 0 .0 0.0 32 .0 72 .0 83 .0 1015 .0 18 90 i .09 1 .03 97 .0 15. .23 6 .89 29. 7 249.9 21 1500 0 .0 0.0 32 .0 72 .0 84 .0 1014 .0 19. 23 i .04 1 . 10 95 .7 15. .04 6 .80 30.7 241.8 22 200O 0. .0 0.0 36 .0 72 .0 84 .0 1090 .0 25. 86 i .71 0 .91 99 .0 20. .73 7.03 25. 9 286.6 23 2000 0 0 0.0 36 .0 72 .0 85 .0 1135 .0 25. 86 1 .48 1 .05 98 .4 20. 62 6 .99 29. 7 249.4 24 2000 0. 0 0.0 36 .0 72 .0 85. .0 1114. .0 26. 19 i .46 1 .08 97 .8 20. 48 6 .94 29. 9 248.2 25 2000 0. 0 0.0 36 .0 72 .0 85, .0 1046 .0 27. 19 1 . 19 1 .36 81 .3 17. .02 5 .77 30. 4 244.0 26 300O 0. 0 0.0 40 .0 72 .0 85. 0 1424 .0 39. 09 2 .54 0 .92 102 .3 32. . 13 7, .26 26. 9 275.3 27 3000 0. 0 0.0 40 .0 72 .0 85. .0 1442 .0 39. 42 2 .38 0. .99 102 .3 32. . 13 7 .26 28. 8 257.6 28 3000 0. 0 0.0 40 .0 72 .0 85. 0 1400. .0 39. 75 2 .23 1 , .07 97 .0 30. .47 6 .89 29. 1 254.7 29 1500 0. 0 0.0 37. 0 72 .0 83. 0 1012. .0 18. 90 1 . 11 1. .02 95 .6 15. 03 6 .79 28. 8 257.2 30 2000 0. 0 0.0 41 . 0 72 .0 83. 0 1130. 0 25. 86 1 . .54 1 . OO 98 .2 20. 57 6. .98 28. 5 260.6 31 3000 0. 0 0.0 45. 0 72 .0 83. 0 1410. 0 39. 42 2 .41 0. 98 101 .4 31 . 85 7. .20 28. 2 262.8 FUEL TYPE ( 1=GAS0LINE,2«NAT. GAS): 2 TEST NO. ENGINE RPM BOOST PRESS, (psi ) BACK PRESS, (psi ) SPARK ADVANCE ( btdc) AMB. TEMP. ( C) INLET TEMP. ( C) EXHAUST TEMP. ( O AIR FLOW g/s FUEL FLOW g/s REL. A/F RATIO TORQUE (Nm) BRAKE POWER (KW) BMEP (bar) EFF. (%) BSFC (g/KWh) 32 2000 0. 0 0.0 32 .0 77 .0 86 .0 1165 .0 25. 32 1 .41 1 .07 101 .7 21 .30 7 .22 31 . 9 232.3 33 20O0 0. 0 0.0 32 .0 72 .0 86 .0 1130 .0 26. 20 1 .51 1 .04 IOO .5 21 .05 7 . 14 29. 6 250.6 34 2000 1. 00 0.0 32 .0 77 .0 112. 0 1201 .0 28. 89 1 .55 1 . 12 115 .2 24. . 14 a . 19 32. 1 230.9 35 2000 1 . 00 0.0 32 .0 72 .0 96. ,0 1220 .0 29. 18 1 .60 1 .09 115 .2 24. . 14 8 . 19 31. 1 238.5 36 2000 2. 00 0.0 32 .0 77 .0 125. .0 1255 .0 32. 78 1 .72 1 . 14 126 . 1 26. 41 8 .96 31 . 6 234.5 37 2000 2. 00 0.0 32 .0 72 .0 106. O 1282 .0 32. 83 1 .73 1 . 14 127 .4 26. .70 9 .05 31 . 8 233. 1 38 200O 3. 00 0.0 32 .0 77 .0 133. 0 1300 .0 49. 26 1 .79 1 .65 135 .6 28. .40 9 .63 32. 8 226.3 39 20OO 3. 00 0.0 32 .0 72 .0 117. ,0 1313 .0 47. 03 1 .79 1 .57 136 .9 28. 68 9 .73 32. 9 225. 1 40 2000 0. 0 1 .00 32 .0 72 .0 78 0 1197 .0 26. 20 1 .47 1 .07 97 .6 20 .45 6 .94 29. 9 248.3 41 2000 0. 0 2.00 32 .0 72 .0 81. 0 1191 .0 25. 87 1 .45 1 .07 96 .0 20. 11 6 .82 29. 7 249.7 42 2000 0. 0 3.00 32 .0 72 .0 82. 0 1190, .0 25. 20 1 .40 1 .07 93 .5 19. 58 6. .64 29. 8 249.0 43 2000 1. OO 0.38 32 .0 77 .0 114. 0 1200 .0 28. 24 1 .55 1 .09 113 .9 23. 86 8 .09 31. 7 233.7 44 2000 2. 00 0.75 32 .0 77 .0 127. 0 1267 . 0 31 . 49 1 .72 1 . 10 122. .0 25. 56 8 .67 30. 6 242.3 45 20O0 3. 00 1.25 32. .0 77 .0 134. 0 1293 .0 36. 01 1 .76 1 .22 124 .7 26. 13 8. .86 30. 5 243.0 FUEL TYPE (1=GAS0LINE,2«NAT. GAS): 2 TEST NO. ENGINE RPM BOOST PRESS. (ps i ) BACK PRESS (psi ) SPARK ADVANCE ( btdc) AMB. TEMP. ( C) INLET TEMP. ( O EXHAUST TEMP. ( O AIR FLOW g/s 46 1500 0 .0 0 .0 27 .0 73 .0 90 .0 1030. 0 19.04 47 2000 0. .0 0 .0 32 .0 73 .0 90 .0 1160. 0 25 .60 48 3000 0. .0 0 .0 35 .0 73 .0 92 .0 1480 .0 38.37 49 1500 0 .0 0 .0 27 .0 74 .0 91 .0 1030 .0 19. 16 50 1500 0 .0 0 .0 27 .0 73 .0 83 .0 1058 .0 19.04 51 1500 0. .0 0 .0 27 .0 73 .0 83 .0 1050 .0 19.04 52 2 OOO 0 .0 0 .0 32 .0 73 .0 84 .0 1185. .0 25 .60 53 3000 O ,o O .0 35 .O 73 .0 85 . 0 1520 .0 39 .03 54 2000 0. 0 0 .0 17 .0 73 .0 85 .0 1235 .0 25 .93 55 30O0 0. 0 0 .0 22 .0 73 .0 85 .0 1610 0 39 .35 56 2000 0. .0 0 .0 32 .0 73 .0 86 .0 1155 0 25 .60 57 2000 1 . 50 0 .0 32 .0 73 .0 111 .0 1250. 0 28 .88 58 2000 3 00 0 .0 32 .0 73 .0 124 .0 1285. 0 40.01 59 1500 1 . 50 0 .0 27 .0 73 .0 115 .0 1058. 0 22 .65 60 30O0 1 50 0 .0 37 .0 73 .0 118 .0 1555 0 43.93 61 2000 1 . .50 1 .25 32 .0 73 .0 115 .0 1222. 0 29.54 FUEL REL. TORQUE BRAKE BMEP EFF. BSFC FLOW A/F (N.m) POWER (bar) (%) (g/KWh) g/s RATIO (KW) 1 .06 1 .07 97. . 1 15. 25 6 .90 30. 1 2 4 6 . 0 1 .41 1 .09 99. . 1 20. ,75 7 ,04 30. 9 239 .8 2 .21 1 .04 99. .9 31 .38 7 .09 29. 8 249 . 1 1 .05 1 .09 97 .4 15 .31 6 .92 30, 9 2 4 0 . 0 1 .06 1 .07 97 .7 15. .35 6 .94 30. 6 2 4 2 . 7 1 . 11 1.03 87. 8 13, .79 6 23 26. 4 2 8 1 . 0 1 .45 1 .06 99. . 1 20 .76 7 .04 30. 2 245 .5 2 . 17 1 .08 lOI .8 31 .98 7 .23 31 . 2 238*. 0 1 .37 1 . 14 86. .6 18 . 14 6 . 15 28. 0 264 .4 2 .38 0 .99 97, . 1 30, .52 6 .90 27. 1 2 7 3 . 9 1 .50 1 .02 99 .3 20. .80 7 .05 29. 3 252 .9 1 .63 1, .06 115. 9 24. 28 8 ,23 30. 8 241 . 1 1 .86 1 .28 130 8 27 .41 9 .29 30. 3 244 .9 1 .37 0 .99 110. .5 17, .36 7. .85 26. 2 283 .3 2 .57 1 .02 117. .3 36. .85 8 ,33 29. 5 251 .5 1 .47 1 .20 107. .8 22 58 7, .66 31 . 5 235. 1 FUEL TYPE ( 1=GAS0LINE,2=NAT. GAS): 2 TEST ENGINE BOOST BACK SPARK AMB. INLET EXHAUST AIR NO. RPM PRESS, (psi ) PRESS (psi ) . ADVANCE ( btdc) TEMP . ( C) TEMP. ( O TEMP ( O FLOW g/s 62 1500 0 .0 0 .0 27 .0 73 .0 74 .0 1011 .0 20 .02 63 2 OOO 0 .0 0 .0 32 .0 73 .0 78 .0 1180 .0 26 .58 64 3000 0 .0 O .0 35 .0 73 .0 81 .0 1528 .0 39 35 65 3000 1 .50 0 .0 35 .0 73 .0 114 .0 1481 .0 43 .60 66 3000 1 .50 0 .0 35 .0 73 .0 1 15 .0 1485 .0 43 .60 67 3000 1 .50 0 0 35 .0 73 .0 1 16 .0 1498 .0 44 .25 68 1750 1 .75 0. 0 30. .0 73 .0 1 15 ,0 1156 .0 26 58 69 1750 1 .75 0. .0 30 .0 73 .0 1 16 .0 1 186 .0 26 91 70 1750 1 .75 0. .0 30 .0 73 .0 1 18. 0 1179 .0 26. 91 71 1750 1 .75 0 .0 30 .0 73 .0 1 19. .0 11 19 .0 27 .24 72 1750 1 .50 0 0 30 .0 73 .0 117. 0 1171 .0 26. 26 73 1750 1 .50 0 0 15 .0 73 .0 118. 0 1180 .0 26 26 74 1750 1 .50 0 0 25. .0 73 .0 119. .0 1197 .0 26. 26 75 1750 1 . .50 0. 0 35, 0 73 .0 120.0 1 165 .0 26. 26 76 1750 1. 50 0. 0 45 .0 73 .0 121. 0 1129. 0 25. 93 77 1750 1 . 50 0. 0 30. 0 73 .0 121 . 0 1150. 0 26. 26 78 2000 0. 0 0. 0 15. .0 73 .0 83. 0 1176. 0 25. 60 79 2000 0. 0 0. 0 25. 0 73 .0 83. 0 1164. 0 25. 60 80 2000 0. 0 0. 0 35. .0 73 .0 83. 0 1131 . 0 25. 60 81 2000 o. 0 0. 0 45. 0 73 .0 83. 0 1100. 0 25. 60 FUEL FLOW g/s REL. A/F RATIO TORQUE (Nm) BRAKE POWER (KW) BMEP (bar) EFF . (7.) BSFC (g/KW 1 . 19 1 .01 96 .8 15 .20 6 .87 27 .2 272.4 1 .58 1 .01 100 .4 21 .04 7 . 13 28 .3 262.3 2 .36 1 .00 103 .3 32 .46 7 .34 29 .2 254. 1 2.87 0 .91 117 .3 36 .85 8 .33 26 .4 280.8 2 .70 0 9r 117 .3 36 .85 8 .33 28 . 1 264. 1 2.57 1 .03 111 .2 34 .93 7 .90 27 .9 265.3 1 .58 1 .01 118 .6 21 .74 a .43 28 .3 262. 1 1 .50 1 .08 1 18 .0 21 .62 8 .38 29 .8 249. 1 1 .32 1 .22 113 .9 20 87 a .09 32 .5 228 . 1 1 . 19 1 .37 101 .0 18 .51 7 . 17 32 .0 231 .9 1 .56 1 .01 1 16 .6 21 . 37 8 .28 28 .2 263.0 1 .'56 1 .01 107 .8 19. .76 7 .66 26 . 1 284.5 1 .56 1 . .01 115 .2 21 . 12 8 . 19 27 .9 266. 1 1 . 56 1 . .01 113 .9 20. 87 8 .09 27 .5 269.2 1 .54 1 . .01 107 .0 19. 61 7 60 26 .2 282.7 1 .56 1 . 01 115 .2 21 . 12 8. 19 27 .9 266. 1 1 .54 1 , 00 99 .0 20. 74 7. .03 28 .5 260.2 1 .54 1 . 00 99 .0 20. 74 7 03 28 .5 260.2 1 .54 1 . .00 95 .0 19. 90 6. ,75 27 .4 271 .0 1 .54 1 . 00 89 .0 18. 65 6. 32 25 .6 289. 1 VO FUEL TYPE (1=GAS0LINE.2=NAT. GAS): 2 TEST NO. ENGINE RPM BOOST PRESS, (psi ) BACK PRESS (psi ) SPARK .ADVANCE ( btdc) AMB. TEMP. ( C) INLET TEMP . ( C) EXHAUST TEMP. ( O AIR FLOW g/s 82 2000 0 .0 0.0 32 .0 73 .0 82.0 1 122 .0 25.27 83 2000 0 .0 0.0 32 .0 73 .0 83.0 1 174 .0 25.93 84 2000 0 .0 0.0 32 .0 73 .0 83.0 1135 .0 25.93 85 2000 0 .0 0.0 32 .0 73 .0 83.0 1102 .0 26.58 86 2 OOO 1 .50 0.0 32 .0 73 .0 114 .0 1210 .0 29.87 87 3000 3. ,00 0.0 35, ,0 73 .0 125.0 1550 .0 47.52 88 3500 3. 00 0.0 35 .0 73 .0 127.0 1607 .0 60.91 FUEL PEL. TORQUE BRAKE BMEP EFF. BSFC FLOW A/F (N.m) POWER (bar) (%) (g/KWh) g/s RATIO (KW) 1 .67 0 .91 97 ,6 20. 44 6 .93 25 .9 286 .0 1 .43 1 .08 99 .0 20. ,74 7 .03 30 .7 241 .9 1 . 32 1 . 17 95 .0 19. .90 6 .75 31 .8 232 .9 1 .24 1 .29 87 . 1 18. .24 6: : 18 31 .2 237 .4 1 .50 1 .20 110 .5 23. . 15 7 .85 31 .9 232 .7 2 .85 1 .00 124 .7 39. , 19 8 .86 28 .3 262 .0 3 .60 1 .01 132 .9 48 . 71 9 ,44 27 .9 266 .2 VO 00 99 APPENDIX C - PROPERTIES OF B.C. NATURAL GAS Composition (Volume %) Methane 94.00 Ethane 3.30 Propane 1.00 Iso-butane 0.15 N-butane 0.20 Iso-pentane 0.02 N-pentane 0.02 Nitrogen 1.00 Carbon Dioxide 0.30 Hexane 0.01 Water content: 3 to 4 l b s / m i l l i o n c u b i c f e e t T h i s composition may be c o n v e n i e n t l y approximated by the f o l l o w i n g composition: % Volume Volume Molecular Mass F r a c t i o n Weight kg/kmol Methane CH4 94.00 0.940 * 16.040 = = 15.078 Ethane C2H6 3.30 0.033 * 30.070 = 0.992 Propane C3H8 1 .00 0.010 * 44.097 « 0.441 Butane C4H10 0.40 0.004 * 58.124 = 0.232 Nitrogen 1 .00 0.010 * 28.013 = 0.280 Carbon Dioxide 0.30 0.003 44.010 = 0.132 100.00 1 .000 M=17.156 I t t h e r e f o r e f o l l o w s that the average molecular weight i s 17.156 and the gas constant = R. = 8.3143 = 0.4846 M 17.156 Hence, d e n s i t y = P/(Z*R*T) = 21.1° C at 1 atm (101.3 kPa). G e n e r a l l y , d e n s i t y at 1 atm = 209 / T (°K) kg/m . 100 V i s c o s i t y T h e v i s c o s i t y o f t h e n a t u r a l g a s a t 0 C may be o b t a i n e d f r o m t h e f o l l o w i n g : I y / * uj * (M; ) ' (M; ) where y ; = mo l f r a c t i o n M; = m o l e c . w t . g i v e n : 1 0 2 . 6 m i c r o p o i s e a t 0 C . 8 4 . 8 7 5 . 0 1 3 9 . 0 1 6 6 . 0 E s t i m a t i n g u a s 7 5 . 0 f o r C4H10 a s w e l l a s C3H8 a n d i n c l u d i n g t h e m o l e f r a c t i o n o f t h e f o r m e r w i t h t h e l a t t e r , t h e c a l c u l a t i o n b e c o m e s : CH4 C2H6 C3H8 C02 N2 V i s c o s i t y 1 0 2 . 6 8 4 . 8 7 5 . 0 1 3 9 . 0 1 6 6 . 0 yj 0 . 9 4 0 0 . 0 3 3 0 . 0 1 4 0 . 0 0 3 0 . 0 1 0 1 6 . 0 4 0 3 0 . 0 7 0 4 8 . 105 4 4 . 0 1 0 2 8 . 0 1 3 ( H i >* 4 . 0 0 5 5 . 4 8 4 6 . 9 3 6 6 . 6 3 4 5 . 2 9 3 M M ; ) * y ; u „ - ( M ; ) 3 . 7 6 5 0 .181 0 . 0 9 7 0 . 0 2 0 0 . 0 5 3 4 . 1 1 6 3 8 6 . 2 9 1 5 . 3 5 7 . 2 8 2 . 7 8 8 . 8 0 4 2 0 . 5 0 w i t h t h e r e s u l t , 4 2 0 . 5 = 1 0 2 . 16 j j p o i s e a t 0 ' C . 4 . 1 1 6 T h e v i s c o s i t y o f n a t u r a l g a s a t o t h e r t e m p e r a t u r e s c a n be o b t a i n e d f r o m , N . G . p = 9 . 8 7 9 * T3/% / (T + 1 6 3 . 1 7 ) T h e r e f o r e v i s c o s i t y o f N . G . a t 7 0 * F ( 2 1 . T O = 1 0 8 . 9 6 > i p o i s e 101 H i g h e r a n d L o w e r H e a t i n g V a l u e s mass mass HHV k g / k m o l (%) ( k J / K g ) CH4 15 .078 0 . 8 7 9 * 55496 48781 C2H6 0 . 9 9 2 0 . 0 5 8 * 51875 3008 C3H8 0.441 0 . 0 2 6 * 50343 1309 C4H10 0 . 2 3 2 0 . 0 1 3 * 49500 644 C02+N2 0 . 4 1 2 0 . 0 2 4 * 0 0 1 7 . 1 5 6 1 . 000 53742 T h e r e f o r e t h e H i g h e r H e a t i n g V a l u e o f B . C . n a t u r a l g a s i s 5 3 , 7 4 2 k J / k g a t 2 5 " C . T h e Lower H e a t i n g V a l u e i s g i v e n b y , ma s s (%) LHV CH4 0 . 8 7 9 * 50010 43959 C2H6 0 . 0 5 8 * 47484 2754 C3H8 0 . 0 2 6 * 46353 1205 C4H10 0 . 0 1 3 * 45714 640 C02+N2 0 . 0 2 4 * 0 0 1 .000 48558 T h e r e f o r e t h e Lower H e a t i n g V a l u e o f B . C . n a t u r a l g a s i s 4 8 , 5 5 8 k J / k g a t 2 5 ° C . 102 APPENDIX D ~ OTTO C Y C L E SIMULATION PROGRAM (COMB) T h i s a p p e n d i x d e s c r i b e s t h e p r o g r a m OTTO w h i c h was w r i t t e n i n o r d e r t o s i m u l a t e an i d e a l f u e l - a i r c y c l e . The m a j o r s e c t i o n s o f t h e p r o g r a m a r e : -a) C a l c u l a t i o n o f m i x t u r e c o m p o s i t i o n a n d e n e r g y a t B . D . C b) A d i a b a t i c c o m p r e s s i o n o f m i x t u r e t o T . D . C . c ) C o n s t a n t v o l u m e c o m b u s t i o n a t T . D . C . d) A d i a b a t i c e x p a n s i o n o f p r o d u c t s t o B . D . C . e ) C a l c u l a t i o n o f e f f i c i e n c y a n d mean e f f e c t i v e p r e s s u r e . E a c h o f t h e m a j o r s e c t i o n s a r e d e s c r i b e d b e l o w a n d i l l u s t r a t e d w i t h f l o w d i a g r a m s a t t h e e n d o f t h e a p p e n d i x . A f u l l l i s t i n g o f t h e p r o g r a m i s a l s o g i v e n a t t h e e n d o f t h e A p p e n d i x . a . I n i t i a l M i x t u r e C o m p o s i t i o n And E n e r g y The m a i n i n p u t s t o t h e p r o g r a m a r e : -F u e l t y p e a n d p r o p e r t i e s I n l e t p r e s s u r e a n d t e m p e r a t u r e A i r f u e l r a t i o C o m p r e s s i o n r a t i o E n g i n e b o r e , s t r o k e , c o n - r o d l e n g t h E x h a u s t g a s r e s i d u a l f r a c t i o n T h e s e v a l u e s a r e u s e d t o d e t e r m i n e t h e p r o p e r t i e s o f t h e m i x t u r e a t b o t t o m d e a d c e n t r e p r i o r t o c o m p r e s s i o n . The c h e m i c a l b a l a n c e e q u a t i o n f o r t h e c o m b u s t i o n o f a h y d r o c a r b o n f u e l i n a i r , a t a g i v e n r e l a t i v e a i r / f u e l r a t i o ( A ) i s : -f u e l ( N C H ) o x y g e n ( N 0 2 ) n i t r o g e n ( N ) (C„ H« ) + ^n + mj . A 0 + 3 . 7 6 2 . ^n + m j . > N 2 n C 0 2 + m H z O + ^n + m j . (A -1 ) O z + 3 . 7 6 2 . ^n + m^. X N 2 c a r b o n w a t e r e x c e s s o x y g e n ( M ) n i t r o g e n ( N ) d i o x i d e (L ) ( K ) (1) where n = number o f c a r b o n a t o m s i n f u e l (CN i n p r o g r a m ) a n d m = number o f h y d r o g e n a t o m s i n f u e l (HM i n p r o g r a m ) 103 The s y m b o l s N C H , N 0 2 , N , K , L & M a r e u s e d i n t h e p r o g r a m t o r e p r e s e n t t h e s t o i c h i o m e t r i c c o e f f i c i e n t s , e . g . , N 0 2 = ( n + m / 4 ) . . , K=n, L=m/2 e t c . A l l o f t h e m i x t u r e c a l c u l a t i o n s i n t h e p r o g r a m a r e b a s e d on one kmol o f h y d r o c a r b o n f u e l , t h e r e f o r e NCH=1, a n d t h e number o f k m o l s o f f r e s h m i x t u r e p e r kmol o f f u e l i s g i v e n b y ; SUMNS = NCH + N02 + N (2) S i n c e r e s i d u a l g a s e s a r e i n c l u d e d i n t h e s i m u l a t i o n , t h e number o f k m o l s o f r e s i d u a l g a s ( N R E S ) , r e l a t i v e t o t h e number o f k m o l s o f f r e s h m i x t u r e (SUMNS) h a s t o be c a l c u l a t e d G i v e n t h e m o l e f r a c t i o n o f r e s i d u a l g a s e s ' F ' , t h e number o f k m o l s o f r e s i d u a l g a s 1 N R E S ' i s g i v e n by NRES = F . ( T o t a l number o f k m o l s ) . . . . ( 3 ) a n d SUMNS = ( 1 - F ) . ( T o t a l number o f k m o l s ) . . . . ( 4 ) t h e r e f o r e NRES = ( F / ( 1 - F ) ) . S U M N S (5) a n d t h e t o t a l number o f k m o l s o f m i x t u r e i n t h e c y l i n d e r p e r kmol o f f u e l (NMIX) i s g i v e n b y : NMIX = SUMNS +. N R E S . (6) G i v e n t h e p e r c e n t a g e c o n c e n t r a t i o n s o f r e s i d u a l g a s e s f r o m t h e i n p u t f i l e , t h e number o f k m o l s o f e a c h r e s i d u a l g a s c o n s t i t u e n t i s now c a l c u l a t e d , a n d a d d e d t o t h e number o f k m o l s o f t h e same s p e c i e s w h i c h were c a l c u l a t e d i n t h e c h e m i c a l b a l a n c e e q u a t i o n 1 a b o v e , e g . N o . o f k m o l s o f = ( p e r c e n t a g e r e s i d u a l o x y g e n ) x r e s i d u a l o x y g e n ( n o . o f k m o l s o f r e s i d u a l ) / l 0 0 o r NR02 = PR02 . NRES / 100 (7) t h e r e f o r e N 0 2 M S l v = NC-2^ + NR02 (8) s i m i l a r l y f o r C 0 2 , H20 a n d N2 T h e e n e r g y o f t h e m i x t u r e i s c a l c u l a t e d u s i n g : E = (H - PV) = (H - RT) (9) SO E R C T = Z Nj ( h f ; + Ah; - RT1 ) . . . . ( 1 0 ) where N,- = number o f k m o l s o f c o n s t i t u e n t ' i ' e g . NCH, N02 e t c . h f j = e n t h a l p y o f f o r m a t i o n o f c o n s t i t u e n t ' i ' i n k J / k m o l a t 298K a n d 1 b a r . 104 Ahj = d i f f e r e n c e i n e n t h a l p y o f c o n s t i t u e n t ' i ' b e t w e e n t e m p e r a t u r e T1 a n d 298K ( o b t a i n e d u s i n g f o r m u l a e g i v e n i n [24] ) . R = u n i v e r s a l g a s c o n s t a n t i n k J / k m o l K a n d T1 = i n l e t t e m p e r a t u r e o f m i x t u r e . T h e e n e r g y ERCT o b t a i n e d a b o v e h a s t h e u n i t s k J / k m o l f u e l a n d i s t h e r e f o r e m u l t i p l i e d by t h e number o f k m o l s o f f u e l p r e s e n t i n t h e c y l i n d e r i n o r d e r t o o b t a i n t h e e n e r g y ENGY1 o f t h e c y l i n d e r c o n t e n t s i n K J . T h e number o f k m o l s o f f u e l p r e s e n t i n t h e c y l i n d e r (MOLFL) i s o b t a i n e d f r o m t h e i d e a l g a s l a w , w h e r e P 1 . V1 = nmol . R . T1 (11) w h e r e nmol = n o . o f k m o l s o f m i x t u r e i n c y l i n d e r = NMIX / k m o l s m i x t u r e \ . MOLFL ( k m o l s f u e l ) \ kmol f u e l / SO MOLFL = (P1 . V 1 ) / (NMIX . R . T1 ) (12) a n d ENGY1 = ERCT . M O L F L . (13) b . A d i a b a t i c C o m p r e s s i o n Of M i x t u r e T h i s s e c t i o n o f t h e p r o g r a m c a l c u l a t e s t h e p r e s s u r e , t e m p e r a t u r e a n d e n e r g y o f t h e m i x t u r e a t 50 s t e p s , s e p e r a t e d by e q u a l v o l u m e d i v i s i o n s , up t o t o p d e a d c e n t r e The f i r s t l aw f o r t h e p r o c e s s g i v e s : dE = dQ - dW . . . . ( 1 4 ) o r E2 = E1 + dQ - pdv . . . . ( 1 5 ) b u t dQ = 0 f o r an a d i a b a t i c c h a n g e . T h e r e f o r e E2 = E1 - pdv . . . . ( 1 6 ) where p d v c a n be a p p r o x i m a t e d by (P1 + P 2 ) . ( V 2 - V1 ) 2 SO E2 = E1 + (P1 + P 2 ) . ( V 2 - V I ) (17) 2 A l s o P2 = P 1 . ^ V 1 _ ^ T 2 j (18) a n d E2 = f ( T 2 ) a s d e s c r i b e d i n t h e p r e v i o u s s e c t i o n f o r E R C T . 105 T h e s e e q u a t i o n s a r e s o l v e d a t e a c h v o l u m e s t e p by an i t e r a t i v e p r o c e d u r e i n w h i c h t h e t e m p e r a t u r e i s i n c r e a s e d i n s t e p s , t h e c o r r e s p o n d i n g p r e s s u r e (P2) a n d e n e r g y (E2) o b t a i n e d , a n d t h e e r r o r E 2 - E 1 + ( ( P 1 + P 2 ) / 2 ) . ( V 2 - V 1 ) = R E M c a l c u l a t e d . T h e t e m p e r a t u r e T2 i s i n c r e a s e d i n s t e p s o f 200K u n t i l t h e s i g n o f t h e r e m a i n d e r c h a n g e s . A t t h i s p o i n t , t h e t e m p e r a t u r e a t w h i c h REM =0 ( i . e . e q u a t i o n (17) i s s a t i s f i e d ) h a s b e e n b r a c k e t e d a n d a p r o p o r t i o n a l c h o p p i n g t e c h n i q u e , b a s e d on t h e r e l a t i v e m a g n i t u d e s o f t h e r e m a i n d e r s , i s u s e d t o f i n d t h e t e m p e r a t u r e (T2) a t w h i c h t h e e q u a t i o n s 17 a n d 18 a r e s a t i s f i e d a n d REM= 0 . T h e v o l u m e i s t h e n i n c r e m e n t e d t h r o u g h a n o t h e r s m a l l d i v i s i o n a n d t h e p r o c e s s r e p e a t e d u n t i l T . D . C . i s r e a c h e d . c . C o n s t a n t V o l u m e C o m b u s t i o n T h i s i s c a l c u l a t e d u s i n g t h e s u b r o u t i n e s COMB a n d ENERGY. F o r c o n s t a n t v o l u m e a d i a b a t i c c o m b u s t i o n , t h e e n e r g y o f t h e p r o d u c t s must be e q u a l t o t h e e n e r g y o f t h e r e a c t a n t s , i . e . Z N j . t h f j + (hjfrz) " h/fr.) ) - R . T 2 ) p r o d u c t s Z Nj . (h f ; r e a c t a n t s + (h^Yn) - h ^ T o " ) ) - R . T 1 ) . . . . ( 1 9 ) a l s o P2 = P I . V 1 . T 2 . / n o . o f m o l s o f p r o d u c t \ . . . . ( 2 0 ) V 2 . T 1 ( n o . o f m o l s o f r e a c t a n t s j T h e e n e r g y o f t h e r e a c t a n t s i s known f r o m t h e l a s t c o m p r e s s i o n s t e p w h i c h l e a v e s t h e t e m p e r a t u r e a f t e r c o m b u s t i o n , (T2 ) a n d t h e c o n c e n t r a t i o n s o f t h e p r o d u c t s o f c o m b u s t i o n ( N j ' s ) a s u n k n o w n s . T h e s u b r o u t i n e COMB i s an i t e r a t i o n r o u t i n e t h a t i n c r e m e n t s t h e p r o d u c t s t e m p e r a t u r e (T2) u n t i l e q u a t i o n s 19 a n d 20 a r e s a t i s f i e d ( e r r o r = 0 ) . T h e p r o d u c t c o n c e n t r a t i o n s a t a g i v e n t e m p e r a t u r e , a n d h e n c e t h e e n e r g y o f t h e p r o d u c t s , b e i n g c a l c u l a t e d by t h e s u b r o u t i n e ENERGY. S u b r o u t i n e ENERGY t a k e s a g i v e n p r o d u c t s t e m p e r a t u r e and p r e s s u r e (T2 & P) t o g e t h e r w i t h t h e u n d i s s o c i a t e d p r o d u c t s c o n c e n t r a t i o n s ( K , L , M , a n d N ) , a n d p r o c e e d s t o c a l c u l a t e t h e t e n d i s s o c i a t e d p r o d u c t c o n c e n t r a t i o n s a n d t h e e n e r g y o f t h e p r o d u c t s EPROD. 106 F o r t h e r e a c t i o n , x„ A + x 8 B = C + x„ D . . . . ( 2 1 ) where t h e x A - X?are t h e s t o i c h o i m e t r i c c o e f f i c i e n t s , t h e g e n e r a l d i s s o c i a t i o n e q u a t i o n h a s t h e f o r m : X^ Xp X c ^"Xp ~ x # y c . y „ = = KA - KF i n x„ x 8 ( p j t h e p r o g r a m . . . . ( 2 2 ) Y* y» where y„ - y„ a r e t h e mol f r a c t i o n s o f t h e c o m p o n e n t s A - D , a n d K i s t h e e q u i l i b r i u m c o n s t a n t f o r t h e r e a c t i o n c o n s i d e r e d . P° i s t h e p r e s s u r e a t s t a n d a r d c o n d i t i o n s = 0.1 M P a . a n d P i s t h e p r e s u r e a t w h i c h t h e r e a c t i o n t a k e s p l a c e . The s i x d i s s o c i a t i o n r e a c t i o n s c o n s i d e r e d w e r e : C02 ^ CO + 1/2 02 (23) ( - A ) (+A) (+1 /2 A) H20 5=* 1/2 H2 + OH (24) ( - B ) (+1/2 B) (+B) H20 ^ H2 + 1/2 02 (25) (-c) (+C) (+1 /2 C) 1/2 N2 + 1/2 02 ^ NO (26) - 1 / 2 D) ( - 1 / 2 D) (+D) H2 ^ 2H (27) ( - E ) (+2E) 02 ^ 20 (28) ( - F ) (+2F) where A - F r e p r e s e n t t h e n o . o f k m o l s o f e a c h s p e c i e s d i s s o c i a t e d . G i v e n t h e o r i g i n a l number o f m o l s o f e a c h p r o d u c t b e f o r e d i s s o c i a t i o n (K = C 0 2 , L = H 2 0 , M = r e s i d u a l 0 2 , N = N 2 ) , t h e number o f m o l s o f t h e p r o d u c t s a f t e r d i s s o c i a t i o n a r e g i v e n b y : P r o g r a m S y m b o l . 1 . N CO = X( 1 ) = K - A 2 . N CO = X ( 2 ) = A 3 . N H 0 = X ( 3 ) = L - B - C 4 . N H X ( 4 ) = C + B / 2 - E 107 5. N 0 = X(5) = M-F+(A+C-D)/2. 6. N N = X(6) = N-D/2 7. N NO = = X(7) = D 8. N OH = = X(8) = B 9. N 0 = X(9) = 2.F 10. N H = X(10) = 2.E (29) And the t o t a l number of kmols of p r o d u c t s (S) i s g i v e n by: S = K+L+M+N+(A+B+C)+E+F (30) 2 (D c a n c e l s o ut) The g e n e r a l d i s s o c i a t i o n e q u a t i o n (22) can now be w r i t t e n f o r each of the s i x d i s s o c i a t i o n r e a c t i o n s c o n s i d e r e d : AV ( M - F + ( A + C- D)/2Vi , V O / I f \ — "-CO, . . . . V J 1 / ' ~7 /B/2 -rC-Ef /BV » \ S ) UJ (JL) - K H 0 ( o H ) ^L-D-Cj' \PV (32) /B/2 +C-EV fo-F+U+C-D)^^ \ S J \ S J fP_y = K H . 0 rod (33) ^L-B-Cj' I P V (§)' ^N-D/2J/x ^M-F+(A+C-D)/2^ I S I ( P \ ^0+6/2 - E j [P'J = K„ z (34) ^M-F+(A+C-D)/2j K-nz ....(35) = K0_ ....(36) V a l u e s f o r the e q u i l i b r i u m c o n s t a n t s K, were o b t a i n e d by f i t t i n g c u r v e s of the form; l n k = A + B. ( l n T ) C t o the d a t a g i v e n i n Ref24, and when m u l t i p l i e d by the ( P ° / P ) terms i n t h e e q u i l i b r i u m e q u a t i o n s , r e s u l t e d i n the e x p r e s s i o n s f o r KA-KF used i n the program. 108 E q u a t i o n s 31 t o 36 a r e s o l v e d f o r A,B,C,D,E and F by assuming i n i t i a l v a l u e s , and s u c c e s s i v e l y i t e r a t i n g towards the t r u e v a l u e s which s a t i s f y the s i x e q u a t i o n s s i m u l t a n e o u s l y , Newton's method b e i n g used f o r each of the s i x e q u a t i o n s . H aving c a l c u l a t e d the c o n c e n t r a t i o n changes A - F, the d i s s o c i a t e d p r o d u c t c o n c e n t r a t i o n s (Nj) a r e de t e r m i n e d u s i n g e q u a t i o n s e t 29 As s t a t e d above, the energy of the p r o d u c t s i s g i v e n by, EPROD = l N j . ( h f J + ( h j ^ - h j ^ ) - R.T2) (37) The hf°j v a l u e s f o r each p r o d u c t ( a t T = 298K) a r e l i s t e d i n the program as UUU(1) t g UUUOO), The DH v a l u e s ( hjfrz)- h j (TB) ) f o r each p r o d u c t a re c a l c u l a t e d u s i n g p o l y n o m i a l e x p r e s s i o n s g i v e n i n Benson and Whitehouse (Ref if) and by i n t e g r a t o n of s p e c i f i c heat e p r e s s i o n s g i v e n i n Van Wylen and Sonntag (Ref24) The s u b r o u t i n e ENERGY c o n c l u d e s by c a l c u l a t i n g the m o l e c u l a r w e i g h t , and the average s p e c i f i c heat of the m i x t u r e of p r o d u c t s . d. A d i a b a t i c E x p a n s i o n Of P r o d u c t s T h i s s e c t i o n of the program c a l c u l a t e s the p r e s u r e , t e m p e r a t u r e , energy and s p e c i e s c o n c e n t r a t i o n s of the p r o d u c t s of combustion a t 50 s t e p s , s e p a r a t e d by e q u a l volume d i v i s i o n s , down t o bottom dead c e n t r e . The f i r s t law f o r the p r o c e s s ; as shown f o r the com p r e s s i o n s t r o k e , g i v e s : E2 = E1 + (P1 + P2).(V2 - V1) (38) 2 a l s o P z = P a . _Vi . Tp.. /number of mols of p r o d u c t s N V x T, Vnumber of mols of r e a c t a n t s , / ....(39) and E a t a g i v e n p r e s s u r e and temperature i s c a l c u l a t e d u s i n g s u b r o u t i n e ENERGY d e s c r i b e d above.The e q u a t i o n s a r e s o l v e d u s i n g a p r o p o r t i o n a l c h o p p i n g i t e r a t i o n ~ p r o c e d u r e by v a r y i n g T2 u n t i l b o t h e q u a t i o n s a r e s a t i s f i e d . The p r o d u c t s c o n c e n t r a t i o n s a re f r o z e n a t 1750K s i n c e no s i g n i f i c a n t change i n c o m p o s i t i o n o c c u r s below t h i s t e m p e r a t u r e . 109 e. C a l c u l a t i o n Of E f f i c i e n c y And MEP The work done d u r i n g the compresion and expansion s t r o k e s i s c a l c u l a t e d u s i n g the e x p r e s s i o n : i = 50 Jpdv = T_ ((P, + P,. )/2).(Vu -V, ) (40) 1 = 1 a l l o w i n g t h e MEP and e f f i c i e n c y t o be c a l c u l a t e d u s i n g : MEP = Jpdv / V (41) where V = swept volume, and E f f i c i e n c y = Jpdv / QVS.MOLFL.Mf (42) where QVS = LHV of f u e l (kJ/kg) MOLFL = Number of kmols of f u e l i n c y l i n d e r Mf = M o l e c u l a r weight of f u e l The program ends by p r i n t i n g out the v a l u e s of the p r e s s u r e , t e m p e r a t u r e , p r o d u c t c o n c e n t r a t i o n s and e n e r g i e s a t each c a l c u l a t i o n s t e p . 110 OTTO CYCLE SIMULATION PROGRAM FLOWCHART INPUT: F U E L TYPE; ENGINE SPEED; A/F RATIO; INTAKE A I R PRESSURE AND TEMPERATURE. ± CALCULATE PROPERTIES OF CYLINDER CONTENTS AT BDC AND AT EACH CRANK ANGLE STEP UP TO TDC, ASSUMING ISENTROPIC COMPRESSION AT TDC, BURN CYLINDER CONTENTS AT CONSTANT VOLUME INCLUDING THE EFFECTS OF DISSOCIATION USING Eproducts=Ereactants AND IDEAL GAS LAW t CALCULATE PROPERTIES C CRANK ANGLE STEP TO EXPANS >F CYLINDER CONTENTS AT EACH BDC, ASSUMING ISENTROPIC ;ION. sfc CALCULATE IMEP AND E F F I C I E N C Y W. PRINT RESULTS AND PLOT GRAPHS STOP 111 1 SAMPLE INPUT F I L E FOR PROGRAM "COMB" 2 ==================================== 3 4 5 003 6 001 0 0 7 1.0 4.0 100.0 300.0 1.00 -74873.0 1 11 8 0.078 0.085 9.00 50 50010.0 3000.0 0.124 1.000 9 0.0000 0.0000 0.0000 0.0000 0.0000 10 3.0 8.0 100.0 300.0 1.00 -103847.0 1 13 11 0.078 0.085 9.00 50 46353.0 3000.0 0.124 1.000 12 0.0000 0.0000 0.0000 0.0000 0.0000 13 8.0 18.0 100.0 300.0 1.00 -208447.0 1 12 14 0.078 0.085 9.00 50 44788.0 3000.0 0.124 1.000 15 0.0000 0.0000 0.0000 0.0000 0.0000 16 ====== 17 NUMBR 18 ================== 19 MODE IPRINT I PLOT 20 ======================================================== 21 CN HM P1 T1 LAMBDA HFO NDISS KFUEL 22 ======================================================== 23 STROK BORE COMPR NDIV QVS SPEED LENG SPKAD 24 ================================================== 25 F PR02 PRC02 PRH20 PRN2 26 1 2 3 4 5 6 7 8 9 .10 1 1 12 13 14 15 16 F U E L ; C 1.0 H 4 . 0 SPEED (RPM) = 3000.0 A I R / F U E L RATIO* 17.17 STOICH. A / F RATIO= 17.17 LAMBDA= 1.00 COMP. RATIO= CONCENTRATION OF COMB. PRODUCTS (KMOLS) STEP VOL 1 49 1 49 497 64 55 488 PRESS 100.0 1595.5 877 1 .9 604 .2 TEMP 300. 619. 2895 . 1791 . C02 0 . 0 0 . 0 7 .682 9 .459 CO 0 . 0 0 . 0 1.711 0 .040 H20 0 .0 0 . 0 18.207 18.977 H2 0 . 0 0 . 0 0 .580 0 .022 02 N2 19.004 7 1 .494 19.004 71 .494 1.146 70 .675 0.031 71.472 NO 0 . 0 0 . 0 0 . 0 0 . 0 OH 0 . 0 0 . 0 0 . 0 0 . 0 9 . 0 0 . 0 0 . 0 0 . 0 0 . 0 H 0 . 0 0 . 0 0 . 0 0 . 0 GAM - 0 . 3 9 9 5 E - 0 1 1 . 244 -0 .8783E+00 POWER= 17.057 I . M . E . P . = 15.415 EFFICIENCY= 44 .95 I . S . F . C . = 160.41 ro TYPICAL OUTPUT FROM PROGRAM "COMB" 113 1 C COMB THIS PROGRAM SIMULATES CONSTANT VOLUME COMBUSTION 2 C ==== IN A SINGLE CYLINDER S.I. ENGINE. IT IS ALSO 3 C CAPABLE OF CALCULATING ADIABATIC FLAME TEMPS. 4 C 5 IMPLICIT REAL*8(A-H.O-Z) 6 REAL*8 K,L,M,N,NO,N2.N02,NCH,KK,NUM,NUM1.NMIX,MOLFL,NM, 7 -NM1,NNM1,NNM2,NN2,NN02,MEP,LENG,MTOT,MWMIX,MFX1,NNCH,MFX2, 8 -MW(14),MMFX2,NRN2,NRES,NR02,NRC02,NRH20,NNFUEL,NNM3,MPV , 9 -MWBMIX,LAMBDA,IGNDEL,ISFC 10 C 11 COMMON /AREA 1/ NCH,N02,K,L,M,N,KFUEL 12 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02,NN2,NNFUEL,KOM 13 COMMON /AREA3/ AREAB,HTEXP,MPV,HTFCN.TWALL,VISC,THCOND 14 COMMON /AREA4/ NDISS,IPRINT 15 C 16 DIMENSION X(10),PP(5,200),VV(5,200),VV2(5,200),VV4(5,200), 17 -PP4(5,200),CC(10),XX(5,200),YY(5,200),PP2(5,200),CPG(10) , 18 -UUU(10),DH(20),CCA(10) 19 C 20 C STATEMENT FUNCTION USED THROUGHOUT PROGRAM TO CALCULATE CYLINDER 21 C VOLUME(DVOL) AT A GIVEN CRANK ANGLE (DALFA). VOLUME OBTAINED MUST 22 C BE ADDED TO THE CLEARANCE VOLUME TO GIVE TOTAL CYLINDER VOLUME. 23 C 24 DVOL(DALFA) = 3. 14 159*((BORE/2. )**2. )*(STR0K/2 . )*(1.-DCOS(DALFA* 25 -0.0174532)+(STR0K/(4.*LENG))*((DSIN(DALFA*0.0174532))**2.)) 26 C 27 C READ NUMBER OF RUNS TO BE MADE 28 C 29 READ(5,999) NUMBR 30 999 FORMAT(IS) 31 C 32 C READ WHAT MODE PROGRAM IS TO OPERATE IN; 33 C IF M0DE=1, PROGRAM WILL RUN AS CONST. VOL. ENGINE SIMULATION 34 C IF M0DE=2, PROGRAM WILL RUN WITHOUT COMP. 8. EXP. STROKES 35 C (I.E. CONSTANT VOLUME COMB. AT INTAKE P 8. T) 36 C IF M0DE=3, PROGRAM WILL CALCULATE ADIABATIC FLAME TEMP. 37 C (I.E. CONSTANT PRESS. COMBUSTION) 38 C IF IPRINT=1 ALL OF THE STEPS OF THE DISSOCIATION CALCULATIONS 39 C WILL BE PRINTED. TO PREVENT THIS IPRINT SHOULD BE SET TO ZERO. 40 C IF IPL0T=1 A P-V DIAGRAM WILL BE PLOTTED. TO PREVENT THIS IPLOT 41 C SHOULD BE SET TO ZERO. 42 C 43 READ(5,998) MODE,IPRINT,IPLOT 44 998 F0RMAT(3I3) 45 C 46 C RUN THROUGH PROGRAM 'NUMBR' OF TIMES; 47 DO 222 IL=1,NUMBR 48 C 49 C READ NUMBER OF MOLES OF CARBON (CN) AND HYDROGEN (HM) IN FUEL; 50 C PRESSURE (P1)(KPA) AND TEMP. (T1)(K) AT START OF COMBUSTION; 51 C REL. AIR/FUEL RATIO (LAMBDA); HFO FOR THE FUEL (HF1); LEVEL OF 52 C ' DISSOCIATION 1,2 OR 3 (NDISS); FUEL TYPE (11=CH4,12=C8H18, 53 C 13=C3H8). 