UBC Theses and Dissertations

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UBC Theses and Dissertations

Study of cylindrical imploding detonations Huni, Jean Paul R. 1970

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A s t u d y of CYLINDRICAL IMPLODING DETONATIONS by J e a n - P a u l R. H u n i B. A. Sc., 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 , 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n t h e department o f PHYSICS We a c c e p t t h i s t h e s i s as c o n f o r m i n g to. t h e r e q u i r e d s t a n d a r d -THE UNIVERSITY OF BRITISH COLUMBIA June, 1970 In presenting th i s thes is in pa r t i a l f u l f i lmen t o f the requirements fo r an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make i t f r ee l y ava i l ab le for reference and study. I fur ther agree that permission for extensive copying o f th i s thes is for scho la r l y purposes may be granted by the Head of my Department or by h is representat ives . It is understood that copying or pub l i ca t ion of th is thes is fo r f inanc ia l gain sha l l not be allowed without my wr i t ten permiss ion. Department of ^ x y £ U S> The Univers i ty of B r i t i s h Columbia Vancouver 8, Canada Date i i ABSTRACT The t h e o r y of i m p l o d i n g d e t o n a t i o n s p r e d i c t s a f o c u s i n g e f f e c t by which the t e m p e r a t u r e , the p r e s s u r e and the f r o n t v e l o c i t y a r e d r a s t i c a l l y i n c r e a s e d as the f r o n t r e a c h e s the c e n t e r of i m p l o s i o n . We have v e r i f i e d t h i s e f f e c t i n c y l i n d r i c a l i m p l o d i n g d e t o n a t i o n s by measuring the f r o n t v e l o c i t y , the p r e s s u r e and the t e m p e r a t u r e . The v e l o c i t y measurements, which a r e the f i r s t of t h e i r k i n d , and the p r e s s u r e measurements, which agree w i t h the p r e v i o u s r e s u l t s o b t a i n e d by Lee e t a l / l / , both c o n f i r m the t h e o r y q u a n t i t a t i v e l y . The t e m p e r a t u r e measurements, on the o t h e r hand, a r e i n c o n c l u s i v e due t o the f a c t t h a t t h a r m a l e q u i l i b r i u m i s not a t t a i n e d i n the v i b r a -t i o n a l l e v e l s of the m o l e c u l e s of the r e a c t i o n p r o d u c t s . Two u s e f u l a p p l i c a t i o n s of the d e t o n a t i o n p r o p e r t i e s a r e p r e s e n t e d : 1) A method of g e n e r a t i n g p l a n e h y p e r s o n i c shock waves w i t h a c y l i n d r i c a l i m p l o d i n g d e t o n a t i o n was develox^ed and 2) plane d e t o n a t i o n s were used t o c a l i b r a t e p i e z o e l e c t r i c p r e s s u r e probes i n a h i g h p r e s s u r e r a n g e . i i i TABLE OF CONTENTS' Pa g e ABSTRACT i i TABLE OF CONTENTS i i i L I S T OF TABLES " v i L I S T OF FIGURES v i i ACKNOWLEDGEMENTS x i i CHAPTER 1 I n t r o d u c t i o n • 1 CHAPTER 2 T h e o r y 4 2-1 P l a n e d e t o n a t i o n s 4 2-2 The C.C.W. m o d e l o f an i m p l o d i n g d e t o n a t i o n 10 CHAPTER 3 G e n e r a t i o n o f c o n c e n t r i c d e t o n a t i o n s - - 23 CHAPTER 4 S p a c e - t i m e m e a s u r e m e n t s -• 28 4-1 Q u a l i t a t i v e s u r v e y w i t h t h e i m a g e c o n v e r t e r 29 4-2 Q u a n t i t a t i v e c o m p a r i s o n o f t h e C.C.W. m o d e l w i t h e x p e r i m e n t 39 4-3 S p a c e - t i m e m e a s u r e m e n t s 48 4-4 S t a b i l i t y 53 4- 5 The l a r g e c hamber 54 CHAPTER 5 P r e s s u r e m e a s u r e m e n t s 57 5- 1 - E x p e r i m e n t a l s e t - u p 57 5-2 Q u a l i t a t i v e r e s u l t s 58 5-3 C o m p a r i s o n w i t h t h e t h e o r y 62 i v CHAPTER 6 S p e c t r u m o f i m p l o d i n g d e t o n a t i o n s 65 6-1 E x p e r i m e n t a l s e t - u p 65 6-2 D i s c u s s i o n o f t h e s p e c t r a 66 6- 3 R i c h a n d l e a n m i x t u r e s 69 CHAPTER 7 T e m p e r a t u r e m e a s u r e m e n t s 71 7- 1 T h e o r y o f m e a s u r e m e n t s 7 2 7-2 Time i n t e g r a t e d t e m p e r a t u r e 76 7-3 S p a c e - t i m e r e s o l v e d " m e a s u r e m e n t s 79 7-4 R e s u l t s 84 7-5 D i s c u s s i o n o f t h e r e s u l t s 87 7- 6 D i s c u s s i o n o f some o t h e r a s s u m p t i o n s 91 AP P L I C A T I O N S 94 CHAPTER 8 An i m p l o d i n g d e t o n a t i o n d r i v e r - 9 5 8- 1 T e r m i n o l o g y 95 8-2 E x p e r i m e n t a l s e t - u p 97 8-3 P e r f o r m a n c e o f t h e s h o c k t u b e 99 8-4 Comments on t h e r e s u l t s 105 8- 5 Summary 111 CHAPTER 9 A p p l i c a t i o n a n d p r o p e r t i e s o f p l a n e d e t o n a t i o n s 112 9- 1 H i g h p r e s s u r e c a l i b r a t i o n o f a p i e z o e l e c t r i c p r o b e 112 9- 2 P r o p a g a t i o n a n d p r o p e r t i e s o f p l a n e d e t o n a t i o n s 117 CHAPTER 10 C o n c l u s i o n s a n d s u g g e s t i o n s f o r f u t u r e w o r k — 12 9 10- 1 C y l i n d r i c a l i m p l o s i o n s 129 10-2 A p p l i c a t i o n s 130 V BIBLIOGRAPHY . 1 3 2 APPENDIX A The d e t o n a t i o n chambers 13 5 APPENDIX B G e n e r a l l a y - o u t and t r i g g e r i n g c i r c u i t l 4 4 APPENDIX C The smear camera 147 APPENDIX D D-l C a l i b r a t i o n of t h e space a x i s 158 D-2 O f f - a x i s e f f e c t s 161 APPENDIX E The p i e z o e l e c t r i c p r e s s u r e probe 164 APPENDIX F The Chapman-Jouguet s t a t e 169 v i LIST OF TABLES T a b l e I F r o n t v e l o c i t y and t o t a l l i n e a r t i m e a t v a r i o u s p r e s s u r e s c o l l a p s e Page 51 v i i LIST OF FIGURES Page 2-1 D i s c o n t i n u i t y f r o n t v i e w e d from a frame o f r e f e r e n c e moving a l o n g w i t h i t 6 2-2 The case o f c y l i n d r i c a l i m p l o s i o n 12 2-3 Gas d e n s i t y b e h i n d an i m p l o d i n g d e t o n a t i o n as f u n c t i o n of r a d i u s 17 2-4 P r e s s u r e o f an i m p l o d i n g d e t o n a t i o n as f u n c t i o n o f r a d i u s 18 2-5 V e l o c i t y o f an i m p l o d i n g d e t o n a t i o n as f u n c t i o n o f r a d i u s 19 2-6 Gas t e m p e r a t u r e b e h i n d an i m p l o d i n g d e t o n a t i o n as f u n c t i o n o f r a d i u s 20 2- 7 T h e o r e t i c a l i m p l o s i o n c u r v e o f a d e t o n a t i o n 22 3- 1 T y p i c a l chamber t o g e n e r a t e i m p l o d i n g d e t o n a t i o n s u s i n g t h e d e f l e c t i o n p l a t e t e c h n i q u e 24 3-2 S e c t i o n o f t h e l a r g e chamber 26 3- 3 S e c t i o n o f t h e s m a l l chamber 26 4- 1 E x p e r i m e n t a l s e t - u p . w i t h t h e image c o n v e r t e r 29 4-2 Image c o n v e r t e r photographs o f an i m p l o d i n g d e t o n a t i o n 31 4-3 r - t p l o t o f an i m p l o d i n g d e t o n a t i o n 32 4-4 I m p l o d i n g d e t o n a t i o n and d e f l a g r a t i o n 34 4-5 I m p l o d i n g d e f l a g r a t i o n a t v a r i o u s p r e s s u r e s showing t h e t r a n s i t i o n t o d e t o n a t i o n 35 4-6 . r-t__.plot-.f.or.„implo.sions a t v a r i o u s p r e s s u r e s 37 4-7 I m p l o s i o n s i n s t o i c h i o m e t r i c oxy-hydrogen 40 4-8 E x p e r i m e n t a l s e t - u p f o r t h e smear camera 42 v i i i 4-9 Low sweep speed smear p h o t o g r a p h o f an i m p l o d i n g d e t o n a t i o n i n e q u i m o l a r oxy-a c e t y l e n e m i x t u r e 43 4-10 I m p l o d i n g d e t o n a t i o n i n r i c h and l e a n m i x t u r e s 45 4-11 C l o s e - u p o f t h e i m p l o s i o n i n l e a n oxy-a c e t y l e n e m i x t u r e 47 4-12 C l o s e - u p o f an i m p l o d i n g d e t o n a t i o n i n -equimolar o x y - a c e t y l e n e m i x t u r e . N e u t r a l d e n s i t y f i l t e r s p l a c e d on t h e s l i t 50 4-13 Enlargement o f a smear p h o t o g r a p h o f an i m p l o d i n g d e t o n a t i o n i n e q u i m o l a r oxy-a c e t y l e n e gas 52 4- 14 I m p l o d i n g d e t o n a t i o n i n t h e l a r g e chamber 56 5- 1 P r e s s u r e d i s t r i b u t i o n i n t h e l a r g e chamber 60 5-2 P r e s s u r e d i s t r i b u t i o n i n t h e s m a l l chamber 61 5- 3 V a r i a t i o n o f t h e d e t o n a t i o n p r e s s u r e w i t h r a d i u s 63 6- 1 E n l a r g e d spectrum o f an i m p l o d i n g d e t o n a t i o n i n e q u i m o l a r o x y - a c e t y l e n e ( N o f o c u s i n g l e n s ) 67 6- 2 S p e c t r a o f i m p l o d i n g d e t o n a t i o n s f o r v a r i o u s gas c o m p o s i t i o n s 68 7- 1 S l o p e o f t h e l o g i n t e n s i t y c u r v e of t h e CN band a t 3810 A 74 7-2 P l o t o f Watson's d a t a on l o g - l o g s c a l e s 74 o 7-3a' P r o f i l e o f t h e 3865.5 A Fe l i n e t a k e n w i t h a 25u s l i t and scanned w i t h a 7u s l i t 77 7-3b Maximum i n t e n s i t y and h a l f - w i d t h o f t h e — -Fe--3-8-65-. 5 A l i n e as a f u n c t i o n o f t h e s l i t w i d t h o f t h e s p e c t r o g r a p h 77 7-4 T y p i c a l p l a t e o f t h e CN v i o l e t system used i n "the' t e m p e r a t u r e measurements 8 0 7-5 E x p e r i m e n t a l s e t - u p f o r t h e t i m e r e s o l v e d t e m p e r a t u r e measurements 80 i x 7-6 T y p i c a l i n t e n s i t y v a r i a t i o n s o f t h e CN band a t 3790 A a t t h r e e r a d i a l p o s i t i o n s 83 7-7 Temperature p r o f i l e s i n t h e chamber 85 7-8 Temperature p r o f i l e s a t R=0 and 10 mm 86 7- 9 I n t e n s i t y o f t h e r o t a t i o n a l l i n e s o f t h e P and R branches i n a r o t a t i o n a l band as f u n c t i o n o f w a v e l e n g t h ' 89 8- 1 S k e t c h o f a p r e s s u r e d r i v e n shock tube 96 8-2 S k e t c h o f a shock tube u s i n g t h e d e t o n a t i o n chamber as a d r i v e r 98 8-3 Smear photographs o f a shock wave 100 8-4 Smear pho t o g r a p h o f a shock wave 100 8-5 Mach number v e r s u s p r e s s u r e r a t i o 102 8-6 Mach number v e r s u s p r e s s u r e r a t i o 103 8-7 Mach number v e r s u s p r e s s u r e r a t i o 104 8-8 Open s h u t t e r p h o t o g r a p h of t h e d r i v e r f i r e d i n open a i r 108 8-9 B r a s s membranes 108 8- 10 One of t h e ' s t r a n g e ' smear ph o t o g r a p h s o b t a i n e d w i t h b r a s s membranes 108 9- 1 P r e s s u r e probe c a l i b r a t i o n s e t - u p 115 9-2 V e l o c i t y o f a p l a n e d e t o n a t i o n v e r s u s p r e s s u r e 116 9-3 P r e s s u r e r a t i o and f i n a l p r e s s u r e v e r s u s i n i t i a l p r e s s u r e f o r a p l a n e d e t o n a t i o n 116 — 9 - 4 Voltage--output o f t h e probe v . s . p r e s s u r e s t e p ( C h e c k on t h e l i n e a r i t y o f probe) 118 9-5 V o l t a g e o u t p u t o f t h e probe v . s . p r e s s u r e s t e p " ( C a l i b r a t i o n c u r ve) 118 X 9-6 P l o t o f 1/PiV 0" 2 v e r s u s V t o check on s s Fay's boundary l a y e r t h e o r y 120 9-7 D e t o n a t i o n s p i n 122 9-8 D e t o n a t i o n and r e f l e c t e d shock wave 124 9-9 V e l o c i t y o f r e f l e c t e d shock wave,V , v e r s u s f r a c t i o n a l d i s t a n c e i n t h e r a r e f a c t i o n wave, x 126 9.