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The influence of swirl and turbulence on flames in lean gaseous mixtures Bauwens, Luc 1986

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THE INFLUENCE OF SWIRL AND TURBULENCE ON FLAMES IN LEAN GASEOUS MIXTURES By LUC BAUWENS Ing. Tech. A . I . E . C A . M . , B r u s s e l s . 1970 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of Mechanical Engineer ing We accept th i s thes i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 1986 (c) Luc Bauwens, 1986 I n 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 m a k e 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 m a y b e g r a n t e d b y t h e h e a d o f my d e p a r t m e n t o r b y 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 b e a l l o w e d w i t h o u t m y 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 1956 M a i n M a l l V a n c o u v e r , C a n a d a V6T 1Y3 D a t e August 28, 1986 D E - 6 n / « n Abstrac t Repeated measurements were made of pressure r i s e , i n a c y l i n d r i c a l constant volume combustion bomb, with c e n t r a l i g n i t i o n , i n s w i r l i n g mixture, for a combination of d i f f e r e n t lean mixtures of propane and a i r and d i f f e r e n t s w i r l s . The s w i r l was obtained by h igh speed charging through an eccentr i c p o r t . D i f f e r e n t flow condi t ions were obtained by v a r y i n g the decay time between the end of charging and i g n i t i o n . Two d i f f e r e n t lean mixtures of propane and a i r were tes ted . V e l o c i t y measurements provided information r e l a t i n g to the flow f i e l d . No large s p a t i a l v a r i a t i o n of the turbulence i n t e n s i t y i s observed, and i t s decay i s approximately descr ibed by the homogeneous, i s o t r o p i c laws. Computing the length sca les according to such a model, one observes that for both mixtures , turbulent burning v e l o c i t i e s appear to vary l i n e a r l y with Re. . A The burning ra te was found to depend s trong ly on the equivalence r a t i o . Even at the h ighest l eve l s obtained of turbulence i n t e n s i t y , the leanest mixture burns at h a l f the speed of the r i c h e r one. No d i f f e r e n c e i n i g n i t i o n delay i s apparent, and the r a t i o of burning v e l o c i t i e s seems to be maintained v i r t u a l l y over the whole combustion time. i i Contents Abs trac t i i L i s t of tables v L i s t of f i gures v i Acknowledgements i x Nomenclature x 1 In troduc t ion 1 1.1 M o t i v a t i o n 1 1.2 Scope 2 1.3 Main features of t h i s experiment 3 1.4 O u t l i n e 3 2 Turbulent premixed flames 4 2.1 Premixed flames 4 2.2 Turbulence 6 2 .3 Turbulent flames 10 2.4 S w i r l 18 2 .5 Summary 21 3 Objec t ives 23 4 The experiment 26 4.1 D e s c r i p t i o n 26 4 .1 .1 Combustion experiments 26 4 .1 .2 Flow measurement 27 4.2 Experimental setup 28 4 .2 .1 General 28 4 .2 .2 Bomb and p i p i n g 29 4 .2 .3 Mixture 30 4 .2 .4 Timing equipment 31 4 . 2 . 5 Charging 32 4 .2 .6 I g n i t i o n 42 4 .2 .7 Pressure measurement 42 4 .2 .8 Temperature measurement 44 4 . 2 . 9 V e l o c i t y measurement 45 4 .2 .9 .1 Equipment 45 4 . 2 . 9 . 2 Hot wire c a l i b r a t i o n 46 4 . 2 . 9 . 3 Data reduct ion 46 4 . 2 . 9 . 4 E v a l u a t i o n of the r e s u l t s 48 4 .2 .10 Data a c q u i s i t i o n and process ing 52 i i i 5 Resul t s 55 5.1 Flow measurements 55 5 .1 .1 A n a l y s i s 55 5 .1 .2 D i s c u s s i o n 58 5.2 Combustion experiments 65 5 .2 .1 A n a l y s i s 65 5 .2 .2 D i s c u s s i o n 67 5 .2 .2 .1 General 67 5 .2 .2 .2 S t a t i s t i c s of i g n i t i o n 68 5 . 2 . 2 . 3 Burning v e l o c i t i e s 71 5 .2 .2 .4 S t a t i s t i c s : v a r i a t i o n dur ing combustion 81 6 Conclus ions 86 7 Further work 89 F igures 91 B i b l i o g r a p h y 127 Appendixes: Computer programs A Data a c q u i s i t i o n : program DATANIC 131 B Hot wire anemometry data reduct ion: program HWRED 136 C S t a t i s t i c s on i g n i t i o n delay C l Convers ion of b inary pressure sequences to time sequences: program STATCOMB 149 C2 C o r r e l a t i o n s : program STAT 161 C3 Mean, standard d e v i a t i o n , skewness, k u r t o s i s : program STATCURVE 166 D Smoothing by s p l i n e s : program SMOOTH 172 i v L i s t of Tables Table I - Charging parameters dur ing combustion tes ts 36 Table II - C o r r e l a t i o n between charging and combustion parameters 37 Table I I I - Homogeneous I s o t r o p i c Assumption 55 Table IV - Combustion Data 74 Table V - C o r r e l a t i o n between combustion data 84 v L i s t o f F i g u r e s 1 The bomb 91 2 I n s t r u m e n t a t i o n a n d c o n t r o l s d i a g r a m 92 3 S t a n d a r d d e v i a t i o n o f p r e s s u r e d u r i n g c h a r g i n g - q u a r t e r - r a d i u s No p l u g 93 4 S t a n d a r d d e v i a t i o n o f t e m p e r a t u r e d u r i n g c h a r g i n g - q u a r t e r - r a d i u s - no p l u g 93 5 I n s t a n t a n e o u s v e l o c i t y t r a c e - q u a r t e r r a d . f r o m c e n t e r -no p l u g 94 6 F i v e s u p e r p o s e d i n s t a n t a n e o u s v e l o c i t y t r a c e s - Q u a r t e r - r a d -no p l u g 94 7 E n s e m b l e a v e r a g e d v e l o c i t y a t t h e c e n t e r o f t h e bomb 95 8 Smoothed e n s e m b l e a v e r a g e d v e l o c i t y a t t h e c e n t e r o f t h e bomb 95 9 Mean v e l o c i t y a n d f l u c t u a t i o n - q u a r t e r - r a d i u s - no p l u g 96 10 Mean v e l o c i t y a n d f l u c t u a t i o n - q u a r t e r - r a d i u s - w i t h p l u g 96 11 T u r b u l e n c e i n t e n s i t y b y ensemble a v e r a g i n g - q u a r t e r - r a d i u s -no p l u g 97 12 T u r b u l e n c e i n t e n s i t y b y ensemble a v e r a g i n g - q u a r t e r - r a d i u s -w i t h p l u g 97 13 Mean v e l o c i t y a n d f l u c t u a t i o n - t h r e e - e i g h t r a d i u s - no p l u g 98 14 Mean v e l o c i t y a n d f l u c t u a t i o n - t h r e e - e i g h t r a d i u s - w i t h p l u g 98 15 T u r b u l e n c e i n t e n s i t y b y ensemble a v e r a g i n g - t h r e e - e i g h t r a d i u s -no p l u g 99 16 T u r b u l e n c e i n t e n s i t y b y ensemble a v e r a g i n g - t h r e e - e i g h t r a d i u s -w i t h p l u g 99 17 Mean v e l o c i t y a n d f l u c t u a t i o n - m i d - r a d i u s - no p l u g 100 18 Mean v e l o c i t y a n d f l u c t u a t i o n - m i d - r a d i u s - w i t h p l u g 100 19 T u r b u l e n c e i n t e n s i t y b y ensemble a v e r a g i n g - m i d - r a d i u s - no p l u g 101 20 T u r b u l e n c e i n t e n s i t y b y ensemble a v e r a g i n g - m i d - r a d i u s -w i t h p l u g 101 v i 21 Mean v e l o c i t y a n d f l u c t u a t i o n - f i v e - e i g h t r a d i u s - no p l u g 102 22 Mean v e l o c i t y a n d f l u c t u a t i o n - f i v e - e i g h t r a d i u s - w i t h p l u g 102 23 T u r b u l e n c e i n t e n s i t y b y ensemble a v e r a g i n g - f i v e - e i g h t r a d i u s -no p l u g 103 24 T u r b u l e n c e i n t e n s i t y b y ensemble a v e r a g i n g - f i v e - e i g h t r a d i u s -w i t h p l u g 103 25 Mean v e l o c i t y a n d f l u c t u a t i o n - t h r e e - q u a r t e r r a d i u s - no p l u g 104 26 Mean v e l o c i t y a n d f l u c t u a t i o n - t h r e e - q u a r t e r r a d i u s - w i t h p l u g 104 27 T u r b u l e n c e i n t e n s i t y b y ensemble a v e r a g i n g - t h r e e - q u a r t e r r a d i u s -no p l u g 105 28 T u r b u l e n c e i n t e n s i t y b y ensemble a v e r a g i n g - t h r e e - q u a r t e r r a d i u s -w i t h p l u g 105 29 Mean v e l o c i t y a n d f l u c t u a t i o n - s e v e n - e i g h t r a d i u s - n o p l u g 106 30 Mean v e l o c i t y a n d f l u c t u a t i o n - s e v e n - e i g h t r a d i u s - w i t h p l u g 106 31 T u r b u l e n c e i n t e n s i t y b y ensemble a v e r a g i n g - s e v e n - e i g h t r a d i u s -no p l u g 107 32 T u r b u l e n c e i n t e n s i t y b y ensemble a v e r a g i n g - s e v e n - e i g h t r a d i u s -w i t h p l u g 107 33 T e m p e r a t u r e p r o f i l e s a t d i f f e r e n t d i s t a n c e s f o r m c e n t e r - no p l u g 108 34 T e m p e r a t u r e p r o f i l e s a t d i f f e r e n t d i s t a n c e s f r o m c e n t e r - w i t h p l u g 108 35 Mean v e l o c i t y a t d i f f e r e n t d i s t a n c e s f r o m c e n t e r - no p l u g 109 36 Mean v e l o c i t y a t d i f f e r e n t d i s t a n c e s f r o m c e n t e r - w i t h p l u g 109 37 T u r b u l e n c e i n t e n s i t y a t d i f f e r e n t d i s t a n c e s f r o m c e n t e r - no p l u g 110 38 T u r b u l e n c e i n t e n s i t y a t d i f f e r e n t d i s t a n c e s f rom c e n t e r - w i t h p l u g 110 39 Mean p r e s s u r e - m i d - r a d i u s - no p l u g 111 40 A n g u l a r v e l o c i t i e s a t d i f f e r e n t d i s t a n c e s f r o m c e n t e r - n o p l u g 112 41 A n g u l a r v e l o c i t i e s a t d i f f e r e n t d i s t a n c e s f r o m c e n t e r - w i t h p l u g 112 42 V e l o c i t y p r o f i l e s - no p l u g 113 43 V e l o c i t y p r o f i l e s - w i t h p l u g 113 v i i 44 Inverse of u ' versus time - no p lug 45 Inverse of u ' versus time - with p lug 46 Combustion pressure curves - 79% f u e l / a i r - delay = 15 ms 47 S t a t i s t i c s of combustion times - 92% f u e l / a i r - delay = 15 ms 48 Standard and median dev ia t ions - 92% f u e l / a i r - delay = 15 ms 49 S t a t i s t i c s of combustion times - 92% f u e l / a i r - delay = 30 ms 50 Standard and median dev ia t ions - 92% f u e l / a i r - delay = 30 ms 51 S t a t i s t i c s of combustion times - 92% f u e l / a i r - de lay = 60 ms 52 Standard and median dev ia t ions - 92% f u e l / a i r - de lay = 60 ms 53 S t a t i s t i c s of combustion times - 92% f u e l / a i r - delay 54 Standard and median dev ia t ions - 92% f u e l / a i r - de lay 55 S t a t i s t i c s of combustion times - 92% f u e l / a i r - de lay (repeated) 120 ms 120 ms 120 ms 56 Standard and median dev ia t ions - 92% f u e l / a i r - delay = 120 ms 63 Combustion pressure versus mean times for d i f f e r e n t decay times before i g n i t i o n - 79% f u e l / a i r 64 pressure increase r a t i o versus mean time for both mixtures -de lay = 15 ms 65 Times for same pressure increase , versus each other , 92% x 79% f u e l / a i r -de lay = 15 ms 66 Turbulent burning v e l o c i t y versus turbulence i n t e n s i t y , nondimensional ized by the laminar burning v e l o c i t y 67 Turbulent burning v e l o c i t y versus Re^ 114 114 115 116 116 117 117 118 118 119 119 120 (repeated) 120 57 S t a t i s t i c s of combustion times - 92% f u e l / a i r - delay - 240 ms 121 58 Standard and median dev ia t ions - 92% f u e l / a i r - de lay = 240 ms 121 59 S t a t i s t i c s of combustion times - 79% f u e l / a i r - de lay = 15 ms 122 60 Standard and median dev ia t ions - 79% f u e l / a i r - de lay 15 ms 122 61 S t a t i s t i c s of combustion times - 79% f u e l / a i r - de lay 30 ms 123 62 Standard and median dev ia t ions - 79% f u e l / a i r - de lay = 30 ms 123 124 125 125 126 126 V l l l Acknow1edgement s I wish to express my g r a t i t u t e to Dr P h i l i p G. H i l l , f o r h i s support and h i s p a r t i c i p a t i o n i n t h i s study, as Thesis Advisor This thesis would not be what i t i s without the many comments and suggestions from Dr H. Daneshyar, during h i s too short stay at the U n i v e r s i t y of B r i t i s h Columbia, over the winter and spring terms 1985-1986. The contributions of Dr I.S. Gartshore, Dr R.L. Evans and Dr E. Hauptmann were a l s o appreciated. I a l s o wish to thank the Faculty, S t a f f and Graduate Students i n the Department of Mechanical Engineering, f o r t h e i r support and assistance. Most of a l l , I am thankful to L i u Chin-Ya and our family, f o r t h e i r patience and understanding, when for many evenings and week-ends, t h e i r husband and father was e i t h e r absent from home, or worse, working at home, and could not be disturbed. i x Nomenclature A, B Constants i n King's law A Area of the wire w K K a r l o v i t z number; a l s o for hot wire anemometry data reduction, thermal conductivity Le Lewis number, defined as heat d i f f u s i v i t y / D i f f u s i v i t y of the reactant Le^ Lewis number of the f u e l Le Lewis number of the oxidant o L x Integral length scale Nu Nusselt number P Pressure measured during combustion experiments P. Pressure at i g n i t i o n time ign Pr Prandtl number R Hot wire resistance R. . Radius of the bomb Domb Re Reynolds number Re^ Reynolds number based on L x Re^ Reynolds number based on u' and X T Temperature Tg Free stream gas temperature T Hot wire temperature w V Hot wire voltage x a, b Constants i n hot wire c o r r e l a t i o n c A p r o p o r t i o n a l i t y constant d Hot wire diameter h Heat transfer c o e f f i c i e n t k, k', k" P r o p o r t i o n a l i t y constants n Exponent i n King's law p Pressure r radius or r a d i a l coordinate t Time u V e l o c i t y u^ Laminar burning v e l o c i t y u^ Turbulent burning v e l o c i t y u* Turbulence i n t e n s i t y (r.m.s v e l o c i t y f l u c t u a t i o n ) v V e l o c i t y of the unburnt mixture, at flame front u x A s p a t i a l coordinate y A s p a t i a l coordinate <$> Equivalence r a t i o a Heat d i f f u s i v i t y P Nondimensional a c t i v a t i o n temperature 6^ Laminar flame thickness e Rate of decay of the turbulent k i n e t i c energy 77 Kolmogorov d i s s i p a t i o n scale X Taylor micro-length scale v Kinematic v i s c o s i t y ir Constant, equal to 3.1415.. x i Density Density of the burnt gases Density of the unburnt mixture x i i 1. In troduct ion 1.1 M o t i v a t i o n The trend toward lean burning i n s p a r k - i g n i t i o n engine design requires techniques to be developed which compensate for the lower burning v e l o c i t i e s of leaner mixtures . Some of the most promising ways to improve the burning rates cons i s t of des igning the i n l e t and combustion chamber with conf igurat ions r e s u l t i n g i n some organized f l u i d motion, among which the most f requent ly r e f e r r e d to are squish and s w i r l . T h i s work w i l l focus on some aspects of s w i r l , i n lean mixtures . The most i n t e r e s t i n g feature of the s w i r l may be that i t tends to conserve k i n e t i c energy i n an organized form, reducing i t s rate of d i s s i p a t i o n dur ing the compression s troke , so that a reasonable amount of energy remains a v a i l a b l e , and may break up i n a more random motion a t combustion time. Depending on the p o s i t i o n of the spark p lug i n r e l a t i o n to the s w i r l , and provided t h i s l a t t e r has not broken up and t r a n s f e r r e d i t s energy into smal ler sca les before i g n i t i o n time, the i g n i t i o n process may be a f f ec ted by the s w i r l i n g motion. Higher v e l o c i t i e s at spark l o c a t i o n may produce more c y c l i c d i s p e r s i o n . C e n t r i f u g a l forces may a l s o a f f e c t the flame propagat ion. 1 T h i s w o r k i s e x p e r i m e n t a l . Though l a m i n a r f l a m e p r o p a g a t i o n i s r e a s o n a b l y w e l l u n d e r s t o o d f rom a t h e o r e t i c a l p o i n t o f v i e w , t h e e f f e c t o f t u r b u l e n t f l u i d m o t i o n o n t h e f l a m e p r o p a g a t i o n i s n o t . E x p e r i m e n t s may p r o v i d e some c l u e s , a n d more i m p o r t a n t l y , t h e y w i l l o f f e r i n f o r m a t i o n n e e d e d b y the d e s i g n e r . I t i s o f i n t e r e s t t o a n a l y z e t h e e f f e c t o f s w i r l o n c o m b u s t i o n i n a n a p p a r a t u s i n w h i c h i t i s e a s i e r t o c o n t r o l a n d o b s e r v e t h a n i n a n e n g i n e , and t o t r y t o i s o l a t e t he d i f f e r e n t e f f e c t s , f o c u s s i n g o n t h e most i m p o r t a n t one , t h a t t h e s w i r l w i l l p r o d u c e a n i n c r e a s e o f t u r b u l e n c e a t i g n i t i o n t i m e . T h i s i s t h e g e n e r a l o b j e c t i v e o f t h e p r e s e n t w o r k . 1 .2 S c o p e The m a i n q u e s t i o n a d d r e s s e d h e r e r e f e r s t o how s w i r l a n d r e s u l t i n g t u r b u l e n c e a f f e c t t h e b u r n i n g t i m e s a n d t h e random v a r i a t i o n s b e t w e e n c y c l e s , o b s e r v e d i n e n g i n e s , a n d what i s t h e i n f l u e n c e o f t h e m i x t u r e c o m p o s i t i o n . The a t t e n t i o n i s r e s t r i c t e d t o s o u r c e s o f c y c l i c d i s p e r s i o n w i t h i n t h e c o m b u s t i o n p r o c e s s i t s e l f . F l u c t u a t i o n s i n i n t a k e f l o w , o r m i x t u r e c o m p o s i t i o n , o r i g n i t i o n a r e n o t c o n s i d e r e d a s b e i n g p a r t o f t h e o b j e c t i v e s ; t o what e x t e n t t h e y a c t u a l l y d i d a f f e c t t h e r e s u l t s w i l l be d i s c u s s e d . 2 1.3 M a i n f e a t u r e s o f t h e e x p e r i m e n t The e x p e r i m e n t i s d e s i g n e d f o r s i m p l i c i t y o f c o n t r o l a n d measurement , and f o r r e p e a t a b i l i t y . S i n c e t h e e m p h a s i s i s o n p r e s s u r e measu remen t s , w h i c h a r e r e l i a b l e a n d e a s y t o r e c o r d , i t i s f e a s i b l e t o r e p e a t t h e same e x p e r i m e n t a l a r g e number o f t i m e s t o p r o v i d e a s u f f i c i e n t number o f s amp le s f o r s t a t i s t i c a l a n a l y s i s . Measu remen t s o f t u r b u l e n c e a r e more d i f f i c u l t t o i m p l e m e n t r e l i a b l y , and i t i s d i f f i c u l t t o a s s e s s t h e i r v a l i d i t y , e v e n when t h e most s o p h i s t i c a t e d methods a r e u s e d . I t i s t h u s r e a s o n a b l e t o l i m i t t h e i r i m p l e m e n t a t i o n t o w h a t e v e r i s n e e d e d f o r e x p l a n a t i o n o f t h e o b s e r v a t i o n s o f t h e p r e s s u r e . H o w e v e r , s i n c e v e l o c i t y i s a l o c a l , t i m e - d e p e n d e n t p r o p e r t y , a n d i s t r e a t e d i n a s t o c h a s t i c m o d e l , r e l a t i v e l y l a r g e numbers o f measurements a r e a l s o n e e d e d t o p r o v i d e a d e q u a t e s a m p l e s . 1 .4 O u t l i n e T h i s w o r k b e g i n s w i t h a b r i e f a p p r a i s a l o f what i s known a b o u t t u r b u l e n t c o m b u s t i o n . N e x t comes a d i s c u s s i o n o f t h e o b j e c t i v e s . T h i s i s f o l l o w e d b y a d e s c r i p t i o n o f t h e e x p e r i m e n t a l s e t - u p , i t s i n s t r u m e n t a t i o n a n d the p r o c e d u r e s b e i n g u t i l i z e d , b o t h f o r c o m b u s t i o n e x p e r i m e n t s a n d v e l o c i t y m e a s u r e m e n t s . The d a t a o b t a i n e d a r e t h e n a n a l y z e d , a n d some c o n c l u s i o n s a r e f i n a l l y p r o p o s e d , c o m p a r i n g t h e d a t a r e f e r r i n g t o f l a m e p r o p a g a t i o n t o the v e l o c i t y s t a t i s t i c s . 3 2. Turbulent premixed flames 2.1 Premixed flames In s t i l l a i r , or where a simple flow f i e l d i s prescribed, laminar flame theory has produced useful r e s u l t s . That work was pioneered by Bush and Fendell [1], 1970, who considered the problem of a steady plane flame, and focussed on such factors as a c t i v a t i o n energy, pressure and temperature, and the Lewis number of the d e f i c i e n t reactant, by singular perturbation techniques, g e n e r a l l y r e f e r r e d to as the method of high a c t i v a t i o n energy asymptotics. Such a method has since been extended, to problems of flame propagation and s t a b i l i t y i n a v a r i e t y of s i t u a t i o n s . (See for instance the monograph by Buckmaster and Ludford [2], and numerous papers, such as [3]-[10]. Among other things, these studies have shown that the balance between molecular transport of heat and reactants required by the planar laminar flame model i s generally unstable, except for a narrow range of Lewis numbers around one, and i n some cases, for a l i m i t e d range of perturbing frequencies [8], [11], [12]. Of p o t e n t i a l relevance here, laminar flame theory has shown that, depending on the Lewis numbers, flame s t r e t c h and s t r a i n by the flow f i e l d a f f e c t the laminar burning v e l o c i t i e s , and p o s s i b l y the l i m i t s of the range of Lewis numbers of the reactants corresponding to s t a b i l i t y of the plane laminar 4 flame. Outside t h i s range, other modes of propagation appear to be possible. They correspond r e s p e c t i v e l y to c e l l u l a r flames, which should be observed when the Lewis number of the d e f i c i e n t reactant i s less that the lower l i m i t of s t a b i l i t y of the planar flame, and to p u l s a t i n g flames, on the other side [11]. Other studies, where a stagnation point flow or some variant was s p e c i f i e d , a l s o show that even for Lewis number within the range of s t a b i l i t y of the plane laminar flame, s t r a i n tends to reduce the laminar burning v e l o c i t y i n mixtures lean i n the heavy reactant. For a c e r t a i n combination of s t r a i n rate and Lewis number, i t s value reaches zero and further, becomes negative. Negative burning v e l o c i t i e s do not make ph y s i c a l sense, and since the model i s very s i m i l a r to the ignition-quenching process i n thermal explosion theories, the expected physical i n t e r p r e t a t i o n i s that the zero of the (stable) strained laminar burning v e l o c i t y corresponds to quenching. (See Daneshyar, Mendes-Lopes, Ludford, Tromans, [3], [4], [8], [10] and a l s o for instance Libby, Linan and Williams [5], Libby and Williams [6], M i k o l a i t i s [13], [14].) M i k o l a i t i s shows that curvature may strengthen considerably the e f f e c t of s t r e t c h and s t r a i n . Experimental evidence confirming the predicted e f f e c t of s t r a i n on the laminar burning v e l o c i t y and quenching, for stagnation point flows, was produced by Daneshyar et a l [3], [4], Sato [15] and Ishizuka and Law [16]. This question, according to some of the authors c i t e d above, may be relevant to turbulent flames, since turbulence w i l l produce a strained flow, with p o s s i b l y strong curvature. 5 The i n f l u e n c e o f s t r a i n i n g i s u s u a l l y c h a r a c t e r i z e d b y a K a r l o v i t z [ 1 7 ] number , o f t h e f o r m f o r a t w o - d i m e n s i o n a l c a s e , where 6^ i s t he l a m i n a r f l a m e t h i c k n e s s , u ^ i 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 du/dy i s t h e g r a d i e n t i n t h e p l a n e t a n g e n t t o t h e f l a m e o f t h e f l o w v e l o c i t y component p a r a l l e l t o t h e d i r e c t i o n o f f l a m e p r o p a g a t i o n . Somet imes m e n t i o n i s made o f a D a m k o h l e r number , w h i c h i s t h e i n v e r s e o f t h e n o r m a l s t r a i n , ( r e l a t e d t o l a t e r a l s t r a i n b y the c o n t i n u i t y e q u a t i o n ) , d i v i d e d b y a c h e m i c a l t i m e , a n d i s t h u s t h e i n v e r s e o f a K a r l o v i t z number . More c o m p l e t e d i s c u s s i o n s o n t h e s t r e t c h f a c t o r , f o r g e n e r a l c a s e s a r e p r o p o s e d b y F . A . W i l l i a m s [ 1 8 ] , p . 4 1 6 , a n d M a t a l o n [ 1 9 ] . 2 . 2 T u r b u l e n c e T u r b u l e n c e s h a l l be c o n s i d e r e d h e r e i n t h e u s u a l way , b a s e d o n t h e R e y n o l d s a p p r o a c h . S u c h a mode l assumes t h e f l o w t o be a n e r g o d i c p r o c e s s , w h i c h i s a r e a s o n a b l e h y p o t h e s i s f o r d e v e l o p e d f l o w s , b u t i s n o t s t r i c t l y v a l i d i n a n e s s e n t i a l l y t r a n s i e n t s i t u a t i o n . However no o t h e r a l t e r n a t i v e i s p r e s e n t l y a v a i l a b l e f o r t h e p r o b l e m u n d e r s t u d y . T h e r e i s a p a r a d o x b e t w e e n the d e t e r m i n i s t i c p h y s i c a l l a w s w h i c h c o n t r o l v i s c o u s f l o w a n d t h e o b s e r v e d r andomness , a n d t h e s t o c h a s t i c m o d e l s t h e r e o f . The N a v i e r - S t o k e s e q u a t i o n s a r e assumed t o p r o v i d e a n a d e q u a t e d e s c r i p t i o n o f t h e f l o w , a n d , g i v e n a p r o p e r s e t o f i n i t i a l a n d b o u n d a r y c o n d i t i o n s , t o have 6 a unique, continuous s o l u t i o n at a l l times. This would not seem to be consistent with a p r o b a b i l i s t i c d e s c r i p t i o n . However i n most cases, the s o l u t i o n i s unstable. Perturbations as small as one wants to the i n i t i a l or boundary conditions w i l l r e s u l t i n flow f i e l d s which tend to become uncorrelated with the unperturbed one as time increases. In the l i m i t , the f u l l y developed flow i s thus independent of i t s i n i t i a l conditions. The hypothesis on which the p r o b a b i l i s t i c model i s based i s that the p r o b a b i l i t y space has become time-independent, and thus, according to the ergodic theorem, has the same p r o b a b i l i t y measure as the space containing the set of instantaneous v e l o c i t y f i e l d s corresponding to a si n g l e event, over an i n f i n i t e length of time. Consequently, time-averaging w i l l converge to the same l i m i t s as ensemble averaging. Thus paradoxically, a c h a r a c t e r i z a t i o n of the f u l l y developed flow as a random process i s not inconsistent with the phys i c a l model. If the flow i s e s s e n t i a l l y unsteady, however, i t s main features n e c e s s a r i l y depend on the i n i t i a l conditions. If these are f u l l y prescribed, the hypothesis of uniqueness of the solutions to a properly posed Navier-Stokes problem r e s u l t s i n one s i n g l e s o l u t i o n at a l l f i n i t e times. According to t h i s , s t r i c t l y speaking, a p r o b a b i l i s t i c d e s c r i p t i o n for an unsteady flow, not yet f u l l y developed and thus at f i n i t e time, could only be obtained as r e s u l t i n g from a p r o b a b i l i s t i c d e s c r i p t i o n of the i n i t i a l conditions. If the concept of turbulent f l u c t u a t i o n i s defined from t h i s point of view, then the proper evaluation technique i s ensemble averaging. 