54 C IF M0DE=1, READ THE FOLLOWING VALUES ALSO:-55 C PISTON STROKE (STROK)(M); PISTON BORE (BORE ) (M); 56 C COMPRESSION RATIO (COMPR); NUMBER OF VOLUME DIVISIONS 57 C IN COMPRESSION STROKE (NDIV); LOWER HEATING VALUE OF FUEL 58 C (0VS)(KJ/KG); ENGINE SPEED (RPM); LENGTH OF CONROD (LENG)(M); 1 14 59 C SPARK ADVANCE ( SPKAD ) (DEG B.T.D.C). 60 C RESIDUAL GAS FRACTION MAY BE INCLUDED OR SET ALL TO ZERO; 61 C RESIDUAL GAS FRACTION (50, (F); PERCENTAGE CONSTITUENTS IN 62 C RESIDUAL FRACTION (PR02,PRC02,PRH20,PRN2). 63 C 64 READ(5,49) CN.HM.P1.T1,LAMBDA,HF1.NDISS,KFUEL 65 IF(MODE.GT.1) GOTO 32 66 READ(5,48) STROK,BORE,COMPR,NDIV,QVS,SPEED,LENG,SPKAD 67 32 READ(5,47) F,PR02,PRC02,PRH20,PRN2 68 49 FORMAT(2F6.1,F7.1,F8.1,F6.2,F11.1,14, 15) 69 48 F0RMAT(2F6.3,F6.2,I3,F8.1,F7.1.2F7.3) 70 47 F0RMAT(5F7.4) 71 RM0L=8.3143 72 JJ=0 73 C CALC. NUMBER OF MOLES OF REACTANTS AND PRODUCTS BEFORE AND 74 C AFTER COMPLETE COMBUSTION OF ONE KMOL OF FUEL. NCH=HYDROCARBON 75 C N02=AVAILABLE OXYGEN N=NITROGEN K=C02 L=H20 M=UNBURNED 76 C OXYGEN.... 77 NCH= 1 78 N02=(CN+HM/4)*LAMBDA 79 N=3.762*(CN+HM/4)*LAMBDA 80 K = CN 81 L=HM/2 82 M=(CN+HM/4)*(LAMBDA-1) 83 C WRITE(6,655) NCH,N02,N,K.L.M 84 C 655 F0RMAT(1H ,'NCH,N02,N,K,L,M=',6F9.5/) 85 SUMNS=NCH+N02+N 86 C CALC. NUMBER OF KMOLS OF RESIDUAL GAS GIVEN VOLUME FRACTION OF 87 c RESIDUAL GASES 'F'.... 88 NRES=(F/(1-F))*SUMNS 89 c CALC NO. OF KMOLES IN CYLINDER PER KMOL OF FUEL... 90 NMIX=SUMNS+NRES 91 SUMNS=NMIX 92 c CALC. NO. OF MOLS OF EACH RESIDUAL GAS... 93 NR02=PR02*NRES 94 NRC02=PRC02*NRES 95 NRH20=PRH20*NRES 96 NRN2=PRN2*NRES 97 c CALC. NEW VALUES FOR NO. OF MOLS OF NITROGEN, OXYGEN, C02 8. H20. 98 N=N+NRN2 99 N02=N02+NR02 100 K=K+NRC02 101 L=L+NRH20 102 M=M+NR02 103 c CALC. STOICH. A/F RATIO (STAFR),AIR/FUEL RATIO (AFR),PERCENTAGE 104 ' c OXYGEN (NN02), NITROGEN (NN2) AND FUEL (NNFUEL) IN MIXTURE... 105 STAFR=((CN+HM/4.)*32.+3.762*(CN+HM/4.)*28.01)/((CN*12)+HM) 106 AFR=STAFR*LAMBDA 107 NN02=(N02/NMIX)*1OO. 108 NN2=(N/NMIX)*100. 109 NNCH=100.-(NN02+NN2) 1 10 NNFUEL=NNCH 1 1 1 c 1 12 c DEFINE MOLECULAR WEIGHTS OF FUELS.. 1 13 MW(11)=16.04 114 MW(12)=114.23 1 15 MW(13)=44.097 1 16 c 115 117 C WRITE(6,655) NCH.N02,N,K,L.M 1 18 C 119 C CALC. ENERGY OF REACTANTS AT INITIAL TEMP. T1.... 120 C 121 DH(1)=((3.096*T1+0.00273*(T1**2)-7.885E-07*(T1**3) 122 1+8.66E-1 1*(T1**4))-1145.0)*RMOL 123 DH(3)=((3.743*T1+5.65GE-04*(T1**2)+4.952E-08*(T1**3) 124 1-1.818E-11*(T1**4))-1167.0)*RM0L 125 DH(5) = ((3.253*T1+G.524E-04*(T1**2)-1.495E-07* ( T1**3) 126 1+1 .539E-11*(T1**4))-1024.0)*RM0L 127 DH(6)=((3.344*T1+2.943E-04*(T1**2)+1.953E-09*(T1**3) 128 1-6.575E-12*(T1**4))-1023.0)*RMOL 129 DH(11)=((1.935*T1+4.965E-03*(T1**2.)-1.244E-06*(T1**3.) 130 1+1 .625E-10*(T1**4. )-8 . 586E-15*(T1 **5.))-985.9)*RMOL 131 DH(12)=((-0.72*T1+4.643E-02*(T1**2.)-1.684E-05*(T1**3.) 132 1+2.67E-09*(T1**4.))-3484.0)*RMOL 133 DH(13)=((1.137*T1+1.455E-02*(T1**2.)-2.959E-06*(T1**3.) 134 1 )-1552.9)*RM0L 135 UUU(1)=-3.93522E05 136 UUU(3)=-2.41827E05 137 C 138 C CALC. TOTAL ENERGY OF MIXTURE (KJ/KMOL FUEL)... 139 ERCT=(NCH*(HF1+DH(KFUEL)-RMOL*T1)+N02*(DH(5)-RMOL*T1) 140 -+N*(DH(6)-RM0L*T1)+NRC02*(UUU(1)+DH(1)-RM0L*T1)+NRH20* 141 -(UUU(3)+DH(3)-RM0L*T1)) 142 C 143 IF(MODE.EO.3) ERCT=NCH*(HF1+DH(KFUEL))+N02*DH(5) 144 C 145 IF(MODE.GT.1) GOTO 105 146 C 147 C CALC. SWEPT VOL.(CYLV),CLEARANCE VOL.(CLRV),TOTAL V0L.(V1), 148 C SIZE OF VOLUME DIV.(DIV),VOLUME CORRESPONDING TO GIVEN SPARK 149 C ADVANCE (DVOLM). 150 CYLV=3.1415926*((BORE/2.)**2.)*STROK 151 CLRV=CYLV/(C0MPR-1.) 152 V1=C0MPR*CLRV 153 NDIV=NDIV-1 154 DIV=CYLV/DFLOAT(NDIV) 155 DALFA=(180.-SPKAD) 156 DV0LM=(V1-DV0L(DALFA)) 157 C NO. OF MOLES OF FUEL IN CYLINDER (MOLFL) 158 M0LFL=(P1*V1)/(NMIX*RMOL*T1) 159 ENGY1=ERCT*MOLFL 160 V1=V1*(1E+06) 161 WRITE(6,652) CN.HM,SPEED 162 652 FORMATdH ,'FUEL; C '.F3.1,' H ', F4 . 1 ,7X,'SPEED (RPM) = ',F7.1/) 163 WRITE(6,813) AFR.STAFR,LAMBDA,COMPR 164 813 FORMATdH , 15HAIR/FUEL RATIO= , F6 . 2 , 3X , 18HST0ICH . A/F RATI0=, 165 -F6.2,3X,7HLAMBDA=,F6.2,3X,12HC0MP. RAT10=,F5.1/) 166 105 WRITE(6,817) 167 817 F0RMAT(1H ,28X,39HC0NCENTRATI0N OF COMB. PRODUCTS (KMOLS)/) 168 WRITE(6,31) 169 31 FORMATdH , 1X ,'STEP', 1X ,'VOL', 3X ,'PRESS', 3X ,'TEMP', 3X ,'C02', 4X 170 -,'CO',5X,'H20',4X,'H2',5X,'02',5X,'N2',5X,'NO',5X,'OH',6X,'0', 171 -6X,'H',5X,'GAM'/) 172 DO 106 KI=1,10 173 X(KI)=0.0 174 106 CONTINUE 116 175 IF(MODE.GT.1) V1=0.0 176 NIT=1 177 WRITE(6,893) NIT,V1,P1,T1,(X(I),1=1,4),NN02,NN2,(X(<J),J = 7, 10) 178 893 F0RMAT(1H ,12 , 1X , F6. 1 ,F7 . 1,F7.1,4F7.2,2F7.3,4F7.2) 179 IF(MODE.GT.1) GOTO 611 180 V1=V1/(1E+06) 181 T2=T1 182 PP2(IL,1)=P1 183 W2( IL, 1 )=V1 184 UJJ=1 185 IC0UNT=2 186 187 C START COMPRESSION STROKE 188 c ======================== 189 C THIS SECTION CALCULATES THE NEW TEMPERATURE AND PRESSURE RESULTING 190 C FROM ADIABATIC COMPRESSION OF THE MIXTURE IN THE CYLINDER. 191 C A PROPORTIONAL CHOPPING ITERATION TECHNIQUE IS USED TO FIND THE 192 C TEMPERATURE AT WHICH THE FIRST-LAW AND IDEAL GAS LAW ARE 193 C SATISFIED. 194 C 195 DO 40 NI=1,NDIV 196 V2=V1-DIV 197 IF(V2.GT.DVOLM) GOTO 51 198 V2=DV0LM 199 J<JJ=2 200 51 NN=0 201 C IDEAL GAS LAW. . . 202 50 P2 = P1*(V1/V2)*(T2/T1 ) 203 DH(1)=((3.096*T2+0.00273*(T2**2)-7.885E-07*(T2**3) 204 1+8.66E-11*(T2**4))-1145.0)*RMOL 205 DH(3)=((3.743*T2+5.656E-04*(T2**2)+4.952E-08*(T2**3) 206 1-1.818E-11*(T2**4))-1167.0)*RM0L 207 DH(5)=((3.253*T2+6.524E-04*(T2**2)-1.495E-07*(T2**3) 208 1 + 1 . 539E-1 1*('T2**4) ) - 1024 .0) *RM0L 209 DH(6)=((3.344*T2+2.943E-04*(T2**2)+1.953E-09*(T2**3) 210 1-6.575E-12*(T2**4))- 1023.0)*RMOL 211 DH(11)=((1.935*T2+4.965E-03*(T2**2.)-1.244E-06*(T2**3.) 212 1 + 1.625E-10*(T2**4. )-8.586E- 15*(T2**5. ))-985.9)*RMOL 213 DH(12)=((-0.72*T2+4.643E-02*(T2**2.)-1.684E-05*(T2**3.) 214 1+2.67E-09*(T2**4.))-3484.0)*RMOL 215 DH(13)=((1.137*T2+1.455E-02*(T2**2.)-2.959E-06*(T2**3.) 216 1)-1552.9)*RM0L 217 ENGY2=M0LFL*(NCH*(HF1+DH(KFUEL)-RMOL*T2)+N02*(DH(5)-RM0L*T2) 218 -+N*(DH(6)-RM0L*T2)+NRC02*(UUU(1 )+DH(1)-RM0L*T2)+NRH20* 219 -(UUU(3)+DH(3)-RM0L*T2) ) 220 C FIRST LAW... 221 REM=ENGY2-ENGY1+((P1+P2)/2)*(V2-V1) 222 C WRITE(6,43) T2,P2,REM,ENGY2 223 C 43 FORMATdH , ' T2 , P2 , REM, ENGY2 '.4E12.4) 224 C 225 IF(NN.EQ.2) GOTO 7 226 IF(NN.EQ.1) GOTO 8 227 REM 1=REM 228 TT1=T2 229 T2=T2+200.0 230 IF(T2.GT.3000.0) STOP 231 NN=1 232 GOTO 50 1 17 233 C 234 8 REM2=REM 235 TT2=T2 236 IF((REM1*REM2).LE.O.O) GOTO 13 237 TT1=T2 238 REM 1=REM2 239 T2=T2+200.0 240 GOTO 50 241 C 242 13 IF(REM2.E0.O.O) GOTO 18 243 T20LD=TT2 244 11 T2=(TT1*REM2-TT2*REM1)/(REM2-REM1) 245 IF(DABS((T2-T20LD)/T2).LT.0.0OO1) GOTO 18 246 T20LD=T2 247 NN=2 248 GOTO 50 249 C 250 7 IF(REM1*REM.LE.O.O) GOTO 12 251 TT1=T2 252 REM1=REM 253 GOTO 11 254 12 TT2=T2 255 REM2=REM 256 GOTO 1 1 257 18 ENGY1=ENGY2 258 PP2(IL.(NI+1))=P2 259 VV2(IL,(NI+1))=V2 260 P1=P2 261 T1=T2 262 V1=V2 263 V2=V2*(1E+06) 264 NIT=NI+1 265 .IC0UNT=IC0UNT+1 266 IF(IC0UNT.E0.50) GOTO 490 267 GOTO 650 268 490 IC0UNT=1 269 WRITE(6,800) NIT,V2,P2,T2,(X(I),1=1,4),NN02,NN2,(X(d),d=7,10) 270 -,ENGY2 271 800 FORMATdH , 12 , 1X , F6 . 1 , F7 . 1 , F7 . 1 ,4F7 . 2 , 2F7 . 3 , 4F7 . 2 , E 14 . 4 ) ' 272 650 V2=V2/(1E+06) 273 IF(ddJ.E0.2) GOTO 610 274 40 CONTINUE 275 276 C START CONSTANT VOLUME BURNING FROM P2 AND T2 277 C ============================================ 278 C 279 C THIS SECTION CALLS A SUBROUTINE TO CALCULATE THE TEMPERATURE 280 C AND PRESSURE RESULTING FROM CONSTANT VOLUME (M0DE=1,2) OR 281 C CONSTANT PRESSURE (M0DE=3) COMBUSTION OF THE MIXTURE. 282 C 283 610 ERCT=ENGY2/M0LFL 284 611 NNN=1 285 CALL C0MB(T1,P1,ERCT,EPROD,SUMNS,SUMXS,T2,P2,CC,X, 286 -GAMMA,LAMBDA,MODE) 287 IF(MODE.GT.1) GOTO 612 288 P3=P2 2§9 PP4(IL,1)=P3 290 VV4(IL,1)=V2 118 291 V3 = V2 292 T3 = T2 293 V3=V3*(1E+06) 294 612 IF(MODE.GT.1) V3=0.0 295 NIT=1 296 WRITE(6,812) NIT,V3,P2,T2,(CC(I ) ,1 = 1 , 10),GAMMA 297 812 F0RMAT(1H ,12,1X,F6.1,F7.1,F7.1,11F7.3) 298 IF(MODE.GT.1) GOTO 222 299 V3=V3/(1E+06) 300 V1=V2 301 P1=P2 302 T1=T2 303 T = T1 304 ENGY1=EPR0D*M0LFL 305 NM1=SUMXS 306 NUT=0 307 IC0UNT=2 308 309 C START EXPANSION STROKE 310 C 311 C THIS SECTION CALCULATES THE TEMPERATURE AND PRESSURE RESULTING 312 C FROM ADIABATIC EXPANSION OF THE PRODUCTS OF COMBUSTION FROM 313 C TDC TO BDC. (NOT USED IF M0DE=2 OR 3). 314 C A PROPORTIONAL CHOPPING ITERATION TECHNIQUE IS USED AT EACH STEP 315 C 316 DO 740 NI=1,NDIV 317 NUT=0 318 NN=0 319 Jd=2 320 V2=V1+DIV 321 TT1=T1-3.0 322 C IDEAL GAS LAW. . . 323 P=P1*(V1/V2)*(TT1/T1)*(SUMXS/NM1) 324 CALL ENERGY(TT1,P,EPROD,SUMXS,CC.X,GAMMA,MODE) 325 ENGY2=EPROD*MOLFL 326 NNM1=SUMXS 327 C FIRST LAW... 328 REM1 = ENGY2-ENGY1 + ((P1+P)/2. )*(V2-V1) 329 C 330 C WRITE(6,409) ENGY1,ENGY2.REM,P,MOLFL,EPROD 331 C 409 FORMATdH , ' ENGY 1 , ENGY 2 ,REM,P, MOLFL, EPROD' , 6E 12 . 4 ) 332 C 333 TT2=T1-100.0 334 IF(T.GT.2500.0) T=T-100.0 335 IF(T.GT.3000.0) T=T-100.0 336 P=P1*(V1/V2)*(TT2/T1)*(SUMXS/NM1) 337 CALL ENERGY(TT2.P,EPROD.SUMXS,CC,X,GAMMA,MODE) 338 ENGY2=EPROD*MOLFL 339 NNM2=SUMXS 340 REM2 = ENGY2-ENGY1 + ((P1+P)/2.)*(V2-V1 ) 341 C 342 TT30LD=TT2 343 719 TT3=(TT1*REM2-TT2*REM1)/(REM2-REM1) 344 SUMXS=(NNM1*REM2-NNM2*REM1)/(REM2-REM1) 345 NUT=NUT+1 346 IF(NUT.GT.100) STOP 347 IF(DABS((TT3-TT30LD)/TT3).LT.0.001) GOTO 718 348 TT30LD=TT3 119 349 P=P1*(V1/V2)*(TT3/T1)*(SUMXS/NM1) 350 CALL ENERGY(TT3.P,EPROD,SUMXS,CC,X,GAMMA,MODE) 351 ENGY2=EPR0D*M0LFL 352 NNM3=SUMXS 353 REM3 = ENGY2-ENGY1 + ((P1+P)/2. )*(V2-V1) 354 IF(REM1*REM3.LE.0.0) GOTO 715 355 TT1=TT3 356 REM1=REM3 357 NNM1=NNM3 358 GOTO 719 359 715 TT2=TT3 360 REM2=REM3 361 NNM2=NNM3 362 GOTO 719 363 C 364 718 ENGY1=ENGY2 365 P1=P 366 T1=TT3 367 V1=V2 368 NM1=SUMXS 369 P4 = P 370 PP4(IL,(NI+1 ) )=P4 371 VV4(IL,(NI+1))=V2 372 V4 = V2 373 V4=V4*(1E+06) 374 NIT=NI+1 375 T4=TT3 376 IC0UNT=IC0UNT+1 377 IF(ICOUNT.E0.50) GOTO 491 378 GOTO 651 , 379 491 IC0UNT=1 : 380 WRITE(6,818) NIT,V4,P4,T4,(CC(I),I=1.10),ENGY2 381 818 F0RMAT(1H ,12,1X.F6.1,F7.1,F7.1,10F7.3.E14.4) 382 651 V4=V4/(1E+06) 383 740 CONTINUE 384 C 385 C MEP,POWER & EFFICIENCY CALCULATIONS 386 C =================================== 387 C THIS SECTION CALCULATES INTEGRAL OF PDV (PDV),MEAN EFFECTIVE 388 C PRESSURE (MEP). POWER, THERMAL EFFICIENCY, AND INDICATED 389 C SPECIFIC FUEL CONSUMPTION (ISFC) (g/kWh). 390 C 391 PDV=0.0 392 DO 300 NI=1,49 393 AREA=(((PP4(IL.NI)+PP4(IL,(NI+1)))/2)-((PP2(IL,(51-NI)) 394 1+PP2(IL.(50-NI)))/2))*DIV 395 300 PDV=PDV+AREA 396 MEP=PDV/(CYLV*100) 397 P0WER=(PDV*SPEED/12O.) 398 EFF=(PDV*100.)/(MOLFL*OVS*(12.*CN+HM)) 399 ISFC=M0LFL*MW(KFUEL)*1OOO/(PDV*2.78E-4) 400 WRITE(6,301) POWER.MEP,EFF,ISFC 401 301 FORMAT(10X,6HP0WER=,F8.3,5X,9HI.M.E.P. = ,F7.3,5X,11HEFFICIENCY= , 402 -F8.2,5X,9HI.S.F.C.=,F8.2//) 403 222 CONTINUE 404 IF(MDDE.GT.1) GOTO 613 405 IF(IPLOT.EO.O) GOTO 613 406 C 120 407 C THIS SECTION GENERATES A P - V DIAGRAM 408 C 409 C 410 DO 605 IL=1,NUMBR 411 DO 605 J = 1 , 1 0 0 412 IF ( J . G T . 5 0 ) GOTO 608 413 V V ( I L , J ) = V V 2 ( I L , J ) * 1 0 0 0 . 414 P P ( I L , J ) = P P 2 ( I L , J ) / 1 0 0 . 415 GOTO 609 416 608 V V ( I L , J ) = V V 4 ( I L , ( J - 5 0 ) ) * 1 0 0 0 . 417 P P ( I L , d ) = P P 4 ( I L , ( J - 5 0 ) ) / 1 0 0 . 418 609 X X ( I L , J ) = ( 5 . * V V ( I L , J ) ) + 2 . 0 419 605 Y Y ( I L , J ) = ( P P ( I L , J ) / 2 0 . ) + 2 . 0 4 2 0 CALL A X I S ( 2 . , 2 . , ' V O L U M E ( L ) ' , - 1 0 , 5 . , 0 . , 0 . , 0 . 2 ) 421 CALL A X I S ( 2 . , 2 . , ' P R E S S U R E ( B A R ) ' , 1 4 , 5 . , 9 0 . , 0 . , 2 0 . ) 422 DO 607 IL=1,NUMBR 423 DO 607 1=1,100 424 607 CALL S Y M B O L ( X X ( I L , I ) , Y Y ( I L . I ) , 0 . 0 5 , I L , 0 . , - 2 ) 425 CALL PLOTND 426 613 STOP 427 END 428 C 429 L»-430 C 431 432 C SUBROUTINE TO C A L C . TEMP. AND PRESS. AFTER COMBUSTION c 433 c 434 SUBROUTINE C O M B ( T 1 , P 1 , E R C T . E P R O D , S U M N S , S U M X S , T 2 , P 2 , C C , X , 435 -GAMMA,LAMBDA,MODE) 436 c 437 R E A L * 8 X F . D X . E P S . P I , E P R O D , S U M X S , S U M N S . E R C T . T t , T 2 , Y 1 , Y 2 , Y 3 , 438 - X 1 , X 2 , X 3 , X 3 0 L D , P 1 , P 2 , P 3 , C C ( 1 0 ) , X ( 1 0 ) , K , L , M , N , G A M M A , N C H , N 0 2 , 439 -KFUEL,LAMBDA 440 c 441 COMMON /AREA 1/ N C H , N 0 2 , K , L , M , N , K F U E L 442 COMMON / A R E A 4 / N D I S S . I P R I N T 443 c 444 X 1 = 2 0 0 0 . 0 445 I F ( L A M B D A . G T . 1 . 2 ) X1=1800 446 X F = 4 5 0 0 . 0 447 DX=500.0 448 EPS=0.001 449 P I = 5 0 0 0 . 0 450 I F ( M 0 D E . E Q . 3 ) PI=P1 451 CALL E N E R G Y ( X 1 . P I , E P R O D , S U M X S , C C , X , G A M M A , M O D E ) 452 Y1=EPROD-ERCT 453 I F ( I P R I N T . E O . 0 ) GOTO 10 454 c-455 W R I T E ( 6 , 2 0 0 ) P 1 . X 1 . Y 1 456 200 F O R M A T d H , ' P , T , Y ' , 2F8 . 1 , E 12 . 3 / ) 457 c-458 10 X2=X1+DX 459 IF ( X 2 . G T . X F ) STOP 460 P 2 = ( S U M X S * X 2 * P 1 ) / ( S U M N S * T 1 ) 461 I F ( M O D E . E O . 3 ) P2=P1 462 CALL E N E R G Y ( X 2 , P 2 , E P R O D , S U M X S , C C , X , G A M M A , M O D E ) 463 Y2=EPR0D-ERCT 464 I F ( I P R I N T . E Q . O ) GOTO 213 121 465 C 466 WRITE(6,200) P2.X2.Y2 467 C 468 213 IF(Y1*Y2.LE.0.) GOTO 20 469 X1=X2 470 Y1=Y2 471 GOTO 10 472 20 IF(Y2.EQ.O.) GOTO 50 473 P3=P2 474 X30LD=X2 475 30 X3=(X1*Y2-X2*Y1 )/(Y2-Y1 ) 476 IF(DABS((X3-X30LD)/X3).LT.EPS) GOTO 60 477 X30LD=X3 478 P3=(SUMXS*X3*P1)/(SUMNS*T1) 479 IF(MODE.EQ.3) P3=P1 480 CALL ENERGY(X3.P3,EPROD.SUMXS,CC,X,GAMMA,MODE) 481 Y3=EPR0D-ERCT 482 IF(IPRINT.EQ.O) GOTO 214 483 C 484 WRITE(6,200) P3.X3.Y3 485 C 486 214 IF(Y1*Y3.LE.O.) GOTO 40 487 X1=X3 488 Y1=Y3 489 GOTO 30 490 40 X2=X3 491 Y2=Y3 492 GOTO 30 493 50 T2=X2 494 GOTO 70 495 60 T2 = X3 496 P2=P3 497 70 RETURN 498 END 499 C 500 C 501 C 502 C SUBROUTINE ENERGY TO CALCULATE THE ENERGY AND COMPOSITION OF 503 C ================= BURNED GAS AT A GIVEN TEMP. (T) AND PRESS. (P), 504 . C INCLUDING THE EFFECTS OF DISSOCIATION. 505 C 506 SUBROUTINE ENERGYCT.P,EPROD,SUMXS,CC,X,GAMMA,MODE) 507 C 508 IMPLICIT REAL*8(A-H,0-Z) 509 REAL*8 K,L,M,N,KE(6),NM,KK,MWBMIX,MW(10),NMIX,NCH,N02,MOLFL, 510 -NN02,NN2,NNFUEL,KC02,KH20,KN2.MPV 511 C 512 COMMON /AREA 1/ NCH.N02,K,L,M,N,KFUEL 513 COMMON /AREA2/ MOLFL.NMIX,HF1,NN02,NN2,NNFUEL,KOM 514 COMMON /AREA3/ AREAB,HTEXP,MPV,HTFCN,TWALL,VISC,THCOND 515 COMMON /AREA4/ NDISS,IPRINT 516 C 517 DIMENSION X(10),CPG(10),UUU(10),DH(10),CC(10).SP(6),RES(6 , 4 ) , 518 -SQT(6),SPP(6,4) 519 C 520 C IF TEMP. LESS THAN 1750K, SKIP DISSOCIATION CALCULATIONS 521 IF(T.LT.1750) GOTO 17 522 IF(NDISS.EQ.O) GOTO 17 122 523 C IPRINT=1 524 C 525 C THE DISSOCIATION CAN INCLUDE THE FOLLOWING REACTIONS; 526 C (1) C02=CO+0.502, 527 C (2) H20=H2+0.502, 528 C (3) H20=OH+0.5H2, 529 C (4) NO=0.5N2+0.502, 530 C (5) H2=2H, 531 C (6) 02=20. 532 C IF NDISS=1, REACTIONS 1 & 2 ARE INCLUDED, 533 C IF NDISS=2, REACTIONS 1,2,3 & 4 ARE INCLUDED, 534 C IF NDISS=3, REACTIONS 1,2,3,4,5 & 6 ARE INCLUDED. 535 C 536 C THE FOLLOWING LINES CALCULATE THE EQUILIBRIUM CONSTANTS FOR EACH 537 C REACTION 1 TO 6, INCLUDING THE (PO/P) TERM, 538 C ALSO, INITIALISE THE DISSOCIATED SPECIES CONCENTRATIONS, 539 C 540 DO 304 1=1,6 541 SP(I)=0.0 542 KE(I)=0.0 543 304 SPP(I,4)=0.0 544 C 545 G0T0(3O2,301,300),NDISS 546 300 KE(6)=DEXP(DLOG(T)**(-6.93319)*(-43428300)+19.3067)*(101 .3/P) 547 KE(5)=DEXP(DLOG(T)**(-6.81208)*(-30743900)+17.8668)*(101.3/P) 548 SP(6)=0.000 549 SP(5)=0.000 550 301 KE(4)=DEXP(DL0G(T)**(-7.33550)*(-16592550)+1.80127) 551 KE(3)=DEXP(DL0G(T)**(-7.04570)*(-30372100)+10.159) 552 -*DSQRT(101.3/P) 553 SP(4)=0.000 554 SP(3)=0.000 555 302 KE(2)=DEXP(DL0G(T)**(-6.86740)*(-18878550)+8.7095) 556 -*DSQRT(101.3/P) 557 KE(1)=DEXP(DLOG(T)**(-7.47210)*(-65549000)+10.53) 558 -*DSQRT(101.3/P) 559 SP(2)=0.1 560 SP(1)=0.1 561 C 562 IF(IPRINT.EQ.O) GOTO 650 563 C 564 WRITE(6,21) (KE(IJK),IJK=1,6) 565 21 F0RMAT(1H ,'KE(1-6) '.6E13.3) 566 C 567 C 568 C DEFINE UNIVERSAL GAS CONSTANT AND SET ITERATION COUNTER TO ZERO, 569 650 RM0L=8.3143 570 NUT=0 571 C 572 C START DISSOCIATION ITERATION ROUTINE. A PROPORTIONAL CHOPPING 573 C ITERATION TECHNIQUE IS USED TO SOLVE FOR THE VARIOUS SPECIES 574 C CONCENTRATIONS AT THE GIVEN TEMPERATURE AND PRESSURE.... 575 C 576 10 QQ=0 577 C 578 C THIS SECTION ENSURES THAT ITERATIONS CANNOT CONTINUE INDEFINATELY, 579 NUT=NUT+1 580 IF(NUT.LT.150) GOTO 400 123 581 WRITE(6 ,401) NUT 582 401 F0RMAT(1H , 'PROGRAM STOP DUE TO ENERGY ITERATIONS EXCEEDING' ,14 ) 583 STOP 584 C 585 400 NSP=2*NDISS 586 C 587 C STEP I FROM 1 TO NUMBER OF DISSOCIATION R E A C T I O N S . . . 588 DO 600 1=1,NSP 589 C 590 NUTT=0 591 IFLAG1=0 592 C 593 S=(SP(1 )+SP(2 )+SP(3 ) ) / 2+ (SP(5 )+SP(6)+K+L+M+N) 594 C 595 I F ( I P R I N T . E Q . O ) GOTO 651 596 C 597 WRITE(6 ,20) I , ( S P ( I J K ) , I J K = 1 , 6 ) , S 598 20 F0RMAT(1H , ' I , S P ( 1 - 6 ) , S ' . I 4 . 7 E 9 . 2 ) 599 C 600 C 601 C IN IT IAL GUESS AT SPECIES CONCENTRATION. . . 602 651 0=1 603 SP( I )=0 .000001 604 S P P ( I . J ) = S P ( I ) 605 G O T O ( 4 5 0 , 4 5 1 , 4 5 2 . 4 5 3 , 4 5 4 , 4 5 5 ) , I 606 1 CONTINUE 607 C 608 I F ( I P R I N T . E Q . O ) GOTO 9 609 C 610 WRITE(6 ,19) I , S P ( I ) , R E S ( 1 , 1 ) 611 19 F O R M A T d H , ' I , S P , R E S 1 ' . I 4 . 2 E 1 0 . 3 ) 612 C 613 C 614 C SECOND AND SUCCESSIVE GUESSES AT SPECIES CONCENTRATION. . . 615 9 d=2 616 STEP=0.1 617 I F ( T . L T . 2 0 0 0 ) STEP=0.02 . 618 SP( I )=SP( I )+STEP 619 I F ( S P ( I ) . G T . 1 0 ) GOTO 500 620 S P P ( I , d ) = S P ( I ) 621 IFLAG1=0 622 G O T O ( 4 5 0 , 4 5 1 , 4 5 2 , 4 5 3 , 4 5 4 , 4 5 5 ) , I 623 2 CONTINUE 624 C 625 I F ( I P R I N T . E Q . O ) GOTO 652 626 C 627 WRITE(6 ,18) I , S P ( I ) , R E S ( I , 1 ) , R E S ( I , 2 ) 628 18 FORMATdH , ' I , SP , RES 1 , RES2 ' , 14 . 3E 1 1 . 3 / ) 629 C 630 C 631 C IF RESIDUAL CROSSES ZERO BETWEEN PREVIOUS AND CURRENT GUESSES 632 C THEN GO TO PROPORTIONAL CHOPPING ROUTINE, OTHERWISE CONTINUE 633 C INCREMENTING SPECIES CONCENTRATION. . . 634 652 I F ( ( R E S ( I , 1 ) * R E S ( I . 2 ) ) . L E . O . O ) GOTO 5 635 R E S ( I , 1 )=RES( I , 2 ) 636 S P P ( I , 1 ) = S P P ( I , 2 ) 637 GOTO 9 638 C 124 639 5 I F ( R E S ( I , 2 ) . E Q . O ) GOTO 500 640 SPOLD=SPP( I ,2 ) 641 J=3 642 C 643 C FIND VALUE OF SPECIES CONCENTRATION ( S P ( I ) ) AT WHICH RESIDUAL 644 C BECOMES SMALL, I . E . WHEN PREVIOUS ' S P ' EQUALS CURRENT ' S P ' TO 645 C WITHIN ONE P E R C E N T . . . 646 6 S P ( I ) = ( S P P ( I , 1 ) * R E S ( I , 2 ) - S P P ( I , 2 ) * R E S ( I , 1 ) ) / ( R E S ( I , 2 ) - R E S ( I , 1 ) ) 647 I F ( D A B S ( ( S P ( I ) - S P O L D ) / S P ( I ) ) . L T . 0 . 0 1 ) GOTO 500 648 SPOLD=SP(I) 649 C 650 G O T O ( 4 5 0 , 4 5 1 , 4 5 2 , 4 5 3 , 4 5 4 , 4 5 5 ) , I 651 3 CONTINUE 652 C 653 I F ( I P R I N T . E Q . O ) GOTO 654 654 C 655 WRITE(6 ,15) I , S P ( I ) , R E S ( 1 , 1 ) , R E S ( I , 3 ) 656 15 FORMAT(1H , ' I , S P , R E S 1,RES3 ' . I 4 . 3 E 1 1 . 3 ) 657 C 658 C 639 654 I F ( R E S ( I , 1 ) * R E S ( I , 3 ) . L E . 0 . 0 ) GOTO 4 660 S P P ( I , 1 )=SP(I ) 661 R E S ( I , 1 ) = R E S ( I , 3 ) 662 GOTO 6 663 4 S P P ( I , 2 ) = S P ( I ) 664 R E S ( I , 2 ) = R E S ( I , 3 ) 665 GOTO 6 666 C 667 C IF VALUE OF S P ( I ) FROM CURRENT SPECIES CALCULATIONS EQUALS THE 668 C VALUE OF S P ( I ) FROM THE PREVIOUS SET OF SPECIES CALCULATIONS AT 669 C THE SAME TEMPERATURE, THEN LEAVE QQ=0, OTHERWISE SET QQ=1 WHICH 670 C WILL CAUSE ANOTHER SET OF CALCULATIONS TO BE PERFORMED. . . 671 500 I F ( D A B S ( ( S P ( I ) - S P P ( I , 4 ) ) / ( S P ( I ) ) ) . G T . 0 . 0 5 ) QQ=1 672 SPP( I ,4 )=SP( I ) 673 GOTO 600 674 C 675 C THIS SECTION CALCULATES THE RESIDUALS FOR EACH SPECIES USING 676 C THE CURRENT VALUES OF S P ( I - G ) . 677 450 S Q T ( 1 ) = M + ( ( S P ( 1 ) + S P ( 2 ) - S P ( 4 ) ) / 2 ) - S P ( 6 ) 678 I F ( S Q T ( 1 ) . L E . 0 . 0 ) GOTO 456 679 R E S ( 1 . J ) = SP(1 ) / ( K - S P ( 1 ) ) * D S Q R T ( S Q T ( 1 ) / S ) - K E ( 1) 680 GOTO 460 681 451 S Q T ( 2 ) = M + ( ( S P ( 1 ) + S P ( 2 ) - S P (4 ) ) / 2 ) - S P ( 6 ) 682 I F ( S Q T ( 2 ) . L E . 0 . 0 ) GOTO 456 683 R E S ( 2 , J ) = ( S P ( 3 ) / 2 + S P ( 2 ) - S P ( 5 ) ) / ( L - S P ( 3 ) - S P ( 2 ) ) * D S Q R T ( S Q T ( 2 ) / S ) 684 1 -KE(2 ) 685 GOTO 460 686 452 S Q T ( 3 ) = S P ( 3 ) / 2 + S P ( 2 ) - S P ( 5 ) 687 I F ( S Q T ( 3 ) . L E . O . O ) GOTO 456 688 R E S ( 3 , d ) = ( S P ( 3 ) ) / ( L - S P ( 3 ) - S P ( 2 ) ) * D S Q R T ( S Q T ( 3 ) / S ) - K E ( 3 ) 689 GOTO 460 690 453 S Q T ( 4 ) = ( N - S P ( 4 ) / 2 ) * ( M - S P ( 6 ) + ( S P ( 1 ) + S P ( 2 ) - S P ( 4 ) ) / 2 ) 691 I F ( S Q T ( 4 ) . L E . O . O ) GOTO 456 692 R E S ( 4 , J ) = S P ( 4 ) / D S Q R T ( S Q T ( 4 ) ) - K E ( 4 ) 693 GOTO 460 694 454 S Q T ( 5 ) = S P ( 3 ) / 2 + S P ( 2 ) - S P ( 5 ) 695 I F ( S Q T ( 5 ) . L E . 0 . 0 ) GOTO 456 696 R E S ( 5 . d ) = ( 4 * S P ( 5 ) * S P ( 5 ) ) / S / S Q T ( 5 ) - K E ( 5 ) 125 697 GOTO 460 698 455 SQT(6)=M-SP(6)+(SP(1)+SP(2)-SP(4))/2 699 IF(S0T(6).LE.O.O) GOTO 456 700 RES(6,J)=(4*SP(6)*SP(6))/S/SQT(6)-KE(6) 701 456 SP(I)=SPP(I,4) 702 GOTO 600 703 460 NUTT=NUTT+1 704 C 705 IF(IPRINT.EO.O) GOTO 655 706 C 707 WRITE(6,22) NUTT,RES(I,J),SOT(I),IFLAG1 708 22 FORMATdH , 'NUT , RES( I , J ) , SQT( I ) , FLAG ' . 13 , 2E 14 . 5 , 13 ) . 709 C 710 C 711 655 IF(NUTT.LT.50) GOTO 16 712 WRITE(6.401) NUTT 713 STOP 714 16 GOTO(1,2,3) ,J 715 C 716 600 CONTINUE 717 C 718 A=SP(1) 719 B=SP(3) 720 C=SP(2) 721 D=SP(4) 722 E=SP(5) 723 F=SP(6) 724 C 725 IF(IPRINT.EO.O) GOTO 656 726 C--727 WRITE(6,14) T,A,B,C,D.E,F 728 14 FORMATdH , ' T , A , B , C , D , E , F ' , F8 . 1 , 6E 10. 3/) 729 C 730 656 IF(00)461,461,10 731 C 732 C 733 461 CONTINUE 734 C 735 C CALCULATING CHANGE IN ENTHALPIES FOR SPECIES 1 TO 10 BET. T AND 289K 736 C C02=1, C0=2, H20=3, H2=4. 02=5, N2=6, N0=7, H=10. 0=9. 0H=8 737 KK=0 738 17 TT=T/100 739 IF (T.GT.3000.0) GOTO 99 740 DH(1)=((3.096*T+0.00273*(T**2)-7.885E-07*(T**3) 741 1+8.66E-11*(T**4))-1145.0)*RMOL 742 DH(2)=((3.317*T+3.77E-04*(T**2)-3.22E-08*(T**3) 743 1-2.195E-12*(T**4))-1022.0)*RMOL 744 DH(3)=((3.743*T+5.656E-04*(T**2)+4.952E-08*(T**3) 745 1-1.818E-11*(T**4))-1167.0)*RM0L 746 DH(4) = ((3.433*T-8.18E-06*(T**2)+9.67E-08* ( T**3) 747 1-1 .444E-11*(T**4))-1025.0)*RMOL 748 DH(5)=((3.253*T+6.524E-04*(T**2)-1.495E-07*(T**3) 749 1+1.539E-11*(T**4))-1024.0)*RMOL 750 DH(6)=((3.344*T+2.943E-04*(T**2)+1.953E-09*(T**3) 751 1-6.575E-12*(T**4))-1023.0)*RMOL 752 DH(7)=((3.502*T+2.994E-04*(T**2)-9.59E-09*(T**3) 753 1-4.904E-12*(T**4))- 1070.0)*RMOL 754 DH(10)=((2.5*T)-745.O)*RMOL 126 755 DH(9)=((2.764*T-2.514E-04*(T**2)+1.002E-07*(T**3) 756 1-1.387E-11*(T**4))-8O4.O)*RM0L 757 DH(8) = ((81.546*TT-47.48*(TT**1.25 )+9.902*(TT**1.75) 758 1-2.133*(TT**2.))* 100-10510) 759 GOTO 91 760 99 DH(1)=((5.208*T+0.00059*(T**2)-5.614E-08*(T**3) 761 1+2.05E-12*(T**4))-1126.0)*RMOL 762 DH(2)=((3.531*T+2.73E-04*(T**2)-3.28E-08*(T**3) 763 1 + 1 .565E-12*(T**4))-1042.0)*RMOL 764 DH(3)=((143.05*TT-146.83*(TT**1.25)+55.17*(TT**1.5) 765 1-1.85*(TT**2.))*100-11945.0) 766 DH(4)=((3.213*T+2.87E-04*(T**2)-2.29E-08*(T**3) 767 1+7.666E-13*(T**4))-1018.0)*RMOL 768 DH(5)=((3.551*T+3.203E-04*(T**2)-2.876E-08*(T**3) 769 1+1.OO5E-12*(T**4))-1O44.O)*RM0L 770 DH(6)=((3.514*T+2.583E-04*(T**2)-2.841E-08*(T**3) 771 1+1.242E-12*(T**4))-1043.0)*RMOL 772 DH(7) = ((3.745*T+1.950E-04*(T**2)- 1.88E-08*(T**3) 773 1+7.703E-13*(T**4))-11O6.O)*RM0L 774 DH(10)=((2.5*T)-745.0)*RMOL 775 DH(9)=((2.594*T-3.843E-05*(T**2)+7.514E-09*(T**3) 776 1-3.209E-13*(T**4))-809.0)*RMOL 777 DH(8)=((81.546*TT-47.48*(TT**1.25)+9.902*(TT**1.75) 778 1-2.133*(TT**2.))*100-10560.) 779 C 780 C CALCULATE CONSTANT PRESSURE SPECIFIC HEATS 781 91 CPG(1)=-3.7357+30.529*(TT**(0.5))-4.1034*TT+0.024198*(TT**2) 782 CPG(2)=69.145-.70463*(TT**(O.75))-200.77*(TT**(-0.5)) 783 -+176.76*(TT**(-0.75)) 784 CPG(3)=143.05-183.54*(TT**(0.25))+82.751*(TT**(0.5)) 785 --3.69889*TT 786 CPG(4)=56.505-702.74*(TT**(-.75))+1165.0/TT-560.7*(TT**(- 1.5)) 787 CPG(5) = 37.432+0.020102*(TT**1.5)- 178.57* ( TT** ( - 1 . 5)) 788 -+236.88*(TT**(-2) ) 789 CPG(6)=39.060-512.79*(TT**(-1.5))+1072.7*(TT**(-2)) 790 --820.4*(TT**(-3)) 791 CPG(7)=59.283-1.7096*(TT**0.5)-70.613*(TT**(-0.5)) 792 -+74.889*(TT**(-1.5)) 793 CPG(8)=81.546-59.35*(TT**0.25)+17.329*(TT**0.75)-4.266*TT 794 C 795 C CALC. NUMBER OF MOLES OF EACH SPECIES AFTER DISSOCIATION 796 X(1)=K-A 797 X(2)=A 798 X(3)=L-B-C 799 X(6)=N-D/2 800 X(7)=D 801 X(4)=C+B/2-E 802 X(5)=M-F+(A+C-D)/2 803 X(10)=2*E 804 X(9)=2*F 805 X(8)=B 806 C 807 C CALC. VISCOSITY & THERMAL CONDUCTIVITY OF PRODUCTS... 808 VC02=((0.019*T+24.2)*X(1)*1E-06)/(X(1)+X(3)+X(6)) 809 KC02=((0.041*T+36.1)*X(1)*1E-03)/(X(1) + X(3)+X (6)) 810 VH20=((0.025*T+15.8)*X(3)*1E-06)/(X(1)+X(3)+X(6)) 811 KH20=((0.130*T-0.60)*X(3)*1E-03)/(X(1)+X(3)+X(6)) 812 VN2 = ((0.019*T+24.1)*X(6)* 1E-06)/(X(1)+X(3)+X(6)) 127 813 KN2=((0.039*T+35.8)*X(6)*1E-03)/(X(1)+X(3)+X(6)) 814 VISC=VC02+VH20+VN2 815 ' THC0ND=KC02+KH20+KN2 816 C 817 C ENTHALPY OF FORMATION FOR EACH SPECIES... 818 UUU( 1 ) = -3.93522E05 819 UUU(2)=-1.10529E05 820 UUU(3)=-2.41827E05 821 UUU(4)=0.00000E00 822 UUU(5)=O.OOOOOEOO 823 UUU(6)=0.00000E00 824 UUU(7)=9.05920EO4 825 UUU(10)=2.17986E05 826 UUU(9)=2.49195E05 827 UUU(8)=39463.0 828 C 829 C MOLECULAR WEIGHT FOR EACH SPECIES... 830 MW(1)=44.01 831 MW(2)=28.01 832 MW(3)=18.01 833 MW(4)=2.02 834 MW(5)=32.00 835 MW(6)=28.01 836 MW(7)=30.00 837 MW(8)=17.00 838 MW(9)=16.00 839 MW(10)=1.00 840 C 841 C CALC. ENERGY OF PRODUCTS 1 TO 10 842 EPROD=0. 843 DO 109 1=1,10 844 ECOMP=X(I)*(UUU(I)+DH(I)-RMOL*T) 845 IF(M0DE.E0.3) ECOMP=X(I)*(UUU(I)+DH(I)) 846 EPROD=EPROD+ECOMP 847 109 CONTINUE 848 C 849 C CALCULATE SUM^OF X VALUES 850 SUMXS=0 851 DO 231 ILG=1,10 852 231 SUMXS=SUMXS+X(ILG) 853 C 854 C CALC PERC. OF PRODUCTS AND MOLECULAR WEIGHT OF MIXTURE 855 MWBMIX=0.0 856 DO 232 ILH=1,10 857 CC(ILH)=(X(ILH)/SUMXS)*100. 858 232 MWBMIX=MWBMIX+(CC(ILH)*MW(ILH)/100.) 859 EB2=EPR0D/MWBMIX/SUMXS 860 VSB2=RM0L*T/(MWBMIX*P) 861 C 862 C CALC. AVERAGE SPECIFIC HEATS FOR MIXTURE... 863 CP=0 864 DO 233 ILF=1,8 865 233 CP=CP+(CC(ILF)*CPG(ILF))/100. 866 CV=CP-RMOL 867 GAMMA=CP/CV 868 C 869 C 870 C ' WRITE(6,889) MWBMIX,EB2,VSB2,GAMMA,NDISS 871 C 889 F0RMAT(1H MWBMIX,EB2,VSB2,GAMMA,NDS '.4E12.4.I3) 872 C 873 C 874 ' RETURN 875 END 128 APPENDIX E - CONSTANT VOLUME BOMB SIMULATION PROGRAM (BOMB) T h i s appendix d e s c r i b e s the program BOMB which s i m u l a t e s a d i a b a t i c , p r o g r e s s i v e b u r n i n g i n e i t h e r a s p h e r i c a l bomb or i n a chamber ha v i n g the same geometry as the Toyota engine c y l i n d e r w i t h f i x e d p i s t o n p o s i t i o n . The main i n p u t s t o the program a r e : 1. F u e l type 2. I n i t i a l p r e s s u r e and temp e r a t u r e 3. A i r / f u e l r a t i o f o r t he s p h e r i c a l bomb, t o g e t h e r w i t h the d i s t a n c e of the p i s t o n from T.D.C. i n the case of the engine c y l i n d e r . G i v e n t h e s e i n p u t v a l u e s and t h e volume of t h e combustion chamber, the program f i r s t c a l c u l a t e s the i n i t i a l m i x t u r e c o m p o s i t i o n , and the t o t a l energy, as d e s c r i b e d i n Appendix D ( s e c t i o n a ) , b e f o r e commencing w i t h the p r o g r e s s i v e b u r n i n g s e c t i o n . To s i m u l a t e p r o g r e s s i v e b u r n i n g the chamber i s s p l i t i n t o burned and unburned zones, s e p a r a t e d by a s p h e r i c a l s h e l l c e n t r e d on the spark p l u g which r e p r e s e n t s the t h i n flame f r o n t . The combustion p r o c e s s i s d i v i d e d i n t o a number of d i f f e r e n t time s t e p s ( t y p i c a l l y 20) and a t each time s t e p , the p r e s s u r e i s incremented u n t i l the c a l c u l a t e d b u r n i n g v e l o c i t y o b t a i n e d from the thermodynamics and geometry of the combustion (CBVEL), becomes e q u a l t o the ' t r u e ' b u r n i n g v e l o c i t y o b t a i n e d from p u b l i s h e d e m p i r i c a l e q u a t i o n s (TBVEL = f ( P U , T M , X ) . The g e n e r a l form of the program i s g i v e n a t the end of the a p p e n d i x , and i t can be seen t h a t the combustion c a l c u l a t i o n s a t each time and p r e s s u r e increment a r e d i v i d e d i n t o 3 s u b r o u t i n e s . a. S u b r o u t i n e ENUFLS The f i r s t s u b r o u t i n e 'ENUFLS' c a l c u l a t e s the temperature (Tu), s p e c i f i c volume (Vu) and s p e c i f i c energy (e ) of the unburned gas by assuming i s e n t r o p i c c o m p r e s s i o n from the p r e s s u r e P1 ( o b t a i n e d from the p r e v i o u s time s t e p ) , t o the newly i t e r a t e d p r e s s u r e P2. (k - 1 ) / k T h e r e f o r e Tu z Tu, (P2/P1) (1) and where 1/k V u z = Vu A . (P2/P1) k = Cp /Cv = Cp /(Cp-R) (2) .... (3) 129 a l s o e M 2 = I n ; (hf° + (hjfr^-h,;<v<a)-RTux ) k J NMIX . MWMIX kg (4) where NMIX = kmols of m i x t u r e / kmols of f u e l and MWMIX = m o l e c u l a r weight of m i x t u r e The v a l u e s of Cp f o r the components of the m i x t u r e a t a g i v e n temperature (Tu1) a r e o b t a i n e d u s i n g e x p r e s s i o n s g i v e n i n Van Wylen and Sonntag [ 2 4 ] . T h i s s u b r o u t i n e a l s o c a l c u l a t e s the ' t r u e ' b u r n i n g v e l o c i t y , TBVEL, based on the average unburned gas temperature (Tu=(Tu1+Tu2)/2) and p r e s s u r e (Pu=(P1+P2)/2) u s i n g e q u a t i o n s g i v e n by M e t g h a l c h i and Keck [17] and [23]) of the form A B TBVEL = Suo . fTu_\ . (5) I 298 i I 100/ f o r propane, o c t a n e , and i n d o l i n e . Other e q u a t i o n s used were; 1 .68 TBVEL = C . (Tu/298) (6) where C = -418 -1287 -1196 +360 - 1 5 . 0 . l o g (Pu) 0 0* ~ F f o r n a t u r a l gas from Agrawal and Gupta (Ref ? ) , and b2 TBVEL = b1 .CPu) . exp (~b3/Tu) (7) f o r methane from Ryan and L e s z t ( R e f 1 6 ) . The v a l u e s o b t a i n e d f o r the unburned gas p r o p e r t i e s and the l a m i n a r b u r n i n g v e l o c i t y a r e r e t u r n e d t o the main program. b. S u b r o u t i n e TEMP T h i s s u b r o u t i n e c o n t a i n s an i t e r a t i o n p r o c e d u r e which v a r i e s the burnt gas te m p e r a t u r e , TB2, u n t i l the f o l l o w i n g two e q u a t i o n s a r e s a t i s f i e d : ETOT/MTOT = x efc + ( 1 - x ) e M (8) VTOT/MTOT = x v b + ( 1 - X ) V m (9) S i n c e v and e ar e known from t h e s u b r o u t i n e ENUFLS, and ETOT, VTOT and MTOT a r e c o n s t a n t s d e t e r m i n e d a t the s t a r t of the program, the v a l u e s of x, eb, and vb remain as unknowns. However, e t= f(TB2) and MWBMIX = f(TB2) ( t h r o u g h the 130 d i s s o c i a t i o n c a l c u l a t i o n s of s u b r o u t i n e ENERGY), t h e r e f o r e vb can be o b t a i n e d u s i n g Vb = RMOL * TB2 / (MWBMIX * P2) (10) The magnitude of the mass f r a c t i o n b u r n t , x, i s t h e r e f o r e o n l y dependant upon the v a l u e of the bur n t gas temperature TB2, and i t i s o b t a i n e d by r e a r r a n g i n g e q u a t i o n s 8 and 9 t o g i v e two e x p r e s s i o n s f o r mass f r a c t i o n b u r n t , namely MFXE = ETOT/MTOT - eu (11) eb - eu and MFXV = VTOT/MTOT - vu (12) vb - vu and the c o r r e c t b u r n t gas temperature i s o b t a i n e d when ERROR = (MFXV-MFXE) = 0. The s u b r o u t i n e ENERGY which i s c a l l e d by TEMP i s i d e n t i c a l t o t h a t d e s c r i b e d i n Appendix 0 f o r the O t t o c y c l e s i m u l a t i o n program. S u b r o u t i n e TEMP r e t u r n s the v a l u e s of x, vb and TB2 t o the main program. c. S u b r o u t i n e CALFLS T h i s s u b r o u t i n e i s used t o o b t a i n the v a l u e of the c a l c u l a t e d b u r n i n g v e l o c i t y CBVEL g i v e n the r e s u l t s of the thermodynamic c a l c u l a t i o n s of the p r e v i o u s two s u b r o u t i n e s (ENUFLS and TEMP), t o g e t h e r w i t h the geometry of the flame p r o p o g a t i o n . F i r s t l y i t c a l c u l a t e s the new bur n t gas volume, VOLB2 = MTOT * x * Vb (13) and then uses an i t e r a t i o n p r o c e d u r e Xo f i n d , 1. The r a d i u s of t h e flame (RB2) r e q u i r e d t o o b t a i n a burned gas volume of VOLB2. 