-10 P r e s s u r e r e c o r d s o f low p r e s s u r e d e t o n a t i o n s t a k e n w i t h a p i e z o e l e c t r i c p r e s s u r e gauge 129 A - l S e c t i o n o f t h e l a r g e chamber 136 A-2 Blow-up v i e w o f t h e s p a r k gap 137 A-3 F r o n t p l a t e used i n t h e p r e s s u r e measurements 138 -A-4 S e c t i o n o f t h e shock tube a t t a c h e m e n t s 139 A-5 Back v i e w o f t h e s m a l l chamber 141 A-6 S e c t i o n A-A' o f t h e s m a l l chamber 142 A-7 S e c t i o n o f t h e q u a r t z window h o l d e r 143 A-8 S e c t i o n o f one o f t h e l u c i t e i n s e r t s used i n t h e p r e s s u r e measurements.close t o t h e c e n t e r o f i m p l o s i o n 143 B - l G e n e r a l l a y - o u t o f t h e a p p a r a t u s 145 B-2 C i r c u i t d i a g r a m o f t h e i g n i t i o n system 146 C - l G e n e r a l l a y - o u t o f t h e camera 148 C-2 R o t o r v i e w a l o n g t h e m i r r o r a x i s 151 C-3 R o t o r , s e c t i o n A-A' 152 C-4 R o t o r , s e c t i o n B-B' 152 C-5 Rotor-motor assembly 154 D - l M a g n i f i c a t i o n v a r i a t i o n s a l o n g t h e s l i t 159 D-2 O f f - a x i s e f f e c t s (not t o s c a l e ) 162 x i E - l D e t a i l s o f t h e probe j u n c t i o n 165 E-2 C o n s t r u c t i o n d e t a i l s o f t h e p r e s s u r e probe h o u s i n g 16 6 E-3 P h o t o g r a p h o f t h e p r e s s u r e probe 167 E-4 T y p i c a l r e s p o n s e o f t h e p r e s s u r e probe t o a p r e s s u r e s t e p g e n e r a t e d by a d e t o n a t i o n .167 F - l A d e t o n a t i o n p r o p a g a t i n g i n a gas i n i t i a l l y a t r e s t 170 F-2 G r a p h i c a l r e p r e s e n t a t i o n o f the Tode l i n e s and Hugoniot a d i a b a t i c s i n a P-v plane 172 X l l ACKNOWLEDGEMENTS I would l i k e t o take t h i s o p p o r t u n i t y t o e x p r e s s my g r a -t i t u d e f o r the i n v a l u a b l e , p a t i e n t and . . e n t h u s i a s t i c g uidance of my r e s e a r c h s u p e r v i s o r , Dr. B. A h l b o r n whose s u g g e s t i o n s and encouragements over a f o u r year span made t h i s work p o s s i b l e . I am a l s o d e e p l y i n d e b t e d t o Dr. F.L. Curzon f o r h a v i n g s u p e r -v i s e d the f i n a l p r e p a r a t i o n of the t h e s i s d u r i n g the absence of Dr. B. A h l b o r n . I am a l s o g r a t e f u l f o r v a l u a b l e comments made by my e x t e r n a l examiner Dr. I . I . G l a s s . •s I would a l s o l i k e t o thank Mr. R. A r d i l a whose c o o p e r a -t i o n i n the p r e s s u r e measurements g r e a t l y f a c i l i t a t e d my t a s k . I am g r a t e f u l f o r the many d i s c u s s i o n s h e l d w i t h most of the members o f the plasma p h y s i c s group, i n p a r t i c u l a r Dr. M. P h i l l i p s and Mr. J.D. S t r a c h a n . I n v a l u a b l e d i s c u s s i o n s were a l s o h e l d w i t h Dr. F.W. Da l b y about the spectrum of the d i s c h a r The c h e e r f u l a s s i s t a n c e of the t e c h n i c a l s t a f f i s g r a t e -f u l l y acknowledged, i n p a r t i c u l a r Mr. D. S t o n e b r i d g e - f o r h a v i n g b u i l d the l a r g e chamber, and Mr. R. H a i n e s - f o r h i s h e l p i n the s t u d e n t machine shop. My thanks a l s o go t o our e l e c t r o n i c t e c h n i c i a n s , Mr. D. S i e b e r g and Mr. J . Aazam f o r b u i l d i n g and m a i n t a i n i n g the e l e c t r o n i c s of the e x p e r i m e n t . F i n a l l y I am g r a t e f u l t o the N a t i o n a l R e s e a r c h C o u n c i l o f Canada f o r the f i n a n c i a l h e l p thoughout the 'course 6f t h i s work. - 1 -CHAPTER 1 INTRODUCTION The s e a r c h f o r h i g h d e n s i t y and t e m p e r a t u r e plasmas r e q u i r e d f o r n u c l e a r f u s i o n l e a d , a t an e a r l y s t a g e , t o the use of f a s t i m p l o d i n g waves. T h e o r e t i c a l models of such waves /I,18,19,20,61,62,63,64/ p r e d i c t v e r y l a r g e i n c r e a s e i n t e m p e r a t u r e , p r e s s u r e and f r o n t v e l o c i t y and s i g n i f i c a n t i n c r e a s e i n d e n s i t y a t the f o c u s of i m p l o s i o n . C o n c e n t r i c i n p l o d i n g waves, m o s t l y c y l i n d r i c a l , have been g e n e r a t e d i n a v a r i e t y of d e v i c e s which may be c l a s s i f i e d i n t h r e e groups a c c o r d i n g t o the type of energy used. T h i s energy can be e l e c t r i c a l , m e c h a n i c a l or c h e m i c a l . Examples of the f i r s t group a r e the w e l l known Z- and 9 - p i n c h e s and more r e c e n t l y the plasma f o c u s . The second c l a s s i s r e p r e s e n t e d by p r e s s u r e d r i v e n shock waves p r o p a g a t i n g i n c o n v e r g i n g c h a n n e l s /65,66/. Machines making use of e i t h e r s o l i d or gaseous e x p l o s i v e s a r e examples of the t h i r d group. For example, a t UTIAS ( U n i v e r s i t y of T o r o n t o I n s t i t u t e f o r A e r o s p a c e S t u d i e s ) c o n v e r g i n g shocks a r e g e n e r a t e d by r e f l e c t i n g r a d i a l l y d i v e r g e n t d e t o n a t i o n waves from the w a l l s of s p h e r i c a l c o n t a i n e r s which a r e e i t h e r m e t a l or m e t a l l i n e d w i t h s o l i d e x p l o s i v e l a y e r s . E x c e l l e n t r e p o r t s , both t h e o r e t i c a l and e x p e r i m e n t a l , can be found i n the UTIAS - 2 -l i t e r a t u r e w hich i s l i s t e d i n the UTIAS A n n u a l P r o g r e s s R e p o r t s . Some of the major c o n t r i b u t o r s are I . I . G l a s s , R. F. F l a g g , A . B e n o i t , A. K. Macpherson, J . C. P o i n s s o t and many o t h e r s . C y l i n d r i c a l i m p l o s i o n s have a l s o been g e n e r a t e d by making use of s o l i d e x p l o s i v e s /67/ and gaseous d e t o n a t i n g m i x t u r e s /1,68/. In c o n t r a s t t o the work done a t UTIAS, we have devoted our a t t e n t i o n t o the dynamics of the i m p l o d i n g d e t o n a t i o n wave i n gaseous m i x t u r e s . A l t h o u g h the o r i g i n a l aim o f p r o d u c i n g a f u s i o n plasma has been p a r t i a l l y l o s t i n t h i s type of r e s e a r c h , the dy-namics of h y d r o c a r b o n d e t o n a t i o n s a r e i n many r e s p e c t s s i m -i l a r t o t h o s e of t h e r m o n u c l e a r d e t o n a t i o n s /2/, t h u s , the s t u d y o f i m p l o d i n g d e t o n a t i o n s i n h y d r o c a r b o n s does not l a c k i n t e r e s t f o r the plasma p h y s i c i s t . The absence of e l e c t r o -magnetic f i e l d s , the e x c e l l e n t s t a b i l i t y and r e p r o d u c i b i l i t y and the ease w i t h which d e t o n a t i o n s can be g e n e r a t e d , make them i d e a l f o r the g e n e r a l s t u d y o f the dynamics of i m p l o s i o n s i n t h e o r y and e x p e r i m e n t s . The v e r y h i g h p r e s s u r e s (about 10^ atm) and moderate t e m p e r a t u r e s (about 1 0 4 °K) d e v e l o p e d a t the i m p l o s i o n f o c u s , y i e l d a plasma not r e a d i l y a t t a i n e d w i t h such cheap f a c i l i t y . These extreme c o n d i t i o n s might prove a t t r a c t i v e f o r s p e c t r o s c o p i c o b s e r v a t i o n s as w e l l as plasma c h e m i s t r y i n y e a r s t o come. ~The - t h e o r e t i c a l model of c y l i n d r i c a l i m p l o d i n g d e t o n a -t i o n s d e v e l o p e d by Lee e t a l /!/, p r e d i c t s the v a r i a t i o n s o f - 3 -t h e f l o w q u a n t i t i e s a t t h e d e t o n a t i o n f r o n t as a f u n c t i o n o f t h e r a d i a l p o s i t i o n o f t h e f r o n t . S i n c e some t h e o r e t i c a l b ackground i s needed i n t h e u n d e r s t a n d i n g o f i m p l o d i n g d e t -o n a t i o n s , we have i n c l u d e d i n the' body of t h i s t h e s i s a d e r i -v a t i o n o f Lee's model c a l c u l a t i o n s i n c h a p t e r 2. — A l t h o u g h a p a r t i a l v e r i f i c a t i o n o f t h i s model was done by Lee h i m s e l f / l / , we s e t o u t t o show t h e r e l e v a n c e o f t h e t h e o r y by d o i n g a comprehensive s t u d y o f t h e i m p l o d i n g d e t -o n a t i o n . T h i s i n v o l v e d s p a c e - t i m e and t e m p e r a t u r e measure-ments ( c h a p t e r s 4 , 6 and 7 ) . Lee's o r i g i n a l p r e s s u r e measure--ments were a l s o r e p e a t e d ( c h a p t e r 5 ) w i t h a h i g h s p a c i a l and t e m p o r a l r e s o l u t i o n p i e z o e l e c t r i c p r e s s u r e probe w h i c h had been c a l i b r a t e d f o r h i g h p r e s s u r e s by making use of p l a n e d e t o n a t i o n s ( c h a p t e r 9 ) . A p r a c t i c a l a p p l i c a t i o n o f t h e h i g h p r e s s u r e and tem-p e r a t u r e plasma at' t h e f o c u s o f t h e i m p l o s i o n i s g i v e n i n c h a p t e r 8 w h i c h p r e s e n t s t h e p e r f o r m a n c e s o f a p r e s s u r e d r i v e n shock tube u s i n g the c y l i n d r i c a l i m p l o d i n g d e t o n a t i o n as a d r i v e r . D e t a i l e d d e s c r i p t i o n of the equipment i s g i v e n i n appen-d i x form. The d e v i c e used i n the p r o d u c t i o n of the i m p l o d i n g d e t o n a t i o n s i s d i s c u s s e d i n c h a p t e r 3. - 4 -CHAPTER 2 THEORY The purpose o f t h i s c h a p t e r i s t o d e v e l o p a s e t o f e q u a t i o n s w h i c h w i l l d e s c r i b e the b e h a v i o u r o f the f l o w q u a n t i t i e s , p r e s s u r e , t e m p e r a t u r e , d e n s i t y , p a r t i c l e and f r o n t v e l o c i t i e s j u s t b e h i n d t h e i m p l o d i n g d e t o n a t i o n f r o n t . I n t h e f i r s t s t e p o f t h i s d e r i v a t i o n , t h e c o n s e r v a t i o n e q u a t i o n s o f mass, momentum and energy a c r o s s a d i s c o n t i -n u i t y f r o n t w i t h energy i n p u t a r e s e t up and t h e g e n e r a l s o l u t i o n s o f t h i s s e t o f e q u a t i o n s , t h e R a n k i n e - H u g o n i o t r e l a t i o n s , a r e s p e c i a l i z e d t o t h e case o f s t r o n g d e t o n a t i o n s . I n t h e second s t e p , t h e c o n s e r v a t i o n e q u a t i o n s a r e used i n c h a r a c t e r i s t i c form t o d e s c r i b e t h e gas f l o w b e h i n d t h e . d i s c o n t i n u i t y f r o n t . The R a n k i n e - H u g o n i o t r e l a t i o n s a r e the n used t o r e l a t e t h e f l o w q u a n t i t i e s o f t h e c h a r a c t e r i s t i c e q u a t i o n s t o t h e c o n d i t i o n s o f t h e u n p e r t u r b e d gas ahead o f t h e d e t o n a t i o n f r o n t . 