7 A less rigorous but sometimes more r e a l i s t i c approach i s to assume that the time elapsed since the o r i g i n of the process i s so large compared to the times c h a r a c t e r i s t i c of the chaotic motion that the r a p i d l y varying motion i s nearly unrelated to the i n i t i a l conditions, even though the flow i s s t i l l unsteady, and the slowly varying features of the flow f i e l d s t i l l depend strongly on the i n i t i a l conditions. If t h i s c o n d i t i o n holds (that i s , i f the experimental data s a t i s f y the condition), a time window can be chosen, narrow enough so that neither the mean features of the flow nor the characters of the random components have changed much, but wide enough so that i t contains a reasonably f u l l d e s c r i p t i o n of the p r o b a b i l i t y d i s t r i b u t i o n of the f l u c t u a t i o n , which by approximation i s assumed to be constant over the window. It i s then possible to measure a slowly varying component and a random component of the motion, and c a l l them r e s p e c t i v e l y the mean v e l o c i t y and the turbulence i n t e n s i t y . While t h i s i s not a proper d e f i n i t i o n of a p h y s i c a l quantity, at least, a measurement procedure i s defined, which would be objective, except that i t depends on one a r b i t r a r i l y chosen parameter, for instance the width of the i n t e r v a l . Since the flame can be expected to depend on the p a r t i c u l a r h i s t o r y of an event, and not on the s t a t i s t i c s of a s e r i e s of events, the second approach, however less rigorous, may be better i n combustion experiments. The ergodic hypothesis i s no more v a l i d because the p r o b a b i l i t y space i s no more time-independent. If the range of f l u c t u a t i o n of the i n i t i a l conditions 8 i s wide, as i n flow measurements i n engines, the f i r s t d e f i n i t i o n w i l l r e s u l t i n higher values. This does not imply that the r e s u l t s of ensemble averaging, over a set of perturbations of the i n i t i a l conditions small enough (but not too small) do not have to be equal to those of window-averaging over a su i t a b l e i n t e r v a l . It i s thus conceivable that the two procedures remain equivalent a l s o f or unsteady flows. The theory of homogeneous, i s o t r o p i c turbulence [20] i s frequently referred to i n turbulent flame studies. The motion i s assumed to be random, with no d i r e c t i o n a l mean and a l l d i r e c t i o n s equiprobable. The Navier-Stokes equations then reduce to some simple e q u a l i t i e s subject to a p r o b a b i l i s t i c d e s c r i p t i o n . The model i s supplemented by empirical observations r e l a t i n g to the rate of decay of turbulent k i n e t i c energy and among i t s r e s u l t s are two simple and use f u l r e l a t i o n s h i p s ( l a t e r mentioned i n chapter 4) between turbulence i n t e n s i t y , i n t e g r a l length scale and Taylor microscale. In most combustion experiments, no or few s p a t i a l l y resolved combustion data are a v a i l a b l e , and v e l o c i t y data are seldom a v a i l a b l e . Further, the accuracy i s not so good as to j u s t i f y the complications which would r e s u l t from the consideration of position-dependent turbulent q u a n t i t i e s . It i s thus usual, and reasonable, i n most s i t u a t i o n s , to adopt the homogeneous, i s o t r o p i c model, as a f i r s t approximation. A u s e f u l represention of homogeneous, i s o t r o p i c turbulence, i s the Tennekes model [21] , [22] , which has been shown to scale properly with the re a l phenomenon, provides an easy, v i s u a l way to characterize i t , and has the 9 a d d i t i o n a l v i r t u e of being i n agreement with the experimental evidence that viscous d i s s i p a t i o n i s not homogeneously d i s t r i b u t e d i n space, but that there i s a structure i n the motion. This i s p a r t i c u l a r l y important, since i t w i l l a f f e c t the flame propagation. 2.3 Turbulent flames Since Mallard and Le C h a t e l i e r , i n the nineteenth century, turbulent f l u i d motion has been known to improve flame propagation. In 1940, Damkohler proposed the s t i l l best known model of turbulent flame propagation, which says turbulence wrinkles the flame and as a r e s u l t the e f f e c t i v e flame area over which molecular propagation mechanisms develop i s increased, r e s u l t i n g i n a f a s t e r global propagation speed. However such a mechanism can only be maintained provided the turbulence i s moderate enough to a f f e c t only gently the flame front. At higher l e v e l s , separate flame sheets are expect to occur, sometimes transported forward i n the unburnt mixture by large turbulent structures. As a consequence of thermal expansion due to the combustion, together with the change of v i s c o s i t y r e s u l t i n g from the temperature d i f f e r e n c e , the flame w i l l a f f e c t the flow f i e l d . The problem i s thus f u l l y coupled, with mutual i n t e r a c t i o n s between the f l u i d mechanics and the diffusional-thermal phenomena. 10 A d e t a i l e d d e s c r i p t i o n of the sources of these ideas i s presented by Andrews, Bradley and Lwakabamba, 1975 [23]. They discuss the d i f f e r e n t models proposed. Some of these works were formulated before a proper understanding of the laminar flame r e a c t i v e - d i f f u s i v e structure had been developed. They consequently r e f e r to the phenomenological concept of the laminar burning v e l o c i t y , as i t r e s u l t s from the observations, without an awareness that more re f i n e d models w i l l propose that the existence and value of the laminar burning v e l o c i t y r e s u l t from the conjunction of many d i f f e r e n t parameters. The proposed empirical r e l a t i o n s h i p s are mostly between u^/u^ and u'/u^. Here u^ r e f e r s to a turbulent burning v e l o c i t y , u' i s the turbulence i n t e n s i t y , defined as the r.m.s. value of the v e l o c i t y f l u c t u a t i o n i n one d i r e c t i o n , assuming the f l u c t u a t i o n to be i s o t r o p i c , u^ i s the a d i a b a t i c laminar burning v e l o c i t y of a plane flame front i n s t i l l mixture, f or the actual mixture composition, 6^ i s a measure, up to a constant of 0(1), of the corresponding flame thickness, with the constant assumed to be such that 6i = - j r ( 2 - 2 ) where a i s the heat d i f f u s i v i t y . L x i s the i n t e g r a l length scale. Damkohler proposes a l i n e a r r e l a t i o n s h i p of the form U t = 1 + k (2.3) where k = 1, v a l i d for L x >> 6^. K a r l o v i t z e t . a l . [17] accept the same 11 expression f o r low values of u' and when u' >> u^ they propose u. u. = 1 + k' u u, 1/2 (2.4) with k' = V 2 , and for strong turbulence, add an a d d i t i o n a l term to u', to consider the e f f e c t of flame-generated turbulence. Shchelkin, and l a t e r , Leason, propose an expression u. u, 1 + k" 1/2 (2.5) Other authors, a l s o mentioned by Andrews, Bradley and Lwakabamba, l i k e Wohl, Kozachenko, Tucker, Richardson, propose some combination between these three basic forms, or va r i a n t s , e i t h e r with d i f f e r e n t c o e f f i c i e n t s or some a d d i t i o n a l terms or corrections. A common feature of a l l these works i s that they assume the equivalence r a t i o and a l l other parameters r e l a t e d to the mixture chemical and molecular transport properties only a f f e c t t h e i r model through the laminar burning v e l o c i t y . Thus f or instance they do not allow for a d i f f e r e n t turbulent behavior between mixtures r e s p e c t i v e l y r i c h and lean, but with the same ad i a b a t i c plane unperturbed laminar burning v e l o c i t y , nor between mixtures of d i f f e r e n t gases, provided u^ i s the same. Such a view i s consistent with the idea that as turbulence increases, the basic (and at the time some of these works were published, s t i l l i n part unknown) model of flame propagation remains the same, but the r o l e of the molecular transport properties tends to be substituted by turbulent ones. 12 These a f f e c t equally heat and reactants, and would thus r e s u l t i n a concept of a general turbulent Lewis number equal to one. However, as pointed out by F.A. Williams i n [18], p.438, burning rates are a c t u a l l y more strongly a f f e c t e d by the temperature i n the r e a c t i o n zone, wich would tend to be reduced by improved turbulent mixing, than by the transport prop e r t i e s . Perhaps as a r e s u l t of such an approach, most of the experimental evidence a v a i l a b l e f o r turbulent combustion r e f e r s to a v a r i e t y of nearly stoi c h i o m e t r i c mixtures, which for many types of f u e l s , tend to have Lewis numbers not too d i f f e r e n t from unity. Consequently most of the data appeared to confirm the assumption of a turbulent Lewis number unity, though i n fact, i t was not r e a l l y tested. This remains true f o r Andrews, Bradley and Lwakabamba's [23] proposals. S u b s t i t u t i n g laminar by turbulent transport c o e f f i c i e n t s i n the burning v e l o c i t y equation, they obtain an equation where the turbulent burning v e l o c i t y v a r i e s with the square root of a Reynolds number based on u" and L x u. u. u •,1/2 Pr (2.6) where Pr i s a Prandtl number. For homogeneous, i s o t r o p i c turbulence, this i s equivalent to u. u. = k . Re, (2.7) where k i s a p r o p o r t i o n a l i t y constant. They then analyze a v a i l a b l e 13 experimental data, and conclude they are reasonably i n agreement with the equation, which appears to be independent of the mixture composition. However they speculate that at higher values of Re^, the wrinkled flame model may not be maintained. B a l l a l and Lefebvre, i n 1975 [24], tested mixtures of propane and a i r with various equivalence r a t i o s . However t h e i r data are sparse (only three tests, at same u', for the lean and for the r i c h mixture, apparently), and they do not discuss s p e c i f i c a l l y the e f f e c t of the equivalence r a t i o , which remains hidden i n c o r r e l a t i o n s of the type already mentioned. Their objectives refer more to the structure of turbulent flame, and a l s o , mostly i n a l a t e r paper by B a l l a l [25], to the question of flame-generated turbulence. Reasoning on the Tennekes model, Chomiak [26], [27], [28] shows that combustion occuring within a region of high viscous d i s s i p a t i o n , of diameter s c a l i n g with the Kolmogorov scale, w i l l produce thermal expansion r e s u l t i n g i n a displacement of the r e a c t i o n zone a x i a l l y along the "vortex tubes" of the Tennekes model, at high v e l o c i t i e s . Within the calmer areas between such zones, s c a l i n g with the Taylor microscale, the flame w i l l complete the combustion at speeds of the order of the laminar burning v e l o c i t y . He does not take into account, however, that during t h e i r t r a v e l , such kernels would s u f f e r large t o t a l heat losses and p o s s i b l y quench, while the heat transferred per u n i t area might not be s u f f i c i e n t to i g n i t e the adjacent material. In e f f e c t , the very large s t r a i n rate implied by Chomiak's hydrodynamic model of propagation must make i t s e n s i t i v e to s t r e t c h , at least when the laminar flame thickness i s less than the Kolmogorov scale. 14 A f t e r a new a n a l y s i s of a v a i l a b l e flame propagation data and turbulence parameters, i n a paper published i n 1980, Abdel-Gayed and Bradley [29] propose another c o r r e l a t i o n between u^/u^, u'/u^ and Re^. Here, the influence of Re^ appears to be important only for lower values of u ' / u ^ and Re^. For larger values, xi^/u^ v a r i e s l i n e a r l y with u'/u^. The equivalence r a t i o s t i l l does not appear i n the c o r r e l a t i o n , except, as i n previous works, i n u^. Daneshyar and H i l l [30] propose an equation which i s consistent with the vortex-bursting concept of Chomiak and an approximately l i n e a r c o r r e l a t i o n of u^ . with u'. The equation i s u t = u e + °-P u .u' (2.8) P b In which subscipt u r e f e r s to unburnt gases, b to burnt gases. They also suggest that the i g n i t i o n delay should scale with X, the Taylor microscale, d i v i d e d by u^. So f a r none of the models discussed takes into account the s p e c i f i c influence of each of the d i f f e r e n t parameters a f f e c t e d by the composition of the mixture, but only t h e i r very s p e c i f i c combination corresponding to the value of u'. In p a r t i c u l a r , they ignore the combined influence of s t r e t c h and of the Lewis number of the c r i t i c a l reactant, which, according the conclusion of several laminar flame models, i s expected to be relevant i n turbulent flames. For instance, Tromans, Daneshyar et a l [3], [4], [8], [10] speculate that above a c e r t a i n l e v e l , turbulence has to r e s u l t i n quenching. Similar conclusions are reached by Libby, Linan and F.A. Williams, i n [5], [6], and a l s o i n chapter 10 of [18]. 15 Abdel-Gayed, Bradley, Hamid and Lawes [31] present new measurements and attempt to include the e f f e c t of s t r a i n i n g i n t h e i r model. They assume that, according to the mentioned theories for stagnation point flows, excessive l o c a l s t r a i n i n g w i l l r e s u l t i n l o c a l quenching. In p a r t i c u l a r , f or a range of mixtures of propane and a i r , they propose values of equivalent Lewis number taking i n t o account the j o i n t e f f e c t of the d i f f u s i v i t y of the f u e l and the oxidant. Apparently, they use an expression derived by J o u l i n and Mitani [11] i n a study of the s t a b i l i t y of an ad i a b a t i c , unstrained laminar flame, v a l i d for (f) = 0(l//3), but not (j) = 0 ( l / p ), (j) being the equivalence r a t i o , and /3 the nondimensional a c t i v a t i o n temperature. The expression depends on the order of the reaction, and the authors s p e c i f i c a l l y mention which terms would have to be a l t e r e d to take curvature, and conceivably s t r a i n , into account. Likewise, i f the expression depends on the order of the r e a c t i o n of an assumed single-step reaction, i t would seem to be reasonable to apply i t not to the Lewis numbers of propane and oxygen, but to those of the reactants i n the most c r i t i c a l step i n the chain-reaction. F i n a l l y , there i s no reason to expect that the combination v a l i d f o r s t a b i l i t y a n a l y s i s w i l l apply also when determining strained laminar burning v e l o c i t i e s . Abdel-Gayed and Bradley do not o f f e r any d e t a i l s on t h e i r procedure, and the assumptions they included. In [32], Abdel-Gayed and Bradley review a v a i l a b l e experimental evidence on l i m i t s of turbulent flame propagation, and propose quenching by turbulent 16 s t r a i n i n g as the c o n t r o l l i n g factor. They propose there i s a c o r r e l a t i o n between burning v e l o c i t y and quenching data and a K a r l o v i t z number based on u'/X. Such a measure of du/dy i s a consequence of Taylor's d e f i n i t i o n of the microlength scale X = ,2 (2-9) (du/dx)2 Chomiak and J a r o s i n s k i [33] perform turbulent quenching experiments i n a test tube and c o r r e l a t e t h e i r data to a K a r l o v i t z number based on u'/L , where L x x i s the i n t e g r a l length scale. No explanation i s given as to why they r e f e r to the i n t e g r a l length scale. If numerous researchers have investigated turbulent combustion, no comprehensive p i c t u r e has emerged. The experimental evidence a v a i l a b l e i s l i m i t e d i n terms of mixture composition, and to some extent, contradictory. This p o s s i b l y r e f l e c t s the fa c t that turbulence and i t s e f f e c t s on the flame are l o c a l and cannot be accurately described by global parameters. Experimental data are thus i n e v i t a b l y dependent on the apparatus; there are mutual i n t e r a c t i o n s between flame and flow, and to a large extent, the r o l e of the chemical and transport properties of the reaction, u n t i l recently l a r g e l y ignored, i s s t i l l v i r t u a l l y unknown. The d i s p e r s i o n between data, when p l o t t e d versus turbulence parameters, and ignoring the other factors except i n the laminar burning v e l o c i t y , i s such that a wide v a r i e t y of empirical c o r r e l a t i o n w i l l f i t almost equally well (or equally badly) the experimental data. 17 2.4 Swirl Swirl has been proposed as one of the mechanisms which might be used to increase burning rates i n engines. It decays more slowly than higher frequency eddies, and i f i t breaks up near i g n i t i o n time, i t w i l l release s i g n i f i c a n t amounts of turbulent k i n e t i c energy when combustion occurs. Swirl a l s o induces buoyancy e f f e c t s , which tend to b r i n g back the l i g h t , burnt gas to the center of the motion, and thus, hopefully, away from the walls of the combustion chamber. The r e s u l t i s that even i f i g n i t i o n occured near the wall of the combustion chamber, the flame i s allowed to propagate i n a l l d i r e c t i o n s ; i t a l s o i n i t i a l l y reduces heat transfer to the walls. While the t o t a l flame speed, given by dx/dt where x i s the d i r e c t i o n of propagation, i s reduced, the laminar burning v e l o c i t y dx/dt| , v being the v e l o c i t y of the u unburnt mixture at the flame front, remains unaffected. Experimental studies on combustion i n s w i r l i n g motion were performed by Hanson and Thomas [34], and a l s o by Dyer [35]. The former observe that i n forced v o r t i c e s , even i f the i g n i t i o n occured o f f the a x i s , the flame kernel moves to the center of the s w i r l , under the e f f e c t of the body forces due to the c e n t r i f u g a l a c c e l e r a t i o n , and that the flame assumes a c y l i n d r i c a l shape. However experiments i n an engine by Witze [36] show that except for very high s w i r l s , c e n t r a l i g n i t i o n r e s u l t s i n f a s t e r combustion. Dyer's experiment has some points i n common with the present one: the swirl i s obtained by f a s t charging through a shrouded port. He measures flow 18 v e l o c i t i e s by laser-doppler anemometry, allowing f or cycle-resolved and d i r e c t i o n a l data. His main objective i s to produce a consistent set of we l l - e s t a b l i s h e d data for reference. The aspect r a t i o i s d i f f e r e n t than here: the diameter i s 80 mm and the length, 29 mm and consequently the e f f e c t of the secondary flow should be d i f f e r e n t than i n the present experiment. Thus no d i r e c t comparison of h i s v e l o c i t y measurements with the present r e s u l t s can be made. He notes that the charging process r e s u l t s i n a temperature increase. However since heat exchange occurs at the walls, the temperature i s not uniform, and a l s o decays with time. The temperature gradients i n r a d i a l d i r e c t i o n s are largest near mid-radius. Both v e l o c i t y and temperature are nearly constant i n d i r e c t i o n s p a r a l l e l to the c e n t e r l i n e . He tests the influence of a spark plug p r o j e c t i n g s l i g h t l y out of the wall, and f i n d s i t s i g n i f i c a n t l y a f f e c t s the flow f i e l d . He a l s o studies the e f f e c t of d i f f e r e n t wall temperatures on the flow and temperature f i e l d s . He observes that nearly 50% of the mass i s burnt i n the 3 mm wide region next to the outside walls, and that the flame appears to propagate at nearly a constant r a d i a l v e l o c i t y outward from the c e n t e r l i n e . Besides h i s thorough i n v e s t i g a t i o n of the flow and temperature f i e l d s , he a l s o performs some combustion experiments, t e s t i n g f a c tors l i k e the spark plug p o s i t i o n , d i f f e r e n t s w i r l s , and d i f f e r e n t wall temperatures, and concludes that h i s combustion r e s u l t s 'are generally as expected'. The only test with a lean mixture i s quiescent. 19 One of the negative aspects of s w i r l i s that when the flame reaches the wall, the high tangential v e l o c i t y w i l l tend to improve convection, and thus increase heat losses. Flame propagation models based on flow representation as homogeneous, i s o t r o p i c turbulence may not be ap p l i c a b l e i n s w i r l i n g motion since the decay of the s w i r l i s accompanied by d i f f u s i o n of turbulent k i n e t i c energy from the boundary layers on the walls and consequently, the l e v e l s of turbulent k i n e t i c energy w i l l r e s u l t from a balance between d i f f u s i o n and viscous d i s s i p a t i o n . Since the s w i r l corresponds to the largest scales possible, however, i t i s reasonable to expect decay to correspond to an i n t e g r a l length scale r e l a t e d to the s i z e of the bomb. The s w i r l a f f e c t s the shape of the flame. This a f f e c t s the pressure r i s e curve, by changing the area/volume r a t i o of the burnt gases, and thus, the area from which the flame can propagate f o r a given quantity of burnt gas. The laminar burning v e l o c i t y i s not d i r e c t l y a f f e c t e d . However the swi r l r e s u l t s i n shear st r e s s or a strained v e l o c i t y f i e l d , i n sofar as i t d i f f e r s from s o l i d body, and at least i n the boundary layer. This s t r a i n i s r a d i a l , with no component perpendicular to the mean d i r e c t i o n of flame propagation, and consequently w i l l not a f f e c t the flame propagation on the points on the flame f r o n t ( s ) where the normal to the flame surface i s i n a plane containing the c e n t e r l i n e . However propagation i n d i r e c t i o n s oblique to the mean flame d i r e c t i o n conceivably w i l l be a f f e c t e d by the s t r a i n . 20 Also, the force f i e l d due to the c e n t r i f u g a l a c c e l e r a t i o n applied on the density d i f f e r e n c e across the flame w i l l tend to reduce the flame wrinkling, l i k e the g r a v i t y f i e l d would do on a downward-propagating flame. Both e f f e c t s tend to reduce the flame wrinkling and laminarize i t . Laminarization i s discussed i n [37], apparently under the second of the mechanisms discussed here. 2.5 Summary There are mutual i n t e r a c t i o n s between the flow and the flame on a large and a small scale. So far no t h e o r e t i c a l model has been developed which would r e s u l t i n a set of general and consistent r e l a t i o n s h i p s . Phenomenological c o r r e l a t i o n s cannot be more accurate than the range of d i s p e r s i o n of the experimental data they are based upon, and w i l l not take into account factors which were not submitted to a s u f f i c i e n t experimental i n v e s t i g a t i o n . The d i f f e r e n t parameters a f f e c t e d by the equivalence r a t i o , the molecular transport p r o p e r t i e s of the reactants and t h e i r r e a c t i o n k i n e t i c properties have not been systematically investigated. Perhaps as a r e s u l t , such factors have been l a r g e l y ignored, i n the c o r r e l a t i o n s which have been proposed so far for turbulent combustion, except i n the combination corresponding to the a d i a b a t i c plane laminar flame v e l o c i t y . This quantity i s a rather complex and s p e c i f i c f unction of the primary phy s i c a l q u a n t i t i e s , and no s o l i d conceptual 21 j u s t i f i c a t i o n as to why t h i s p a r t i c u l a r function, and only t h i s , should be so relevant to turbulent combustion has been proposed. The inadequacies of the only model a v a i l a b l e to characterize and measure turbulence would be s u f f i c i e n t to explain the scatte r between experimental data. This does not n e c e s s a r i l y implies there are no other reasons. Recent t h e o r e t i c a l works show that the structure of laminar flames i s s e n s i t i v e to c e r t a i n f a c tors which depend on the flow f i e l d , and should not be expected to become i r r e l e v a n t when the flow i s turbulent. It i s thus not unreasonable to conjecture that part of the scatte r i n the a v a i l a b l e c o r r e l a t i o n s may be due to the neglect of some of the several parameters which r e s u l t to the laminar flame structure. Recently some studies have begun to consider such f a c t o r s , without very c l e a r r e s u l t s so f a r . 22 3 Objectives The b a s i c purpose of t h i s work was to investigate the e f f e c t of turbulence due to s w i r l , and mixture composition, on turbulent burning rates. With that purpose i n mind, two v a r i a b l e s were investigated: the stoichiometry of a propane-air mixture, and the decay time of an unsteady s w i r l i n g motion produced by the intake configuration. D i f f e r e n t decay times r e s u l t i n d i f f e r e n t turbulence l e v e l s . The r e s u l t s were.compared with predictions r e s u l t i n g from current models for engine combustion simulation, and the hypotheses such models are based upon were discussed, i n the l i g h t of the experimental evidence. P a r t i c u l a r a t t e n t i o n was paid to the range within which the experimental r e s u l t s vary, and f i t with the proposed models The s w i r l was of i n t e r e s t p r i m a r i l y as the mechanism generating the turbulent motion. I t may be d i f f i c u l t to i s o l a t e , i n t h i s kind of experiment, e f f e c t s due d i r e c t l y to the s w i r l from those due to swirl-generated turbulence. The two s p e c i f i c questions one wanted to answer were: (1). How do d i f f e r e n t s w i r l s , and t h e i r respective turbulence parameters a f f e c t the flame propagation^, and how regular are such e f f e c t s : Flame propagation i s characterized simply by the time i t takes to reach c e r t a i n pressure l e v e l s . 