2. The a r e a of the flame f r o n t a t t h i s r a d i u s (AREA2). The i t e r a t i o n procedes by v a r y i n g the v a l u e of the flame r a d i u s RB2 u n t i l the volume o b t a i n e d from s u b r o u t i n e 'VOL' i s eq u a l t o the b u r n t gas volume VOLB2 o b t a i n e d from e q u a t i o n 13. S u b r o u t i n e VOL c o n t a i n s e q u a t i o n s which e x p r e s s the bur n t gas volume and flame f r o n t a r e a as a f u n c t i o n of flame r a d i u s . In the case of the s p h e r i c a l bomb w i t h c e n t r a l i g n i t i o n , 131 the b u r n t volume and flame a r e a a r e g i v e n s i m p l y by; VOLB = (4/3) * TT * (RB2) (13) and AREA2 = 4 * TT * (RB2) (14) However the e x p r e s s i o n s become more i n v o l v e d i n the case of a h e m i s p h e r i c a l head combustion chamber w i t h c e n t r a l i g n i t i o n . In t h i s case the flame i s c o n s i d e r e d t o expand i n the manner shown i n F i g , where i t can be seen t h a t d i f f e r e n t e x p r e s s i o n s a r e i n v o l v e d f o r each of the v a r i o u s s t a g e s of e x p a n s i o n . Having o b t a i n e d the flame a r e a a t the end of the c u r r e n t combustion time s t e p (AREA2), the c a l c u l a t e d b u r n i n g v e l o c i t y i s o b t a i n e d u s i n g the e q u a t i o n , CBVEL = MTOT * x * V u ( a v g ) (15) AVERAGE FLAME AREA where x = mass b u r n i n g r a t e = (x, +x t)/2 v M ( a v g ) = the average v a l u e of the unburned gas s p e c i f i c volumes from the c u r r e n t (VSU2) and p r e v i o u s (VSU1) time s t e p s = (VSU1+VSU2)/2 and AVG. FLAME AREA = (AREAF1 + AREAF2)/2. The v a l u e of CBVEL i s r e t u r n e d t o the main program. Having o b t a i n e d the v a l u e s of TBVEL and CBVEL at a g i v e n time s t e p and p r e s s u r e u s i n g s u b r o u t i n e s ENUFLS, TEMP and CALFLS, th e ERROR=(TBVEL-CBVEL) i s c a l c u l a t e d , and the p r e s s u r e incremented u n t i l ERROR=0 u s i n g a p r o p o r t i o n a l c h o p p i n g i t e r a t i o n p r o c e d u r e . At the end of each time s t e p , the v a l u e s o f ; Time P r e s s u r e Mass f r a c t i o n burned Burned gas temperature and volume and Unburned gas temperature and volume ar e p r i n t e d o u t , and the program proceeds t o the next time s t e p . C a l c u l a t i o n s a t each f r a c t i o n b u r n t (x) e q u a l s time s t e p u n i t y , a t c o n t i n u e u n t i l the mass which p o i n t the i t e r a t i o n s 132 a r e stopped, and graphs of P r e s s u r e , Mass F r a c t i o n burned and B u r n i n g v e l o c i t y v e r s e s t i m e , are g e n e r a t e d . 133 CONSTANT VOLUME BOMB SIMULATION PROGRAM FLOWCHART INPUT: FUEL TYPE; A/F RATIO; INITIAL MIXTURE PRESSURE AND TEMPERATURE. CALCULATE INITIAL MIXTURE COMPOSITION AND ENERGY AT NEXT TIME STEP; ASSUME NEW PRESSURE IN BOMB ASSUME UNBURNED GAS COMPRESSED ISENTROPICALLY TO DETERMINE NEW TEMPERATURE AND ENERGY, FROM THESE OBTAIN LAMINAR BURNING VELOCITY.(ENUFLS) ITERATE BURNED GAS TEMPERATURE UNTIL MASS AND ENERGY OF BURNED AND UNBURNED GASES BALANCE.(TEMP) OBTAIN MASS FRACTION BURNED, FLAME RADIUS & FLAME SPEED, AND HENCE BURNING VELOCITY.(CALFLS) NO IS CALCULATED BURNING VELOCITY EQUAL TO LAMINAR BURNING VELOCITY? NO IS MASS FRACTION BURNED GREATER THAN UNITY? PRINT RESULTS AND PLOT GRAPHS STOP 134 1 SAMPLE INPUT F I L E FOR PROGRAM "BOMB" 3 4 5 003 6 001 0 0 7 1.0 4 . 0 1 0 0 . 0 3 0 0 . 0 1 .00 - 7 4 8 7 3 . 0 1 11 8 0 . 0 7 8 0 . 0 8 5 9 . 0 0 50 5 0 0 1 0 . 0 3 0 0 0 . 0 0 . 1 2 4 1 .000 9 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 10 3 . 0 8 . 0 1 0 0 . 0 3 0 0 . 0 1 .00 - 1 0 3 8 4 7 . 0 1 13 11 0 . 0 7 8 0 . 0 8 5 9 . 0 0 50 4 6 3 5 3 . 0 3 0 0 0 . 0 0 . 1 2 4 1 .000 12 0.0000 0.0000 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 13 8 . 0 1 8 . 0 1 0 0 . 0 3 0 0 . 0 1 .00 - 2 0 8 4 4 7 . 0 1 12 14 0 . 0 7 8 0 . 0 8 5 9 . 0 0 50 4 4 7 8 8 . 0 3 0 0 0 . 0 0 . 1 2 4 1 .000 15 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 16 ====== 17 NUMBR 18 ================== 19 MODE IPR INT I P L O T 20 ======================================================== 21 CN HM P1 T1 LAMBDA HFO NDISS K F U E L 22 ======================================================== 23 STROK BORE COMPR NDIV QVS SPEED LENG SPKAD 24 ================================================== 25 F PR02 PRC02 PRH20 PRN2 26 FUEL; C 8.0 H 18.0 AIR/FUEL RATI0= 15.06 STOICH. A/F RATIO* 15.06 LAMBDA= 1.00 INITIAL PRESSURE = 900.0 kPa INITIAL TEMPERATURE5 500.0 K P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, P2.MFX2, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, TBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, CBV, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, V0LB2, TU2.TB2 TU2,TB2 TU2.TB2 TU2,TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2,TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 TU2.TB2 0 9035E+03 0 8056E-03 0 5860E+00 0 6269E+00 0 2321E -06 0 5005E+03 0 2455E+04 0 9178E+03 0 3747E-02 0 5883E+00 0 6110E+00 0 1064E -05 0 5025E+03 0 2459E-I-04 0 9481E+03 o 9856E-02 O 5938E+00 0 5995E+00 0 2720E -05 0 5066E+03 0 2466E+04 0 1001E+04 0 2052E-01 0 6035E+O0 0 6113E+00 0 5394E -05 0 5133E+03 0 2479E+04 0 1082E+04 0 3717E-01 0 6186E+00 0 6217E+00 0 91 14E -05 0 5232E+03 0 2498E+04 0 1199E+04 0 6073E-01 0 6395E+00 0 6410E+00 0 1356E -04 0 5363E+03 0 2522E+04 0 1344E+04 0 9056E-01 0 6653E+00 0 6659E+00 0 1825E -04 0 5513E+03 0 2549E+04 0 1515E+04 0 1264E+00 0 6942E+00 0 6992E+00 O 2285E -04 0 5674E+03 0 2578E+04 0 1717E+04 0 1682E+00 0 7255E+00 0 7254E+00 0 2713E -04 0 5846E+03 0 2605E+04 0 1946E+04 0 2164E+00 0 7585E+00 0 7589E+00 0 31 15E -04 0 6021E+03 0 2634E+04 0 2203E+04 0 2712E+00 0 7924E+00 0 7928E+00 0 3488E -04 0 6198E+03 0 2662E+04 0 2483E+04 0 3319E+00 0 82G7E+00 0 8235E+00 0 3829E -04 0 6373E+03 0 2689E+04 0 2802E+04 0 3987E+00 0 8615E+00 0 8611E+00 O 4 1 13E -04 0 6554E+03 0 2715E+04 0 3144E+04 0 471 1E+00 0 8969E+00 0 8964E+00 0 4372E -04 0 6729E+03 0 2740E+04 0 3489E+04 0 5474E+00 0 9307E+00 0 9306E+00 0 4619E -04 0 6891E+03 0 2763E+04 0 3835E+04 o 6257E+00 0 9623E+00 0 9656E+00 0 4843E -04 0 7041E+03 0 2784E+04 0 4204E+04 0 7038E+00 0 9926E+00 0 9921E+00 0 5003E -04 0 7189E+03 0 2802E+04 0 4402E+04 o 7429E+00 0 1016E+01 0 1014E+01 0 5058E -04 0 7263E+03 0 2811E+04 0 4592E+04 0 7801E+00 0 1030E+01 0 9734E+00 0 5108E -04 0 7332E+03 0 2819E+04 0 4735E+04 0 8178E+00 0 1042E+01 0 1039E+01 0 5209E -04 0 7382E+03 0 2827E+04 0 4894E+04 0 8531E+00 0 1053E+01 0 1051E+01 0 5270E -04 0 7437E+03 0 2835E+04 0 5042E+04 0 8862E+00 0 1064E+01 0 1061E+01 0 5327E -04 0 7486E+03 0 2841E+04 0 5175E+04 0 9164E+00 0 1074E+01 0 1070E+01 0 5379E -04 0 7530E+03 0 2847E+04 0 5293E+04 0 9433E+00 0 1082E+01 0 1076E+01 0 5423E -04 0 7567E+03 0 2852E+04 0 5394E+04 0 9664E+00 0 1089E+01 0 1079E+01 0 5461E -04 0 7599E+03 o 2856E+04 0 5476E+04 0 9850E+00 0 1095E+01 0 1076E+01 0 5490E -04 0 7624E+03 0 2859E+04 0 5549E+04 0 1000E+01 0 1100E+01 o 1100E+01 0 5506E -04 0 0 0 2862E+04 to cn TYPICAL OUTPUT FROM PROGRAM "BOMB" 136 1 C BOMB THIS PROGRAM SIMULATES PROGRESSIVE BURNING 2 C ===== IN A CONSTANT VOLUME, SPHERICAL BOMB. A 3 C CYLINDRICAL BOMB, OR A HEMISPHERICAL 4 C COMBUSTION CHAMBER WITH THE SAME GEOMETRY 5 C AS THE TOYOTA ENGINE. 6 C 7 IMPLICIT REAL*8(A-H,0-Z) 8 REAL*8 K,L,M,N,NO,N2.N02,NCH,KK,NUM,NUM1,NMIX,MOLFL,NM.NM1, 9 -NNM1,NNM2,NN2,NN02,MEP,LENG,MTOT,MWMIX,MFX1,NNCH,MFX2,MW(14), 10 -MMFX2,NRN2,NRES.NR02,NRC02,NRH20,NNFUEL,LAMBDA,MWBMIX 1 1 C 12 COMMON /AREA1/ NCH,N02,K,L.M.N,KFUEL 13 COMMON /AREA2/ MOLFL,NMIX,HF 1 ,NN02.NN2,NNFUEL,KOM 14 COMMON /AREA4/ NDISS,IPRINT 15 C 16 DIMENSION X(10),PP(5,200),VV(5,200).VV2(5.200),VXX(5,200), 17 -DH(20),CPG(20),PP2(5,200),CC(10),DI(5,200),TIM(5,200), 18 -XX(5,200),CCA(10),DL(5,200),ZZ(5,200),DC(5,200),YY(5,200), 19 -UUUOO) 20 C 21 INTEGER IPRES(5,200) 22 C 23 C WHEN THE PROGRAM IS RUN TO SIMULATE THE TOYOTA COMBUSTION CHAMBER, 24 C STATEMENT FUNCTION USED THROUGHOUT PROGRAM TO CALCULATE CYLINDER 25 C VOLUME (DVOL) AT A GIVEN CRANK ANGLE (DALFA). VOLUME OBTAINED MUST 26 C ' BE ADDED TO THE CLEARANCE VOLUME TO GIVE TOTAL CYLINDER VOLUME 27 C 28 DVOL(DALFA) = 3 . 14159*((BORE/2. )**2.)*((STROK/2.)*(1.-DCOS(DALFA* 29 -0.0174532))+LENG*(1.-DSORT(1.-(DSIN(DALFA*0.0174532)*DSIN(DALFA 30 -*0.0174532)*((STROK/2./LENG)**2.))))) 31 C 32 C READ NUMBER OF RUNS TO BE MADE.... 33 C 34 READ(5,999) NUMBR,IPRINT 35 999 F0RMAT(2I3) 36 DO 222 IL=1,NUMBR 37 JZZ=1 38 JXX=1 39 C 40 C READ NUMBER OF MOLES OF CARBON (CN) AND HYDROGEN (HM) IN FUEL; 41 C PRESSURE (P1)(KPA) AND TEMP. (T1)(K) AT START OF COMBUSTION; 42 C (LAMBDA); AND HFO FOR FUEL; FUEL TYPE (KFUEL) (11=CH4. 43 C 12=C8H18,13=C3H8); TIME INTERVAL BETWEEN COMBUSTION STEPS (DTIME) 44 C IN SECONDS; FLAME FACTOR (FFF); NO.OF DISS. CALCS. (NDISS=1,2,3); 45 C INITIAL PRESSURE INCREMENT (PIN); SUCCESSIVE PRESSURE INCREMENTS 46 C (DPX); ITERATION LIMITING ERROR (EPS); NO. OF STEPS TO ITERATE 47 C TO (IPDX); RADIUS OF BOMB (RADBMB); 48 C PISTON DISTANCE FROM TDC (DIST); TYPE OF COMBUSTION CHAMBER: 49 C (1=SPHERICAL BOMB,2=CYLINDRICAL BOMB,3=T0Y0TA ENGINE) (KTYPE). 50 C 51 READ(5,49) CN.HM,P1,T1.LAMBDA,HF1.KFUEL,DTIME,FFF,NDISS 52 49 FORMAT(4F7.1,F7.3.F11.2,I3,F7.4,F5.2,I3) 53 READ(5,48) PIN,DPX,EPS,IPDX,IJUMP,RADBMB,DIST,KTYPE 54 48 F0RMAT(2F7.2,F8.5,2I4.F7.4,F9.6,I3) 55 C 56 C GAS CONSTANT (KJ/KMOL K) 57 C 58 RM0L=8.3143 137 59 JJ=0 60 C 61 C CALC. NUMBER OF KMOLS OF REACTANTS AND PRODUCTS BEFORE AND AFTER 62 c COMBUSTION RELATIVE TO ONE KMOL OF FUEL 63 c (NOT INCLUDING DISSOCIATION). NCH=HYDR0CARB0N 64 c N02=AVAILABLE OXYGEN N=NITROGEN, K=C02, L=H20, M=UNBURNT OXYGEN 65 c 66 NCH= 1 67 N02 =(CN+HM/4)* LAMBDA 68 N=3.762*(CN+HM/4)*LAMBDA 69 K=CN : 70 L=HM/2 71 M=(CN+HM/4)*(LAMBDA-1) 72 c 73 c WRITE(6,655) NCH,N02.N,K,L,M 74 c 655 F0RMAT(1H ,'NCH,N02,N,K,L,M='.6F9.5/) 75 c 76 c CALC. NUMBER OF KMOLS OF REACTANTS... 77 SUMNS=NCH+N02+N 78 c 79 c CALC. ENTHALPY OF REACTANTS AT INLET TEMP; 5=02, 6=N2, 11=CH4 80 c 12=C8H18, 13=C3H8 (IN KJ/KMOL OF FUEL) 81 DH(5) = ((3.253*T1+6.524E-04*(T1**2)- 1.495E-07*(T1**3) 82 1+1.539E-11*(T1**4))-1O24.O)*RM0L 83 DH(6)=((3.344*T1+2.943E-04*(T1**2)+1.953E-09*(T1**3) 84 1-6.575E-12*(T1**4))-1O23.O)*RM0L 85 DH( 11) = ((1.935*T1+4.965E-03*(T1 **2.)-1.244E-06*(T1**3.) 86 1+1.625E-10*(T1**4.)-6.586E-15*(T1**5.))-985.9)*RM0L 87 DH(12)=((-0.72*T1+4.643E-02*(T1*"*2.)-1.684E-05*(T1**3.) 88 1+2.67E-09*(T1**4.))-3484.0)*RMOL 89 DH(13)=((1.137*T1+1.455E-02*(T1**2.)-2.959E-06*(T1**3.) 90 1)-1552.9)*RM0L 91 c CALC. TOTAL ENERGY OF MIXTURE (KJ/KMOL FUEL) 92 ERCT = (NCH*(HF1+DH(KFUEL)-RM0L*T1 )+N02*(DH(5)-RMOL*T1 ) 93 -+N*(DH(6)-RM0L*T1 ) ) 94 c 95 c CALC. VOLUME OF GIVEN COMBUSTION CHAMBER TYPE... 96 IF(KTYPE.EO• 1) V1 = (4./3.)*3.14159*(RADBMB**3. ) 97 IF(KTYPE.EO.2) V1=405.19E-06 98 IF(KTYPE.E0.3) V1=55.3264E-06+3.14159*(0.00180625)*DIST 99 TIME=0.0 100 c 101 c CALC. NO. OF KMOLS OF MIXTURE/KMOL OF FUEL, AND CALC. THE NO. 102 c OF KMOLS OF FUEL IN THE CYLINDER.... 103 NMIX=(1.0+4.762*(CN+HM/4)*LAMBDA) 104 M0LFL=(P1*V1)/(NMIX*RM0L*T1) 105 c 106 c ENERGY OF CYLINDER CONTENTS IN KJ 107 ET0T2=ERCT*M0LFL 108 c 109 c CALC. STOICH. A/F RATIO (STAFR),AIR/FUEL RATIO (AFR ),PERCENTAGE 1 10 c OXYGEN (NN02) AND NITROGEN (NN2) IN MIXTURE. 111 STAFR=((CN+HM/4.)*32.+3.762*(CN+HM/4.)*28.01)/((CN*12)+HM) 112 AFR=STAFR*LAMBDA 113 NN02=(N02/NMIX)*1OO. 1 14 NN2=(N/NMIX)*100. 115 NNCH=100.-(NN02+NN2) 1 16 c 138 117 C GIVEN MOLECULAR WEIGHTS OF FUELS, CALC. MOLECULAR WEIGHT OF 118 C MIXTURE (MWMIX); TOTAL MASS OF MIXTURE (MTOT); AND SPECIFIC 119 C VOLUME OF MIXTURE 120 MW(11)=16.04 121 MW(12)=114.23 122 MW(13)=44.097 123 MWMIX=(NN02*32.0/100.)+(NN2*28.0/100.)+(NNCH*MW(KFUEL)/100.) 124 MT0T=(P1*V1*MWMIX)/(T1*RM0L) 125 VT0T1=V1 126 VSU1=VT0T1/MT0T 127 C 128 C CALC. ENERGY OF CYLINDER CONTENTS IN KJ/KG.... 129 ET0T1=ERCT/MWMIX/NMIX 130 C 131 C WRITE(6,734) ERCT,ETOT1,ET0T2,NMIX,MWMIX,MOLFL 132 C 734 FORMATdH f ERCT , ET 1 , ET2 . NMIX , MWMX , MOLFL ;', 6E 12 . 4//) 133 C 134 WRITE(6,652) CN,HM 135 652 FORMATdH ,'FUEL; C '.F3.1,' H '.F4.1/) 136 WRITE(6,813) AFR , STAFR,LAMBDA 137 813 FORMATdH ,15HAIR/FUEL RAT10=,F6.2,3X,18HST0ICH. A/F RATIO=, 138 -F6.2,3X,7HLAMBDA=,F6.2/) 139 WRITE(6,817) 140 817 FORMATdH ,28X,39HC0NCENTRATI0N OF COMB. PRODUCTS (KMOLS)/) 141 WRITE(6,31) 142 31 FORMATdH , 1X ,' STEP ', 1X ,' VOL ', 3X ,' PRESS ', 3X ,' TEMP ', 3X ,' C02 ', 4X 143 -,'CO',5X,'H20',4X,'H2',5X,'02',5X,'N2',5X,'NO',5X,'OH',6X,'0', 144 -6X,'H',4X,'TIME'/) 145 DO 106 KI=1,10 146 X(KI)=0.0 147 106 CONTINUE 148 NIT=1 149 V1=VT0T1*(1E+06) 150 WRITE(6,893) NIT,V1,P1,T1,(X(I),I=1,4),NN02,NN2,(X(J),J=7,8) 151 -,ETOT1,TIME 152 893 F0RMAT(1H ,12,1X,F6. 1 ,F7 . 1 , F7 . 1 , 4F7.2,2F7.3,2F7.2,E12.4,F9.6) 153 TU1=T1 154 PP2(IL,1)=P1/100.0 155 TIM(IL,1)=TIME 156 JJJ=1 157 C 158 C START OF PROGRESSIVE BURNING 159 C ============================ 160 C 161 C INITIALISE VALUES USED IN THIS SECTION... 161.5 DELP=0.0 162 IDTM=1 163 IMX=1 164 MFX1=0.0 165 IV0L=1 165.5 C 166 DO 5 J=1,IPDX 166.5 C 166.7 C 167 NUT=0 168 PX1=P1+PIN 169 PXF=10000.0 170 C 139 j y -f ^ n II it II n it II n II n n n 11 n tt n n n 11 n n n n u n u 11 n n n it 11 n n rt n n n 11 n u 11 " ti n n n n M u n n n n n n n n n it n u n 172 CALL ENUFLS(PX1,P1,TU1,VSU1 ,MWMIX,TU2,VSU2,EU2,FFF,TBVEL) ^73 ^ II II ti II n n II it ti II II II II II it H II it II II n n n n II II II n II n n n rt t* n ti tt n it n n t> ti n n n II II n n n M n •• n n n II i> n ti tt 174 CALL TEMP(PX1,TB2,CC,MFX2,MTOT,EU2,VSU2,VTOT1,ETOT1.VSB2) ^ "75 Q ti ti II it ti II n it it it II II ti it II it ti it II ii II ii ti II II tt n n n it n n II II tl II ti ti n n •• « it it it ti II n n u ti n it ti II II II II u n II u 176 CALL CALFLS(MFX1,MFX2,VSB2,MTOT,DTIME,FFF,VSU2,CBVEL,VSU1 , 177 -AREAF1,VOLB2,IVOL,VOLB1,AREAF2,RB1,RB2,RADBMB,DIST,KTYPE) •J "7Q £ 1 1 1 1 1 1 1 1 n II ti it II n II ti it n II II II n II n II n II II II M II II II II n II it II tt ti ti ti ti II II II II II it ti II ti n it n II II n II II II II II II n II n 179 C 180 Y1=TBVEL-CBVEL 181 Z1=1.0-MFX2 181.5 IF(DELP.GT.DPX) DPX=DELP/2 182 10 PX2=PX1+DPX 183 IF (PX2.GT.PXF) STOP 184 C -| g g £ II II tt n ti it II II II it ti II II II n II II tt it it n II it n ti n ti ti ti n n it n n rt H II II it n it ti n n n n it it ti ti ti it it II II it ti it ti n u n n 186 502 CALL ENUFLS(PX2,P1,TU1,VSU1,MWMIX,TU2,VSU2,EU2,FFF,TBVEL) ^Qf Q tt ti II II n it ti ti ii tt II n rt ri II tr n ti it it it ti n n n n n n n n ti n n M n n u n n n n ti II n n n it n it ti ti tt it ti n it ti n II n n n n 188 CALL TEMP(PX2,TB2,CC,MFX2,MTOT,EU2,VSU2,VTOT1,ETOT1,VSB2) 4j gg £ o II II n II it ti II it ti ti H II ii tt it II ti II II ti it ti ti ti II ii it ii » it it ti n it tt rt n II II II it H ti n II II II II II II II ti ti n II n n n it it tt it 190 C 191 IF(IMX.E0.2) GOTO 503 192 IF(MFX2.LT.1.0) GOTO 501 193 Z2=1-MFX2 194 PX2 = (PX1*Z2-PX2*Z1 )/(Z2-Z1 ) 195 IMX=2 196 GOTO 502 197 C ^ gg Q II it tt II II it II ti ti ti it II n n II it it II II rr it it n II n II N u tt II n II ti n n ii it ti it it ti ti n n n n n n n u u n it II n n n n n n u n n 199 501 CALL CALFLS(MFX1.MFX2.VSB2,MTOT,DTIME,FFF,VSU2,CBVEL.VSU1, 200 -AREAF1,V0LB2,IV0L.V0LB1,AREAF2,RB1,RB2,RADBMB,DIST,KTYPE) 20 ^  C " " " " " " " " " " " " " " " " " " " " " " " " " M 1111 " " " " " " " " " " " 11 " 11 " u " " " " " " " " " " " " " " " " " " " 202 C 203 Y2=TBVEL-CBVEL 204 IF(Y1*Y2.LE.O.) GOTO 20 205 PX1=PX2 206 Y1=Y2 207 GOTO 10 208 20 IF(Y2.EQ.O.) GOTO 50 209 PX30LD=PX2 210 30 PX3 = (PX1*Y2-PX2*Y1 )/(Y2-Y1 ) 211 NUT=NUT+1 212 IF (NUT.LT.50) GOTO 80 213 WRITE(6,90) NUT 214 90 F0RMAT(1H .'PROGRAM STOP DUE TO PRO BN ITERATIONS EXCEEDING',14) 215 STOP 216 80 IF(DABS((PX3-PX30LD )/PX3 ) .LT.EPS) GOTO 60 217 PX30LD=PX3 218 C 2^9 £ II u II II it it II II ii ii II tt ii ii II II ii II rt it tt II n it it II n II n n rt n ti it II ii » ti it n n n n n n n it it n it n n u n n n n n II n ti II II 220 CALL ENUFLS(PX3,P1,TU1,VSU1.MWMIX,TU2.VSU2,EU2,FFF,TBVEL) ^ II n II II II II n H II II n II n II n II II n it H n I M I n II II n n rt n rt « n n it II it n tt it tt n n II •• i n II n n it n n it n n n n 222 CALL TEMP(PX3,TB2,CC,MFX2,MTOT,EU2,VSU2,VTOT1,ETOT1,VSB2) 223 Q II II It II It II II It II H It II II tl It II II tt It ft II 11 II H 11 11 II It 11 It II II fl tl tl II 11 II II II II It 11 1 II II II II tt 11 tl H 11 II 11 II II II II II 224 CALL CALFLS(MFX1.MFX2.VSB2.MTOT,DTIME.FFF.VSU2,CBVEL.VSU1 , 225 -AREAF1.V0LB2,IVOL,VOLB1.AREAF2,RB1.RB2.RADBMB,DIST,KTYPE) 226 £ II n n II ir it II it II n II » II •• II II ti tt t> II it ti it ti rt it n it n II it n n ti n II ti n n n it II ti it II ti n n n n it it n it ti II II II ti u n n n 227 C 140 228 . Y3=TBVEL-CBVEL 229 IF(Y1*Y3.LE.O.) GOTO 40 230 PX1=PX3 231 Y1=Y3 232 GOTO 30 233 40 PX2=PX3 234 Y2=Y3 235 GOTO 30 236 50 P2=PX2 237 GOTO 70 238 60 P2=PX3 239 70 V0LU2=VT0T1-V0LB2 240 C 241 503 IFUMX.EQ.1) GOTO 504 242 MFX2=1.0 243 P2=PX2 244 CBVEL=TBVEL 245 TU2=0.0 246 V0LU2=0.0 247 VSUAVG=(VSU1+VSU2)/2.0 248 XD0T=CBVEL*(AREAF1/2.)/(MTOT*VSUAVG) 249 DTIME=(1.0-MFX1)/XDOT 250 C 251 504 TIME=TIME+DTIME 252 FLMSPD=(RB2-RB1)/DTIME 253 VFRBNT=(V0LB2/VT0T1)*100.0 254 WRITE(6,100) P2,MFX2,TBVEL,CBVEL,V0LB2.TU2,TB2 255 100 F0RMAT(1H ,'P2,MFX2,TBV,CBV,V0LB2,TU2,TB2: '.7E12.4) 256 WRITE(6,101) VFRBNT,FLMSPD,V0LU2,TIME,DTIME 257 101 FORMATdH ,'VFRBNT , FLMSPD . V0LU2 , TIME . DTIME'. F7 . 2 , 4E 12 . 4//) 258 PP2(IL,(d+1))=P2/100.0 259 TIM(IL,(d+1))=TIME*1000.0 260 V0LB1=V0LB2 261 AREAF1=AREAF2 262 RB1=RB2 263 TU1=TU2 264 MFX1=MFX2 265 VSU1=VSU2 265.5 DELP=P2-P1 266 P1=P2 267 IV0L=2 268 IF(IDTM.E0.2) GOTO 3 269 IF(MFX2.LT.0.70) GOTO 3 270 DTIME=DTIME/2.0 271 C DPX=DPX/2.0 272 IDTM=2 273 3 IF(MFX2.GT.0.999) GOTO 222 274 NID=J+1 275 5 CONTINUE 276 C 277 222 CONTINUE 278 NID=NID+1 279 280 IF(IJUMP.EQ.2) GOTO 599 281 C 282 C THIS SECTION GENERATES A PRESSURE-TIME DIAGRAM 283 C ============================================== 284 C 141 285 387 DO 605 IL=1,NUMBR 286 DO 605 d= 1,NID 287 Y Y ( I L , J ) = ( P P 2 ( I L , J ) / 2 . 0 ) + 2 . 0 288 Z Z ( I L , J ) = T I M ( I L , d ) / 2 0 . + 2 . 0 289 605 CONTINUE 290 CALL A X I S ( 2 . , 2 . , ' T I M E ( M S E C ) ' , - 1 1 , 5 . 0 , 0 . , 0 . 0 , 2 0 . ) 291 CALL A X I S ( 2 . , 2 . , ' P R E S S U R E ( B A R ) ' , 1 4 , 6 . , 9 0 . , 0 . , 2 . ) 292 DO 415 IL=1,NUMBR 293 DO 415 1=1,NID 294 415 CALL S Y M B O L ( Z Z ( I L , I ) . Y Y ( I L , I ) , 0 . 0 5 , I L , 0 . , - 2 ) 295 C CALL L I N E ( Z Z ( 1 , I ) , Y Y ( 1 , I ) , 8 4 , 1 ) 296 CALL PLOTND 297 599 STOP 298 END 299 C 300 C SUBROUTINE TEMP CALCULATES TEMP. OF BURNT GAS AND MASS FRACTION 301 C =============== BURNED. 302 C 303 SUBROUTINE T E M P ( P 1 , T B 2 , C C , M F X , M T O T , E U 2 , V S U 2 , V T O T 1 , E T 0 T 1 , V S B 2 ) 304 C 305 COMMON /AREA 1 / N C H , N 0 2 , K , L , M , N , K F U E L 306 COMMON / A R E A 2 / MOLFL,NMIX.HF1,NN02,NN2,NNFUEL , KOM 307 COMMON / A R E A 4 / NDISS, IPRINT 308 C 309 R E A L * 8 X F , D X , E P S , Y 1 , Y 2 , Y 3 , X X 2 , Y Y 2 , M O L F L , H F 1 , N N 0 2 , N N 2 , N N F U E L , 310 - X 1 , X 2 , X 3 , X 3 0 L D , P 1 , P 2 , P 3 , C C ( 1 0 ) , X ( 1 0 ) , K , L , M , N . G A M M A , M F X . M T O T . 311 - E U 2 , V S U 2 , V T O T 1 , V S B 2 , E B 2 , T B 2 . E T O T 1 , V T D T C , N M I X , M F X E , M F X V , N 0 2 , N C H 312 C 313 NUT=0 314 JDX=1 315 IDX=1 316 X1=2000.0 317 XF=4000.0 318 DX=100.0 319 EPS=0.001 320 £ tr tl II tt ll ll it il ll ll ll ll li ll n || ll ll it ll ll it ll ll ll ll ll ll ll ll ll II ll ll ll ll ll ll 321 5 CALL E N E R G Y ( X 1 , P 1 , C C , X , E B 2 , V S B 2 ) 322 C " " *' " 11 " " " " " " " 1 1 1 1 " " " " " " " " 11 " " " " " n H " " H " " " " " 323 M F X E = ( E T 0 T 1 - E U 2 ) / ( E B 2 - E U 2 ) 324 C WRITE(6 ,777) X 1 , E T O T 1 , V T O T 1 , P 1 , E B 2 325 C 777 F0RMAT(1H , ' X 1 , E T O T 1 , V T O T 1 , P 1 , E B 2 , ' , 5 3 E 1 2 . 4 ) 326 I F ( M F X E . G T . O . 0 ) GOTO 10 327 X1=X1+DX 328 I F ( X I . G T . X F ) RETURN 329 0DX=2 330 GOTO 5 331 10 MFXV=(VT0T1 /MT0T-VSU2) / (VSB2-VSU2) 332 Y1=MFXV-MFXE 333 I F ( J D X . E O . I ) GOTO 30 334 IF ( Y 1 . L T . 0 . 0 ) GOTO 30 335 DX=-DX/2 . 336 IDX=2 337 30 X2=X1+DX 338 I F ( X 2 . G T . X F ) RETURN Q it tt it II •> II II it II n it H u n it II n II » n » if n >i n II n II tt it tt » n it n it n » 340 20 CALL E N E R G Y ( X 2 , P 1 , C C , X , E B 2 , V S B 2 ) 34 TJ Q it II ti ti II II II II II it ii ii H ii it fi II II II II II II II M ii ii ii ii n II •• •• II n II II n II 342 M F X E = ( E T 0 T 1 - E U 2 ) / ( E B 2 - E U 2 ) 142 343 C 747 FORMATC1H ,'X2,MFXE,MFXV,VSB2,VSU2,EB2,EU2;',7E10.3) 344 IFCMFXE.GT.0.0) GOTO 15 345 DX=DX/2. 346 IDX=2 347 X2=X2-DX 348 NUT=NUT+1 349 IF(NUT.GT.50) GOTO 91 350 GOTO 20 351 15 IFUDX.EQ.1) GOTO 16 352 DX=DX/2. 353 16 MFXV=(VT0T1/MT0T-VSU2)/(VSB2-VSU2) 354 Y2=MFXV-MFXE 355 C WRITE(6,747) X2,MFXE,MFXV,VSB2,VSU2,EB2,EU2 356 IF(Y1*Y2.LE.O.O) GOTO 25 357 X1=X2 358 Y1=Y2 359 NUT=NUT+1 360 IF(NUT.GT.80) .GOTO 91 361 GOTO 30 362 25 IF(Y2.EO.0.0) GOTO 50 363 IF(X2.GT.X1) GOTO 35 364 XX2=X2 365 YY2=Y2 366 X2=X1 367 Y2=Y1 368 X1=XX2 369 Y1=YY2 370 35 IF(MFXE.LT.10.0) GOTO 36 371 DX=DX/10.0 372 X2=X2-DX 373 GOTO 20 374 36 X30LD=X2 375 40 X3=(X1*Y2-X2*Y1 )/(Y2-Y1 ) 376 NUT=NUT+1 377 IF (NUT.LT.150) GOTO 80 378 91 WRITE(6,90) NUT 379 90 FORMATdH .'PROGRAM STOP DUE TO TEMP ITERATIONS EXCEEDING'. 14) 380 . RETURN 381 80 IF(DABS((X3-X30LD )/X3 ) . LT .EPS) GOTO 60 382 X30LD=X3 3Q3 ^ M II H H II ti it II II H tt tt II II M II II H II it II H H it it II II it II M n II H II II II n II 384 CALL ENERGY(X3,P1,CC,X,EB2,VSB2) 3Q5 ^ II II II ii II II II II II II it it II II II II II II II II II II ll ll tt ii ll ll ll ll ll •• II II II II II II 386 MFXE=(ET0T1-EU2)/(EB2-EU2) 387 MFXV=(VT0T1/MT0T-VSU2)/(VSB2-VSU2) 388 Y3=MFXV-MFXE 389 C WRITE(6,767) X3,MFXE,MFXV,Y3 390 C 767 FORMAT(1H ,'X3,MFXE,MFXV,Y3',4E12.4) 391 IF(Y1*Y3.LE.O.) GOTO 45 392 X1=X3 393 Y1=Y3 394 GOTO 40 395 45 X2=X3 396 Y2=Y3 397 GOTO 40 398 50 TB2=X2 399 GOTO 70 400 60 TB2=X3 143 401 70 MFX=(MFXE+MFXV)/2.0 402 IF(IPRINT.EQ.O) GOTO 365 403 C 404 WRITE(6,112) TB2,MFXE,MFXV,EB2,VSB2 405 112 FORMATdH , 'TB2 , MFXE ,MFXV, EB2 , VSB2 ; ' , 5E 12 . 4 ) 406 C 407 365 RETURN 408 END 409 C 410 C 411 C SUBROUTINE ENERGY TO CALCULATE THE ENERGY AND COMPOSITION OF 412 C ================= BURNED GAS AT A GIVEN TEMP. (T) AND PRESS. (P), 413 C INCLUDING THE EFFECTS OF DISSOCIATION. 414 C 415 SUBROUTINE ENERGY(T,P,CC,X,EB2,VSB2) 416 C 417 IMPLICIT REAL*8(A-H,0-Z) 418 REAL*8 K,L,M,N,KE(6),NM,KK,MWBMIX,MW(10),NMIX,NCH,N02,MOLFL, 419 -NN02,NN2,NNFUEL,KC02,KH20,KN2,MPV 420 C 421 COMMON /AREA1/ NCH,N02,K,L,M,N,KFUEL 422 COMMON /AREA2/ MOLFL,NMIX,HF1.NN02,NN2,NNFUEL,KOM 423 COMMON /AREA4/ NDISS,IPRINT 424 C 425 DIMENSION X(10),CPG(10),UUU(10),DH(10),CC(10).SP(6),RES(6,4), 426 -S0T(6),SPP(6,4) 427 C 428 C IF TEMP. LESS THAN 1750K, SKIP DISSOCIATION CALCULATIONS 429 IF(T.LT . 1750) GOTO 17 430 IF(NDISS.EO.O) GOTO 17 431 C IPRINT=0 432 C 433 C THE DISSOCIATION CAN INCLUDE THE FOLLOWING REACTIONS; 434 C (1) C02=C0+0.502, 435 C (2) H20=H2+0.502, 436 C (3) H20=0H+O.5H2, 437 C (4) N0=O.5N2+O.502. 438 C (5) H2=2H, 439 C (6) 02=20. 440 C IF NDISS=1, REACTIONS 1 & 2 ARE INCLUDED, 441 C IF NDISS=2. REACTIONS 1,2,3 & 4 ARE INCLUDED, 442 C IF NDISS=3, REACTIONS 1,2,3,4,5 & 6 ARE INCLUDED. 443 C 444 C THE FOLLOWING LINES CALCULATE THE EQUILIBRIUM CONSTANTS FOR EACH 445 C REACTION 1 TO 6, INCLUDING THE (PO/P) TERM, 446 C ALSO, INITIALISE THE DISSOCIATED SPECIES CONCENTRATIONS, 447 C 448 DO 304 1=1,6 449 SP(I)=0.0 450 KE(I)=0.0 451 304 SPP(I,4)=0.0 452 C 453 G0T0(302,301,300),NDISS 454 300 KE(6)=DEXP(DL0G(T)**(-6.93319)*(-434283OO)+19.3067)*(101.3/P) 455 KE(5)=DEXP(DL0G(T)**(-6.81208 )*(-30743900)+17.8668)*(101.3-/P) 456 SP(6)=0.000 457 SP(5)=0.000 458 301 KE(4)=DEXP(DL0G(T)**(-7.3355O)*(-1659255O)+1.80127) 144 459 KE(3)=DEXP(DL0G(T)**(-7.O457O)*(-3O3721OO)+1O.159) 460 -*DSQRT(101.3/P) 461 SP(4)=0.000 462 SP(3)=0.000 463 302 KE(2)=DEXP(DL0G(T)**(-6.86740)*(-18B78550)+8.7095) 464 -*DSQRT(101.3/P) 465 KE(1)=DEXP(DL0G(T)**(-7.4721O)*(-655490OO)+10.53) 466 -*DSQRT(101.3/P) 467 SP(2)=0.1 468 SP(1)=0.1 469 C 470 IF(IPRINT.EQ.O) GOTO 650 471 C 472 WRITE(6,21) (KE(IJK),IJK=1,6) 473 '21 F0RMAT(1H ,'KE(1-6) '.6E13.3) 474 C 475 C 476 C DEFINE UNIVERSAL GAS CONSTANT AND SET ITERATION COUNTER TO ZERO, 477 650 RM0L=8.3143 478 NUT=0 479 C 480 C START DISSOCIATION ITERATION ROUTINE. A PROPORTIONAL CHOPPING 481 C ITERATION TECHNIQUE IS USED TO SOLVE FOR THE VARIOUS SPECIES 482 C CONCENTRATIONS AT THE GIVEN TEMPERATURE AND PRESSURE.... 483 C 484 , 10 QQ=0 485 C 486 C THIS SECTION ENSURES THAT ITERATIONS CANNOT CONTINUE INDEFINATELY, 487 NUT=NUT+1 488 IF(NUT.LT.150) GOTO 400 489 WRITE(6,401) NUT 490 401 FORMATdH .'PROGRAM STOP DUE TO ENERGY ITERATIONS EXCEEDING',14) 491 STOP 492 C 493' 400 NSP=2*NDISS 494 C 495 C STEP I FROM 1 TO NUMBER OF DISSOCIATION REACTIONS... 496 DO 600 1=1,NSP 497 C 498 NUTT=0 499 IFLAG1=0 500 C 501 S=(SP(1 )+SP(2)+SP(3))/2+(SP(5)+SP(6)+K+L+M+N) 502 C 503 IF(IPRINT.EQ.O) GOTO 651 504 C 505 WRITE(6,20) I , ( SP( I JK ) , I JK = 1 , 6 ) , S 506 20 FORMATdH , ' I , SP ( 1-6 ) , S '.I4.7E9.2) 507 C 508 C 509 C INITIAL GUESS AT SPECIES CONCENTRATION... 510 651 J=1 511 SP(I)=0.OOOOO1 512 SPP(I,J)=SP(I) 513 GOTO(450,451,452,453,454,455 ) ,I 514 1 CONTINUE 515 C 516 IF(IPRINT.EQ.O) GOTO 9 145 517 518 WRITE(6,19) I,SP(I ) ,RES(1,1) 519 19 F0RMAT(1H ,'I,SP,RES1 '.I4.2E10.3) 520 C 521 C 522 C SECOND AND SUCCESSIVE GUESSES AT SPECIES CONCENTRATION... 523 9 d=2 524 STEP=0.1 525 IF(T.LT.2000) STEP=0.02 525.5 IF(KFUEL.GT.11) STEP=.3 526 SP(I)=SP(I)+STEP 527 IF(SP(I).GT.10) GOTO 500 528 SPP(I,d)=SP(I) 529 IFLAG1=0 530 G0TO(450,451,452,453,454,455), I 531 2 CONTINUE 532 C 533 IF(IPRINT.EO.O) GOTO 652 534 C 535 WRITE(6,18) I,SP(I).RES(I.1 ) .RES(I,2) 536 18 FORMATdH , ' I , SP , RES 1 , RES2 ' , 14 , 3E 1 1 . 3/) 537 C 538 C 539 C IF RESIDUAL CROSSES ZERO BETWEEN PREVIOUS AND CURRENT GUESSES 540 C THEN GO TO PROPORTIONAL CHOPPING ROUTINE, OTHERWISE CONTINUE 541 C INCREMENTING SPECIES CONCENTRATION... 542 . 652 IF((RES(I,1)*RES(I,2)).LE.0.0) GOTO 5 543 RES(I,1)=RES(I,2) 544 SPP(I,1)=SPP(I,2) 545 GOTO 9 546 C 547 5 IF(RES(I,2).EQ.O) GOTO 500 548 SP0LD=SPP(I,2) 549 d=3 550 C 551 C FIND VALUE OF SPECIES CONCENTRATION (SP(D) AT WHICH RESIDUAL 552 C BECOMES SMALL, I.E. WHEN PREVIOUS 'SP' EQUALS CURRENT 'SP' TO 553 C WITHIN ONE PERCENT... 554 6 SP(I ) = (SPP(I.1 )*RES(I,2)-SPP(I,2)*RES(1,1))/(RES(I,2)-RES (1, 1)) 555 IF(DABS((SP(I)-SP0LD)/SP(I)).LT.O.O1) GOTO 500 556 SPOLD=SP(I) 557 C 558 GOTO(450,451,452,453,454,455),I 559 3 CONTINUE 560 C 561 IF(IPRINT.EQ.O) GOTO 654 562 C 563 WRITE(6,15) I,SP(I).RES(I,1),RES(I,3) 564 15 F0RMAT(1H , 'I,SP,RES 1,RES3 '.I4.3E11.3) 565 C 566 C 567 654 IF(RES(I,1)*RES(I,3).LE.0.0) GOTO 4 568 SPP(I,1)=SP(I) 569 RES(I,1 )=RES(I,3) 570 GOTO 6 571 4 SPP(I,2)=SP(I) 572 RES(I,2)=RES(I,3) 573 GOTO 6 146 574 C 575 C IF VALUE OF S P ( I ) FROM CURRENT SPECIES CALCULATIONS EQUALS THE 576 C VALUE OF S P ( I ) FROM THE PREVIOUS SET OF SPECIES CALCULATIONS AT 577 C THE SAME TEMPERATURE, THEN LEAVE QQ=0, OTHERWISE SET QQ=1 WHICH 578 C WILL CAUSE ANOTHER SET OF CALCULATIONS TO BE P E R F O R M E D . . . 579 500 I F ( D A B S ( ( S P ( I ) - S P P ( I , 4 ) ) / ( S P ( I ) ) ) . G T . 0 . 0 5 ) QQ=1 580 S P P ( I , 4 ) = S P ( I ) 581 GOTO 600 582 C 583 C THIS SECTION CALCULATES THE RESIDUALS FOR EACH SPECIES USING 584 C THE CURRENT VALUES OF S P ( l - 6 ) . 585 450 S Q T ( 1 ) = M + ( ( S P ( 1 ) + S P ( 2 ) - S P ( 4 ) ) / 2 ) - S P ( 6 ) 586 I F ( S Q T ( 1 ) . L E . O . O ) GOTO 456 587 R E S ( 1 , d ) = S P ( 1 ) / ( K - S P ( 1 ) ) * D S Q R T ( S Q T ( 1 ) / S ) - K E ( 1 ) 588 GOTO 460 589 451 S Q T ( 2 ) = M + ( ( S P ( 1 ) + S P ( 2 ) - S P ( 4 ) ) / 2 ) - S P ( 6 ) 590 I F ( S Q T ( 2 ) . L E . 0 . 0 ) GOTO 456 591 R E S ( 2 , J ) = ( S P ( 3 ) / 2 + S P ( 2 ) - S P ( 5 ) ) / ( L - S P ( 3 ) - S P ( 2 ) ) * D S Q R T ( S Q T ( 2 ) / S ) 592 1 - K E ( 2 ) 593 GOTO 460 594 452 S Q T ( 3 ) = S P ( 3 ) / 2 + S P ( 2 ) - S P ( 5 ) 595 I F ( S Q T ( 3 ) . L E . O . O ) GOTO 456 596 R E S ( 3 , J ) = ( S P ( 3 ) ) / ( L - S P ( 3 ) - S P ( 2 ) ) * D S Q R T ( S Q T ( 3 ) / S ) - K E ( 3 ) 597 GOTO 460 598 453 S Q T ( 4 ) = ( N - S P ( 4 ) / 2 ) * ( M - S P ( 6 ) + ( S P ( 1 ) + S P ( 2 ) - S P ( 4 ) ) / 2 ) 599 I F ( S Q T ( 4 ) . L E . 0 . 0 ) GOTO 456 600 R E S ( 4 , J ) = S P ( 4 ) / D S Q R T ( S Q T ( 4 ) ) - K E ( 4 ) 601 GOTO 460 602 454 S Q T ( 5 ) = S P ( 3 ) / 2 + S P ( 2 ) - S P ( 5 ) 603 I F ( S Q T ( 5 ) . L E . O . O ) GOTO 456 604 R E S ( 5 , J ) = ( 4 * S P ( 5 ) * S P ( 5 ) ) / S / S Q T ( 5 ) - K E ( 5 ) 605 GOTO 460 606 455 S Q T ( 6 ) = M - S P ( 6 ) + ( S P ( 1 ) + S P ( 2 ) - S P ( 4 ) ) / 2 607 I F ( S Q T ( 6 ) . L E . 0 . 0 ) GOTO 456 608 R E S ( 6 , d ) = ( 4 * S P ( 6 ) * S P ( 6 ) ) / S / S Q T ( 6 ) - K E ( 6 ) 609 456 S P ( I )=SPP(I , 4 ) 610 GOTO 600 61 1 46Q NUTT=NUTT+1 612 C 613 I F ( I P R I N T . E Q . O ) GOTO 655 614 c-615 W R I T E ( 6 , 2 2 ) N U T T , R E S ( I , d ) , S Q T ( I ) , I FLAG 1 616 22 F0RMAT(1H , ' N U T , R E S ( I . d ) , S Q T ( I ) , F L A G ' , 1 3 , 2 E 1 4 . 5 , 1 3 ) 617 / 618 c 619 655 I F ( N U T T . L T . 5 0 ) GOTO 16 620 W R I T E ( 6 , 4 0 1 ) NUTT 621 STOP 622 16 G O T O ( 1 , 2 , 3 ) , 0 623 c 624 600 CONTINUE 625 c 626 A = SP( 1 ) 627 B=SP(3) 628 C=SP(2) 629 D=SP(4) 630 E=SP(5) 631 F=SP(6) 147 632 C 633 IF(IPRINT.EQ.O) GOTO 656 634 C 635 WRITE(6,14) T,A,B,C,D.E,F 636 14 FORMATdH , 'T, A, B,C ,D, E , F ' , F8 . 1, 6E 10. 3/) 637 C 638 656 IF(00)461,461,10 639 C 640 C 641 461 CONTINUE 642 C 643 C CALCULATING CHANGE IN ENTHALPIES FOR SPECIES 1 TO 10 BET. T AND 289K 644 C C02=1, C0=2, H20=3, H2=4, 02=5, N2=6, N0=7, H=10, 0=9, 0H=8 645 KK=0 646 17 TT=T/100 647 IF (T.GT.3000.0) GOTO 99 648 DH(1)=((3.096*T+0.00273*(T**2)-7.885E-07*(T**3) 649 1+8.66E-11*(T**4))-1145.0)*RMOL 650 DH(2)=((3.317*T+3.77E-04*(T**2)-3.22E~08*(T**3) 651 1-2. 