2-1 PLANE DETONATIONS: — D e t o n a t i o n waves a r e o b s e r v e d i n many c o m b u s t i b l e gases w i t h i n a c e r t a i n range o f c o m p o s i t i o n . S e l f - s u p p o r t e d d e t -o n a t i o n s p r o p a g a t e w i t h a c o n s t a n t , s u p e r s o n i c v e l o c i t y w h i c h i s dependent on the gas m i x t u r e but r e l a t i v e l y i n s e n s i t i v e t o v a r i a t i o n s of the i n i t i a l p r e s s u r e . A l a r g e p r e s s u r e - 5 -i n c r e a s e i s a l s o o b s e r v e d i n t h i s mode o f co m b u s t i o n . These f a c t s were r e p o r t e d i n the f i r s t papers on d e t o n a t i o n s /3,4/. S i n c e t h e n , d e t o n a t i o n s have been s t u d i e d e x t e n s i v e l y and many well-documented a c c o u n t s can be found./5 t o 13/. One o f t h e f i r s t problems e n c o u n t e r e d i n t h e s t u d y o f t h i s mode o f combustion was t o f i n d a mechanism w h i c h would r a i s e t h e te m p e r a t u r e o f t h e c o l d gas above t h e spontaneous t h e r m a l i g n i t i o n p o i n t . From p u r e l y p h y s i c a l arguments /14/, and more r i g o r o u s m a t h e m a t i c a l t r e a t m e n t / 5 / , i t can be shown t h a t t h e r m a l c o n d u c t i o n and d i f f u s i o n e f f e c t s a r e n e g l i g i b l e i n d e t o n a t i o n s . T h i s , a l o n g w i t h t h e i r s u p e r s o n i c speed and h i g h p r e s s u r e s , makes d e t o n a t i o n s more a k i n t o shock waves t h a n t o o r d i n a r y f l a m e s . A d e t o n a t i o n c o n s i s t s o f a shock wave i m m e d i a t e l y f o l l o w e d by a zone i n whi c h t h e c h e m i c a l r e a c t i o n t a k e s p l a c e . The shock wave h e a t s and compresses the c o l d gas t o a s t a t e above spontaneous c o m b u s t i o n . The main " d i f f e r e n c e between a d e t o n a t i o n and a shock wave l i e s i n t h e i r mode of p r o p a g a t i o n . An a d i a b a t i c p r e s s u r e d r i v e n shock wave d e r i v e s i t s energy from t h e r a p i d i s e n t r o p i c ex-p a n s i o n o f a h i g h p r e s s u r e - g a s i n t o a low p r e s s u r e r e g i o n . Thus by v a r y i n g t h e r a t i o o f t h e s e p r e s s u r e s , a c o n t i n u o u s - r a n g e o f f r o n t v e l o c i t i e s i s p o s s i b l e . The p r o p a g a t i o n o f a d e t o n a t i o n , on t h e o t h e r hand, depends on t h e d i f f e r e n c e b e t w e e n ' t h e e n e r g y ' r e l e a s e d p e r u n i t mass by t h e c h e m i c a l -— r e a c t i o n and t h e ene r g y - a b s o r b e d t o hea t t h e gas. The d i f f e r -ence i s used t o d r i v e t h e shock wave. S i n c e t h e s e p r o c e s s e s - 6 -a r e a l l n e a r l y l i n e a r l y dependent on the mass d e n s i t y , the speed and te m p e r a t u r e of a d e t o n a t i o n a r e p r a c t i c a l l y i n d e -pendent of the i n i t i a l p r e s s u r e i n which the wave p r o p a g a t e s . The u n i q u e n e s s o f t h e f r o n t v e l o c i t y and o f t h e f i n a l s t a t e o f t h e r e a c t i o n p r o d u c t s i n s e l f - s u s t a i n e d d e t o n a t i o n s have been d i s c u s s e d i n g r e a t d e t a i l by Z e l d o v i c h and o t h e r a u t h o r s /6 t o 15/. I t i s s u f f i c i e n t t o say he r e t h a t t h e c o n d i t i o n o f t h e gas b e h i n d t h e d e t o n a t i o n i s g i v e n by t h e Chapman-Jouguet (C.J.) s t a t e w h i c h c o r r e s p o n d s t o t h e l o w e s t p o s s i b l e wave v e l o c i t y c o m p a t i b l e w i t h t h e c o n s e r v a t i o n equa-t i o n s . T h i s c o n d i t i o n can be s t a t e d i n a n o t h e r but e q u i v a -l e n t way, namely: t h e speed o f a C . J . d e t o n a t i o n w i t h r e s p e c t t o t h e r e a c t i o n p r o d u c t s i s e q u a l t o t h e speed o f sound i n t h i s gas. See Appendix F f o r a d i s c u s s i o n of the C . J . s t a t e . To s e t up the i n t e g r a t e d e q u a t i o n s of c o n s e r v a t i o n , c o n -s i d e r a d i s c o n t i n u i t y w i t h a heat s o u r s e i n a frame of r e f e r -ence i n which the f r o n t i s s t a t i o n a r y as i n f i g u r e 2-1. P 2 ,T 2 , P 2 , h 2 ; U: P i i T i , P i h i Ui D i s c o n t i n u i t y f r o n t F i g u r e 2-1: D i s c o n t i n u i t y f r o n t v iewed from a frame o f r e f e r -ence moving a l o n g w i t h i t . Assuming o n e - d i m e n s i o n a l p l a n e wave geometry, t h e i n t e g r a t e d c o n s e r v a t i o n e q u a t i o n s can be w r i t t e n a s : Mass: P i U i = p 2 U 2 (2-1) Momentum: P i + P1U1 = P 2 + p 2U 2 (2-2) Energy: h i + Q + |u? = h 2 + |u| (2-3) where p, U, P, h and Q a r e t h e d e n s i t y , gas v e l o c i t y , p r e s s u r e , e n t h a l p y and energy r e l e a s e d p e r u n i t mass a t t h e f r o n t . The s u b s c r i p t s 1 and 2 r e f e r t o t h e c o n d i t i o n s o f t h e gas ahead and b e h i n d t h e d i s c o n t i n u i t y f r o n t r e s p e c t i v e l y . These t h r e e e q u a t i o n s c o n t a i n f i v e unknowns, p 2, P 2 , U?_, U i , and h 2 , t h u s one needs two o t h e r r e l a t i o n s i n o r d e r t o s o l v e them e x a c t l y . One r e l a t i o n i s p r o v i d e d by t h e e q u a t i o n o f s t a t e w h i c h can be w r i t t e n a s : ^ - Y P (2-4) Y - l p f o r an i d e a l gas. y i s t h e s p e c i f i c heat r a t i o and i s a c o n s t a n t . I n t h e case o f r e a l g a s e s , however, y i s n o t cons-t a n t and t h e e n t h a l p y can be used t o d e f i n e an e f f e c t i v e a d i a b a t i c exponent, g, such t h a t /16/: (2-4 1) g - i p H e n c e g t a k e s a f u n c t i o n a l dependence on p r e s s u r e and temp-e r a t u r e , i e : g = g ( P , T ) . The second m i s s i n g r e l a t i o n w i l l be i n t r o d u c e d l a t e r - 8 -by making use o f t h e . C . J . c o n d i t i o n w h i c h c o n s i s t s i n making ' t h e f r o n t v e l o c i t y a minimum f o r a g i v e n energy i n p u t , Q. To t h i s end, one f i r s t s o l v e s t h e c o n s e r v a t i o n e q u a t i o n s g e n e r a l l y , k e e p i n g t h e wave v e l o c i t y , U i , as a p a r ameter. The g e n e r a l s o l u t i o n o f e q u a t i o n s ( 2 - 1 ) , ( 2 - 2 ) , (2-3) and (2-4') can be w r i t t e n as / l l / : U2. = £ i _ = l + n ( l . + u ) . (2-5) Ul P2 |i- = 1 - g i M f n ( 1 + u ) (2-6) where _ ( g 2 / giM? ) - 1 o-n\ n ~ g 2 + 1 ' V - [ 1 + e - ? g f M * < g i ~ L\£ 1 4 (2-8) H ( g i - l ) ( g a - g i M i P h i . c = 2 ( g a+D (gi-g2 ) M?gi c?-cj\ ( g i - D ( g 2 - g i M f ) z l z y ; Mi = S i . . a? = g i £ l * (2-10) d l p i where Mi i s t h e Mach number of t h e f r o n t and a j t h e speed of sound i n t h e u n p e r t u r b e d g a s e s . I n s t r o n g d e t o n a t i o n s l i k e o x y - a c e t y l e n e , t h e Mach num-ber i s a t l e a s t 8 so t h a t terms w i t h ^2 may be n e g l e c t e d . W i t h t h i s a p p r o x i m a t i o n , e q u a t i o n s ( 2 - 7 ) , (2-8) and (2-9) r e d u c e t o : 1 (2-11) " . g 2 + 1 * T h i s r e l a t i o n h o l d s e x a c t l y f o r i d e a l gases ( g=y ) but i s o n l y an a p p r o x i m a t i o n f o r r e a l g a s e s . - 9 -y = E !'+ e_ i i a i i p Z i i ] I ( 2_ 1 2 ) e.= 0 (2-13) H e n c e , t h e p r e s s u r e , g a s d e n s i t y a n d g a s v e l o c i t y r a t i o f o r s t r o n g d e t o n a t i o n s r e d u c e t o : U * - £i = i - _ i _ t i + U - 2 ( g l - l ) Q / a f } i ] ( 2 _ 1 4 ) U i p 2 g 2 + l ' M E.2 = 9 ' M i r 1 + I 1 2 ( g l - 1 ) Q/a 2 x ^ l r o - m x P i g 2 + l : Ml ' J J-^; Now we c a n i n t r o d u c e t h e C . J . c o n d i t i o n , t h a t i s , m a k e t h e f r o n t v e l o c i t y U i a minimum. T h i s minimum i s o b t a i n e d when t h e s q u a r e r o o t , i e : y, i n e q u a t i o n (2-14) i s i d e n t i -c a l l y z e r o . L e t t i n g y = 0 i n (2-14) a n d (2-15) we o b t a i n : U 2 = P i = 92 ( 2 _ 1 6 ) U i p 2 g 2 + 1 1.2 = a i M l ' (2-17) P i g i + i ^ ±/; and f r o m y=0 we h a v e t h e s p e e d o f a C . J . d e t o n a t i o n : U i = V C J = [ 2 ( g | - l ) Q ] T (2-18) U s i n g e q u a t i o n s ( 2 - 1 6 ) , (2-17) a n d t h e d e f i n i t i o n (2-9) o f t h e s p e e d o f s o u n d , a 2 c a n be w r i t t e n a s : • a 2 = (Sill) 2 = — 2 2 u i (2-19) p 2 g 2 + 1 . F r o m e q u a t i o n (2-19) a nd e q u a t i o n (2-16) we h a v e , U 2 = a 2 , h e n c e t h e e q u i v a l e n c e o f t h e two s t a t e m e n t s o f t h e C . J . c o n -d i t i o n . T h e d e v i a t i o n s o f y f r o m t h e v a l u e z e r o i n e q u a t i o n - 10 -(2-14) i s t h e r e f o r e a measure o f t h e d e p a r t u r e o f t h e d e t o n a -t i o n .from t h e C.J. s t a t e . 2-2 THE C.C.W. MODEL OF AN IMPLODING DETONATION: I n t h e i m p l o s i o n s o f s u p e r s o n i c waves, one wants t o know th e v a r i a t i o n s o f t h e f r o n t v e l o c i t y and o f p r e s s u r e , d e n s i t y and t e m p e r a t u r e b e h i n d t h e f r o n t as a f u n c t i o n o f t h e r a d i a l p o s i t i o n . Such c a l c u l a t i o n s were f i r s t c a r r i e d o u t by Lee e t a l / l / f o r t h e case o f d e t o n a t i o n s . The model d e v e l o p e d by Lee f o l l o w e d t h e c a l c u l a t i o n s o f C h e s t e r /18/, C h i s n e l l /19/ and Whitham /20/. T h i s "C.C.W." model i s r e d e r i v e d h e r e i n th e form used by Lee. The d i f f e r e n t i a l c o n s e r v a t i o n e q u a t i o n s f o r a q u a s i -one d i m e n s i o n a l gas f l o w w i t h no heat s i n k o r s o u r c e terms can be w r i t t e n a s : Mass d f p D U j p U _ 0 d t > 3 r * r Momentum dU + UjHJ 1 2>P _ Q (2-20) d t T a r T p ?>r w (2-21) Energy de _ P dp _ Q to-oo) d t p 5 d t ^ where p , U, P have t h e same meaning as i n t h e p r e v i o u s s e c t i o n , r and e a r e t h e s p a c i a l c o o r d i n a t e and t h e i n t e r n a l energy r e s p e c t i v e l y , and j i s a c o n s t a n t ( j = 0 , l , 2 f o r p l a n a r , c y l i n -d r i c a l and s p h e r i c a l geometry ). The t o t a l d e r i v a t i v e o f a q u a n t i t y B i s g i v e n by: - 1 1 -| B = | B + U | B = + U B * dr 9t dr t r W i t h t h e e q u a t i o n o f s t a t e and t h e speed o f sound d e f i n i t i o n , e q u a t i o n s (2-20) t o (2-22) r e d u c e t o : P t + Up r + j p S = 0 (2-24) U. + UU +• = 0 (2-25) t r p P . + UP + a 2 ( p , _ + Up- ) = 0 (2-26) t r t M r M a n i p u l a t i n g t h e s e e q u a t i o n s a c c o r d i n g t o t h e e x p r e s s i o n : '[a 2 x eq. (2-24) + eq. (2-26) ] + [±ap x eq.(2-25)] t h e f o l l o w i n g e q u a t i o n i s o b t a i n e d : [ P +(U±a)P ] ± p a [ U +(U±a)U ] + p U a A r = 0 (2-27) t - I" "C 3T A where A=rA^ i s t h e a r e a t h r o u g h w h i c h t h e gas f l o w s i n c y l i n -d r i c a l geometry. E q u a t i o n (2-27) i s e a s i l y r e c o g n i z e d as t h e c o n s e r v a t i o n e q u a t i o n a l o n g the c o n t o u r l i n e s dr/dt=U+a , w h i c h a r e c a l l e d t h e C + and the C~ c h a r a c t e r i s t i c s . E q u a t i o n (2-27) may be r e w r i t t e n as: -it * + ^  • ° <2-2s» The l a s t t e r m o f t h i s e q u a t i o n can be changed from a s p a c i a l *For c o n v e n i e n c e we w i l l use t h e s u b s c r i p t n o t a t i o n t o i n d i -c a t e p a r t i a l d e r i v a t i v e s . t o a t i m e d e r i v a t i v e a l o n g t h e c h a r a c t e r i s t i c s a nd b e c o m e s : pUa 2A y. _ p U a 2 A f A (U±a)A (2-29) I n t r o d u c i n g (2-29) i n e q u a t i o n (2-28) and, w r i t i n g (2-28) i n i n c r e m e n t a l f o r m r a t h e r t h a n i n d i f f e r e n t i a l f o r m we h a v e : JCT-, J . m , p U a 2 6A . 