23 How well does the v a r i a t i o n i n turbulence i n t e n s i t y explain differences i n flame propagation? Does one observe an influence on the burning speed of the scales of turbulence? How the data compare with previous observations, and how well do they follow established empirical r e l a t i o n s h i p s p r e d i c t i n g the burning times, based on the turbulence i n t e n s i t y and scales? Do turbulence-related parameters a f f e c t the d i s p e r s i o n between experiments? Can the combustion process be modeled by d e f i n i n g an i g n i t i o n delay, with a s t o c h a s t i c d e s c r i p t i o n , followed by a d e t e r m i n i s t i c combustion time, a l b e i t dependent on turbulence? Is i t p o s s i b l e to d i s t i n g u i s h any e f f e c t d i r e c t l y a t t r i b u t a b l e to swirl? . To what extent does the mixture composition a f f e c t the flame propagation: Previous works conclude that the mixture composition has l i t t l e i nfluence on the turbulent burning v e l o c i t y , provided that the d i f f e r e n c e s i n laminar burning v e l o c i t i e s are taken into account. Is this conf irmed? 24 Or i f not, i s the influence of the mixture composition on the burning v e l o c i t i e s i n the same proportion as the v a r i a t i o n of laminar burning v e l o c i t y due to s t r a i n i n g by a v e l o c i t y gradient? Does the mixture a f f e c t the c y c l i c d i s p e r s i o n and the i g n i t i o n delay? If so, i s the e f f e c t r e l a t e d to a d i f f e r e n c e i n laminar burning v e l o c i t i e s , i n strained laminar burning v e l o c i t i e s , i n the Lewis numbers, or what other parameters? Is the influence of the mixture composition, on the burning times and the c y c l i c d ispersion, a f f e c t e d by turbulence, and how? Is i t a f f e c t e d by the s w i r l , and how? 25 4.The experiment 4.1 D e s c r i p t i o n 4.1.1 Combustion experiments The s w i r l i n g motion was obtained by r a p i d l y charging the previously evacuated bomb through an ec c e n t r i c port. A l l experiments were performed with the same charging sequence, with a l l parameters constant, w i t h i n the l i m i t s of r e p e a t a b i l i t y allowed by the equipment. D i f f e r e n t flow f i e l d s during the combustion were obtained by s e t t i n g d i f f e r e n t time i n t e r v a l s between the end of charging and i g n i t i o n . I g n i t i o n was produced by a spark between electrodes with the gap at the center of the bomb. Two d i f f e r e n t mixture compositions were tested, with respective equivalence r a t i o s of 0.92 and 0.79. With the f i r s t batch of mixture, approximately 100 i d e n t i c a l experiments were repeated f o r delay times between end of charging and i g n i t i o n of r e s p e c t i v e l y 15 ms, 30 ms, 60 ms, 120 ms and 240 ms. With the second batch, f o r only two values of the delay, 15 ms and 30 ms, was the experiment repeated a hundred times. However, delays of 0, 5, 10, 60, 120 and 240 ms were investigated with smaller samples, of ten tests for each delay. For each experiment, the charging pressure-time h i s t o r y and the combustion pressure trace were recorded. This allowed v e r i f i c a t i o n a - p o s t e r i o r i of the 26 extent to which the parameters measuring non-repeatability i n charging were co r r e l a t e d to the parameters c h a r a c t e r i z i n g combustion. Also, an accurate record of the pressure at i g n i t i o n time remained a v a i l a b l e for zero c o r r e c t i o n . The pressure i n the charging tank, the i n i t i a l vacuum i n the bomb, the c o n t r o l l e d times, and the other parameters a f f e c t i n g charging and combustion, described i n the next sections, were monitored.during the experiments. 4.1.2 Flow measurements The purpose of the flow measurements was to provide information on the flow f i e l d , i t s s p a t i a l d i s t r i b u t i o n and turbulence parameters, at the d i f f e r e n t decay times tested i n the combustion experiments. The experiments were e s s e n t i a l l y the same as i n the combustion experiments, except that the combustible mixture was replaced by a i r , and that instrumentation for flow measurement was i n s t a l l e d . The flow measurement technique i s hot wire anemometry. Seven d i f f e r e n t hot wire locations were investigated, a l l i n the c e n t r a l plane of symmetry of the bomb, at radius r a t i o s r / I ^ b equal to 0, 0.25, 0.375, 0.5, 0.625, 0.75 and 0.825. For each lo c a t i o n , the experiment was repeated approximately f i f t y times, to provide data f o r ensemble averaging. At a l l locations, the set of experiments was r e a l i z e d twice, with and without the spark plug i n place. Synchronized with the hot wire s i g n a l , the pressure and temperature h i s t o r y 27 were a l s o recorded, as described i n sections 4.2.7 and 4.2.8. However, the temperature could not be measured at the hot wire lo c a t i o n , but only at approximately the same distance from the wall, i n another r a d i a l d i r e c t i o n , i n the c e n t r a l plane of symmetry. Pressure, temperature and hot wire data were recorded from the beginning of the charging process, defined as the time a push-button i s depressed on a timing c o n t r o l device, described i n Section 4.2.4, i n i t i a t i n g the sequence of operations. 4.2 Experimental setup 4.2.1 General The experimental set-up used here was designed and u t i l i z e d i n i t i a l l y by Roger Milane [38], and suffered only minor a l t e r a t i o n s , except for the charging c o n t r o l , which was exhaustively tested and modified, t i l l i t s r e p e a t a b i l i t y was found to be adequate for the purpose of the intended s t a t i s t i c a l a n a l y s i s . The i n l e t design was a l s o modified, to reduce the c a v i t y i n the i n l e t , between the c y l i n d r i c a l part of the bomb and the check valve. 28 4.2.2 Bomb and Piping The combustion bomb i s shown on Figure 1. It i s c y l i n d r i c a l , with a diameter of 89 mm by a length of 45 mm. I t i s made of s t a i n l e s s s t e e l , with transparent quartz windows on i t s f l a t sides. Besides the admission i n l e t , with i t s c e n t e r l i n e located i n the cent r a l plane of symmetry, orthogonal to the c y l i n d e r c e n t e r l i n e , and i t s lower generatrix tangent to the cylin d e r , a number of ports are a v a i l a b l e , for the ou t l e t to the vacuum pump, for the hot wire probe, the spark plug and for the pressure sensor. The pip i n g i s i l l u s t r a t e d on the control and instrumentation diagram, Figure 2. An i n l e t g r i d with s i z e 2 mm i s placed in s i d e the piping, together with an in s e r t , continuing to the check valve, of same cross s e c t i o n as the g r i d , reducing as f a r as p r a c t i c a l the c a v i t i e s i n the part of the charging l i n e which remains i n communication with the bomb, where a substantial amount of mixture w i l l be pushed i n by the flame and burn a f t e r the flame reaches the cy l i n d e r walls. The i n l e t g r i d i s made of a long, s o l i d c y l i n d e r , with bored holes of the desired g r i d s i z e of 2 mm diameter. The actual t o t a l volume, of the cylinder and the c a v i t y i n the i n l e t , which remains i n communication with the bomb during combustion, was measured by f i l l i n g the bomb with a measured volume of l i q u i d , of 287 ml, with a reading error within ±5 ml. Since the volume of the cy l i n d e r i s approximately 280 ml, the c a v i t y i n the i n l e t would appear to be of no more than 12 ml. 29 The aspect r a t i o has a strong influence on the flow f i e l d . Here, the length of the c y l i n d r i c a l chamber was h a l f the diameter, r e s u l t i n g from a compromise between the two extremes, r e s p e c t i v e l y the f l a t disk, maybe more representative of a combustion chamber at top dead center, and the long c y l i n d e r , more l i k e the case of bottom dead center. An i n t e r e s t i n g feature of t h i s range of aspect r a t i o s i s the secondary flow e f f e c t . The spiral-shaped boundary layer on the f l a t walls r e c i r c u l a t e s f l u i d from the boundary layer on the c y l i n d r i c a l wall, which does not grow as would be expected i n the one-dimensional case of a long c y l i n d e r . Vortex shedding by the spark plug a f f e c t s the flow f i e l d s u b s t a n t i a l l y . Since i t i s important to r e l a t e the combustion r e s u l t s to the actual flow f i e l d , t h i s matter was deemed to merit a f u l l i n v e s t i g a t i o n , hence the d u p l i c a t i o n of a l l v e l o c i t y measurements with and without the plug i n . 4.2.3 Mixture Two batches of mixture were prepared, with each large enough to allow for a l l t e s t i n g with the respective composition, and stored i n a high pressure c y l i n d e r , at a pressure such that a combustion within the c y l i n d e r would not r e s u l t i n a peak pressure higher than the b o t t l e design pressure. The mixture was made by c o n t r o l l i n g the p a r t i a l pressures, as for ideal gases. The composition was then checked by gas chromatography. The a i r was drawn from a b o t t l e of commercially designated extra dry a i r , with 10 ppm 30 maximum moisture. The propane was instrument grade, with minimum p u r i t y of 99.5% i n the l i q u i d phase. The gas chromatography a n a l y s i s was repeated several times for the same mixture, with r e s u l t s which would keep f l u c t u a t i n g , within approximately 1%. Most errors may be due to the sample manipulation procedures, and since conceivably a i r from the ambient could leak into the sample, but not f u e l , tests g i v i n g the r i c h e s t r e s u l t s were generally believed to be the most r e l i a b l e . The uncertainty i n composition i s reckoned to be within 1% of the f u e l / a i r r a t i o . One of the two batches was re-checked three months a f t e r the f i r s t a n a l y s i s , and no change i n composition was observed, confirming that s t r a t i f i c a t i o n i n the b o t t l e was not a problem. The influence of impurities i n the a i r and propane i s not expected to be s i g n i f i c a n t , when compared to the range of inaccuracies from other sources. Both batches of mixture were prepared from the same a i r and propane b o t t l e s . Since the a i r used was extra dry i t was assumed that the e f f e c t of water vapor on the burning v e l o c i t i e s could not have been s i g n i f i c a n t . 4.2.4 Timing Equipment An analogue timing device, already mentioned i n Section 4.1.2, triggered by a push-button, supplies three timing references, and controls the whole 31 process. The f i r s t timer t r i g g e r s a DC output, and has a range from approximately 10 to 100 ms. The output i s switched on by depressing the button, and o f f by the timer. The second timer provides the delay between charging and i g n i t i o n ; i t controls the time at which the i g n i t i o n i s triggered. The t h i r d timer allows for s e t t i n g the length of the pulse which t r i g g e r s the i g n i t i o n . The timing device was r e g u l a r l y checked, using a N i c o l e t o s c i l l o s c o p e , described i n s e c t i o n 4.2.10, as a reference, and was never found to have d r i f t e d more than the N i c o l e t sampling i n t e r v a l , i . e . 1/2000 of the set delay value. 4.2.5 Charging The charging system consists of a pressure tank, and the p i p i n g which connects i t to the bomb, where the charging valve i s i n s t a l l e d , c o n t r o l l e d by the timing device. This valve i s not designed to be exposed to the conditions during combustion, and would l e t the flame propagate, through a p i l o t hole i n i t s diaphragm, to the charging tank. To avoid t h i s , a high pressure rating, spring operated check valve was i n s t a l l e d i n the l i n e , downstream of the charging valve. During charging, the charging tank was i s o l a t e d and i n thermal equilibrium with the atmosphere. Before each test, i t was replenished with new mixture from the same batch, up to the same i n i t i a l pressure, of approximately 32 340 kPa absolute. Since by the end of charging, the absolute pressure i n the bomb was approximately 180 kPa, the flow remained choked during most of the charging duration at the valve throat, the smallest s e c t i o n i n the charging l i n e . The pressure was monitored by an absolute pressure transducer (Sensym model LX1830AZ), i n s t a l l e d i n the piping. The expansion from the higher pressure i n the storage tank to pressure i n the charging tank r e s u l t s i n some change i n temperature, but the time i t takes for the charging tank to reach e q u i l i b r i u m with the atmosphere i s less than the time required to store the data. While the charging tank was being replenished, the bomb was evacuated, by opening a valve which connects i t to a vacuum pump. The vacuum i s monitored on a s p i r a l c o i l vacuum gage. When the absolute pressure was below 2 kPa, which was te best vacuum the equipment would provide, the valve was closed, and the c y c l e would begin, by pushing the button on the timing box. Great care was taken to check that the charging process was repeatable. The c r i t i c a l element i s the control valve which opens and closes the l i n e . For c o n t r o l of the charging process, AC operated solenoid valves are obviously not s u i t a b l e , since operating times have to be c o n t r o l l e d within a margin of erro r s u b s t a n t i a l l y less than one period of the 60 Hz power supply. 33 DC solenoid valves were t r i e d , but were found to be unsatisfactory. Commercially a v a i l a b l e DC solenoid valve i n the range needed are pilot-operated; they are designed i n such a way for the power required by the c o i l and consequently, the forces on the diaphragm, to be as small as pos s i b l e . However here, the valve i s expected to close while choked or nearly so, and i n t h i s condition, the valve does not perform w e l l . The operation should remain repeatable within an error of the order of one millisecond. Extensive t e s t i n g showed t h i s to be out of reach with that type of actuator. A more s a t i s f a c t o r y r e s u l t was obtained with an air-operated valve, c o n t r o l l e d by a d i r e c t a c t i o n , three-way solenoid valve triggered by the timing device, and s e t t i n g the a i r pressure at the highest allowable l e v e l . The a i r valve (ASCO model P210C94) i s a c t u a l l y a l s o p i l o t operated. But a much higher energy i s used to trigg e r i t , and the spring which closes the valve i s stronger. The a i r pressure was 900 kPa (gauge). The DC signal supplied by the timers to the solenoid valve (ASCO model 8321A1) was 15 V. The length of the pulse during which the solenoid valve c o i l remained energized f o r charging was 40 ms i n a l l the te s t s . The selected flow measurement technique does not allow cycle-resolved measurements, that i s , flow measurement during the act u a l combustion tests, permitting c o r r e l a t i o n s to be computed, since the hot wire cannot be exposed to the flame temperature, and thus, no data are a v a i l a b l e to c o r r e l a t e flame growth parameters with cycle-resolved v e l o c i t y data and evaluate d i r e c t l y the influence of non-repeatable v e l o c i t i e s . 34 But charging pressure traces were recorded during the combustion experiments, and c o r r e l a t i o n c o e f f i c i e n t s were computed between charging and combustion data.The charging data considered are: - peak charging pressure; - time to peak charging pressure; - pressure at i g n i t i o n time; - times f o r charging pressure increase by 1, 2, 5, 10, 20, 50% of the r i s e at peak. The combustion data are: - peak combustion pressure; - time from i g n i t i o n to peak pressure; - times from i g n i t i o n to a sequence of pressure increase r a t i o s . Table I presents the mean values and standard deviations of the charging parameters, and Table II, the c o r r e l a t i o n c o e f f i c i e n t s , f o r a l l combustion experiments. T y p i c a l l y , the c o r r e l a t i o n c o e f f i c i e n t s between charging and combustion parameters were low, at least for the cases where one hundred or more repeated experiments were performed. T y p i c a l values were under 0.30 and most of them below 0.20; only i n a few cases, values between 0.30 and 0.40 were noted, mostly i n tests with the leaner mixture. Conversely, c o r r e l a t i o n 35 Table I - Charging parameters monitored dur ing combustion experiments Case Max Pressure Time to max Press at Time for press increase of Pressure i g n i t i o n time 2% 10% 50% equiv Delay Mean Std d Mean Std d Mean Std d Mean Std d Mean S td d Mean Std d % (ms) (kPa) (ms) (kPa) (ms) (ms) (ms) 15 183.1 1 .5 110.2 1 .33 177. .7 1, .2 64.99 1.65 70.63 0.27 80.88 0.29 30 178.8 1 .6 109.6 1 .10 161. ,0 1, .6 64.91 1.12 70.88 0.56 81.11 0.56 60 178.4 1 .1 110.3 1 .34 166. .8 0 .9 64.48 0.64 71.17 0.34 81.40 0.34 120 181.1 1 .3 109.7 1 .24 165. ,7 1 .1 64.84 0.55 70.97 0.34 81.10 0.29 120 181.4 1 .3 109.6 1 .20 165. .8 1, .2 64.89 1.61 70.66 0.42 80.89 0.40 240 178.6 1 .7 109.8 1 .13 160. .3 1, .1 64.22 0.65 71.40 0.47 81.56 0.47 79 15 183.9 1.6 110.0 1.84 178.4 1.7 64.81 1.00 69.21 0.63 80.80 0.61 30 179.6 1.9 109.1 1.45 171.1 2.0 65.71 0.88 72.39 0.78 82.05 0.75 Table II - C o r r e l a t i o n c o e f f i c i e n t s between charging and combustion parameters (When absolute value larger than 0.20) Parameter Time to Press at Time for charg. Peak Time to Time for comb max charg i g n i t i o n press increase by combust peak comb press increase pressure time 2% 10% 50% pressure press by 20% by 100% in u e d io Max charging press - 0.84 -0.60 - -0.35 -0.34 1 - 1 Time to max charg. press - - 0 . 3 3 - - - - _ S " Press at i g n i t i o n time -0.58 - -0.28 -0.28 t 4 H cJ Time for charg press incr by 2% 0.65 - - - - " eg "a! Time for charg press incr by 10% 0.77 - - - -0 1 ° Time for charg press incr by 50% - -u e Max charging press - 0.85 c3 o Time to max charg press -Press at i g n i t i o n time Time for charg press incr by 2% c? Time for charg press incr by 10% c5 U Time for charg press incr by 50% -0.35 0.22 -0.43 0.34 -0.23 0.22 -0.33 0.36 0.94 0.21 (Continues) Table II - C o r r e l a t i o n c o e f f i c i e n t s between charging and combustion parameters (When absolute value larger than 0.20) - Continued Parameter Time to Press at Time for charg. Peak Time to Time for comb max charg i g n i t i o n press increase by combust peak comb press increase pressure time 2% 10% 50% pressure press by 20% by 100% cn '3 o Max ch press - 0.84 - 0.34 ^Time to max charg. press - - - - - -% 11 Press at i g n i t i o n time -0.30 -0.35 -0.33 ime f o r charg press incr by 2% 0.68 0.66 - -CN cuTime f or charg press incr by 10% 0.91 -0 9 °Time f o r charg press incr by 50% -u f§Max ch press 0.27 0.87 -0.37 n) oTime to max charg press 0.23 — i £nPress at ign time -0.35 3 nTime f or charg press incr by 2% >>Time for charg press incr by 10% eg -^Time f or charg press incr by 50% o •0.49 -0.34 -0.26 0. .24 -0.26 -0.29 •0.54 -0.41 -0.27 -0.28 -0.31 0.55 0.56 0.52 -0. .27 - -0.77 0.33 - -0.29 -0. 20 0.22 0.25 (Continues) Table II - C o r r e l a t i o n c o e f f i c i e n t s between charging and combustion parameters (When absolute value larger than 0.20) - Continued Case/parame ter Time to Press at Time for charg. Peak max charg i g n i t i o n press increase by combust pressure time 2 % 1 0 % 5 0 % pressure Time to Time f or comb peak comb press increase press by 2 0 % by 1 0 0 % a, J3 w M a x ch press - 0.82 ^ gTime to max charg. press -§ 0 Press at i g n i t i o n time *** ^  Time for charg press incr by 2 % ^ HTime for charg press incr by 1 0 % 0 5 ^Time for charg press incr by 5 0 % ro r—I p -0.47 -0.42 -0.27 -0.45 0.38 -0.29 0.21 0.85 -0.22 -0.22 gMax ch press - 0.59 - - 0 . 2 3 o Time to max charg press 0.21 -^ £JPress at i g n i t i o n time -0.33 -0.32 - - 0 . 2 3 ^ „ Time for charg press incr by 2% 0.61 0.59 *** .^Time for charg press incr by 1 0 % 0.89 -c^J^Time for charg press incr by 5 0 % (Continues) Table II - C o r r e l a t i o n c o e f f i c i e n t s between charging and combustion parameters (When absolute value larger than 0.20) - Continued Parameter Time to Press at Time for charg. Peak Time to Time for comb max charg i g n i t i o n press increase by combust peak comb press increase pressure time 2% 10% 50% pressure press by 20% by 100% to u B rt in Max ch press 0.31 0.88 '"'Time to max charg. press -3 Press at i g n i t i o n time dTime f or charg press incr by 2% °<j> a; Time f or charg press incr by 10% ^ Q T i m e f or charg press incr by 50% -0.48 -0.44 -0.70 -0.68 0.63 -0.64 -0.64 0.62 0.95 -0.27 -0.34 0.26 0.30 -0.27 0.21 -0.22 -0.29 0.22 0.24 o u eMax ch press 0.40 0.97 d oTime to max charg press 0.34 5^ 0 0 Press at ign time 3 Time for charg press incr by 2% t w cjTime f o r charg press incr by 10% cn "oTime f or charg press incr by 50% -0.75 -0.68 -0.27 -0.22 -0.71 -0.65 0.96 -0.25 0.45 -0.32 -0. .22 -0. 22 -0.32 -0. .22 -0. 22 0.46 0. .30 0. 30 0.35 0. 35 c o e f f i c i e n t s between d i f f e r e n t charging process parameters were higher, i n a range between 0.50 and 0.90. The standard d e v i a t i o n observed i n the combustion tests, of the actual time i n t e r v a l from the s t a r t of the sequence to the time at which the valve closes varied, from one sample to another, i n a range between 1.1 and 1.8 ms. S t a t i s t i c s were a l s o computed on the pressure and temperature reached at a sequence of values for the time coordinate. The standard d e v i a t i o n of the pressure and temperature charging are presented r e s p e c t i v e l y on Figure 3 and 4. They show t y p i c a l values of less than 1% of the pressure reached at o the end of charging, and of no more than 1 C for temperature. In the case of temperature, t h i s c e r t a i n l y r e f l e c t s the range of f l u c t u a t i o n i n i n i t i a l or ambient temperature, and for both pressure and temperature, zero errors, and thus only part of that f l u c t u a t i o n i s due to imperfections i n the charging system. At the beginning of charging, however, when the valve has started to open, o these f i g u r e s reach peaks of about 4% and 2 to 3 r e s p e c t i v e l y . The peaks are very sharp and of short duration, as one can see on f i g u r e s 3 and 4. They occur at a time where pressure and temperature r i s e at a very f a s t rate, when s l i g h t v a r i a t i o n s of the valve opening time produce large pressure f l u c t u a t i o n s . 41 The adopted d e f i n i t i o n of turbulence i n t e n s i t y r e s u l t s i n the t o t a l i t y of the standard d e v i a t i o n of the v e l o c i t y to be accounted for as turbulence i n t e n s i t y . There may conceivably be a r e l a t i o n s h i p between the v e l o c i t y h i s t o r y of each p a r t i c u l a r test and the corresponding combustion performance. But the flow measurement technique and the conceptual framework adopted here would make i t impossible to i d e n t i f y such a c o r r e l a t i o n . 4.2.6 I g n i t i o n A standard c a p a c i t i v e discharge i g n i t i o n c i r c u i t (Heathkit model CP 1060) i s used. A standard automotive c o i l i s used, and a 12 V battery. A l l combustion experiments were performed with the same spark plug and gap (1 mm). No a l t e r a t i o n of the electrode ends was noticed. However, no measurements were done to assess the r e p e a t a b i l i t y of the spark, and t h i s may have contributed to some extent to the observed randomness i n the flame development. 4.2.7 Pressure measurement The pressure was measured by a piezometric transducer ( K i s t l e r type 6213 AZ). The charge s i g n a l produced by the transducer was fed into a K i s t l e r type 5004 42 dual mode a m p l i f i e r , which converts the signal into a voltage output and am p l i f i e s i t . The output signal i s then supplied to the N i c o l e t scope. The a m p l i f i e r time constant was set i n the p o s i t i o n "long" to r e f l e c t c o r r e c t l y the s t a t i c pressure gradient over time i n t e r v a l s of up to 400 ms. The pressure transducer conversion factor was set .according to c a l i b r a t i o n data supplied by the manufacturer for the p a r t i c u l a r u n i t ( S e r i a l number 177004), at -157 pC/Pa. Piezometric elements v i r t u a l l y do not depend on displacement of mechanical components and t h e i r i n e r t i a , and consequently, are s u i t a b l e f or measurement of r a p i d l y changing pressure. The pressure signal provided by piezometric elements i s d i f f e r e n t i a l only, and always needs to be r e f e r r e d to a known i n i t i a l value, which corresponds the signal at i n i t i a l time. The r e s u l t s may not be r e l i a b l e i n terms of s t a t i c pressure, i f the i n i t i a l pressure i s not known or recorded by some other means, and need to be reset before each experiment. Since the bomb was i n i t i a l l y evacuated, the i n i t i a l voltage recorded at the beginning of the charging sequence corresponds to the i n i t i a l vacuum. The p r e c i s e value of the corresponding low pressure (about 2 kPa) was not recorded, and the i n i t i a l voltage was set to correspond to zero pressure. This r e s u l t s i n a systematic error of approximately 1% on the peak charging pressure, and 0.2% on combustion Piezometric pressure transducers are known to be susceptible to thermal loading. For that reason, the pressure sensor i s mounted s l i g h l y recessed i n the c y l i n d r i c a l wall; the recess i s not deep enough, to produce s i g n i f i c a n t acoustic resonance. A choice was made not to use rubber s i l i c o n coatings, as 43 suggested f o r instance i n [39]; the consistency of the r e s u l t s was deemed to be more important than th e i r accuracy, and one would a n t i c i p a t e such a coating to progr e s s i v e l y degrade as a r e s u l t of i t s exposure to the flame. Besides, the emphasis, here, i s on the i n i t i a l part of the pressure trace, well before the flame would a f f e c t the transducer. 