195E-12*(T**4))-1O22.O)*RM0L 652 DH(3)=((3.743*T+5.656E-04*(T**2)+4.952E-08*(T**3) 653 1-1.818E-11*(T**4))-1167.O)*RM0L 654 DH(4)=((3.433*T-8.18E-06*(T**2)+9.67E-08*(T**3) 655 1-1.444E-11*(T**4))-1O25.O)*RM0L - 656 DH(5) = ((3.253*T+6.524E-04*(T**2)-1.495E-07*(T**3) 657 1+1.539E-11*(T**4))-1O24.O)*RM0L 658 DH(6) = ((3.344*T+2.943E-04*(T**2)+1.953E-09* ( T**3) 659 1-6.575E-12*(T**4))-1023.0)*RM0L 660 DH(7)=((3.502*T+2.994E-04*(T**2)-9.59E-09*(T**3) 661 1-4.904E-12*(T**4))-1070.0)*RMOL 662 DH(1O)=((2.5*T)-745.O)*RM0L 663 DH(9) = ((2.764*T-2.514E-04*(T**2) + 1.002E-07* ( T**3) 664 1-1 .387E-11*(T**4))-804.0)*RM0L 665 DH(8) = ((81.546*TT-47.48*(TT**1.25)+9.902*(TT* * 1.75) 666 1-2. 133*(TT**2.))* 100-10510) 667 GOTO 91 668 99 DH(1) = ((5.208*T+0.00059*(T**2)-5.614E-08* (T**3) 669 1+2.05E-12*(T**4))-1126.0)*RMOL 670 DH(2)=((3.531*T+2.73E-04*(T**2)-3.28E-08*(T**3) 671 1+1.565E-12*(T**4))-1042.0)*RMOL 672 DH(3)=((143.05*TT-146.83*(TT**1.25)+55.17*(TT**1.5) 673 1-1.85*(TT**2.))*100-11945.0) 674 DH(4)=((3.213*T+2.87E-04*(T**2)-2.29E-08*(T**3) 675 1+7.666E-13*(T**4))-1018.0)*RMOL 676 DH(5)=((3.551*T+3.203E-04*(T**2)-2.876E-08*(T**3) 677 1+1.OO5E-12*(T**4))-1O44.O)*RM0L 678 DH(6)=((3.514*T+2.583E-04*(T**2)-2.841E-08*(T**3) 679 1+1 . 242E-12*(T**4))-1043.0)*RMOL 680 DH(7) = ((3.745*T+1.950E-04*(T**2)- 1.88E-08*(T**3) 681 1+7.703E-13*(T**4))-1106.0)*RMOL 682 DH(1O)=((2.5*T)-745.O)*RM0L 683 DH(9) = ((2.594*T-3.843E-05*(T**2) + 7.514E-09* (T**3) 684 1-3.209E-13*(T**4))-809.O)*RMOL 685 DH(8) = ((81.546*TT-47.48*(TT** 1.25)+9.902*(TT* * 1.75) 686 1-2.133*(TT**2.))*100-10560.) 687 C 688 C CALCULATE CONSTANT PRESSURE SPECIFIC HEATS 689 91 CPG(1)=-3.7357+30.529*(TT**(0.5))-4.1034*TT+0.024198*(TT**2) 148 690 CPG(2)=69.145-.70463*(TT**(0.75))-200.77*(TT** (-0.5)) 691 -+176.76*(TT**(-0.75)) 692 CPG(3) = 143.05-183.54*(TT**(0.25))+82.751 * (TT** (0. 5)) 693 --3.69889*TT 694 CPG(4) = 56.505-702.74*(TT**(-.75))+1165.0/TT-560.7*(TT** ( - 1 .5)) 695 CPG(5)=37.432+0.020102*(TT**1.5)- 178.57*(TT** ( - 1.5)) 696 -+236.88*(TT**(-2)) 6^7 CPG(6) = 39.060-512.79*(TT**(-1.5)) +1072.7*(TT** (-2)) 698 --820.4*(TT**(-3)) 699 CPG(7)=59.283-1.7096*(TT**0.5)-70.613*(TT* *(-0.5)) 700 -+74.889*(TT**(-1.5)) 701 CPG(8)=81.546-59.35*(TT**0.25)+17.329*(TT**0.75)-4.266*TT 702 C 703 C CALC. NUMBER OF MOLES OF EACH SPECIES AFTER DISSOCIATION 704 X(1)=K-A 705 X(2)=A 706 X(3)=L-B-C 707 X(6)=N-D/2 708 X(7)=D 709 X(4)=C+B/2-E 710 X(5)=M-F+(A+C-D)/2 711 X(10)=2*E 712 X(9)=2*F 713 X(8)=B 714 C 715 C CALC. VISCOSITY & THERMAL CONDUCTIVITY OF PRODUCTS... 716 VC02=((0.019*T+24.2)*X(1)* 1E-06)/(X(1)+ X(3) + X(6)) 717 KC02=((0.041*T+36.1)*X(1)* 1E-03)/(X(1) + X(3) + X(6)) 718 VH20=((0.025*T+15.8)*X(3)*1E-06)/(X(1)+X(3)+X(6)) 719 KH20=((O.130*T-0.60)*X(3)*1E-03)/(X(1)+X(3)+X(6)) 720 VN2=((0.019*T+24.1)*X(6)* 1E-06)/(X(1) + X(3) + X (6)) 721 KN2=((0.039*T+35.8)*X(6)* 1E-03)/(X(1)+X( 3)+ X(6)) 722 VISC=VC02+VH20+VN2 723 THC0ND=KC02+KH20+KN2 724 C 725 C ENTHALPY OF FORMATION FOR EACH SPECIES... 726 UUU(1)=-3.93522E05 727 UUU(2)=-1.10529E05 728 UUU(3)=-2.41827E05 729 UUU(4)=0.00000E00 730 UUU(5)=0.00000E00 731 UUU(6)=0.00000E00 732 UUU(7)=9.05920E04 733 UUU(10)=2.17986E05 734 UUU(9)=2.49195E05 735 UUU(8)=39463.0 736 C 737 C MOLECULAR WEIGHT FOR EACH SPECIES... 738 MW(1)=44.01 739 MW(2)=28.01 740 MW(3)=18.01 741 MW(4)=2.02 742 MW(5)=32.00 743 MW(6)=28.01 744 MW(7)=30.00 745 MW(8)=17.00 746 MW(9)=16.00 747 MW(10)=1.00 149 748 C 749 C CALC. ENERGY OF PRODUCTS 1 TO 10 750 EPR0D=O. 751 DO 109 1 = 1 , 10 752 ECOMP=X(I)*(UUU(I)+DH(I)-RMOL*T) 753 IF(M0DE.E0.3) ECOMP=X(I)*(UUU(I)+DH(I)) 754 EPROD=EPROD+ECOMP 755 1 09 CONTINUE 75S c 757 c CALCULATE SUM OF X VALUES 758 SUMXS=0 759 DO 231 ILG=1,10 760 231 SUMXS=SUMXS+X(ILG) 761 c 762 c CALC PERC. OF PRODUCTS AND MOLECULAR WEIGHT OF MIXTURE 763 MWBMIX=0.0 764 DO 232 ILH=1.10 765 CC(ILH) = (X(ILH)/SUMXS)* 100. 766 232 MWBMIX=MWBMIX+(CC(ILH)*MW(ILH)/100.) 767 EB2=EPR0D/MWBMIX/SUMXS 768 VSB2=RM0L*T/(MWBMIX*P) 769 c 770 c CALC. AVERAGE SPECIFIC HEATS FOR MIXTURE... 771 CP=0 772 DO 233 ILF=1,8 773 233 CP=CP+(CC(ILF)*CPG(ILF))/100. 774 CV=CP-RMOL 775 GAMMA=CP/CV 776 c 777 778 c WRITE(6,889 ) MWBMIX,EB2,VSB2,GAMMA,NDISS 779 c 889 F0RMAT(1H ,'MWBMIX,EB2,VSB2,GAMMA.NDS '.4E12.4.I3) 780 781 c 781 . 5 c IPRINT=1 782 RETURN 783 END 784 c 785 c SUBROUTINE CALFLS THIS IS USED TO OBTAIN THE CALCULATED 786 c ================= BURNING VELOCITY 787 c 788 SUBROUTINE CALFLS(MFX1.MFX2,VSB2,MTOT,DTIME,FFF,VSU2,CBVEL, 789 -VSU1,AREA 1,V0LB2,IVOL,VOLB1,AREA2,RB1,RB2,RADBMB,DIST,KTYPE) 790 c 791 COMMON /AREA4/ NDISS,IPRINT 792 c 793 REAL*8 RF,DR,EPS,Y1,Y2,Y3,BORE,D,XDOT,ARAVG,AREA, 794 -R1,R2,R3,R30LD,DTIME,RMAX.R,VOLB1,MFX2,AREA 1,AREA2,RB1,RB2, 795 -FFF,MFX,VSB2,VSU2,MTOT,MFX1,V0LB2,VOLB,CBVEL,VSUAVG,VSU1,RADBMB 796 -.DIST 797 c 798 D=RADBMB*2.0 799 V0LB2=MT0T*MFX2*VSB2 800 c CALC. MAXIMUM RADIUS WHICH FLAME CAN ATTAIN IN THE SPHERICAL 801 c BOMB (1), THE CYLINDRICAL BOMB (2). OR THE ENGINE CYLINDER 802 c GIVEN THE POSITION OF THE PISTON IN THE CYLINDER (DIST)... 803 IF(KTYPE.EO.1 ) RMAX=D/2.0 804 IF(KTYPE.EQ.2) RMAX=0.1034528 150 805 IF(KTYPE.EO•3) RMAX=DSORT(((0.018358+DIST)**2)+(O.0425**2)) 806 IF(IV0L.EQ.2) GOTO 546 807 RB1=0.0001 808 CALL V0L(RB1.DIST.AREA,VOLB,KTYPE) 809 VOLB1=VOLB 810 AREA 1 =AREA 811 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 812 C 546 WRITE(6,201) V0LM1,AREA 1,RMAX,VOLB2 813 C 201 F0RMAT(1H ,'V0LM1,AREA 1,RMAX,V0LB2. '.4E12.5) 814 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 815 C 816 C ITERATION PROCEDURE FINDS RADIUS AND AREA OF NEW BURNT VOLUME 817 546 NUT=0 818 R1=0.OOO1O00 819 RF=RMAX 820 DR=0.01 821 EPS=0.0001 822 CALL V0L(R1.DIST,AREA,VOLB,KTYPE) 823 Y1=V0LB2-V0LB 824 10 R2=R1+DR 825 IF(R2.GT.RF) R2=RF 826 CALL V0L(R2,DIST,AREA,VOLB,KTYPE) 827 Y2=V0LB2-V0LB 828 IF(Y1*Y2.LE.O.) GOTO 20 829 R1=R2 830 Y1=Y2 831 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 832 C WRITE(6,2CO) R2.Y2 833 C 200 FORMATdH ,'R2,Y2 = '.2E14.6/) 834 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 835 NUT=NUT+1 836 IF (NUT.LT.20) GOTO 13 837 WRITE (6,90) NUT 838 STOP 839 13 GOTO 10 840 20 IF(Y2.EO.O.) GOTO 50 841 R30LD=R2 842 30 R3=(R1*Y2-R2*Y1)/(Y2-Y1) 843 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 844 C WRITE(6,303) R3 845 C 303 F0RMAT(1H ,'R3 = '.E12.5) 846 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 847 NUT=NUT+1 848 IF (NUT.LT.150) GOTO 80 849 WRITE(6.90) NUT 850 90 FORMATdH ,'PROGRAM STP DUE TO CALFLS ITERATIONS EXCEEDING',14) 851 STOP 852 80 IF(DABS((R3-R30LD)/R3).LT.EPS) GOTO 60 853 R30LD=R3 854 CALL V0L(R3,DIST.AREA,VOLB,KTYPE) 855 Y3=V0LB2-V0LB 856 IF(Y1*Y3.LE.O.) GOTO 40 857 R1=R3 858 Y1=Y3 859 GOTO 30 860 40 R2=R3 861 Y2=Y3 862 GOTO 30 151 863 50 RB2=R2 864 GOTO 99 865 60 RB2=R3 866 99 CALL VOL(RB2,DIST,AREA,VOLB,KTYPE) 867 AREA2=AREA 868 VSUAVG=(VSU1+VSU2)/2. 869 ARAVG=(AREA1+AREA2)/2. 870 XD0T=(MFX2-MFX1)/DTIME 871 CBVEL=MTOT*XDOT*VSUAVG/ARAVG 872 IF(IPRINT.EO.O) GOTO 70 873 L. 874 WRITE(6,221 ) VOLB1.V0LB2.RB1,RB2,AREA 1,AREA2,CBVEL 875 221 FORMAT(1H ,'V1,V2,R1,R2,AR1,AR2,CBVEL:',7E12.4/) 876 *p 877 70 RETURN 878 END 879 c 880 c SUBROUTINE VOL TO CALCULATE THE VOLUME AND AREA OF BURNT GAS 881 c ============ IN A SPHERICAL BOMB (1), CYLINDRICAL BOMB (2), 882 c OR THE TOYOTA ENGINE COMBUSTION CHAMBER (3), 883 c GIVEN THE FLAME RADIUS.... 884 c 885 SUBROUTINE VOL(BRAD,DIST,AREA,VOLB,KTYPE) 886 c 887 REAL*8 BRAD,DIST,AREA,VOLB,BORE,R,D.H,HTCLRV,RDASH,CLRV,HA, 888 -HVOL,RMAX,DD 889 c 890 IF(KTYPE.EO.1) GOTO 201 891 IF(KTYPE.EQ.2) GOTO 202 892 IF(KTYPE.EQ.3) GOTO 203 893 c 894 c TO CALCULATE THE VOLUME OF BURNT GAS IN A 895 c SPHERICAL BOMB GIVEN THE FLAME RADIUS... 896 c 897 201 V0LB=(4./3. )*3.14159*(BRAD**3. ) 898 AREA = 4 . *3. 14159*(BRAD**2.) 899 RETURN 900 c 901 c 902 c TO CALCULATE THE VOLUME OF BURNT GAS IN A 903 c CYLINDRICAL BOMB GIVEN THE FLAME RADIUS... 904 c 905 202 B0RE=0.073 906 R=B0RE/2. 907 D=0.0968 908 IF(BRAD.GT . R ) GOTO 10 909 V0LB=3.14159*(2./3.)*(BRAD**3.) 910 AREA=2.*3.14159*(BRAD**2.) 911 GOTO 50 912 10 H=DSQRT((BRAD**2.)-(R**2.)) 913 IF(BRAD.GT.D) GOTO 20 914 V0LB=(2./3. )*3.14159*((BRAD**3.)-(H**3.)) 915 AREA=2.*3.14159*BRAD*(BRAD-H) 916 GOTO 50 917 20 V0LB=(3.14159/3.)*(3.*(BRAD**2.)*D-(D**3.)-2.*(H**3.)) 918 AREA=2.*3.14159*BRAD*(D-H) 919 cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 920 c 50 WRITE(6,100) VOLB,AREA 152 921 C 100 F0RMAT(1H ,'VOL. SUBROUTINE: VOLB = '.E12.4,' AREA= ',E12.4) 922 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 923 50 RETURN 924 C 925 C 926 C TO CALC. THE VOLUME BURNT AND FLAME AREA IN 927 C THE TOYOTA ENGINE COMBUSTION CHAMBER GIVEN THE 928 C RADIUS OF THE FLAME.... 929 C 930 C 931 203 B0RE=O.O85 932 HTCLRV=18.358E-03 933 RDASH=58.3737E-03 934 CLRV=55.3264E-06 935 R=B0RE/2. 936 RMAX=DSQRT((HTCLRV**2)+(R**2)) 937 DD=HTCLRV+DIST 938 C 939 IF(BRAD.GT.RMAX) GOTO 310 940 HV0L=O.25*3.14159*(BRAD**3)*(BRAD/RDASH) 941 HA=3.14159*(BRAD**2)*(BRAD/RDASH) 942 H=0.0 943 IF(BRAD.GT.DD) GOTO 320 944 D=BRAD 945 GOTO 350 946 320 D=HTCLRV+DIST 947 GOTO 350 948 C 949 310 HV0L=(3.14159*(R**2)*HTCLRV)-CLRV 950 HA=0.0 951 H=DSORT((BRAD**2)-(R**2)) 952 IF(BRAD.GT.DD) GOTO 330 953 D=BRAD 954 GOTO 350 955 330 D=HTCLRV+DIST 956 C 957 350 V0LB=(3.14159/3.0)*(3.*(BRAD**2)*D-(D**3)-2.*(H**3))-HVOL 958 AREA=2.0*3.14159*BRAD*(D-H)-HA 959 C 960 C WRITE(6,300) BRAD,HVOL,AREA,VOLB.RMAX,D,HA.H 961 C 300 FORMAT(1H ,'BRAD,HVOL,AREA,VOLB,RMAX,D,HA,H',8E10.3) 962 C 963 RETURN 964 END 965 C 966 C 967 C SUBROUTINE ENUFLS THIS CALCULATES THE PROPERTIES OF THE UNBURNT 968 C ================= GAS AT THE GIVEN PRESS. BY FIRST CALCULATING 969 C GAMMA AND THEN ASSUMING ISENTROPIC COMPRESSION 970 C THE BURNING VELOCITY IS THEN CALCULATED USING THE UNBURNT GAS 971 C TEMP. AND PRESS. USING PUBLISHED FORMULAE FOR GIVEN FUEL. 972 C 973 SUBROUTINE ENUFLS(P2.P 1 ,T1,VSU1,MWMIX,TU2.VSU2,EU2,FFF,TBVEL) 974 C 975 COMMON /AREA 1 / NCH,N02.K,L.M,N.KFUEL 976 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02,NN2,NNFUEL,KOM 977 COMMON /AREA4/ NDISS,IPRINT 978 C 153 979 REAL*8 P1,T1,NN02.NN2,NMIX,TU2,VSU2,EU2,TBVEL,TT,NNFUEL,FFF, 980 -CPG(14),CP.CV,GAMU,DH(14),ENGY,N02.N,RMOL,VSU1,POW1,P0W2,NCH, 981 -MWMIX,PU,TU,SUO,ALPHA,BETA,PBAR2,P2,HF1,T,T2,P0W3,C4,AF,PBAR1 982 -,K,L,M,MOLFL 983 C 984 RM0L=8.3142 985 C 986 C CALC. GAMMA FOR THE UNBURNT ELEMENTS.... 987 C 988 NNFUEL=100.-(NN02+NN2) 989 TT=T1/100. 990 CPG(5) = 37.432+0.020102*(TT**1.5)-178.57* ( TT** ( - 1 .5)) 991 -+236.88*(TT**(-2)) 992 CPG(6)=39.060-512.79*(TT**(-1.5))+1072.7*(TT**(-2)) 993 --820.4*(TT**(-3)) 994 CPG(11)=-672.87+439.74*(TT**0.25)-24.875*(TT**0.75)+323.88* 995 -(TT**(-0.5)) 996 CPG(13) = -4.042+30.46*TT-1.571 *(TT**2.)+0.03171 *(TT**3.) 997 T=TT*100. 998 CPG(12)=8.3143*(-0.72+0.09285*T1-5.05E-05*(T1**2.)+1.068E-08* 999 "(T1**3)) 1000 CP=(NN02*CPG(5)+NN2*CPG(6)+NNFUEL*CPG(KFUEL))/100. 1001 CV=CP-8 .3143 1002 GAMU=CP/CV 1003 C 1004 P0W1=(GAMU-1.)/GAMU 1005 P0W2=1./GAMU 1006 T2 = T*( (P2/P1')**P0W1 ) 1007 TU2=T2 1008 VSU2=VSU1*((P1/P2)**P0W2) 1009 C 1010 C CALC. ENTHALPY OF REACTANTS AT GIVEN TEMP; 5=02, 6=N2, 11=CH4 101 1 C 12=C8H18, 13=C3H8.... 1012 DH(5)=((3.253*T2+6.524E-04*(T2**2)-1.495E-07*(T2**3) 1013 1+1.539E-11*(T2**4))-1024.0)*RMOL 1014 DH(6)=((3.344*T2+2.943E-04*(T2**2)+1.953E-09*(T2**3) 1015 1-6.575E- 12*(T2**4))-1023.0)*RMOL 1016 . DH( 11) = ((1.935*T2+4.965E-03*(T2**2. )- 1.244E-06*(T2**3.) 1017 1 + 1.625E-10*(T2**4. )-8.586E- 15*(T2**5. ))-985.9)*RMOL 1018 DH(12)=((-0.72*T2+4.643E-02*(T2**2.)-1.684E-05*(T2**3.) 1019 1+2.67E-09*(T2**4.))-3484.0)*RMOL 1020 DH(13)=((1.137*T2+1.455E-02*(T2**2.)-2.959E-06*(T2**3.) 1021 1)-1552.9)*RM0L 1022 C CALC. ENERGY OF UNBURNT GAS AT TEMP. T2 IN KJ/KMOL FUEL... 1023 ENGY = (1.0*(HF1+DH(KFUEL)-RM0L*T2)+N02*(DH(5)-RMOL*T2) 1024 -+N*(DH(6)-RM0L*T2)) 1025 C WRITE(6,889) ENGY 1026 C CONVERT TO KJ/KMOL MIXTURE... 1027 ENGY=ENGY/NMIX 1028 C WRITE(6,889) ENGY 1029 C CONVERT TO KJ/KG MIXTURE... 1030 EU2=ENGY/MWMIX 1031 C WRITE(6,889) EU2 1032 C 889 F0RMAT(1H ,E12.4) 1033 C CALC. AVERAGE UNBURNT TEMP. AND PRESS. 1034 PU=(P1+P2)/2. 1035 TU=(T1+T2)/2. 1036 C 1 54 1037 C CALCULATE LAMINAR BURNING VELOCITY: 1038 C METGHALCHI AND KECK'S EQUATIONS FOR 0CTANE(12) AND PR0PANE(13) 1039 C 1040 IF(KFUEL.NE.12) GOTO 500 1041 SU0=27.O 1042 ALPHA=2.26 1043 BETA=-0.18 1044 GOTO 505 1045 500 IF(KFUEL.NE.13) GOTO 501 1046 SU0=31.9 1047 ALPHA=2.13 1048 BETA=-0.17 1049 505 TBVEL=SU0*((TU/298.)**ALPHA)*((PU/100.)**BETA) 1050 GOTO 510 1051 C 1052 C ANDREWS AND BRADLEYS EQUATION FOR METHANE(11)... 1053 C 1054 C 501 PBAR1=PU/100. 1055 C TBVEL = (10.0+0.000371*(TU**2.)*(PBAR1 * *(-0.5))) 1056 C 1057 C AGRAWAL AND GUPTAS EQUATION FOR METHANE... 1058 C 1059 501 AF=1 .0 1060 PBAR1=PU/100.0 1061 C4=-418.0+1287.0/AF-1196.0/(AF**2)+360.0/(AF**3)-15.0*AF* 1062 -DL0G1O(PBAR1) 1063 J>0W3=1 . 68*DSQRT ( AF ) 1064 IF(AF.GT.1.) GOTO 65 1065 P0W3=1.68/DSQRT(AF) 1066 65 TBVEL=C4*((TU/3OO.O)**P0W3) 1067 C 1068 C MULT. LAMINAR FLAME SPEED BY 'FLAME FACTOR' TO ACCOUNT FOR 1069 C TURBULENCE, AND DIVIDE BY 100 TO CONVERT FROM CM/S TO M/S...' 1070 C 1071 510 TBVEL=FFF*TBVEL/100. 1072 C 1073 IF(IPRINT.EQ.O) GOTO 35 1074 1075 WRITE(6,100) TBVEL,VSU2.EU2,PU,TU,P2,T2 1076 100 FORMAT(1H ,'TBV,VSU2,EU2,PU,TU,P2,T2 =',7E12.4) 1077 *p -1078 35 RETURN 1079 END 155 APPENDIX F ~ ENGINE SIMULATION PROGRAM (SIM) T h i s program combines r o u t i n e s d e v e l o p e d i n the COMB and BOMB programs, i n order t o s i m u l a t e p r o g r e s s i v e b u r n i n g i n a spark i g n i t i o n e n g ine w i t h h e m i s p h e r i c a l head combustion chamber, h a v i n g the same di m e n s i o n s as the Toyota used i n t h e engine e x p e r i m e n t s . The main s e c t i o n s of the program a r e , a) C a l c u l a t i o n of m i x t u r e compostion and energy a t B.D.C. b) Compression of m i x t u r e up t o spark t i m e . c) P r o g r e s s i v e b u r n i n g t h r o u g h T.D.C. t o a l l b u r n t . d) E x p a n s i o n of p r o d u c t s t o B.D.C. e) C a l c u l a t i o n of e f f i c i e n c y and mean e f f e c t i v e p r e s s u r e . Each of these major s e c t i o n s a r e d i s c u s s e d below; and i l l u s t r a t e d w i t h f l o w diagrams a t the end of the appen d i x . A f u l l l i s t i n g of the program i s a l s o g i v e n a t the end of the Appendix. a. I n i t i a l M i x t u r e C o m p o s i t i o n And Energy The main i n p u t s t o the program a r e : F u e l type and p r o p e r t i e s I n l e t p r e s s u r e and temp e r a t u r e A i r / f u e l r a t i o . Spark advance Exhaust gas r e s i d u a l f r a c t i o n . These v a l u e s a r e used t o de t e r m i n e the p r o p e r t i e s of the m i x t u r e a t bottom dead c e n t r e i n the same manner as d e s c r i b e d i n Appendix C f o r the OTTO c y c l e s i m u l a t i o n . A d d i t i o n a l c a l c u l a t i o n s i n c l u d e , d e t e r m i n a t i o n of the m o l e c u l a r weight of the m i x t u r e (MWMIX); the t o t a l mass of the m i x t u r e (MTOT); the s p e c i f i c volume (VSU1) and the t o t a l energy of the c y l i n d e r c o n t e n t s i n k J (ET0T1). b. Compression Of M i x t u r e T h i s i s a l s o s i m i l a r t o t h e method used i n the OTTO program, however the c a l c u l a t i o n s t e p s a r e s e p a r a t e d by e q u a l crank a n g l e d i v i s i o n s r a t h e r than volume d i v i s i o n s . The s i z e of the crank a n g l e d i v i s i o n s can be s e l e c t e d i n the i n p u t f i l e , and ar e n o r m a l l y 1 or 2 de g r e e s . The c y l i n d e r volume a t a g i v e n c r a n k a n g l e i s o b t a i n e d u s i n g , 156 VOLUME = DIST . TT. BORE2" + CLRV (1) 4 where CLRV = C l e a r a n c e volume, and DIST = d i s t a n c e of p i s t o n from TDC which i s g i v e n by, DIST = STROK.(1+ LENG - Cos 6 - / LENG - S i n B ) 2 { (STROK/2) 7 STROK/2 / (2) where 8 = a n g l e of c r a n k (6 = 0°at TDC) LENG = c o n n e c t i n g r o d l e n g t h and STROK = s t r o k e of p i s t o n ( = 2 x crank r a d i u s ) . These e x p r e s s i o n s a r e combined i n a F u n c t i o n S u b r o u t i n e d e f i n e d a t the s t a r t of the program, and c a l l e d by u s i n g , volume (d 9 ) = DVOL ( 8 ) . The volumes a t the b e g i n n i n g (V1) and end (V2) of a g i v e n crank a n g l e s t e p are t h e r e f o r e c a l c u l a t e d , and the new p r e s s u r e (P2) temperature (T2) and energy (ENGY2) a r e o b t a i n e d by the i t e r a t i o n p r o c e d u r e c o n t a i n e d i n s u b r o u t i n e COMP. S u b r o u t i n e COMP i s e s s e n t i a l l y the same i t e r a t i o n p r o c e d u r e used f o r the c o m p r e s s i o n s t o k e d e s c r i b e d i n Appendix C f o r the OTTO c y c l e s i m u l a t i o n . U s i n g the f i r s t law e q u a t i o n and the i d e a l gas law, the p r e s s u r e , temperature and energy of the m i x t u r e a r e c a l c u l a t e d a t each crank a n g l e s t e p , up t o the spark advance a n g l e (ANG). c. P r o g r e s s i v e B u r n i n g T h i s s e c t i o n f o l l o w s the same method as t h a t o u t l i n e d i n Appendix D f o r the BOMB s i m u l a t i o n program, and u t i l i z e s the same s u b r o u t i n e s , ENUFLS, TEMP and CALFLS as d e s c r i b e d p r e v i o u s l y . A g a i n , the c o n t e n t s of the combustion chamber a r e d i v i d e d i n t o two zones; burned, and unburned. The zones b e i n g s e p a r a t e d by a s p h e r i c a l l y expanding flame f r o n t c e n t r e d on the spark p l u g . The c a l c u l a t i o n s t e p s c o n t i n u e t o be s e p a r a t e d by e q u a l c r a n k a n g l e i n t e r v a l s as i n the compression s t r o k e . The main d i f f e r e n c e between t h i s program and t h e BOMB s i m u l a t i o n program i s t h a t the volume, and hence th e t o t a l energy of the c y l i n d e r charge changes d u r i n g the combustion p r o c e s s . The volume change i s o b t a i n e d s i m p l y from the v a r i a t i o n of p i s t o n motion w i t h c r a n k a n g l e ; VTOT2 = VTOT1-DVOL( 6 ) . 157 The energy change i s o b t a i n e d by c o n s i d e r i n g the 1 s t . Law f o r the c o n t r o l mass i n the c y l i n d e r , i . e . dE = dQ - dw ....(5) or ET0T2 = ETOT1 + ^P1+P2j.(V2-V1) - dQ (6) where DQ i s o b t a i n e d u s i n g Annand's heat t r a n s f e r e q u a t i o n [26] of the form, b DQ = AREAW . a . /_k \ . (Re) .(T2 - TWALL).At (4) {BORE/ where AREAW = Area of a c y l i n d e r and p i s t o n e n c l o s i n g m i x t u r e k = Thermal c o n d u c t i v i t y of the m i x t u r e a & b = C o n s t a n t s Re = Reynolds number =/MPV . BORE> v v . v i s e / and MPV = mean p i s t o n v e l o c i t y = (Engine rpm . s t r o k e ) 3000 V = s p e c i f i c volume of the m i x t u r e VISC = Dynamic v i s c o s i t y of the m i x t u r e (Ns / m M The heat i s assumed t o be t r a n s f e r e d o n l y from the burnt gas r e g i o n , s i n c e t h i s heat t r a n s f e r i s up t o 10-15 tim e s the amount l o s t from the unburnt r e g i o n . T h i s a l l o w s the assumption of i s e n t r o p i c compression of the unburned gas t o be m a i n t a i n e d . At each crank a n g l e s t e p , the new c y l i n d e r volume i s f i r s t c a l c u l a t e d , and then the c y l i n d e r p r e s s u r e i s r a i s e d t o a new v a l u e . The s u b r o u t i n e ENUFLS d e s c r i b e d i n Appendix D i s used t o o b t a i n v a l u e s f o r the s p e c i f i c volume ( v M ) and s p e c i f i c energy ( e M ) of the unburned gas r e s u l t i n g from i s e n t r o p i c compression t o the newly assumed c y l i n d e r p r e s s u r e . The ' t r u e ' b u r n i n g v e l o c i t y (TBVEL) i s a l s o c a l c u l a t e d . The new energy of the c y l i n d e r c o n t e n t s (ETOT2) i s now o b t a i n e d u s i n g the f i r s t law as d e s c r i b e d above, b e f o r e c a l l i n g t he s u b r o u t i n e TEMP t o c a l c u l a t e the burned gas tempe r a t u r e (TB2), the s p e c i f i c volume of the bu r n t gas ( v y ) and the mass f r a c t i o n burned ( x ) . U s i n g t h e s e v a l u e s , s u b r o u t i n e CALFLS c a l c u l a t e s the burned gas volume (VOLB2), the r a d i u s of the flame f r o n t (RB2), and the ' c a l c u l a t e d ' b u r n i n g v e l o c i t y (CBVEL) The v a l u e s a r e r e t u r n e d t o the main program, where the c a l c u l a t e d b u r n i n g v e l o c i t y CBVEL i s compared w i t h the t r u e b u r n i n g v e l o c i t y TBVEL, and i f the d i f f e r e n c e i s g r e a t e r than the a l l o w e d e r r o r , then the program i t e r a t e s t o a new c y l i n d e r p r e s s u r e and r e p e a t s the above c a l c u l a t i o n s u s i n g s u b r o u t i n e s ENUFLS, TEMP, and CALFLS When the p r e s s u r e has been found where TBVEL = CBVEL, the 158 i t e r a t i o n p r o c e d u r e s t o p s , and the v a l u e s of the r e l e v e n t parameters a r e p r i n t e d out b e f o r e moving on th r o u g h the next c r a n k a n g l e d i v i s i o n , and r e p e a t i n g the above proce d u r e a t the new c y l i n d e r volume. The p r o g r e s s i v e b u r n i n g c a l c u l a t i o n s c o n t i n u e u n t i l the mass f r a c t i o n b u r n t e q u a l s 1.0, a t which p o i n t the c y l i n d e r i s c o n s i d e r e d t o c o n t a i n a homogeneous m i x t u r e of the p r o d u c t s of combustion d. E x p a n s i o n Of P r o d u c t s T h i s s e c t i o n i s e s s e n t i a l l y the same as t h a t used i n the OTTO program, i n t h a t the F i r s t Law i s s a t i s f i e d a t each crank a n g l e s t e p , i n o r d e r t o o b t a i n the new t e m p e r a t u r e , p r e s s u r e and energy of t h e c y l i n d e r c o n t e n t s as the p i s t o n moves down t o bottom dead c e n t r e . In t h i s program, however, heat t r a n s f e r c o n t i n u e s t o be i n c l u d e d , and r e s u l t s i n a f i r s t law e q u a t i o n of the form; where DQ i s a g a i n c a l c u l a t e d u s i n g the e x p r e s s i o n g i v e n by Annand. The v a l u e of the gas temperature i s a d j u s t e d by an i t e r a t i o n p r o c e d u r e i n s u b r o u t i n e EXP, u n t i l t he f i r s t law e q u a t i o n above, and the i d e a l gas law a r e s a t i s f i e d . D i s s o c i a t i o n i s acc o u n t e d f o r i n the c a l c u l a t i o n s , u n t i l t he temperature of the gas i s too low f o r d i s s o c i a t i o n t o be i m p o r t a n t , a t which p o i n t the c o m p o s i t i o n of the m i x t u r e i s f r o z e n . e. C a l c u l a t i o n Of E f f i c i e n c y And M.E.P. These c a l c u l a t i o n s a r e performed i n the same way as d e s c r i b e d i n Appendix C f o r the COMB program, by c a l c u l a t i n g the a r e a under the p r e s s u r e volume diagram t o o b t a i n the work done, and hence the c y c l e e f f i c i e n c y and the mean e f f e c t i v e p r e s s u r e . ENGY2 = ENGY1 (7) The program c o n c l u d e s by g e n e r a t i n g p r e s s u r e / v o l u m e and p r e s s u r e / c r a n k a n g l e diagrams. 159 SIMULATION PROGRAM FLOWCHART INPUT: FUEL TYPE; ENGINE SPEED; A/F RATIO; INTAKE AIR PRESSURE AND TEMPERATURE; SPARK ADVANCE; BOOST PRESSURE & C u r VERSUS MASS FRACTION BURNED CURVE. CALCULATE PROPERTIES OF CYLINDER CONTENTS AT BDC AND AT EACH CRANK ANGLE STEP UP TO IGNITION ASSUMING ISENTROPIC COMPRESSION AT NEXT CRANK ANGLE STEP: ASSUME NEW CYLINDER PRESSURE ASSUME UNBURNED GAS COMPRESSED ISENTROPICALLY TO DETERMINE NEW TEMPERATURE AND ENERGY, FROM THESE OBTAIN LAMINAR BURNING VELOCITY. ' I CALCULATE NEW TOTAL ENERGY OF CYLINDER CONTENTS FROM 1ST LAW - ENERGY2^ENERGY 1 + JPDV-DQ ITERATE BURNED GAS TEMPERATURE UNTIL MASS AND ENERGY OF BURNED AND UNBURNED GASES BALANCE. OBTAIN MASS FRACTION BURNED, FLAME RADIUS & FLAME SPEED, AND TURBULENT BURNING VELOCITY. NO IS CALCULATED BURNING VELOCITY EQUAL TO S/.+Cur ? i NO IS MASS FRACTION BURNED GREATER THAN UNITY? CALCULATE PROPERTIES OF CYLINDER CONTENTS AT EACH CRANK ANGLE TO BDC. CALCULATE IMEP AND EFFICIENCY PRINT RESULTS AND PLOT GRAPHS H Z STOP 160 1 SAMPLE INPUT F I L E FOR PROGRAM "SIM" 2 =================================== 3 4 5 001 0 6 11 82.0 300.0 3000.0 9.00 1.20 34.00 0.00 8.00 7 0.050 0.735 9.174 18.326 71.758 1 2.00 0.800 0.70 8 12 82.2 296.0 3000.0 9.00 1.00 22.00 0.00 4.00 9 0.050 0.029 12.428 14.027 73.409 1 2.00 0.800 0.70 10 12 87.0 298.0 3000.0 9.00 1.00 16.00 7.50 1.000 0.80 11 0.050 0.029 12.428 14.027 73.409 1 4.00 500.0 12 13 100.0 298.0 3000.0 9.00 1.00 20.00 8.00 1.000 0.70 13 0.000 0.000 0.000 0.000 0.000 2- 4.00 500.0 1 4 C 15 C KFUEL PI T1 SPEED COMPR AF SPKAD FFF. IGNDEL 16 C 17 C F PR02 PRC02 PRH20 PRN2 NDISS PDCA HTFCN HTEXP 18 C 19 C "I 1 2 3 4 5 6 7 8 37 38 39 FUEL TYPE:- OCTANE C 8 . 0 H 18 .0 SPEED (RPM) = 3000 .0 SPARK ADVANCE (DEG. BTDC) = 22 .00 AIR/FUEL RATIO= 15.06 STOICH. A/F RATIO= 15.06 LAMBDA= 1.00 COMP. RATIO* 9 . 0 STEP VOL PRESS TU TB MFX VFRBNT CBVEL TBVEL FLMSPD FSR RADF AREAF C.A. ENERGY 9 in 1 497 9 82 2 296 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 180 0 - 0 16533 1U 1 1 83 66 6 1121 9 554 0 2661 9 0 0004 0 19 4 519 0 739 35 02 6 12 0 399 0 97 344 0 - 0 05649 12 84 63 9 1187 9 561 2 2567 2 0 0015 0 77 4 056 0 753 20 50 5 39 0 627 2 34 346 0 - 0 05352 13 85 61 7 1258 2 568 3 2547 1 0 0039 1 93 4 071 0 768 19 57 5 30 0 844 4 16 348 0 - 0 05082 14 86 59 7 1334 1 575 6 2530 8 0 0076 3 69 3 875 0 783 17 66 4 95 1 041 6 20 350 0 - 0 04843 15 87 58 2 1416 3 583 1 2523 5 0 0132 6 15 3 859 0 798 16 92 4 83 1 229 8 49 352 0 - 0 0464 1 16 88 56 9 1506 4 590 8 2519 5 0 0208 9 33 3 832 0 814 16 08 4 71 1 407 10 94 354 0 - 0 04482 17 89 56 0 1604 6 598 8 2520 7 0 0310 13 24 3 839 0 831 15 53 4 62 1 580 13 56 356 0 -o 04372 18 90 55 5 1731 7 608 7 2527 6 0 0473 18 94 4 679 0 850 18 30 5 50 1 783 16 93 358 0 - 0 04322 19 91 55 3 1904 8 621 1 2538 3 0 0722 26 47 5 687 0 874 20 52 6 51 2 01 1 18 82 360 0 -0 04352 20 92 55 5 2127 8 635 6 2554 3 0 1070 35 28 6 792 0 903 22 84 7 52 2 265 19 92 362 0 -o 04482 21 93 56 0 2390 5 651 2 2572 6 0 1518 44 42 7 608 0 935 23 21 8 13 2 523 20 66 364 0 - 0 04744 22 94 56 9 2697 1 667 7 2591 4 0 2084 53 60 8 536 0 97 1 23 47 8 79 2 783 20 99 366 0 - 0 05183 23 95 58 2 3023 5 683 6 2609 0 0 2740 61 98 8 950 1 007 22 28 8 89 3 031 20 92 368 0 -0 05803 24 96 59 7 3355 1 698 4 2622 9 0 3469 69 16 9 2 15 1 041 20 44 8 85 3 258 20 56 370 0 - 0 06662 25 97 61 7 3658 3 710 9 2632 5 0 4244 75 44 9 292 1 072 19 51 8 67 3 475 19 94 372 0 - 0 07779 26 98 63 9 3922 4 721 0 2637 1 0 5032 80 66 9 190 1 098 18 03 8 37 3 675 19 18 374 0 - 0 09171 27 99 66 5 4127 1 728 4 2636 5 0 5800 84 87 8 884 1 1 18 16 49 7 95 3 858 18 39 376 0 - 0 10845 28 100 69 5 4259 1 733 1 2630 3 0 6514 88 21 8 333 1 132 14 85 7 36 4 023 17 67 378 0 - 0 12791 29 101 72 8 4319 4 735 2 2619 2 0 7156 90 82 7 623 1 139 13 20 6 69 4 170 17 12 380 0 - 0 14985 30 102 76 3 4315 4 735 0 2606 3 0 7702 92 81 6 590 1 142 1 1 41 5 77 4 297 16 87 382 0 -0 17162 31 103 80 2 4253 1 732 9 2588 5 0 8180 94 40 5 851 1 139 10 05 5 14 4 408 16 90 384 0 - 0 19594 32 104 84 4 4150 8 729 3 2567 6 0 8583 95 66 4 950 1 132 8 72 4 37 4 505 17 28 386 0 - 0 22134 33 105 88 9 4016 8 724 5 2544 6 0 8934 96 76 4 280 1 123 7 92 3 81 4 593 17 92 388 0 - 0 24764 34 106 93 7 3866 9 719 0 2519 4 0 9228 97 49 3 676 1 1 1 1 6 24 3 31 4 663 17 43 390 0 - 0 27459 36 180 497 8 371 1 0 0 1299 1 0 9228 97 49 0 0 0 0 0 0 0 0 0 0 0 0 538 0 -1 03291 POWER= 12.225 I.M.E.P. 11.048 EFFICIENCY= 37.77542 cn TYPICAL OUTPUT FROM PROGRAM "SIM" 162 1 C SIM THIS PROGRAM SIMULATES PROGRESSIVE BURNING IN ONE 2 C === CYLINDER OF THE TOYOTA 4 CYLINDER S.I. ENGINE. THE 3 C COMBUSTION CHAMBER HAS A HEMISPERICAL HEAD GEOMETRY. 4 C 5 IMPLICIT REAL*8(A-H,0-Z) 6 REAL*8 MPV, K.L.M.N, NO, N2.N02, NCH, KK.NUM, NUM1 , NMIX, MOLFL, 7 -NM.NM1,NNM1,NNM2,NN2,NN02,MEP,LENG,MTOT,MWMIX,MFX1,NNCH, 8 -MFX2,MW(14),MMFX2,NRN2,NRES,NR02.NRC02,NRH20,NNFUE L, 9 -MF(5,200),IGNDEL,MWBMIX,LAMBDA,MFXMAX,LBVEL 10 C 11 COMMON /AREA1/ NCH,N02,K,L,M,N,KFUEL 12 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02,NN2,NNFUEL,KOM 13 COMMON /AREAS/ AREAB,HTEXP,MPV,HTFCN,TWALL,VISC,THCOND 14 COMMON /AREA4/ NDISS,IPRINT 15 C 16 DIMENSION X(10),PP(5,200),VV(5,200),VV2(5,200),VVX(20), 17 -DH(20),CPG(20),PP2(5,200),DI(5,200),TIM(5,200),XX(5,200), 18 -CCA(10),DL(5,200),ZZ(5,200),DC(5,200),YY(5,200),POUT(180), 19 -UUU(10),CC(10),PDAT(5.200),CB(5,200),TB(5,200), 20 -FS(5,200),RB(5,200) 21 C 22 INTEGER IPRES(5,200) 23 C 24 C STATEMENT FUNCTION USED THROUGHOUT PROGRAM TO CALCULATE CYLINDER 25 C VOLUME (DVOL) AT A GIVEN CRANK ANGLE (DALFA). VOLUME OBTAINED MUST 26 C BE ADDED TO THE CLEARANCE VOLUME TO GIVE TOTAL CYLINDER VOLUME 27 C 28 DVOL(DALFA ) =3.14159*((BORE/2. )**2. )*((STROK/2.)*(1.-DCOS(DALFA* 29 -0.0174532))+LENG*(1.-DSQRT(1.-(DSIN(DALFA*0.0174532)*DSIN(DALFA 30 -*0.0174532)*((STROK/2./LENG)**2.))))) 31 C 32 C READ NUMBER OF RUNS TO BE MADE.... 33 C 34 READ(5,999) NUMBR,IPRINT 35 999 F0RMAT(2I3) 36 DO 222 IL=1,NUMBR 37 C 38 C READ TYPE OF FUEL (11=CH4, 12=C8H18, 13=C3H8 ); 39 C PRESSURE (P1)(KPA) AND TEMP. (T1)(K) AT START OF COMBUSTION; 40 C ENGINE SPEED (RPM); COMPRESSION RATIO (COMPR); REL. AIR/FUEL 41 C RATIO (LAMBDA); SPARK ADVANCE (SPKAD) (DEG. B. T.D.C); 42 C TURBULENT FLAME FACTOR (FFF); IGNITION DELAY (IGNDEL); 43 C 44 C RESIDUAL GAS FRACTION (%),(F); PERCENTAGE CONSTITUENTS IN 45 C RES. FRACTION (PR02,PRC02,PRH20,PRN2); 46 C WHETHER FULL DISSOCIATION (NDISS=2) OR PARTIAL (NDISS=1); 47 C CRANK ANGLE ITERATION INCREMENT (PDCA); HEAT TRANSFER MULTIPLIER 48 C (HTFCN); HEAT TRANSFER EXPONENT (HTEXP). 49 C 50 READ(5.47) KFUEL,P1,T1.SPEED,COMPR,LAMBDA,SPKAD.FFF,IGNDEL 51 47. F0RMAT(I3,3F7.1.5F6.2) 52 READ(5,46) F,PR02,PRC02,PRH20,PRN2,NDISS,PDCA,HTFCN,HTEXP 53 46 F0RMAT(5F7.3,I3,F6.2,F6.3,F5.2) 54 C 55 C SPECIFY FUEL PROPERTIES: MOL.WEIGHT. LOWER HEATING VALUE, 56 C ENTHALPY OF FORMATION... ^ 57 C 58 IF(KFUEL.GT.11) GOTO 10 163 59 CN=1.0 60 HM=4.0 61 MW(11)=16.04 62 QVS=50050.0 63 HF1=-74873.0 64 WRITE(6,45) CN.HM 65 45 F0RMAT(1H .'FUEL TYPE:- METHANE C '.F3.1,' H '.F3.1/) 66 GOTO 30 67 C 68 10 IF(KFUEL.GT.12) GOTO 20 69 CN=8.0 70 HM=18.0 71 MW(12)=114.14 72 QVS=43500.0 73 HF1=-208447.0 74 WRITE(6,43) CN.HM 75 43 FORMATdH .'FUEL TYPE:- OCTANE C '.F3.1,' H '.F4.1/) 76 GOTO 30 77 C 78 20 IF(KFUEL.GT.13) STOP 79 CN=3.0 80 HM=8.0 81 MW(13)=44.097 82 0VS=46353.0 83 HF1=-103847.0 84 WRITE(6,44) CN.HM 85 44 FORMATdH ,'FUEL TYPE:- PROPANE C '.F3.1,' H ',F3.1/) 86 C 87 C SPECIFY ENGINE PARAMETERS... 