6 P ± p a 6 U + -Tu±a)A = 0 (2-30) A t t h i s p o i n t we h a v e t o e x a m i n e t h e f l o w t o w h i c h we w a n t t o a p p l y t h i s r e l a t i o n . E q u a t i o n (2-30) r e l a t e s t h e f l o w q u a n t i t i e s i n a r e g i o n w h i c h d o e s n o t c o n t a i n d i s c o n t i n u i t y f r o n t s . I n t h e c a s e o f c y l i n d r i c a l i m p l o d i n g d e t o n a t i o n s t h i s r e g i o n l i e s o u t s i d e t h e p o s i t i o n o f t h e f r o n t R , i e : r>R a s i n f i g u r e 2-2. s ^ D i s c o n t i n u i t y , f r o n t (5=1) d e s c r i b e d by t h e jump c o n d t i o n s . F l o w f i e l d d e s c r i b e d by t h e h a r a c t e r i s t i c e q . F i g u r e 2-2: The c a s e o f c y l i n d r i c a l i m p l o s i o n . - 13 -Whitham has shown /20/ t h a t f o r a c o n v e r g e n t f r o n t the p o s i t i v e c h a r a c t e r i s t i c must be a p p l i e d t o the f l o w q u a n t i t i e s a t o r r i g h t b e h i n d the f r o n t ( + s i g n i n e q u a t i o n (2-30) ) . But t h e s e q u a n t i t i e s have been o b t a i n e d i n s e c t i o n 2-1 i n terms o f t h e Mach number o f t h e f r o n t and o f t h e c o n d i t i o n s ahead of i t ( e q u a t i o n s (2-14) and ( 2 - 1 5 ) ) . Thus on s u b s t i t u t i o n o f t h e s e r e l a t i o n s i n e q u a t i o n (2-30) , we o b t a i n an e q u a t i o n r e -l a t i n g t h e Mach number o f t h e wave t o t h e a r e a change. T h i s e q u a t i o n can t h e n be i n t e g r a t e d t o f i n d t h e v a r i a t i o n s o f t h e Mach number o f t h e wave w i t h t h e a r e a changes. The i n t e g r a t i o n c o n s t a n t i s found from t h e jump c o n d i t i o n s a t l a r g e r a d i i , where t h e d e t o n a t i o n f r o n t s t i l l behaves v e r y much l i k e a p l a n e s e l f - s u p p o r t e d d e t o n a t i o n . I n o r d e r t o s i m p l i f y t h e f i n a l r e s u l t s , we i n t r o d u c e t h e f o l l o w i n g d i m e n s i o n l e s s p a r a m e t e r s /!/: i|>(5,MJ = p ( r , t ) / P l <j> (E,M ) =' U ( r , t ) / R s s f( E , M ) = P ( r , t ) / P l R 2 £ = r / Rr M = R / a i , s s' ' € > 1 R = — s s 3t (2-31) where R g i s t h e f r o n t v e l o c i t y . The l i m i t p l a c e d on t h e d i -m e n s i o n l e s s r a d i u s , i e : £>1 , i m p l i e s t h a t a l l p o i n t s i n t h e d e t o n a t e d gas a r e i n c l u d e d . W r i t i n g e q u a t i o n (2-30) i n terms - 14 -of t h e s e new v a r i a b l e s and k e e p i n g o n l y t h e p o s i t i v e c h a r a c -t e r i s t i c , we o b t a i n : R Sf + 2fSR + /gT^cbfiR + R 64,) + x | A = 0 (2-32) o too ——— p± d>+/gf/ij> The jump e q u a t i o n s (2-14) and (2-15) can a l s o be w r i t t e n i n terms o f t h e new v a r i a b l e s a s : TM1,MJ = (g 2 +D / g 2 ( i - a ) 4>(1,M ) = f (1,M )• = ( l + g 2 a ) / ( g 2 + D u / I n 2 ( g i - l ) Q / a f , y where a - y / g 2 = [1- M z 1 (2-33) (2-34) s i n c e £=1 a t t h e f r o n t . A c c o r d i n g t o Whitham, e q u a t i o n (2-32) can be a p p l i e d a t t h e f r o n t ( i e : 5=1) where e q u a t i o n s i (2-33) must h o l d as w e l l . T h e r e f o r e s u b s t i t u t i n g e q u a t i o n s (2-33) i n e q u a t i o n (2-32) we o b t a i n an e q u a t i o n w h i c h r e l a t e d t h e change i n a r e a t o t h e v a r i a b l e a; t h i s e q u a t i o n i s : F(a) 6a + ^ 0 where _ , » l+g 2a+g? V ( l+g 2 ) (1-a) r , . , m-, \~m r\ F(o) = ^ ( 14; a ) ( i + g 2 a ) ^ x U + g 2 a + / ( l + g 2 a ) / ( l - a ) } ^ (2-35) I n o r d e r t o i n t e g r a t e t h e above e q u a t i o n , we need t o know t h e i n t e g r a t i o n c o n s t a n t , t h e v a l u e o f g 2 and t h e form o f 6A/A. The i n t e g r a t i o n c o n s t a n t can be o b t a i n e d from t h e s t a t e o f t h e d e t o n a t i o n a t l a r g e r a d i i where t h e f r o n t i s e x p e c t e d t o behave v e r y much l i k e a p l a n e s e l f - s u p p o r t e d d e t o n a t i o n . - 15 -T h e r e f o r e we can a p p l y t h e C.J. c o n d i t i o n s , e q u a t i o n s (2-16) t o ( 2 - 1 8 ) , t o f i n d t h e i n t e g r a t i o n c o n s t a n t . That i s we p u t ar=0 a t r=R s=RQ. The n u m e r i c a l v a l u e o f g 2 i s v e r y much i n q u e s t i o n and i s p r o b a b l y n o t a c o n s t a n t f o r t h e whole f l o w f i e l d due t o r e a l gas e f f e c t s , however, we s h a l l see t h a t t h e n u m e r i c a l v a l u e s o f t h e f l o w q u a n t i t i e s , w i t h t h e e x c e p t i o n o f t h e t e m p e r a t u r e and t h e d e n s i t y , a r e n o t v e r y dependent on t h e e x a c t v a l u e o f g 2 . From t h e c y l i n d r i c a l geometry, we can e a s i l y f i n d 6A/A t o be: 6A 6f ~ _ R s A ~r . ' r R Q OnCe t h e dependence of a i s found as a f u n c t i o n o f f , t h e f l o w q u a n t i t i e s can be found f rom e q u a t i o n s (2-33) and (2-34) as a f u n c t i o n o f t h e r a d i a l p o s i t i o n o f t h e d e t o n a t i o n f r o n t . I n o r d e r t o p r e s e n t t h e r e s u l t s i n a more g e n e r a l form, we n o r m a l i z e t h e f l o w q u a n t i t i e s w i t h t h e C.J. v a l u e s . These re d u c e d f l o w q u a n t i t i e s a r e g i v e n by: P = p / p C J = pTl C J = l / d - « ) (2-36) T T R <t> ^ U = £ = = ( l + g 2 a ) / / l - g i a ^ (2-37) CJ V C J V C J ~ P P l R s f P = i = n . v ^ f = V ( l - g 2 a ) (2.-38). F C J p i V C J r C J ^ = V V C J = U C J ( l " g 2 a ) = (2-39) - 1 6 -The e x p r e s s i o n f o r t h e t e m p e r a t u r e can be o b t a i n e d from t h e speed o f sound: 2 P, k T 2 a, = g, —2- = g, — -2 2 P 2 2 m 2 Where m2 i s t h e mean m o l e c u l a r w e i g h t o f t h e r e a c t i o n p r o d u c t s . Reducing t h i s t e m p e r a t u r e w i t h t h e C.J. t e m p e r a t u r e , we o b t a i n : T = 5j-~a) , (2-40) ( l - a g 2 ) The v a r i a b l e a was o b t a i n e d as a f u n c t i o n o f f by s o l v i n g e q u a t i o n (2-35) on t h e computer. Then, s u b s t i t u t i n g a i n e q u a t i o n s (2-36) t o ( 2 - 4 0 ) , we g e t t h e gas parameters as a f u n c t i o n o f r . These c o m p u t a t i o n s were c a r r i e d o u t f o r t h r e e v a l u e s o f g 2 ( g 2 = l . l , 1.235, 1.4). The v a l u e s 1.1 and 1.4 were chosen t o c o v e r t h e range o f g 2 p o s s i b l e i n t h e r e a c t i o n p r o d u c t s /46/. The v a l u e g 2=l.235±0.015 was o b t a i n e d from e q u a t i o n (2-18) u s i n g t h e measured v a l u e s o f . U j (2.73 t o 2.96 Km/sec) and t h e b e s t e s t i m a t e o f t h e energy i n p u t , Q, f o r e q u i m o l a r o x y - a c e t y l e n e m i x t u r e s , Q=7.72xi0 6 J o u l e s / K g /60/. The p l o t s o f p, P, V, and T a r e shown i n f i g u r e s 2-3 t o 2-6 r e s p e c t i v e l y . From t h e s e , we can see t h a t t h e dependence o f P and V on g 2 i s v e r y s m a l l , however, p and p a r t i c u l a r l y T, do depend v e r y much on the v a l u e of z^. As t h e r a d i u s o f t h e i m p l o s i o n becomes s m a l l , a->-l/g2 ( e q u a t i o n (2-35)) t h e r e f o r e , P, V, and-T i n c r e a s e w i t h o u t bounds a t t h e c e n t e r o f i m p l o s i o n , p, on t h e o t h e r hand, approaches t h e c o n s t a n t v a l u e o f g 2 / ( g 2 - l ) a t t h e c e n t e r . - 17 -0-0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 9 8 7 6 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1 0 - 18 -0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 - 19 -0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 - 20 -°-0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -. 21 -These a r e t h e f o c u s i n g e f f e c t s w h i c h make i m p l o s i o n s such i n t e r e s t i n g phenomena. S i n c e t h e v e l o c i t y i n c r e a s e i s o n l y a.second o r d e r e f f e c t ( e q u a t i o n (2-39)) and becomes s i g n i f i -c a n t o n l y v e r y c l o s e t o t h e c e n t e r o f i m p l o s i o n , i t i s more c o n v e n i e n t t o i n t e g r a t e t h e v e l o c i t y t o o b t a i n t h e p a t h o f t h e f r o n t i n an f - t p l a n e . T h i s c u r v e can t h e n be d i r e c t l y compared w i t h t h e smear p h o t o g r a p h s o f t h e i m p l o s i o n s as i t i s done i n c h a p t e r 4. The p o s i t i o n o f t h e f r o n t as a f u n c t i o n of t i m e i s found from: t = r d r 0 ^ > (2-41) The r e s u l t i n g c u r v e i s shown i n f i g u r e 2-7. S i n c e t h e v e l o c i t y i n c r e a s e i s o n l y n o t i c e a b l e f o r s m a l l r a d i i , t h i s c u r v e d e v i -a t e s o n l y -very s l i g h t l y from t h e s t r a i g h t l i n e ; f o r t h a t r e a s o n , t h e t i m e d i f f e r e n c e A t , between t h e l i n e a r p a t h and t h e C.C.W. model i m p l o s i o n c u r v e , i s a l s o g i v e n i n f i g u r e 2-7 i n an e n l a r -ged t i m e s c a l e . Here a g a i n t h e dependence on g 2 i s v e r y s m a l l . I t i s one o f t h e aims o f t h i s t h e s i s t o compare t h i s mo-d e l o f an i m p l o d i n g d e t o n a t i o n w i t h a c omplete s e t o f measure-ments o f t h e p r e s s u r e , t h e v e l o c i t y and t h e t e m p e r a t u r e . Four c h a p t e r s ( c h a p t e r s 4, 5, 6, and 7) a r e d e v o t e d t o t h i s i n v e s -t i g a t i o n . But f i r s t i t i s n e c e s s a r y t o g i v e some d e t a i l s o f t h e e x p e r i m e n t a l way i n w h i c h t h e i m p l o d i n g d e t o n a t i o n s a r e g e n e r a t e d . - 22 -F i g u r e 2-7: T h e o r e t i c a l i m p l o s i o n c u r v e o f a d e t o n a t i o n . 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-- 23 -CHAPTER 3 • GENERATION OF CONCENTRIC DETONATIONS The aim o f t h i s s h o r t c h a p t e r i s t o f a m i l i a r i z e t h e r e a d e r w i t h t h e method used t o g e n e r a t e i m p l o d i n g d e t o n a t i o n s . The d e t a i l s o f the a p p a r a t u s are i n c l u d e d i n a p p e n d i x form, a p p e n d i c e s A, B, C, and E. The problem i n p r o d u c i n g c y l i n d r i c a l i m p l o d i n g d e t o -n a t i o n s l i e s i n t h e f a c t t h a t t h e gas has t o be i g n i t e d u n i f o r m l y and s i m u l t a n e o u s l y o v e r t h e whole r i m o f t h e cham-ber i n w h i c h t h e d e t o n a t i o n i s t o be o b s e r v e d . ..Lee e t a l / l / , f i r s t s o l v e d t h i s p r o b lem by making use of a d i v e r -g i n g d e t o n a t i o n which was t u r n e d around a " d e f l e c t i o n p l a t e " t o i g n i t e t h e i m p l o d i n g wave. A s k e t c h o f a chamber r e q u i r e d by t h i s so c a l l e d "de-f l e c t i o n p l a t e " t e c h n i q u e i s shown i n f i g u r e 3-1. The c e n t e r p l a t e , o r d e f l e c t i o n p l a t e , i s f a s t e n e d t o t h e back p l a t e by means o f s i x screws c o v e r e d w i t h d o u b l e wedges. The purpose of t h e wedges i s t o p r o v i d e t h e s p a c i n g between t h e back and c e n t e r p l a t e s , t h e d o u b l e wedge shape was — c h o s e n f o r t h e s e s p a c e r s i n an a t t e m p t ~ t o m i n i m i z e "the p e r -t u r b a t i o n s due t o the p r e s e n c e of t h e s e s p a c e r s . The s p a r k gap, d e s c r i b e d i n a p p endix A, was d e s i g n