4.2.8 Temperature measurement As noted by Dyer [35], the temperature i n the bomb during and a f t e r charging i s higher than the ambient temperature, maintained i n the charging tank. In e f f e c t , f o r an i n f i n i t e l y large charging tank, considering the mixture as an ide a l gas, and neglecting heat exchange at the walls, the absolute temperature i n the bomb, immediately a f t e r i n j e c t i o n , would reach a value equal to T (the s p e c i f i c heat r a t i o ) times the i n i t i a l temperature'- the energy balance shows that the enthalpy of the f l u i d entering the bomb i s equal to the i n t e r n a l energy of the f l u i d i n the bomb a f t e r charging. Even for a moderate volume r a t i o between the bomb and the charging tank, the temperature r a t i o , while s l i g h t l y less than nr, remains high, and the peak o temperatures measured i n the bomb were over 100 C above ambient. Heat exchange at the walls r e s u l t s i n strong temperature gradients and a decay somewhat slower than the decay of the s w i r l i n g flow. The temperature signal was provided by a chromel-constantan thermocouple. The probe was made using an Omega "Cement-on" s t y l e II thermocouple, catalogue number C02-E. To improve the response time, the junction, however designed to 44 be glued to a support, was l e f t f r e e . The leads were passed through the holes i n a double hole ceramic i n s u l a t o r , which was placed ins i d e a s t a i n l e s s steel tube, sealed with high temperature epoxy glue. The output was fed to the data a c q u i s i t i o n system through a c o l d junction compensator (Omega type E), g i v i n g an output proportional to the temperature i n °C, and a DC a m p l i f i e r (Omega model Omni-IIA), with a gain set at 100, and i n the p o s i t i o n V/V. The junction i s 0.013 mm thick, which corresponds to a response time i n a i r of the order of the mil l i s e c o n d . 4.2.9 V e l o c i t y measurement 4.2.9.1 Equipment V e l o c i t i e s were measured by hot wire anemometry. The hot wire i s a standard DISA probe, type 55P11, platinum-coated tungsten, diameter 5 pm, length 1.25 mm. I t i s i n s t a l l e d with the wire c e n t e r l i n e p a r a l l e l to the ce n t e r l i n e of the bomb. The hot wire control set consists of a DISA 55M01 u n i t , with a 55M10 bridge. This equipment contains a l l c i r c u i t r y required for e s t a b l i s h i n g a constant-temperature hot wire anemometer. The chosen overheat r a t i o was 1.8. 45 4.2.9.2 Hot wire c a l i b r a t i o n The hot wire was c a l i b r a t e d i n a wind tunnel before being placed i n the bomb. The range of v e l o c i t i e s was from 2 m/s to 16 m/s. The c a l i b r a t i o n was done at atmospheric pressure and ambient temperature. The v e l o c i t y i n the wind tunnel was measured with a P i t o t tube. There were no f a c i l i t i e s a v a i l a b l e for c a l i b r a t i o n at other pressures and temperature, as de s i r a b l e as t h i s might be. E x t r a p o l a t i o n was thus required, based on t h e o r e t i c a l considerations. A l l the tests were done with the same wire. No evidence of d r i f t was noticed. 4.2.9.3 Data reduction The conversion from hot wire voltage data to v e l o c i t y data i s done on the computer, according to King's law Where A and B are functions of pressure and temperature, as r e s u l t i n g from c a l i b r a t i o n . V i s the voltage across the wire and u i s the v e l o c i t y which i s to be determined. The hypothesis i s that the Nusselt number r e l a t i n g to the forced convection around the hot wire i s a l i n e a r function of power n of the Reynolds number based on the wire diameter and the v e l o c i t y , considering bulk properties, unaffected by the wire. That i s , A + B u n (4.1) Nu = a + b Re n (4.2) 46 Neglecting conduction through the prongs, an energy balance around the wire r e s u l t s i n V 2 - 5 - = h A (T - T ) (4.3) R w v w g 7 v ' R being the wire resistance and thus maintained constant, h the heat transfer h*d c o e f f i c i e n t ( r e l a t e d to the Nusselt number by Nu= i n which K i s the f l u i d thermal condu c t i v i t y and d i s the cy l i n d e r diameter), T the wire ' w temperature and, the bulk f l u i d temperature. At atmospheric pressure and ambient temperature, a range of n (the exponents of the v e l o c i t y i n King's law) between 0.45 and 0.5 f i t s well the c a l i b r a t i o n data. At other pressures and temperatures, i t was found, though, that the corrections according to the procedure described below, with values larger than 0.45, app l i e d to voltages measured i n s t i l l a i r , r e s u l t e d i n v e l o c i t y errors much larger than the error expected from free convection. The value of 0.45 was thus adopted. The Reynolds number can be expressed i n terms of dynamic v i s c o s i t y and density, and these properties can be r e l a t e d to pressure and temperature. Assuming the f l u i d to be an i d e a l gas and the dynamic v i s c o s i t y to be independent of pressure and proportional to the power 0.76 of the absolute temperature, i t may be shown that T> u - u 1 _,-1.76 IA A\ Re = j = k.p.u.T (4.4) d.p In which k i s a p r o p o r t i o n a l i t y constant. 47 F i n a l l y , e l i m i n a t i n g Nu and Re and assuming that K (the f l u i d thermal conductivity) i s proportional to the power 0.8 of the temperature, one obtains V 2 = a ( T w - T g ) T ° - 8 + p ( T w - T g ) 0 - 0 0 8 ( p.u ) 4 5 (4.5) Where a l l p r o p o r t i o n a l i t y constants are included i n a and j3, whose numerical value r e s u l t s from c a l i b r a t i o n . At the adopted wire temperature, conduction through the prongs i s usually neglected. 4.2.9.4 Evaluation of the r e s u l t s A comprehensive c r i t i c a l evaluation of hot wire anemometry for engines measurements was published by Witze [40], and some of h i s observations apply to the present measurements. No other experimental data are a v a i l a b l e comparing d i r e c t l y r e s u l t s from high temperature c a l i b r a t i o n to the extr a p o l a t i o n from c a l i b r a t i o n data at ambient pressure and temperature. Among the questions addressed by Witze, the v a l i d i t y of the temperature c o r r e c t i o n procedure, the p o s i t i o n at which the temperature i s measured and the e f f e c t of temperature f l u c t u a t i o n s are relevant here. The c o r r e c t i o n procedure follows Witze's recommendation that for both the v i s c o s i t y and conduc t i v i t y corrections, the mainstream gas temperature should be used. 48 As mentioned i n 4 . 2 . 9 . 3 , at the low overheat r a t i o of 1.8 chosen here, conduction through the prongs i s small i n r e l a t i o n to convection to the gas, and normally neglected, while at the high wire temperatures ( t y p i c a l l y 650oC) required f or measurement i n engines, t h i s would lead to a considerable error. Thus on that respect, Witze's conclusions do not apply. A non-uniform temperature f i e l d r e s u l t s here, as i t does i n engines, from the combined e f f e c t s of a s p a t i a l l y d i s t r i b u t e d temperature change due to compression and heat exchange at the walls. Consequently, the p o s i t i o n of the probe has to be important, as he shows. In engines, and i n p o s i t i o n s a f f e c t e d by the intake j e t , he shows actual measurements to be better than bulk temperatures estimated from pressure measurements, assuming a p o l y t r o p i c compression. Comparing to the engine case, here, by symmetry, a better approximation of the wire temperature can be obtained by p l a c i n g the temperature probe at the same r a d i a l p o s i t i o n as the hot wire. According to Witze's conclusion, the procedure adopted here i s the best p o s s i b l e within the l i m i t a t i o n s of hot wire anemometry, and should provide a reasonable estimate of the mean v e l o c i t y . A p o t e n t i a l l y more serious problem, a l s o studied by Witze, i s the e f f e c t of temperature f l u c t u a t i o n s . The strong r a d i a l temperature gradient (See f i g u r e s 33 and 34) , r e s u l t i n g from the temperature increase due to compression and heat exchange at the wall, exposed to the turbulent flow, w i l l produce some temperature f l u c t u a t i o n s . An estimate of the range of f l u c t u a t i o n by X*vT, for X = 1 mm and vT = 4o/mm, gives a f i g u r e of 4o, i n a t y p i c a l frequency range given by u'/X, equal to 1000 Hz for u' = 2 m/s. 49 However f a s t , neither the thermocouple used here, nor those the resistance thermometry techniques implemented by Witze have a s u f f i c i e n t l y low thermal i n e r t i a to provide a measure of such a f l u c t u a t i o n . In consequence, the f l u c t u a t i o n cannot but be ignored i n the c o r r e c t i o n . If the hot wire c o r r e l a t i o n were l i n e a r , v e l o c i t y f l u c t u a t i o n s at a given frequency would only be a f f e c t e d by temperature f l u c t u a t i o n s at the same frequency. The error due to negl e c t i n g the temperature f l u c t u a t i o n would depend on the phase angle between the two waves. If the phase d i f f e r e n t was randomly d i s t r i b u t e d , the averaging would r e s u l t i n an absolutely co r r e c t estimate. However the strong n o n l i n e a r i t y of the c o r r e l a t i o n introduces a bias, r e s u l t i n g i n estimated turbulence i n t e n s i t i e s (u') higher than r e a l , since a hot wire voltage increase i s tr a n s l a t e d into a v e l o c i t y increase larger than the decrease which would r e s u l t from a voltage decrease of the same magnitude. Witze's r e s u l t s confirm t h i s . Figure 20 of h i s paper shows u' estimated by hot wire anemometry up to twice as high as those r e s u l t i n g from laser-doppler measurements, and p r a c t i c a l l y never lower. It can be shown that an unaccounted for temperature f l u c t u a t i o n of 3 to 4°C w i l l r e s u l t i n an estimated range of f l u c t u a t i o n of the instantaneous v e l o c i t y going, depending on the random phase angle between the unknown temperature wave and the v e l o c i t y wave, from approximately 50% below r e a l to approximately 100% above normal. The ensemble averaging procedure applied to a sample with a random error i n that range w i l l r e s u l t i n a systematic error of the order of 30% to 50%. 50 Even though he recognizes h i s hot wire used as a resistance thermometer does not have a frequency response i n the range of 1 kHz, Witze presents an estimate of temperature f l u c t u a t i o n computed by ensemble averaging, of up to 14 oC. Since h i s thermometer f i l t e r s out the high frequencies, such a standard d e v i a t i o n has to r e f l e c t low frequency f l u c t u a t i o n s , which i n h i s terminology would be c a l l e d c y c l i c v a r i a t i o n s , and could be corrected by cycle-resolved measurements i f the hot wire and temperature probes were at the same p o s i t i o n . Here the standard deviations are no more than 1©C (Figure 4). This observation does not imply that no high frequencies are present, e s p e c i a l l y considering that the c e n t r i f u g a l forces due to the s w i r l reduce more strongly the low frequency f l u c t u a t i o n s . In engines, the uncertainty about the flow d i r e c t i o n makes a hot wire signal d i f f i c u l t to i n t e r p r e t . Here the s w i r l provides a known mean flow d i r e c t i o n , with a mean v e l o c i t y s u f f i c i e n t l y higher than the f l u c t u a t i o n to v a l i d a t e the assumption that the e f f e c t of components i n other d i r e c t i o n s on the hot wire voltage are n e g l i g i b l e . By symmetry, at the center of the bomb, a l l r a d i a l v e l o c i t y d i r e c t i o n s have to be equiprobable, and the a x i a l component has to have a zero mean. The mean v e l o c i t y must then be zero. This observation i s not incompatible, though, with the notion that a vortex might have a h e l i c a l a x i s . In any case, at the center a l l of what the hot wire sees i s deemed to be f l u c t u a t i o n . Since before charging, the bomb i s evacuated, choking occurs n e c e s s a r i l y at some p o s i t i o n i n the charging l i n e . And i n the conditions chosen here, 51 choking must p e r s i s t nearly t i l l the end of the charging process. The v e l o c i t i e s measured during charging reach values of the order of Mach 0.3 to 0.35, which are thus not inconceivable. According to Bradshaw [41], p. 158, for Mach numbers above 0.5, the c o r r e l a t i o n given i n equation (4.1) should include the Mach number, besides the Reynolds number and the Nusselt, and generally, hot wire anemometry has not been used above that value, except at much higher Mach numbers. 4.2.10 Data a c q u i s i t i o n and processing A l l measured s i g n a l s , of pressure, v e l o c i t y , temperature and hot wire voltage were fed to N i c o l e t 3091 d i g i t i z i n g o s c i l l o s c o p e s , triggered by pulses supplied by the timing device. The N i c o l e t acquires, d i g i t i z e s and stores i n i t s memory a t o t a l a 4000 data points, at a set sampling frequency, adjustable between 5 mHz to 1 MHz, r e s u l t i n g i n a sweep time between 4 ms and approximately 10 days. The sweep time was set here at 400 ms (or 0.1 ms/point, that i s , 10 kHz) for the hot wire measurements, and at 20 ms for the combustion measurements, except when the peak combustion pressure was reached at times over 15 ms, when a value of 40 ms was chosen. For monitoring the pressure during charging, the sweep times were 200 ms, except when i t was set at 400 ms, for delays of 120 ms and 240 ms between the time the charging valve closes and i g n i t i o n . The corresponding r e s o l u t i o n gives a conservative estimate of the accuracy of the times measurements. 52 The d i g i t i z e d and stored signals were then transferred, through an RS-232 asynchronous communications i n t e r f a c e , to an I n t e l 8088 based microcomputer, working i n MS-DOS. The data were l a t e r transferred, processed and analyzed on a VAX 11-750 minicomputer. The N i c o l e t d i g i t i z e s the f u l l scale y-coordinate i n 4096 steps, t r a n s l a t i n g i t i n two-byte data. Some of the f i r s t combustion experiments were performed with the zero of the y-scale at the center of the screen. This reduces the r e s o l u t i o n of the y-information by a factor 2, and i n subsequent tests, the more advisable procedure was chosen, to locate the zero at the bottom of the screen, g i v i n g a f u l l screen r e s o l u t i o n . The best scale was generally chosen, minimizing the d i g i t i z a t i o n error. Both temperature and hot wire signal are absolute data, where the accuracy of the zero i s important. In p a r t i c u l a r , the hot wire signal i s so highly nonlinear that a small zero d r i f t read as a change i n v e l o c i t y w i l l r e s u l t i n a much larger error on a high v e l o c i t y value than on smaller ones. The N i c o l e t was found to s u f f e r from noticeable zero d r i f t s , e s p e c i a l l y when heating up. Consequently, t h i s was monitored c l o s e l y during the experiments, but even so some s i g n i f i c a n t errors may have happened, whose range one cannot quantify e a s i l y . The data a c q u i s i t i o n software was designed to allow for checking that the transmission occurred without error, by p l o t t i n g on the screen the same image as shown by the o s c i l l o s c o p e , before the storage on a d i s k e t t e i s i n i t i a t e d . 53 The program, c a l l e d DATANIC, and shown i n Appendix A, i s very simple; the very simple v e r s i o n of the RS-232C communication protocol used by the Ni c o l e t o s c i l l o s c o p e makes i t convenient f o r i t to be wr i t t e n i n BASIC without penalty i n terms of e f f i c i e n c y . The c r i t i c a l f a ctor i s the transmission time, l i m i t e d by the hardware at 9600 Bauds. 54 5 Results 5.1 Flow measurements. 5.1.1 Analysis Instantaneous v e l o c i t i e s were computed from hot wire signals at each of the 4000 data points, with temperature and pressure c o r r e c t i o n s , according to eq. (4.5), based on pressure and temperature measurements simultaneously recorded for each cycle, for each of the f i f t y hot wire signals obtained for each of the s i x p o s i t i o n s , with and without the spark plug. The f i f t y traces were then ensemble averaged. The mean and the standard d e v i a t i o n of the pressure and the temperature were a l s o computed. The respective codes are i n Appendix B, under the name HWRED. Data were acquired and stored for both procedures o u t l i n e d i n chapter 2, and ensemble averaging and s i n g l e trace processing were compared. I t was found that as a r e s u l t of the r e p e a t a b i l i t y of the charging process, and p o s s i b l y of the a p p l i c a t i o n of cycle-resolved pressure and temperature corrections (that i s , based on simultaneous measurements), the ranges of f l u c t u a t i o n of the instantaneous v e l o c i t y traces superpose very well onto each other. Figures 5 and 6 show t y p i c a l instantaneous v e l o c i t y traces, f i v e of them being superposed on Figure 6. A comparison between Figure 5 and 6 shows that a l l instantaneous v e l o c i t y traces f i t within a r e l a t i v e l y narrow band, and further, that the largest 55 f l u c t u a t i o n s they contain tend to f i l l most of the width of that band and thus, the ensemble averaging process provides a good estimate of the v e l o c i t y f l u c t u a t i o n . But the large structures observed on most s i n g l e traces are so large when compared to the decay time of the high frequencies, and a l s o i n r e l a t i o n to the unsteadiness of the flow, that s i n g l e trace processing and Fourier a n a l y s i s do not give good r e s u l t s . In e f f e c t , one cannot d i s t i n g h i s h , on a s i n g l e trace, what part of the f l u c t u a t i o n i s due to a change i n mean, and what could be a t t r i b u t e d to turbulence. Some c r i t e r i a could be defined, l i k e a c u t - o f f frequency, or an a r b i t r a r i l y chosen degree of smoothing on a s p l i n e function, but the r e s u l t s would be so s e n s i t i v e to such a r b i t r a r y parameters, that they would i n f a c t r e f l e c t more the choice of c r i t e r i a than the randomness of the phenomenon. Flames are expected to be s e n s i t i v e to the range of v a r i a t i o n of v e l o c i t i e s during each p a r t i c u l a r event, and s i n g l e trace processing would i n p r i n c i p l e be more d i r e c t l y r e l a t e d to that. However, since the mean appears to be repeatable, such a range i s well r e f l e c t e d here by ensemble averaging. Single trace processing w i l l produce e i t h e r means very d i f f e r e n t between events, or an almost a r b i t r a r i l y prescribed mean, v i r t u a l l y uncorrelated to the event, and p o s s i b l y r e s u l t i n g i n an overestimation of the turbulence l e v e l . Fourier transforms are appropriate when the sig n a l i s s t a t i s t i c a l l y steady. To apply such a procedure for unsteady phenomena implies that over the time i n t e r v a l , the energy spectrum has not changed much. But here, small scales decay so f a s t when compared to the largest scales that i f one considers a 56 large i n t e r v a l , the highest frequencies vary so much over the i n t e r v a l , that the r e s u l t w i l l be some average over the i n t e r v a l , but w i l l not r e f l e c t the i n i t i a l high c o n t r i b u t i o n of the high frequency, nor the f a c t that near the end, they have already decayed to nearly i n s i g n i f i c a n t l e v e l s . Thus the most i n t e r e s t i n g information, r e l a t e d to how the spectrum changes, w i l l not be produced. But f o r a narrow i n t e r v a l , while the high frequencies are adequate, most of the energy i s i n frequencies with period larger than the length of the i n t e r v a l , and thus excluded from the r e s u l t i n g spectrum. One a c t u a l l y can see on the screen of the o s c i l l o s c o p e how f a s t the high frequencies decay. As a r e s u l t , a l l data a n a l y s i s based on s i n g l e - t r a c e processing was abandoned, and only ensemble-averaged data w i l l be presented and discussed further on. Figures 7 and 8 show the ensemble-averaged v e l o c i t y a t the center, with and without smoothing by cubic s p l i n e s . Since the probes would i n t e r f e r e with the spark plug, t h i s test could only be performed without the plug. To some extent, however, the probes must a f f e c t the flow f i e l d i n a way not unlike the plug would. Figures 9 to 32 show the mean and standard d e v i a t i o n of the instantaneous v e l o c i t i e s , a t d i f f e r e n t p o s i t i o n s along the same radius, with and without the spark plug i n s t a l l e d . The locations correspond approximately to 1/4, 3/8, 1/2, 5/8, 3/4 and 7/8 r a d i i from the center. The accuracy i n p o s i t i o n i s 57 reckoned to be within ±1 or 2 mm. In a l l p l o t s r e f e r r e d to i n Section 5.1, the time reference o r i g i n i s the time at which the c y c l e i s i n i t i a t e d , and the data a c q u i s i t i o n process i s triggered. The charging valve a c t u a l l y opens somewhat a f t e r t = 60 ms, and closes for t ^ 109 i 1 or 2 ms.(See Table I, i n chapter 4). For each p o s i t i o n , two figures are shown for each case, with and without the plug; the f i r s t shows mean and f l u c t u a t i o n and the other, only the f l u c t u a t i o n , u s u a l l y c a l l e d turbulence i n t e n s i t y , as r e s u l t i n g from ensemble averaging, without smoothing. Figures 33 and 34 show the mean temperature p r o f i l e s at the various p o s i t i o n s . Figure 4 shows the standard d e v i a t i o n of temperature, and Figure 5, that of pressure. Figure 35 and 36 contain smoothed mean v e l o c i t y traces at a l l p o s i t i o n s , while Figure 37 and 38 show the smoothed turbulence i n t e n s i t i e s . Figure 39 shows a t y p i c a l mean charging pressure trace. These are t y p i c a l l y undistinguishable from each other, except as noted i n Section 4. 5.1.2 Discussion Three main observations w i l l be discussed: the d i f f e r e n c e between v e l o c i t y p r o f i l e s with and without spark plug, the shape of the s w i r l , and the s p a t i a l d i s t r i b u t i o n and decay of turbulence i n t e n s i t y . 58 The presence of the spark plug r e s u l t s i n a very d i f f e r e n t flow f i e l d . The dif f e r e n c e s may be more evident during charging than a f t e r the valve i s closed. Peak v e l o c i t i e s , near the wall, are very high when no spark plug i s i n the way of the incoming j e t , reaching values of p o s s i b l y 110 m/s for the mean v e l o c i t i e s , and instantaneous v e l o c i t i e s of up to 130 m/s. With the spark plug, the mean v e l o c i t y s t i l l reaches nearly 80 m/s. The peak occurs e a r l i e r . This i s not s u r p r i s i n g since the spark plug i s positioned r i g h t i n the way of the incoming j e t . At the time the charging valve closes, the e f f e c t of the plug on the flow f i e l d i s large. During charging, the peak mean v e l o c i t i e s are lower when the plug i s i n s t a l l e d , and thus i t s presence r e s u l t s i n energy transfer from the main s w i r l to smaller length scales or higher modes, which decay f a s t e r . The shape of the s w i r l can be analyzed by comparing the angular v e l o c i t i e s at d i f f e r e n t locations, as on Figure 40, with no plug and Figure 41 with the plug i n place, or on Figures 42 and 43, which show v e l o c i t y p r o f i l e s . Without the plug, the angular v e l o c i t y i s i n i t i a l l y larger at the center but decays f a s t e r there, so that the s w i r l tends to s o l i d body r o t a t i o n . The peak v e l o c i t y appears to occur i n i t i a l l y between 1/4 and 3/8 r a d i i from the wall, and l a t e r to move toward the wall. Thus the boundary layer on the c y l i n d r i c a l wall does not grow; p o s s i b l y because of the secondary flow e f f e c t , the spiral-shaped boundary layer on the f l a t ends of the c y l i n d e r keeps the boundary layer on the c y l i n d r i c a l surface thin. 59 With the spark plug i n s t a l l e d , at the end of charging, the v e l o c i t y gradients are larger at least i n r e l a t i v e terms, as a proportion to the peak v e l o c i t y . The v e l o c i t y i s higher at 3/8 than at 1/2 radius from the center and then increases sharply toward the w a l l . This cannot be a t t r i b u t e d to inaccuracies i n probe p o s i t i o n s , since the probe p o s i t i o n s were not changed between the two s e r i e s of tests, with and without spark plug, and i n the case without the plug, the values of the v e l o c i t y at these p o s i t i o n s are as one would expect, while an er r o r would a f f e c t equally the two cases. The v e l o c i t y measured by the hot wire i s not n e c e s s a r i l y tangential, and another component, r e l a t i v e l y large to the tangential v e l o c i t y , due p o s s i b l y to vortex shedding by the spark plug would produce such an e f f e c t . The p l o t s of the standard d e v i a t i o n of the instantaneous v e l o c i t y , generally r e f e r r e d to here as the turbulence i n t e n s i t y , and represented by u', show a r a p i d decay i n v i r t u a l l y a l l cases. P l o t s of t h e i r inverse, versus time, as on Figure 44 and 45, are more i l l u s t r a t i v e . Experimental evidence indicates [20] that for homogeneous, i s o t r o p i c turbulence, the rate of decay e of the turbulent k i n e t i c energy obeys an equation of the type .3i e= k- u L x (5.1) Where u' i s the turbulence i n t e n s i t y and L^, the i n t e g r a l length scale, k i s a constant of order 1. Since i t i s assumed the v e l o c i t y f l u c t u a t i o n i s the 60 same i n a l l d i r e c t i o n s , the rate of decay of the turbulent k i n e t i c energy i s given by Assuming k = 1.5, a f t e r s u b s t i t u t i n g e between (5.1) and (5.2), an i n t e g r a t i o n assuming remains constant shows that 1/u' increases l i n e a r l y with time, and that the slope of the p l o t of 1/u' versus time equals l / ( 2 - L x ) . An inconvenient feature of t h i s presentation, however, i s that i t appears to make relevant data r e l a t i n g to longer times when v e l o c i t i e s and their standard d e v i a t i o n are very small, and when t h i s l a s t parameter possibly r e f l e c t s more random errors and inaccuracies than inherent aspects of the flow. For t h i s reason, the p l o t s on Figures 44 and 45 only show a time i n t e r v a l of 100 ms a f t e r the end of charging, where u' has not decayed yet to a very low value. The p l o t s show that near the wall, u" s t a r t s decaying before the end of the charging process, and that when the valve closes, u' i s larger near the center, where, however, i t decays f a s t e r . P l ots of 1/u" versus time are not r e a l l y l i n e a r , e s p e c i a l l y near the center, but t h e i r curvature i s not strong. Within experimental accuracy, one could say that the slope of the curves i s approximately independent of space and time. Though t h i s i s only a f i r s t approximation, i t i s not unreasonable to treat the decay of the turbulence i n t e n s i t y as i f i t were l i n e a r and homogeneous, providing a global measure of the disorder of the flow, even though i n r e a l i t y , turbulence i n t e n s i t y i s a l o c a l property. 