88 C 89 30 CONTINUE 90 STR0K=O.O78 91 B0RE=O.O85 92 LENG=0.124 93 RDASH=58.3737E-03 94 HTCLRV=18.358E-03 95 CLRV=55.3264E-06 96 TWALL=450.0 97 C 98 C GAS CONSTANT (KJ/KMOL K) 99 C 100 RM0L=8.31434 101 JJ=0 102 C 103 C CALC. NUMBER OF KMOLS OF REACTANTS AND PRODUCTS BEFORE AND AFTER 104 C COMBUSTION RELATIVE TO ONE KMOL OF FUEL 105 C (NOT INCLUDING DISSOCIATION). NCH=HYDROCARBON 106 C N02=AVAILABLE OXYGEN, N=NITROGEN. K=C02, L=H20, M=UNBURNT OXYGEN 107 C 108 NCH=1 109 N02=(CN+HM/4)*LAMBDA 1 10 N=3.762*(CN+HM/4)*LAMBDA 1 1 1 K=CN 112 L=HM/2 113 M=(CN+HM/4)*(LAMBDA-1 ) 1 14 C 1 15 WRITE(6,655) NCH,N02,N,K,L,M 1 16 655 FORMATdH , ' NCH, N02 . N, K , L , M= ' . 6F9 . 5/ ) 164 117 C 1 18 C CALC. TOTAL NUMBER OF KMOLS OF FRESH MIXTURE PER KMOL OF FUEL . 119 SUMNS=NCH+N02+N 120 C CALC. NO. OF KMOLS OF RESIDUAL GAS GIVEN THE VOLUME FRACTION OF 121 C RESIDUAL GASES ' F'. . . . 122 NRES=(F/(1-F))*SUMNS 123 C CALC. NO. OF KMOLS IN CYLINDER PER KMOL OF FUEL... 124 NMIX=SUMNS+NRES 125 SUMNS=NMIX 126 C CALC. NO OF KMOLS OF EACH RESIDUAL GAS... 127 NR02=PR02*NRES/100.0 128 NRC02=PRC02*NRES/100.0 129 NRH20=PRH20*NRES/100.0 130 NRN2=PRN2*NRES/100.0 131 C CALC. NEW VALUES FOR THE TOTAL NO. OF KMOLS OF N2, 02, C02.& H20 132 C PER KMOL OF FUEL... 133 N=N+NRN2 134 N02=N02+NR02 135 K=K+NRC02 136 L=L+NRH20 137 M=M+NR02 138 WRITE(6,655) NCH,N02,N.K,L,M 139 C 140 C CALC. ENERGY OF REACTANTS AT INLET TEMP; 5=02. 6=N2, 11= CH4 141 C 12=C8H18, 13=C3H8, 1=C02, 3=H20,... (IN KJ/KMOL OF FUEL) 142 DH(1)=((3.096*T1+0.00273*(T1**2)-7.885E-07*(T1**3) 143 1+8.66E-11*(T1**4))-1145.0)*RMOL 144 DH(3)=((3.743*T1+5.656E-04*(T1**2)+4.952E-08*(T1**3) 145 1-1.818E-11*(T1**4))-1167.O)*RM0L 146 DH(5)=((3.253*T1+6.524E-04*(T1**2)-1.495E-07*(T1**3) 147 1+1.539E-11*(T1**4))-1024.0)*RM0L 148 DH(6)=((3.344*T1+2.943E-04*(T1**2)+1.953E-09*(T1**3) 149 1-6.575E-12*(T1**4))-1O23.O)*RM0L 150 DH( 1 1 ) = ((1.935*T1+4.965E-03*(T1**2.)-1.244E-06*(T1**3. ) 151 1+1.625E-10*(T1**4.)-8.586E-15*(T1**5.))-985.9)*RMOL 152 DH(12)=((-0.72*T1+4.643E-02*(T1**2.)-1.684E-05*(T1**3. ) 153 1+2.67E-09*(T1**4.))-3484.0)*RMOL 154 DH(13)=((1.137*T1+1.455E-02*(T1**2.)-2.959E-06*(T1**3. ) 155 1)-1552.9)*RM0L 156 UUU(1)=-3.93522E05 157 UUU(3)=-2.41827E05 158 C CALC. TOTAL ENERGY OF MIXTURE (KJ/KMOL FUEL) 159 ERCT=(NCH*(HF1+DH(KFUEL )-RM0L*T1)+N02*(DH(5)-RM0L*T1) 160 -+N*(DH(6)-RM0L*T1)+NRC02*(UUU(1)+DH(1)-RMOL*T1)+NRH20* 161 -(UUU(3)+DH(3)-RM0L*T1)) 162 C 163 C CALC. SWEPT VOL.(CYLV),CLEARANCE VOL.(CLRV),TOTAL V0L.(V1), 164 C VOLUME CORRESPONDING TO GIVEN SPARK ADVANCE (DVOLM)... 165 CYLV = 3. 1415926*((B0RE/2. )**2.)*STROK 166 CLRV=CYLV/(C0MPR-1.) 167 V1=C0MPR*CLRV 168 VT0TAL=V1 169 MPV=SPEED*STR0K/30.0 170 C SUBT. SPK ADV. ANGLE FROM 360' 171 ANG=(360.-SPKAD+IGNDEL) 172 C INITIALISE CRANK ANGLE COUNTER AT B.D.C. & SET TIME TO ZERO 173 DLF1=180.0 174 TIME=0.0 165 175 C CALC. VOLUME IN CYLINDER AT SPARK TIME (USED LATER) 176 DVOLM=(CLRV+DVOL(ANG)) 177 TIME=0.0 178 C TOTAL NO. OF MOLS IN CYL.=NO. OF MOLS OF FUEL*(1+4.76(CN+HM/4) 179 C *LAMBDA) 180 C WHERE (1+4.76(CN+HM/4).LAMBDA)=NMIX. 181 C I.E. NT0T=M0LFL*NMIX 182 C BUT P1.V1=NT0T.RM0L.T1 OR NTOT=P1.V1/RM0L.T1 = MOLFL.NMIX 183 C THEREFORE NO. OF MOLS OF FUEL IN CYL. = P1 . V1/NMIX.RMOL.T1 184 M0LFL=(P1*V1)/(NMIX*RM0L*T1) 185 C ENERGY OF CYLINDER CONTENTS IN KJ 186 ENGY1=ERCT*MOLFL 187 C CALC. STOICH. A/F RATIO (STAFR),AIR/FUEL RATIO (AFR),PERCENTAGE 188 C OXYGEN (NN02), NITROGEN (NN2) AND FUEL (NNCH) IN MIXTURE... 189 STAFR=((CN+HM/4.)*32.+3.762*(CN+HM/4.)*28.01)/((CN*12)+HM) 190 AFR=STAFR*LAMBDA 191 NN02=(N02/NMIX)*1OO. 192 NN2=(N/NMIX)*100. 193 NNCH=100.-(NN02+NN2) 194 NNFUEL=NNCH 195 C GIVEN MOLECULAR WEIGHTS OF FUELS, CALC. MOLECULAR WEIGHT OF 196 C MIXTURE (MWMIX); TOTAL MASS OF MIXTURE (MTOT); AND SPECIFIC 197 C VOLUME OF MIXTURE 198 MW(11)=16.04 199 MW(12)=114.23 200 MW(13)=44.097 201 MWMIX=(NN02*32.0/1OO.)+(NN2*28.0/100.)+(NNCH*MW(KFUEL)/100.) 202 MT0T=(P1*V1*MWMIX)/(T1*RM0L) 203 VT0T1=V1 204 VSU1=VT0T1/MTOT 205 ET0T1=ERCT/MWMIX/NMIX 206 WRITE(6,735) MPV,TWALL,HTFCN 207 735 F0RMAT(1H ,'MPV,TWALL,HTFCN '.3E12.4/) 208 WRITE(6,734) ERCT,ENGY1,NMIX,MWMIX,MOLFL,MTOT 209 734 FORMATdH , ' ERCT , EG1 . NMIX ,MWMX ,MOLFL . MTOT ; ' , 6E 12 . 4//) 210 C 211 WRITE(6,652) SPEED,SPKAD,FFF 212 652 FORMATdH .'SPEED (RPM) = '.F7.1, 213 -7X, 'SPARK ADVANCE (DEG. BTDC) =' ,F7 . 2,3X, 'FLAME FACTOR =',F7.2/) 214 WRITE(6,813) AFR,STAFR,LAMBDA,COMPR 215 813 FORMATdH ,,15HAIR/FUEL RATIO=,F6.2,3X,18HST0ICH. A/F RATIO=, 216 -F6.2,3X,7HLAMBDA=,F6.2,3X,12HC0MP . RATIO=,F5.1/) 217 WRITE(6,31) 218 31 FORMATdH , 1X ,' STEP ', 1X ,' VOL ', 3X ,' PRESS ', 3X ,' TU ', 5X ,' TB ', 5X 219 -,'MFX',4X,'VFRBNT',2X.'CBVEL',3X,'TBVEL',3X,'FLMSPD',2X, 220 -'FSR',3X,'RADF ' ,2X,'AREAF',3X,'C.A. ',3X,'ENERGY'/) 221 DO 106 KI=1,10 222 X(KI)=0.0 223 106 CONTINUE 224 NI=1 225 V1=V1*(1E+06) 226 WRITE(6,893) NI,V1,P1,T1,(X(I),I=1,9),DLF1,ENGY1 227 893 F0RMAT(1H ,13,1X,F6. 1.3F7.1,F9.4,F7.2,2F8.3.F7.2.F7.2,F7.3, 228 -F7.2.F7.1.F10.5) 229 TU1=T1 230 V1=V1/(1E+06) 231 T2=T1 232 PP2(IL,1)=P1 166 233 V V 2 ( I L , 1 ) = V 1 234 T I M ( I L , 1 ) = T I M E 235 M F ( I L , 1 ) = 0 . 0 236 C B ( I L , 1 ) = 0 . 0 237 T B ( I L , 1 ) = 0 . 0 238 F S ( I L , 1 ) = 0 . 0 239 R B ( I L , 1 ) = 0 . 0 240 JJJ=1 241 NUT=0 242 DCA=PDCA 243 NDCA=(180./DCA) 244 C 245 C START COMPRESSION STROKE 246 C 247 C 248 C THIS SECTION CALCULATES P R E S S . , V O L . , T E M P . , & ENERGY UP TO START 249 C OF COMBUSTION IN EVEN STEPS OF CRANK ANGLE CHANGE (DCA) 250 C 251 DO 40 NI=2,NDCA 252 C 253 C ITERATION CONTROLS 254 NN=0 255 NUT=0 256 C C A L C . VOLUME D I V I S I O N (DIV). FOR GIVEN C . A . DIVISION (DCA) 257 DIV=DV0L(DLF1)-DVOL(DLF1+DCA) 258 C • C A L C . NEW VOLUME IN CYLINDER & RESET C . A . COUNTER TO NEW VALUE 259 V2=V1-DIV 260 DLF1=DLF1+DCA 261 C IF NEW C . A . < SPK. A D V . , CONTINUE WITH COMP. STROKE CALCS. 262 IF (DLF 1 . GE . ANG) J J J = 2 263 C C A L C . CURRENT T I M E ; AND PRESS. AT GIVEN VOL. & TEMP. 264 51 T I M E = ( D L F 1 - 1 8 0 . ) / ( 6 . 0 * S P E E D ) 265 CALL C 0 M P ( P 1 , V 1 , T 1 , P 2 , V 2 , T 2 , E N G Y 1 , E N G Y 2 , N R C 0 2 . N R H 2 0 ) 266 ENGY1=ENGY2 267 C RECORD PERMANENT VALUES OF P R E S S . , V O L . , T I M E , VOL. DIV, AND 268 C C . A . D I V , AT END OF EACH C . A . S T E P . . . 269 P P 2 ( I L . N I ) = P 2 270 V V 2 ( I L . N I ) = V 2 271 T I M ( I L . N I ) = T I M E 272 D I ( I L , ( N I - 1 ) ) = D A B S ( D I V ) 273 M F ( I L , N I ) = 0 . 0 274 C B ( I L , N I ) = 0 . 0 275 T B ( I L . N I ) = 0 . 0 276 R B ( I L . N I ) = 0 . 0 277 F S ( I L , N I ) = 0 . 0 278 KTDC=0 279 c x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 280 c W R I T E ( 6 . 3 1 2 ) N I , K T D C , P 2 , V 2 , T I M E , D I V , D L F 1 281 P1=P2 282 T1=T2 283 V1=V2 284 c ADJUST MAGNITUDE OF VOLUME FOR WRITE S T A T E M E N T . . . 285 V2=V2*(1E+06) 286 287 W R I T E ( 6 , 8 9 3 ) N I , V 2 , P 2 , T 2 , ( X ( I ) , I = 1 , 9 ) , D L F 1 , E N G Y 2 288 289 650 V2=V2/(1E+06) 290 I F ( J J J . E 0 . 2 ) GOTO 610 167 291 40 CONTINUE 292 610 VT0T1=V1 293 TU1=T1 294 VSU1=V1/MTOT 295 C 296 C START OF PROGRESSIVE BURNING 297 C 298 C 299 NG=0 300 KOM=0 301 IS=1 302 NED= 1 303 JJJ=1 304 NDC=1 305 IDTM=1 306 IMX=1 307 MFX1=0.0 308 NNN= 1 309 IV0L=1 310 KTDC=0 31 1 NUTT=0 312 SUMXS=NMIX 313 TB2=2400.0 314 DPX=4OO.0 315 EPS=0.001 316 THC0ND=0.1 317 VISC=0.5E-04 318 VSB2=0.5 319 MFXMAX=0.95 320 C 321 C 322 DO 333 LMN=1,50 323 C 324 C 325 C CALC. TIME TAKEN FOR PISTON TO TRAVEL THROUGH 'DCA' DEGREES C.A. 326 C 327 NI=NI+1 328 508 DTIME=DCA/(6.0*SPEED) 329 C UPDATE TIME AND CRANK ANGLE COUNTER... 330 TIME=TIME+DTIME 331 DLF 1 =DLF1+DCA 332 c CALC. DISTANCE FROM PISTON TOP TO T.D.C 333 DIST=DV0L(DLF1 )/(3 . 14159*((BORE/2. )**2)) 334 c CALC. CHANGE IN VOLUME DUE TO PISTON MOTION... 335 DIV=DV0L(DLF1-DCA)-DV0L(DLF1 ) 336 c CALC. NEW TOTAL VOLUME.... 337 V2=V1-DIV 338 VT0T1=V2 339 c WRITE(6.461 ) DTIME,TIME,DLF1,DIST,DIV,V2 340 c 461 F0RMAT(1H ,'DTIME,TIME,DLF1,DIST.DIV,V2=',6E11.4) 341 • c UPDATE ITERATION COUNTER AND FIND NO. OF ITERATION AT T.D.C. 342 IF(KTDC.GT.0) GOTO 350 343 IF(DLF1.GE.360.0) KTDC=NI 344 c 345 c START BURNING... 346 c 347 c CALC. NEW PRESS.RESULTING FROM ADIABATIC COMPRESSION OR EXPANSION 348 c OF THE CYLINDER GASES RESULTING FROM PISTON MOTION. THIS PRESS. 168 349 C (P I2 ) IS USED AS THE MINIMUM VALUE FROM WHICH TO ITERATE TO FIND 350 C THE NEW C Y L . PRESS. AFTER C O M B U S T I O N . . . . 351 350 I F ( M F X 1 . L T . 0 . 0 5 ) GOTO 401 352 I F ( M F X 1 . G T . 0 . 8 ) GOTO 352 353 PI2=P1 354 GOTO 353 355 C 352 WRITE(6 ,360) P 1 , V 1 , T B 2 , V 2 , E N G Y 1 , E N G Y 2 356 C 360 FORMATdH , ' P 1 . V 1 , T B 2 . V 2 , E N G Y 1 , E N G Y 2 ' , 6 E 1 2 . 4 ) 357 352 CALL E X P ( P 1 , V 1 , T B 2 , P I 2 , V 2 , T 2 , C C , S U M X S , E N G Y 1 , E N G Y 2 , 358 -ATOT,DT IME) 359 DPX=50 360 GOTO 353 361 401 I F ( D L F 1 . L T . 3 6 0 . 0 ) GOTO 403 362 PI2=P1 363 GOTO 353 364 403 CALL C O M P ( P 1 , V 1 , T 1 , P I 2 , V 2 , T 2 , E N G Y 1 , E N G Y 2 , N R C 0 2 , N R H 2 0 ) 365 GAM=DL0G1O(PI2 /P1) /DLOG10(V1/V2) 366 NG=NG+1 367 IF ( N G . G T . 2 ) GAM=0.0 368 C 392 WRITE(6 ,390) P 1 . T 1 . P I 2 . T 2 369 C 390 FORMATdH , ' P1 , T 1 , PI2 , T2 ' , 4E 12 . 4 ) 370 C 371 C INCREASE PRESSURE SLIGHTLY TO START ITERATION PROCEDURE.. 372 353 PX1=PI2+0.2 373 PXF=10000.0 374 I F ( N G . E O . I ) AREAB=0.0 3 "7 g Q II II II Ii II II H II H ll It II If It it Ii II II Ii II II rl 11 11 It II 11 II n II 11 It II II It M II tl II 11 II II 11 ii ti 11 II II II II II II II II 11 ll II H ll 11 I) II II I I ll II 376 CALL E N U F L S ( P X 1 , P 1 , T U 1 , V S U 1 , M W M I X , T U 2 , V S U 2 , E U 2 , F F F . L B V E L , L A M B D A , 377 -GAM,NRC02,NRH20) 37Q ^ ti it II II II II n II it it it n u n ti ti it ti II ti it II it it it it M H it n it II n it it it it H it tt ii II II II it it it ti II II ti it n II n n ti II II II II it II II ti II II ti n 379 H T C 0 E F = ( T H C 0 N D / B 0 R E ) * ( ( M P V * B 0 R E / ( V S B 2 * V I S C ) ) * * H T E X P ) / 1 0 0 0 . 0 380 DO=HTCOEF*AREAB*(TB2-TWALL)*HTFCN*DTIME 381 PDV=( (P1+PX1) /2 . ) *D IV 382 ENGY2=ENGY1+PDV-DQ 383 C WRITE(6 ,737) ENGY2,ENGY1,PDV,DO,HTCOEF 384 C737 F O R M A T d H , ' E2 , E 1 , PDV, DO, HTCOEF ' . 5 E 1 2 . 4 ) 385 ETOT1=ENGY2/MT0T 3Qg Q 11 11 11 II 11 II tl II tt fl II II 11 II tl tt H It It 11 11 II tl tt 11 tt ft tl It tl It fl II M 11 II II tl II II It tt tl II II II II II II II It II II It It tl II tl tl II II II II 11 II 387 CALL T E M P ( P X 1 , T B 2 , C C , M F X 2 , M T O T , E U 2 , V S U 2 , V T O T 1 , E T O T 1 , V S B 2 , I S ) 3gg Q II M II ti ti II H it ti n it ti it ti it it n n II II II ti it ti it it H it H II H it n it H « tt it H II n II H M II ti n n it II ti II II n n II II n M II II II tt ti ti 389 CALL C U T ( L B V E L , T B V E L . M F X 2 ) 3gQ Q •' '• '* « " •• tt •• " « « x 1 1 " •• 1 1 1 1 " >• •< " " *t tl II ti II II ti n ll 391 I F ( I S . E O . I ) GOTO 560 392 PI2=PI2+0.5 393 GOTO 353 394 560 MMFX2=MFX2 395 C 396 IF (MFX2.LT.MFXMAX) GOTO 394 397 UJJ=1 398 NUT=0 399 T1=TB2 400 NNN=1 401 GOTO 396 402 Q " 11 " " 11 " " " 11 " " " 1111 " " 11 " 11 " " " " N " 11 H " " " " " " " " " " 11 " " " 11 " " " 11 " " " " " " " " " " 11 " " " " " " 403 394 CALL C A L F L S ( M F X 1 , M F X 2 , V S B 2 , M T O T , D T I M E , F F F , V S U 2 , C B V E L , V S U 1 , 404 - A R E A F 1 , V 0 L B 2 , I V O L , V O L B 1 . A R E A F 2 . R B 1 , R B 2 , D I S T , T B V E L ) ^05 C " " " " " " 11 " " " " " " " " " " " 1 1 1 1 " " " " 1 1 1 1 " " " n " M " M 11 " " " " " " " " " " " " " " " " " " " " " " " " 11 " " " 406 KOM=0 169 407 C 408 C CALC. ERROR BETWEEN BURNING VELOCITIES TAKEN FROM PUBLISHED 409 C EQUATIONS (TBVEL) AND THOSE CALCULATED AT A GIVEN PRESSURE (CBVEL). 410 Y1=TBVEL-CBVEL 411 C INCREMENT PRESSURE... 412 910 IF(CBVEL.LT.TBVEL) GOTO 354 413 PX2=PX1-DPX 414 GOTO 502 415 354 PX2=PX1+DPX 416 IF(PX2.GT.PXF) GOTO 91 417 IF(PX2.LT.100.0) GOTO 91 4 TJ g Q it ii ii ii ii ii II ii it n n II II ti II it ii n II II n II II n II it it n II II ii n n it it n n it ii it n n it n it it u n n n 11 n n n n n n n n n » n tt n n u n n ti 419 502 CALL ENUFLS(PX2,P1,TU1.VSU1,MWMIX,TU2,VSU2.EU2,FFF,LBVEL,LAMBDA, 420 .-GAM,NRC02,NRH20) 421 C " 11 " " " " " " 11 " " " " " 11 " " " " " " M " " " " " " " n " 11" " " M " 11 " " " " 11 " 11 " " " " " " 11 " " 11" " " " " " 11 " " 11 " " " " 422 HTC0EF=(THCDND/B0RE)*((MPV*B0RE/(VSB2*VISC))**HTEXP)/1000.0 423 DQ=HTCOEF *AREAB*(TB2-TWALL)*HTFCN*DTIME 424 PDV=((P1+PX2)/2. )*DIV 425 ENGY2=ENGY1+PDV-DQ 426 C WRITE(6,738) ENGY2,ENGY1,PDV,DQ,HTCOEF 427 C738 FORMATdH , ' E2 . E 1 . PDV . DQ .HTCOEF '.5E12.4) 428 ETOT1=ENGY2/MT0T 423 Q II II II n II ti II II ft II II II ii ii ti ii H ii it ti it it II II ti II H n II n n n II n II ii II n II II II II it ii II II II it it ti tt it tt ti II it II ii n II II II II II n 430 CALL TEMP(PX2,TB2,CC,MFX2,MTOT,EU2,VSU2,VTOT1,ETOT1,VSB2,IS) 4 3 ^ Q II II II II it it II II II II II II II II it II II II II it II II II ti ti it it n if u II it II n II II n it II ti ti II n II II II it if II II n II II it ti II II II II M II •• II II 432 CALL CUT(LBVEL,TBVEL,MFX2) 4 3 3 Q II ii II ii ii ii ii it ii ii ii ii ii it it n it ti it it it n n it II II II n n II 434 IF(MFX2.LT.MFXMAX) GOTO 501 435 IF(NED.EQ.2) GOTO 365 436 DPX=DPX*(1.0-MMFX2)/(MFX2-MMFX2)-20.0 437 NED=2 438 GOTO 910 4 3 9 Q ii II II ti II it II II it it tt II II II it n it it tt II tt it it n H ti n ti n II II if if it tt if n II n II it it it II II II n II II it II n II n II n II it II it II II II 440 501 CALL CALFLS(MFX1,MFX2,VSB2,MTOT,DTIME,FFF,VSU2,CBVEL,VSU1, 441 -AREAF1,V0LB2,IVOL,VOLB1,AREAF2,RB1,RB2,DIST,TBVEL) 442 Q n II II II II II II II II II II II ti II II n n II ti II II II ti tt tt it n n ii ti II II if II n II II II II II II i< fi II II II II II II II II II II II II II II II II II II •• •• 443 IF(NED.EQ.1) GOTO 368 444 IF(CBVEL.LT.TBVEL) GOTO 365 445 368 Y2=TBVEL-CBVEL 446 IF(Y1*Y2.LE.O.) GOTO 920 447 PX1=PX2 448 Y1=Y2 449 GOTO 910 450 C 451 C HAVING BRACKETED THE PRESSURE WHERE ERROR (Y)=0.0 ITERATE TO 452 C FIND EXACT PRESS. AND TEMP. 453 C 454 920 IF(Y2.EQ.O.) GOTO 950 • 455 PX30LD=PX2 456 930 PX3=(PX1*Y2-PX2*Y1 )/(Y2-Y1 ) 457 NUT=NUT+1 458 IF (NUT.LT.25) GOTO 980 459 91 WRITE(6,90) NUT 460 90 FORMATdH .'PROGRAM STOP DUE TO PRO BN ITERATIONS EXCEEDING'.14) 461 STOP 462 980 IF(DABS((PX3-PX30LD)/PX3).LT.EPS) GOTO 960 463 PX30LD=PX3 AC A P " 1 1 *' 1 1 " " " " " M " " " " " " " " " >• >• » II tt tt tl tt it H it H it II it ll II n it ft it II ti II II II II n II II II n II II II ii.ii n II n II II II II n II it ti ti II 170 465 CALL ENUFLS(PX3.P1,TU1,VSU1,MWMIX,TU2,VSU2,EU2,FFF,LBVEL,LAMBDA, 466 -GAM,NRC02,NRH20) 4g*7 ^ II II H ll ii ii ii ii ii ii ii ii ii ii ii ii ii u ii ii ii ii ii ii ii ii tt ii n it ii ti ll it it it tt ti •• ti II II II II II II ti it ii II it it it ti ti it ti ti n II ll II II ii II II II II II 468 HTCOEF=(THCOND/BORE)*((MPV*BORE/(VSB2*VISC))**HTEXP)/1000.0 469 DO=HTCOEF*AREAB*(TB2-TWALL)*HTFCN*DTIME 470 PDV=((P1+PX3)/2.)*DIV 471 .ENGY2 = ENGY 1+PDV-DO 472 C WRITE(6,739) ENGY2,ENGY1,PDV,DO,HTCOEF 473 C739 F0RMAT(1H ,'E2,E1,PDV,DO,HTCOEF '.5E12.4) 474 ETOT1=ENGY2/MT0T 4*75 Q it ii ii ii ii ii ii ii ii ii ii ii ii ii it ii ti ii ii ii ti n ii ii tt ii n n ti n n n n n ti n n n tt it it 11 n n n 11 it » n n n II it II it ti it ti n n n n n ti n 476 CALL TEMP(PX3,TB2,CC,MFX2,MTOT.EU2.VSU2,VTOT1,ETOT1,VSB2.IS) Q II II II tt 11 II tl ll ll ll tl tl II 11 II It It II II H tl tl It tt II ll N rl II 11 11 It 11 11 tl tt It II 11 It II tl tt II II II II ll ll II II II 11 fl 11 It II II II II II II'M II II 478 CALL CUT(LBVEL,TBVEL,MFX2) 4*7g Q H n u it H ii H II II tt ti n n II n II ti H ti ti tt H n it ti II tt n tt II it H it it ti ti ti II n II II u n ti H H H H II H H H it II H ti ti ti H II n II n 480 CALL CALFLS(MFX1,MFX2,VSB2,MTOT,DTIME,FFF.VSU2,CBVEL,VSU1, 481 -AREAF1,V0LB2,IVOL,VOLB1,AREAF2,RB1,RB2,DI ST,TBVEL) 4Q2 Q II II II II II tt II II tl II II II II It II II II tl ft tt II II It II 11 H It ft It 11 II U It II 11 11 II 11 H 11 II II tl 11 II II II II II II It II tl II II 11 11 II II II II II II 483 Y3=TBVEL-CBVEL 484 IF(Y1*Y3.LE.O.) GOTO 940 485 PX1=PX3 486 Y1=Y3 487 GOTO 930 488 940 PX2=PX3 489 Y2=Y3 490 GOTO 930 491 950 P2=PX2 492 GOTO 970 493 960 P2=PX3 494 970 V0LU2=VT0T1-V0LB2 49^ 5 FLMSPD = ( RB2-RB 1 ) / ( DT I ME ) 496 VFRBNT=(V0LB2/VT0T1)*100.0 497 FSR=CBVEL/LBVEL 498 PRB2=RB2*100.0 499 PAREAF=AREAF2*10000.0 500 V2=V2*(1E+06) 501 C ' 502 . WRITE(6,893) NI,V2,P2,TU2,TB2,MFX2,VFRBNT,CBVEL,LBVEL, 503 -FLMSPD,FSR,PRB2,PAREAF,DLF1,ENGY2 504 C 505 C WRITE(6,102) TB2,VISC,THCOND 506 C 102 FORMATdH ,'TB2 , VI SC , THCOND '.3E14.6//) 507 C 508 V2=V2/(1E+06) 509 PP2(IL,NI)=P2 510 TIM(IL.NI)=TIME 511 VV2(IL.NI)=V2 512 DI(IL,(NI-1))=DABS(DIV) 513 MF(IL.NI)=MFX2 514 CB(IL,NI)=CBVEL 515 TB(IL.NI)=LBVEL 516 FSUL.NI ) = FLMSPD 517 RB(IL,NI)=RB2*100.0 518 C 519 V0LB1=V0LB2 520 AREAF 1 =AREAF2 521 RB1=RB2 522 TU1=TU2 171 523 MFX1=MFX2 524 VSU1=VSU2 525 P1=P2 526 V1=V2 527 T1=T2 528 ENGY1=ENGY2 529 T1=T2 530 DCA=PDCA 531 IV0L=2 532 NUT=0 533 NED=1 534 533 NUTT=NUTT+1 535 IF(NUTT.LT.50) GOTO 333 536 WRITE(6.90) NUTT 537 STOP 538 333 CONTINUE 539 C 540 C 541 365 T1=TB2 542 MFX2=MFX1 543 NUT=0 544 ddd=1 545 NNN =1 546 IF(NED.E0.2) GOTO 396 547 548 C START EXPANSION STROKE 549 C ====================== 550 C 551 310 DIV=DVOL(DLF1+DCA)-DVOL(DLF1) 552 V2=V1+DIV 553 IF(V2.LT.497.0E-06) GOTO 851 554 DLF1=DLF1+DCA 555 IF(DLF1.GE.540) ddd=2 556 TIME=(DLF1-180.0)/(6.0*SPEED) 557 NI=NI+1 558 P2=P1*(V1/V2) 559 GOTO 718 560 851 DLF1=DLF1+DCA 561 DIST=DV0L(DLF1)/(3.14159*((BORE/2.)**2)) 562 TIME=(DLF1-180.0)/(6.0*SPEED) 563 NI=NI+1 564 NUT=NUT+1 565 IF(NUT.GT.80) STOP 566 396 AT0T = 3. 14159*(2.*RDASH*HTCLRV+((BORE/2. )**2 ) + 2.*(BORE/2.)*DIST) 567 CALL EXP(P1,V1,T1,P2,V2,T2,CC,SUMXS,ENGY1.ENGY2.AT0T,DTIME) 568 718 ENGY1=ENGY2 569 P1=P2 570 T1=T2 571 V1=V2 572 P4=P2 573 PP2(IL,NI)=P4 574 VV2(IL.NI)=V2 575 TIM(IL,NI)=TIME 576 DI(IL,(NI-1))=DABS(DIV) 577 MF(IL,NI)=MFX2 578 CB(IL,NI)=0.0 579 TB(IL,NI)=0.0 580 FS(IL,NI)=0.0 172 581 RB(IL,NI)=0.0 582 C 583 V4 = V2 584 T4=T1 • 585 V4=V4*(1E+06) 586 C 587 WRITE(6,893) NI,V4,P4,X(1),T4,MFX2,VFRBNT,(X(I),1=1,6),DLF1, 588 -ENGY2 589 C 590 DCA=PDCA 591 IF (ddd.EQ.1) GOTO 310 592 C 593 C THIS SECTION CALCULATES INTEGRAL OF PDV (PDV),MEAN EFFECTIVE 594 C PRESSURE (MEP),POWER AND THERMAL EFFICIENCY. 595 C 596 C 597 304 PDV=0.0 598 SUMDI=0.0 599 AREA1=0.0 600 AREA3=0.0 601 MTDC=KTDC-1 602 DO 300 d=1,MTDC 603 300 AREA1=AREA1+(PP2(IL,d)+PP2(IL,(d+1)))*DI(IL,d)/2.0 604 NTDC=KTDC+1 605 NID=NI-1 606 DO 302 d=NTDC,NID 607 302 AREA3 = AREA3+(PP2(IL,d)+PP2(IL,(d+1 ) ))*DI(IL,d)/2.0 608 DO 303 d=1,MTDC 609 303 SUMDI=SUMDI+DI(IL,d) 610 VA1=CYLV-SUMDI 61 1 VA2=DI(IL,KTDC)-VA1 612 PPTDC=PP2(IL,KTDC)+((VA1/DI(IL,KTDC))*(PP2(IL,NTDC)-613 -PP2(IL,KTDC))) 614 AREA2=(PPTDC+PP2(IL,KTDC) )*VA1/2.0 615 AREA4=(PPTDC+PP2(IL,NTDC))*VA2/2.0 616 WRITE(6,486) AREA 1,AREA2,AREA3,AREA4,VA1,VA2,PPTDC,PDV 617 486 FORMAT(1H ,'A1,A2,A3,A4.VA1,VA2,PTDC,PDV'.8E12.4/) 618 PDV=(AREA3+AREA4)-(AREA1+AREA2) 619 MEP=PDV/(CYLV*100.0) 620 POWER=(PDV*SPEED/120.) 621 622 EFF=(PDV*100.)/(MOLFL*QVS*(12.*CN+HM)) C 623 WRITE(6,301) POWER,MEP,EFF 624 301 FORMAT(10X,6HP0WER=,F8.3,5X,9HI.M.E.P.=,F7.3,5X,11HEFFICIENCY; 625 -FIO.5///) 626 c 627 c 628 NUMM=1 629 ISPK=IDINT(SPKAD) 630 WRITE(6,933) NUMM,SPEED.ISPK,KFUEL 631 933 FORMAT(14,F8.1,14,13) 632 DO 478 dK=1,180 633 WRITE(6,480) PP2(IL,JK),MF(IL,JK) ,CB(IL,dK),TB(IL,dK), -634 -FS(IL,dK),RB(IL,dK) 635 480 FORMAT(6F10.4) 636 478 CONTINUE 637 c 638 222 CONTINUE 173 839 C = 640 C 641 C 642 C THIS SECTION GENERATES A P-V DIAGRAM AND A 643 C PRESSURE-CRANK ANGLE DIAGRAM. 644 C 645 C 646 387 DO 605 IL=1,NUMBR 647 DLF=180.0 648 ZZ(IL,1)=2.0 649 DO 605 d=1,NID 650 VV(IL,d)=VV2(IL,d)*1000. 651 PP(IL,d)=PP2(IL,d)/100. 652 DLF=DLF+PDCA 653 DL(IL,(d+1))=DLF 654 c XX(IL.d) = (5. * W ( I L , d ) )+2.0 655 YY(IL,d)=(PP(IL.J) /20. )+2.0 656 ZZ(IL,(d+1))=((DL(IL,(J+1))-180.0)/60.0)+2.0 657 605 CONTINUE 658 659 c CALL AXIS(2. ,2 . , 'VOLUME (L ) ' , - 10.5. , 0 . , 0 . . 0 . 2 ) 660 c CALL AXIS(2. ,2. , 'PRESSURE (BAR ) ' , 1 4 , 5 . , 9 0 . , 0 . , 2 0 . ) 661 c DO 607 IL=1,NUMBR 662 c DO 607 1=1,NID 663 c 607 CALL SYMBOL(XX( IL , I ) ,YY( IL , I ) ,0 .05 , IL ,0 . , -1 ) 664 c CALL LINE(XX(1, I ) ,YY(1, I ) ,NID,1) 665 666 CALL PLOT(10 . ,0 . , -3 ) 667 CALL AXIS(2. .2. ,'CRANK ANGLE' , -11 ,6 .0 ,0 . ,180. ,60.) 668 CALL AXIS(2. ,2. , 'PRESSURE (BAR ) ' , 14,5. ,90. , 0 . ,20 . ) 669 DO 415 IL=1.NUMBR 670 DO 415 1=1,NID 671 415 CALL SYMB0L(ZZ( IL , I ) ,YY( IL , I ) ,O .05 , IL ,0 . , -2 ) 672 c CALL LINE(ZZ(1, I ) ,YY(1, I ) .84,1) 673 CALL PLOTND 674 599 STOP 675 END 676 c 677 678 c 679 c SUBROUTINE TEMP CALCULATES TEMP. OF BURNT GAS AND MASS FRACTION 680 c =============== BURNED. 681 c 682 SUBROUTINE TEMP(P1,TB2,CC,MFX,MTOT,EU2,VSU2,VTOT1,ET0T,VSB2, 683 -is) 684 c 685 COMMON /AREA 1/ NCH,N02,K,L,M,N,KFUEL 686 COMMON /ARE*A2/ MOLFL , NMIX , HF 1 , NN02 , NN2 , NNFUEL , KOM 687 COMMON /AREA4/ NDISS,IPRINT 688 c 689 REAL*8 XF.DX.EPS,Y1,Y2,Y3.XX2,YY2, 690 -X1,X2,X3,X30LD,P1,P2,P3,CC(10),X(10),K,L,M,N,GAMMA,MFX,MTOT 691 -,EU2,VSU2,VTOT1,VSB2,EB2,TB2,ETOT,VTOTC,NMIX,MFXE,MFXV 692 -,EPROD,SUMXS,NCH,N02,MOLFL,HF1,NN02,NN2,NNFUEL 693 c 694 K0M=K0M+1 695 IF(KOM.GT.10) GOTO 93 696 NUT=0 174 697 JDX=1 698 IDX=1 699 X1=1900.0 700 XF=3300.0 701 DX=200.0 702 EPS=0.001 703 5 CALL ENERGY(X1,P1,EPROD,SUMXS,CC,X,EB2,VSB2 704 MFXE=(ET0T-EU2)/(EB2-EU2) 705 C WRITE(6,777) X1 .ETOT,VTOT1,P1,EB2,MFXE 706 C 777 FORMAT(1H ,'X1,ETOT,VTOT1,P1,EB2,MFXE',6E12 707 IF(MFXE.GT.O.O) GOTO 10 708 X1=X1+DX 709 IF(XI.GT.XF) GOTO 91 710 . JDX = 2 711 GOTO 5 712 10 MFXV=(VT0T1/MT0T-VSU2)/(VSB2-VSU2) 713 Y1=MFXV-MFXE 714 IFCJDX.EO.1 ) GOTO 30 715 IF (Y1.LT.O.O) GOTO 30 716 DX=-DX/2. 717 IDX = 2 718 30 X2=X1+DX 719 IFCX2.GT.XF) GOTO 91 720 20 CALL ENERGYCX2.P1.EPROD,SUMXS,CC,X,EB2,VSB2 721 MFXE=(ET0T-EU2)/(EB2-EU2) 722 C 747 FORMATC1H ,'X2,MFXE.MFXV,VSB2,VSU2,EB2,EU2; 723 IF(MFXE.GT.O.O) GOTO 15 724 DX=DX/2. 725 IDX = 2 726 X2=X2-DX 727 NUT=NUT+1 728 IF(NUT.GT.30) GOTO 91 729 GOTO 20 730 15 IF(IDX.EQ. 1 ) GOTO 16 731 DX=DX/2. 732 16 MFXV=(VT0T1/MT0T-VSU2)/(VSB2-VSU2) 733 Y2=MFXV-MFXE 734 C WRITE(6,747) X2,MFXE,MFXV,VSB2,VSU2,EB2,EU2 735 IFCY1*Y2.LE.O.O) GOTO 25 736 X1=X2 737 Y1=Y2 738 NUT=NUT+1 739 IF(NUT.GT.60) GOTO 91 740 GOTO 30 741 25 IF(Y2.EQ.0.0) GOTO 50 742 IF(X2.GT.X1 ) GOTO 35 743 XX2=X2 744 YY2=Y2 745 X2 = X1 746 Y2 = Y1 747 X1=XX2 748 Y1=YY2 749 35 IF(MFXE.LT.10.0) GOTO 36 750 DX=DX/10.0 751 X2=X2-DX 752 GOTO 20 753 36 X30LD=X2 754 40 X3 = (X1*Y2-X2*Y1 )/(Y2-Y1 ) 175 755 NUT=NUT+1 756 IF (NUT.LT.150) GOTO 80 757 91 IS = 2 758 RETURN 759 93 WRITE(6,90) KOM 760 90 F0RMAT(1H .'PROGRAM STOP DUE TO TEMP ITERATIONS EXCEEDING'.14) 761 STOP 762 80 IF(DABS((X3-X30LD)/X3).LT.EPS) GOTO 60 763 X30LD=X3 764 CALL ENERGY(X3.P1,EPROD,SUMXS,CC,X,EB2.VSB2) 765 MFXE=(ET0T-EU2)/(EB2-EU2) 766 MFXV=(VT0T1/MT0T-VSU2)/(VSB2-VSU2) 767 Y3=MFXV-MFXE 768 C WRITE(6,767) X3,MFXE,MFXV,Y3 769 c 767 FORMATdH , ' X3, MFXE, MFXV, Y3' .4E12.4) 770 IF(Y1*Y3.LE.O.) GOTO 45 771 X1=X3 772 Y1=Y3 773 GOTO 40 774 45 X2 = X3 775 Y2 = Y3 776 GOTO 40 777 50 TB2=X2 778 GOTO 70 779 60 TB2=X3 780 70 MFX=(MFXE+MFXV)/2.0 781 \* 782 IF(IPRINT.NE.2) GOTO 765 783 WRITE(6, 112) TB2,MFXE,MFXV,EB2.VSB2 784 112 FORMAT(1H ,'TB2,MFXE,MFXV,EB2,VSB2;'.5E12.4) 785 786 765 IS=1 787 RETURN 788 END 789 c 790 c 791 c 792 c SUBROUTINE ENERGY TO CALCULATE THE ENERGY AND COMPOSITION OF 793 c =============== BURNED GAS AT A GIVEN TEMP. (T) AND PRESS. (P) 794 c INCLUDING THE EFFECTS OF DISSOCIATION. 795 c 796 SUBROUTINE ENERGY(T,P,EPROD,SUMXS,CC,X,EB2,VSB2) 797 c 798 IMPLICIT REAL*8(A-H,0-Z) 799 REAL*8 K,L,M,N,KE(6),NM,KK,MWBMIX,MW(10),NMIX,NCH,N02,MOLFL, 800 -NN02,NN2,NNFUEL,KC02,KH20,KN2,MPV 801 c 802 COMMON /AREA 1/ NCH,N02.K,L,M,N,KFUEL 803 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02,NN2,NNFUEL,KOM 804 COMMON /AREA3/ AREAB,HTEXP,MPV,HTFCN,TWALL,VISC,THCOND 805 COMMON /AREA4/ NDISS,IPRINT 806 c 807 DIMENSION X(10),CPG(10),UUU(10),DH(10),CC(10),SP(6),RES(6,4), 808 -SQT(6),SPP(6,4) 809 c 810 c IF TEMP. LESS THAN 1750K, SKIP DISSOCIATION CALCULATIONS 811 IF(T.LT.1750) GOTO 17 812 IF(NDISS.EO.O) GOTO 17 176 813 C IPRINT=1 814 C 815 C THE DISSOCIATION CAN INCLUDE THE FOLLOWING REACTIONS; 81G C (1) C02=CO+0.502, 817 C (2) H20=H2+0.502, 818 C (3) H20=OH+0.5H2, 819 C (4) NO=0.5N2+0.502, 820 C (5) H2=2H, 821 C (6) 02=20. 822 C IF NDISS=1, REACTIONS 1 & 2 ARE INCLUDED, 823 C IF NDISS=2, REACTIONS 1,2,3 & 4 ARE INCLUDED, 824 C IF NDISS=3, REACTIONS 1,2,3,4,5 & 6 ARE INCLUDED. 825 C 82G C THE FOLLOWING LINES CALCULATE THE EQUILIBRIUM CONSTANTS FOR EACH 827 C REACTION 1 TO 6, INCLUDING THE (PO/P) TERM, 828 C ALSO, INITIALISE THE DISSOCIATED SPECIES CONCENTRATIONS, 829 C 830 DO 304 1=1,6 831 SP(I)=0.0 832 KE(I)=0.0 833 304 SPP(I,4)=0.0 834 C 835 GOTO(302,301,300).NDISS 836 300 KE(6)=DEXP(DL0G(T)**(-6.93319)*(-434283OO)+19.3O67)*(101.3/P) 837 KE(5)=DEXP(DL0G(T)**(-6.81208)*(-30743900)+17.8668)*(101.3/P) 838 SP(6)=0.000 839 SP(5)=0.000 840 301 KE(4)=DEXP(DL0G(T)**(-7.3355O)*(-1659255O)+1.80127) 841 KE(3)=DEXP(DL0G(T)**(-7.04570)*(-30372100)+10.159) 842 -*DSQRT(101.3/P) 843 SP(4)=0.000 844 SP(3)=0.000 845 302 KE(2)=DEXP(DLOG(T)**(-6.86740)*(-18878550)+8.7095) 846 -*DSQRT(101.3/P) 847 KE(1)=DEXP(DL0G(T)**(-7.4721O)*(-6554900O)+10.53) 848 -*DSQRT(101.3/P) 849 SP(2)=0.1 850 SP(1)=0.1 851 C 852 IF(I PRINT.NE. 1) GOTO 650 853 C 854 WRITE(6,21) (KE(IJK),IJK=1,6) 855 21 FORMAT(1H ,'KE(1-6) '.6E13.3) 856 C 857 C 858 C DEFINE UNIVERSAL GAS CONSTANT AND SET ITERATION COUNTER TO ZERO, 859 650 RM0L=8.3143 860 NUT=0 861 C 862 C START DISSOCIATION ITERATION ROUTINE. A PROPORTIONAL CHOPPING 863 C ITERATION TECHNIQUE IS USED TO SOLVE FOR THE VARIOUS SPECIES 864 C CONCENTRATIONS AT THE GIVEN TEMPERATURE AND PRESSURE.... 865 C 866 10 QQ=0 867 C 868 C THIS SECTION ENSURES THAT ITERATIONS CANNOT CONTINUE INDEFINATELY, 869 NUT=NUT+1 870 IF(NUT.LT.150) GOTO 400 177 871 WRITE(6,401) NUT 872 401 F0RMAT(1H .'PROGRAM STOP DUE TO ENERGY ITERATIONS EXCEEDING'.14) 873 STOP 874 C 875 400 NSP=2*NDISS 876 C 877 C STEP I FROM 1 TO NUMBER OF DISSOCIATION REACTIONS... 878 DO 600 I=1,NSP 879 C 880 NUTT=0 881 IFLAG1=0 882 C 883 S=(SP(1)+SP(2)+SP(3))/2+(SP(5)+SP(6)+K+L+M+N) 884 C 885 IF(IPRINT.NE.1) GOTO 651 886 C 887 WRITE(6.20) I , ( SP(IJK),IJK=1,6 ) ,S 888 20 FORMATdH . ' I , SP( 1-6 ) . S '.I4.7E9.2) 889 C 890 C 891 C INITIAL GUESS AT SPECIES CONCENTRATION... 892 651 J=1 893 SP(I)=0.000001 894 SPP(I,J)=SP(I) 895 GOTO(450,451,452,453,454,455),I 896 1 CONTINUE 897 C 898 IF(IPRINT.NE.1) GOTO 9 899 C 900 WRITE(6.19) I,SP(I),RES(I,1) 901 19 FORMATdH , ' I , SP , RES 1 '.I4.2E10.3) 902 C 903 C 904 C SECOND AND SUCCESSIVE GUESSES AT SPECIES CONCENTRATION... 905 9 J=2 906 STEP=0.1 907 IF(T.LT.2000) STEP=0.02 908 IF(T.GT.2400) STEP=0.4 909 SP(I)=SP(I)+STEP 910 IF(SP(I).GT.10) GOTO 500 911 SPP(I.J)=SP(I ) 912 IFLAG1=0 913 GOTO(450,451,452,453,454.455),I 914 2 CONTINUE 915 C 916 IF(IPRINT.NE.1) GOTO 652 917 C 918 WRITE(6,18) I,SP(I),RES(I,1).RES(I.2) 919 18 FORMATdH . ' I , SP . RES 1 , RES2 ' , 14 , 3E 1 1 . 3/) 920 C '• 921 C 922 C IF RESIDUAL CROSSES ZERO BETWEEN PREVIOUS AND CURRENT GUESSES 923 C THEN GO TO PROPORTIONAL CHOPPING ROUTINE, OTHERWISE CONTINUE 924 C INCREMENTING SPECIES CONCENTRATION... 925 652 IF((RES(I,1 )*RES(I,2)).LE.0.0) GOTO 5 926 RES(I,1)=RES(I,2) 927 SPP(I,1 ) =SPP(1,2) 928 GOTO 9 178 929 C 930 5 IF(RES(I,2).E0.O) GOTO 500 931 SPOLD=SPP(I,2) 932 J=3 933 C 934 C FIND VALUE OF SPECIES CONCENTRATION (SP(I)) AT WHICH RESIDUAL 935 C BECOMES SMALL, I.E. WHEN PREVIOUS 'SP' EQUALS CURRENT 'SP' TO 936 C WITHIN ONE PERCENT... 937 6 SP(I)=(SPP(I,1)*RES(I,2)-SPP(I,2)*RES(I,1))/(RES(I,2)-RES(I,1)) 938 IF(DABS((SP(I)-SP0LD)/SP(I)).LT.O.O1) GOTO 500 939 SPOLD=SP(I) 940 C 941 GOTO(450,451,452,453,454,455),I 942 3 CONTINUE 943 C 944 IF(IPRINT.NE.1) GOTO 654 945 C 946 WRITE(6,15) I , SP(I ) ,RES(I,1),RES(I,3) 947 15 F0RMAT(1H ,'I,SP,RES 1.RES3 '.I4.3E11.3) 948 C 949 C 950 654 IF(RES(I,1)*RES(I,3).LE.0.0) GOTO 4 951 SPP(I.1 )=SP(I) 952 RES(I,1 )=RES(I,3) 953 GOTO 6 954 4 SPP(I,2)=SP(I) 955 RES(I,2)=RES(I,3) 956 GOTO 6 957 C 958 C IF VALUE OF SP(I) FROM CURRENT SPECIES CALCULATIONS EQUALS THE 959 C VALUE OF SP(I) FROM THE PREVIOUS SET OF SPECIES CALCULATIONS AT 960 C THE SAME TEMPERATURE, THEN LEAVE QQ=0, OTHERWISE SET QQ=1 WHICH 961 C WILL CAUSE ANOTHER SET OF CALCULATIONS TO BE PERFORMED... 962 500 IF(DABS((SP(I )-SPP(I.4) )/(SP(I))).GT.0.05) QQ=1 963 SPP(I,4 ) = SP(I ) 964 GOTO 600 965 C 966 C THIS SECTION CALCULATES THE RESIDUALS FOR EACH SPECIES USING 967 C THE CURRENT VALUES OF SP(1-6). 968 450 SQT(1)=M+((SP(1)+SP(2)-SP(4))/2)-SP(6) 969 IF(SQT(1).LE.O.O) GOTO 456 970 RES(1,J)=SP(1)/(K-SP(1))*DSQRT(SQT(1)/S)-KE(1) 971 GOTO 460 972 451 SQT(2)=M+((SP(1)+SP(2)-SP(4))/2)-SP(6) 973 IF(SQT(2).LE.O.O) GOTO 456 974 RES(2,J) = (SP(3)/2+SP(2)-SP(5) )/(L-SP(3)-SP(2))*DSQRT(SQT(2)/S) 975 1-KE(2) 976 GOTO 460 , 977 452 SQT(3)=SP(3)/2+SP(2)-SP(5) 978 IF(SQT(3) .LE.O.O) GOTO 456 979 RES(3,d)=(SP(3))/(L-SP(3)-SP(2))*DSQRT(SQT(3)/S)-KE(3) 980 GOTO 460 981 453 SQT(4)=(N-SP(4)/2)*(M-SP(6)+(SP(1)+SP(2)-SP(4))/2) 982 IF(SQT(4).LE.O.O) GOTO 456 983 RES(4,J)=SP(4)/DSQRT(SQT(4))-KE(4) 984 GOTO 460 985 454 SQT(5)=SP(3)/2+SP(2)-SP(5) 986 IF(SQT(5).LE.O.O) GOTO 456 179 987 RES(5.J)=(4*SP(5)*SP(5))/S/SOT(5)-KE(5) 988 GOTO 460 989 455 SQT(6)=M-SP(6)+(SP(1)+SP(2)-SP(4))/2 990 IF(S0T(6).LE.0.0) GOTO 456 991 RES(6,J)=(4*SP(6)*SP(6))/S/SOT(6)-KE(6) 992 456 SP(I)=SPP(I,4) 993 GOTO 600 994 460 NUTT=NUTT+1 995 C 996 IF(IPRINT.NE.1) GOTO 655 997 C 998 WRITE(6,22) NUTT.RES(I,0),SQT(I),IFLAG1 999 22 F0RMAT(1H ,'NUT,RES(I,J),5QT(I),FLAG ',13,2E14.5,13) 1000 C 1001 C 1002 655 IF(NUTT.LT.50) GOTO 16 1003 WRITE(6,401) NUTT 1004 STOP 1005 16 GOTO(1,2,3),d 1006 C 1007 600 CONTINUE 1008 C 1009 A=SP(1) 1010 B=SP(3) 1011 C=SP(2) 1012 D=SP(4) 1013 E=SP(5) 1014 F=SP(6) 1015 C 1016 IF(IPRINT,NE.1) GOTO 656 1017 C 1018 WRITE(6,14) T , A , B,C.D,E,F 1019 .14 F0RMAT(1H , ' T , A ,B , C , D , E , F ' , F8 . 1 , 6E 10. 3/) 1020 C 1021 656 IF(00)461,461 , 10 1022 C 1023 C 1024 461 CONTINUE 1025 C 1026 C CALCULATING CHANGE IN ENTHALPIES FOR SPECIES 1 TO 10 BET. T AND 289K 1027 C C02=1, C0=2, H20=3. H2=4, 02=5, N2=6, N0=7, H=10, 0=9, 0H=8 1028 KK=0 1029 17 TT=T/100 1030 IF (T.GT.3000.0) GOTO 99 1031 DH(1)=((3.096*T+O.O0273*(T**2)-7.885E-07*(T**3) 1032 1+8.66E-11*(T**4))-1145.0)*RMOL 1033 DH(2)=((3.317*T+3.77E-04*(T**2)-3.22E-08*(T**3) • 1034 1-2.195E-12*(T**4))-1022.0)*RM0L 1035 DH(3)=((3.743*T+5.656E-04*(T**2)+4.952E-08*(T**3) 1036 1-1 .818E-11*(T**4))-1167.0)*RM0L 1037 DH(4)=((3.433*T-8.18E-06*(T**2)+9.67E-08*(T**3) 1038 1-1.444E-11*(T**4))- 1025.0)*RM0L 1039 DH(5)=((3.253*T+6.524E-04*(T**2)-1.495E-07*(T**3) 1040 1+1.539E-11*(T**4))-1024.0)*RMOL 1041 DH(6) = ((3.344*T+2.943E-04*(T**2)+1.953E-09* (T**3) 1042 1-6.575E-12*(T**4))- 1023.0)*RMOL 1043 DH(7)=((3.502*T+2.994E-04*(T**2)-9.59E-09*(T**3) 1044 ' 1-4.904E-12*(T**4))-1070.0)*RM0L 180 1045 DH(10)=((2.5*T)-745.0)*RM0L 1046 DH(9)=((2.764*T-2.514E-04*(T**2)+1.002E-07*(T**3) 1047 1-1.387E-11*(T**4))-804.0)*RM0L 1048 DH(8) = ((81. 