e d t o produce a s p a r k on t h e a x i s o f t h e chamber. For o p e r a t i o n , t h e chamber i s f i r s t e v a c u a t e d and t h e n F i g u r e 3-1: T y p i c a l chamber t o g e n e r a t e i m p l o d i n g d e t o n a t i o n s u s i n g t h e d e f l e c t i o n p l a t e t e c h n i q u e . B- Back p l a t e , E- E x p l o s i o n s i d e , D- D e f l e c t i o n p l a t e , I - I m p l o s i o n s i d e , F- F r o n t p l a t e , S- Spark gap, W- Double wedges s p a c e r s . - 25 -f i l l e d t o t h e d e s i r e d p r e s s u r e w i t h t h e d e t o n a t i o n g a s w h i c h i s m i x e d i n a f i v e l i t e r e x t e r n a l t a n k . The g a s i s t h e n i , g n i t e d by t h e s p a r k w h i c h p r o d u c e s a u n i f o r m d i v e r g i n g c y -l i n d r i c a l d e t o n a t i o n f r o n t . T h i s f r o n t , u p o n r e a c h i n g t h e r i m o f t h e c h a m b e r , i s t u r n e d a r o u n d t h e c e n t e r p l a t e t o p r o d u c e t h e i m p l o d i n g d e t o n a t i o n . Two c h a m b e r s w e r e b u i l t . B e s i d e s d i f f e r i n g i n s i z e , t h e y a l s o d i f f e r e d i n t h e way t h e d e t o n a t i o n i s t u r n e d a r o u n d t h e d e f l e c t i o n p l a t e . The f i r s t a n d l a r g e r c h a m b e r , h a s a n i n n e r d i a m e t e r o f 19 cm. F i g u r e 3-2 shows a s c a l e d r a w i n g o f a s e c t i o n o f t h e c h a m b e r . The hope was t o be a b l e t o t u r n t h e wave a r o u n d i n t h i s w i d e c h a n n e l w i t h o u t much d i s t o r t i o n . H o w e v e r , i t was f o u n d t h a t t h i s c o n f i g u -r a t i o n l e a d t o m u l t i p l e r e f l e c t i o n s i n s i d e t h e c h a n n e l a n d a l t h o u g h t h e f r o n t was f o u n d t o be w e l l b e h a v e d c l o s e t o t h e c e n t e r o f i m p l o s i o n , i t was v e r y much p e r t u r b e d a t l a r g e r a d i i . T h u s a s e c o n d i m p r o v e d c hamber was b u i l t . T h i s c h amber i s s m a l l e r a n d h a s a s e c t i o n shown i n f i g u r e 3-3. The i n n e r d i a m e t e r o f t h i s c h amber i s a b o u t 14 cm. I n t h i s c h a m b e r , t h e d i v e r g i n g d e t o n a t i o n i s f i r s t o v e r d r i v e n by c o n s t r i c t i n g i t l a t e r a l l y b e f o r e c h a n n e l l i n g i t i n t o t h e n a r r o w p a s s a g e w h i c h c o n n e c t s t h e two s i d e s o f t h e c h a m b e r . S i n c e t h e w i d t h o f t h i s c h a n n e l i s much s m a l l e r t h a n t h e r a d i u s o f c u r v a t u r e , t h e wave c a n be t u r n e d a r o u n d t h e c e n -t e r p l a t e w i t h o u t d i s t o r t i o n s . The f r o n t t h e n g o e s t h r o u g h a l a t e r a l e x p a n s i o n p h a s e b e f o r e e n t e r i n g t h e u n i f o r m r e g i o n - 26 -F i g u r e 3-2: ca Q ^ S e c t i o n o f t h e 6 0 . y mm . , l a r g e chamber. . P o i n t A (Ref: Chap. 4) f 51.3 mm F i g u r e 3-3 : S e c t i o n o f t h e s m a l l chamber. 1 o f i m p l o s i o n . I n b o t h chambers, t h e r a d i u s , , i s t a k e n t o be t h e p o s i t i o n a t w h i c h t h e u n i f o r m i m p l o s i o n r e g i o n s t a r t s . RQ=69.8 mm and 5 1 . 3 mm f o r t h e l a r g e and s m a l l chambers r e s p e c t i v e l y . - 28 -CHAPTER 4 SPACE-TIME MEASUREMENTS One o f t h e most i m p o r t a n t p r o p e r t i e s o f an i m p l o d i n g d e t o n a t i o n i s i t s i m p l o s i o n c h a r a c t e r i s t i c * t h a t i s , t h e p a t h o f t h e f r o n t i n a s p a c e - t i m e p l a n e . I n t h i s c h a p t e r , we s e t o u t t o o b t a i n t h i s c u r v e by means o f o p t i c a l o b s e r -v a t i o n s made w i t h an image c o n v e r t e r and a smear camera. In t h e c o u r s e o f t h i s i n v e s t i g a t i o n we a l s o l e a r n about t h e symmetry, s t a b i l i t y and d e t o n a t i o n l i m i t s i n t h e chambers and a r e a b l e t o make a f i r s t c o m p a r i s o n between t h e t h e o r e t i c a l r e s u l t s and t h e e x p e r i m e n t a l b e h a v i o u r o f c y l i n d r i c a l i m p l o d i n g d e t o n a t i o n s . F o r a f i r s t q u a l i t a t i v e s u r v e y o f t h e c y l i n d r i c a l b e h a v i o u r , t h e image c o n v e r t e r i s most c o n v e n i e n t . To -complete t h i s p r e l i m i n a r y i n v e s t i g a t i o n , we used a smear -camera and o b t a i n e d s p a c e - t i m e c u r v e s f o r a q u a n t i t a t i v e c o m p a r i s o n w i t h t h e t h e o r y . The p r o p e r t i e s o f t h e d e t o n a t i o n were m a i n l y s t u d i e d i n t h e s m a l l chamber. Some comments a r e made on t h e b e h a v i o u r o f t h e f r o n t i n t h e l a r g e chamber. • I m p o r t a n t s i n c e i t i s one o f the most e a s i l y o b s e r v a b l e . - 29 -4-1 QUALITATIVE SURVEY WITH THE IMAGE CONVERTER: The image c o n v e r t e r i s a TRW camera model 1-D f i t t e d w i t h a submicrosecond 5 frame, p l u g - i n u n i t model 26-B. A TRW t r i g g e r d e l a y g e n e r a t o r model 46-A i s used t o o b t a i n p r o p e r t i m i n g . Chamber Rogowski c o i l t=0 TRW 46-A TRW 26-B TRW 1-D t=0 t=t F i g u r e 4 - 1 : E x p e r i m e n t a l s e t - u p w i t h t h e image c o n v e r t e r . F i g u r e 4-1 shows a b l o c k d i a g r a m o f t h e e x p e r i m e n t a l s e t - u p . The camera i s f o c u s e d onto a p l a n e j u s t b e h i n d t h e f r o n t p l a t e o f t h e chamber. A Rogowski c o i l , p l a c e d around t h e i g n i t i o n d i s c h a r g e l e a d s , p r o v i d e s a v e r y r e p r o d u c i b l e r e f e r e n c e p u l s e . T h i s p u l s e i s used t o t r i g g e r t h e d e l a y g e n e r a t o r w h i c h , i n t u r n , t r i g g e r s t h e camera a t t h e d e s i r e d t i m e , t ^ . The exposure t i m e =50, 100, 200. or 500 nsec) - 30 -and the i n t e r f r a m e time ( t ^ , v a r i a b l e from 0.5 t o 20 \isec) a r e s e t d i r e c t l y on the camera. SPACE-TIME CURVE: F i g u r e 4-2a shows a t y p i c a l i m p l o d i n g d e t o n a t i o n i n a s t o i c h i o m e t r i c m i x t u r e of oxygen and a c e t y l e n e a t an i n i t i a l p r e s s u r e of 300 T o r r . F i g u r e 4-2b i s a c l o s e up view of the l a s t 3 usee of the i m p l o s i o n s t a g e . The f r o n t i s seen t o be v e r y s h a r p l y d e f i n e d and p e r f e c t l y s y m m e t r i c a l as w e l l as e x t r e m e l y r e p r o d u c i b l e . The d i s t o r t i o n s a r e due t o a m i s a d j u s t m e n t of the image c o n v e r t e r camera. The r a d i a l p o s i t i o n o f the f r o n t , as measured from the p hotographs of f i g u r e 4-2, i s p l o t t e d v e r s u s time i n f i g u r e 4-3. The p a t h f o l l o w e d by the d e t o n a t i o n i n t h i s r - t diagram i s n o n - l i n e a r and r e s e m b l e s v e r y c l o s e l y the t h e o r e t i c a l c u r v e o f f i g u r e 2-7. The time t a k e n by the d e t o n a t i o n f r o n t t o advance from the edge of the chamber t o the c e n t e r o f c o l l a p s e i s 19.8 usee ( f i g u r e 4-3). The time d i f f e r e n c e between the a c t u a l c o l l a p s e time and the p r o j e c t e d l i n e a r c o l l a p s e , 6>t, i s 0.7^0.1 usee w h i c h r e p r e s e n t s a p p r o x i m a t e l y 3.5% of the c o l l a p s e t i m e . The c o r r e s p o n d i n g v a l u e o b t a i n e d from the t h e o r e t i c a l i m p l o s i o n c u r v e s o f f i g u r e 2-7 v a r i e s from 3.6% t o 4.0% of the t o t a l c o l l a p s e time depending on the v a l u e of g2« The d e t o n a t i o n speed measured a t l a r g e r a d i u s i s 2.42 t.0.04 Km/sec. T h i s i s s l i g h t l y h i g h e r than the 2.39 Km/sec - 31 -t . = i n t e r - f r a m e t i m e . t e x = e x p o s u r e time o f each frame. ex '—- r I 1 - r |—'—- r 1.2 cm 1.2 cm 1.2 cm F i g u r e 4-2: Image c o n v e r t e r photographs of an i m p l o d i n g d e t o n a t i o n . ( S t o i c h i o m e t r i c o x y - a c e t y l e n e ) Pi=300 T o r r - 33 -q u o t e d i n S o k o l i k / 9 / , h o w e v e r , e x p e r i m e n t a l e r r o r s due t o t h e s m a l l s i z e a n d p o o r q u a l i t y o f t h e i m a g e a s w e l l a s t h e c a l i b r a t i o n o f t h e image c o n v e r t e r , a r e q u i t e l a r g e a n d c a n e a s i l y a c c o u n t f o r s u c h a d i s c r e p a n c y . DETONATION L I M I T S : A t l o w i n i t i a l p r e s s u r e s ( P i < 1 8 0 T o r r ) , a d i f f e r e n t mode o f p r o p a g a t i o n i s o b s e r v e d . F i g u r e 4-4 i l l u s t r a t e s t h e d i f f e r e n c e b e t w e e n t h e s e two modes o f p r o p a g a t i o n . F o r P i > 1 8 0 T o r r , t h e f r o n t i s b r i g h t a n d s h a r p a n d moves a t a c o n s t a n t s p e e d e x c e p t f o r t h e r e g i o n v e r y c l o s e t o t h e c e n t e r o f i m p l o s i o n . F o r P i < 1 8 0 T o r r , o n t h e o t h e r h a n d , t h e f r o n t i s d i f f u s e a n d n o t v e r y b r i g h t a n d s p e e d s up m a r k e d l y a s i t moves t o w a r d s t h e a x i s . A s t h e d i f f u s e f r o n t g e t s c l o s e r t o t h e c e n t e r o f t h e c h a m b e r , we o b s e r v e t h e f o r m a t i o n o f b r i g h t s h a r p b u t i r r e g u l a r l u m i n o s i t y f r o n t s ( f i g u r e 4 - 5 a ) . T h e s e a r e i d e n t i f i e d a s t r a n s i t i o n s f r o m d e f l a g r a t i o n t o d e t o n a t i o n . A s t h e i n i t i a l p r e s s u r e i s i n c r e a s e d , t h e t r a n s i t i o n becomes more r e g u l a r a n d o c c u r s a t l a r g e r r a d i i ( f i g u r e 4 - 5 b , c , d ) . DEFLAGRATION: The t r a n s i t i o n f r o m d e f l a g r a t i o n t o d e t o n a t i o n h a s b e e n e x t e n s i v e l y s t u d i e d i n p l a n a r g e o m e t r y /I/. I t i s e x p l a i n e d b y t h e p r e s e n c e o f a s h o c k wave w h i c h d e v e l o p s a h e a d o f t h e f l a m e f r o n t a s i t a c c e l e r a t e s a n d becomes s u p e r s o n i c w i t h r e s p e c t t o t h e l a b o r a t o r y f r a m e o f r e f e r e n c e . T h i s s h o c k wave e v e n t u a l l y becomes s t r o n g e n o u g h t o h e a t a nd c o m p r e s s t h e u n b u r n t g a s e s t o a s t a t e a t w h i c h s p o n t a n e o u s c o m b u s t i o n o c c u r s . The s h o c k wave i s ( S t o i c h i o m e t r i c o x y - a c e t y l e n e ) 60 T o r r 55 t 50 45 h 5 cm r->-F i g u r e 4-4: I m p l o d i n g d e t o n a t i o n (Pi=200), and d e f l a g r a t i o n (Pi=150 Tor r ) - 35 -t •* d) Pi=150 T o r r , t =50 y s e c , t.