61 Assuming thus that 1/u' i s l i n e a r , and that the slope of i t s p l o t versus time i s equal to l / ( 2 * L x ) , and applying that to the r e s u l t s without spark plug, one finds values of L x of 45 mm when considering the p l o t of u' near the wall , and somewhat lower values near the center, where decay i s f a s t e r . With the spark plug, the same pattern holds, but the decay i s generally f a s t e r . S p a t i a l average values of u' are 1.6 m/s a f t e r a decay time of 15 ms, 1.1 m/s a f t e r 30 ms and around 0.7 m/s a f t e r 60 ms. This corresponds to a constant i n t e g r a l length scale smaller than i n the case without the plug, of approximately 29 mm. This value i s approximately equal to the gap between the spark plug and the wall, which appears to be reasonable, since the in t e g r a l length scale i s u s u a l l y expected to be r e l a t e d to the s i z e of the ve s s e l . At the center of the bomb, i f a l l flow d i r e c t i o n s are equiprobable, the mean v e l o c i t y i n any d i r e c t i o n has to be zero. Further, i f turbulence i s assumed to be i s o t r o p i c i n a l l r a d i a l d i r e c t i o n s , f o r the hot wire placed p a r a l l e l to the c e n t e r l i n e of the bomb, then a measure of u' i s provided by the ensemble-averaged mean of the measured v e l o c i t i e s . According to Appendix C of Checkel [42], assuming the components i n two orthogonal d i r e c t i o n s to be normally d i s t r i b u t e d , the ensemble average of the hot wire signal corresponds to the r.m.s. f l u c t u a t i o n i n one d i r e c t i o n , times VTT/2 . This r e s u l t s i n a value of u' at the center much higher during charging than given by measurements at quarter-radius from the center. During the decay period, u' at the center i s s i m i l a r to the values obtained without plug, away from the center. 62 If during charging, large departures are observed, during the decay period, wi t h i n the experimental accuracy, the data are i n agreement with a homogeneous, i s o t r o p i c representation, and further on, the turbulence parameters w i l l be assumed to f i t within such model. The s w i r l represents the largest scale of the motion and w i l l decay more slowly than more disorganized motion would. Turbulent k i n e t i c energy i s d i f f u s e d from the boundary layers, and thus the homogeneous, i s o t r o p i c assumption i s at best a f i r s t approximation, j u s t i f i e d by the inaccuracy of the data. The Kolmogorov dissapation scale i s given by the expression And for homogeneous, i s o t r o p i c turbulence, the Taylor micro length scale i s given by Resulting i n the f i g u r e s shown i n table I I I , where the data r e f e r r e d to as s w i r l are the mean angular v e l o c i t i e s at mid-radius, measured with the spark plug i n place. The decay time r e f e r s to the d i f f e r e n t delays between the time at which the charging valve closes, when the s w i r l , the turbulence and the temperature begin to decay, t i l l i g n i t i o n i n the tests r e f e r r e d to i n the next section. n = ( u 3 / e ) 1/4 (5.3) (5.4) 63 Table III - Homogeneous Isotropic Assumption Time (ms) 110 125 Decay time^(ms) 0 15 u' (m/s) 2.8 1.6 A (mm) 1.33 1.76 n (mm) 0.046 0.070 R e A 213 161 R e L 4570 2600 2 Swi r1 (rev/s) 97 65 140 170 230 350 30 60 120 240 1.1 0.7 0.41 0.22 2.13 - 2.67 3.48 4.76 0.093 0.131 0.196 0.312 134 107 82 60 1800 1140 670 360 44 30 16 5.5 However approximate, these values represent probably the best estimate of the turbulent q u a n t i t i e s as r e s u l t i n g from the measurements, and the flame data w i l l be compared to them. It i s acknowledged that the ext r a p o l a t i o n of the hypothesis of a constant i n t e g r a l length scale on the smaller decay time side, to estimate A at the time the charging valve closes, i s p a r t i c u l a r l y questionable. Following valve closure. i 'At mid-radius. 64 5.2 Combustion experiments 5.2.1 Analysis The primary measurement r e s u l t i n g from the combustion experiments i s the pressure h i s t o r y r e l a t e d of each test. Such data vary noticeably from experiment to experiment, even when the charging process i s well c o n t r o l l e d ; i t i s thus natural to perform a s t a t i s t i c a l a n a l y s i s . A f i r s t o bjective of the s t a t i s t i c a l a n a l y s i s was to see i f f l u c t u a t i o n s i n the charging process contribute s i g n i f i c a n t l y to the d i s p e r s i o n i n the observed pressure r i s e times. This was dealt with i n Chapter 4. The second i s to provide a p r o b a b i l i s t i c d e s c r i p t i o n of the combustion process, and compare i t with the p r o b a b i l i s t i c d e s c r i p t i o n of turbulence. Figure 46 i s an sample of pressure vs time curves. In most cases, such curves appear to be nearly i d e n t i c a l , except for a uniform time s h i f t . This implies that the randomness i s i n the i g n i t i o n delay, not the burning v e l o c i t y . The method used to examine t h i s randomness was to perform the s t a t i s t i c a l a n a l y s i s on the time i t takes, s t a r t i n g from i g n i t i o n , to reach given pressure l e v e l s . The codes performing these operations, c a l l e d STATCOMB, STAT and STATCURVE, are presented i n Appendix C. Figures 47 to 62 show the combustion s t a t i s t i c s computed f o r the d i f f e r e n t sets of combustion experiments. Shown i n these graphs i s the pressure r i s e r a t i o P/P. f i n which P. i s the pressure at i g n i t i o n time), a c t u a l l y the ign v ign 65 independent v a r i a b l e , versus the corresponding mean time, measured from i g n i t i o n . Also shown are the standard deviation, skewness and k u r t o s i s of the pressure r i s e times, p l o t t e d versus the mean time. Kurtosis means here the fourth order moment, nondimensionalized by the fourth power of the standard deviation, minus three; t h i s quantity would be zero f o r a normally d i s t r i b u t e d random v a r i a b l e . Pressure i s u s u a l l y nondimensionalized i n combustion data by the peak combustion pressure. The proper quantity would be the ad i a b a t i c pressure. But wide v a r i a t i o n s of peak pressure were observed here (See Table V), making i t unsuitable. Consequently, pressures were normalized by the pressure at i g n i t i o n time, and the range of the r e s u l t i n g r a t i o s i s from 1 to around 5. Figure 47 to 58 r e f e r to the tests with the r i c h e r mixture, with an equivalence r a t i o of 0.92. For a delay time between end of charging and i g n i t i o n of 120 ms, the whole s e r i e s of 100 experiments was repeated, to confirm the unexpected shape of the standard d e v i a t i o n curve, and the two sets of r e s u l t s are presented, r e s p e c t i v e l y on Figures 53 and 54, and on Figures 55 and 56. For each case, two figures are presented, showing the f i r s t four moments for the whole range of pressure increase r a t i o s , and a comparison between mean and median. Figures 59 to 62 show the corresponding r e s u l t s f o r the leaner mixture, with equivalence r a t i o of 0.79. Figure 63 a l s o includes the mean times r e s u l t i n g from experiments at other decay times, repeated only ten times. Samples of ten tests are not s u f f i c i e n t to produce other valuable s t a t i s t i c s . 66 Figures 64 and 65 r e f e r to a 15 ms delay. They compare the mean burning times of the two mixtures. Figure 65 shows the two curves on Figure 64 p l o t t e d against each other. Such p l o t s for other decay times are s i m i l a r . A l l combustion times are measured s t a r t i n g at i g n i t i o n time, including on the f i g u r e s , and the delay between charging and i g n i t i o n was set considering that the end of charging occured 110 ms a f t e r the s t a r t of the charging sequence. According to Table I, the actual time at which the valve closed, detected by a sudden change of the slope of the pressure curve, was nearer to 109 ms i n most experiments. No s i g n i f i c a n t number of m i s f i r e s was noted; even with the leanest mixture, m i s f i r e d i d not occur i n more than two tests i n one hundred. 5.2.2 Discussion 5.2.2.1 General The questions to be addressed now are: Whether an i g n i t i o n delay i s observed, with what p r o b a b i l i s t i c d e s c r i p t i o n ; How the mean burning times are a f f e c t e d by the mixture composition and the turbulent q u a n t i t i e s ; A f t e r the i g n i t i o n delay, i s a p r o b a b i l i s t i c d e s c r i p t i o n of the flame 67 growth duration a l s o needed? 5.2.2.2 S t a t i s t i c s of i g n i t i o n The s t a t i s t i c s show that at the smallest measurable pressure increase, well-defined p r o b a b i l i s t i c d e s c r i p t i o n s already emerge, which have to be due e i t h e r to i g n i t i o n proper, or to the i n c i p i e n t flame development. At least for the leanest mixture, such i n i t i a l pattern does not change much during the subsequent flame growth. For the other mixture, while i n i t i a l standard deviations are low, increased randomness r e s u l t s from the flame growth, to be l a t e r reduced to a l e v e l r e l a t e d to the i n i t i a l value ( t h i s w i l l be discussed i n 5.2.2.4). Thus a model based on i g n i t i o n delay and subsequent flame growth does not t r u l y describe the phenomenon, and i n p a r t i c u l a r , i s not s u i t a b l e for a study of the mean burning times, which appear to be c o n t r o l l e d by the same fa c t o r s during the whole process. Only with the leaner mixture, does most of the d i s p e r s i o n between cycles seem to r e s u l t from the e a r l y stage of the process, which i s thus worthwile of a n a l y s i s . Samples of more than 50 elements are generally considered as large samples i n s t a t i s t i c a l a n a l y s i s . However here, with 100 elements or more, no clear p a t t e r n seems to emerge from the d i f f e r e n t t e s t s . In most cases, the d i s t r i b u t i o n appears to be skewed, but the t h i r d and fourth moments converge to d i f f e r e n t values i n d i f f e r e n t cases. The skewness and k u r t o s i s s t a r t at 68 d i f f e r e n t values i n d i f f e r e n t cases and then vary without any consistent pattern. In most cases, among the 100 or so tests, a few appear to be d i f f e r e n t and i t i s tempting to consider them as due to some undesired, ac c i d e n t a l cause, unrelated to the subject being investigated, and to eliminate them. A closer look shows that i n v i r t u a l l y a l l of these tests, a l l monitored parameters were quite normal; i n most of them, burning times are longer than normal. However i n the flow measurement tests, a l l r e s u l t s are as expected, and there i s no reason to beli e v e that occasionally, the charging process would behave abnormally. The i g n i t i o n equipment i s simple and r e l i a b l e , and thus, there i s no reason to assume that these apparent o u t l i e r s do not r e f l e c t some bona f i d e character of the process. More robust s t a t i s t i c a l procedures are less e f f i c i e n t [43], but provide r e s u l t s which tend to be v a l i d regardless of the nature of the odd cases. The simplest robust measure of p o s i t i o n on a d i s t r i b u t i o n i s the median. Here i t i s found that the median v i r t u a l l y coincides with the mean, which i s thus not biased by the extreme points. Even f o r a normally d i s t r i b u t e d random v a r i a b l e , the de v i a t i o n with respect to the mean would not be normal, but i t s p r o b a b i l i t y d i s t r i b u t i o n i s one-sided and consequently, the median of the de v i a t i o n would not be equal even i n that case to the standard deviation. (A proper robust measure of di s p e r s i o n would generally r e f e r to the dev i a t i o n from the median, but since mean and median are nearly equal, here, to which one one r e f e r s does not 69 matter.) No consistent r e l a t i o n s h i p i s observed between the two measures of dis p e r s i o n , as on Figure 48, 50, 52, 54, 56, 58, 60 and 62; i n some cases, they seem to follow the same pattern, i n others, they do not. The robust estimates, supposedly more i n s e n s i t i v e to contamination, do not provide a d i f f e r e n t p i c t u r e than the standard estimates, as they would i f the suspect elements i n the samples were t r u l y o u t l i e r s . They consequently must be assumed to belong to a t r u t h f u l representation of the process. This implies that besides there being extreme points, the p r o b a b i l i t y d i s t r i b u t i o n of the i g n i t i o n delay i s d i f f e r e n t i n the d i f f e r e n t cases. But the data r e f e r to a l i m i t e d number of cases over a wide range and no s p e c i f i c trend can be observed. The presence of extreme points implies that the p r o b a b i l i t y d i s t r i b u t i o n of the time needed for the mixture to i g n i t e properly, or to i g n i t e and propagate, may have a long and t h i n t a i l , on the large time side. The t o t a l p r o b a b i l i t y of an event to belong to the t a i l might be high enough for three or four cases i n one hundred to appear abnormally long; i f , however, the p r o b a b i l i t y density, i n the t a i l , i s very low and nearly constant i n a wide range of time delays, each sample of a hundred tests w i l l contain some events from the t a i l , which may well be very d i f f e r e n t from one case to the others. In e f f e c t , the s t a t i s t i c s computed over the 100 events w i l l be c r i t i c a l l y influenced by the p o s i t i o n of these few events, and much larger samples would then be needed, with enough events from the t a i l , to see the s t a t i s t i c s converging. This i s impractical here, and the d e t a i l s of the structure of the t a i l are l a r g e l y i r r e l e v a n t . I t s existence, and the t o t a l p r o b a b i l i t y of an event to happen i s the t a i l , are more important. 70 The data show that depending on the mixture, the randomness i n burning times e i t h e r r e s u l t s mostly from a random i g n i t i o n delay or from the subsequent flame growth period. This l a s t case w i l l be discussed i n Section 5.2.2.4. 5.2.2.3 Burning v e l o c i t i e s The more important observation i n t h i s work i s that, as shown on Figures 66 and 67, the leaner mixture, exposed to the same flow f i e l d , burns at roughly h a l f the speed of the r i c h e r one, while the d i f f e r e n c e i n laminar burning v e l o c i t i e s would be no more than 20 to 30%. This c o n t r a d i c t s many generally accepted models, which imply that at least f o r moderate Reynolds numbers, u t = u^ + k*u'. The present experiments were repeated over one hundred times i n two d i f f e r e n t , well c o n t r o l l e d flow conditions. Figure 66 shows a p l o t of u^/u^ versus u'/u^, and Figure 67, u^/u^ versus Re.. The turbulent q u a n t i t i e s r e s u l t from an assumed homogeneous, i s o t r o p i c A d e s c r i p t i o n , and were established i n Section 5.1.2. The p l o t t e d values of the turbulent burning v e l o c i t y were not computed according to a combustion model, which would require assumptions on the flame shape, on the i n i t i a l temperature d i s t r i b u t i o n and on the amount of heat transfer at the wall. Instead, a more d i r e c t procedure was used. 71 The slope at any point on pressure x time curve, as Figure 64, i s equal to a mean burning v e l o c i t y across the flame front, d i v i d e d by a factor which depends on the pressure l e v e l , the flame shape and the properties of the mixture. Assuming the flame shape to depend only on the pressure l e v e l , at least for a given mixture, then for a given mixture, the p r o p o r t i o n a l i t y constant at any given pressure l e v e l s i s the same for a l l t e s t s . Furthermore, any of the pressure curves obtained, f o r a given mixture, at d i f f e r e n t delay times, as on Figure 63, can nearly be obtained by m u l t i p l y i n g one such curve 3 by a p r o p o r t i o n a l i t y constant . As a r e s u l t , not only w i l l the slope at any point on these curves, but a l s o the inverse of any time i n t e r v a l w i l l provide a measure of the burning v e l o c i t y , up to an unknown p r o p o r t i o n a l i t y constant, dependent only of the mixture. Figure 67 was obtained by p l o t t i n g the inverse of the time from i g n i t i o n t i l l a the pressure increased by 10% (See Table IV) and assuming that the l i n e a r i t y observed extrapolates, f o r small Re.. , t i l l A the i n t e r s e c t i o n with the v e r t i c a l a x i s . At t h i s point, u^ = u^, or i f u^/u^ i s the parameter on the y ax i s , the ordinate i s unity. This l i n e of reasoning can be ap p l i e d separately to each mixtures, and the data on Figures 66 and 67 r e s u l t , and are expected to compare favorably, i n terms of accuracy, with estimates produced by combustion modeling, which would require dubious hypotheses about the flame shape. Figures 64 and 65 show that the dependence of the turbulent v e l o c i t y on the equivalence r a t i o i s a c t u a l l y well d i s t r i b u t e d across the whole combustion The same i s true f o r mean pressure r i s e curves obtained, for a given value of the delay, and the d i f f e r e n t mixtures, as seen on Figure 65. 72 time, and the i g n i t i o n delays vary i n the same proportion as the subsequent combustion times. On Figure 65, mean times corresponding to the same pressure increase, with the two d i f f e r e n t mixtures, i n tests with the same flow f i e l d , are p l o t t e d against each other. Except at the end, when the r i c h e r mixture i s known to behave somewhat e r r a t i c a l l y , the p l o t i s nearly l i n e a r , and appears to extrapolate to the o r i g i n of the coordinate system. Thus the slopes of the pressure r i s e curves and consequently, the burning v e l o c i t i e s remain nearly proportional from the time at which the smallest pressure increase i s detected, and p o s s i b l y from i g n i t i o n time, t i l l peak pressure i s reached. Figure 64 and 65 r e f e r to a delay of 15 ms, but the pattern i s the same for a l l delays tested. The a v a i l a b l e data do not permit a conclusion on whether the s w i r l plays an important r o l e , or whether the noted d i f f e r e n c e i n burning v e l o c i t i e s r e s u l t s simply from the combined e f f e c t of the stoichiometry and the swirl-generated turbulence, nor do they ind i c a t e the e f f e c t s of i n i t i a l pressure and temperature. Table 4 presents the times to given pressure increase r a t i o s , f o r two values of these r a t i o s , and t h e i r standard deviation. The standard deviations are indica t e d only for the cases where approximately 100 tests were performed; i n the other cases, with samples of only 10 tests, standard deviations cannot be r e l i a b l y evaluated, and even the estimate of the mean time may not be very accurate. Only the mean times w i l l be discussed i n t h i s section. The standard deviations r e f e r to matters discussed i n 5.2.2.4. 73 Table IV - Combustion Data Mixture Delay 10% pressure increase 100% pressure increase (%) (ms) mean time std dev mean time std dev (ms) (ms) (ms) (ms) 79 0 7.53 11.28 5 8.18 • . . 12.08 • • • 10 8.05 • • • 12.14 . . . 15 8.43 .865 12.81 .913 30 9.18 .672 14.04 .735 60 9.40 • • • 14.85 • • » 120 11.36 . . . 18.30 • • • 240 11.11. • . • 19.39 • • • 92 15 4.06 .218 6.15 .441 30 4.58 .197 7.24 .270 60 5.09 .326 8.25 .394 120 5.76 .269 9.75 .372 120 5.77 .243 9.58 .323 240 6.47 .318 11.19 .333 Figures 66 and 67 show that f or both mixtures tested, the r e l a t i o n s h i p appears to much more l i n e a r between the burning v e l o c i t y and Re^ than u'/u^. However u' r e s u l t s d i r e c t l y from measurements, and u^ i s a constant. Thus the shape on Figure 66 r e s u l t s d i r e c t l y from the measurements, except that the value of u' r e s u l t s from a somewhat h e u r i s t i c s p a t i a l average over the domain. But on Figure 67, the values of A considered i n Re^ depend on the v a l i d i t y of the homogeneous, i s o t r o p i c assumption, which admittedly may be i n v a l i d . On both f i g u r e s , as observed e a r l i e r , the p l o t s are quite d i f f e r e n t for the d i f f e r e n t mixtures, showing that the improvement i n burning v e l o c i t y due to turbulence i s s e n s i t i v e to the mixture composition. 74 In t h e i r 1975 paper, Andrews, Bradley and Lwakabamba [23] d i d not observe any influence of the mixture on turbulent burning v e l o c i t y . Based on a simple model, which disregards the f a c t that improved turbulent mixing may a f f e c t negatively the flame temperature, they suggested turbulent burning v e l o c i t i e s should vary l i n e a r l y with Re^, and independent of the mixture strength. In 1980, Abdel-Gayed and Bradley [29] proposed another model, r e s u l t i n g i n a c o r r e l a t i o n between u^/u^, u'/u^ and Re^ such that for constant L x (as i n f e r r e d here), and thus for Re^ increasing with u', u^/u^ should increase f a s t e r for larger values of u'/u^, on the p l o t of the former as a function of the l a t t e r , t i l l Re^ reaches values of 3000 to 4000 when the c o r r e l a t i o n becomes l i n e a r and independent of Re^. The curvature observed on fi g u r e 66 goes i n the other d i r e c t i o n : f o r larger u', u^ . increases more slowly. As described i n Section 2.1 and 2.3, more recent works [3], [4], [5], [6], [8], [10], [15] propose that flame s t r e t c h by the v e l o c i t y gradients due to turbulence w i l l a f f e c t turbulent burning v e l o c i t i e s d i f f e r e n t l y f o r d i f f e r e n t mixtures. In p a r t i c u l a r , Abdel-Gayed and Bradley [31], [32 ] present some data from which they conclude that for a given mixture, turbulent s t r a i n w i l l p r o g r e s s i v e l y hamper the turbulent flame propagation, so that as u' increases, u^ increases less and le s s , reaches a maximum and decreases t i l l supposedly a point w i l l be reached where the flame cannot propagate anymore as quenching occurs. However i n the present data, provided the values of Re^ r e s u l t i n g from the homogeneous, i s o t r o p i c turbulence model r e f l e c t the r e a l i t y , then the l i n e a r i t y observed on Figure 67 would imply that no quenching w i l l occur. The 75 turbulent s t r a i n , assuming t h i s mechani sm i s the source of the differ e n c e between the two mixtures, would a f f e c t the slope of the curve, but not so strongly as to change i t s sign. Another hypothesis may provide a better explanation for the unexpected v a r i a t i o n of the slope of the curve of u^/u^ versus u'/u^. The largest turbulence i n t e n s i t y corresponds a l s o to high s w i r l i n g v e l o c i t y . The r e s u l t i n g c e n t r i f u g a l a c c e l e r a t i o n , a p p l i e d to burnt and unburnt mixtures with a large density change w i l l reduce the flame wrinkling and the extent to which the flame structure i s c e l l u l a r . This 'laminarization' [37] w i l l reduce the burning v e l o c i t y a t the points where u' i s larger, and explains why the burning v e l o c i t y increase i s not l i n e a r with u', here. In r e l a t i o n to the Abdel-Gayed and Bradley data [31], [32], though, u'/u^ i s f a i r l y low here, and the p o s s i b i l i t y remains that the e f f e c t s of s t r a i n might become apparent only i n a higher range. Summmarizing, the present data do not confirm the previous observation; they show a strong influence of the mixture, and an influence of u' of a unexpected shape. The present observations compare tests i n the same equipment, with the same procedures, and i n the same flow conditions for both mixtures, They are consistent; the experiment i s simple and the pressure measurement technique i s r e l i a b l e . S t r a i n i n g by turbulence and po s s i b l y the s w i r l i n g motion i s the most l i k e l y cause of the d i f f e r e n c e i n burning v e l o c i t y f o r d i f f e r e n t equivalence r a t i o s . 