546*TT-47.48*(TT**1.25)+9.902* ( TT** 1 .75) 1049 1-2.133*(TT**2.))* 100-10510) 1050 GOTO 91 1051 99 DH(1)=((5.208*T+0.00059*(T**2)-5.614E-08*(T**3) 1052 1+2.05E-12*(T**4))-1126.0)*RMOL 1053 DH(2)=((3.531*T+2.73E-04*(T**2)-3.28E-08*(T**3) 1054 1 + 1.565E-12*(T**4))- 1042.0)*RM0L 1055 DH(3)=((149.05*TT-146.83*(TT**1.25)+55.17*(TT**1.5) 1056 1-1.85*(TT**2.))*100-11945.0) 1057 DH(4)=((3.213*T+2.87E-04*(T**2)-2.29E-08*(T**3) 1058 1+7.666E-13*(T**4))-1018.0)*RMOL 1059 DH(5)=((3.551*T+3.203E-04*(T**2)-2.876E-08*(T**3) 1060 1+1.005E-12*(T**4))-1044.0)*RMOL 1061 DH(6)=((3.514*T+2.583E-04*(T**2)-2.841E-08*(T**3) 1062 1 + 1 .242E-12*(T**4))-1043.0)*RM0L 1063 DH(7) = ((3.745*T+1.950E-04*(T**2)- 1.88E-08* (T**3) 1064 1+7.703E-13*(T**4))-1106.0)*RM0L 1065 DH(10)=((2.5*T)-745.0)*RM0L 1066 DH(9)=((2.594*T-3.843E-05*(T**2)+7.514E-09*(T**3) 1067 1-3.2O9E-13*(T**4))-8O9.O)*RM0L 1068 DH(8) = ((81.546*TT-47.48*(TT**1.25)+9.902* (TT**1.75) 1069 1-2.133*(TT**2.))*100-10560.) 1070 C 1071 C CALCULATE CONSTANT PRESSURE SPECIFIC HEATS 1072 91 CPG( 1 ) = -3.7357+30.529*(TT**(0.5))-4.1034*TT+0.024198* ( TT**2) 1073 CPG(2)=69.145-.70463*(TT**(0.75))-200.77 *(TT**(-0.5)) 1074 -+176.76*(TT**(-0.75)) 1075 CPG(3) = 143.05-183.54*(TT**(0.25))+82.751*(TT**(0. 5)) 1076 --3.69889*TT 1077 CPG(4) = 56.505-702.74*(TT**(-.75))+1165.0/TT-560.7*(TT**(- 1.5)) 1078 CPG(5)=37.432+0.020102*(TT**1.5)- 178.57*(TT**(- 1.5)) 1079 -+236.88*(TT**(-2)) 1080 CPG(6)=39.060-512.79*(TT**(-1.5))+1072.7*(TT**(-2)) 1081 --820.4*(TT**(-3)) 1082 CPG(7) = 59.283-1.7096*(TT**0.5)-70.613*(TT* *(-0. 5)) 1083 -+74.889*(TT**(-1.5)) 1084 CPG(8)=81.546-59.35*(TT**0.25)+17.329*(TT**0.75)-4.266*TT 1085 C 1086 C CALC. NUMBER OF MOLES OF EACH SPECIES AFTER DISSOCIATION 1087 X(1)=K-A 1088 X(2)=A 1089 X(3)=L-B-C 1090 X(6)=N-D/2 1091 X(7)=D 1092 X(4)=C+B/2-E 1093 X(5)=M-F+(A+C-D)/2 1094 X(10)=2*E 1095 X(9)=2*F 1096 X(8)=B 1097 C 1098 C CALC. VISCOSITY & THERMAL CONDUCTIVITY OF PRODUCTS... 1099 VC02=((0.019*T+24.2)*X(1)* 1E-06)/(X(1)+X(3)+X(6)) 1100 KC02=((0.041*T+36.1)*X(1)*1E-03)/(X(1)+X(3)+X(6)) 1 101 VH20=((0.025*T+15.8)*X(3)*1E-06)/(X(1)+X(3) + X(6)) 1 102 KH20=((O.130*T-0.60)*X(3)*1E-03)/(X(1)+X(3) + X(6)) 181 1103 VN2 = ((0.019*T+24.1)*X(6)* 1E-06)/(X(1) + X(3)+X(6)) 1104 KN2=((0.039*T+35.8)*X(6)*1E-03)/(X(1)+X(3) + X (6)) 1105 VISC=VC02+VH20+VN2 1106 THC0ND=KC02+KH20+KN2 1107 C 1108 C ENTHALPY OF FORMATION FOR EACH SPECIES... 1109 UUU(1)=-3.93522E05 1110 UUU(2)=-1.10529E05 1111 UUU(3)=-2.41827E05 1112 UUU(4)=0.00000E00 1113 UUU(5)=0.00000E00 1114 UUU(6)=0.00000E00 1115 UUU(7)=9.05920E04 1116 UUU(10)=2.17986E05 1117 UUU(9)=2.49195E05 1118 UUU(8)=39463.0 1119 C 1120 C MOLECULAR WEIGHT FOR EACH SPECIES... 1121 MW(1)=44.01 1122 MW(2)=28.01 1123 MW(3)=18.01 1124 MW(4)=2.02 1125 MW(5)=32.00 1126 MW(6)=28.01 1127 MW(7)=30.00 1128 MW(8)=17.00 1129 MW(9)=16.00 1130 MW(10)=1.00 1131 C 1132 C CALC. ENERGY OF PRODUCTS 1 TO 10 1133 EPROD=0. 1134 DO 109 1=1,10 1135 ECOMP=X(I)*(UUU(I)+DH(I)-RMOL*T) 1136 IF(M0DE.E0.3) ECOMP = X(I)*(UUU(I)+DH( I ) ) 1137 EPROD=EPROD+ECOMP 1138 109 CONTINUE 1 139 C 1140 C CALCULATE SUM OF X VALUES 1141 SUMXS=0 1 142 ,D0 231 ILG=1,10 1143 231 SUMXS=SUMXS+X(ILG) 1 144 C 1145 C CALC PERC. OF PRODUCTS AND MOLECULAR WEIGHT OF MIXTURE 1146 MWBMIX=0.0 1147 DO 232 ILH=1,10 1148 CC(ILH)=(X(ILH)/SUMXS)*100. 1149 232 MWBMIX=MWBMIX+(CC(ILH)*MW(ILH)/100.) 1150 EB2=EPR0D/MWBMIX/SUMXS 1151 VSB2=RM0L*T/(MWBMIX*P) 1152 C 1153 C CALC. AVERAGE SPECIFIC HEATS FOR MIXTURE... 1154 CP=0 1155 DO 233 ILF=1,8 1156 233 CP=CP+(CC(ILF)*CPG(ILF))/100. 1157 CV=CP-RM0L 1158 GAMMA=CP/CV 1159 C 1160 C 182 1161 IF(IPRINT.NE.1) GOTO 764 1162 WRITE(6,B89) MWBMIX,EB2.VSB2,GAMMA,NDISS 1163 889 FORMAT(1H ,'MWBMIX,EB2.VSB2,GAMMA,NDS '.4E12.4.I3) 1164 C 1 165 C 1166 764 RETURN 1167 END 1168 C 1 169 C 1170 C SUBROUTINE CALFLS THIS IS USED TO OBTAIN THE CALCULATED 1171 C ================= BURNING VELOCITY 1 172 C 1173 SUBROUTINE CALFLS(MFX1,MFX2,VSB2,MTOT,DTIME,FFF,VSU2.CBVEL, 1174 -VSU1,AREA 1,V0LB2,IVOL,VOLB1,AREA2,RB1,RB2,DIST,TBVEL) 1175 C 1176 REAL*8 RF,DR,EPS,Y1,Y2,Y3.BORE,D,XDOT,ARAVG,AREA, 1177 -R1,R2.R3,R30LD,DTIME,RMAX,R,VOLB1,MFX2,AREA 1,AREA2.RB1,RB2, 1178 -FFF,MFX,VSB2.VSU2,MTOT,MFX1,V0LB2,VOLB,CBVEL,VSUAVG,VSU1.RADBMB 1179 -,DIST,TBVEL 1180 C 1181 COMMON /AREA4/ NDISS,IPRINT 1182 C 1183 V0LB2=MT0T*MFX2*VSB2 1184 C CALC. MAXIMUM RADIUS WHICH FLAME CAN ATTAIN 1185 C GIVEN THE POSITION OF THE PISTON IN THE CYLINDER (DIST)... 1186 RMAX=DSORT(((0.018358+DIST)**2)+(0.0425**2)) 1187 IF(IVOL.E0.2) GOTO 546 1188 RB1=0.0001 1189 CALL V0L(RB1,DIST,AREA,VOLB) 1190 V0LB1=V0LB 1191 AREA 1=AREA 1192 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1193 C 546 WRITE(6,201) VOLM1,AREA 1,RMAX,V0LB2 1194 C 201 F0RMAT(1H ,'VOLM1,AREA 1,RMAX,V0LB2, '.4E12.5) 1195 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1196 C 1197 C ITERATION PROCEDURE FINDS RADIUS AND AREA OF NEW BURNT VOLUME 1198 546 NUT=0 1199 R1=0.0001000 1200 RF=RMAX 1201 DR=0.01 1202 EPS=0.0001 1203 CALL V0L(R1.DIST,AREA,VOLB) 1204 Y1=V0LB2-V0LB 1205 10 R2=R1+DR 1206 IF(R2.GT.RF) R2=RF 1207 CALL V0L(R2,DIST,AREA,VOLB) 1208 Y2=V0LB2-V0LB 1209 IF(Y1*Y2.LE.O.) GOTO 20 1210 R1=R2 1211 Y1=Y2 1212 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1213 C WRITE(6,200) R2.Y2 1214 C 200 F0RMAT(1H ,'R2,Y2 = '.2E14.6/) 1215 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX .1216 NUT=NUT+1 1217 IF (NUT.LT.20) GOTO 13 1218 WRITE (6,90) NUT 183 1219 STOP 1220 13 GOTO 10 1221 20 I F ( Y 2 . E 0 . O . ) GOTO 50 1222 R30LD=R2 1223 30 R 3 = ( R 1 * Y 2 - R 2 * Y 1 ) / ( Y 2 - Y 1 ) 1224 c x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 1225 c W R I T E ( 6 , 3 0 3 ) R3 1226 c 303 F O R M A T d H , ' R 3 = ' . E 1 2 . 5 ) 1227 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1228 NUT=NUT+1 1229 IF ( N U T . L T . 1 5 0 ) GOTO 80 1230 W R I T E ( 6 , 9 0 ) NUT 1231 90 F O R M A T d H .'PROGRAM STP DUE TO C A L F L S ITERATIONS E X C E E D I N G ' , 1 4 ) 1232 STOP 1233 80 " I F ( D A B S ( ( R 3 - R 3 0 L D ) / R 3 ) . L T . E P S ) GOTO 60 1234 R30LD=R3 1235 CALL V 0 L ( R 3 , D I S T , A R E A , V O L B ) 1236 Y3=V0LB2-V0LB 1237 I F ( Y 1 * Y 3 . L E . O . ) GOTO 40 1238 R1=R3 1239 Y1=Y3 1240 GOTO 30 1241 40 R2 = R3 1242 Y2 = Y3 1243 GOTO 30 1244 50 RB2=R2 1245 GOTO 99 1246 60 RB2=R3 1247 99 CALL V 0 L ( R B 2 , D I S T . A R E A , V O L B ) 1248 AREA2=AREA 1249 ARAVG=(AREA1+AREA2)/2. 1250 VSUAVG=(VSU1+VSU2)/2. 1251 XDOT=(MFX2-MFX1)/DTIME 1252 CBVEL=MTOT*XDOT*VSUAVG/ARAVG 1253 «— L. 1254 I F ( I P R I N T . N E . 2 ) GOTO 70 1255 W R I T E ( 6 , 2 2 1 ) V O L B 1 , V 0 L B 2 , R B 1 , R B 2 , A R E A 1 , A R E A 2 , C B V E L , T B V E L 1256 221 FORMAT(1H , ' V 1 , V 2 , R 1 , R 2 , A R 1 , A R 2 , C B V E L : ' , 8 E 1 2 . 4 / ) 1257 /"> _ L» -1258 70 RETURN 1259 END 1260 c 1261 c SUBROUTINE VOL TO CALCULATE THE VOLUME AND AREA OF BURNT GAS 1262 c ============ IN THE TOYOTA ENGINE COMBUSTION CHAMBER 1263 c GIVEN THE FLAME R A D I U S . . . . 1264 c 1265 SUBROUTINE V O L ( B R A D , D I S T , A R E A F , V O L B ) 1266 c 1267 COMMON / A R E A 3 / A R E A B , H T E X P , M P V , H T F C N , T W A L L . V I S C , T H C O N D 1268 c 1269 R E A L * 8 B R A D , D I S T , A R E A F , V O L B , B O R E , R , D , H , H T C L R V , R D A S H , C L R V , H A , 1270 • H V O L , R M A X , D D , A T O T , A R E A B , A R E A U , M P V , H T F C N , T W A L L , V I S C , T H C O N D 1271 • , H T E X P 1272 c 1273 c TO C A L C . THE VOLUME BURNT AND FLAME AREA IN 1274 c THE TOYOTA ENGINE COMBUSTION CHAMBER GIVEN THE 1275 c RADIUS OF THE F L A M E . . . . 1276 c 184 1277 203 B0RE=O.O85 1278 H T C L R V = 1 8 . 3 5 8 E - 0 3 1279 RDASH=58.3737E-03 1280 C L R V = 5 5 . 3 2 6 4 E - 0 6 1281 R=B0RE/2. 1282 R M A X = D S Q R T ( ( H T C L R V * * 2 ) + ( R * * 2 ) ) 1283 DD=HTCLRV+DIST 1284 A T 0 T = 3 . 1 4 1 5 9 * ( 2 . * R D A S H * H T C L R V + ( R * * 2 ) + 2 . * R * D I S T ) 1285 C 1286 I F ( B R A D . G T . R M A X ) GOTO 310 1287 H V 0 L = 0 . 2 5 * 3 . 1 4 1 5 9 * ( B R A 0 * * 3 ) * ( B R A D / R D A S H ) 1288 H A = 3 . 1 4 1 5 9 * ( B R A D * * 2 ) * ( B R A D / R D A S H ) 1289 H = 0 . 0 1290 I F ( B R A D . G T . D D ) GOTO 320 1291 D=BRAD 1292 AREAB = 3 . 1 4 1 5 9 * ( B R A D * * 2 ) 1293 GOTO 350 1294 320 D=HTCLRV+DIST-1295 AREAB = 3 . 1 4 1 5 9 * ( 2 . * ( B R A D * * 2 ) - ( D * * 2 ) ) 1296 GOTO 350 1297 C 1298 310 H V 0 L = ( 3 . 1 4 1 5 9 * ( R * * 2 ) * H T C L R V ) - C L R V 1299 HA=0.0 1300 H = D S Q R T ( ( B R A D * * 2 ) - ( R * * 2 ) ) 1301 I F ( B R A D . G T . D D ) GOTO 330 130'2 D=BRAD 1303 A R E A B = 3 . 1 4 1 5 9 * ( ( R M A X * * 2 ) + 2 . * R * ( H - H T C L R V ) ) 1304 GOTO 350 1305 330 D=HTCLRV+DIST 1306 A R E A B = 3 . 1 4 1 5 9 * ( ( R M A X * * 2 ) + 2 . * R * ( H - H T C L R V ) + ( B R A D * * 2 ) - ( D * * 2 ) ) 1307 C 1308 350 V 0 L B = ( 3 . 1 4 1 5 9 / 3 . 0 ) * ( 3 . * ( B R A D * * 2 ) * D - ( D * * 3 ) - 2 . * ( H * * 3 ) ) - H V O L 1309 A R E A F = 2 . 0 * 3 . 1 4 1 5 9 * B R A D * ( D - H ) - H A 1310 AREAU=ATOT-AREAB 1311 1312 C W R I T E ( 6 . 3 0 0 ) B R A D , A R E A F , V O L B , A R E A B , A T O T 1313 C 300 F O R M A T d H , ' B R A D . A R E A F , V O L B , A B , A T ' . 5 E 1 2 . 4 ) 1314 t> 1315 RETURN 1316 END 1317 c 1318 c 1319 c SUBROUTINE ENUFLS THIS CALCULATES THE PROPERTIES OF THE UNBURNT 1320 c =============== GAS AT THE GIVEN PRESS. BY FIRST CALCULATING 1321 c GAMMA AND THEN ASSUMING ISENTROPIC COMPRESSION 1322 c THE BURNING VELOCITY IS THEN CALCULATED USING THE UNBURNT GAS 1323 c TEMP. AND PRESS. USING PUBLISHED FORMULAE FOR GIVEN F U E L . 1324 c 1325 SUBROUTINE E N U F L S ( P 2 , P 1 , T 1 , V S U 1 , M W M I X , T U 2 , V S U 2 , E U 2 , F F F , T B V E L , A F 1326 •GGAM,NRC02,NRH20) 1327 c 1328 COMMON /AREA 1/ N C H , N 0 2 , K , L , M , N , K F U E L 1329 COMMON / A R E A 2 / M O L F L , N M I X , H F 1 , N N 0 2 , N N 2 , N N F U E L , K O M 1330 COMMON / A R E A 4 / N D I S S , I P R I N T 1331 c 1332 R E A L * 8 P 1 , T 1 , N N 0 2 , N N 2 , N M I X , T U 2 . V S U 2 . E U 2 , T B V E L , T T , N N F U E L , F F F , 1333 • C P G ( 1 4 ) , C P , C V , G A M U , D H ( 1 4 ) , E N G Y , N 0 2 , N , R M O L , V S U 1 , P O W 1 , P 0 W 2 , T T 2 , 1334 • M W M I X , P U , T U , P B A R 2 , P 2 , H F 1 , T , T 2 , P 0 W 3 , C 4 , A F , P B A R 1 , G G A M , B 1 , B 2 , B 3 , 185 1335 -NCH,K,L,M,MOLFL,FI,SUO(15),ALPHA(15) .BETA(15),NRC02,NRH20,UUU(3) 1336 C 1337 RM0L=8.31434 1338 NUT=0 1339 C 1340 C CALC. GAMMA, FOR THE UNBURNT ELEMENTS 1341 C 1342 NNFUEL=100.-(NN02+NN2) 1343 TT=T1/100. 1344 CPG(5) = 37.432+0.020102*(TT**1.5)-178.57*(TT**(- 1.5)) 1345 -+236.88*(TT**(-2)) 1346 CPG(6)=39J060-512.79*(TT**(-1.5))+1072.7*(TT**(-2)) 1347 --820.4*(TT**(-3)) 1348 CPG(11)=-672.87+439.74*(TT**0.25)-24.875*(TT**0.75)+323.88* 1349 -(TT**(-0.5)) 1350 CPG(13)=-4.042+30.46*TT-1.571*(TT**2.)+0.03171 *(TT**3.) 1351 CPG(12)=8.3143*(-0.72+0.09285*T1-5.05E-05*(T1**2.)+1.068E-08* 1352 -(T1**3)) 1353 CP=(NN02*CPG(5)+NN2*CPG(6)+NNFUEL*CPG(KFUEL))/100. 1354 CV=CP-RMOL 1355 GAMU=CP/CV 1356 IF (GGAM.GT.0.0) GAMU=GGAM 1357 C 1358 P0W1=(GAMU-1.)/GAMU 1359 P0W2=1./GAMU 1360 TT2=T1*((P2/P1)**P0W1 ) 1361 IF (GGAM.EO.0.0) GOTO 20 1362 T2=TT2 1363 GOTO 10 1364 20 CALL GAM(TT2,T1,GAMU) 1365 P0W1=(GAMU-1.0)/GAMU 1366 T2 = T1*((P2/P1 )**P0W1) 1367 c WRITE(6,30) T1 ,T2,TT2,GAMU 1368 c 30 FORMATdH , 'T 1 , T2 ,TT2 . GAMU ' , 4E 12 . 4 ) 1369 IF(DABS(TT2-T2).LE.1.0) GOTO IO 1370 NUT=NUT+1 1371 IF(NUT.GT.20) STOP 1372 TT2=T2 1373 GOTO 20 1374 10 P0W2=1.O/GAMU 1375 TU2=T2 1376 VSU2=VSU1*((P1/P2)**P0W2) 1377 c 1378 c CALC. ENTHALPY OF REACTANTS AT GIVEN TEMP. 1379 DH(1)=((3.096*T2+0.00273*(T2**2)-7.885E-07*(T2**3) 1380 1+8.66E-11*(T2**4))-1145.0)*RM0L 1381 DH(3)=((3.743*T2+5.656E-04*(T2**2)+4.952E-08*(T2**3) 1382 1-1.818E-1 1*(T2**4))-1167.0)*RMOL 1383 DH(5)=((3.253*T2+6.524E-04*(T2**2)-1.495E-07*(T2**3) 1384 1+1.539E-11*(T2**4))-1024.0)*RMOL 1385 DH(6)=((3.344*T2+2.943E-04*(T2**2)+1.953E-09*(T2**3) 1386 1-6.575E-12*(T2**4))- 1023.0)*RMOL 1387 DH(11)=((1.935*T2+4.965E-03*(T2**2.)-1.244E-06*(T2**3.) 1388 1+1.625E-10*(T2**4.)-8.586E-15*(T2**5.))-985.9)*RMOL 1389 DH(12)=((-0.72*T2+4.643E-02*(T2**2.)-1.684E-05*(T2**3.) 1390 1+2.67E-09*(T2**4.))-3484.O)*RMOL 1391 DH(13)=((1.137*T2+1.455E-02*(T2**2.)-2.959E-06*(T2**3.) 1392 1)-1552.9)*RM0L 186 1393 UUU(1)=-3.93522E05 1394 UUU(3)=-2.41827E05 1395 C CALC. TOTAL ENERGY OF MIXTURE (KJ/KMOL FUEL) 139G ENGY=(NCH*(HF1+DH(KFUEL)-RM0L*T2)+N02*(DH(5)-RM0L*T2) 1397 -+N*(DH(6)-RM0L*T2)+NRC02*(UUU(1)+DH(1)-RM0L*T2)+NRH20* 1398 -(UUU(3)+DH(3)-RM0L*T2) ) 1399 C CONVERT TO KJ/KMOL MIXTURE... 1400 ENGY=ENGY/NMIX 1401 c CONVERT TO KJ/KG MIXTURE... 1402 EU2=ENGY/MWMIX 1403 c CALC. AVERAGE UNBURNT TEMP. AND PRESS. 1404 PU=(P1+P2)/2. 1405 TU=(T1+T2)/2. 1406 c 1407 c CALCULATE LAMINAR BURNING VELOCITY: 1408 c 1409 c METGHALCHI & KECK'S EQN.S FOR PR0PANE(13), 0CTANE(12), 1410 c AND IND0LINEO4) 1411 c 1412 IF(KFUEL.EO.11) GOTO 501 1413 ' FI=1./AF 1414 IF(FI.GT.0.90) GOTO 87 1415 DATA SUO(13),SUO(12),SUO(14)/23.20,19.25,19.15/ 1416 DATA ALPHA(13),ALPHA(12),ALPHA(14)/2.27,2.36,2.27/ 1417 DATA BETA(13).BETA(12),BETA(14)/-0.23,-0.22,-0.17/ 1418 GOTO 89 1419 87 IF(FI.GT.1.10) GOTO 88 1420 DATA SUO(13),SUO(12),SUO(14)/31.90.27.00.25.21/ 1421 DATA ALPHA(13),ALPHA(12),ALPHA(14)/2. 13,2 . 26,2 . 19/ 1422 DATA BETA(13) ,BETA(12) .BETA(14)/-0.17,-0.18,-0.13/ 1423 GOTO 89 1424 88 CONTINUE 1425 DATA SUO(13),SUO(12),SUO(14)/33.80,27.63,28.14/ 1426 DATA ALPHA(13),ALPHA(12),ALPHA(14)/2.06.2.03,2.02/ 1427 DATA BETA(13).BETA(12) ,BETA(14 )/-0. 17,-0. 11,-0.087/ 1428 89 TBVEL=SUO(KFUEL)*((TU/298.)**ALPHA(KFUEL))* 1429 -((PU/100. )**BETA(KFUEL) ) 1430 GOTO 510 1431 c 1432 c ANDREWS AND BRADLEYS EQUATION FOR METHANE(11)... 1433 c 1434 c PBAR1=PU/100. 1435 c TBVEL=(10.0+0.000371*(TU**2. )*(PBAR1 * *(-0.5))) 1436 c 1437 c RYAN AND LESTZ'S EQN. FOR METHANE(11)... 1438 c 1439 501 B1=9655.5 1440 B2=-0.623 1441 B3=-2144.5/TU 1442 TBVEL=B1*((PU/100.)**B2)*DEXP(B3) 1443 GOTO 510 1444 c 1445 c AGRAWAL AND GUPTAS EQUATION FOR METHANE... 1446 c 1447 c 701 PBAR 1=PU/1(50.0 1448 c C4 = -418.0+1287.O/AF-1196.0/(AF**2) + 360.0/(AF* *3)-15.0*AF* 1449 c -DL0G10(PBAR1) 1450 c P0W3=1.68*DSQRT(AF) 187 1451 C IF(AF.GT.L) GOTO 65 1452 C POW3=1.68/DS0RT(AF) 1453 C 65 TBVEL=C4*((TU/300.0)**POW3) 1454 C 1455 C DIVIDE BY 100 TO CONVERT FROM CM/S TO M/S... 1456 C 1457 510 TBVEL=TBVEL/100.0 1458 C 1459 IF(IPRINT.NE.2) GOTO 763 1460 WRITE(6,100) TBVEL,VSU2,EU2,PU,TU,P2,T2 1461 100 FORMATdH . ' TBV, VSU2 , EU2 , PU. TU, P2 , T2 =',7E12.4) 1462 C 1463 763 RETURN 1464 END 1465 C 1466 C 1467 C SUBROUTINE GAM THIS CALCULATES THE AVERAGE RATIO OF SPECIFIC 1468 C ============== HEATS (GAMMA) OF AN UNBURNED GAS MIXTURE 1469 C BETWEEN TWO GIVEN TEMPERATURES. 1470 C 1471 SUBROUTINE GAM(T2,T1,GAMU) 1472 • C 1473 COMMON /AREA 1/ NCH,N02,K,L,M,N,KFUEL 1474 COMMON /AREA2/ MOLFL.NMIX.HF1,NN02.NN2,NNFUEL,KOM 1475 C 1476 REAL*8 T2.T1,NN02,NN2,NNFUEL,GAMU,TI,CPA(14),A 1.A2,R1,R2,S1.S2. 1477 -C1,C2,D1,D2,E1,E2,RMOL,CPAV,TT,NCH,N02,K.L,M,N,MOLFL,NMIX,HF1 1478 C 1479 C CALC. VALUES OF CP FOR THE COMBUSTIBLE MIXTURE; 1480 C 5=02. 6=N2, 11=CH4, 12 = C8H18, 13=C3H8, 14 = IND0LINE .'. . 1481 C 1482 RM0L=8.31434 1483 TT=T2/100. 1484 TI=T1/100.0 1485 C 1486 A1=(37.432*TT+8.041E-03*(TT**2.5)+357.14/0SQRT(TT)-236.88/TT) 1487 A2=(37.432*TI+8.041E-03*(TI **2.5) + 357. 14/DSORT(TI)-236.88/TI) 1488 CPA(5)=(NN02/(T2-T1))*(A1-A2) 1489 C 1490 R1 = (39.06*TT+1025.58/DSQRT(TT)- 1072.7/TT+410.2/( TT**2)) 1491 R2=(39.06*TI+1025.58/DS0RT(TI)-1072.7/TI+410.2/(TI**2)) 1492 CPA(6)=(NN2/(T2-T1))*(R1-R2) 1493 C 1494 S1=-672.87*TT+351 .8*(TT**1.25)-14.214*(TT**1.75)+647.76 1495 -*DSORT(TT) 1496 S2=-672.87*TI+351.8*(TI**1.25)-14.214*(TI**1.75)+647.76 1497 -*DSQRT(TI) 1498 CPA(11)=(NNFUEL/(T2-T1))*(S1-S2) 1499 C 1500 C1=(-4.042*TT+15.23*(TT**2)-0.5237*(TT**3)+7.9275E-03*(TT**4)) 1501 C2=(-4.042*TI+15.23*(TI**2)-0.5237*(TI**3)+7.9275E-03*(TI**4)) 1502 CPA(13)=(NNFUEL/(T2-T1))*(C1-C2) 1503 C 1504 TT=TT*100. 1505 TI=TI*100. 1506 C 1507 D1=RM0L*(-0.72*TT+4.643E-02*(TT**2)- 1.684E-05*(TT**3)+ 2.67E-09* 1508 -(TT**4)) 188 1509 D2 = RM0L*(-0.72*TI+4.643E-02*(TI**2)- 1.684E-05*(TI **3) + 2.67E-09* 1510 -(TI**4)) 1511 CPA(12)=(NNFUEL*0.01/(T2-T1))*(D1-D2) 1512 C 1513 E1=RM0L*(-O.72*TT+4.643E-O2*(TT**2)-1.684E-05*(TT**3)+2.67E-09* 1514 -(TT**4)) 1515 E2=RM0L*(-O.72*TI+4.643E-02*(TI**2)- 1.684E-05*(TI**3) + 2.67E-09* 1516 -(TI**4)) 1517 CPA(14)=(NNFUEL*0.01/(T2-T1))*(E1-E2) 1518 C 1519 C CALC. CP, GAMMA, AND HENCE PRESSURE(P) AT TEMP. T(J) ASSUMING 1520 C ISENTROPIC COMPRESSION 1521 1522 CPAV=CPA(5)+CPA(6)+CPA(KFUEL) 1523 GAMU=CPAV/(CPAV-RMOL) 1524 RETURN 1525 END 1526 C 1527 C 1528 C SUBROUTINE COMP THIS CALCULATES THE PRESS. AND TEMP. AFTER 1529 C =============== ADIABATIC COMPRESSION OF THE FUEL-AIR MIXTURE. 1530 C 1531 SUBROUTINE COMP(P1,V1,T1,P2,V2,T2,ENGY1,ENGY2,NRC02,NRH20) 1532 C 1533 COMMON /AREA 1 / NCH,N02.K,L,M,N.KFUEL 1534 COMMON /AREA2/ MOLFL.NMIX,HF1,NN02,NN2,NNFUEL,KOM 1535 C 1536 REAL*8 P1,V1,T1,P2,V2.T2,NCH,N02,N,ENGY1,ENGY2,DH(14),RMOL, 1537 -REM,REM 1,TT1,REM2,TT2,HF1,MOLFL,DLF1,K,L,M,NMIX,NN02,NN2,NNFUEL 1538 -,UUU(10),T20LD,NRC02,NRH20 1539 C 1540 RM0L=8.31434 1541 NN=0 1542 NUT=0 1543 C 1544 50 P2 = P1*(V1/V2)*(T2/T1 ) 1545 0H(1) = ((3.096*T2+0.00273*(T2**2)-7.885E-07*(T2**3) 1546 1+8.66E-11*(T2**4))-1145.0)*RMOL 1547 DH(3)=((3.743*T2+5.656E-04*(T2**2)+4.952E-08*(T2**3) 1548 1-1.818E-11*(T2**4))-1167.O)*RM0L 1549 DH(5)=((3.253*T2+6.524E-04*(T2**2)-1.495E-07*(T2**3) 1550 1+1.539E-11*(T2**4))-1O24.O)*RM0L 1551 DH(6)=((3.344*T2+2.943E-04*(T2**2)+1.953E-09*(T2**3) 1552 1-6.575E-12*(T2**4))-1023.0)*RMOL 1553 DH(11)=((1.935*T2+4.965E-03*(T2**2.)-1.244E-06*(T2**3.) 1554 1 + 1.625E-10*(T2**4 . )-8.586E-15*(T2**5.))-985.9)*RMOL 1555 DH(12) = ((-0.72*T2+4.643E-02*(T2**2. )-1 . 684E-05*(T2**3. ) 1556 1+2.67E-09*(T2**4.))-3484.O)*RMOL 1557 DH(13)=((1.137*T2+1.455E-02*(T2**2.)-2.959E-06*(T2**3.) 1558 1 )-1552.9)*RM0L 1559 UUU(1)=-3.93522E05 1560 UUU(3)=-2.41827E05 1561 C CALC. TOTAL ENERGY OF MIXTURE (KJ/KMOL FUEL).... 1562 ENGY2=M0LFL*(NCH*(HF1+DH(KFUEL)-RM0L*T2)+N02*(DH(5)-RM0L*T2) 1563 -+N*(DH(6)-RM0L*T2)+NRC02*(UUU(1)+DH(1)-RM0L*T2)+NRH20* 1564 -(UUU(3)+DH(3)-RM0L*T2)) 1565 REM=ENGY2-ENGY1 + ((P1+P2)/2 )*(V2-V1) 1566 C WRITE(6,43) T2,P2,REM,ENGY2,ENGY1 189 1567 C 43 F0RMAT(1H ,'T2,P2,REM,E2,E1 '.5E12.4) 1568 NUT=NUT+1 1569 IF(NUT.GT.100) STOP 1570 C 1571 IF(NN.EQ.2) GOTO 7 1572 IF(NN.EQ.1) GOTO 8 1573 REM 1=REM 1574 ' TT1=T2 1575 T2=T2+200.0 1576 IF(T2.GT.4000.0) STOP 1577 NN=1 1578 GOTO 50 1579 C 1580 8 REM2=REM 1581 TT2=T2 1582 IF((REM1*REM2).LE.O.O) GOTO 13 1583 TT1=T2 1584 REM 1=REM2 1585 T2=T2+200.0 '1586 GOTO 50 1587 C 1588 13 IF(REM2.E0.0.0) GOTO 18 1589 T20LD=TT2 1590 11 T2=(TT1*REM2-TT2*REM1)/(REM2-REM1) 1591 IF(DABS((T2-T20LD)/T2).LT.0.001) GOTO 18 1592 T20LD=T2 1593 NN=2 1594 GOTO 50 1595 C 1596 7 IF(REM1*REM.LE.O.O) GOTO 12 1597 TT1=T2 1598 REM1=REM 1599 GOTO 11 1600 12 TT2=T2 1601 REM2=REM 1602 GOTO 11 1603 10 RETURN 1604 END 1605 C 1606 C 1607 C SUBROUTINE EXP THIS CALCULATES THE PRESS. AND TEMP. AFTER 1608 C ============== ADIABATIC EXPANSION OF THE PRODUCTS OF 1609 C COMBUSTION. 1610 C 1611 SUBROUTINE EXP(P1,V1,T1,P,V2,TT3,CC,SUMXS,ENGY1,ENGY2, 1612 -ATOT.DTIME) 1613 C 1614 COMMON /AREA 1/ NCH,N02,K,L.M.N,KFUEL 1615 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02,NN2,NNFUEL,KOM 1616 COMMON /AREA3/ AREAB,HTEXP,MPV,HTFCN,TWALL,VISC,THCOND 1617 C 1618 REAL*8 P1,V1,T1,P2,V2,T2,SUMXS,K,L,N,M,NMIX,NM1,TT1,P.EPROD, 1619 -CC(10),X(10),ENGY1,ENGY2,MOLFL,REM1,REM2,TT2,TT3,TT30LD,NNM1 , 1620 -NNM3,REM3,NCH,N02,HF1,NN02,NN2,NNFUEL,NNM2,EB2,VSB2,BORE 1621 -.AREAB,ATOT,MPV,HTFCN,TWALL,PDV,DO,HTCOEF,VISC.THCOND,HTEXP 1622 -,DTIME 1623 C 1624 C WRITE(6,777) P1,V1,T1,V2,ENGY1 190 1625 C 777 FORMAT(1H , 'P1,V1 ,T1,V2,ENGY1',5E12.4/) 1626 B0RE=O.O85 1627 NUT=0 1628 NN=0 1629 NM1=SUMXS 1630 TT1=T1 1631 C WRITE(6,888) MOLFL 1632 C 888 FORMATdH , 'MOLFL ' , E 12 . 4 ) 1633 C 1634 P=P1*(V1/V2)*(TT1/T1)*(SUMXS/NM1) 1635 CALL ENERGY(TT1,P,EPROD,SUMXS,CC,X,EB2,VSB2) 1636 ENGY2=EPR0D*M0LFL 1637 NNM1=SUMXS 1638 HTC0EF=(THC0ND/B0RE)*((MPV*B0RE/(VSB2*VISC))**HTEXP)/1000.0 1639 D0=HTCOEF*ATOT*(TT1-TWALL)*HTFCN*DTIME 1640 REM1=ENGY2-ENGY1+((P1+P)/2.)*(V2-V1 )+DQ 1641 C 1642 C WRITE(6,409) ENGY1,ENGY2,REM1,P,MOLFL,EPROD 1643 C 409 FORMATdH ,'ENGY1,ENGY2,REM,P,MOLFL,EPROD',6E12.4) 1644 C 1645 TT2=T1-100.0 1646 IF(TT2.GT.2500.0) TT2=TT2-100.0 1647 IF(TT2.GT.3000.0) TT2=TT2-100.0 1648 P=P1*(V1/V2)*(TT2/T1)*(SUMXS/NM1) 1649 CALL ENERGY(TT2,P,EPROD,SUMXS,CC,X,EB2,VSB2) 1650 ENGY2=EPR0D*M0LFL 1651 NNM2=SUMXS 1652 HTC0EF=(THC0ND/B0RE)*((MPV*B0RE/(VSB2*VISC))**HTEXP)/1000.0 1653 D0=HTCOEF*AT0T*(TT2-TWALL)*HTFCN*DTIME 1654 REM2=ENGY2-ENGY1+((P1+P)/2.)*(V2-V1)+D0 1655 C 1656 TT30LD=TT2 1657 719 TT3=(TT1*REM2-TT2*REM1)/(REM2-REM1) 1658 SUMXS=(NNM1*REM2-NNM2*REM1)/(REM2-REM1) 1659 NUT=NUT+1 1660 IF(NUT.GT.100) STOP 1661 IF(DABS((TT3-TT30LD)/TT3).LT.0.001) GOTO 718 1662 TT30LD=TT3 1663 P=P1*(V1/V2)*(TT3/T1)*(SUMXS/NM1) 1664 CALL ENERGY(TT3,P,EPROD,SUMXS,CC,X,EB2,VSB2) 1665 ENGY2=EPR0D*M0LFL 1666 NNM3=SUMXS 1667 HTCOEF=(THCOND/BORE)*((MPV*B0RE/(VSB2*VISC))**HTEXP)/1000.0 1668 D0=HTC0EF *ATOT *(TT3-TWALL)*HTFCN*DTIME 1669 PDV=((P1+P)/2.)*(V2-V1) 1670 REM3=ENGY2-ENGY1+PDV+DQ 1671 C WRITE(6,10) ENGY2,ENGY1.PDV,DO,HTCOEF 1672 C 10 FORMAT(1H ,'E2,E1,PDV,DQ,HTCOEF '.5E12.4) 1673 IF(REM1*REM3.LE.O.O) GOTO 715 1674 TT1=TT3 1675 REM 1=REM3 1676 NNM1=NNM3 1677 GOTO 719 1678 715 TT2=TT3 1679 REM2=REM3 1680 NNM2=NNM3 1681 GOTO 719 1682 718 RETURN 191 1683 END 1684 C 1685 C CUT THIS SUBROUTINE CALCULATES THE TURBULENT BURNING 1686 c = = = VELOCITY GIVEN THE LAMINAR BURNING VELOCITY AND 1687 c THE SHAPE OF THE (TURBULENT-LAMINAR) BURNING 1688 c VELOCITY CURVE FOR THE ENGINE RUNNING AT 3000RPM 1689 c 1690 SUBROUTINE CUT(LBVEL,TBVEL,MFX2) 1691 c 1692 REAL*8 LBVEL,TBVEL.MFX2.CU,FRACTN.A(11),B(11),NCH,N02,K,L 1693 M,N 1694 c 1695 COMMON /AREA 1 / NCH,N02,K,L,M,N,KFUEL 1696 c 1697 DATA A(1),A(2),A(3).A(4),A(5),A(6),A(7),A(8),A(9),A(10), 1698 •A(11)/5.8,7.5,8.1,8.2,8.1,7.7,6.7,5.0,3.0,1.0,0.0/ 1699 DATA B(1),B(2).B(3),B(4),B(5),B(6),B(7),B(8),B(9),B(10) 1700 /1.0,2.0,2.8,3.5,3.9,4.3,4.7,5.2,5.6,5. 8/ 1701 c 1702 IF(MFX2.GE.0.04) GOTO 20 1703 c 1704 c CU=MFX2*100 1705 IF(KFUEL.GT.11) GOTO 10 1706 CU=5.0 1707 GOTO 50 1708 10 CU=3.0 1709 GOTO 50 1710 c 1711 20 IF(MFX2.GE.O.10) GOTO 30 1712 INTMFX=IDINT(MFX2*100) 1713 FRACTN=MFX2*100-DFLOAT(INTMFX) 1714 CU=B(INTMFX ) + FRACTN*(B(INTMFX+1)-B(INTMFX)) 1715 GOTO 50 1716 c 1717 30 INTMFX=IDINT(MFX2*10) 1718 FRACTN=MFX2*10-DFLOAT(INTMFX) 1719 CU = A(INTMFX) + FRACTN*(A(INTMFX+1)-A( INTMFX)) 1720 c 1721 50 TBVEL=LBVEL+CU 1722 RETURN 1723 END 192 APPENDIX G - BURNING RATE ANALYSIS PROGRAM (MB) The b u r n i n g r a t e a n a l y s i s program was w r i t t e n t o o b t a i n v a l u e s of mass f r a c t i o n burned and t u r b u l e n t b u r n i n g v e l o c i t y v e r s e s engine r o t a t i o n i n degrees crank a n g l e . The major assumptions made i n the program a r e the same as t h o s e made by Keck [29] and L a v o i e [ 3 0 ] , namely; ( i ) The combustion chamber i s d i v i d e d i n t o two zones by a t h i n , s p h e r i c a l l y expanding flame f r o n t s e p a r a t i n g the burned gas f r a c t i o n (x) from the unburned gas f r a c t i o n ( 1 - x ) . ( i i ) B o th the burned and unburned gases have v a r y i n g s p e c i f i c h e a t s and obey the i d e a l gas law. ( i i i ) The unburned gas i s i s e n t r o p i c a l l y compressed by the expanding burned gases. ( i v ) The p r e s s u r e i s u n i f o r m throughout the combustion chamber. The assumption of a s p h e r i c a l l y expanding flame f r o n t i s s u p p o r t e d i n [25] which p r e s e n t s combustion photographs taken i n s i d e an engine h a v i n g a combustion chamber of the same shape as the Toyota used i n t h i s s t u d y . Assumptions ( i ) t o ( i v ) a l l o w the f o l l o w i n g p r o c e d u r e t o be used i n which c a l c u l a t i o n s a re performed a t each degree c r a n k a n g l e . The t o t a l mass of f u e l - a i r m i x t u r e c o n t a i n e d i n the c y l i n d e r i s o b t a i n e d from measured a i r and f u e l f l o w r a t e s , and the i n i t i a l m i x t u r e c o m p o s i t i o n c a l c u l a t i o n s a l l o w f o r exhaust gas r e s i d u a l f r a c t i o n . At each s t e p of the combustion p r o c e s s the v a l u e s of energy, temperature an volume are known f o r both the burned an unburned gases a t the p r e v i o u s c a l c u l a t i o n s t e p ( s u b s c r i p t 1) and t h e s e a r e used as t h e s t a r t i n g p o i n t f o r c a l c u l a t i n g v a l u e s f o r the c u r r e n t s t e p ( s u b s c r i p t 2 ) . From the assumption of i s e n t r o p i c c ompression of the unburned g a s e s , '/k v M 2. = v M 1 ( P, / P x ) (1 ) Assuming i d e a l gas b e h a v i o u r , T « = Pi v M 1 / M« R (2) Which a l l o w s the s p e c i f i c energy of the unburned gas t o be c a l c u l a t e d , e M t = ZN„ ( h/j + ( hjfar hux)) - R L ) ....(3) 193 Where the v a l u e s f o r h ^ ) ar e o b t a i n e d from formulae r e p r e s e n t i n g curve f i t s t o p u b l i s h e d e n t h a l p y d a t a f o r each c o n s t i t u e n t . The new combustion chamber volume (Vz) i s o b t a i n e d from the volume/crank a n g l e r e l a t i o n s h i p f o r the e n g i n e , and the new t o t a l energy of the c o n t r o l mass c o n t a i n e d i n the combustion chamber i s g i v e n by the f i r s t law, E z = E x - P.dV + dQ (4) The P dV term i s a p p r o x i m a t e d by (Pi + P i ) / 2 . ( V z . - V, ) and dQ i s o b t a i n e d u s i n g Annands [ 2 6 ] heat t r a n s f e r e q u a t i o n , dQ = hw a (k/B) (Re) f c(T, - T~) dt (5) S i n c e t h e unburned gases a r e compressed i s e n t r o p i c a l l y , heat i s o n l y l o s t from the burned gases, hence T ? = T* and A^ eq u a l s the a r e a of the combustion chamber i n c o n t a c t w i t h the burned gases c a l c u l a t e d i n the p r e v i o u s s t e p . T ^ i s taken t o be 450K, a = 0.8 and b = 0.7 These v a l u e s f o r a and b were o b t a i n e d by v a r y i n g them u n t i l the f o l l o w i n g e q u a t i o n b a l a n c e d , ( I n t . Energy a t spark - I n t . Energy a t combustion end) = ( t o t a l Work Done + t o t a l Heat L o s t ) over t h i s p e r i o d From the c o n s e r v a t i o n of mass and energy, V 2 / m = x z v b i + (1-x ) v M X . . . . ( 6 ) E z / m = X i e ^ t (1-x ) e M X ....(7) The v a l u e s of x x , V i , Z r & e n a r e unknown a t t h i s t h i s p o i n t , however vfcx = f(T / i 2.Pz) and et,x= f ( T ^ x P z ) a c c o r d i n g t o the f o l l o w i n g r e l a t i o n s h i p s , = Mfei R T t z / P z . ....(8) and e ^ = J_ N; ( h/j + ( h j - t r h j n ) - R T A i) (9) The program t h e r e f o r e p roceeds by i t e r a t i n g t he burned gas temperature Tbx u n t i l the v a l u e s of e*»x and v£x c a l c u l a t e d by e q u a t i o n s 8 & 9 s a t i s f y e q u a t i o n s 6 & 7. At t h i s ~ p o i n t the mass f r a c t i o n burned Xz, i s o b t a i n e d . The b u r n i n g v e l o c i t y S 7 - i s c a l c u l a t e d u s i n g the f o l l o w i n g r e l a t i o n s h i p , Sr- = m x v M / hf ....(10) The v a l u e of hf i s o b t a i n e d from a geometry s u b r o u t i n e which t a k e s and the d i s t a n c e of the p i s t o n from TDC as i n p u t s 194 and c a l c u l a t e s ry , A^ and A/ based on the assumption of s p h e r i c a l flame p r o p a g a t i o n c e n t r e d a t the spark p l u g . The above proce d u r e i s r e p e a t e d a t each degree crank a n g l e u n t i l e i t h e r the mass f r a c t i o n burned becomes e q u a l t o 1 , or - x, becomes l e s s than a p r e d e f i n e d l i m i t . Laminar b u r n i n g v e l o c i t i e s a r e c a l c u l a t e d a t each s t e p u s i n g e q u a t i o n s g i v e n i n [15] f o r n a t u r a l gas and e q u a t i o n s g i v e n i n [17] f o r g a s o l i n e . 195 BURNING RATE ANALYSIS PROGRAM FLOWCHART INPUT: FUEL TYPE; ENGINE SPEED; A/F RATIO; INTAKE AIR FLOWRATE AND TEMPERATURE; SPARK ADVANCE; BOOST PRESSURE & MEASURED CYLINDER PRESSURE RECORD. I CALCULATE VOLUMETRIC EFFICIENCY AND SCALE & SMOOTH CYLINDER PRESSURE DATA. CALCULATE PROPERTIES OF CYLINDER CONTENTS AT BDC AND AT END OF EACH CRANK ANGLE STEP UP TO IGNITION. I AT NEXT CRANK ANGLE STEP: ASSUME UNBURNED GAS COMPRESSED ISENTROPICALLY TO DETERMINE NEW TEMPERATURE AND ENERGY, FROM THESE OBTAIN LAMINAR BURNING VELOCITY. CALCULATE NEW TOTAL ENERGY OF CYLINDER CONTENTS FROM 1ST LAW - ENERGY2=ENERGY1+/PDV-DQ ITERATE BURNED GAS TEMPERATURE UNTIL MASS AND ENERGY OF BURNED AND UNBURNED GASES BALANCE. OBTAIN MASS FRACTION BURNED, FLAME RADIUS & FLAME SPEED, AND TURBULENT BURNING VELOCITY. NO IS MASS FRACTION BURNED GREATER THAN UNITY? CALCULATE PROPERTIES OF CYLINDER CONTENTS AT EACH CRANK ANGLE TO BDC. I CALCULATE IMEP AND EFFICIENCY i PRINT RESULTS AND PLOT GRAPHS ~ X STOP 196 1 SAMPLE INPUT F I L E FOR PROGRAM "MB" 3 4 5 001 0 0 6 12 296.0 3000.0 9.00 1.00 21.00 0.800 0.70 7 0.050 0.029 12.428 14.027 73.409 1 2.00 450.0 8 99.6 43.48 4.00 5.00 0 0.00 9 15 15 15 15 15 10 17 16 1 4 15 1 5 1 1 1 4 15 15 1 4 1 5 1 2 15 15 15 1 5 15 13 15 15 16 17 16 14 17 16 16 17 16 15 17 18 18 18 19 16 18 20 19 19 20 17 21 21 22 21 23 18 23 23 25 26 27 19 29 29 29 31 31 20 33 35 36 38 40 21 40 44 45 47 51 22 53 56 60 62 67 23 70 74 80 85 91 24 98 103 1 1 1 119 127 25 1 36 147 156 169 179 26 189 201 21 1 224 239 27 254 273 298 327 368 28 416 469 525 574 61 1 29 639 653 657 651 635 30 614 589 560 531 500 31 470 442 414 389 366 32 343 322 304 286 270 33 255 241 229 217 206 34 196 186 178 170 162 35 1 55 1 50 143 139 133 36 128 124 119 1 15 113 37 109 106 104 100 98 38 96 93 92 89 87 39 86 83 82 81 78 40 78 77 74 74 72 41 70 70 68 67 67 42 65 64 63 61 61 43 59 58 59 57 55 44 55 52 51 50 47 45 46 45 43 42 40 46 41 38 34 33 33 1 FUEL TYPE:- OCTANE C 8.0 H 18.0 2 3 SPEED (RPM) = 3000.0 SPARK ADVANCE (DEG. BTDC) = 21.00 4 5 AIR/FUEL RATIO* 15.06 STOICH. A/F RATIO* 15.06 LAMBDA= 1.00 COMP. RAT10= 9.0 6 7 a STEP VOL PRESS TU TB MFX VFRBNT CBVEL TBVEL FLMSPD FSR RADF AREAF C.A ENERGY o 9 4 r\ 1 497 9 82 2 296 0 0 0 0 0 0 0 0 0 0 0 O 0 0 0 0 0 0 0 180 0 -0 16520 1U 1 1 83 66 6 1199 3 573 8 2753 9 0 0013 0 71 7 050 0 787 54 76 8 96 0 618 2 28 344 0 -0 04760 12 84 63 9 1270 1 580 9 2749 4 0 0026 1 34 2 482 0 802 12 24 3 09 0 754 3 35 346 0 -0 04442 13 85 61 7 1343 5 587 9 2700 5 0 0046 2 32 2 803 0 817 12 92 3 43 0 898 4 68 348' 0 -0 04151 14 86 59 7 1418 8 594 8 2659 7 0 0077 3 70 2 94 1 0 832 12 96 3 53 1 042 6 21 350 0 -0 03892 15 87 58 2 1500 9 601 9 2622 5 0 0127 5 84 3 461 0 847 14 80 4 09 1 207 8 20 352 0 -0 03673 16 88 56 9 1594 6 609 7 2596 8 0 0206 9 02 3 990 0 863 16 59 4 62 1 391 10 7 1 354 0 -0 03497 17 89 56 0 1706 8 618 5 2582 5 0 0327 13 49 4 465 0 881 17 91 5 07 1 590 13 72 356 0 - O 03373 18 90 55 5 1848 2 629 0 2578 8 0 0509 19 52 4 970 0 902 19 08 5 51 1 802 17 25 358 0 -0 03309 19 91 55 3 2030 4 64 1 5 2584 2 0 0773 27 13 5 744 0 927 20 57 6 20 2 030 18 92 360 0 -0 03315 20 92 55 5 2262 0 656 1 2595 9 0 1 140 35 97 6 817 0 957 22 83 7 12 2 284 19 98 362 0 -0 03419 21 93 56 0 2543 4 672 2 261 1 4 0 1622 45 34 7 786 0 991 23 70 7 86 2 548 20 69 364 0 -0 03649 22 94 56 9 2862 0 688 7 2628 1 0 221 1 54 45 8 481 1 027 23 29 8 25 2 806 20 97 366 0 -0 04040 23 95 58 2 3198 5 704 5 2643 4 0 2894 62 77 8 944 1 064 22 18 8 41 3 053 20 86 368 0 -0 04627 24 96 59 7 3531 6 718 8 2655 7 0 3644 70 01 9 210 1 099 20 71 8 38 3 283 20 43 370 0 -0 05444 25 97 61 7 3839 0 731 0 2664 0 0 4438 76 23 9 366 1 129 19 46 8 29 3 499 19 76 372 0 -0 06518 26 98 63 9 4099 4 740 7 2667 6 0 5239 81 38 9 304 1 155 18 02 8 06 3 699 18 95 374 0 -0 07865 27 99 66 5 4293 2 747 6 2666 0 0 6007 85 53 8 981 1 174 16 47 7 65 3 882 18 1 1 376 0 -0 09489 28 100 69 5 4407 0 751 5 2658 8 0 6703 88 79 8 331 1 187 14 73 7 02 4 046 17 37 378 O -0 1 1374 29 101 72 8 4440 5 752 6 2646 4 0 7308 91 29 7 460 1 193 12 95 6 26 4 190 16 83 380 0 -0 13492 30 102 76 3 4403 2 751 4 2629 3 0 7817 93 20 6 469 1 192 1 1 23 5 43 4 315 16 58 382 0 -0 15802 31 103 80 2 4307 3 748 1 2608 4 0 8234 94 69 5 425 1 187 9 68 4 57 4 422 16 66 384 0 -0 18260 32 104 84 4 4 166 5 743 1 2584 1 0 8562 95 78 4 311 1 177 8 OO 3 66 4 51 1 17 17 386 0 -0 2082 1 33 105 88 9 3993 4 736 8 2556 9 0 8813 96 59 3 265 1 164 6 61 2 80 4 585 18 08 388 0 -0 23440 34 106 93 7 3799 3 729 4 2527 4 0 8995 97 14 2 364 1 148 5 37 2 06 4 644 18 67 390 0 -0 26080 35 107 98 8 3594 2 721 3 2496 1 0 9123 97 53 1 770 ' 130 5 1 1 1 57 4 701 17 50 392 0 -0 28712 3D 37 i a 180 497 8 286 7 0 0 1043 8 0 9207 97 53 0 0 0 0 0 0 0 0 0 0 0 0 538 0 -1 16269 oo 39 POWER= 12.442 I M E.P = 1 1 245 EFFICIENCY5 38 47779 40 TYPICAL OUTPUT FROM PROGRAM "MB" 198 1 C MB THIS PROGRAM CALCULATES MASS BURNING RATE AND 2 C === FLAME SPEED FROM MEASURED PRESSURE DATA TAKEN 3 C FROM THE TOYOTA 4-CYL. ENGINE. 