=2 y s e c , t =100 nsec. d i ex I'igure 4-5: I m p l o d i n g d e f l a g r a t i o n s a t v a r i o u s p r e s s u r e s shov/ing the t r a n s i t i o n t o d e t o n a t i o n . A l l i n s t o i c h i o m e t r i c o x y - a c e t y l e n e m i x t u r e . - 36 -t h e n i m m e d i a t e l y f o l l o w e d by a r e a c t i o n z o n e and t h e r e f o r e becomes a d e t o n a t i o n . I n t h e c h a m b e r , t h e f l a m e d e v e l o p s f r o m t h e q u e n c h i n g o f t h e d e t o n a t i o n ( s e e f i g u r e 4-6 and t h e f o l l o w i n g a r g u -m e n t s ) a n d i s a l w a y s o b s e r v e d t o be s u p e r s o n i c . T h e r e f o r e one w o u l d e x p e c t t h e same t r a n s i t i o n m e c h a n i s m t o be i n v o l v e d h e r e , h o w e v e r , t h e a c c e l e r a t i o n o f t h e f l a m e and s t r e n g t h e n i n g o f t h e s h o c k wave i s s p e e d e d up by t h e f o c u s i n g e f f e c t s o f t h e c y l i n d r i c a l g e o m e t r y . S T A B I L I T Y : I t i s i n t e r e s t i n g t o n o t e t h a t e v e n t h o u g h t h e d e t o n a t i o n t r a n s i t i o n o c c u r s v e r y i r r e g u l a r l y a r o u n d t h e f r o n t , t h e f i n a l s t a g e o f t h e i m p l o s i o n i s a l w a y s f a i r l y -s y m m e t r i c a l a s shown i n f i g u r e s 4-5b a n d 4-5c, i n d i c a t i n g t h e p r e s e n c e o f a s t r o n g s t a b i l i z i n g m e c h a n i s m w h i c h i s r e s p o n s i b l e f o r t h e g o o d s y m m e t r y a n d r e p r o d u c i b i l i t y o f t h e i m p l o s i o n a t h i g h e r p r e s s u r e s . We w i l l come b a c k t o t h i s s t a b i l i z i n g m e c h a n i s m l a t e r i n t h i s c h a p t e r . TRANSITION FROM DETONATION TO DEFLAGRATION: I n f i g u r e 4-6, t h e f r o n t p o s i t i o n i s p l o t t e d v e r s u s t i m e f o r v a r i o u s i n i t i a l p r e s s u r e s . I f t h e s e c u r v e s a r e e x t r a p o l a t e d b a c k w a r d s i n t i m e , t h e y a l l seem t o c r o s s a t a p o i n t A, * 53 mm f r o m t h e c e n t e r . The a v e r a g e s p e e d o f t h e f r o n t f r o m t h e i g n i t i o n p o i n t on t h e b a c k o f t h e chamber t o p o i n t A i s 2.38 Km/sec. T h i s i s t h e s p e e d o f t h e d e t o n a t i o n a n d The e x t r a p o l a t i o n o f t h e c u r v e f o r P i = 8 0 T o r r i s some-what u n c e r t a i n , h o w e v e r , t h e f o l l o w i n g a r g u m e n t s do n o t d e p e n d c r i t i c a l l y on i t . - 38 -t h e r e f o r e , up t o p o i n t A, the wave t r a v e l s as a d e t o n a t i o n . From f i g u r e 3-3, one can see t h a t p o i n t A i s s t i l l i n the l a t e r a l e x p a n s i o n phase of the f r o n t s i d e of the chamber; i t i s not u n t i l r = R 0 = 5 1 . 3 mm t h a t t h i s e x p a n s i o n i s c o m p l e t e d . I t i s t h e r e f o r e i n t h i s phase t h a t the d e t o n a t i o n f r o n t changes over t o a d e f l a g r a t i o n . The r e a s o n f o r t h i s t r a n s i t i o n t o o c c u r o n l y a t low p r e s s u r e s can be u n d e r s t o o d by c o n s i d e r i n g boundary l a y e r e f f e c t s . \ BOUNDARY LAYER EFFECTS, a c c o u n t i n g o n l y f o r the mechani-c a l l o s s e s due t o the v i s c o s i t y of the gas, a r e most pronoun-ced a t low p r e s s u r e s and i n s m a l l c h a n n e l s /21/. Thus when the d e t o n a t i o n , ( which has been o v e r - d r i v e n by the l a t e r a l c o m p r e s s i o n s t a g e i n the back of the chamber), emerges from the narrow c h a n n e l , i t has been weakened from i t s o v e r - d r i v e n s t a t e by some amount i n v e r s e l y p r o p o r t i o n a l t o the i n i t i a l p r e s s u r e . For h i g h p r e s s u r e s , P-^  > 180 T o r r , i t i s s t i l l s t r o n g enough t o m a i n t a i n a d e t o n a t i o n t h r o u g h o u t the e x p a n s i o n phase. F o r lower p r e s s u r e s , however, the e x p a n s i o n phase r e d u c e s the s t r e n g t h of the c o m p r e s s i o n wave so much t h a t i t can no l o n g e r shock i g n i t e the gas. The r e a c t i o n zone t h e r e f o r e s e p a r a t e d from the shock f r o n t and the wave p r o p a g a t e s as a f a s t d e f l a g r a t i o n . F o r even lower p r e s s u r e s , the d e f l a g r a t i o n may s t a r t i n the c h a n n e l i t s e l f ( p o i n t B ) . The f a c t t h a t the d e t o n a t i o n s w i t c h e s over t o a d e f l a -*A s u c c e s s f u l e x p e r i m e n t a l v e r i f i c a t i o n of t h i s i n t e r p r e -t a t i o n was done r e c e n t l y i n our l a b o r a t o r y by P a u l R e d f e r n . - 3 9 -g r a t i o n a t low i n i t i a l p r e s s u r e s , g i v e s a v e r y good i n d i c a -t i o n t h a t the d e t o n a t i o n a t r = R Q , t h a t i s j u s t a f t e r the l a t e r a l e x p a n s i o n , i s i n d e e d i n the C.J. s t a t e or v e r y c l o s e t o i t f o r i n i t i a l p r e s s u r e s g r e a t e r t h a n 180 T o r r . OTHER GAS MIXTURES: The image c o n v e r t e r was used t o i n v e s t i g a t e the i m p l o s i o n p r o p e r t i e s of o t h e r oxy-a c e t y l e n e m i x t u r e s and of m i x t u r e s of oxygen w i t h hydrogen, e t h a n e , methane or propane. I t was found t h a t e q u i m o l a r o x y - a c e t y l e n e m i x t u r e s a r e a l s o v e r y s t a b l e , p r o d u c i n g s y m m e t r i c a l and r e p r o d u c i b l e i m p l o d i n g d e t o n a t i o n s . On t h e o t h e r hand, i t was i m p o s s i b l e t o o b t a i n an i m p l o d i n g d e t o n a t i o n w i t h any o f the o t h e r gases when used i n the s m a l l chamber even though t h e y d i d produce good i m p l o s i o n s i n t h e l a r g e chamber. F i g u r e s 4-7a and 4-7b a r e two s e t s of image c o n -v e r t e r photographs of an i m p l o s i o n i n the s m a l l and l a r g e chambers under i d e n t i c a l c o n d i t i o n s . I t i s c o n c l u d e d t h a t the narrow c h a n n e l t h r o u g h which the d e t o n a t i o n i s f o r c e d i n the s m a l l chamber quenches t h e d e t o n a t i o n b e f o r e i t r e a c h e s the i m p l o s i o n s i d e , and, s i n c e the q u e n c h i n g e f f e c t i s due t o a boundary e f f e c t w hich i s dependent on the r e a c t i o n zone t h i c k n e s s /21/, t h e s e gas m i x t u r e s must have a l o n g e r r e a c t i o n zone than o x y - a c e t y l e n e m i x t u r e s . 4-2 QUANTITATIVE COMPARISON OF THE CCW MODEL WITH EXPERIMENT In the p r e v i o u s s e c t i o n , we were a b l e t o show the e x c e l l e n t symmetry and r e p r o d u c i b i l i t y of the i m p l o s i o n . We - 40 -a) S m a l l chamber 2 H 2 + 0 2 Pi=760 T o r r t =55 ysec d t.=3 usee l t =200 nsec. | 1 r 2. 6 cm b) Large chamber 2 H 2 + 0 2 Pi=760 T o r r + t^=95 ysec t t^=2 ysec t =500 nsec. ex F i g u r e 4-7: I m p l o s i o n s i n s t o i c h i o m e t r i c oxy-hydrogen gas. a) S m a l l chamber b) Large chamber. - 4 1 -a l s o made a q u a l i t a t i v e v e r i f i c a t i o n o f t h e t h e o r e t i c a l i m p l o s i o n c u r v e o f f i g u r e 2-7 ( f i g u r e 4 - 3 ) , h o w e v e r , t h e i m a g e c o n v e r t e r p h o t o g r a p h s w e r e t o o s m a l l and d i s t o r t e d t o g i v e a c c u r a t e r e s u l t s . We a l s o h a d t o r e l y on t h e s h o t -t o - s h o t r e p r o d u c i b i l i t y o f t h e i m p l o s i o n t o b u i l d up t h e i m p l o s i o n c u r v e . I n o r d e r t o c o m p l e m e n t t h i s t h e o r y -e x p e r i m e n t c o m p a r i s o n b y q u a l i t a t i v e r e s u l t s , a smear c a m e r a was u s e d . The smear c a m e r a i s d e s c r i b e d i n a p p e n d i x C. Smear p h o t o g r a p h s a r e b e t t e r f o r t h i s c o m p a r i s o n s i n c e t h e y a r e d i r e c t s p a c e - t i m e r e c o r d o f t h e p o s i t i o n o f t h e f r o n t V e r s u s t i m e r a t h e r t h a n d i s c r e t e s n a p - s h o t s o f t h e c h a m b e r . The s m e a r s a l s o do n o t n e e d t h e s h o t - t o - s h o t r e p r o d u c i b i l i t y s i n c e t h e w h o l e i m p l o s i o n c u r v e c a n be o b t a i n e d i n one e x p o -s u r e . H o w e v e r , t h e i n v e s t i g a t i o n w i t h t h e image c o n v e r t e r was n e c e s s a r y t o show t h e symmetry o f t h e i m p l o s i o n . T h i s i n f o r m a t i o n c a n n o t be o b t a i n e d f r o m a one s l i t smear c a m e r a . A l s o , t h e i n t e r p r e t a t i o n o f t h e s m e a r s w h i c h a r e r e c o r d s o f t h e l u m i n o s i t y p a t t e r n a l o n g a d i a m e t e r o f t h e c h a m b e r , r e l y on t h e g o o d symmetry o f t h e f r o n t , h e n c e a p r e v i o u s know-l e d g e o f t h e i m p l o s i o n s y m m e t r y was n e c e s s a r y . F i g u r e 4-8 shows t h e e x p e r i m e n t a l s e t - u p . The s l i t o f t h e c a m e r a i s f o c u s e d v i a two a c h r o m a t i c l e n s e s ( f o c a l l e n g t h o f 1 5 " , f : 5 ) o n t o a d i a m e t e r o f t h e c h a m b e r . The t i m i n g e l e c t r o n i c s o f t h e c a m e r a p r o v i d e a t r i g g e r p u l s e w h i c h a l l o w s one t o i g n i t e t h e d e t o n a t i o n a t any d e s i r e d t i m e . - 42 -Hi-—r —»< ' Chamber J L e n s e s T r i g - D e l a y g e n e r a t o r Smear c a m e r a J l —t 1— fcT fcm J l m F i g u r e 4 - 8 : E x p e r i m e n t a l s e t - u p f o r t h e smear c a m e r a . INTERPRETATION OF THE SMEARS: A smear p h o t o g r a p h t a k e n a t v e r y l o w sweep s p e e d i s r e p r o d u c e d i n f i g u r e 4 - 9 . I t i l l u s t r a t e s t h e l o n g t i m e b e h a v i o u r o f t h e i m p l o s i o n and f o l l o w i n g r e f l e c t i o n s . The b l a c k v e r t i c a l l i n e s are-c e n t i m e t e r m a r k s p l a c e d o n t h e f r o n t p l a t e o f t h e c h amber i n o r d e r t o o b t a i n t h e m a g n i f i c a t i o n o f t h e o p t i c a l s y s t e m . S t r a y l i g h t f r o m t h e i g n i t i o n s p a r k c a n be s e e n b e f o r e t h e a r r i v a l o f t h e i m p l o s i o n , i t i s i d e n t i f i e d by t h e l e t t e r S i n f i g u r e 4 - 9 . The s t r u c t u r e f o l l o w i n g t h e i n i t i a l i m p l o s i o n and s u b s e q u e n t r e f l e c t e d s h o c k i s q u i t e c o m p l e x due t o m u l t i p l e r e f l e c t i o n s a t r=R^ a n d a l s o r e f l e c t i o n s c o m i n g f r o m t h e b a c k s i d e o f t h e c h a m b e r . The r e p r o d u c i b i l i t y o f - 4 3 -F i g u r e 4-9: Low sweep speed smear p h o t o g r a h of an i m p l o d i n g d e t o n a t i o n i n e q u i m o l a r o x y - a c e t y l e n e m i x t u r e . Pi=300 T o r r , camera s l i t width=0.1 mm. - 44 -th e d e t o n a t i o n i s q u i t e r e m a r k a b l e . The p h o t o g r a p h o f f i g u r e 4-9 i s a c t u a l l y a c o m p o s i t e of two smears t a k e n w i t h d i f f e r e n t d e l a y s and l a t e r matched by c o r r e l a t i n g t h e ti m e on b o t h smears. From t h e l u m i n o s i t y p a t t e r n we see t h a t t h e gas does not undergo l a r g e m o t i o n s , b u t r a t h e r has a s m a l l p u l s a t i n g b e h a v i o u r . The v e r y i n t e n s e c e n t e r s p o t o b t a i n e d p r e v i o u s l y i s r e a d i l y o b s e r v a b l e a t a l l convergence p o i n t s e s p e c i a l l y a t t h e i n i t i a l i m p l o s i o n . RICH AND LEAN MIXTURES: The two smears o f f i g u r e 4-10 i l l u s t r a t e t h e g r e a t dependence of t h e e m i s s i o n o f v i s i b l e r a d i a t i o n on t h e e x a c t c o m p