76 Differences due to a v a r i a t i o n i n mixture composition involve n e c e s s a r i l y the k i n e t i c s of r e a c t i o n and thus molecular processes, and i t i s d i f f i c u l t to conceive what other factor r e l a t e d to the flow f i e l d could i n t e r f e r e with the molecular processes. In the boundary layer, near the wall, where most of the combustion occurs, s t r a i n rates due to the s w i r l are high, but the v e l o c i t y gradient i s p a r a l l e l to the mean d i r e c t i o n of flame propagation. Besides, Figure 65 shows the d i f f e r e n c e between the two mixture to be i d e n t i c a l before and a f t e r the flame w i l l reach the boundary layer, and that i f anything, i t would be reduced i n the boundary layer. The c e n t r i f u g a l forces due to the s w i r l are high for short delays between charging and i g n i t i o n , but are reduced by approximately a factor 100 for the longest delays (See Figure 41), when they are thus i n s i g n i f i c a n t . Yet substantial d i f f e r e n c e s between burning v e l o c i t i e s of the two mixtures are observed for a l l delays. Thus such forces are not l i k e l y to be a f a c t o r . At t h i s point, the mechanism of s t r a i n needs to be analyzed i n more d e t a i l , and compared to the observation. In chapter 2, mention was made of the f a c t laminar flames lean i n the heavier reactant are more susceptible to quenching due to flame s t r e t c h , as discussed i n [3], [4], [8] and [33]. Table III shows that while at the end of charging, the Kolmogorov scale i s estimated as 0.046 mm, i t increases and reaches 0.312 mm 240 ms l a t e r . The 77 flame thickness, evaluated by v/5g, assuming thus a Prandtl number of order 1, i s approximately 0.037 mm for the mixture with equivalence r a t i o 0.92 and 0.045 for the mixture with (J) = 0.79. Since the Kolmogorov scale n i s larger than the laminar flame thickness, i t i s not unreasonable to assume, as most of the mentioned models do, that l o c a l l y , within a distance r e l a t e d to n, the flame or flamelet should have a structure determined by molecular transport. Thus to some extent, the flamelets w i l l behave l o c a l l y l i k e a the laminar flame, with a t h i n reaction zone, preceded by a region where molecular transport mechanisms, susceptible to s t r a i n i n g e f f e c t s , r e s u l t i n heat and concentration gradients, ult i m a t e l y d e f i n i n g the burning v e l o c i t y . These gradients w i l l be p r o g r e s s i v e l y more a f f e c t e d by turbulent motion, at increasing distances to the r e a c t i o n zone. But the l o c a l nearly laminar flame w i l l be more s e n s i t i v e to what happens nearer to the r e a c t i o n zone, where the gradients are larger. The already mentioned studies of the e f f e c t of s t r a i n i n g on laminar flames show that the s t r a i n rate corresponding to a zero i n the laminar burning and quenching i s expected to happen, i s p a r t i c u l a r l y s e n s i t i v e to the Lewis number (thermal conductivity of the m i x t u r e / d i f f u s i v i t y of the specie i n the mixture) of the d e f i c i e n t reactant. The l o c a l rates of turbulent s t r a i n i n g may be described by a p r o b a b i l i t y d i s t r i b u t i o n , and i f l o c a l l y , the threshold value of the s t r a i n , correponding to the l i m i t of propagation, i s reached and quenching occurs, for an i n c r e a s i n g l y larger turbulence i n t e n s i t y , such a threshold w i l l be reached 78 over a larger proportion of the flame area. But at the same time, improved turbulent transport s t i l l works i n favor of a speed increase. Scales may be a fa c t o r a l s o : i f they are large, there may be regions i n a h i g h l y strained f i e l d where the s t r a i n rates are low, and the flame conceivably would propagate through such regions. To the author's knowledge, studies of strained laminar flame s t a b i l i t y have not been extended to nearly stoichiometric cases, but so far, o n l y consider mixtures s u f f i c i e n t l y f a r away from stoichiometry to v a l i d a t e the assumption that only the d e f i c i e n t reactant i s relevant. However i t i s known that for the laminar burning v e l o c i t i e s , when the mixture i s i n a range around stoichiometry, the d i f f u s i v i t i e s of both f u e l and oxidant become important [9], [11], and t h i s a l s o should be expected to be the case for the l i m i t of s t a b i l i t y . Thus even though here both mixtures tested are lean i n propane, for the r i c h e r one, the Lewis number of the oxidant should be expected to play a larger r o l e , and the leaner mixture to be more susceptible to quenching by a strained flow f i e l d . In the present conditions, the Lewis number for propane should be near 2, and for oxygen, the value must be below unity. As discussed i n Section 2.3, some questions a r i s e on the process Abdel-Gayed, Bradley e t . a l . [31] used i n th e i r computation of the Lewis numbers combining f u e l and oxidant of 0.88 for propane-air mixtures with equivalence r a t i o (J) = 1.1, 1.97 for (J) = 0.9 and 1.98 for (J) = 0.8. the combination they propose appear to r e s u l t from an unstrained flame s t a b i l i t y study [11], but another combination should be required for strained burning v e l o c i t y computation. While t h i s i s not 79 a v a i l a b l e , a better procedure would be to r e f e r to the three conceptually well-defined q u a n t i t i e s : equivalence r a t i o and both Lewis numbers, for the f u e l and the oxidant. S t r e t c h i s u s u a l l y q u a n t i f i e d as a K a r l o v i t z number as i n equation (2.1).In the case of s t r e t c h i n g by turbulence, as suggested e a r l i e r by Andrews, Bradley and Lwakabamba [23], Abdel-Gayed and Bradley [32] propose to compute the K a r l o v i t z number based on the mean v e l o c i t y gradient, as given by the d e f i n i t i o n of the Taylor microscale X: ' du 2 ' u'" . dx . . X . (5.5) This approach appears to better than the one taken by Chomiak and Ja r o s i n s k i [33], who measure the s t r a i n rate by u'/L x. They do not give t h e i r reasons for doing so. When the s t r a i n rate i s expressed by u'/X, the r e s u l t i n g K a r l o v i t z number i s u' .6, K = u^ .X (5.6) K a r l o v i t z s t r e t c h f actors computed accordingly decay from 0.25 to 0.005 for the mixture with (J) = 0.79, and for a delay from 0 to 240 ms, and from 0.17 to 0,004 for (j) = 0.92. The observations, together with the speculation that turbulent s t r a i n i n g explains the d i f f e r e n c e between the mixtures, suggests the constant of p r o p o r t i o n a l i t y c i n the Daneshyar and H i l l equation (2.8) to have a form: c = F(K,Le f ,Le o,<l)) (5.7) Where the subscipts f and o on the Lewis numbers r e l a t e r e s p e c t i v e l y to fue l 80 and oxygen. If the mixture i s far away from stoichiometry, F would tend to depend only on the Lewis number of the d e f i c i e n t reactant. If the turbulent burning v e l o c i t y depends on the composition of the mixture, then c y c l i c d i s p e r s i o n i n an engine may be influenced by v a r i a t i o n s i n the a i r / f u e l r a t i o , which according to the present evidence, may r e s u l t i n burning rates f l u c t u a t i n g i n a wider range than the d i f f e r e n c e s i n laminar burning v e l o c i t i e s would ind i c a t e . That would a l s o e x plain experimental evidence (See for instance Heywood, J.B., [44]), that lean mixtures seem to be more susceptible to c y c l i c d i s persion. Both a better t h e o r e t i c a l understanding and e s p e c i a l l y , more experimental evidence i s needed before any strong conclusion can be made regarding the e f f e c t of s t r e t c h and s t r a i n on turbulent flames. So f a r , neither the present data nor the mentioned previous work are s u f f i c i e n t l y conclusive to a t t r i b u t e to such f a c t o r s any c l e a r influence on burning v e l o c i t y and quenching, with a reasonable l e v e l of confidence; at best they provide the most reasonable speculation. 5.2.2.4 S t a t i s t i c s : v a r i a t i o n during combustion The d i s p e r s i o n between experiments appears to be larger with the lean mixture, and i n roughly the same r a t i o as the flame growth times. It i s d i f f i c u l t , however, to d i s t i n g u i s h any trend i n the dispersion, f or a given mixture, between d i f f e r e n t s w i r l decay times: the standard deviations of the 81 burning times shown i n Table IV appear to be more r e l a t e d to the mixture than to the flow conditions. From one mixture to the other, a c l e a r d i f f e r e n c e i s noticeable, while for a given flow at d i f f e r e n t turbulence l e v e l s , and d i f f e r e n t values of the Taylor microscale, no s i g n i f i c a n t change i s observed. The range of v a r i a t i o n between these d i f f e r e n t cases i s not inconsistent with the observation suggested e a r l i e r , that the p r o b a b i l i t y d i s t r i b u t i o n must have a long, t h i n t a i l , and that as a r e s u l t , more tes t s would be needed to provide for more accurate estimates. With the r i c h e r mixture ((() = 0 . 9 2 ) , the d i s p e r s i o n of the time to reach given pressure l e v e l s i s i n i t i a l l y small, and grows s t e a d i l y , to reach values of around one h a l f of those with the leaner mixture. A f t e r that, i t decreases, sometimes to a value comparable to what i t was i n i t i a l l y , and f i n a l l y , at a time when the flame i s well inside the boundary layer, i t increases again. For the leaner mixture ((J) = 0 . 7 9 ) , at the lowest measurable pressure increase, the d i s p e r s i o n i s already high, and seems to increase very s l i g h t l y , with a slope nearly constant over the whole combustion duration, except that at the end, when the flame i s very near the wall, i t increases. The c o r r e l a t i o n c o e f f i c i e n t s between combustion times, shown on Table V, t e l l a s i m i l a r story. For the leaner mixture, the combustion appears to occur i n an ord e r l y manner, where, a f t e r some randomness already present at the lower measurable pressure increases, a l l combustion times, i n c l u d i n g the time to peak pressure, are well correlated. 8 2 For the r i c h e r mixture, not only are the c o r r e l a t i o n c o e f f i c i e n t s much lower, e s p e c i a l l y f or the time to peak pressure, but i n some cases, paradoxical trends are noted, where the times to reach high pressure l e v e l s , of three or four times the i g n i t i o n pressure, are better c o r r e l a t e d with the times to low pressure increases, of 5% or 10%, than with the pressures, larger, corresponding to the peaks i n the d e v i a t i o n p l o t s . Thus eventually, the flame appears to remember i t s i n i t i a l condition, and i s more influenced by i t than by i t s more recent past. However t h i s i s noted only with the r i c h e r mixture. Such an e f f e c t i s thus r e l a t e d to the stoichiometry, and probably to the strong d i f f e r e n c e i n burning v e l o c i t i e s discussed i n section 5.2.2.3. The same trends are observed for a wide range of s w i r l s , and the c e n t r i f u g a l forces being proportional to the square of the v e l o c i t i e s , they are probably not d i r e c t l y r e l a t e d to the s w i r l . The peaks i n the d e v i a t i o n p l o t s , and the minima i n the c o r r e l a t i o n c o e f f i c i e n t s are observed at a time when the flame i s around mid-radius, thus not yet near the boundary layer, and where the s w i r l i s s t i l l nearly s o l i d body-like. A p o s s i b l e explanation may be r e l a t e d to a turbulent s t r a i n i n g and the s p a t i a l non-homogeneity i n turbulence i n t e n s i t y and scales, which must e x i s t but are not q u a n t i f i a b l e here, due to the measurement techniques and the adoption of the homogeneous, i s o t r o p i c turbulence model. 83 Table V - C o r r e l a t i o n between combustion data (When larger than 0.20) Time to peak Times to pressure increase of press 5% 10% 20% 50% 100% 200% 300% 400% <j) = 92% - Delay = 15 ms Peak press 0.850 - - 0. 223 0. 230 0. 234 0. 232 0.224 Time to peak pr 0.268 0. 250 - - - - - -time to 5% pr in c r 0. 848 0. 595 0. 415 0. 379 0. 370 0. 375 0.406 10% press i n c r 0. 926 0. 823 0. 793 0. 785 0. 787 0.804 20% press i n c r 0. 973 0. 955 0. 947 0. 948 0.952 50% press i n c r 0. 995 0. 990 0. 990 0.985 100% press i n c r 0. 998 0. 996 0.991 200% press i n c r 0. 999 0.993 300% press i n c r 0.997 (J) = 92% - Delay = 30 ms Peak press - - - - - - 0. 204 0. 249 0.256 Time to peak pr 0.466 0. 451 0. 404 0. 394 0. ,427 0. 440 0. 428 0.451 time to 5% pr in c r 0. 885 0. 772 0. 672 0. ,658 0. 654 0. 655 0.652 10% press i n c r 0. ,956 0. ,899 0. ,879 0. ,868 0. 858 0.847 20% press i n c r 0. ,977 0. ,955 0. ,938 0. ,928 0.908 50% press i n c r 0. .989 0. .974 0. 962 0.939 100% press i n c r 0. .993 0. ,984 0.963 200% press i n c r 0. ,992 0.971 300% press i n c r 0.987 (f> = 92% - Delay = 60 ms Peak press - - - - - - 0. .209 -Time to peak pr 0.533 0. .447 0 .386 0 .361 0 .409 0 .487 0. .566 0.641 time to 5% pr in c r 0, .980 0, .954 0 .928 0 .927 0 .927 0. .921 0.879 10% press i n c r 0 .991 0 .975 0 .970 0 .957 0 .933 0.893 20% press i n c r 0 .993 0 .984 0 .965 0 .935 0.885 50% press i n c r 0 .995 0 .975 0 .941 0.886 100% press i n c r 0 .989 0 .962 0.914 200% press incr 0 .988 0.953 300% press i n c r 0.983 (j> = 92% - Delay = 120 ms Peak press - 0 .229 0 .2 0 .265 - - -Time to peak pr 279 - -0 .219 -0 .341 -0 .272 - 0 .427 0.577 time to 5% pr in c r 0 .887 0 .769 0 .652 0 .677 0 .799 0 .801 0.685 10% press i n c r 0 .969 0 .910 0 .914 0 .899 0 .729 0.540 20% press i n c r 0 .980 0 .976 0 .900 0 .655 0.440 50% press i n c r 0 .992 0 .871 0 .567 0.339 100% press i n c r 0 .917 0 .639 0.418 200% press i n c r 0 .877 0.713 300% press i n c r 0.937 (Continues) 84 Table V - C o r r e l a t i o n between combustion data (when larger than 0.20) - (continued) Time to peak Times to pressure increase of press 5% 10% 20% 50% 100% 200% 300% 400% (J) = 92% - Delay = 120 ms (repeated) Peak press -0.391 - - - - - - - 0. 226 Time to peak pr - -0. 234 -0. 299 -0. 350 -0. 288 - 0.391 0. 532 time to 5% pr in c r 0. 949 0. 892 0. 830 0. 851 0. 903 0.753 0. 532 10% press i n c r 0. 982 0. 950 0. 955 0. 907 0.633 0. 382 20% press i n c r 0. 987 0. 984 0. 884 0.554 0. 293 50% press i n c r 0. 992 0. 854 0.484 0. 222 100% press i n c r 0. 900 0.554 0. 296 200% press i n c r 0.839 0. 633 300% press i n c r 0. 910 (j) = 92% - Delay = 240 ms Peak press - 0. 236 0. 269 0. 298 0. 312 0. 316 0. 332 0.234 0. 239 Time to peak pr 0. ,389 0. 401 0. 385 0. 375 0. 365 0. 450 0.509 0. 556 time to 5% pr incr 0. 978 0. 941 0. 881 0. 851 0. 882 0.850 0. 766 10% press i n c r 0. 985 0. 938 0. 912 0. 907 0.845 0. 752 20% press i n c r 0. ,974 0. 955 0. 924 0.836 0. 735 50% press i n c r 0. 983 0. 930 0.825 0. 718 100% press i n c r 0. 953 0.844 0. 750 200% press i n c r 0.950 0. 858 300% press i n c r 0. 941 (j) = 79% - Delay = 15 ms Peak press 0.260 0. .201 0. .211 0. .219 0. .223 0. .215 0. 222 0.219 0. 220 Time to peak pr 0, .895 0. .906 0. .916 0. .929 0. .939 0. .946 0.949 0. ,956 time to 5% pr in c r 0. .997 0. .991 0. .979 0. .968 0. .958 0.952 0. ,939 10% press i n c r 0. .997 0. .988 0. .978 0. .969 0.963 0. ,951 20% press i n c r 0. .995 0. .987 0. .979 0.974 0. .961 50% press i n c r 0 .997 0. .991 0.986 0. .974 100% press i n c r 0, .997 0.993 0, .983 200% press i n c r 0.998 0, .990 300% press i n c r 0 .995 (}) = 79% - Delay = 30 ms Peak press - - - - - — — — — Time to peak pr 0 .863 0 .885 0 .900 0 .919 0 .926 0 .936 0.946 0 .956 time to 5% pr in c r 0 .995 0 .987 0 .972 0 .956 0 .943 0.933 0 .915 10% press i n c r 0 .996 0 .983 0 .968 0 .957 0.948 0 .931 20% press i n c r 0 .993 0 .980 0 .969 0.961 0 .945 50% press i n c r 0 .995 0 .986 0.980 0 .963 100% press i n c r 0 .996 0.991 0 .973 200% press i n c r 0.997 0 .983 300% press i n c r 0 .991 85 6 Conclusions The answers emerging from the experimental evidence and i t s a n a l y s i s are: (1) The equivalence r a t i o a f f e c t s strongly the combustion of a lean mixture of propane and a i r i n s w i r l i n g flow i n a constant volume bomb. The rate of increase of turbulent burning v e l o c i t y with turbulence i n t e n s i t y i s strongly dependent on mixture strength at a l l l e v e l s of turbulence. The turbulent burning v e l o c i t y f or equivalence r a t i o 0.92 i s approximately twice that of the mixture with equivalence r a t i o 0.79. C y c l i c d i s p e r s i o n patterns a l s o depend markedly on mixture strength. For the leaner mixture, the randomness i s contained i n a p r o b a b i l i s t i c i g n i t i o n delay, while for the r i c h e r mixture, the randomness increases progressively, from a low value a f t e r i g n i t i o n , reaches a peak and f i n a l l y decreases. The nearly constant value of the d i s p e r s i o n between experiments for the leaner mixture i s approximately twice the peak d i s p e r s i o n observed for the r i c h e r mixture. (2) For both mixtures, the slope of the p l o t s of the turbulent burning v e l o c i t y versus turbulence i n t e n s i t y decreases with increasing turbulence i n t e n s i t y . P lots of the turbulent burning v e l o c i t y versus a turbulent Reynold number based on the Taylor microscale appear to be l i n e a r . However the values of the microlength scale were not measured, but derived assuming a homogeneous, i s o t r o p i c turbulence model. 86 No r e l a t i o n s h i p was observed between the d i s p e r s i o n of the time to given pressure r i s e s and the turbulence i n t e n s i t y or scales. The s i z e of the samples, of one hundred tests i n each case, does not appear to be s u f f i c i e n t to provide an accurate estimate of the d i s p e r s i o n of the i g n i t i o n delay. The range of v a r i a t i o n f or the d i f f e r e n t turbulence l e v e l s seems to be within the margin of uncertainty of the estimate. The observed d i f f e r e n c e s between mixtures are too large to be a t t r i b u t e d s o l e l y to a d i f f e r e n c e i n laminar burning v e l o c i t i e s . Previous works [3]-[8],[10], [31], [32] mention p o s s i b l e e f f e c t s of turbulent s t r a i n i n g as a factor a f f e c t i n g the turbulent v e l o c i t y . At the r e l a t i v e l y low l e v e l of turbulence produced here, they do not p r e d i c t such e f f e c t to be important. But here, the burning v e l o c i t i e s are already d i f f e r e n t between the two mixtures for low turbulence, and no tendency of the burning v e l o c i t y to l e v e l of as the turbulence increases i s noted. The experimental evidence i n the l i t e r a t u r e shows considerable scatter. Comparisons between data measured i n d i f f e r e n t apparati may not be v a l i d . At the same time, the present t h e o r e t i c a l knowledge of the e f f e c t s of s t r a i n i s s t i l l very l i m i t e d . In the absence of any other p o t e n t i a l explanation, s t r a i n e f f e c t s on the flame, due to turbulence and p o s s i b l y the s w i r l , appears to remain the most 87 reasonable cause of the observed dif f e r e n c e s between the two tested s t o i c h i o m e t r i c s . The models described i n Chapter 2, based on the Tennekes turbulence model, would p r e d i c t that the c y c l i c d i s p e r s i o n r e s u l t s from the e a r l y flame development, and scales with the microscale, divided by the laminar burning v e l o c i t y . However inaccurate the present estimate of the scale may be, and even considering the p o s s i b l y large error on the measurement of the c y c l i c d i s persion, such a r e l a t i o n s h i p i s not confirmed by the present evidence. 88 7 Further work To take further the present work, the following g u i d e l i n e s should be considered'-F i r s t of a l l , i t has to be determined whether the s w i r l i s an important factor i n the d i f f e r e n c e between the mixtures, or simply the turbulence i t produces. Thus the present combustion tests should be repeated with an i n l e t c o n f i g u r a t i o n producing turbulence, but no s w i r l . Supposing turbulence without s w i r l r e s u l t s i n s i m i l a r e f f e c t s as here, the next step i s to investigate whether and how the i n t e r a c t i o n between the mixture composition and turbulence i s a f f e c t e d by the Lewis numbers. A wider range of mixture compositions could be t r i e d , and the r e s u l t i n g burning v e l o c i t i e s compared to the Lewis numbers. The region around stoichiometry, where both Lewis number, of the f u e l and the oxidant, are expected to be s i g n i f i c a n t , should be p a r t i c u l a r l y well covered. Propane i s probably an i n t e r e s t i n g f u e l to consider, since i t s Lewis number i s rather high. Tests with other f u e l s for which t h i s i s not the case may provide some clues too. V e l o c i t y measurements simultaneous with the combustion tests, not possible by hot wire anemometry, may explain most of the c y c l i c d i s p e r s i o n observed here. That would confirm a hypothesis that the d i s p e r s i o n may not be inherent to turbulent combustion, but the r e s u l t of measurable d i f f e r e n c e s between 89 cycles, and that i n engines, mixture composition f l u c t u a t i o n may play an important r o l e . F i n a l l y , flow measurements with a better s p a t i a l r e s o l u t i o n should be implemented, and the v a l i d i t y of the homogeneous, i s o t r o p i c hypothesis should be assessed, under the l i g h t of more accurate experimental v e l o c i t y data. Also, a range of length scales should be investigated. This can be done simply by s u b s t i t u t i o n of the i n l e t g r i d . 90 INLET GRID ( B R A S S ) Figure \- THE BOMB . 91 Pressure Regulator Vacuum Pump ro m i 1 L E G E N D = bd. Normally open Valve H Normally closed Valve N Check Valve [s| Selenoid Control Air Electr ical Signal 4r Ground o IIOV AC 1 «"i r Hot Wire Probe | | 1 H. W. Control r Air operated Charging Valve Temperature Probe—> J Pressure i ! Signal ^ 0 ! i i — i JL 12V Battery Switch^ T i m e r s I Signal I I a . t = 0 t=40ms Signal 2- Adjustable Delay after Signal I (only for Combustion Tests) © -Capacitive Oischarge Module zr (Comb.Tests)*-i — ; " I Trigger o r ©"Ur Nicolet Oscilloscope # I Signol 2 Digital Oata Nicolet Osclllo scope # 2 Microcomputer I Diskette ^(Comb.Tests) Trigger: Signal 2 for Combustion Tests Signal I for H.W. Tests * Not used in Combustion Tests Figure 2= PIPING AND I N S T R U M E N T A T I O N DIAGRAM Figure 3 - S t anda rd dev ia t ion of p r e s s u r e dur ing cha r g i ng — q u a r t e r — r a d . — no plug Time ms F igure 4 — S t anda rd dev ia t i on of t e m p e r a t u r e du r ing cha r g i n g - q u a r t e r - r a d - no p lug 3 I 5-2-5-1-5 93 Figure 6 - F ive s u p e r p o s e d in s tantaneous ve loc i ty t r a c e s Q u a r t e r - r a d i u s - no p lug T i m e m s Figure 5 - Instantaneous ve loc i ty t r a c e Q u a r t e r - r a d i u s - no plug 40 I — — 35-Time m s 94 Figure 7 - E n s e m b l e a v e r a g e d ve loc i ty at cen te r e i T i m e m s Figure 8 — S m o o t h e d e n s e m b l e a v e r a g e d ve loc i ty at cen te r 7-1 o 4 - ^ J , , , , , , I 50 100 150 200 250 500 550 400 T i m e m s 95 Figure 9 - Mean veloc i ty a n d r.m.s. f l uc tuat ion Q u a r t e r - r a d i u s - no plug T i m e m s Figure 10 — Mean ve loc i ty a n d r.m.s. f l uc tua t i on Qua r t e r— rad i u s — with p lug Time m s 96 Figure 11 - Turbulence intensity by e n s e m b l e a ve rag i n g Q u a r t e r - r a d i u s - no plug Figure 13 - Mean veloc i ty a n d r.m.s. f l uc tuat ion t h r e e - e i g h t r ad . - no plug Time ms Figure 14 - Mean veloc i ty a n d r.m.s. f l uc tua t i on T h r e e - e i g h t r a d - with plug 25 Time ms 98 Figure 15 - Turbulence intensity by e n s e m b l e a ve rag i n g t h r e e - e i g h t r ad . - no plug 200 250 Time ms 400 Figure 16 - Turbulence intensity by e n s e m b l e a v e r a g i n g T h r e e - e i g h t r a d — with p lug 99 Figure 17 - Mean ve loc i ty a n d r.m.s. f l uc tuat ion M i d - r a d i u s - no plug Time ms Figure 18 - Mean ve loc i ty a n d r.m.s. f l uc tua t i on m i d - r a d i u s - with plug Time ms 100 Figure 17 - Mean veloc i ty a n d r.m.s. f l uc tuat ion M i d - r a d i u s - no plug 200 250 Time ms Figure 18 - M e a n ve loc i ty a n d r.m.s. f l uc tua t i on m i d - r a d i u s - w i th p lug 200 250 Time ms 100 Figure 19 - Turbulence intensity by e n s e m b l e a v e r a g i n g M i d - r a d i u s - no plug B-t — — — . 7-Time ms Figure 2 0 - Turbulence intensity by e n s e m b l e a v e r a g i n g M i d - r a d i u s — with p lug Time ms 101 F igure 21 - Mean veloc i ty a n d r.m.s. f l uc tuat ion F i v e - e i g h t r ad . - no plug Time m s Figure 2 2 - Mean ve loc i ty a n d r.m.s. f l uc tua t i on F i v e - e i g h t r ad . - with p lug T i m e m s 102 Figure 2 3 - Turbulence intensity by e n s e m b l e a ve rag i n g F i v e - e i g h t r ad . - no plug 200 250 Time m s 400 Figure 24 — Turbulence intensity by e n s e m b l e a v e r a g i n g F i v e - e i g h t r ad . — with p lug 103 Figure 2 5 - Mean velocity a n d r.m.s. f l uc tua t i on T h r e e - q u a r t e r r ad . - no plug 80 T i m e m s Figure 2 6 - Mean ve loc i ty a n d r.m.s. f l uc tua t i on T h r e e - q u a r t e r r ad . — wi th p lug 60 - i " T i m e m s 104 Figure 2 7 - Turbulence intensity by e n s e m b l e a ve r a g i n g T h r e e - q u a r t e r r ad . - no plug 200 250 Time ms 400 Figure 2 8 - Turbulence intensity by e n s e m b l e a ve r a g i n g T h r e e - q u a r t e r r ad . - with p lug 200 250 Time ms 400 105 Figure 2 9 - Mean veloc i ty a n d r.m.s. f l uc tuat ion S e v e n - e i g h t r ad . — no plug 120 T — Time ms Figure 3 0 - Mean veloc i ty a n d r.m.s. f l uc tua t i on s e v e n - e i g h t r ad . - with p lug Time ms 106 Figure 31 - Turbulence intensity by e n s e m b l e a ve r a g i n g S e v e n - e i g h t r ad . - no plug JO-1 • — — " 25-Time ms Figure 3 2 - Turbulence intensity by e n s e m b l e a ve r a g i n g Seven—eight r ad . — wi th p lug 20 - i ' i i I I I I ' 50 100 150 200 250 S00 350 400 Time ms 107 Figure 3 3 - Tempera tu re prof i les - No plug At d i f ferent d i s t ance s f r o m cen te r 280+-50 100 I 150 200 250 T i m e MS 300 350 400 108 Figure 3 5 - Mean ve loc i ty - No plug at d i f ferent d i s t ance s f r o m center Distance Figure 3 6 - Mean ve loc i ty - Wi th p lug at d i f ferent d i s t ance s f r o m cente r Distance 1/4 rod. Time ms 109 F igure 3 7 — Turbulence intensity — No plug at d i f ferent d i s t ance s f r o m cente r Distance Time m s F igure 3 8 — Turbulence intensity - With p lug at d i f ferent d i s t ance s f r o m cen te r Distance 110 I l l Absolute Pressure kpa _» _» to tn o o o o o o o 500 Figure 4 0 — Angu l a r ve loc i t ies - No plug At d i f ferent d i s t ance s f r o m cente r Distance Time ms 112 113 1 1 4 SIX Figure 4 8 — S t anda rd dev i a t i on a n d Med ian dev ia t i on 9 2 % fue l/a i r - de lay = 15 m s 00 0.0-1 1 1 1 j 1 I i 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 Mean time ITIS 116 F igure 5 0 — S t anda rd dev ia t i on a n d Med ian dev ia t i on 9 2 % fue l/a i r — de lay = 3 0 m s Legend Stondord deviation Median deviation 6 7 Mean time ms 1 0 117 Figure 51 - Stat i st ics of c o m b u s t i o n t i m e s 9 2 % fuel/a i r - de lay = 6 0 m s F igure 5 2 - S t anda rd dev ia t i on a n d Med ian dev ia t i on 9 2 % fue l/a i r - de lay = 6 0 m s ^ ^ ^ ^ ^ ^ Legend Stondord devioiion Median devlotion 0 . 