4 C 5 IMPLICIT REAL*8(A-H,0-Z) 6 REAL*8 MPV,K,L,M,N,NO,N2,N02,NCH,KK,NUM,NUM1,NMIX,MOLFL, 7 -NM,NM1,NNM1,NNM2,NN2,NN02,MEP,LENG,MTOT.MWMIX,MFX1.NNCH, 8 -MFX2,MW(14).MMFX2.NRN2,NRES,NR02,NRC02,NRH20,NNFUEL 9 -,MF(5,200),IGNDEL,MWBMIX,LAMBDA 10 C 11 COMMON /AREA1/ NCH,N02.K,L.M,N,KFUEL 12 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02,NN2,NNFUEL,KOM 13 COMMON /AREA3/ AREAB,HTEXP,MPV,HTFCN,TWALL,VISC,THCOND 14 COMMON /AREA4/ NDISS,IPRINT 15 C 16 DIMENSION X(10),PP(5,200),VV(5,200),VV2(5,200),VVX(20), 17 -DH(20),CPG(20),PP2(5,200),DI(5,200),TIM(5,200),XX(5,200), 18 -CCA(10),DL(5,200),ZZ(5,200),DC(5,200),YY(5.200),POUT(180), 19 -UUU(10),CC(10),PDAT(5,200),CB(5,200),TB(5,200), 20 -FS(5,200),RB(5.200) 21 C 22 INTEGER IPRES(5,200) 23 C 24 C STATEMENT FUNCTION USED THROUGHOUT PROGRAM TO CALCULATE CYLINDER 25 C VOLUME (DVOL) AT A GIVEN CRANK ANGLE (DALFA") . VOLUME OBTAINED MUST 26 C BE ADDED TO THE CLEARANCE VOLUME TO GIVE TOTAL CYLINDER VOLUME 27 C 28 DVOL(DALFA)=3.14159*((BORE/2. )**2. )*((STROK/2. )*(1.-DCOS(DALFA* 29 -0.0174532))+LENG*(1.-DSQRT(1.-(DSIN(DALFA*0.0174532)*DSIN(DALFA 30 -*O.O174532)*((STR0K/2./LENG)**2. ) ) ) ) ) 31 C 32 C READ NUMBER OF RUNS TO BE MADE.... 33 C 34 READ(5,999) NUMBR,IPRINT,IGRAPH 35 999 FORMAT(313) 36 ' DO 222 IL=1.NUMBR 37 C 38 C 39 C READ TYPE OF FUEL (11=CH4, 12=C8H18, 13=C3H8 ); 40 C TEMP. (T1)(K) OF INLET AIR; 41 C ENGINE SPEED (RPM); COMPRESSION RATIO (COMPR); REL. AIR/FUEL 42 C RATIO, (LAMBDA) ; SPARK ADVANCE (SPKAD ) (DEG . B.T.D.C); 43 C HEAT TRANSFER MULTIPLIER (HTFCN); 44 C HEAT TRANSFER EXPONENT (HTEXP); 45 C RESIDUAL GAS FRACTION (%),(F); PERCENTAGE CONSTITUENTS IN 46 C RES. FRACTION (PR02,PRC02,PRH20.PRN2); 47 C WHETHER FULL DISSOCIATION (NDISS=2). OR PARTIAL (NDISS=1); 48 C CRANK ANGLE ITERATION INCREMENT (PDCA); CYL. WALL TEMP. (TWALL); 49 C AMBIENT AIR PRESSURE (PAMB); AIR FLOWRATE (G/S); 50 C IGNITION DELAY (DEG. C.A.)(IGNDEL); BOOST PRESS (PSI)(PBOOST) 51 C 52 REA0(5,47) KFUEL,T1,SPEED,COMPR,LAMBDA,SPKAD,HTFCN,HTEXP 53 47 F0RMAT(I3.2F7.1,3F6.2,F6.3,F5.2 ) 54 READ(5,46) F,PR02.PRC02,PRH20,PRN2,NDISS,PDCA,TWALL 55 46 FORMAT(5F7.3,I3,F6.2,F7.1) 56 READ(5,2) PAMB,AlRFLO,IGNDEL,SCONST,IPRNTS,PBOOST 57 2 F0RMAT(F6.1,3F6.2,I3,F6.2) 58 C 199 59 C READ IN PRESSURE DATA AND SMOOTH IT USING SUBROUTINE 'SMOOTH' 60 c 61 CALL SM00TH(POUT,SCONST, IPRNTS) 62 c 63 DO 658 KJ=1,180 64 P D A T ( I L , K J ) = P O U T ( K J ) 65 658 CONTINUE 66 c 67 c DETERMINE FUEL PROPERTIES: MOL.WEIGHT, LOW HEAT V A L . , 68 c ENTHAL. OF FORMATION 69 c 70 I F ( K F U E L . G T . 1 1 ) GOTO 10 71 CN=1.0 72 HM=4.0 73 MW(11)=16.04 74 QVS=50050.0 75 HF1=-74873 .0 76 WRITE(6 ,45) CN.HM 77 45 FORMATdH . ' F U E L T Y P E : - METHANE C ' . F 3 . 1 . ' H ' , F 3 . 1/) 78 GOTO 30 79 c 80 10 I F ( K F U E L . G T . 1 2 ) GOTO 20 81 CN=8.0 82 HM=18.0 83 MW(12) = 1 14 . 14 84 QVS=43500.0 85 HF1=-208447 .0 86 WRITE(6 ,43) CN.HM 87 43 FORMATdH , ' F U E L T Y P E : - OCTANE C ' . F 3 . 1 , ' H ' , F 4 . 1/) 88 GOTO 30 89 c 90 20 I F ( K F U E L . G T . 1 3 ) STOP 91 CN=3.0 92 HM=8.0 93 MW(13)=44.097 94 0VS = 46353 .0 95 HF1=-103847 .0 96 WRITE(6 ,44) CN.HM 97 44 FORMATdH . ' F U E L T Y P E : - PROPANE C ' . F 3 . 1 , ' H ' , F 3 • 1/) 98 c 99 c ENGINE PARAMETERS 100 c 101 30 CONTINUE 102 STR0K=O.O78 103 B0RE=O.O85 104 LENG=0.124 105 RDASH=58.3737E-03 106 HTCLRV=18.355E-03 107 CLRV=55.3264E-06 108 c 109 c GAS CONSTANT (KJ/KMOL K) 1 10 c 1 1 1 RM0L=8.31434 112 JJ=0 113 c 1 14 c 115 c CALC STOICH A / F RATIO(STAFR) AND A I R / F U E L RATIO(AFR) 116 c 200 117 STAFR=((CN+HM/4.)*32.+3.762*(CN+HM/4.)*28.01)/((CN*12)+HM) 118 AFR=STAFR*LAMBDA 1 19 C 120 C CALCULATE VOLUMETRIC EFFICIENCY FROM AIR MASS FLOW(g/sec), 121 C INLET TEMP(K) AND PRES(kpa), RPM, AND DENSITY FACTOR 122 C FOR GASEOUS FUELS 123 C VOLEFF=AIRFLOW/(P/RT)*FACTOR*SPEED*(SWEPT VOL./2) 124 C (FROM TAYLOR P149) 125 C FACTOR=DENSITY CORRECTION FOR FUEL VAPOUR IN CHARGE 126 C INLET PRESS.=AMBIENT PRESS.+BOOST PRESS.-2.7KPA 127 C 128 PB00ST = PB00ST*6 .9 129 PINLET = PAMB+PB00ST-2 . 7 130 FACTOR* 1 131 IF(KFUEL.EO.12) GOTO 700 132 FACT0R=1.0+(1.0/AFR)*(29.0/(MW(KFUEL))) 133 C 134 700 V0LEFF=19.145*FACT0R*AIRFL0*T1/(SPEED*PINLET) 135 C 136 C CALC. PRESSURE P1 WHICH REPRESENTS THE PRESSURE IN THE 137 C CYCLINDER AT BDC. 138 C CONVERT PRESSURE DATA IN BAR TO KPA, AND CORRECT DATA FOR 139 c VOL. EFF. 140 c 141 P1=V0LEFF*PINLET 142 PDIFF=(101.3+PB00ST)-P1 143 WRITE(6,701) P1.VOLEFF,FACTOR,PDIFF 144 701 FORMATdH ,'P1 , VOLEF F , FACTOR , PDIFF '.4F10.3/) 145 DO 267 1 = 1 ,180 146 PDAT(IL,I ) = PDAT(IL,I)* 100.0-PDIFF 147 267 CONTINUE 148 c 149 c 150 c CALC. NUMBER OF KMOLS OF REACTANTS AND PRODUCTS BEFORE AND AFTER 151 c COMBUSTION RELATIVE TO ONE KMOL OF FUEL 152 c (NOT INCLUDING DISSOCIATION). NCH=HYDROCARBON 153 c N02=AVAILABLE OXYGEN, N=NITROGEN, K=C02, L=H20, M=UNBURNT OXYGEN 154 c 155 NCH=1 156 N02=(CN+HM/4)*LAMBDA 157 N=3.762*(CN+HM/4)*LAMBDA 158 K=CN 159 L=HM/2 160 M=(CN+HM/4)*(LAMBDA-1) 161 c 162 WRITE(6,655) NCH,N02,N,K,L,M 163 655 FORMATdH , 'NCH, N02 ,N,K , L ,M= ' , 6F9 . 5/ ) 164 c 165 c CALC. TOTAL NUMBER OF KMOLS OF REACTANTS... 166 SUMNS=NCH+N02+N 167 c CALC. NO. OF KMOLS OF RESIDUAL GAS GIVEN THE VOLUME FRACTION OF 168 c RESIDUAL GASES 'F' . . . . 169 NRES=(F/(1-F))*SUMNS 170 c CALC. NO. OF KMOLS IN CYLINDER PER KMOL OF FUEL... 171 NMIX=SUMNS+NRES 172 SUMNS=NMIX 173 c CALC. NO OF KMOLS OF EACH RESIDUAL GAS... 174 NR02=PR02*NRES/100.0 201 175 NRC02=PRC02*NRES/100.0 176 NRH20=PRH20*NRES/100.0 177 NRN2=PRN2*NRES/100.0 178 C CALC. NEW VALUES FOR THE TOTAL NO. OF KMOLS OF N2, 02, C02.& H20 179 N=N+NRN2 180 N02=N02+NR02 181 K=K+NRC02 182 L=L+NRH20 183 M=M+NR02 184 WRITE(6,655) NCH,N02,N,K,L,M 185 C 186 C CALC. ENERGY OF REACTANTS AT INLET TEMP; 5=02, 6=N2, 11= CH4 187 C 12=C8H18, 13=C3H8. 1=C02, 3=H20,... (IN KJ/KMOL OF FUEL) 188 DH(1)=((3.096*T1+0.00273*(T1**2)-7.885E-07*(T1**3) 189 1+8.66E-11*(T1**4))-1145.0)*RMOL 190 DH(3)=((3.743*T1+5.656E-04*(T1**2)+4.952E-08*(T1**3) 191 1-1.818E-11*(T1**4))-1167.0)*RMOL 192 DH(5)=((3.253*T1+6.524E-04*(T1**2)-1.495E-07*(T1**3) 193 1+1.539E-11*(T1**4))-1024.0)*RMOL 194 DH(6) = ((3.344*T1+2.943E-04*(T1**2)+1.953E-09*(T1 * *3) 195 1-6.575E-12*(T1**4))-1023.0)*RMOL 196 DH(11)=((1.935*T1+4.965E-03*(T1**2.)-1.244E-06*(T1**3. ) 197 1+1.625E-10*(T1**4.)-8.586E-15*(T1**5.))-985.9)*RMOL 198 DH(12)=((-0.72*T1+4.643E-02*(T1**2.)-1.684E-05*(T1**3. ) 199 1+2.67E-09*(T1**4.))-3484.0)*RMOL 200 DH(13) = (( 1 . 137*T1 + 1.455E-02*(T1**2. )-2.959E-06*(T1 **3. ) 201 1)-1552.9)*RM0L 202 UUU(1)=-3.93522E05 203 UUU(3)=-2.41827E05 204 C CALC. TOTAL ENERGY OF MIXTURE (KJ/KMOL FUEL) 205 ERCT = (NCH*(HF1+DH(KFUEL ) -RMOL*T1 )+N02*(DH(5)-RMOL*T1) 206 -+N*(DH(6)-RM0L*T1)+NRC02*(UUU(1)+DH(1)-RM0L*T1)+NRH20* 207 -(UUU(3)+DH(3)-RM0L*T1)) 208 C 209 C CALC. SWEPT VOL.(CYLV).CLEARANCE VOL.(CLRV),TOTAL V0L.(V1), 210 C VOLUME CORRESPONDING TO GIVEN SPARK ADVANCE (DVOLM)... 211 CYLV=3.1415926*((BORE/2. )**2.)*STROK 212 CLRV=CYLV/(COMPR-1.) 213 V1=C0MPR*CLRV 214 VT0TAL=V1 215 MPV=SPEED*STR0K/3O.O 216 C SUBT. SPK ADV. ANGLE FROM 360'AND ADD IGNITION DELAY... 217 ANG=(360.0-SPKAD+IGNDEL) 218 C INITIALISE CRANK ANGLE COUNTER AT B.D.C. & SET TIME TO ZERO 219 DLF1=180.0 220 TIME=0.0 221 C CALC. VOLUME IN CYLINDER AT SPARK TIME (USED LATER) 222 DVOLM=(CLRV+DVOL(ANG)) 223 TIME=0.0 224 C TOTAL NO. OF MOLS IN CYL.=NO. OF MOLS OF FUEL*(1+4.76(CN+HM/4) 225 C *LAMBDA) 226 C WHERE (1+4.76(CN+HM/4).LAMBDA)=NMIX. 227 C I.E. NTOT=MOLFL*NMIX 228 C BUT P1.V1=NT0T.RM0L.T1 OR NT0T=P1.V1/RMOL.T1 = MOLFL.NMIX 229 C THEREFORE NO. OF MOLS OF FUEL IN CYL. = P1.V1/NMIX.RMOL.T1 230 M0LFL=(P1*V1)/(NMIX*RM0L*T1) 231 C ENERGY OF CYLINDER CONTENTS IN KJ 232 ENGY1=ERCT*MOLFL 202 233 C CALC. STOICH. A/F RATIO (STAFR),AIR/FUEL RATIO (AFR) ,PERCENTAGE 234 C OXYGEN (NN02), NITROGEN (NN2) AND FUEL (NNCH) IN MIXTURE... 235 STAFR=((CN+HM/4.)*32.+3.762*(CN+HM/4.)*28.01)/((CN*12)+HM) 236 AFR=STAFR*LAMBDA 237 NN02=(N02/NMIX)*1OO. 238 NN2=(N/NMIX)*100. 239 NNCH=100.-(NN02+NN2) 240 NNFUEL=NNCH 241 C GIVEN MOLECULAR WEIGHTS OF FUELS, CALC. MOLECULAR WEIGHT OF 242 C MIXTURE (MWMIX); TOTAL MASS OF MIXTURE (MTOT); AND SPECIFIC 243 C VOLUME OF MIXTURE 244 MWMIX=(NN02*32.0/100.)+(NN2*28.0/100.)+(NNCH*MW(KFUEL)/100.) 245 MTOT=(PDAT(IL,1)*V1*MWMIX)/(T1*RMOL) 246 VT0T1=V1 247 VSU1=VT0T1/MT0T 248 ET0T1=ERCT/MWMIX/NMIX 249 C 250 C 251 WRITE(6,735) MPV,TWALL,HTFCN,HTEXP 252 735 F0RMAT(1H ,'MPV,TWALL,HTFCN,HTEXP '.4E12.4/) 253 WRITE(6,734) ERCT,ENGY1,NMIX.MWMIX,MOLFL,MTOT 254 734 FORMATdH , ' ERCT , EG 1 , NMIX , MWMX , MOLFL , MTOT ; ' , GE 12 . 4//) 255 C 256 WRITE(6,652) SPEED,SPKAD 257 652 FORMATdH .'SPEED (RPM) = '.F7.1, 258 -7X,'SPARK ADVANCE (DEG. BTDC) =',F7.2,3X/) 259 WRITE(6,813) AFR,STAFR,LAMBDA,COMPR 260 813 F0RMAT(1H ,15HAIR/FUEL RATIO=,F6.2,3X,18HST0ICH. A/F RATIO=, 261 -F6.2,3X,7HLAMBDA=,F6.2,3X,12HC0MP. RATI0=,F5.1/) 262 WRITE(6,31 ) 263 31 FORMATdH , 1X ,'STEP', 1X ,'VOL', 3X ,'PRESS', 3X ,'TU', 5X ,'TB', 5X 264 -,'MFX',4X,'VFRBNT',2X.'CBVEL',3X,'TBVEL',3X,'FLMSPD'.2X, 265 -'FSR',3X,'RADF',2X,'AREAF',3X,'C.A.',3X,'ENERGY'/) 266 DO 106 KI = 1, 10 267 X(KI)=0.0 268 106 CONTINUE 269 NI = 1 270 V1=V1*(1E+06) 271 WRITE(6,893) NI,V1,PDAT(IL,NI),T1.(X(I),I=1.9). 272 -DLF1.ENGY1 273 893 F0RMAT(1H ,13, 1X , F6.1,3F7. 1,F9.4,F7.2,2F8.3,F7.2,F7.2,F7.3, 274 -F7.2.F7.1.F9.5) 275 TU1=T1 276 V1=V1/(1E+06) 277 T2 = T1 278 PP2(IL,1)=PDAT( IL, 1 ) 279 VV2(IL,1)=V1 280 TIM(IL,1)=TIME 281 MF(IL.1)=0.0 282 CB(IL,1)=0.0 283 TB(IL,1)=0.0 284 FS(IL,1)=0.0 285 RB(IL,1)=0.0 286 UJd=1 287 NUT=0 288 DCA=PDCA 289 NDCA=(360./DCA) 290 C 203 291 C START COMPRESSION STROKE 292 C 293 C 294 c THIS SECTION CALCULATES ADIABATIC PRESSURE RISE AT EACH CRANK 295 c ANGLE INTERVAL AND COMPARES THE RESULT WITH THE CORRESPONDING 296 c MEASURED PRESSURE VALUE TO DETERMINE IF COMBUSTION HAS STARTED 297 c 298 DO 40 NI=2,NDCA 299 c 300 c CALC. VOLUME DIVISION (DIV) FOR GIVEN C.A. DIVISION (DCA) 301 DIV=DV0L(DLF1)-DVOL(DLF1+DCA) 302 c CALC. NEW VOLUME IN CYLINDER & RESET C.A. COUNTER TO NEW VALUE 303 V2=V1-DIV 304 DLF1=DLF1+DCA 305 DTIME=DCA/(6.0*SPEED) 306 DIST=DV0L(DLF1 )/(3.14159*((BORE/2. )**2)) 307 c 308 c CALC. NEW MIXTURE TEMPERATURE USING P.V = R.T 309 T2=(MWMIX*PDAT(IL,NI)*V2)/(MTOT*RMOL) 310 CALL C0MP(T2,ENGY2,NRC02.NRH20) 311 c 312 c IF NEW C.A. < SPK. ADV., CONTINUE WITH COMP. STROKE CALCS. 313 IF(DLF1.GE.ANG) GOTO 610 314 c IF NEW C.A. > SPK. ADV., CALCULATE ADIABATIC PRESSURE RISE 315 c AND COMPARE RESULT WITH MEASURED VALUE.. 316 c 317 c IF(IPRINT.EQ.O) GOTO 393 318 CALL GAM(T2,T1,GAMU) 319 PISEN=((V1/V2)**GAMU)*PDAT(IL,(NI-1)) 320 c WRITE(6,257) PDAT(IL,NI),PI SEN.T2,GAMU 321 c 257 F0RMAT(1H , 'PDAT,PI SEN,T2,GAMU '.4F10.3) 322 c 323 f* L. / 324 c IF(IDELP.EQ.2) GOTO 217 ) 325 c DELP1=(PDAT(IL.NI)-PISEN) ) 326 c IDELP=2 ) 327 c GOTO 51 ) 328 c ) 329 C217 DELP2=(PDAT(IL,NI)-PISEN) ) 330 C IF((DELP2-DELP1).GT.PTHRES) GOTO 610 ) 331 L. -332 c 333 c CALC. CURRENT TIME; AND PRESS. AT GIVEN VOL. & TEMP. 334 393 TIME=(DLF1-180.)/(6.0*SPEED) 335 c RECORD PERMANENT VALUES OF PRESS., VOL., TIME, VOL. DIV, AND 336 c C.A. DIV, AT END OF EACH C.A. STEP... 337 PP2(IL,NI)=PDAT(IL.NI) 338 VV2(IL,NI)=V2 339 TIM(IL,NI)=TIME 340 DI(IL,(NI-1))=DABS(DIV) 341 DC(IL,(NI-1))=DCA 342 MF(IL,NI)=0.0 343 CB(IL,NI)=0.0 344 TB(IL.NI)=0.0 345 FS(IL.NI)=0.0 346 RB(IL.NI)=0.0 347 DELP1=DELP2 348 KTDC=0 204 349 T1=T2 350 V1=V2 351 C ADJUST MAGNITUDE OF VOLUME FOR WRITE S T A T E M E N T . . . 352 V2=V2*(1E+06) 353 C-354 W R I T E ( 6 , 8 9 3 ) N I , V 2 , P D A T ( I L , N I ) , T 2 , ( X ( I ) , I = 1 , 9 ) , 355 - D L F 1 . E N G Y 2 356 n \* 357 650 V2=V2/(1E+06) 358 40 CONTINUE 359 610 TU1=T1 360 VSU1=V1/MTOT 361 c CALCULATE ENERGY OF MIXTURE JUST BEFORE START OF COMBUSTION 362 c 363 CALL COMP(T1,ENGY1,NRC02,NRH20) 364 KZZ = 2 365 c 366 c START OF PROGRESSIVE BURNING 367 c 368 c 369 c ITERATION CONTROLS AND I N I T I A L I S A T I O N 370 NG=0 371 KOM=0 372 NED= 1 373 J J J = 1 374 NDC-1 375 IDTM=1 376 IMX=1 377 MFX1=0.0 378 NNN= 1 379 IV0L=1 380 KTDC=0 381 SUMXS=NMIX 382 T B 2 = 2 4 0 0 . 0 383 THC0ND=O.1 384 V I S C = 0 . 5 E - 0 4 385 VSB2=0.5 386 DOSUM=0.0 387 PDVSUM=0.0 388 ESPARK=ENGY1 389 c 390 c 391 DO 333 LMN=1,50 392 c 393 c 394 c C A L C . TIME TAKEN FOR PISTON TO TRAVEL THROUGH ' D C A ' DEGREES C. 395 c 396 c IF FIRST TIME THROUGH FROM COMPRESSION STROKE, SKIP VOLUME 397 c C A L C U L A T I O N S . . . . 398 c 399 I F ( K Z Z . E 0 . 2 ) GOTO 727 400 NI=NI+1 401 508 D T I M E = D C A / ( 6 . 0 * S P E E D ) 402 c UPDATE TIME AND CRANK ANGLE C O U N T E R . . . 403 TIME=TIME+DTIME 404 DLF1=DLF1+DCA 405 c C A L C . DISTANCE FROM PISTON TOP TO T . D . C 406 D I S T = D V 0 L ( D L F 1 ) / ( 3 . 1 4 1 5 9 * ( ( B O R E / 2 . ) * * 2 ) ) 205 407 C CALC. CHANGE IN VOLUME DUE TO PISTON MOTION... 408 DIV=DV0L(DLF1-DCA)-DV0L(DLF1) 409 C CALC. NEW TOTAL VOLUME.... 410 V2=V1-DIV 411 727 VT0T1=V2 412 C WRITE(6,461) DTIME,TIME,DLF1,DIST,DIV,V2 413 C 461 F0RMAT(1H ,'DTIME,TIME,DLF1,DIST,DIV,V2=',6E11.4) 414 C UPDATE ITERATION COUNTER AND FIND NO. OF ITERATION AT T.D.C. 415 IF(KTDC.GT.0) GOTO 350 416 IF(DLF1.GE.360.0) KTDC=NI 417 C 418 C START BURNING... 419 c *************** 420 C 421 350 IF(NG.EQ.O) AREAB=0.0 422 C 423 PDT1=PDAT(IL,(NI-1)) 424 PDT2=PDAT(IL,NI) 425 Q II u II II II II II II ll ll ll ll ll tl II II II II II II II II n II II n it II II II II II n tl ll ll fl ii it II II II II n t i tl ti ii ti i i it 426 CALL ENUFLS(PDT2,PDT1,TU1,VSU1,MWMIX,TU2,VSU2. 427 -EU2,TBVEL,LAMBDA,T2,NRC02,NRH20) 423 Q n n H it II it II II ti II II II II n n II II II II it II II it n II II ii ti fl tl tl ll ll tl ll II •• II II II II H II II II II II ti II II •> 429 HTCOEF=(THCOND/BORE)*((MPV*BORE/(VSB2*VISC))**HTEXP)/1000.0 430 DO=HTCOEF *AREAB*(TB2-TWALL)*HTFCN*DTIME 431 NG=1 432 PDV=((PDAT(IL.NI)+PDAT(IL,(NI- 1 ) ) ) / 2 . ) * D I V 433 ENGY2=ENGY1+PDV-DQ 434 PDVSUM=PDVSUM+PDV 435 DOSUM=DOSUM+DO 436 TRT=(MWBMIX*PDAT(IL.NI)*V2)/(MTOT*RMOL) 437 C 438 IF(IPRINT.EO.O) GOTO 971 439 WRITE(6,73») ENGY2,ENGY1,PDV,DQ,HTCOEF,TRT 440 737 FORMATdH ,' E2 , E 1 , PDV , DO, HTCOEF ' , 5E 12 . 4 , F8 . 1 ) 441 C 442 971 ETOT1=ENGY2/MT0T 442 ^ tt n H ti H n H H n II ti ti H it II ti H H it H it n ti it ti ti n H H H ti H H H n H ti ti II n II H it ti i i II n II n II 444 CALL TEMP(PDT2,TB2,CC,MFX2,MT0T,EU2,VSU2, 445 -VTOT1,ETOT1,VSB2.MWBMIX) 44g Q II II n I I n n II II II ti tt tl II II it II ri II ti II n II it it II II it II II n it ii tt tt it it n it ti II n II n II t i ti <i it ti t< 447 IF(MFX2.LT.0.5) GOTO 394 448 IF(MFX2.GT.0.98) GOTO 312 449 IF((MFX2-MFX1).GT.0.01) GOTO 394 450 312 KZZ=2 451 GOTO 365 452 C " " " " " 1 1 " " " " " " n " " " n ** n " ** n n •• ti II II ti n n tt ti ti tt II ti ti II M •• i i •• n H it H II •• M H H •• II 453 394 CALL CALFLS(MFX1.MFX2,VSB2,MTOT,DTIME,VSU2,CBVEL,VSU1, 454 -AREAF 1 ,V0LB2,IVOL,VOLB1,AREAF2,RB1,RB2,DIST) 4 5 5 Q it II II n II II it it n II II n ti ti n it II ii n n n II n n ti II ti H ti it II n n II II it n it ti tt H II II II it it II t i it it ti H ti H ti n II it ti 456 KOM=0 457 C 458 970 V0LU2=VT0T1-V0LB2 459 FLMSPD=(RB2-RB1)/(DTIME) 460 VFRBNT=(V0LB2/VT0T1)*100.0 461 FSR=CBVEL/TBVEL 462 V=VT0T1*(1E+06) 463 PRB2=RB2*100.0 464 PAREAF=AREAF2*10000.0 206 465 C 466 WRITE(6,893) NI,V,PDAT(IL.NI),TU2,TB2,MFX2,VFRBNT.CBVEL, 467 -TBVEL,FLMSPD,FSR,PRB2,PAREAF,DLF1,ENGY2 468 C 469 PP2(IL.NI)=PDAT(IL.NI) 470 TIM(IL,NI)=TIME 471 VV2(IL,NI)=V2 472 DI(IL,(NI-1))=DABS(DIV) 473 DC(IL.(NI-1))=DCA 474 MF(IL,NI)=MFX2 475 CB(IL,NI)=CBVEL 476 TB(IL.NI)=TBVEL 477 FS(IL.NI)=FLMSPD 478 RB(IL,NI)=PRB2 479 C 480 V0LB1=V0LB2 481 AREAF1=AREAF2 482 RB1=RB2 483 TU1=TU2 484 MFX1=MFX2 485 VSU1=VSU2 486 V1=V2 487 T1=T2 488 ENGY1=ENGY2 489 KZZ=1 490 IV0L=2 491 333 CONTINUE 492 C 493 365 T1=MFX2*TB2+(1-MFX2)*TU2 494 ECEND=ENGY2 495 C WRITE(6,266) MWBMIX,PDAT(IL,NI).V2,MTOT,RMOL 496 C 266 FORMAT(1H .5E12.4/) 497 TRT= (MWBMIX*PDAT(IL.NI)*V2)/(MTOT*RMOL) 498 CALL ENERGY(TRT,PDAT(IL.NI).EPROD,SUMXS.NNN,CC,X,EB2,VSB2, 499 -GAMMA,MWBMIX) 500 TENGY = EPROD*MOLF L 501 TDO=(ESPARK-TENGY)-PDVSUM 502 WRITE(6.265 ) ESPARK,ECEND.TENGY,PDVSUM.DOSUM,TDO,T1.TRT 503 265 F0RMAT(1H ,'ESPK,ECND,TENG,PDVS,DOS,T1,TRT ',6F10.6,2F7.1/) 504 DO 249 KKI = 1, 10 505 249 X(KKI)=0.0 506 NUT=0 507 JdU=1 508 NNN= 1 509 IF(KZZ.E0.2) GOTO 396 510 511 C START EXPANSION STROKE 512 C 513 C 514 310 DIV=DV0L(DLF1+DCA)-DV0L(DLF1) 515 V2=V1+DIV 516 IF(V2.LT.497.0E-06) GOTO 851 517 DLF1=DLF1+DCA 518 IF(DLF1.GE.538 ) J J J = 2 519 TIME=(DLF1-180.0)/(6.0*SPEED) 520 NI=NI+1 521 GOTO 718 522 851 DLF1=DLF1+DCA 207 523 DIST=DVOL(DLF1)/(3.14159*((BORE/2.)**2)) 524 DTIME=DCA/(6.0*SPEED) 525 TIME=(DLF1-180.0)/(6.0*SPEED) 526 NI=NI+1 527 NUT=NUT+1 528 IF(NUT.GT.80) STOP 529 396 AT0T = 3.14 159*(2.*RDASH*HTCLRV+((BORE/2.)**2) + 2.*(BORE/2) 530 -*DIST) 531 CALL EXP(PDAT(IL,(NI-1)),V1,T1,PDAT(IL,NI),V2,T2,NNN,CC, 532 -SUMXS,ENGY1,ENGY2.ATOT.DTIME,MTOT.MWBMIX) 533 718 ENGY1=ENGY2 534 T1=T2 535 V1=V2 536 PP2(IL.NI)=PDAT(IL.NI) 537 VV2(IL.NI)=V2 538 TIM(IL,NI)=TIME 539 DI(IL,(NI-1))=DABS(DIV) 540 DC(IL.(NI-1))=DCA 541 MF(IL,NI)=MFX2 542 CB(IL,NI)=0.0 543 TB(IL,NI)=0.0 544 FS(IL.NI)=0.0 545 RB(IL,NI)=0.0 546 V4=V2 547 T4=T1 548 V4=V4*(1E+06) 549 C 285 IF(JJJ.EQ.2) GOTO 277 550 C IF(NUT.GT.2) GOTO 817 551 C 552 277 WRITE(6,893) NI,V4.PDAT(IL,NI).X(1),T4,MFX2,VFRBNT,(X( I ),I = 1 , 6) , 553 -DLF1,ENGY2 554 C 555 817 IF (JJJ.E0.1) GOTO 310 556 C 557 WRITE(6,818) (CC(I ) ,I = 1,8) 558 818 F0RMAT(1H ,'%C02=',F7.3,' %C0=',F7.3,' %H20=',F7.3,' %H2=',F7.3, 559 -' %02='.F7.3.' %N2=',F7.3,' %N0=',F7.3,' %0H=',F7.3/) 560 C 561 C 562 C THIS SECTION CALCULATES INTEGRAL OF PDV (PDV),MEAN EFFECTIVE 563 C PRESSURE (MEP),POWER AND THERMAL EFFICIENCY. 564 C ============================================================ 565 C 566 304 PDV=0.0 567 SUMDI=0.0 568 AREA1=0.0 569 AREA3=0.0 570 MTDC=KTDC-1 571 DO 300 J=1,MTDC s 572 300 AREA1=AREA1+(PP2(IL,d)+PP2(IL,(J+1)))*DI(IL,J)/2.0 573 NTDC=KTDC+1 574 NID=NI-1 575 DO 302 <J=NTDC, NID 576 302 AREA3=AREA3+(PP2(IL.U)+PP2(IL,(J+1)))*DI(IL,J)/2.0 577 DO 303 d=1,MTDC 578 303 SUMDI=SUMDI+DI(IL,J) 579 VA1=CYLV-SUMDI 580 VA2=DI(IL,KTDC)-VA1 208 581 P P T D C = P P 2 ( I L , K T D C ) + ( ( V A 1 / D I ( I L , K T D C ) ) * ( P P 2 ( I L , N T D C ) -582 - P P 2 ( I L . K T D C ) ) ) 583 A R E A 2 = ( P P T D C + P P 2 ( I L , K T D C ) ) * V A 1 / 2 . 0 584 A R E A 4 = ( P P T D C + P P 2 (IL , N T D C ) ) * V A 2 / 2 . 0 585 I F ( I P R I N T . E Q . O ) GOTO 269 586 WRITE(6 .486) AREA 1 , A R E A 2 , A R E A 3 , A R E A 4 , V A 1 , V A 2 , P P T D C , P D V 587 486 FORMAT(1H , 'A 1 , A 2 , A 3 , A 4 , V A 1 , V A 2 , P T D C , P D V ' , 8 E 1 2 . 4 / ) 588 269 PDV=(AREA3+AREA4)-(AREA1+AREA2) 589 MEP=PDV/ (CYLV*100 .0 ) 590 POWER=(PDV*SPEED/120. ) 591 E F F = ( P D V * 1 0 0 . ) / ( M O L F L * Q V S * ( 1 2 . * C N + H M ) ) 592 C -593 WRITE(6 ,301) POWER,MEP,EFF 594 301 F O R M A T ( 1 0 X , 6 H P 0 W E R = , F 8 . 3 , 5 X , 9 H I . M . E . P . = , F 7 . 3 , 5 X , 1 1HEF FICIENC Y = , 595 - F 1 0 . 5 / / / ) 596 C 597 C WRITE VALUES OF PRESSURE. MASS FRACTION BURNT, C A L C . BURNING 598 C VELOCITY , LAMINAR BURNING VELOCITY, AND FLAME SPEED FOR USE 599 C BY THE PLOTTING PROGRAM ' D P 2 ' . . . . 600 C 601 IJUMP 1=0 602 IJUMP2=0 603 IJUMP3=0 604 IJUMP4=1 605 NUMM=1 606 ISPK=IDINT(SPKAD) 607 I F ( I L . G T . I ) GOTO 799 608 C WRITE(6 ,933) NUMBR,IJUMP 1 , IJUMP2, IJUMP3, IJUMP4 609 C933 F0RMAT(5I3) 610 799 WRITE(6 ,934) NUMM,SPEED, ISPK,KFUEL 611 934 F 0 R M A T ( I 4 , F 8 . 1 , 1 4 , 1 3 ) 612 DO 928 JK=1 ,180 613 WRITE(6 ,929) P P 2 ( I L , J K ) , M F ( I L , J K ) , C B ( I L , J K ) , T B (I L , J K ) , FS ( IL , JK) 614 - , R B ( I L , J K ) 615 929 F0RMAT(6F10 .4 ) 616 928 CONTINUE 617 C 618 C 619 C 620 222 CONTINUE 621 C 622 C0####################*##n</!'#^ 623 C 624 C 625 C THIS SECTION GENERATES A P-V DIAGRAM AND A 626 C PRESSURE-CRANK ANGLE DIAGRAM. 627 C ========================================== 628 C 629 I F ( I G R A P H . E O . O ) GOTO 599 630 387 DO 605 IL=1,NUMBR 631 DLF=180 .0 632 Z Z ( I L , 1 ) = 2 . 0 633 DO 605 J=1,NID 634 V V ( I L , J ) = V V 2 ( I L , J ) * 1 0 0 0 . 635 P P ( I L , J ) = P P 2 ( I L , J ) / 1 0 0 . 636 DLF=DLF+DC( IL ,J ) 637 D L ( I L , ( J + 1 ) ) = D L F 638 C X X ( I L . J ) = ( 5 . * V V ( I L , J ) ) + 2 . 0 209 639 YY(IL.d)=(PP(IL,d)/20.)+2.0 640 ZZ(IL,(d+1 )) = ((DL(IL,(d+1))-180.0)/60.0) + 2.0 641 605 CONTINUE 642 643 C CALL AXIS(2.,2.,'VOLUME ( L ) ' , - 10.5..0.,0.,0.2) 644 C CALL AXIS(2. ,2. . 'PRESSURE (BAR)',14,5 . ,90. ,0. ,20. ) 645 c DO 607 IL=1.NUMBR 646 c DO 607 1=1,NID 647 c 607 CALL SYMBOL(XX(IL,I),YY(IL,I),0.05,IL,0. ,- 1) 648 c CALL LINE(XX(1,I),YY(1,I),NID,1) 649 f 650 CALL PL0T(1O.,0.,-3) 651 CALL AXIS(2.,2. , 'CRANK ANGLE',- 11,6.0,0., 180.,60.) 652 CALL AXIS(2.,2., 'PRESSURE (BAR)',14,5.,90. ,0. ,20. ) 653 DO 415 IL=1.NUMBR 654 DO 415 1=1,NID 655 415 CALL SYMBOL(ZZ(IL,I),YY(IL,I),0.05,IL,0..-2) 656 c CALL LINE(ZZ(1,I),YY(1,I),84,1) 657 CALL PLOTND 658 599 STOP 659 END 660 c 661 662 c 663 c SUBROUTINE TEMP CALCULATES TEMP. OF BURNT GAS AND MASS FRACTION 664 c ============= BURNED. 665 c 666 SUBROUTINE TEMP(P1,TB2,CC,MFX,MTOT,EU2,VSU2,VTOT1,ET0T,VSB2, 667 -MWBMIX) 668 c 669 COMMON /AREA 1/ NCH,N02.K,L,M,N.KFUEL 670 COMMON /AREA2/ MOLFL,NMIX.HF1,NN02.NN2.NNFUEL,KOM 671 COMMON /AREA4/ NDISS,IPRINT 672 c 673 REAL*8 XF,DX,EPS.Y1,Y2,Y3,XX2,YY2, 674 -X1,X2,X3,X30LD.P1,P2,P3,CC(10),X(10),K,L.M.N,GAMMA,MFX,MTOT 675 -,EU2,VSU2.VTOT1,VSB2,EB2,TB2,ETOT,VTOTC,NMIX,MFXE,MFXV 676 -,EPROD.SUMXS,NCH,N02,MOLFL,HF1,NN02.NN2,NNFUEL,GA,MWBMIX 677 c 678 NNN= 1 679 K0M=K0M+1 680 IF(KOM.GT.10) GOTO 93 681 NUT=0 682 dDX=1 683 IDX=1 684 X1=1900.0 685 XF=4000.0 686 DX=1O0.0 687 EPS=0.00010 688 5 CALL ENERGY(X1,P1,EPROD,SUMXS,CC.X,EB2,VSB2,GA,MWBMIX) 689 MFXE=(ET0T-EU2)/(EB2-EU2) 690 c WRITE(6,777) X1,ETOT,VTOT1,P1,EB2.MFXE 691 c 777 FORMATdH , ' X 1 , ETOT , VTOT 1 ,P1 .EB2.MFXE' .6E12.4) 692 IF(MFXE.GT.O.O) GOTO 10 693 X1=X1+DX 694 IF(X1.GT.XF) GOTO 91 695 dDX = 2 696 GOTO 5 210 G97 10 MFXV=(VTOT1/MT0T-VSU2)/(VSB2-VSU2) 698 Y1=MFXV-MFXE 699 IF(JDX.EQ.1) GOTO 30 700 IF (Y1.LT.O.O) GOTO 30 701 DX=-DX/2. 702 IDX = 2 703 30 X2=X1+DX 704 IF(X2.GT.XF) GOTO 91 705 20 CALL ENERGY(X2,P1,EPROD,SUMXS.CC,X,EB2,VSB2,GA,MWBMIX) 706 MFXE=(ET0T-EU2)/(EB2-EU2) 707 C 747 FORMAT(1H ,'X2,MFXE.MFXV,VSB2,VSU2.EB2,EU2;'.7E10.3) 708 IF(MFXE.GT.O.O) GOTO 15 709 DX=DX/2. 710 IDX = 2 711 X2=X2-DX 712 NUT=NUT+1 713 IF(NUT.GT.30) GOTO 91 714 GOTO 20 715 15 IF(IDX.EO.1) GOTO 16 716 DX=DX/2. 717 16 MFXV=(VT0T1/MT0T-VSU2)/(VSB2-VSU2) 718 Y2=MFXV-MFXE 719 ' C WRITE(6,747) X2.MFXE.MFXV,VSB2,VSU2.EB2,EU2 720 IF(Y1*Y2.LE.O.O) GOTO 25 721 X1=X2 722 Y1=Y2 723 NUT=NUT+1 724 IF(NUT.GT.60) GOTO 91 725 GOTO 30 726 25 IF(Y2.E0.0.0) GOTO 50 727 IF(X2.GT.X1) GOTO 35 728 XX2=X2 729 YY2=Y2 730 X2 = X1 731 Y2 = Y1 732 X1=XX2 733 Y1=YY2 734 35 IF(MFXE.LT.10.0) GOTO 36 735 DX=DX/10.0 736 X2=X2-DX 737 GOTO 20 738 36 X30LD=X2 739 40 X3=(X1*Y2-X2*Y1)/(Y2-Y1 ) 740 NUT=NUT+1 741 IF (NUT.LT.150) GOTO 80 742 91 IS = 2 743 RETURN 744 93 WRITE(6,90) KOM 745 90 FORMAT(1H .'PROGRAM STOP DUE TO TEMP ITERATIONS EXCEEDING',14) 746 STOP 747 80 IF(DABS((X3-X30LD)/X3).LT.EPS) GOTO 60 748 X30LD=X3 749 CALL ENERGY(X3,P1,EPROD,SUMXS,CC,X,EB2,VSB2,GA,MWBMIX) 750 MFXE=(ET0T-EU2)/(EB2-EU2) 751 MFXV=(VTOT1/MTOT-VSU2)/(VSB2-VSU2) 752 Y3=MFXV-MFXE 753 C WRITE(6,767) X3,MFXE,MFXV,Y3 754 C 767 FORMAT(1H .'X3.MFXE,MFXV.Y3'.4E12.4) 21 1 755 IF(Y1*Y3.LE.O.) GOTO 45 75G X1=X3 757 Y1=Y3 758 GOTO 40 759 45 X2=X3 760 Y2=Y3 761 GOTO 40 762 50 TB2=X2 763 GOTO 70 764 60 TB2=X3 765 70 MFX=(MFXE+MFXV)/2.0 766 IF(IPRINT.EO.O) GOTO 225 767 C :  768 WRITE(6,112) TB2,MFXE,MFXV,EB2,VSB2,GA 769 112 F0RMAT(1H ,'TB2,MFXE,MFXV,EB2,VSB2,GA;',6E12.4) 770 C 771 225 IS=1 772 RETURN 773 END 774 C 775 C 776 C SUBROUTINE ENERGY TO CALCULATE THE ENERGY AND COMPOSITION OF 777 C ================= BURNED GAS AT A GIVEN TEMP. (T) AND PRESS. (P), 778 C INCLUDING THE EFFECTS OF DISSOCIATION. 779 C 780 SUBROUTINE ENERGY(T,P,EPROD,SUMXS,CC,X,EB2,VSB2,GAMMA,MWBMIX) 781 C 782 IMPLICIT REAL*8(A-H,0-Z) 783 REAL*8 K,L,M,N,KE(6).NM,KK,MWBMIX.MW(10),NMIX,NCH,N02,MOLFL, 784 -NN02,NN2,NNFUEL,KC02,KH20,KN2,MPV 785 C 786 COMMON /AREA 1/ NCH,N02,K,L,M,N,KFUEL 787 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02,NN2,NNFUEL,KOM 788 COMMON /AREA3/ AREAB.HTEXP,MPV,HTFCN,TWALL,VISC,THCOND 789 COMMON /AREA4/ NDISS.IPRINT 790 C 791 DIMENSION X(10),CPG(10),UUU(10),DH(10),CC(10),SP(6),RES(6,4), 792 -S0T(6),SPP(6,4) 793 C 794 C IF TEMP. LESS THAN 1750K, SKIP DISSOCIATION CALCULATIONS 795 IF(T.LT.1750) GOTO 17 796 IF(NDISS.EQ.O) GOTO 17 797 JZ IPRINT=1 798 C 799 C THE DISSOCIATION CAN INCLUDE THE FOLLOWING REACTIONS; 800 C (1) C02=CO+0.502, 801 C (2) H20=H2+0.502, 802 C (3) H20=0H+O.5H2, 803 C (4) NO=0.5N2+0.502, 804 C (5) H2=2H, 805 C (6) 02=20. 806 C IF NDISS-1, REACTIONS 1 & 2 ARE INCLUDED, 807 C IF NDISS=2, REACTIONS 1,2,3 & 4 ARE INCLUDED, 808 C IF NDISS=3, REACTIONS 1,2,3,4,5 & 6 ARE INCLUDED. 809 C 810 C THE FOLLOWING LINES CALCULATE THE EQUILIBRIUM CONSTANTS FOR EACH 811 C REACTION 1 TO 6, INCLUDING THE (PO/P) TERM, 812 C' ALSO, INITIALISE THE DISSOCIATED SPECIES CONCENTRATIONS, 212 813 C 814 00 304 1=1,6 815 SP(I)=0.0 816 KE(I)=0.0 817 304 SPP(I.4)=0.0 818 C 819 GOTO(302,301,300),NDISS 820 300 KE(6)=DEXP(DL0G(T)**(-6.93319)*(-43428300)+19.3067)*(101.3/P) 821 KE(5)=DEXP(DLOG(T)**(-6.81208)*(-30743900)+17.8668)*(101.3/P) 822 SP(6)=0.000 823 SP(5)=0.000 824 301 KE(4)=DEXP(DL0G(T)**(-7.33550)*(-16592550)+1.80127) 825 KE(3)=DEXP(DLOG(T)**(-7.04570)*(-30372100)+10.159) 826 -*DSQRT(101.3/P) 827 SP(4)=0.000 828 SP(3)=0.000 829 302 KE(2)=DEXP(DLOG(T)* *(-6.86740)*(- 18878550)+8.7095) 830 -*DSORT(101.3/P) 831 KE(1)=DEXP(DL0G(T)**(-7.47210)*(-65549000)+10.53) 832 -*DSQRT(101.3/P) 833 SP(2)=0.1 834 SP(1)=0.1 835 c 836 IF(IPRINT.EQ.O) GOTO 650 837 c-838 WRITE(6.21) (KE(IJK),IdK=1,6) 839 21 FORMAT(1H ,'KE(1-6) '.6E13.3) 840 c-841 c 842 c DEFINE UNIVERSAL GAS CONSTANT AND SET ITERATION COUNTER TO ZERO, 843 650 RM0L=8.3143 844 NUT=0 845 c 846 c START DISSOCIATION ITERATION ROUTINE. A PROPORTIONAL CHOPPING 847 c ITERATION TECHNIQUE IS USED TO SOLVE FOR THE VARIOUS SPECIES 848 c CONCENTRATIONS AT THE GIVEN TEMPERATURE AND PRESSURE.... 849 c 850 10 QQ=0 851 c 852 c THIS SECTION ENSURES THAT ITERATIONS CANNOT CONTINUE INDEFINATELY, 853 NUT=NUT+1 854 IF(NUT.LT.150) GOTO 400 855 WRITE(6,401) NUT 856 401 FORMATdH .'PROGRAM STOP DUE TO ENERGY ITERATIONS EXCEEDING',14) 857 STOP 858 c 859 400 NSP=2*NDISS 860 c 861 c STEP I FROM 1 TO NUMBER OF DISSOCIATION REACTIONS... 862 DO 600 I=1,NSP 863 c 864 NUTT=0 865 IFLAG1=0 866 c 867 S=(SP(1 ) + SP(2)+SP(3))/2+(SP(5)+SP(6)+K+L+M+N) 868 c 869 IF(IPRINT.EQ.O) GOTO 651 870 c-213 871 WRITE(6,20) I,(SP(IJK),IJK =1,6) ,S 872 20 F0RMAT(1H ,'I,SP(1-6),S '.I4.7E9.2) 873 r* 874 c 875 c INITIAL GUESS AT SPECIES CONCENTRATION... 876 651 J=1 877 SP(I)=0.000001 878 SPP(I,J)=SP(I) 879 GOTO(450,451,452,453,454,455) , I 880 1 CONTINUE 881 c 882 IF(IPRINT.EO.O) GOTO 9 883 f u 1 884 WRITE(6,19) I,SP(I).RES(I.1) 885 19 FORMATdH ,'I,SP,RES1 '.I4.2E10.3) 886 r» 887 c 888 c SECOND AND SUCCESSIVE GUESSES AT SPECIES CONCENTRATION... 889 9 J = 2 890 STEP=0.1 891 IF(T.LT.2000) STEP=0.02 892 SP(I)=SP(I)+STEP 893 IF(SP(I).GT.10) GOTO 500 894 SPP(I,J) =SP(I) 895 IFLAG1=0 896 GOTO(450,451,452,453,454,455 ) .I 897 2 CONTINUE 898 c 899 IF(IPRINT.EQ.O) GOTO 652 900 901 WRITE(6,18) I,SP(I),RES(I,1),RES(I,2) 902 18 FORMATdH , ' I , SP , RES 1 , RES2 ' , 14 , 3E 1 1 . 3/) 903 904 c 905 c IF RESIDUAL CROSSES ZERO BETWEEN PREVIOUS AND CURRENT GUESSES 906 c THEN GO TO PROPORTIONAL CHOPPING ROUTINE. OTHERWISE CONTINUE 907 c INCREMENTING SPECIES CONCENTRATION... 908 652 IF((RES(I,1)*RES(I,2)).LE.0.0) GOTO 5 909 RES(I.1)=RES(1,2) 910 SPP(I,1 ) = SPP(I,2) 91 1 GOTO 9 912 c 913 5 IF(RES(I.2).EQ.O) GOTO 5CO 914 SPOLD=SPP(I,2) 915 J = 3 916 c 917 c FIND VALUE OF SPECIES CONCENTRATION (SP(I)) AT WHICH RESIDUAL 918 c BECOMES SMALL, I.E. WHEN PREVIOUS 'SP' EQUALS CURRENT 'SP' TO 919 c WITHIN ONE PERCENT... 920 6 SP(I)=(SPP(I,1)*RES(I,2)-SPP(I,2)*RES(I.1))/(RES(I,2)-RES(I 921 IF(DABS((SP(I)-SP0LD)/SP(I)).LT.O.O1) GOTO 500 922 SPOLD=SP(I) 923 c 924 GOTO(450,451,452,453,454,455 ) ,I 925 3 CONTINUE 926 c 927 IF(IPRINT.EQ.O) GOTO 654 928 c-214 929 WRITE(6,15) I,SP(I),RES(1,1),RES(I,3) 930 15 FORMATdH , ' I , SP , RES 1 , RES3 '.I4.3E11.3) 931 C 932 C 933 654 IF(RES(I. 1)*RESU.3).LE.O.O) GOTO 4 934 SPP(I,1)=SP(I) 935 RES(I,1)=RES(I,3) 936 GOTO 6 937 4 SPP(I,2)=SP(I ) 938 RESd ,2)=RES(I ,3) 939 GOTO 6 940 C 941 C IF VALUE OF SP(I) FROM CURRENT SPECIES CALCULATIONS EQUALS THE 942 C VALUE OF SP(I) FROM THE PREVIOUS SET OF SPECIES CALCULATIONS AT 943 C THE SAME TEMPERATURE. THEN LEAVE QQ=0. OTHERWISE SET QQ=1 WHICH 944 C WILL CAUSE ANOTHER SET OF CALCULATIONS TO BE PERFORMED... 