o s i t i o n o f t h e m i x t u r e near e q u i m o l a r c o n c e n t r a t i o n . (I s h a l l r e f e r t o r i c h and l e a n m i x t u r e s depending on whether t h e ex c e s s gas i s a c e t y l e n e o r oxygen) . A s l i g h t l y l e a n m i x t u r e (51.6% 0 2) p r a c t i c a l l y does n o t r a d i a t e i n t h e v i s i b l e e x c e p t f o r a f a i n t glow a t t h e d e t o n a t i o n f r o n t i t s e l f and a b r i g h t f l a s h a t t h e c o l l a p s e - p o i n t . A s l i g h t l y r i c h m i x t u r e (48.4% 0 2 ) , on t h e o t h e r hand, i s luminous t h r o u g h o u t t h e whole f a c e o f t h e chamber. These g r e a t d i f f e r e n c e s i n l u m i n o s i t y p a t t e r n s w i l l be d i s -c u s s e d i n c h a p t e r 6 wh i c h d e a l s w i t h t h e spectrum o f t h e d i s c h a r g e . A p a r t from l i g h t e m i s s i o n , t h e b e h a v i o u r o f t h e d e t o n a t i o n i n - r i c h and l e a n m i x t u r e s appears t o be the.same. In -both c a s e s the i m p l o s i o n speed i s 2.77±1.5% Km/sec a t a - p r e s s u r e o f 300 T o r r , i n d i c a t i n g t h a t w i t h i n the e x p e r i m e n t a l r e s o l u t i o n , the system behaves i d e n t i c a l l y . In f i g u r e 4-10a - 45 -a) R i c h mix: 48.4% 0 2 12.5 ysec 1 cm b) Lean mix: 51.6% 0 2 12.5 ysec 1 cm F i g u r e 4-10: I m p l o d i n g d e t o n a t i o n s i n r i c h and l e a n m i x t u r e s . Pi=300 T o r r , sweep speed=12.5 ysec/cm, 1 cm m a r k e r s , camera s l i t width=0.1 mm. - 4 6 -a - s m a l l d i s t u r b a n c e i s s e e n t o f o l l o w t h e i m p l o d i n g f r o n t ' ~ " h o w e v e r , i t i s ' f a r f r o m t h e d e t o n a t i o n and t h e r e f o r e s h o u l d "?" n o t p e r t u r b t h e i m p l o s i o n c h a r a c t e r i s t i c s o f t h e wave. MODIFICATION OF THE CHAMBER: A f t e r a number o f s h o t s , a s m a l l b u t n o t i c e a b l e l e n s e f f e c t was o b s e r v e d a t t h e c e n t e r o f t h e f r o n t p l a t e . T h i s was due t o d e f o r m a t i o n s o f t h e l u c i t e u n d e r t h e h i g h p r e s s u r e s and t e m p e r a t u r e s d e v e l o p e d a t t h e c e n t e r o f t h e c o l l a p s e . I n o r d e r t o a v o i d o p t i c a l d i s t o r -t i o n s , a q u a r t z window was i n s e r t e d a t t h e c e n t e r o f t h e p l a t e . A l t h o u g h t h i s w indow d i d n o t d e f o r m , i t had t o be c h a n g e d p e r i o d i c a l l y b e c a u s e s m a l l c r a c k s d e v e l o p e d i n i t . The b r a s s h o l d e r u s e d t o s e c u r e t h e window i s d e s c r i b e d i n a p p e n d i x A.• R E P R O D U C I B I L I T Y : F i g u r e 4 - l l a shows a smear o f an i m p l o s i o n i n a l e a n m i x t u r e a t an i n i t i a l p r e s s u r e o f 500 T o r r , t a k e n t h r o u g h a q u a r t z window. The b r i g h t f l a s h a t t h e c e n t e r i s now v e r y v i s i b l e a n d t h e n o n - l i n e a r i m p l o s i o n c u r v e o f t h e d e t o n a t i o n i s o b v i o u s . U n d e r t h i s h i g h r e s o l u t i o n , i t was f o u n d t h a t a l l s h o t s d i d n o t i m p l o d e on t h e g e o m e t r i c c e n t e r o f t h e chamber b u t w a n d e r e d o f f t h a t p o i n t by a s much as 1.5 mm. The p h o t o g r a p h s o f f i g u r e s l i b and 1 1 c i l l u s -t r a t e t h i s e f f e c t . T h e s e s m e a r s r e p r e s e n t r a t h e r e x t r e m e c a s e s i n w h i c h t h e c o l l a p s e o c c u r r e d o f f a x i s b u t on t h e s l i t i m a ge ( f i g u r e 4 - l l b ) a n d o f f t h e s l i t ( f i g u r e 4 - l l c ) . One r e a s o n f o r t h i s b e h a v i o u r c a n be t r a c e d b a c k t o t h e i g n i t i o n e l e c -t r o d e s . T h e s e b r a s s e l e c t r o d e s a r e 3 mm i n d i a m e t e r a n d t e n d - 47 -c) O f f c e n t e r - o f f s l i t , 6 ysec F i g u r e 4-11: Close-up o f t h e i m p l o s i o n i n l e a n (51.6% O2) o x y - a c e t y l e n e m i x t u r e . Pi=500 T o r r , sweep speed=6 ysec/cm, s l i t width=0.2mm. 48 -t o w e a r o f f t o a s m o o t h s l i g h t l y r o u n d e d s h a p e a f t e r a f e w f i r i n g s . H e n c e , t h e r e i s no g u a r a n t e e t h a t t h e i n i t i a l s p a r k c h a n n e l , w h i c h f o r m s u p o n t r i g g e r i n g , i s a t t h e c e n t e r o f t h e e l e c t r o d e s . The i g n i t i o n , t h e r e f o r e , c o u l d be a s much a s 1.5 mm o f f c e n t e r . T h i s e c c e n t r i -c i t y i s p r o p a g a t e d t o t h e f r o n t s i d e o f t h e chamber a nd r e s u l t s i n o f f c e n t e r i m p l o s i o n s . On t h e a v e r a g e , one o u t o f s i x s h o t s was on c e n t e r o r s o c l o s e t o i t t h a t i t c o u l d be c o n s i d e r e d so w i t h i n t h e e x p e r i m e n t a l r e s o l u t i o n w h i c h i s d i c t a t e d by t h e s l i t w i d t h o f t h e c a m e r a . a n d t h e s h a r p n e s s o f t h e p h o t o g r a p h s . 4-3 SPACE-TIME MEASUREMENTS: The s m e a r s u s e d f o r q u a n t i t a t i v e c o m p a r i s o n w i t h t h e t h e o r e t i c a l r e s u l t s w e r e t a k e n on Kodak T r i - X f i l m w h i c h was d e v e l o p e d i n Kodak D-19; t h e d e v e l o p e r i n c r e a s e s t h e s p e e d o f t h e e m u l s i o n t o a b o u t ASA 2 5 0 0 , t h u s e n a b l i n g e x p o s u r e s t o be made w i t h a n a r r o w s l i t ( 0 . 1 mm). Two s e r i e s o f s m e a r s w e r e t a k e n . The f i r s t s e r i e s was t a k e n t h r o u g h a 2.38 cm d i a m e t e r w i n d o w u s i n g r i c h a n d l e a n m i x t u r e s a t an i n i t i a l p r e s s u r e o f 200<Pi<500 T o r r . The s e c o n d s e r i e s was t a k e n t h r o u g h a 5 cm window i n e q u i -m o l a r m i x t u r e a t i n i t i a l p r e s s u r e s o f 200 a n d 300 T o r r . •Two n e u t r a l d e n s i t y f i l t e r s ( d e n s i t y = 0 . 1 a n d 0.4) w e r e p l a c e d a t t h e c e n t e r o f t h e s l i t o f t h e c a m e r a d u r i n g t h e - 4 9 -second r u n i n an a t t e m p t t o p r e v e n t g r o s s o v e r e x p o s u r e o f the f i l m near t h e c e n t e r o f c o l l a p s e . F i g u r e 4 - l l a i s a t y p i c a l smear o f t h e f i r s t s e r i e s , w h i l e f i g u r e 4 - 1 2 i s a t y p i c a l smear o f t h e second s e r i e s . The average chamber-t o - f i l m m a g n i f i c a t i o n i s 1 . 6 7 2 ( ± 0 . 3 % ) and 1 . 1 0 1 ( ± 0 . 2 % ) r e s p e c t i v e l y . Only an e x a c t v a l u e 'of t h e average m a g n i f i c a t i o n i s needed as s m a l l v a r i a t i o n s i n t h e m a g n i f i c a t i o n a c r o s s t h e s l i t have v e r y l i t t l e e f f e c t s on t h e f r o n t p a t h (appendix D ) . The n e g a t i v e s were e n l a r g e d i n o r d e r t o t r a c e t h e l u m i n o s i t y f r o n t on s e m i - t r a n s p a r e n t p a p e r . The t r a c i n g s o f d i f f e r e n t d e t o n a t i o n s i n t h e same i n i t i a l p r e s s u r e were found t o be i d e n t i c a l w i t h i n t h e t h i c k n e s s o f t h e p e n c i l l i n e s . The e x a c t c e n t e r o f i m p l o s i o n and t i m e a x i s were found by f o l d i n g t h e t r a c i n g s i n such a way as t o make b o t h s i d e s o f t h e i m p l o s i o n c u r v e match e x a c t l y . The r a d i a l a x i s was t h e n drawn p e r p e n d i c u l a r t o t h e t i m e a x i s . These were i n t u r n c a l i b r a t e d u s i n g t h e sweep speed of the camera, t h e enlargement and t h e c h a m b e r - t o - f i l m m a g n i f i c a t i o n . I n o r d e r t o p l o t t h e t h e o r e t i c a l c u r v e on t h e s e t r a c i n g s , t h e d e t o n a t i o n speed, V g , a t l a r g e r a d i u s had t o be known. T h i s v a l u e was o b t a i n e d from t h e smears o f t h e whole chamber ( f i g u r e 4 - 1 0 ) . The c o l l a p s e t i m e , TQ, f o r l i n e a r c o l l a p s e i s t h e n c a l c u l a t e d from T =R„/V , where R = 5 1 . 3 mm i s t h e 0 0' s 0 r a d i u s o f t h e s m a l l chamber. These r e s u l t s a r e t a b u l a t e d i n t a b l e I . - 50 -— j t=0 -- 6 ysec t r 2.5 cm F i g u r e 4-12: Close-up o f an i m p l o d i n g d e t o n a t i o n i n e q u i -molar o x y - a c e t y l e n e m i x t u r e . N e u t r a l d e n s i t y f i l t e r s p l a c e d on t h e s l i t . Pi=200 T o r r , sweep speed=6 ysec/cm, s l i t width=0.1 mm. - 5 1 -TABLE I F r o n t v e l o c i t y and t o t a l l i n e a r c o l l a p s e time a t v a r i o u s p r e s s u r e s . P 0 (Torr) 2 0 0 ( ± 5 % ) 3 0 0 4 0 0 5 0 0 V G (Km/sec) 2.7.3 ( ± 1 . 5 % ) 2 . 7 7 2 . 7 9 2 . 8 1 T Q (ysec) 1 8 . 8 6 ( ± 1 . 5 % ) 1 8 . 5 9 1 8 . 46 1 8 . 3 3 The a c c u r a c y o f the s e measurements i s d i c t a t e d m a i n l y by the s y s t e m a t i c e r r o r ( 0 . 5 % ) of the c a l i b r a t i o n of the smears and s e c o n d l y by the e r r o r i n the e s t i m a t e of the s l o p e o f the f r o n t on the s t r e a k p h o t o g r a p h s . Repeated measurements performed on t h e same smear and measurements made from smear t o smear , have a s c a t t e r o f about 1%. Thus t h e r e i s a p o s s i b l e 1 . 5 % u n c e r t a i n t y i n T^. T h i s f a i r l y l a r g e e r r o r can be t o l e r a t e d s i n c e t h e e r r o r a t any t i m e , t , i s n o t 1 . 5 % o f T Q, but 1 . 5 % of t h e v a l u e o f t , w h i c h i s measured from t h e i n s t a n t o f c o l l a p s e . T h e r e f o r e t h e e r r o r b a r s d e c r e a s e w i t h t and be-come v e r y s m a l l i n t h e r e g i o n where t h e e x p e r i m e n t a l r e s u l t s a r e compared w i t h t h e t h e o r y . Knowing T^, R^, and t h e s c a l e s on t h e ti m e and r a d i a l a x i s o f t h e e n l a r g e m e n t s , t h e t h e o r e t i c a l c u r v e can now be p l o t t e d u s i n g t h e v a l u e s c a l c u l a t e d i n c h a p t e r 2. F i g u r e 4 - 1 3 shows an enlargement o f a t y p i c a l smear o f th e second r u n . I t shows t h e l a s t 1.5 cm o f t h e i m p l o s i o n i n an e q u i m o l a r o x y - a c e t y l e n e m i x t u r e a t an i n i t i a l p r e s s u r e o f 2 0 0 T o r r . The ti m e a x i s on t h e s e smears i s c o n v e n i e n t l y o b t a i n e d from t h e marks l e f t by t h e n e u t r a l d e n s i t y F i g u r e 4-13: Enlargement o f a smear photograph o f an i m p l o d i n g d e t o n a t i o n i n e q u i m o l a r o x y - a c e t y l e n e gas. P =200 T o r r . C.C.W. model i m p l o s i o n c u r v e , L i n e a r i m p l o s i o n , i—i P r e d i c t e d f r o n t t h i c k n e s s . f i l t e r s p l a c e d on t h e s l i t o f the camera. The r a d i a l a x i s i s drawn as a d o u b l e l i n e t o i n d i c a t e t h e w i d t h o f the s l i t (100 u ) . The t h e o r e t i c a l c u r v e ( dashed l i n e ) and l i n e a r c o l l a p s e c u r v e ( s o l i d l i n e ) have been drawn on t h e p r i n t . We see t h a t t h e t a i l o f the r e c o r d e d l u m i n o s i t y f r o n t f o l l o w t h e t h e o r e t i c a l c u r v e v e r y c l o s e l y . T h i s a g r e e s w i t h t h e o f f a x i s e f f e c t s c o n s i d e r e d i n appendix D. A l s o shown i n t h i s f i g u r e i s t h e p r e d i c t e d t h i c k n e s s o f t h e f r o n t a t 5, 10 and 15 mm from t h e c e n t e r o f i m p l o s i o n . These v a l u e s were c a l c u l a t e d from t h e e x p r e s s i o n d e r i v e d i n appendix D u s i n g t h e d a t a r e l e v a n t t o the smear. The a l l around ex-c e l l e n t agreement between p r e d i c t i o n s and e x p e r i m e n t a l r e s u l t s , g i v e s good e v i d e n c e t h a t t h e C.C.W. model does i n d e e d p r e d i c t v e r y w e l l t h e b e h a v i o u r o f t h e i m p l o s i o n f r o n t . I t a l s o shows t h a t t h e d e t o n a t i o n f r o n t i n oxy-a c e t y l e n e i s e x t r e m e l y t h i n s i n c e t h e c a l c u l a t e d t h i c k n e s s shown i n f i g u r e 4-13 were o b t a i n e d ' a s s u m i n g an i n f i n i t e s i -maly t h i n f r o n t . 