0 0 -10 12 Mean time 118 F igure 5 3 — Stat ist ics of c o m b u s t i o n t i m e s 9 2 % fuel/a i r - de lay = 120 m s Mean time ms Figure 5 4 - S t anda rd dev ia t i on a n d Med ian dev ia t i on 9 2 % fue l/a i r - de lay = 120 m s 0.7 I — •—• * 0 0 ) i i i i I I I I I * 5 6 7 B 9 10 11 12 13 Mean time ms 119 F igure 5 5 — Stat i s t ics of c o m b u s t i o n t i m e s 9 2 % fuel/a i r - de lay = 120 m s (repeated) Mean time m S Figure 5 6 - S t anda rd dev i a t i on a n d Med ian dev ia t i on 9 2 % fue l/a i r - de lay = 120 m s (repeated) 0.6 0.1-i I I I I I I I I I ' 4 5 6 7 8 9 10 11 12 13 14 Mean time ms 120 Figure 5 7 — Stat i st ics of c o m b u s t i o n t i m e s 9 2 % fue l/a i r - de lay = 240 m s F igure 5 8 - S t anda rd dev ia t i on a n d Med ian dev ia t i on 9 2 % fue l/a i r - de lay = 240 m s 0.6 o.o H . , , , , , , 1 4 6 6 10 12 14 16 18 M e a n l i m e ms-121 Figure 5 9 — S tat i s t ics of c o m b u s t i o n t i m e s 7 9 % fuel/a i r - de lay = 15 m s Legend P/Pign. Std dev. Slowness Kurtosis 6 7 8 9 10 11 12 13 14 15 16 17 Mean t i m e ms Figure 6 0 — S t anda rd dev ia t i on a n d Med ian dev ia t i on 7 9 % fuel/air - de lay = 15 m s Legend Stondord deviation Median deviation —r-15 16 10 11 12 1' M e a n l i m e ms - r -14 17 122 F igure 61 — Stat i st ics of c o m b u s t i o n t i m e s 7 9 % fue l/a i r - de lay = 3 0 m s Legend Mean iime ms Figure 6 2 — S tanda rd dev ia t i on a n d Med ian dev ia t i on 7 9 % fue l/a i r - de lay = 3 0 m s Legend Standard devlotion Median deviation i i i i i i i i i i i 7 6 9 10 11 12 13 14 15 16 17 16 Mean iime ms 123 Pressure/Pressure at ignition time Figure 6 4 - P r e s s u r e i n c r ea s e rat io x m e a n t i m e 79% f u e l / a i r and 92% f u e l / a i r - d e l a y = 15 ms Time F igure 6 5 - T i m e s fo r s a m e p r e s s u r e i n c rea se , v e r s u s e a c h other, 7 9 % fue l/a i r x 9 2 % fuel a i r - de lay = 15 m s IB Time for the 92% fuel/air mixture ms 125 Figure 6 6 - Turbulent bu rn ing veloc i ty v e r s u s Turbulence intensity, n o n - d i m e n s i o n a l i z e d by the l am ina r burn ing velocity Turbulence i n t e n s i t y / l a m i n a r b u r n i n g v e l o c i t y Figure 6 7 - Tubulent bu rn ing ve loc i ty v e r s u s Reyno ld n u m b e r b a s e d on the Taylor m i c r o s c a l e S.5 I • 0.5-- i 1 I I I I 0 50 100 150 200 250 300 R e y n o l d s n u m b e r 126 Bibliography [ I ] Bush, W.B., and Fendell, F.E. 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[12] Matalon, M. , and Matkowsky, B.J., On the s t a b i l i t y of plane and curved flames, SIAM Journal on Applied Mathematics, 1984, Vol.46, pp. 327-343. 127 [13] M i k o l a i t i s , D.W., The i n t e r a c t i o n of Flame Curvature and Stretch, Part I I : The Convex Premixed Flame, Combustion and Flame, 58:23-29 (1984). [14] M i k o l a i t i s , D.W., Premixed Flames i n Combination Shear and S t r a i n i n g Flows, Combust. S c i . and Tech., 1984, Vol. 41, pp 211-218. [15] Sato, J . , E f f e c t s of Lewis number on e x t i n c t i o n behavior of premixed flames i n a stagnation flow, Nineteenth Symposium (International) on Combustion/The Combustion I n s t i t u t e , 1982, pp 1541-1548. [16] Ishizuka, S. and Law, C.K., An experimental study on e x t i n c t i o n and s t a b i l i t y of stretched premixed flames, Nineteenth Symposium (International) on Combustion/The Combustion I n s t i t u t e , 1982, pp 327-335. [17] K a r l o v i t z , B. , Denniston, D.W. Knapschaefer, D.H. and Wells, F.E. , Fourth Symposium (International) on Combustion, Williams and Wilkins, Baltimore, 1953, pp 613-620. [18] Williams, F.A., Combustion Theory, 2d e d i t i o n , The Benjamin/Cummings Publishing Co, Inc, 1985. [19] Matalon, M., On Flame Stretch, combustion S c i . and Tech., 1983, Vol. 31, pp. 169-181. [20] Batchelor, G.K., The Theory of Homogeneous Turbulence, Cambridge U n i v e r s i t y Press, 1953. [21] Tennekes, H., Phys. F l u i d s 11:669 (1968). [22] Tennekes, H. and Lumley, J.L., A F i r s t Course i n Turbulence, MIT Press, Cambridge, Mass, 1972. [23] Andrews, G.E., Bradley, D. and Lwakabamba, S.B., Turbulence and Turbulent Flame Propagation-A C r i t i c a l Appraisal, Combustion and Flame, 24, 285-304(1975). [24] B a l l a l , D.R. and Lefebvre, A.H., The structure and propagation of turbulent flames, Proc. R. Soc. Lond. A. 344,217-234(1975). 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[37] Zawadzki, A. and J a r o s i n s k i , J. , Laminarization of Flames i n Rotating Flow, Combust. S c i . and Tech., 1983, Vol.35, pp. 1-13. [38] Milane, R. , Evans, R.L. and H i l l , P.G., Combustion and Turbulence Structure i n a Closed Chamber with S w i r l , accepted f o r p u b l i c a t i o n by Combustion S c i and Tech. [39] Kach, R.A. and Adamczyk, A.A., E f f e c t s of thermal loading on pressure measurement i n a combustion bomb, Rev.Sci.Instrum.56(6), June 1985. [40] Witze, A., A C r i t i c a l Comparison of Hot-Wire Anemometry and Laser Doppler Velocimetry for I.C. Engine App l i c a t i o n s , SAE Technical Paper Series 800132, 1982. [41] Bradshaw, P., Introduction to Turbulence and i t s Measurement, Oxford, Pergamon Press, 1971. 129 [42] Checkel, M.D., Turbulence enhanced combustion of lean mixtures, Ph.D. Thesis, Cambridge Uni v e r s i t y , 1981. [43] Barnett, V. and Lewis, T. , O u t l i e r s i n S t a t i s t i c a l Data, 2d ed, John Wiley and Sons, 1984. [44] Heywood, J.B. and V i l c h i s , F.R., Comparison of Flame Development i n a Spark-Ignition Engine Fueled with Propane and Hydrogen, Combust. S c i and Tech, 1984, v o l 38, pp. 313-324. 130 Appendix A Data a c q u i s i t i o n : Program DATANIC Function: The program DATANIC i s a BASIC program, designed to run on a microcomputer under MS-DOS. I t receives the data transferred from a N i c o l e t d i g i t i z i n g o s c i l l o s c o p e , p l o t s them on screen and stores them i n a binary form on a d i s k e t t e . The d i g i t i z e d data send by the N i c o l e t , using a simple version of the RS-232C communication protocol, consist of a sequence of 4000 integers i n 2-byte binary format, i n a range between -2047 and +2048. The zero corresponds to the c e n t r a l p o s i t i o n on the screen of the N i c o l e t , but the value of the s i g n a l at that point depends on the o f f s e t adjusted before data a c q u i s i t i o n . The scale informations supplied by the N i c o l e t are stored by DATANIC, but were not used further i n t h i s work. Inputs The operation of the program requires only answers to the prompts given by the program. A f t e r the trace i s p l o t t e d on the screen, the operator has to press the Return key. 131 Outputs The output on d i s k e t t e i s a l s o stored as integers i n binary format. This output i s ready to be transferred to a Vax 11/750 using Kermit communication sof tware. 132 10 PRINT " Program DATANIC inputs data from N i c o l e t o s c i l l o s c o p e . " 20 PRINT " ======================================================" 30 PRINT 40 PRINT 50 PRINT "This program reads one screen f u l l of information stored on the" 60 PRINT "Nicolet Oscilloscope and reproduces i t on t h i s monitor. " 70 PRINT " I f requested, the data can be stored on a floppy disk i n drive B. " 80 PRINT 90 DEFINT A 100 DIM A(4100) 110 DIM N(8) 120 PRINT "In order to transfer data, check that the o s c i l l o s c o p e i s i n " 130 PRINT "the 'STORE' mode." 140 PRINT "Press 'P' to open communications, then press the RS232 button" 150 PRINT "on the o s c i l l o s c o p e a f t e r the tone." 160 PRINT "Communications remain open u n t i l the DATA ACQUISITION COMPLETE" 170 PRINT "message appears ( t h i s takes approx. 2 minutes)." 180 PRINT 190 IVF=0 200 PRINT 210 PRINT " TAKE DATA,ENTER P AT KEYBOARD," 220 PRINT " THEN PRESS RS-232 ON NICOLET AFTER TONE." 230 PRINT 240 PRINT 250 B$=INPUT$(1) 260 IF B$="p" THEN 280 270 IF B$="P" THEN 280 ELSE 250 280 PRINT "COMMUNICATIONS OPEN..." 290 ' Open l i n e to ramdrive C through f i l e #2 300 ' Open communications f i l e to RS232 port ( f i l e #1), 310 ' 9600 baud, no p a r i t y check, 7 data b i t s , ignore CTS and DSR , 320 OPEN "C0M1:9600,S,7.1,CS,DS" AS #1 330 ' Input character s t r i n g from communications b u f f e r . . . 340 ' Write character s t r i n g to ramdrive ( f i l e #2)... 350 ' P r i n t character s t r i n g s on screen... 360 SOUND 880,25 370 INPUT ttl, I :PRINT I 380 FOR J=3 TO 4002 390 A(J)=VAL(INPUT$(5,1)) 400 NEXT J 410 A$=INPUT$(1,1) 420 FOR L=l TO 8 430 N(L)=VAL(INPUT$(5,1)) 440 NEXT L 450 PRINT 460 CLOSE ttl 470 PRINT "DATA ACQUISITION COMPLETE" 480 SOUND 880,10 490 PRINT 133 500 HZER0=N(4) 510 V1=(N(5)-5)*10~(N(6)-12) 520 H1=(N(7)-5)*10~(N(8)-12) 530 HEND=H1*4000 540 HMID=HEND/2 550 VPOS=V1*2000 560 VP0S2=VP0S/2 570 VNEG=-VP0S 580 VNEG2=VNEG/2 590 PRINT 600 ANS$="Y" 610 TTL$=" NICOLET OSCILLOSCOPE RECORD " 620 YAX$="V0LTS" 630 XAX$="TIME (SEC.)" 640 IF ANS$="y" GOTO 720 650 IF ANS$="Y" GOTO 720 660 PRINT 670 INPUT; "ENTER TITLE ", TTL$ 680 PRINT 690 INPUT; "X-AXIS UNITS ", XAX$ 700 PRINT 710 INPUT; "Y-AXIS UNITS ", YAX$ 720 KEY OFF 730 SCREEN 2,,0,0 740 LINE (100,90)-(600,90) 750 LINE (100,1)-(600,1) 760 LINE (100,180)-(600,180) 770 LINE (100,1)-(100,180) 780 LINE (600,1)-(600,180) 790 LINE (100,45)-(105,45) 800 LINE (600,45)-(595.45) 810 LINE (600,135)-(595,135) 820 LINE (100,135)-(105,135) 830 LINE (350,180)-(350,176) 840 LOCATE 12,8,0 :PRINT "0.00"; 850 LOCATE 1,6,0 :PRINT USING "tttttt.m";VPOS; 860 LOCATE 6,6,0 :PRINT USING "###.##";VP0S2; 870 LOCATE 23,6,0 :PRINT USING "tttttt.tttt";VNEG; 880 LOCATE 18,6,0 :PRINT USING "###.##";VNEG2; 890 LOCATE 25,52,0 :PRINT XAX$; 900 LOCATE 9,1,0 :PRINT YAX$; 910 LOCATE 1,28,0 :PRINT TTL$; 920 LOCATE 24,12,0 :PRINT "0.0"; 930 LOCATE 24,42,0 :PRINT HMID; 940 LOCATE 24,73,0 :PRINT HEND; 950 LOCATE 1,1,0 960 FOR X=100 TO 600 970 Y=90-A((X-99)*8-5)/22.75 980 PSET(X.Y) 990 NEXT X 1000 INPUT; ST$ 1010 SCREEN 0 1020 PRINT 134 1030 PRINT "THE DATA ARE BEING STORED ON DISKETTE IN DRIVE B" 1040 INPUT "Name of the f i l e ",INF$ 1050 VD$="B:"+INF$+".DAT" 1060 HW$="B:U-"+INF$+".DAT" 1070 OPEN "R", #3, VD$, 2 1080 FIELD #3, 2 AS X$ 1090 FOR 1=3 TO 4002 1100 LSET X$=MKI$(A(I)) 1110 PUT #3 1120 NEXT I 1130 CLOSE #3 1140 OPEN "R", #3, HW$, 8 150 FIELD #3, 4 AS Hl$, 4 AS Vl$ 1160 LSET H1$=MKS$(H1) 1170 LSET V1$=MKS$(V1) 1180 PUT #3 1190 CLOSE #3 1200 IVF=IVF+1 1210 PRINT "Number of stored data f i l e s : ",IVF 1220 SOUND 880,10 1230 PRINT 1240 INPUT; "INPUT ANOTHER DATA SET (Y/N)"; AN$ 1250 IF AN$="N" GOTO 1280 1260 IF AN$="n" GOTO 1280 1270 GOTO 200 1280 PRINT :PRINT "PROGRAM ENDED" 1290 END 135 Appendix B Hot wire anemometry data reduction: Program HWRED Function HWRED reads binary f i l e s t ransferred from the N i c o l e t to a microcomputer and then from the microcomputer to the VAX 11/750, for which HWRED i s designed, through Kermit communication software. Series of simultaneous pressure, temperature and hot wire voltage f i l e s are read and processed. Each corresponding v e l o c i t y trace i s computed, according to the procedure described i n 4.2.9.3. Temperature and pressure data are needed for the corrections described. Besides instantaneous v e l o c i t y traces, the program a l s o computes mean and standard deviations between a l l traces, at a l l 4000 time data points recorded by the N i c o l e t . A range of values of the exponent i n the c o r r e l a t i o n (n i n eq (4.2)) can be t r i e d . Inputs The names of the f i l e s to be processed are read from an ASCII text f i l e , named FILENAMES.LST which can be prepared using an ed i t o r . On each record, four f i l e names w i l l be read, corresponding r e s p e c t i v e l y to the three 136 matching input f i l e s , containing pressure, temperature and hot wire traces. The fourth f i l e name w i l l be given by the program to the ASCII f i l e i t w i l l create, containing the corresponding instantaneous v e l o c i t y f i l e . Other informations must be given by answering prompts. They include - scale f a c t o r s and o f f s e t for the three types of data f i l e s . These values depend on the scale factor and o f f s e t used on the N i c o l e t and the primary device, and have to be computed accordingly. In p a r t i c u l a r , f o r temperature, the c o l d j u n c t i o n compensator gives a signal proportional to the temperature i n oC, while the program expects absolute temperatures. For other v a r i a b l e s , the o f f s e t w i l l generally correspond to the o f f s e t of the zero scale set on the N i c o l e t at the time of data a c q u i s i t i o n . (The best r e s o l u t i o n i s obtained when the zero i s at the bottom, say 2000 d i g i t i z a t i o n steps from the zero). -The names of the f i l e s where sequences of hot wire c a l i b r a t i o n data, r e s p e c t i v e l y voltages, and i n the same sequences, the corresponding v e l o c i t i e s must be given, and a l s o the temperature and pressure of c a l i b r a t i o n , and the set wire temperature. -The range of exponents to be investigated. Output The instantaneous v e l o c i t y traces go to new f i l e s with the names given i n FILENAMES.LST. Besides, output f i l e s are created, with the names MEAN.DAT and STDD.DAT, containing r e s p e c t i v e l y the mean v e l o c i t y and i t s standard 137 d e v i a t i o n at the 4000 time references. These are the f i l e s p l o t t e d Figures 9 to 32. 138 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 x x x x x x x x x x x x x x x x x x x x x x x c c Program HWRED c c This program reads pressure, temperature and HW voltage traces, c and computes v e l o c i t y traces c 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 x x x x x x x x x x x x x x x x x x x x x x x c c character*20 InputFile, + A n s w e r , f i l e v o l t , f i l e v e l , + O u t p u t f i l e , + filenames(120,4) integer*4 Data(4000).ncalmax,jfile,ipri, + ilength,ilengthy,in,nfmax,np(4000) real*4 offtemp,offvolt.offpress real*8 sf temp, s f v o l t , sfpress, v o l t c a l ( 3 0 ) , + sv(4000),sv2(4000) REAL*4 vo11(4000,50),pres s(4000,50),temp(4000,50) REAL*8 aa.bb, + vel(4000),velcal(30).n.nmax,int, + velcln(30),a,b,alpha,beta, + caltemp,calpress,wiretemp,m c 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 x x x x x x x x x x x x x x x x x x x x x x x c COMMON/DAT A/da ta, nvalues Common/outputf ile / o u t p u t f i l e c 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 x x x x x x x x x x x x x x x x x x x x x x x c c c c ncalmax=30 j f i l e = l c c write(6,8002) 8002 format(' Enter the scale factor f o r voltage, and the o f f s e t +: ',$) read(6,8040)sfvolt,offvolt 6001 format(a) 6002 format(i6) write (6,8020) 8020 format(/' Enter the scale factor for pressure, and the o f f s e +t: '$) 139 read(6,8040)sfpress,of fpress 8040 format(f5.0) c c write(6,2335) 2335 format(/,' Enter the scale factor f o r temperature, and the o f f s e t +: ',$) read(6,8040)sf temp,off temp write(6,6500) 6500 format(/,' Enter the c a l i b r a t i o n data filenames: Voltage ',$) read(6,6600)f i1evo11 6600 format(a20) write(6,6700) 6700 f o r m a t f V e l o c i t y (m/s) ',$) read(6,6600)f ileve1 write(6,6740) 6740 format(/,' Enter the c a l . temp and pressure and the wire temp') read(6,6760)caltemp,calpress.wiretemp 6760 format(fl0.5) write(6,6800) 6800 format(/,' Enter now the range of exponents to test') read (6,6900)n,nmax,int 6900 format(f5.3) c c c c c Reading the pressure,temp,voltage f i l e s c c c c a l l readfile(filenames,nfmax) c c 5 c a l l r e a d b i n a r y ( f i l e n a m e s ( j f i l e , 1 ) ) do 10 i=l,4000 temp(i,jf ile)=sftemp*data(i)+offtemp 10 end do cal1 readbinary(f ilenames(jf i l e , 2 ) ) do 20 i=l,4000 p r e s s ( i , j f ile)=sfpress*data(i)+offpress 20 end do cal1 readbinary(f ilenames(jf i l e , 3 ) ) do 30 i=l,4000 v o l t ( i , j f i l e ) = s f v o l t * d a t a ( i ) + o f f v o l t 30 end do j f i l e = j f i l e + 1 i f ( j f i l e . l e . n f m a x ) goto 5 c c c c 140 C a l i b r a t i o n data: c a l c u l a t i o n of alpha and beta c a l l o p e n f i l e ( f i l e v e l . v e l c a l , i l e n g t h ) c a l l o p e n f i l e ( f i l e v o l t , v o l t e a l , i l e n g t h y ) i f ( i l e n g t h y . I t . i l e n g t h ) ilength=ilengthy do 300 i = l , i l e n g t h i i = i l e n g t h - i + l i f ( v e l c a l ( i i ) . l t . 5 0 . ) goto 300 goto 400 300 end do 400 i n = i i - l do 500 i = l , i n v o l t e a l ( i ) = v o l t e a l ( i ) * * 2 500 end do 600 continue do 700 i = l , i n v e l c l n ( i ) = v e l c a l ( i ) * * n 700 end do c a l l l i n ( v e l c l n , v o l t c a l , i n . b . a ) m=n*l.76-.8 a1pha=a/(ca1temp**.8)/(wiretemp-ca1temp) beta=b*(caltemp»^m)/(calpress**n)/(wiretemp-caltemp) write(6,3550)alpha,beta 3550 format(/,' alpha = '.£10.9.' beta = \ f 7 . 6 ) Computation of the v e l o c i t i e s do 60 i=l,4000 sv(i)=0. sv2(i)=0. np(i)=nfmax 60 end do do 80 jfile=l.nfmax i p r i = l do 70 i=l,4000 write(6,5555)temp(i,jf i l e ) , p r e s s ( i , j f i l e ) , v o l t + ( i , j f i l e ) 5555 format(3fl2.4) aa=alpha*(temp(i,jfile)**(.8+m))/beta 141 b b = ( v o l t ( i , j f i l e ) * * 2 ) * ( t e m p ( i . j f i l e ) * * m ) / b e t a bb=(bb/(wi re temp-temp(i.jfile)))-aa i f (bb.le.O.) then vel( i ) = 0 . n p ( i ) = n p ( i ) - l i f ( i p r i . e q . 1 ) then write(6,7775)i,jf i l e ipri=0 end i f goto 70 end i f v e l ( i ) = ( b b * * ( l / n ) ) / p r e s s ( i , j f i l e ) s v ( i ) = s v ( i ) + v e l ( i ) s v 2 ( i ) = s v 2 ( i ) + v e l ( i ) * v e l ( i ) i f ( i p r i . e q . O ) then i p r i = l w r ite(6,7776)i,vel(i) end i f 70 end do 7775 format(' V e l o c i t y negative for i from ', + 15,' f i l e tt 1,i3,$) 7776 format(' t i l l i= ',15,' when velo c i t y = \ f 6 . 2 ) open(unit=9,f ile=filenames(jf ile,4),status='new') write(9,7700)(vel(i),i=l,4000) 7700 format(10f8.2) close(9) 80 end do do 85 i=1,4000 i f ( n p ( i ) . l e . l ) then sv(i)=0. sv2(i)=0. goto 85 end i f s v 2 ( i ) = d s q r t ( ( s v 2 ( i ) - ( s v ( i ) * s v ( i ) ) / n p ( i ) ) / ( n p ( i ) -s v ( i ) = s v ( i ) / n p ( i ) 85 end do open(unit=9,f ile='mean.dat',status='new') wri te(9,7700)(sv(i).i=l,4000) close(9) open(unit=9,f ile='stdd.dat',status='new') write(9,7700)(sv2(i),i=l,4000) close(9) 90 n=n+int i f (n.lt.nmax) goto 600 end 142 cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c c c c c c c c c c c c c c SUBROUTINE readbinary(Inputfile) Programmer: Gary Lepp May 1, 1985 Copyright 1985, Gary Lepp Permission i s hereby given to f r e e l y use and or/modify t h i s program If t h i s program i s copied or modified, t h i s copyright notice must be retained i n any and a l l copies made. Description: This program reads binary f i l e s transfered from the N i c o l e t data a c q u i s i t i o n system. byte byte_values( 510,16 ) integer*2 data_yalues( 4000 ) integer*4 data(4000) character*20 InputFile equivalence ( byte_values(l,1), data_yalues(l) ) c common/data/data,nvalues C. open ( unit=l, f i l e = I n p u t F i l e , + form='unformatted', + recordtype='variable', + status='old', + readonly ) C Determine the input and output f i l e name lengths c c a l l s t r $ t r i m ( i n p u t F i l e , i n p u t F i l e , IFlength ) C Read the input f i l e ( maximum 16, 510 byte records ) write ( 6,6001 ) InputFile c 6001 formatC Reading f i l e ', a<IFlength> ) 6001 formatC Reading f i l e ',a20) nvalues = 4000 do 101 j = 1,16 read( l,err=103 ) ( b y t e _ v a l u e s ( i , j ) , i = 1,510 ) 101 end do goto 103 c 102 write (6,6004 ) i , j c 6004 formate Err o r reading - i= ' , i 3 , ' j=',i2) 103 NBytes = 510*j+i-1001 143 c n v a l u e s = n b y t e s / 2 c w r i t e ( 6 , 6 0 0 2 ) n B y t e s c 6 0 0 2 f o r m a t ( ' ' , i 5 , ' B y t e s r ead* ) c w r i t e ( 6 , 6 0 0 3 ) ( d a t a _ v a l u e s ( j ) , j = l , 4 0 0 0 ) c 6003 f o r m a t ( 1 0 i 6 ) C c l o s e ( u n i t = l ) do 200 j = l , n v a l u e s d a t a ( j ) = d a t a _ v a l u e s ( j ) 200 end do c  r e t u r n end 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 x x x x x x x x x x x x x x x x x x x x x x x 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 x x x x x x x x x x x x x x x x x x x x x x x c c s u b r o u t i n e r e a d f i l e ( n a m e s . n f i l e ) c c 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 x x x x x x x x x x x x x x x x x x x x x x x x c c c h a r a c t e r * 2 0 n a m e s ( 1 2 0 , 4 ) , + a n s w e r , i n p u t f i l e 3 c h a r a c t e r * 2 0 i n p u t f i l e i , i n p u t f i l e 2 , o u t p u t f i l e i n t e g e r * 4 n f i l e c c 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 x x x x x x x x x x x x x x x x x x x x x x x x c n f i l e = 0 o p e n ( u n i t = 9 , f i l e = ' f i l e n a m e s . 1 s t ' , f o r m = " f o r m a t t e d ' , + s t a t u s = ' o l d * . r e a d o n l y ) 10 r e a d ( 9 , 8 0 0 1 ) I n p u t f i l e i , i n p u t f i l e 2 , i n p u t f i l e 3 , o u t p u t f i l e 8001 f o r m a t ( 4 a 2 0 ) A n s w e r = i n p u t f i l e i c a l l s t r $ u p c a s e ( A n s w e r . A n s w e r ) i f ( A n s w e r ( l : l ) . n e . ' E ' ) t h e n n f i l e = n f i l e + l n a m e s ( n f i l e , l ) = i n p u t f i l e l n a m e s ( n f i l e , 2 ) = i n p u t f i l e 2 n a m e s ( n f i l e , 3 ) = i n p u t f i l e 3 n a m e s ( n f i l e , 4 ) = o u t p u t f i l e g o t o 10 end i f c l o s e ( 9 ) r e t u r n end c 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 x x x x x x x x x x x x x x x x x x x x x x x x 144 cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c Subroutine l i n ( x , y , i n , s l o p e , i n t e r c e p t ) c Linear regression between two f i l e s c c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c real*8 x(30),y(30) real*8 s l o p e , i n t e r c e p t , c o r r e l integer*4 i n real*8 sx,sy,ssx,ssy,ssxy c c c-c c c c c c sx=0. sy=0. ssx=0. ssy=0. ssxy=0. do 500 i = l , i n sx=sx+x(i) sy=sy+y(i) ssx=ssx+x(i)*x(i) ssy=ssy+y(i)*y(i) ssxy=ssxy+x(i)*y ( i ) 500 end do c c c c c slope=(in*ssxy-sx*sy)/(in*ssx-sx*sx) intercept=( sy-sx*s l o p e ) / i n correl=( in*ssxy-sx*sy)/dsqr t( ( in*ssx-sx*sx)*( in*ssy-sy*sy) ) write(6,7000)slope,intercept,correl,in 7000 format(///,' Results of l i n e a r regression :',/,' slope= ' , f l 0 . 5 , +' intercept= ' , f l 0 . 5 , ' c o r r e l a t i o n coeff = ' , f l 0 . 8 , / , +' No. of points= ',i4,/) end c c c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c 145 c c subroutine openfile(name,x,il) c c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c character*20 name real*8 x(30) integer*4 i1 c c c c c open(unit=9,f ile=name,status='old',readonly) read(9,1000.err=100)(x(i),i=l,30) 1000 format(10f8.0) write(6,1100) 1100 format(/' No end of f i l e detected a f t e r reading 30 points ') 100 i l = i - l close(9) return end c c c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c 146 Data input to HWRED: Sample of f i l e FILENAMES.LST t703al. dat p703al.dat v703al. dat v a l . dat t703a2. dat p703a2.dat v703a2. dat va2. dat t703a3. dat p703a3.dat v703a3. dat va3. dat t703a4. dat p703a4.dat v703a4. dat va4. dat t703a5. dat p703a5.dat v703a5. dat va5. dat t703a6. dat p703a6.dat v703a6. dat va6. dat t703a7. dat p703a7.dat v703a7. dat va7. dat t703a8. dat p703a8.dat v703a8. dat va8. dat t703a9. dat p703a9.dat v703a9. dat va9. dat t703a0. dat p703a0.dat v703a0. dat vaO. dat t703aa. dat p703aa.dat v703aa. dat vaa. dat t703ab. dat p703ab.dat v703ab. dat vab. dat t703ac. dat p703ac.dat v703ac. .dat vac. .dat t703ad. ,dat p703ad.dat v703ad. dat vad. .dat t703ae. .dat p703ae.dat v703ae. dat vae. . dat t703af. dat p703af.dat v703af. .dat vaf. .dat t703ag.dat p703ag.dat v703ag.dat vag. .dat t703ah. .dat p703ah.dat v703ah. .dat vah. .dat t703ai. dat p703ai.dat v703ai. .dat v a i . .dat t703aj. .dat p703aj.dat v703aj. dat vaj. .dat t703ak. .dat p703ak.dat v703ak. .dat vak. .dat t703al. ,dat p703al.dat v703al. dat v a l . dat t703am. .dat p703am.dat v703am.dat vara. dat t703an. .dat p703an.dat v703an. .dat van. .dat t703ao. .dat p703ao.dat v703ao. .dat vao. .dat t703ap.dat p703ap.dat v703ap.dat vap. dat t703aq.dat p703aq.dat v703aq.dat vaq. dat t703ar. .dat p703ar.dat v703ar. .dat var. dat t703as. dat p703as.dat v703as. .dat vas. .dat t703at. .dat p703at.dat v703at. .dat vat. dat t703au. .dat p703au.dat v703au, .dat vau. dat t703av. .dat p703av.dat v703av. .dat vav. dat t703aw. .dat p703aw.dat v703aw. dat vaw. dat t703ax. .dat p703ax.dat v703ax. .dat vax. .dat t703ay.dat p703ay.dat v703ay.dat vay. .dat t703az. .dat p703az.dat v703az. .dat vaz, .dat t703bl, .dat p703bl.dat v703bl. .dat vbl. .dat t703b2 .dat p703b2.dat v703b2, .dat vb2 .dat t703b3 .dat p703b3.dat v703b3 .dat vb3 .dat t703b4 .dat p703b4.dat v703b4 .dat vb4 .dat t703b5 .dat p703b5.dat v703b5 .dat vb5 .dat t703b6 .dat p703b6.dat v703b6 .dat vb6 .dat t703b7 .dat p703b7.dat v703b7 .dat vb7 .dat t703b8 .dat p703b8.dat v703b8 .dat vb8 .dat t703b9 .dat p703b9.dat v703b9 .dat vb9 .dat 147 t703b0.dat t703ba.dat t703bb.dat t703bc.dat t703bd.dat End p703b0.dat p703ba.dat p703bb.dat p703bc.dat p703bd.dat v703b0.dat v703ba.dat v703bb.dat v703bc.dat v703bd.dat vbO.dat vba.dat vbb.dat vbc.dat vbd.dat 148 Appendix C S t a t i s t i c s of Combustion C l Conversion of the pressure traces: Program STATCOMB Function STATCOMB reads the sequence of correponding charging pressure and combustion pressure traces, prepares sums for s t a t i s t i c a l a n a l y s i s , and ASCII f i l e s containing the values of the times corresponding to a sequence of pressure increase r a t i o s , s t a r t i n g at 1.02 and with increments .005. Zero corrections are performed i n both traces, assuming that the i n i t i a l value of pressure a t beginning of charging i s zero (Absolute); the value of the pressure given on the combustion pressure trace, at i g n i t i o n time, can then be corrected, since a correct value at that time i s given by the charging pressure traces. A c t u a l l y , the program considers means of the respective values over a short i n t e r v a l . The program assumes the length of the charging pressure trace i s 200 ms, and the length of the combustion pressure trace i s 20 ms. If t h i s i s not so, the times i n the r e s u l t s w i l l be scaled by the corresponding f a c t o r s . 