945 500 IF(DABS((SP(I)-SPP(I,4))/(SP(I))).GT.0.05) QQ=1 946 SPP(I,4)=SP(I ) 947 GOTO 600 948 C 949 C THIS SECTION CALCULATES THE RESIDUALS FOR EACH SPECIES USING 950 C THE CURRENT VALUES OF SP(1-6). 951 450 SQT(1)=M+((SP(1)+SP(2)-SP(4))/2)-SP(6) 952 IF(SQT(1).LE.0.0) GOTO 456 953 RES(1,J)=SP(1)/(K-SP(1 ) )*DSQRT(SQT(1)/S)-KE(1) 954 GOTO 460 955 451 SQT(2)=M+((SP(1)+SP(2)-SP(4))/2)-SP(6) 956 IF(SQT(2).LE.O.O) GOTO 456 957 RES(2,J)=(SP(3)/2+SP(2)-SP(5))/(L-SP(3)-SP(2))*DSQRT(SQT(2)/S) 958 1-KE(2) 959 GOTO 460 960 452 SQT(3)=SP(3)/2+SP(2)-SP(5) 961 IF(SQT(3).LE.0.0) GOTO 456 962 RES(3.J) = (SP(3))/(L-SP(3)-SP(2))*DSQRT(SQT(3)/S)-KE(3) 963 GOTO 460 964 453 SQT(4)=(N-SP(4)/2)*(M-SP(6)+(SP(1)+SP(2)-SP(4))/2) 965 IF(SQT(4).LE.O.O) GOTO 456 966 RES(4,J)=SP(4)/DSQRT(SQT(4))-KE(4) 967 GOTO 460 968 454 SQT(5)=SP(3)/2+SP(2)-SP(5) 969 IF(SQT(5).LE.0.0) GOTO 456 . 970 RES(5.d)=(4*SP(5)*SP(5))/S/SQT(5)-KE(5) 971 GOTO 460 972 455 SQT(6)=M-SP(6)+(SP(1)+SP(2)-SP(4))/2 973 IF(SQT(6).LE.0.0) GOTO 456 974 RES(6,d) = (4*SP(6)*SP(6) )/S/SQT(6)-KE(6) 975 456 SP(I ) = SPP(I,4) 976 GOTO 600 977 460 NUTT=NUTT+1 978 C 979 IF(IPRINT.EQ.O) GOTO 655 980 C 981 WRITE(6,22) NUTT,RES(I,J) .SQT(I),I FLAG 1 982 22 FORMATdH , ' NUT , RES( I . J) , SQT( I ) , FLAG ' , 13 , 2E 14 . 5 , 13 ) 983 C 984 C 985 655 IF(NUTT.LT.50) GOTO 16 986 WRITE(6,401) NUTT 215 987 STOP 988 16 G0T0(1,2,3) , J 989 C 990 600 CONTINUE 991 C 992 A=SP(1) 993 B=SP(3) 994 C=SP(2) 995 D=SP(4) 996 E=SP(5) 997 F=SP(6) 998 C 999 IF(IPRINT.EQ.O) GOTO 656 1000 C 1001 WRITE(6,14) T.A.B.C.D.E.F 1002 14 FORMATdH , 'T , A , B , C , D, E , F ' , F8 . 1 , 6E 10 . 3/) 1003 C 1004 656 IF(00)461,461,10 1005 C 1006 C 1007 461 CONTINUE 1008 C 1009 C CALCULATING CHANGE IN ENTHALPIES FOR SPECIES 1 TO 10 BET. T AND 289K 1010 C C02=1, C0=2, H20=3, H2=4, 02=5, N2=6, N0=7, H=10, 0=9, 0H=8 10tl KK=0 1012 17 TT=T/100 1013 IF (T.GT.3000.0) GOTO 99 1014 DH(1)=((3.096*T+0.00273*(T**2)-7.885E-07*(T**3) 1015 1+8.66E-11*(T**4))-1145.0)*RMOL 1016 DH(2)=((3.317*T+3.77E-04*(T**2)-3.22E-08*(T**3) 1017 1-2.195E-12*(T**4))-1022.O)*RM0L 1018 DH(3)=((3.743*T+5.656E-04*(T**2)+4.952E-08* (T**3) 1019 1-1.818E-11*(T**4))-1167.O)*RM0L 1020 DH(4) = ((3.433*T-8.18E-06*(T**2)+9.67E-08* ( T* *3) 1021 1-1 .444E-11*(T**4))- 1025.0)*RMOL 1022 DH(5) = ((3.253*T+6.524E-04*(T**2)-1.495E-07* (T**3) 1023 1 + 1 .539E-11*(T**4))-1024.0)*RMOL 1024 DH(6)=((3.344*T+2.943E-04*(T**2)+1.953E-09*(T**3) 1025 1-6 .575E-12*(T**4))-1023.0)*RMOL 1026 DH(7)=((3.502*T+2.994E-04*(T**2)-9.59E-09*(T**3) 1027 1-4.904E-12*(T**4))-1070.0)*RMOL 1028 DH(10)=((2.5*T)-745.O)*RMOL 1029 DH(9) = ((2.764*T-2.514E-04*(T**2)+1.002E-07* ( T**3) 1030 1-1.387E-11*(T**4))-8O4.O)*RM0L 1031 DH(8) = ((81.546*TT-47.48*(TT**1.25)+9.902*(TT** 1.?5) 1032 1-2.133*(TT**2.))* 100-10510) 1033 GOTO 91 1034 99 DH(1)=((5.208*T+0.0O059*(T**2)-5.614E-08*(T**3) 1035 1+2.O5E-12*(T**4))-1126.O)*RM0L 1036 DH(2)=((3.531*T+2.73E-04*(T**2)-3.28E-08*(T**3) 1037 1+1.565E-12*(T**4))-1O42.O)*RM0L 1038 DH(3) = ((143.05*TT-146.83*(TT**1.25)+55.17*(TT**1 .5) 1039 1-1.85*(TT**2.))*100-11945.0) 1040 DH(4)=((3.213*T+2.87E-04*(T**2)-2.29E-08*(T**3) 1041 1+7.666E-13*(T**4))-1018.0)*RMOL 1042 DH(5)=((3.551*T+3.203E-04*(T**2)-2.876E-08*(T**3) 1043 1+1.OO5E-12*(T**4))-1O44.O)*RM0L 1044 DH(6)=((3.514*T+2.583E-04*(T**2)-2.84 1E-08*(T**3) 216 1045 1 + 1 .242E-12*(T**4)) -1043.0)*RM0L 1046 DH(7)=((3.745*T+1.950E-04*(T**2)- 1.88E-08*(T**3) 1047 1 + 7.703E-13*(T**4))- 1106.0)*RM0L 1048 DH(1O)=((2.5*T)-745.O)*RM0L 1049 DH(9)=((2.594*T-3.843E-05*(T**2)+7.514E-09*(T**3) 1050 1-3.209E-13*(T**4))-809.0)*RM0L 1051 DH(8)=((81.546*TT-47.48*(TT**1.25)+9.902*(TT**1.75) 1052 1-2.133*(TT**2.))*100-10560.) 1053 C 1054 C CALCULATE CONSTANT PRESSURE SPECIFIC HEATS 1055 91 CPG(1)=-3.7357+30.529*(TT**(0.5))-4.1034*TT+0.024198*(TT**2) 1056 CPG(2)=69.145-.70463*(TT**(0.75))-200.77*(TT**(-O.5)) 1057 -+176.76*(TT**(-0.75)) 1058 CPG(3)=143.05-183.54*(TT**(0.25))+82.751*(TT**(0.5)) 1059 --3.69889*TT 1060 CPG(4) = 56.505-702.74*(TT**(-.75)) + 1165.0/TT-560.7*(TT**(- 1.5)) 1061 CPG(5)=37.432+0.020102*(TT**1.5)-178.57*(TT**(- 1.5)) 1062 -+236.88*(TT**(-2)) 1063 CPG(6)=39.060-512.79*(TT**(-1.5))+1072.7*(TT** (-2)) 1064 --820.4*(TT**(-3)) 1065 CPG(7)=59.283-1.7096*(TT**0.5)-70.613*(TT**(-O.5)) 1066 -+74.889*(TT**(-1.5)) 1067 CPG(8)=81.546-59.35*(TT**0.25)+17.329*(TT**0.75)-4.266*TT 1068 C 1069 C CALC. NUMBER OF MOLES OF EACH SPECIES AFTER DISSOCIATION 1070 X(1)=K-A 1071 X(2)=A 1072 X(3)=L-B-C 1073 X(6)=N-D/2 1074 X(7)=D 1075 X(4)=C+B/2-E 1076 X(5)=M-F+(A+C-D)/2 1077 X(10)=2*E 1078 X(9)=2*F 1079 X(8)=B 1080 C 1081 C CALC. VISCOSITY 8. THERMAL CONDUCTIVITY OF PRODUCTS... 1082 VC02=((0.019*T+24.2)*X(1)* 1E-06)/(X(1)+X(3) + X(6)) 1083 KC02 = ((0.041*T + 36.1)*X(1)* 1E-03)/(X(1) + X(3)+X (6)) 1084 VH20=((0.025*T+15.8)*X(3)*1E-06)/(X(1)+X(3) + X ( 6)) 1085 KH20=((0.130*T-0.60)*X(3)*1E-03)/(X(1)+X ( 3) + X( 6)) 1086 VN2 = ((0.019*T+24.1)*X(6)* 1E-06)/(X(1)+X(3) + X(6)) 1087 KN2 = ((0.039*T+35.8)*X(6)* 1E-03)/(X(1)+X(3) + X(6)) 1088 VISC=VC02+VH20+VN2 1089 THC0ND=KC02+KH20+KN2 1090 C 1091 C ENTHALPY OF FORMATION FOR EACH SPECIES... 1092 UUU(1)=-3.93522E05 1093 UUU(2)=-1.10529E05 1094 UUU(3)=-2.41827E05 1095 UUU(4)=O.OOOOOEOO 1096 UUU(5)=O.OOOOOEOO 1097 UUU(6)=O.OOOOOEOO 1098 UUU(7)=9.05920E04 1099 UUU(10)=2.17986E05 1100 UUU(9)=2.49195E05 1101 UUU(8)=39463.0 1102 C 217 1103 C MOLECULAR WEIGHT FOR EACH SPECIES... 1104 MW(1)=44.01 1105 MW(2)=28.01 1106 MW(3)=18.01 1107 MW(4)=2.02 1108 MW(5)=32.00 1109 MW(6)=28.01 1110 MW(7)=30.00 1111 MW(8)=17.00 1112 MW(9)=16.00 1113 MW(10)=1.00 1114 C 1115 C CALC. ENERGY OF PRODUCTS 1 TO 10 1116 EPROD=0. 1117 DO 109 1 = 1 , 10 1118 ECOMP=X(I)*(UUU(I)+DH(I)-RMOL*T) 1119 IF(MODE.EO.3) ECOMP=X(I)*(UUU(I)+DH(I)) 1120 EPROD=EPROD+ECOMP 1121 109 CONTINUE 1 122 C 1123 C CALCULATE SUM OF X VALUES 1124 SUMXS=0 1125 DO 231 ILG=1.10 1126 231 SUMXS=SUMXS+X(ILG) 1 127 C 1128 C CALC PERC. OF PRODUCTS AND MOLECULAR WEIGHT OF MIXTURE 1129 MWBMIX=0.0 1130 DO 232 ILH=1.10 1131 CC(ILH)=(X(ILH)/SUMXS)*100. 1132 232 MWBMIX=MWBMIX+(CC(ILH)*MW(ILH)/100.) 1133 EB2=EPR0D/MWBMIX/SUMXS 1134 VSB2=RM0L*T/(MWBMIX*P) 1 135 C 1136 C CALC. AVERAGE SPECIFIC HEATS FOR MIXTURE... 1137 CP=0 1138 DO 233 ILF = 1 ,8 1139 233 CP=CP+(CC(ILF)*CPG(ILF))/100. 1140 CV=CP-RMOL 1141 GAMMA=CP/CV 1 142 C 1143 C-1144 C WRITE(6,889) MWBMIX,EB2,VSB2,GAMMA,NDISS 1145 C 889 F0RMAT(1H ,'MWBMIX,EB2,VSB2,GAMMA,NDS '.4E12.4.I3) 1146 C ' 1147 C 1148 RETURN 1149 END 1 150 C 1151 C SUBROUTINE CALFLS THIS IS USED TO OBTAIN THE CALCULATED 1152 C ================= BURNING VELOCITY 1 153 C 1154 SUBROUTINE CALFLS(MFX1,MFX2,VSB2.MTOT,DTIME,VSU2,CBVEL, 1155 -VSU1,AREA 1,V0LB2,1VOL,VOLB1,AREA2,RB1,RB2,DI ST) 1156 C 1157 COMMON /AREA4/ NDISS,IPRINT 1158 C 1159 REAL*8 RF,DR,EPS,Y1,Y2,Y3,BORE,D,XDOT,ARAVG,AREA, 1160 -R1,R2.R3.R30LD,DTIME,RMAX,R,VOLB1,MFX2,AREA 1,AREA2,RB1 ,RB2, 218 1 161 -FFF,MFX,VSB2.VSU2,MTOT,MFX1.VOLB2,VOLB,CBVEL,VSUAVG,VSU1.RADBMB 1162 -,DIST 1 163 C 1164 VOLB2=MTOT*MFX2*VSB2 1165 C CALC. MAXIMUM RADIUS WHICH FLAME CAN ATTAIN 1166 C GIVEN THE POSITION OF THE PISTON IN THE CYLINDER (DIST)... 1167 ' RMAX=DSQRT(((0.018358+DIST)**2)+(0.0425**2)) 1168 IF(IV0L.EQ.2) GOTO 546 1169 RB1=0.0001 1170 CALL V0L(RB1.DIST.AREA,VOLB) 1171 VOLB1=VOLB 1172 AREA 1 =AREA 1 173 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1174 C 546 WRITE(6,201) V0LM1,AREA 1,RMAX,V0LB2 1175 C 201 FORMAT(1H ,'VOLM1,AREA 1,RMAX,V0LB2, '.4E12.5) 1176 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1177 C 1178 C ITERATION PROCEDURE FINDS RADIUS AND AREA OF NEW BURNT VOLUME 1179 546 NUT=0 1180 R1=0.OO01000 1181 RF=RMAX 1182 DR=0.01 1183 EPS=0.0001 1184 CALL V0L(R1,DIST,AREA,VOLB) 1185 Y1=V0LB2-V0LB 1186 10 R2=R1+DR 1187 IF(R2.GT.RF ) R2 = RF 1188 CALL V0L(R2,DIST,AREA,VOLB) 1189 Y2=V0LB2-V0LB 1190 IF(Y1*Y2.LE.O.) GOTO 20 1191 R1=R2 1192 Y1=Y2 1193 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1194 C WRITE(6,200) R2.Y2 1195 C 200 FORMAT(1H ,'R2,Y2 = '.2E14.6/) 1196 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1197 NUT=NUT+1 1198 IF (NUT.LT.20) GOTO 13 1199 WRITE (6,90) NUT 1200 STOP 1201 13 GOTO 10 ° 1202 20 IF(Y2.E0.0.) GOTO 50 1203 R30LD=R2 1204 30 R3=(R1*Y2-R2*Y1)/(Y2-Y1 ) 1205 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1206 C WRITE(6,303) R3 1207 C 303 FORMATdH ,'R3 = '.E12.5) 1208 CXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX '1209 NUT=NUT+1 1210 IF (NUT.LT.150) GOTO 80 1211 WRITE(6,90) NUT 1212 90 FORMATdH ,'PROGRAM STP DUE TO CALFLS ITERATIONS EXCEEDING',14) 1213 STOP 1214 80 IF(DABS((R3-R30LD)/R3).LT.EPS) GOTO 60 1215 R30LD=R3 1216 CALL V0L(R3,DIST,AREA,VOLB) 1217 Y3=V0LB2-V0LB 1218 IF(Y1*Y3.LE.O.) GOTO 40 219 1219 R1=R3 1220 Y1=Y3 1221 GOTO 30 1222 40 R2=R3 1223 Y2=Y3 1224 GOTO 30 1225 . 50 RB2=R2 1226 GOTO 99 1227 ' 60 RB2=R3 1228 99 CALL VOL(RB2,DIST,AREA,VOLB) 1229 AREA2=AREA 1230 ARAVG=(AREA1+AREA2)/2. 1231 VSUAVG=(VSU1+VSU2)/2. 1232 XDOT=(MFX2-MFX1)/DTIME 1233 CBVEL=MT0T*XD0T*VSU2/ARAVG 1234 IF(IPRINT.EO.O) GOTO 70 1235 c====================================================== 1236 WRITE(6,221) VOLB1.V0LB2,RB1,RB2,AREA 1,AREA2,CBVEL 1237 221 F0RMAT(1H , 'V1,V2,R1,R2,AR 1 ,AR2,CBVEL: ' ,7E12.4/) 1238 c====================================================== 1239 70 RETURN 1240 END 1241 C 1242 C SUBROUTINE VOL TO CALCULATE THE VOLUME AND AREA OF BURNT GAS 1243 C ============== IN THE TOYOTA ENGINE COMBUSTION CHAMBER 1244 C GIVEN THE FLAME RADIUS.... 1245 C 1246 SUBROUTINE VOL(BRAD,DIST,AREAF,VOLB) 1247 C 1248 COMMON /AREA3/ AREAB,HTEXP,MPV,HTFCN,TWALL , VI SC , THCOND 1249 C 1250 REAL*8 BRAD,DIST,AREAF,VOLB,BORE.R,D,H,HTCLRV,RDASH,CLRV,HA , 1251 -HVOL,RMAX,DD,ATOT,AREAB.AREAU,MPV.HTFCN,TWALL,VISC,THCOND 1252 -,HTEXP 1253 C 1254 C TO CALC. THE VOLUME BURNT AND FLAME AREA IN 1255 C THE TOYOTA ENGINE COMBUSTION CHAMBER GIVEN THE 1256 C RADIUS OF THE FLAME.... 1257 C 1258 203 B0RE=O.O85 1259 HTCLRV=18.358E-03 1260 RDASH=58.3737E-03 1261 CLRV=55.3264E-06 i 1262 R=B0RE/2. 1263 RMAX=DSQRT((HTCLRV**2)+(R**2)) 1264 DD=HTCLRV+DIST 1265 AT0T = 3.14 159*(2.*RDASH*HTCLRV+(R**2) + 2.*R*DIST) 1266 C 1267 IF(BRAD.GT.RMAX ) GOTO 310 1268 HVDL=0.25*3.14159*(BRAD**3)*(BRAD/RDASH) 1269 HA=3.14159*(BRAD**2)*(BRAD/RDASH) 1270 H=0.0 1271 IF(BRAD.GT,DD) GOTO 320 1272 D=BRAD 1273 AREAB = 3. 14 159*(BRAD**2) 1274 GOTO 350 , 1275 320 D=HTCLRV+DIST 1276 AREAB=3.14159*(2.*(BRAD**2)-(D**2)) 220 1277 GOTO 350 1278 C 1279 310 HV0L=(3.14159*(R**2)*HTCLRV)-CLRV 1280 HA=0.0 1281 H=DSQRT((BRAD**2)-(R**2)) 1282 IF(BRAD.GT.DD) GOTO 330 1283 D=BRAD 1284 AREAB=3.14159*((RMAX**2)+2.*R*(H-HTCLRV)) 1285 GOTO 350 1286 330 D=HTCLRV+DIST 1287 AREAB=3.14159*((RMAX**2)+2.*R*(H-HTCLRV)+(BRAD**2)-(D**2)) 1288 C 1289 350 V0LB=(3.14159/3.0)*(3.*(BRAD**2)*D-(D**3)-2.*(H**3))-HVOL 1290 AREAF=2.0*3.14159*BRAD*(D-H)-HA 1291 AREAU=ATOT-AREAB 1292 /-U " 1293 C WRITE(6,300) BRAD,AREAF,VOLB,AREAB,ATOT 1294 C 300 FORMATdH .'BRAD,AREAF,VOLB, AB,AT '.5E12.4) 1295 -1296 RETURN 1297 END 1298 c 1299 c 1300 c SUBROUTINE ENUFLS THIS CALCULATES THE PROPERTIES OF THE UNBURNT 1301 c =============== GAS AT THE GIVEN PRESS. BY FIRST CALCULATING 1302 c GAMMA AND THEN ASSUMING ISENTROPIC COMPRESSION 1303 c THE BURNING VELOCITY IS THEN CALCULATED USING THE UNBURNT GAS 1304 c TEMP. AND PRESS. USING PUBLISHED FORMULAE FOR GIVEN FUEL. 1305 c 1306 SUBROUTINE ENUFLS(P2.P1,T1,VSU1,MWMIX,TU2,VSU2,EU2,TBVEL,AF. 1307 -T2.NRC02.NRH20) 1308 c 1309 COMMON /AREA 1/ NCH,N02,K,L,M,N,KFUEL 1310 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02,NN2,NNFUEL,KOM 1311 COMMON /AREA4/ NDISS,IPRINT 1312 c 1313 REAL*8 P1,T1,NN02.NN2,NMIX.TU2,VSU2,EU2,TBVEL,TT,NNFUEL,FFF, 1314 -CPG(14),CP,CV,GAMU,DH(14),ENGY,N02,N,RMOL,VSU1,P0W1.P0W2.TT2, 1315 -MWMIX,PU,TU,PBAR2.P2,HF1,T,T2,P0W3,C4,AF,PBAR1,GGAM,B1,B2.B3, 1316 -NCH.K,L.M,MOLFL,FI,SUO(15),ALPHA(15),BETA(15),NRC02,NRH20,UUU(3) 1317 c 1318 RM0L=8.31434 1319 NUT=0 1320 c 1321 c CALC. GAMMA FOR THE UNBURNT ELEMENTS.... 1322 c 1323 NNFUEL=100.-(NN02+NN2) 1324 TT=T1/100. 1325 CPG(5) = 37.432+0.020102*(TT**1.5)- 178.57*(TT** ( - 1 .5)) 1326 -+236.88*(TT**(-2)) 1327 CPG(6)=39.060-512.79*(TT**(-1.5))+1072.7*(TT**(-2)) 1328 --820.4*(TT**(-3)) 1329 CPG( 11 ) = -672.87+439.74*(TT**0.25)-24.875*(TT**0.75)+323.88* 1330 -(TT**(-0.5)) 1331 CPG(13) = -4.042+30.46*TT-1.571 *(TT**2.)+0.03171 *(TT**3.) 1332 CPG(12)=8.3143*(-0.72+0.09285*T1-5.05E-05*(T1**2.)+1.068E-08* 1333 -(T1**3)) 1334 CP=(NN02*CPG(5)+NN2*CPG(6)+NNFUEL*CPG(KFUEL))/100'. 221 1335 CV=CP-RM0L 1336 GAMU=CP/CV 1337 C 1338 P0W1=(GAMU-1.)/GAMU 1339 P0W2=1./GAMU 1340 TT2=T1*((P2/P1)**P0W1) 1341 20 CALL GAM(TT2,T1.GAMU) 1342 POW1=(GAMU-1.0)/GAMU 1343 T2=T1*((P2/P1)**P0W1) 1344 IF(DABS(TT2-T2).LE.1.0) GOTO 10 1345 NUT=NUT+1 1346 IF(NUT.GT.20) STOP 1347 TT2=T2 1348 GOTO 20 1349 10 P0W2=1.O/GAMU 1350 TU2=T2 1351 VSU2=VSU1*((P1/P2)**P0W2) 1352 C 1353 C CALC. ENTHALPY OF REACTANTS AT GIVEN TEMP. 1354 DH(1)=((3.096*T2+0.00273*(T2**2)-7.885E-07*(T2**3) 1355 1+8.66E-11*(T2**4))-1145.0)*RMOL 1356 DH(3)=((3.743*T2+5.656E-04*(T2**2)+4.952E-08*(T2**3) 1357 1-1 . 818E-1 1*(T2**4))-1167.0)*RMOL 1358 DH(5)=((3.253*T2+6.524E-04*(T2**2)-1.495E-07*(T2**3) 1359 1+1.539E-11*(T2**4))-1O24.O)*RM0L 1360 DH(6)=((3.344*T2+2.943E-04*(T2**2)+1.953E-09*(T2**3) 1361 1-6.575E-12*(T2**4))-1023.0)*RMOL 1362 DH(11)=((1.935*T2+4.965E-03*(T2**2.)-1.244E-06*(T2**3. ) 1363 1+1.625E-10*(T2**4.)-8.586E-15*(T2**5.))-985.9)*RMOL 1364 DH(12)=((-0.72*T2+4.643E-02*(T2**2.)-1.684E-05*(T2**3. ) 1365 1+2.67E-09*(T2**4.))-3484.0)*RMOL 1366 DH(13)=((1.137*T2+1.455E-02*(T2**2.)-2.959E-06*(T2**3. ) 1367 1)-1552.9)*RM0L 1368 UUU( 1 ) = -3.93522E05 1369 UUU(3)=-2.41827E05 1370 C CALC. TOTAL ENERGY OF MIXTURE (KJ/KMOL FUEL).... 1371 ENGY=(NCH*(HF1+DH(KFUEL)-RMOL*T2)+N02*(DH(5)-RMOL*T2) 1372 -+N*(DH(6)-RM0L*T2)+NRC02*(UUU(1)+DH(1)-RMOL*T2)+NRH20* 1373 -(UUU(3)+DH(3)-RM0L*T2)) 1374 C CONVERT TO KJ/KMOL MIXTURE... 1375 ENGY=ENGY/NMIX 1376 C CONVERT TO KJ/KG MIXTURE... 1377 EU2=ENGY/MWMIX 1378 C CALC. AVERAGE UNBURNT TEMP. AND PRESS. 1379 PU=(P1+P2)/2. 1380 TU=(T1+T2)/2. 1381 C 1382 C CALCULATE LAMINAR BURNING VELOCITY: 1383 c 1384 c METGHALCHI 8. KECK'S EON.S FOR PR0PANE(13), 0CTANE(12), 1385 c AND IND0LINE(14) 1386 c 1387 IF(KFUEL.EO.11) GOTO 501 1388 FI = 1 ./AF 1389 IF(FI.GT.0.90) GOTO 87 1390 DATA SUO(13) ,SUO( 12),SUO( 14)/23.20D0,19.25D0,19.15D0/ 1391 DATA ALPHA(13) .ALPHA(12) ,ALPHA(14)/2.27DO.2.36D0.2.27D0/ 1392 DATA BETA(13),BETA(12),BETA(14)/-0.23DO,-0.22D0.-0.17D0/ 222 1393 GOTO 89 1394 87 IF(FI.GT.1.10) GOTO 88 1395 DATA SUO( 13),SUO(12),SUO(14)/31.9000,27.OODO,25.21D0/ 1396 DATA ALPHA(13),ALPHA(12),ALPHA(14)/2.13D0,2.26D0,2.19D0/ 1397 DATA BETA(13),BETA( 12),BETA(14)/-0. 17D0,-0. 18D0,-0.13D0/ 1398 GOTO 89 1399 88 CONTINUE 1400 DATA SUO( 13) ,SUO( 12),SUO( 14 )/33.80D0,27.63D0,28.14D0/ 1401 DATA ALPHA ( 13) , ALPHA ( 12) , ALPHA ( 14 )/2 .06DO, 2 .03D0,'2 .02DO/ 1402 DATA BETA(13),BETA(12),BETA(14)/-0.17D0,-0.11D0,-0.087DO/ 1403 89 TBVEL=SU0(KFUEL)*((TU/298.)**ALPHA(KFUEL))* 1404 -((PU/100.)**BETA(KFUEL )) 1405 GOTO 510 1406 C 1407 C ANDREWS AND BRADLEYS EQUATION FOR METHANE(11)... 1408 C 1409 C PBAR1=PU/100. 1410 C TBVEL=(10.0+0.000371 *(TU**2.) *(PBAR1 **J-0.5))) 1411 C 1412 C RYAN AND LESTZ'S EQN. FOR METHANE(11)... 1413 C 1414 C 501 B1=9655.5 1415 C B2=-0.623 1416 C B3=-2144.5/TU 1417 C TBVEL=B1*((PU/100.)**B2)*DEXP(B3) 1418 C GOTO 510 1419 C 1420 C AGRAWAL AND GUPTAS EQUATION FOR METHANE ... 1421 C 1422 501 PBAR1=PU/100.0 1423 C4 = -418.0+1287.0/AF-1196.0/(AF**2) + 360.0/(AF**3)- 15.0*AF* 1424 -DL0G10(PBAR1) 1425 P0W3=1.68*DSQRT(AF ) 1426 IF(AF.GT.1.) GOTO 65 1427 P0W3=1.68/DS0RT(AF) 1428 65 TBVEL=C4*((TU/300.0)**P0W3) 1429 C 1430 C DIVIDE BY 100 TO CONVERT FROM CM/S TO M/S... 1431 C 1432 510 TBVEL=TBVEL/100. 1433 C 1434 IF(IPRINT.EQ.O) GOTO 225 1435 • 1436 WRITE(6,100) TBVEL,VSU2,EU2,PU,TU.P2,T2 1437 100 F0RMAT(1H ,'TBV,VSU2,EU2,PU,TU,P2,T2 =',7E12.4) 1438 c -L. 1439 225 RETURN 1440 END 1441 c 1442 c 1443 c SUBROUTINE GAM THIS CALCULATES THE AVERAGE RATIO OF SPECIFIC 1444 c ============== HEATS (GAMMA) OF AN UNBURNED GAS MIXTURE 1445 c BETWEEN TWO GIVEN TEMPERATURES. 1446 c 1447 SUBROUTINE GAM(T2,T1,GAMU) 1448 c 1449 COMMON /AREA 1/ NCH,N02,K,L.M,N.KFUEL 1450 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02,NN2,NNFUEL,KOM 223 1451 C 1452 REAL*8 T2.T1,NN02,NN2,NNFUEL,GAMU,TI,CPA(14),A 1,A2,R1,R2,S1,S2, 1453 -C1,C2,D1.D2.E1,E2,RMOL,CPAV.TT,NCH,N02,K,L,M,N,MOLFL,NMIX.HF1 1454 C 1455 C CALC. VALUES OF CP FOR THE COMBUSTIBLE MIXTURE; 1456 C 5=02, 6=N2, 11=CH4, 12=C8H18, 13=C3H8, 14=IND0LINE... 1457 C 1458 RM0L=8.31434 1459 TT=T2/100. 1460 TI=T1/100.0 1461 C 1462 A1 = (37.432*TT+8 . 041E-03*(TT**2.5) + 357.14/DSQRT(TT)-236.88/TT) 1463 A2 = (37.432*TI+8.041E-03*(TI**2.5)+357.14/DSQRT(TI)-236.88/TI ) 1464 CPA(5)=(NN02/(T2-T1))*(A1-A2) 1465 C 1466 R1=(39.06*TT+1025.58/DS0RT(TT)-1072.7/TT+410.2/(TT**2)) 1467 R2=(39.06*TI+1025.58/DS0RT(TI)-1072.7/TI+410.2/(TI**2)) 1468 CPA(6)=(NN2/(T2-T1))*(R1-R2) 1469 C 1470 S1 = -672.87*TT+351.8*(TT**1.25)- 14.214*(TT** 1.75)+647.76 1471 -*DSQRT(TT) 1472 S2=-672.87*TI+351.8*(TI**1.25)-14.214*(TI**1.75)+647.76 1473 -*DSORT(TI) 1474 CPA(11)=(NNFUEL/(T2-T1))*(S1-S2) 1475 C 1476 C1=(-4.042*TT+15.23*(TT**2)-0.5237*(TT**3)+7.9275E-03*(TT**4)) 1477 C2=(-4.042*TI+15.23*(TI**2)-0.5237*(TI**3)+7.9275E-03*(TI**4)) 1478 CPA(13)=(NNFUEL/(T2-T1))*(C1-C2) 1479 C 1480 TT=TT*100. 1481 TI=TI*100. 1482 C 1483 D1=RM0L*(-O.72*TT+4.643E-O2*(TT**2)-1.684E-05*(TT**3)+2.67E-09* 1484 -(TT**4)) 1485 D2 = RM0L*(-0.72*TI+4.643E-02*(TI**2)- 1 .684E-05*(TI **3) + 2.67E-09* 1486 -(TI**4)) 1487 CPA(12)=(NNFUEL*0.01/(T2-T1))*(D1-D2) 1488 C 1489 E1=RM0L*(-0.72*TT+4.643E-02*(TT**2)-1.684E-05*(TT**3)+2.67E-09* 1490 -(TT**4) ) 1491 E2 = RM0L*(-O.72*TI+4.643E-02*(TI **2)- 1.684E-05*(TI **3) + 2.67E-09* 1492 -(TI**4)) ! 1493 CPA(14)=(NNFUEL*0.01/(T2-T1))*(E1-E2) 1494 C 1495 C CALC. CP, GAMMA, AND HENCE PRESSURE(P) AT TEMP. T(J) ASSUMING 1496 c ISENTROPIC COMPRESSION 1497 1498 CPAV=CPA(5)+CPA(6)+CPA(KFUEL) 1499 GAMU=CPAV/(CPAV-RMOL) 1500 RETURN 1501 END 1502 c 1503 c 1504 c SUBROUTINE COMP THIS CALCULATES THE SPECIFIC ENERGY OF THE 1505 c =============== UNBURNED MIXTURE. 1506 c 1507 SUBROUTINE COMP(T2,ENGY2,NRC02,NRH20) 1508 c 224 1509 COMMON /AREA 1/ NCH,N02,K,L,M,N,KFUEL 1510 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02.NN2,NNFUEL,KOM 1511 C 1512 REAL*8 PI,V1,T1,P2.V2.T2.NCH,N02.N,ENGY1,ENGY2,DH(14),RMOL, 1513 -REM,REM 1,TT1,REM2,TT2,HF1.MOLFL,DLF1,K,L,M,NMIX,NN02,NN2,NNFUEL 1514 -,UUU(10),T20LD,NRC02,NRH20 1515 C 1516 RM0L=8.31434 1517 C 1518 DH(1)=((3.096*T2+0.00273*(T2**2)-7.885E-07*(T2**3) 1519 1+8.66E-11*(T2**4))-1145.0)*RM0L 1520 DH(3)=((3.743*T2+5.656E-04*(T2**2)+4.952E-08*(T2**3) 1521 1-1.818E-11*(T2**4))-1167.0)*RM0L 1522 DH(5)=((3.253*T2+6.524E-04*(T2**2)-1.495E-07*(T2**3) 1523 1+1.539E-11*(T2**4))-1024.0)*RMOL 1524 DH(6)=((3.344*T2+2.943E-04*(T2**2)+1.953E-09*(T2**3) 1525 1-6.575E-12*(T2**4))-1O23.O)*RM0L 1526 DH(11)=((1.935*T2+4.965E-03*(T2**2.)-1.244E-06*(T2**3.) 1527 1+1.625E-10*(T2**4.)-8.586E- 15*(T2**5.))-985.9)*RMOL 1528 DH( 12) = ((-0.72.*T2+4.643E-02*(T2**2. )-1 . 684E-05* (T2* *3 . ) 1529 ' 1+2.67E-09*(T2**4.))-3484.0)*RMOL 1530 DH(13)=((1.137*T2+1.455E-02*(T2**2.)-2.959E-06*(T2**3.) 1531 1)-1552.9)*RM0L 1532 UUU(1)=-3.93522E05 1533 UUU(3)=-2.41827E05 1534 C CALC. TOTAL ENERGY OF MIXTURE (Kd).... 1535 ENGY2=M0LFL*(NCH*(HF1+DH(KFUEL)-RM0L*T2)+N02*(DH(5)-RM0L*T2) 1536 -+N*(DH(6)-RM0L*T2)+NRC02*(UUU(1)+DH(1)-RM0L*T2)+NRH20* 1537 -(UUU(3)+DH(3)-RM0L*T2)) 1538 C 1539 RETURN 1540 END 1541 C 1542 C 1543 C SUBROUTINE EXP THIS CALCULATES THE TEMP. AND CONCENTRATION OF 1544 C ============== THE PRODUCTS OF COMBUSTION DURING THE EXPANSION 1545 C STROKE. 1546 C 1547 SUBROUTINE EXP(P1,V1,T1,P2,V2,T2,NNN,CC,SUMXS,ENGY1,ENGY2. 1548 -ATOT.DTIME,MTOT.MWBMIX) 1549 C 1550 COMMON /AREA 1/ NCH,N02,K,L,M,N,KFUEL 1551 COMMON /AREA2/ MOLFL,NMIX,HF1,NN02,NN2,NNFUEL,KOM 1552 COMMON /AREA3/ AREAB,HTEXP,MPV,HTFCN.TWALL.VISC,THCOND 1553 COMMON /AREA4/ NDISS,IPRINT 1554 C 1555 REAL*8 P1.V1,T1,P2,V2.T2,SUMXS,K,L,N,M,NMIX,NM1,TT1,P,EPROD, 1556 -CC(10),X(10),ENGY1,ENGY2,MOLFL,REM1,REM2,TT2,TT3,TT30LD,NNM1, 1557 -NNM3,REM3,NCH,N02,HF1,NN02,NN2,NNFUEL,NNM2,EB2,VSB2,BORE 1558 -,AREAB,ATOT,MPV.HTFCN,TWALL.PDV,DO.HTCOEF.VISC.THCOND,HTEXP 1559 * -,DOMEAS,DTIME,GAMMA,MWBMIX,MTOT 1560 c 1561 B0RE=0.085 1562 NUT=0 1563 NN=0 1564 c 1565 T2=(MWBMIX*P2*V2)/(MT0T*8.31434) 1566 c 225 1567 CALL ENERGY(T2.P2,EPROD,SUMXS,CC,X,EB2,VSB2,GAMMA,MWBMIX) 1568 C 1569 ENGY2=EPROD*MOLFL 1570 HTC0EF=(TH(J0ND/B0RE)*((MPV*B0RE/(VSB2*VISC))**HTEXP)/1000.0 1571 DQ=HTCOEF*ATOT*(T2-TWALL)*HTFCN*DTIME 1572 PDV=((P1+P2)/2.0)*(V2-V1) 1573 DOMEAS=ENGY2-ENGY1+PDV 1574 C 1575 PISEN=((V1/V2)**GAMMA)*P1 1576 C 1577 IF(IPRINT.EO.O) GOTO 4 1578 C 1579 WRITE(6,409) ENGY1,ENGY2,PDV,DO,DQMEAS,PI SEN 1580 409 F0RMAT(1H ,'ENGY1,ENGY2,PDV,DO,DOMEAS '.6E12.4) 1581 C 1582 4 CONTINUE 1583 C 1584 RETURN 1585 END 1586 C 1587 C SUBROUTINE SMOOTH THIS READS IN THE INTEGER PRESSURE VALUES 1588 C ================= AND SMOOTHS THEM USING MTS LIBRARY ROUTINES 1589 C 1590 SUBROUTINE SMOOTH(POUT.SCONST.IPRNTS) 1591 C . 1592 IMPLICIT REAL*8(A-H.0-W) 1593 C 1594 DIMENSION PIN(180), DPDTH(180), T0L(180), ANGLE(180), PD1(180) 1595 DIMENSION PD2(180), W(2000), IPIN(200), P0UT(180), D2PDTH(180) 1596 C 1597 C 1598 SVAL=5.0 1599 CONST1=SC0NST 1600 C0NST2=SC0NST 1601 IBEG=60 1602 IEND=120 1603 C 1604 C READ IN PRESSURE DATA... 1605 C 1606 K=1 1607 DO 11 IL=1,38 1608 READ(5,20) IPIN(K),IPIN(K+1),IPIN(K+2),IPIN(K+3),IPIN(K+4) 1609 20 F0RMAT(5I6) 1610 K=K+5 1611 11 CONTINUE 1612 C 1613 C DO 600 Id=1 ,190 1614 C WRITE(6,601) IPIN(Id) 1615 C 601 F0RMAT(1H ,110) 1616 C 600 CONTINUE 1617 . C 1618 C CONVERT PRESSURE DATA TO REAL NUMBERS AND BAR 1619 C 1620 DO 12 Id=1,180 1621 PIN(Id)=DFL0AT(IPIN(Id+2))/14.7D0 1622 ANGLE(IJ)=DFLOAT(Id) 1623 12 CONTINUE 1624 C 226 BASED ON VARIATION OVER RANGE I 492 DO 15 IT=4.177 dS=IT-3 dF=IT+3 AV=0.0 DO 16 d=dS,dF 16 AV=AV+D2PDTH(d) AV=AV/7.0 SA=0.0 DO 17 d=dS,dF 17 SA=SA+DABS(D2PDTH(d) -AV)**2 SD=DS0RT(SA/6) 1625 C CALCULATE dP/dTHETA AT EACH DATA POINT... 1626 C 1627 490 DO 5 d = 2,179 1628 5 DPDTH(d)=(PIN(d+1)-PIN(J-1))/2.0D0 1629 DPDTH(1)=0.0 1630 DPDTH(180)=DPDTH(179) 1631 C 1632 C 1633 C CALCULATE d2P/d(THETA)**2 AT EACH DATA POINT... 1634 C 1635 491 DO 6 d = 2,179 1636 6 D2PDTH(d)=(DPDTH(d+1)-DPDTH(d-1))/2.0D0 1637 D2PDTH(1)=0.0 1638 D2PDTH(180)=D2PDTH(179) 1639 C 1640 C 1641 C CALCULATE STANDARD DEVIATION OF THE SLOPE AT EACH CRANK ANGLE 1642 C 1643 C 1644 1645 1646 1647 1648 1649 1650 C 1651 1652 C 1653 1654 1655 1656 1657 IF(IT.LT.IBEG.OR.IT.GT.IEND) GOTO 431 1658 T0L(IT)=SD*C0NST2+O.OOO1 1659 GOTO 15 1660 431 T0L(IT)=SD*C0NST1+0.0O01 1661 15 CONTINUE 1662 C 1663 DO 18 IT=1,3 1664 18 T0L(IT)=T0L(4) 1665 C 1666 DO 19 IT=178,180 1667 19 TOL(IT)=TOL(177) 1668 CCCCCCCCCCCCCCCCCCCCCCCCCCCCC 1669 C DO 88 IT=1,180 1670 C WRITE(6,87) TOL(IT) 1671 C 87 FORMATdH .F12.5) 1672 C 88 CONTINUE 1673 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 1674 C 1675 C CALL LIBRARY CURVE FITTING ROUTINES... 1676 C 1677 493 CALL DSPLFT(ANGLE,PIN,TOL,SVAL,180,W,&100) 1678 CALL DSPLN(ANGLE,POUT,PD1,PD2, 180,& 100) 1679 C 1680 GOTO 92 1681 100 WRITE(6,101) 1682 101 FORMATdH .'ERROR IN CURVE FITTING ROUTINE' ) 1683 STOP 1 1684 C 1685 92 IF(IPRNTS.EO.O) GOTO 933 1686 DO 45 dK=1,180 1687 WRITE(6,602) PIN(dK),POUT(dK) 1688 602 FORMATdH .2F12.5) 1689 45 CONTINUE 1690 C 1691 933 RETURN 1692 END 227 APPENDIX H - DEFINITION OF PROGRAM SYMBOLS AFR A i r / f u e l r a t i o ANG Spark advance a n g l e AREA 1-4 - Used i n c a l c . a r e a under p r e s s u r e c u r v e AREAF1-2 - Area of flame f r o n t (m2-) AREAB Area of burned gas i n c o n t a c t w i t h w a l l (m a) AREAU Area of unburned gas i n c o n t a c t w i t h w a l l (m z) ATOT T o t a l w a l l a r e a i n s i d e c y l i n d e r (mM BORE C y l i n d e r bore (m) CBVEL C a l c u l a t e d b u r n i n g v e l o c i t y (m/s) CC P e r c e n t a g e p r o d u c t c o n c e n t r a t i o n CLRV C l e a r a n c e volume (m 3) CN Number of carbon atoms i n f u e l COMPR Compression r a t i o CP S p e c i f i c heat a t c o n s t a n t p r e s s u r e (kJ/kmol.K) CPG(I) S p e c i f i c h e a t s of m i x t u r e components CV S p e c i f i c heat a t c o n s t a n t volume (kJ/kmol.K) CYLV Swept c y l i n d e r volume (m 3) DALFA Crank a n g l e DCA Crank a n g l e increment DH Change i n e n t h a l p y from r e f . v a l . a t 298K DI Record of v o l . d i v . a t each c a . d i v i s i o n DIST D i s t a n c e of p i s t o n from T.D.C. DIV Volume d i v i s i o n (m 3) DLF 1 Crank a n g l e c o u n t e r DPIN P r e s s u r e increment a t s t a r t of combustion (kPa) DPX P r e s s u r e increment d u r i n g comb, c a l c u l a t i o n s (kPa) DQ Heat l o s t t o w a l l of combustion chamber ( k J ) DTIME Time increment (sec.) DVOL F u n c t i o n s u b r o u t i n e ( t o c a l c . volume change) DVOLM Volume of c y l i n d e r a t spark a n g l e (m 5) EFF E f f i c i e n c y (%) ENGB Burned gas energy (kJ) ENGU Unburned gas energy ( k J ) ENGY1-2 - Energy of c y l i n d e r c o n t e n t s ( k J ) EPROD Energy of the p r o d u c t s of combustion (kJ/kmol f u e l ) ERCT Energy of the r e a c t a n t s (kJ/kmol f u e l ) ERR E r r o r q u a n t i t y used i n i t e r a t i o n r o u t i n e s ETOT1-2 - T o t a l energy of c y l . c o n t e n t s / t o t a l mass (kJ/kg) EU2 S p e c i f i c energy of the unburned gas (kJ/kmol) F Volume f r a c t i o n of r e s i d u a l gases FFF T u r b u l a n t flame speed m u l t i p l i e r FLMSPD Flame speed (m/s) GAM R a t i o of s p e c i f i c h eats GAMA R a t i o of s p e c i f i c h eats GAMMA R a t i o of s p e c i f i c h eats GAMU R a t i o of s p e c i f i c h eats (unburned m i x t u r e ) HF 1 E n t h a l p y of f o r m a t i o n of f u e l (298K,1bar)(kJ/kmol.K) HM Number of hydrogen atoms i n f u e l HTCOEF Heat t r a n s f e r c o e f f i c i e n t HTEXP Exponent i n Annand's heat t r a n s f e r e q u a t i o n HTFCN Constant i n Annand's heat t r a n s f e r e q u a t i o n IPRES I n t e g e r p r e s s u r e data f o r s t o r i n g i n f i l e 228 K Number of kmols of carbon d i o x i d e per kmol of f u e l KFUEL Type of f u e l KOM - Counts TEMP s u b r o u t i n e i t e r a t i o n s L Number of kmols of water per kmol of f u e l LAMBDA - A i r / f u e l r a t i o r e l a t i v e t o s t o i c h i o m e t r i c LENG Length of con-rod (m) M Number of kmols of e x c e s s oxygen per kmol of f u e l MEP Mean e f f e c t i v e p r e s s u r e (kPa) MFX1-2 Mass f r a c t i o n burned MOLFL Number of kmols of f u e l i n c y l i n d e r MPV - Mean p i s t o n v e l o c i t y (m/s) MTOT - T o t a l mass of gases i n c y l i n d e r MW(I ) M o l e c u l a r weight of f u e l MWMIX M o l e c u l a r weight of unburned m i x t u r e N Number of kmols of N i t r o g e n per kmol of f u e l NDISS Number of d i s s o c i a t i o n r e a c t i o n s i n c l u d e d NN2 Pe r c e n t a g e N i t r o g e n i n m i x t u r e NCH Number of kmols of f u e l (=1) NI Crank a n g l e i t e r a t i o n c o u n t e r NO 2 Number of kmols of oxygen per kmol of f u e l NM Number of kmols of m i x t u r e / k m o l s of f u e l NMI Number of kmols of m i x t u r e / k m o l s of f u e l NMIX - No. of kmols m i x t u r e ( i n c . r e s i d u a l s ) / kmol f u e l NNCH Pe r c e n t a g e of f u e l i n m i x t u r e NNM1-2 Number of kmols of mi x t u r e / k m o l of f u e l NN02 Per c e n t a g e of oxygen i n m i x t u r e NRC02 Number of kmols of r e s i d u a l C02 NRES Number of kmols of r e s i d u a l gases NRH20 Number of kmols of r e s i d u a l H20 NRN2 Number of kmols of r e s i d u a l N2 NR02 Number of kmols of r e s i d u a l 02 NUM I t e r a t i o n c o u n t e r NUM1 I t e r a t i o n c o u n t e r P P r e s s u r e (kPa) P1-4 P r e s s u r e s (P1 = i n i t i a l c y l i n d e r p r e s s u r e ) (kPa) PDCA I n t e r a t i o n i n t e r v a l i n degrees c r a n k a n g l e • PDV - Work done = i n t e g r a l of P dV (kJ) PIN P r e s s u r e Increment (kPa) PNEW I n t e r m e d i a t e p r e s s u r e i n i t e r a t i o n r o u t i n e (kPa) PNEW1 I n t e r m e d i a t e p r e s s u r e i n i t e r a t i o n r o u t i n e (kPa) POW1-2 - Exponent POWER Power d e v e l o p e d ( k J ) PPTDC - P r e s s u r e a t TDC (kPa) PP2(I ) P r e s u r e s s t o r e d a t each c a l c u l a t i o n s t e p (kPa) PRC02 Per c e n t a g e r e s i d u a l C02 PRH20 Pe r c e n t a g e r e s i d u a l H20 PRO 2 Per c e n t a g e r e s i d u a l 02 PRN2 Per c e n t a g e r e s i d u a l N2 PXF Max p r e s s u r e f o r i t e r a t i o n (kPa) QQ D i s s o c i a t i o n R o u t i n e i t e r a t i o n f l a g QVS Lower h e a t i n g v a l u e of f u e l (kJ/kg) RADBMB Radiu s of combustion bomb (m) RB1-2 Burned volume r a d i i (m) REM1-2 - Used i n i t e r a t i o n r o u t i n e s 229 RES1-2 - Used i n i t e r a t i o n r o u t i n e s RM1-2 - Used i n i t e r a t i o n r o u t i n e s RMOL - M o l a r u n i v e r s a l gas c o n s t a n t (kJ/kmol.K) SPEED - Engine speed ( r.p.m.) SPKAD - Spark advance a n g l e STAFR - S t o i c h i o m e t r i c a i r / f u e l r a t i o STROK - P i s t o n s t r o k e (m) SUMDI - Sum of the volume d i v i s i o n s SUMNS - Number of kmols of f r e s h m i x t u r e per kmol f u e l SUMXS - Number of kmols of burned m i x t u r e T - Temperature (K) T1-4 - I n t e r m e d i a t e Temperatures i n i t e r a t i o n r o u t i n e s (K) TB2 - Temperature of the burned gas a t s t a t e 2 (K) TBVEL - True b u r n i n g v e l o c i t y (m/s) TIM(I) - Record of time a f t e r BDC a t each degree c a . (s) TIME - Time a f t e r BDC (s) THCOND - Thermal c o n d u c t i v i t y of burned gas TNEW - New temperature used i n i t e r a t i o n r o u t i n e (K) TT J - Burnt gas temp, T/100 TT1-2 - Temps used i n i t e r a t i o n r o u t i n e s (K) TU1-2 - Unburned gas t e m p e r a t u r e s (K) TWALL - C y l i n d e r w a l l t e m p e r a t u r e (K) UUU1-10 - Heats of f o r m a t i o n of burned gas c o n s t i t u e n t s V1-4 - Volumes (m ) W 2 ( I ) - C y l i n d e r volume r e c o r d a t each deg. c a . (m 5) VFRBNT - Volume f r a c t i o n burned VSB2 - S p e c i f i c volume of burned gas (m'/kg) VSUAG - Average s p e c i f i c volume of unburned gas (m*/kg) VSU1-2 - S p e c v o l . of unburned gas a t s t a t e s 1 & 2 (mVkg) V0LB1-2 - Burned gas volume a t s t a t e s 1 £ 2 (m*) V0LU1-2 - Unburned gas volume a t s t a t e s 1 & 2 (m 3) VISC - V i s c o s i t y of burned gas VTOT - T o t a l volume of chamber (m*) VT0T1-2 - T o t a l volume a t crank a n g l e p o s i t i o n s 1 & 2 (my) X - Number of kmols of each s p e c i e s a f t e r d i s s o c i a t i o n XX - A r r a y used i n p l o t t i n g r o u t i n e XDOT - Rate of change of mass f r a c t i o n burned (kg/s) YY - A r r a y used i n p l o t t i n g r o u t i n e ZZ - A r r a y used i n p l o t t i n g r o u t i n e 

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