149 Inputs The program asks f o r the p o s i t i o n (integer: the n point) i n the charging pressure f i l e , of i g n i t i o n . The names of the binary data f i l e s from the Niocolet are read, l i k e i n HWRED, from a text f i l e c a l l e d FILENAMES.LST. Outputs A f i l e c a l l e d STATOUTPUT.OUT, l a t e r read by STAT, and f i l e s containing a sequence of times corresponding to the sequence of pressure l e v e l s . The names must be supplied i n FILENAMES.LST. These f i l e s w i l l be read by STATCURVE. 150 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c Program STATCOMB c c This program reads charging and combustion pressure traces, and c prepares data f o r s t a t i s t i c a l evaluation of the process c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c character*20 InputFile, + Answer, + Out p u t f i l e , + filenames(120,3) integerx-4 ChargingPressure (4000), + CombustionPressure (4000), + Data(4000) real*8 CombPRatio(4000), + Time(2000) integer*4 jj(9).nfmax, + StatArray(120,33), + RatioTest(lO), + Ratioq(4) integer*4 zeroshif t .denom, i p t e s t , i z e r o s h i f t real*8 jratio.ddaa,sigma.a,sc,c(24) c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c common/ChargingPressure/ChargingPressure,jign COMMON/DATA/data,nvalues Common/ou tpu t f i1e/ou tpu t f i1e c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c Data jj/1.2,5,10,20.30,40,50,500/ Data RatioTest/10200,10500,11000,12000, +15000,20000,30000,40000,50000,1000000/ data r a t i o q /10020,10050,10100,10200/ c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c jtime=3000 n f i l e = 1 c c write(6,8002) 8002 formatC Enter the p o s i t i o n , i n the charging pressure f i l e , of i g +nition time: ',$) read(6,6002)jign 6001 format(a) 6002 format(i6) write (6,8020) 151 8020 format(/' Enter the scale factor r a t i o (comb/charg): '$) read(6,8040)sfratio 8040 format(f5.0) c c write(6,2335) 2335 format(/, ' Enter the slope regression weighing parameter *• ' ,$) read(6,8040)sigma sc=0. do 2 i i z = l , 2 4 a = - l . * ( ( f l o a t ( i i z ) / s i g m a ) * * 2 ) c(iiz)=dexp(a) sc=sc+c(iiz) 2 end do sc=l.+2.*sc do 3 i i z = l , 2 4 c ( i i z ) = c ( i i z ) / s c 3 end do c c a l l readfile(filenames,nfmax) c c 10 write(6,3344)((filenames(iu,ju),ju=l,3),iu=l,nfmax) c 3344 formatC ,,3a20) 10 c a l l r e a d b i n a r y ( f i l e n a m e s ( n f i l e . l ) ) Maxpress=0 jpmax=0 i z e r o s h i f t=0 do 15 j = 2 , l l i z e r o s h i f t = i z e r o s h i f t + d a t a ( j ) 15 end do i z e r o s h i f t=izeroshif t/10 i f ( i z e r o s h i f t . n e . d a t a ( l ) ) write(6,8045)izeroshift,data(l) 8045 format(' F i r s t data point on charging trace d i f f e r e n t ' , +' from average of next 10 points:',/,' Ten points average= ', +i7,' f i r s t point= *,i7) do 20 j=l,jign+3 ChargingPressure(j)=Data(j)-izeroshif t i f (j.gt.jign-50) goto 211 i f (ChargingPressure(j).gt.maxpress) Then Maxpress=ChargingPressure(J) Minpress=maxpress min=maxpress jpmax=j End i f 211 i f (j.gt.jpmax+10) then min=min+chargingpressure(j)/10-chargingPressure(j-10)/10 e l s e min=min+chargingpressure(j)/10-maxpress/10 end i f i f (min.le.minpress) then minpress=min jpmin=j end i f 152 20 end do 25 StatArray(nfile,l)=Maxpress StatArray(nf ile,2)=jpmax StatArray(nf ile,3)=ChargingPressure(jign) StatArray(nf ile,4)=minpress statarray(nf ile,5)=jpmin pressmax=df1oat(maxpress) jmax=jign do 30 j=l,8 jk=j+5 c a l l T e s t r a t i o ( p r e s s m a x , j j ( j ) , s t a t a r r a y ( n f i l e , j k ) ) 30 end do nvall=nvalues C a l l readbinary(filenames(nfile,2)) i f (nValues.gt.nvall) nvalues=nvall PCMax=0 TCMax=0 jtest=10250 j j t e s t = l joutputStat=l z e r o s h i f t=0 denom=0 zero s h i f t=minpress do 38 j=1.40 denom=denom+data(j) 38 end do zero s h i f t=zeroshif t/sfratio-denom/40 wr i te(6,9876)denom,zeroshi f t 9876 formatC denom= * , i 6 , ' zeroshift= ' ,i6) ddaa=data(l)+zeroshif t do 40 ju=l,nvalues+25 combustionPressure(ju)=data(ju)+zeroshif t Jratio=10000.*CombustionPressure(Ju) CombPRa t i o ( j u ) = j r a t i o/ddaa j=ju-25 i f (j.It.100) goto 40 If (CombPRatio(J).gt.pcmax) Then PCMax=Combprat i o(J) TCMax=J j i jmax=j j tes t+500 do 440 j i j = j j t e s t , j i j m a x if(Combpratio(j) .ge.jtest) Then jtest=jtest+50 e l s e goto 450 153 440 450 end i f end do continue do 455 j j k = j j t e s t , j i j - 1 time(j j k ) = j - l + d f l o a t ( j j k - j j test+1)/(j i j - j j tes t) 455 end do j j t e s t = j i j If (CombPRatio(j).ge.RatioTest(JoutputStat)) Then j ja=JoutputStat+15 StatArray(nf i l e , j j a ) = j Jou tpu tS ta t=Jou tpu tS ta t+1 sxy=0. sx2=0. do 33 jku=l,24 sx2=2.*c(jku)*jku*jku+sx2 jplu=j+jku jmin=j-jku st=(combpratio(jplu)-combpratio(jmin))*jku sxy=sxy+c(jku)*st 33 end do j jb=jou tput s tat+23 isl=ifix(100.*sxy/sx2) statarray(nf i l e , j j b ) = i s l Endif Endif 40 End do StatArray(nfile,14)=PCMax StatArray(nfile,15)=TCMAx j j o u t = j j t e s t - l i f ( j j o u t . I t . j t i m e ) jtime=jjout outputf ile = f i l e n a m e s ( n f i l e , 3 ) open(UNIT=9, f ile=outputfile,form=*formatted',status='new') write(9,8011)(time(j),j=l,jjout) 8011 format (10fl0.3) close(9) i f ( n f i l e . I t . nfmax) then nf ile=nf ile+1 goto 10 endif outputf i l e = ' s t a t f i l e . o u t ' open (unit=9,file=outputfile,form='formatted', +status='new') write(9,8030)((statarray(i,j),i=l,120),j=l,33) 8030 format(lOi12) close(9) c a l l stat(statarray,nfmax) 154 c 90 end c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c Subroutine TestRatio(datamax,j,jout) c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c integer*4 datal(4000), + data2(4000),j real*8 a.atest c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c common/ChargingPressure/datal,jmax common /data/data2,nvalues c c_ jout=4001 a t e s t = d f l o a t ( j ) do 10 ji=l,jmax a=100.*dfloat(datal(j i ) ) a=a/da tamax i f (a.ge.atest) then jout=ji goto 20 endif 10 end do 20 return end cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x-cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x-c c c c c c c c c c SUBROUTINE readbinary(Inputfile) Programmer: Gary Lepp May 1, 1985 Copyright 1985, Gary Lepp Permission i s hereby given to f r e e l y use and or/modify t h i s program. If t h i s program i s copied or modified, t h i s copyright notice must be retained i n any and a l l copies made. 155 c c c c c +-c D e s c r i p t i o n This program reads binary f i l e s transfered from the N i c o l e t data a c q u i s i t i o n system. byte byte_values( 510,16 ) integer*2 data_values( 4000 ) integer*4 data(4000) character*20 InputFile equivalence ( byte_values(1,1), data_values(l) ) c  c c common/da ta/da ta,nvalues C. open ( uni t = l , f i l e = I n p u t F i l e , + form='unformatted', + recordtype='variable', + status=*old', + readonly ) C Determine the input and output f i l e name lengths c c a l l s t r $ t r i m ( i n p u t F i l e , i n p u t F i l e , IFlength ) C Read the input f i l e ( maximum 16, 510 byte records ) write ( 6,6001 ) InputFile c 6001 formatC Reading f i l e ', a<IFlength> ) 6001 formatC Reading f i l e ',a20) nvalues = 3500 do 101 j = 1,16 read( l,err=103 ) ( b y t e _ v a l u e s ( i , j ) , i = 1,510 ) 101 end do goto 103 c 102 write (6,6004 ) i , j c 6004 format(' E r r o r reading - i= ' , i 3 , ' j=',i2) 103 KBytes = 510*j+i-1001 c nvalues = nbytes/2 c write ( 6,6002 ) nBytes c 6002 format (' ', i 5 , ' Bytes read' ) c write (6,6003)(data_values(j),j=l,4000) c 6003 format(10i6) C close ( unit=l ) do 200 j=l,nvalues da ta(j)=data_va1ue s ( j ) 200 end do 156 c-return end Cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx * c c subroutine readfile(names,nfile) c c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c character*20 names(120,3), + answer characterx-20 inputf i l e i , inputf ile2,outputf i l e integer*4 n f i l e c c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c nfile=0 open(unit=9,file="filenames.1st*,form=*formatted', +status=*old'.readonly) 10 r e a d ( 9 . 8 0 0 1 ) I n p u t f i l e i . i n p u t f i l e 2 , o u t p u t f i l e 8001 format(3a20) Answer=inputf i l e l c a l l str$upcase(Answer.Answer) i f ( Answer(l:l) .ne. 'E') then nfile=nfile+1 n a m e s ( n f i l e , l ) = i n p u t f i l e l names(nf ile,2)=inputf i l e 2 names(nf i l e , 3 ) = o u t p u t f i l e goto 10 end i f close(9) return end c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 157 Data input to STATCOMB: Sample of f i l e FILENAMES.LST pal274.dat cal274. dat t a l . dat pa2274.dat ca2274. dat ta2. dat pa3274.dat ca3274. dat ta3. dat pa4274.dat ca4274. dat ta4. dat pa5274.dat ca5274. dat ta5. dat pa6274.dat ca6274. dat ta6. dat pa7274.dat ca7274. dat ta7. dat pa8274.dat ca8274. dat ta8. dat pa9274.dat ca9274. dat ta9. dat pa0274.dat ca0274. dat taO. dat paa274.dat caa274. dat taa. dat pab274.dat cab274. dat tab. dat pac274.dat cac274. dat tac. dat pad274.dat cad274. dat tad. dat pae274.dat cae274. dat tae. dat paf274.dat caf274. dat taf. dat pag274.dat cag274.dat tag. dat pah274.dat cah274. dat tah. .dat pai274.dat cai274. dat t a i . .dat paj274.dat caj274.dat ta j .dat pak274.dat cak274. dat tak. .dat pal274.dat cal274. dat t a l . .dat pam274.dat cam274. dat tarn. .dat pan274.dat can274. .dat tan .dat pao274.dat cao274. .dat tao .dat pap274.dat cap274.dat tap .dat paq274.dat caq274.dat taq .dat par274.dat car274, .dat tar .dat pas274.dat cas274 .dat tas .dat pat274.dat cat274, .dat tat .dat pau274.dat cau274 .dat tau .dat pav274.dat cav274 .dat tav .dat paw274.dat caw274, .dat taw .dat pax274.dat cax274, .dat tax .dat pay274.dat cay274.dat tay .dat paz274.dat caz274 .dat taz .dat pbl274.dat cbl274, .dat t b l .dat pb2274.dat cb2274 .dat tb2 .dat pb3274.dat cb3274 .dat tb3 .dat pb4274.dat cb4274, .dat tb4 .dat pb5274.dat cb5274. .dat tb5 .dat pb6274.dat cb6274, .dat tb6 .dat pb7274.dat cb7274. .dat tb7 .dat pb8274.dat cb8274. .dat tb8 .dat pb9274.dat cb9274.dat tb9 .dat pb0274.dat cb0274, .dat tbO .dat pba274.dat cba274. .dat tba .dat pbb274.dat cbb274, .dat tbb, .dat pbc274.dat cbc274, .dat tbc .dat 158 pbd274.dat cbd274. dat tbd.dat pbe274.dat cbe274. dat tbe.dat pbf274.dat cbf274. dat tbf.dat pbg274.dat cbg274.dat tbg.dat pbh274.dat cbh274. dat tbh.dat pbi274.dat cbi274. dat tbi.dat pbj274.dat cbj274.dat tbj.dat pbk274.dat cbk274. dat tbk.dat pbl274.dat cbl274. dat tbl.dat pbm274.dat cbm274. dat tbm.dat pbn274.dat cbn274. dat tbn.dat pbo274.dat cbo274. dat tbo.dat pbp274.dat cbp274.dat tbp.dat pbq274.dat cbq274.dat tbq.dat pbr274.dat cbr274. dat tbr.dat pbs274.dat cbs274. dat tbs.dat pbt274.dat cbt274. dat tbt.dat pbu274.dat cbu274. dat tbu.dat pbv274.dat cbv274. dat tbv.dat pbw274.dat cbw274. dat tbw.dat pbx274.dat cbx274. dat tbx.dat pby274.dat cby274.dat tby.dat pbz274.dat cbz274. dat tbz.dat pcl274.dat ccl274. dat t c l . d a t pc2274.dat cc2274. dat tc2.dat pc3274.dat cc3274. dat tc3.dat pc4274.dat cc4274. dat tc4.dat pc5274.dat cc5274. dat tc5.dat pc6274.dat cc6274. dat tc6.dat pc7274.dat cc7274. .dat tc7.dat pc8274.dat cc8274. .dat tc8.dat pc9274.dat cc9274. .dat tc9.dat pc0274.dat cc0274 .dat tcO.dat pca274.dat cca274 .dat tea.dat pcb274.dat ccb274 .dat tcb.dat pcc274.dat ccc274 .dat tec.dat pcd274.dat ccd274 .dat ted.dat pce274.dat cce274 .dat tee.dat pcf274.dat ccf274 .dat tcf.dat pcg274.dat ccg274.dat teg.dat pch274.dat cch274 .dat tch.dat pci274.dat cci274.dat t c i . d a t pcj274.dat ccj274.dat t c j . d a t pck274.dat cck274 .dat tck.dat pcl274.dat ccl274 .dat t c l . d a t pcm274.dat ccm274 .dat tern.dat pcn274.dat ccn274 .dat ten.dat pco274.dat cco274 .dat tco.dat pcp274.dat ccp274.dat tcp.dat pcq274.dat ccq274.dat tcq.dat pcr274.dat ccr274 .dat tcr.dat pcs274.dat ccs274 .dat tcs.dat pct274.dat cct274 .dat tct.dat 159 pcu274.dat pcv274.dat pcw274.dat pcx274.dat pcy274.dat pcz274.dat end of f i l e ccu274.dat ccv274.dat ccw274.dat ccx274.dat ccy274.dat ccz274.dat tcu.dat tcv.dat tew.dat tcx.dat tcy.dat tcz.dat 160 C2 C o r r e l a t i o n c o e f f i c i e n t s : Program STAT Function From data supplied by STATCOMB, STAT computes c o r r e l a t i o n c o e f f i c i e n t s between a matrix of charging and combustion data, and a l s o the f i r s t four moments of the p r o b a b i l i t y d i s t r i b u t i o n of each of theses data sets. Inputs The data are read from a f i l e created by STATCOMB, c a l l e d STATFILE.OUT, and a prompt asks the number of f i l e s to consider (The f i r s t n f i l e s w i l l be selected), and whether some f i l e s are to be disconsidered. In that case, they w i l l be substituted by the l a s t ones. The indicated number of f i l e s must be less or equal to the t o t a l number minus the ones eliminated. Output A readable f i l e containing the indicated informations, c a l l e d STATOUTPUT.OUT. 161 cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx X* c c c Subroutine Stat(input,imax) c c computes s t a t i s t i c s on flame development and propagation c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx integer*4 input(120,33) integer*4 ielim(120),imax real*8 output(120) real*8 sums(33) real* 8 cross(33,33),si(33,33),sll real*8 scale(33) real*8 s3sums(33) real * 8 k4sums(33) characterx-40 names (33) character*120 answer data names /'Max. Charging Pressure','Time to max ch. Pressure', +' Pressure at set i g n i t i o n time','pressure detected at i g n i t i o n + time/peak ch. press.','detected i g n i t i o n time",'time f o r ch. + press, increase by 1%', +'Time for ch. press, increase by 2%',' Time + for ch. press, increase by 5%','Time for ch. press, increase + by 10%','Time f or ch. press, increase by 20%', 'Time f or + ch. press, increase by 30%','Time for ch. press, increase by 40%' +,'Time for ch. press increase by 50%','Peak Combustion Pressure", +'Time to peak combustion pressure', 'Time to 2 +% combustion pressure rise','Time to 5% combustion pressure r i s e ' , +'Time to 10% combustion pressure rise','Time to 20% combustion press +ssure rise','Time to 50% combustion pressure rise','Time to 100% com +ombustion pressure r i s e * , 'Time to 200% combustion pressure r i s +se' , 'Time for 300% combustion pressure r i s e " , 'Time for 400% + combustion pressure rise','Slope at 2% pr. rise','Slope at 5% pr + r i s e " , ' s l o p e at 10% pr. r i s e ' , " s l o p e at 20% pr. r i s e " , ' s l o p e at + 50% pr. r i s e ' , ' s l o p e at 100% pr. r i s e ' , ' s l o p e at 200% pr. r i s e ' , +'slope at 300% pr. r i s e ' , ' s l o p e at 400% pr. r i s e * / data scale/2000.,20.,2000.,100.,20.,20.,20.,20.,20.,20.,20.,20., +20. ,10000. ,100. ,100. ,100. ,100. ,100. ,100. ,100. ,100. ,100. ,100. , +10000. , 10000. , 10000. , 10000. , 10000. , 10000. , 10000. , 10000. , 10000./ c c c c c c open(unit=9,file='statfile.out*,form='formatted',status='old', 162 +readonly) read(9,6001)((input(i,j),i=l,120),j=l,33) 6001 format(10i12) close(9) write(6,7001) 7001 format(/' Enter the number of f i l e s to process: ',$) read(6,7002)imax 7002 format(i6) ii=0 write(6,7003) 7003 format(' Do you want to eliminate some f i l e s ? ',$) 50 read(6,7004)Answer 7004 format(a) c a l l str$upcase(Answer,answer) i f (Answer(l:l) .Eq. 'Y' ) then i i = i i + l write(6,7006) 7006 formatC Enter the f i l e number: ',$) read(6,7002)ielim(ii) write(6,7005) 7005 format(' Do you want to eliminate more f i l e s ? ',$) goto 50 end i f open(uni t=9,f ile='statoutput.out',form='formatted', +status='new') write(9,7500) 7500 format(//,' Combustion S t a t i s t i c s ' , / / / , +10x,' Data',//) ishit=imax+ii do 97 i = l , i s h i t input(i,4)=10000*input(i,4)/input(i,1) 97 end do do 100 j=l,33 sums(j)=0. s3sums(j)=0. k4sums(j)=0. do 110 jj=l,33 c r o s s ( j , j j ) = 0 . 110 end do do 105 i = l . i i i n put(ielim(i),j)=input(imax+i,j) 105 end do do 109 i=l,imax o u t p u t ( i ) = i n p u t ( i , j ) / s c a l e ( j ) 109 end do 115 write(9.6999)names(j),(output(i),i=l,imax) 6999 format(/,* ',a40,/,12(10f8.3,/)) write(6,7000)names(j),(output(i),i=l,imax) 7000 format(/,' ',a40,/,12(10f8.3./)) 100 end do do 20 i=l,imax do 10 j=l,33 sums(j)=sums(j)+dfloat(input(i,j)) 163 do 30 j j = l , j c r o s s ( j , j j ) = c r o s s ( j , j j ) + d f l o a t ( i n p u t ( i , j ) ) * d f l o a t ( i n p u t ( i , j j 30 end do 10 end do 20 end do do 300 j=l,33 sums(j)=sums(j)/imax do 310 i=l,imax k4sums(j)=k4sums(j)+(dfloat(input(i,j))-sums(j))**4 s3sums(j)=s3sums(j)+(dfloat(input(i,j))-sums( j ))**3 310 end do cross(j,j)=dsqrt(cross(j,j)/imax-sums(j)*sums(j)) i f ( c r o s s ( j , j ) . e q . 0 . ) then k4sums(j)=0. s3sums ( j ) =0. goto 295 endif k4sums(j)=k4sums(j)/imax/(cross(j,j)**4) s3sums(j)=s3sums(j)/imax/(cross(j,j)**3) 295 jmax=j-1 do 200 jj=l,jmax i f ( ( c r o s s ( j , j ) . e q . 0 . ) . o r . ( c r o s s ( j j , j j ) . e q . 0 . ) ) then c r o s s ( j , j j ) = l . s l ( j , j j ) = 0 . goto 200 endif mum=cross ( j , j j )/imax-sums ( j )x-sums ( j j ) c r o s s ( j , j j ) = r n u m / ( c r o s s ( j , j ) * C r o s s ( j j . j j ) ) s1l=rnum/(cross(Jj,j j ) * c r o s s ( j j , j j ) ) s 1 ( j . j j ) = s 1 l * s c a l e ( j j ) / s c a l e ( j ) 200 end do 300 end do write(9,7099) write(6,7099) 7099 format(///,10x, ' f i l e \ 2 7 x , ' mean std dev', +' skew, k u r t o s i s ',/) do 500 j=l,33 sums(j)=sums(j)/seale(j) c r o s s ( j , j ) = c r o s s ( j , j ) / s c a l e ( j ) write(6,7100)names(j),sums(j),cross(j,j),s3sums(j),k4sums(j) 550 write(9,7100)names(j),sums(j),cross(j,j),s3sums(j),k4sums(j) 7100 formatC ,,a40,4f9.3) 500 end do write(9,7300) write(6,7300) 7300 format(//' xxxxxxxxxxxxxx C O R R E L A T I O N S ',30('*'). do 700 j=2,33 write(9,7350)names(j) write(6,7350)names(j) 7350 format(//,' The c o r r e l a t i o n coeff. between ',a40,' and') jmax=j-l do 600 jj=l,jmax i f ( d a b s ( c r o s s ( j , j j ) ) . l t . . 2 ) goto 600 164 w r i t e ( 9 , 7 4 0 0 ) n a m e s ( j j ) , c r o s s ( j , j j ) , s l ( j , j j ) i f ( d a b s ( c r o s s ( j , j j ) ) . I t . . 5 ) goto 600 wr i te(6,7400)names(j j ) , c r o s s ( j , j j ) , s 1 ( j , j j ) 600 end do 700 end do 7400 format(' •^40,' i s '^6.4, ' The slope i s \ f l 0 . 5 ) close(9) end c c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 165 3 Curves of mean, s t . deviation, skewness and k u r t o s i s : program STATCURVE Function Reading from the i n d i v i d u a l sequences of times to given pressure increase r a t i o s computed by STATCOMB, STATCURVE computes the s t a t i s t i c s , for the whole sequence of pressure increase r a t i o s . Input A l l input data are e x i s t i n g f i l e s : the names f i l e FILENAMES.LST that STATCOMB reads, and the data f i l e s created by STATCOMB. Output Four f i l e s c a l l e d MEAN.DAT, STDD.DAT, SKEW.DAT and KURT.DAT, containing sequences r e s p e c t i v e l y of the mean times, t h e i r standard deviation, skewness and k u r t o s i s , f o r the sequence of pressure increase r a t i o s . These f i l e s are p l o t t e d on Figures 47 to 62. 166 c xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c Program STATCURV c c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx character*120 InputFile(120), + Answer, + O u t p u t f i l e real*8 Sum (2000), + ssl(2000),ss2(2000),ss3(2000),ss4(2000), + Suml, + Sum2, + Sum3, + Sum4, + h a l f , l a s t , z e r o , a j f i l e r e a l * 8 two,three, four,six,ddata(120,2000) integer*4 data(2000) i n t e g e r s jmax, j f i 1 e, iaa, jk, j j j , j j i real*4 disp(120),datal(120),y(120) real*8 median,smed(2000),med(2000) c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c data scale /504000./ data half/.5d00/ data zero/.0d00/ data two/2.d00/ data three/3.dOO/ data four/4.dOO/ data six/6.dOO/ c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c c a l l r e a d f i l e ( I n p u t F i l e . j f i l e ) a j f i l e = d f l o a t ( j f i l e ) jmax=2000 do 110 j=l,jmax sum(j)=zero 110 end do c do 120 j f = l , j f i l e write(6,7600)InputFile(jf) 7600 formatC Opening f i l e \a60) cal1 inputf(InputFile(jf),data,jmax) do 120 j=l,jmax d d a t a ( j f , j ) = d f l o a t ( d a t a ( j ) ) / s c a l e sum ( j ) =sum ( j ) +ddata ( j f, j ) 167 120 end do write(6,123)l,sum(2) write(6,123)2,sum(2) write(6,123)5.sum(10) write(6,123)10,sum(20) write(6,123)20,sum(40) write(6,123)50,sum(lOO) write(6,123)100,sum(200) write(6,123)200,sum(400) write(6,123)300,sum(600) write(6,123)400,sum(600) 123 format(i5,' lOC^meanV , f8.2) do 1000 j=l,jmax suml=sum(j)/ajf i l e sum2=zero sum3=zero sum4=zero do 500 j k = l , j f i l e datal(jk)=ddata(jk,j) y ( j k ) = f l o a t ( j k ) sum2=sum2+(ddata(jk,j)-suml)**2 sum3=sum3+(ddata(jk,j)-suml)**3 sum4=sum4+(ddata(jk,j)-suml)**4 500 end do sum2=dsqrt(sum2/ajf i1e) sum3=sum3/ajfile sum4=sum4/ajf i l e sum3=sum3/sum2**3 sum4=sum4/sum2H^4-3 c a l l s s o r t ( d a t a l , y , j f i l e , 2 ) j j j = j f i l e / 2 i f ( 2 * j j j . e q . j f i l e ) then median=.5*(datal(j j j ) + d a t a l ( j j j+1)) el s e median=datal(j j j+1) end i f med(j)=median do 450 j j i = l , j f i l e d i sp(j j i)=dabs(ddata(j j i,j)-med(j)) 450 end do c a l l s s o r t ( d i s p , y , j f i l e , 2 ) j j j = j f i l e / 2 i f ( 2 * j j j . e q . j f i l e ) then median=.5*(disp(j j j)+di sp(j j j+1)) el s e median=di s p ( j j j+1) end i f smed(j)=median wr i te(6,8000)suml,sum2,sum3,sum4,med(j),smed(j) 8000 format(6(fl2.7,x)) ss2(j)=sum2 168 ss3(j)=sum3 ss4(j)=sum4 ssl(j)=suml 1000 end do c c c c open(unit=3,file='statcurve.out',status='new') c w r i t e ( 3 , 1 5 6 0 ) j f i l e c 1560 format(//' S t a t i s t i c s on pressure trace',//, c +' Number of sets i n sample:',i4,//, c +' P/P at ign. time (%) Mean (ms) ', c +5x,' Standard Deviation (ms)',5x,' Skewness f a c t o r ' , c +10x,' Kurtosis',/) c do 155 j=l,jmax c aa=float(j)/2 c w r i t e ( 3 , 1 5 7 0 ) a a , s s l ( j ) , s s 2 ( j ) , s s 3 ( j ) , s s 4 ( j ) c 1570 format(5x,f7.1.2x,3(12x,f8.3)) c 155 end do c close(3) outputf ile='kurt.dat' c a l l storereal(outputfile,ss4,jmax) outputf ile='skew.dat' cal1 storereal(outputf ile,ss3,jmax) outputfile='stdd.dat' cal1 storereal(outputf ile,ss2,jmax) outputf ile='mean.dat' c a l l s t o r e r e a l ( o u t p u t f i l e , s s l , j m a x ) outputf ile='med.dat' cal1 storereal(outputf ile,med,jmax) outputf ile='smed.dat' c a l l storereal(outputfile,smed,jmax) 90 end c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c Subroutine Storereal(filename,data,j) c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c CharacterX-120 Filename real*8 Data(2000) c c c c c open(unit=9,f ile=f ilename,form='formatted',status='new') w r i t e ( 9 , 1 0 ) ( d a t a ( i ) , i = l , j ) 10 format(10fl2.6,' ') 169 close(9) return end c c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c Subroutine inputf(filename,data,j) c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c Character*120 Filename Integer*4 data(2000), + J character*120 t r a s h l integer*4 trash2 real*4 datal(2000) c c c c Open (unit=9,file=filename,form=*formatted*,status='old") read(9,10,err=20)(datal(i),i=l,j) 10 format(10fl0.3) goto 30 20 continue j = i - l 30 close(9) do 40 j j = l , j d a t a ( j j ) = i f i x ( d a t a l ( j j)*2520) 40 end do return end c c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c subroutine readfile(names,nfile) c c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c character*120 names(120), + answer character*20 InputFilei,InputFile2,outputf i l e integer*4 n f i l e c c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 170 nf ile=0 open(unit=9,f ile = ' f ilenames.1st *,form='formatted', +status='old',readonly) 10 read(9,8001)InputFilei,InputFile2,outputfile 8001 format(3a20) Answer=InputFilei c a l l str$upcase(Answer.Answer) i f ( Answer(l:l) .ne. 'E') then nfile=nf ile+1 names(nfile)=outputfile goto 10 endif close(9) return end c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 171 Appendix D Smoothing by spl i n e s : Program SMOOTH Function To smooth data f i l e s l i k e the v e l o c i t y traces, producing p l o t s more e a s i l y d i s t i n g u i s h a b l e between d i f f e r e n t cases. Input Names of the f i l e s to be read, and of the f i l e s containing smooth data, to be created. The x - f i l e i s not a data f i l e , but the sequence of x-values to which the sequence of y-values corresponds, and can e a s i l y be created by a simple program. Output The f i l e of smoothed data, with a s p e c i f i e d number of points, abd the name given i n answer to the prompts. 172 cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx C C c c Program SMOOTH smooths data by cubic s p l i n e s c c c cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx c c real*4 x(4000),y(4000),b(2004),w(40000),work(12) rea l * 4 xmin.xx.xl,xd,sd(4000),t(2020) integer*4 n, imax, iout, i i , i , im, j ,k, inev, i a t ,nbk character*20 inputx,inputy,output,answer,outputx c c c data sd/4000*0.0/ c c c write(6,8000) 8000 format(//,* Enter the names of the x - f i l e , the y - f i l e + and the o u t p u t f i l e s ' ) read(6,8010)inputx,inputy,output,outputx 8010 format(a20) write(6,8030) 8030 format(/,' How many points do you want, s t a r t i n g x>than? ' + ,$) read(6,8040)imax,xmin 8040 format(i5,/fl0.3) write(6,8045) 8045 format(' How many p o i n t s / i n t e r v a l s ? ',$) read(6,8300)iat i f (imax.gt.3999) imax=3999 open(uni t=3,f ile=inputx,status='old',readonly) read(3,8050,err=100)(x(i),i=l.3999) close(3) 100 im=i-l open(unit=3,f ile=inputy,status='old',readonly) read(3,8050,err=l10)(y(i),i=l,im) 110 im=i-l 8050 format(10f8.0) close(3) do 200 i=l,im if(x(i).ge.xmin) goto 210 200 end do stop 210 i f ( i . e q . l ) then i f (imax.gt.im) imax=im goto 301 endif 173 do 300 ii=i,i+imax-1 i f ( i i . g t . i m ) goto 299 x ( i i - i + l ) = x ( i i ) y ( i i - i + l ) = y ( i i ) 300 end do goto 301 299 imax=im-i 301 continue write (6,7777)im,i,imax 7777 format(* im=', i 6 , ' i= ' , i 6 , ' imax= ',i6) c write(6,7778)(i,x(i),y(i).i=l,imax) c 7778 format(i6,2fl0.4) do 305 i=4,2005 i f (iat*(i-4)+l.gt.imax) goto 306 t ( i ) = x ( i a t * ( i - 4 ) + l ) 305 end do 306 nbk=i+3 do 307 i=nbk-3,nbk t ( i ) = 2 * t ( i - l ) - t ( i - 2 ) 307 end do do 310 1=1.3 t ( 4 - i ) = 2 * t ( 5 - i ) - t ( 6 - i ) 310 end do write(6,7779)(t(i),i=l.nbk) 7779 format(10f8.2) write(6,8300)nbk cal1 efc(imax,x,y,sd,4.nbk,t,1,m,b,40000,w) write(6,8200) 8200 format(' How many data points i n the output? ',$) read(6,8300)iout 8300 format(i5) xd=(x(imax)-x(1))/(iout-1) x l = x ( l ) inev=l do 400 i = l , i o u t xx=xl+(i-l)*xd y(i)=bvalu(t,b,nbk-4,4,0,xx,inev,work) write(6,7000)xx,y(i) 7000 format(10f8.3) x(i)=xx 400 end do open(unit=3,f ile=output,form="formatted',status= +'new') write ( 3 , 7 1 0 0 ) ( y ( i ) , i = l , i o u t ) close(3) open(unit=3,f ile=outputx,form=* formatted',status= +'new') write(3,7100)(x(i),i=l,iout) close(3) 7100 format(2fl0.4) end 174 

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