4-4 STABILITY: The image c o n v e r t e r p h otographs o f s e c t i o n 4-1, showed t h a t g r o s s l y d i s t o r t e d f r o n t s t e n d t o become r e g u l a r as t h e r a d i u s becomes s m a l l e r . Hence a s t a b i l i z i n g mechanism must be p r e s e n t . Now t h a t t h e f r o n t has been shown t o behave i n a way p r e d i c t e d by t h e C.C.W. model, t h i s mechanism can be a s s o c i a t e d w i t h t h e i n c r e a s e i n d e t o n a t i o n v e l o c i t y as t h e - 54 -r a d i u s d e c r e a s e s . A l t h o u g h t h i s r e s u l t a p p l i e s t o a r e g u -l a r f r o n t a s a w h o l e and d e p e n d s on t h e r e l a t i v e c h a n g e o f c u r v a t u r e , t h e same g e n e r a l r e s u l t a p p l i e s l o c a l l y by e x -t e n s i o n o f t h e m o d e l . D i s t o r t i o n s i n t h e c i r c u l a r f r o n t , p r o d u c e l o c a l v a r i a -t i o n s o f t h e r a d i u s o f c u r v a t u r e . The r e g i o n s o f h i g h c u r -v a t u r e a r e a l s o t h o s e l a g g i n g b e h i n d t h e c i r c u l a r s h a p e . S i n c e by t h e C.C.W. m o d e l p r e d i c t i o n s , t h e s e r e g i o n s a r e a l s o t h o s e h a v i n g a h i g h e r s p e e d t h a n t h e . r e g i o n s ' o f l e s s e r c u r v a t u r e , t h e y t e n d t o c a t c h up w i t h t h e r e s t o f t h e f r o n t t o r e s t o r e t h e c i r c u l a r s h a p e o f t h e wave. The r e v e r s e e f f e c t h o l d s f o r t h o s e r e g i o n s a h e a d o f t h e c i r c u l a r s h a p e w h i c h h a v e a l o w e r c u r v a t u r e t h a n t h e a v e r a g e . H e n c e , d i s -t o r t e d f r o n t s t e n d t o become r e g u l a r a s t h e d e t o n a t i o n moves i n w a r d s . T h i s p i c t u r e , h o w e v e r , i s f a r f r o m c o m p l e t e . I n t h e t h e o r y c h a p t e r , o n l y t h e m a c r o s c o p i c p r o p e r t i e s o f t h e d e t -o n a t i o n w e r e c o n s i d e r e d . M i c r o s c o p i c i n v e s t i g a t i o n s h a v e shown t h a t d e t o n a t i o n f r o n t s a r e n o t p l a n e and u n i f o r m b u t a r e made up o f s m a l l i n t e r s e c t i o n w a v e l e t s w i t h a w e l l m a r k e d t r a n s v e r s e wave p a t t e r n . L e e e t a l /22/ h a v e shown t h a t t h e s e m i c r o s c o p i c t r a n s v e r s e waves p r o d u c e a s t r o n g s t a b i -l i z i n g m e c h a n i s m i n c o n c e n t r i c i m p l o d i n g d e t o n a t i o n s . 4-5 THE LARGE CHAMBER: T h i s s h o r t s e c t i o n i s i n c l u d e d t o show t h e a d v a n t a g e s - 55 -o f t h e s m a l l chamber i n w h i c h t h e d e t o n a t i o n i s o v e r - d r i v e n and c h a n n e l l e d i n t o a narrow passage b e f o r e b e i n g t u r n e d around t h e c e n t e r p l a t e . Smear photographs o f t h e i m p l o s i o n i n t h e s m a l l chamber r e v e a l e d o n l y one s m a l l p e r t u r b a t i o n q u i t e f a r b e h i n d t h e d e t o n a t i o n f r o n t ( f i g u r e 4-10a). On a s i m i l a r smear t a k e n o f t h e i m p l o s i o n i n t h e l a r g e chamber ( f i g u r e 4-14), we see a t l e a s t two w e l l marked p e r t u r b a t i o n f r o n t s ( f r o n t P i and P 2 ) -The f i r s t l u m i n o s i t y f r o n t w h i c h c a t c h e s up w i t h t h e d e t o n a t i o n f r o n t , i s not a p e r t u r b a t i o n but an o p t i c a l e f f e c t s i m i l a r t o t h e one d i s c u s s e d i n a p p e n d i x D. The p e r t u r b a t i o n s seem t o o r i g i n a t e from r e f l e c t i o n s o c c u r r i n g i n t h e wide c h a n n e l w h i c h c o n n e c t s t h e two s i d e s o f t h e chamber ( f i g u r e 3-2). These p e r t u r b a t i o n s not o n l y show up on t h e smears but a l s o i n t h e p r e s s u r e p r o f i l e s o f c h a p t e r 5. D e s p i t e t h e s e l a r g e p e r t u r b a t i o n s , t h e m o t i o n of t h e f r o n t c l o s e t o t h e c e n t e r o f i m p l o s i o n , i s s t i l l v e r y w e l l behaved and can be a c c u r a t e l y p r e d i c t e d by t h e C.C.W. model. T h i s was c o n f i r m e d e x p e r i m e n t a l l y f o r s e v e r a l gas m i x t u r e s (oxygen w i t h hydrogen, ethane, o r propane) and has been r e p o r t e d p r e v i o u s l y /23/. A t l a r g e r a d i i , however, t h e p r e s s u r e -measured a t t h e - f r o n t , c h a p t e r 5, i s much l a r g e r t h a n t h e p r e d i c t e d p r e s s u r e i n d i c a t i n g t h a t t h e f r o n t i t s e l f i s q u i t e p e r t u r b e d by t h e t u r n i n g phase. - 56 -F:"gure 4 - 1 4 : Imploding d e t o n a t i o n i n t h e l a r g e chamber. Eq u i m o l a r o x y - a c e t y l e n e m i x t u r e , i n i t i a l pressure=500 T o r r , sweep speed=8 usec/cm - 57 -CHAPTER 5 PRESSURE MEASUREMENTS The p h o t o g r a p h i c o b s e r v a t i o n s o f t h e p r e v i o u s c h a p t e r gave a good s u r v e y of t h e dynamics o f t h e c o n c e n t r i c i m p l o -d i n g d e t o n a t i o n and they a l s o p r o v i d e d a f i r s t q u a n t i t a t i v e check o f th e C.C.W. model. The second t e s t o f t h e t h e o r y i s t o measure t h e p r e s -s u r e b e h i n d t h e d e t o n a t i o n as a f u n c t i o n o f t h e r a d i u s and compare i t w i t h t h e p r e d i c t i o n s . Such a t e s t was f i r s t p e r -formed by Lee h i m s e l f / l / . R e c e n t l y , we succeded i n c a l i -b r a t i n g p i e z o e l e c t r i c p r e s s u r e probe by a n o v e l t e c h n i q u e u s i n g w e l l d e f i n e d l a r g e a m p l i t u d e p r e s s u r e p u l s e s o f s h o r t r i s e - t i m e . D e t a i l s of t h i s c a l i b r a t i o n can be found i n c h a p t e r 9. I t was t h e r e f o r e f e l t a p p r o p r i a t e t o measure t h e e n t i r e p r e s s u r e d i s t r i b u t i o n ' d u r i n g t h e i m p l o s i o n and * subsequent e x p a n s i o n phase . The p r e s s u r e v a l u e s immedia-t e l y b e h i n d t h e d e t o n a t i o n f r o n t were t h e n compared w i t h t h e th e C.C.W. model. Our r e s u l t s agree v e r y w e l l w i t h our nu-m e r i c a l s o l u t i o n o f the C.C.W. model, however, an u n e x p l a i n e d - d i s c r e p a n c y was found between Lee 1 s - s o l u t i o n and o u r s . 5-1 EXPERIMENTAL SET-UP: < * I am g r a t e f u l t o Mr. R. A r d i l a f o r h a v i n g t a k e n most o f the d a t a and reduced i t . - 58 -The p r e s s u r e d i s t r i b u t i o n was m e a s u r e d i n t h e two cham-b e r s . . The l a r g e c hamber b e i n g m o s t c o n v e n i e n t f o r m e a s u r e -m e n t s a t l a r g e r a d i i w h i l e t h e s m a l l one y i e l d e d t h e p r e s s u r e d i s t r i b u t i o n f o r s m a l l v a l u e s o f t h e r a d i u s . LARGE CHAMBER: The f r o n t p l a t e o f t h e l a r g e chamber was r e d e s i g n e d t o a c c o m o d a t e t h e p r e s s u r e p r o b e s d e s c r i b e d i n a p p e n d i x E. T h i s 3.7 5 cm t h i c k l u c i t e p l a t e was b u i l t w i t h t e n h o l e s t o f i t t h e p r o b e a t v a r i o u s r a d i a l p o s i t i o n s , f r o m r=R o=69.8 mm t o r=12.7 mm ( f i g u r e 3 - 2 ) . The p l a t e i s d e s c r i b e d i n a p p e n d i x A. "The p r e s s u r e was o b s e r v e d a t one s t a t i o n a t a t i m e , t h e r e m a i n i n g n i n e h o l e s b e i n g c l o s e d o f f by s p e c i a l l y made b r a s s p l u g s . The p r o b e o u t p u t was d i s p l a y e d on a n o s c i l l o s c o p e i n t h e same way u s e d i n t h e p r e s s u r e c a l i b r a t i o n ( c h a p t e r 9 ) . The o s c i l l o s c o p e t r a c e s w e r e r e c o r d e d o n T r i - X f i l m so t h a t t h e y c o u l d be e a s i l y e n l a r g e d . SMALL CHAMBER: The p r e s s u r e p r o f i l e s i n t h e s m a l l c h a m b e r w e r e r e c o r d e d a t f i v e p o s i t i o n s c l o s e t o t h e c e n t e r o f i m p l o s i o n . F i v e l u c i t e i n s e r t s w h i c h c o u l d be f i t t e d i n t h e q u a r t z w i n d o w h o l d e r w e r e made f o r t h i s p u r p o s e . E a c h i n s e r t h a s a h o l e t o f i t t h e p r o b e a t a g i v e n r a d i a l p o s i -t i o n , 0<r<12.2 mm ( f i g u r e 3 - 3 ) . T h e s e i n s e r t s a r e a l s o d e s -c r i b e d i n a p p e n d i x A. 5-2 QUALITATIVE RESULTS: T y p i c a l p r e s s u r e r e c o r d s i n t h e l a r g e a n d s m a l l c h a m b e r s - 59 -a r e shown i n f i g u r e 5-1 and f i g u r e 5-2 r e s p e c t i v e l y . I n t h e s e d i a g r a m s , t h e t i m e v a r i a t i o n o f t h e p r e s s u r e i s shown f o r t h e v a r i o u s o b s e r v a t i o n p o s i t i o n s a l o n g t h e r a d i u s o f t h e c h a m b e r s . The s c a l e o f t h e p r e s s u r e a x i s was o b t a i n e d f r o m t h e c a l i b r a t i o n c u r v e o f t h e p r e s s u r e p r o b e ( f i g u r e 9 - 5 ) . B o t h o f t h e s e f i g u r e s w e r e o b t a i n e d i n e q u i m o l a r o x y - a c e t y -l e n e d e t o n a t i o n s a t an i n i t i a l p r e s s u r e o f 400 T o r r . LARGE CHAMBER ( f i g u r e 5 - 1 ) : The l u m i n o s i t y f r o n t s o b s e r v e d i n t h e smear p h o t o g r a p h s o f t h e d e t o n a t i o n i n t h e l a r g e c h a m b e r ( f i g u r e 4-14) c a n be s e e n t o c o r r e s p o n d t o w e l l m a r k e d p e r t u r b a t i o n s i n t h e p r e s s u r e p r o f i l e s o f t h e d e t o n a t i o n , t h e s e a r e l a b e l l e d P i and P 2 a s i n t h e smear o f f i g u r e 4-14. T h e s e d i s t u r b a n c e s seem t o d e v e l o p i n t o s e c o n -d a r y s h o c k waves i n t h e r e a c t i o n p r o d u c t s a s t h e d e t o n a t i o n moves c l o s e r t o t h e c e n t e r . The v e r y s h a r p r a r e f a c t i o n wave f o l l o w i n g t h e d e t o n a t i o n f r o n t i s g r a d u a l l y f i l l e d i n a s t h e f r o n t sweeps i n w a r d s , c r e a t i n g a r e g i o n o f a l m o s t c o n s t a n t p r e s s u r e b e h i n d i t . T h i s e f f e c t i s due t o t h e c y l i n d r i c a l g e o m e t r y a s t h e r e a c t i o n p r o d u c t s , w h i c h f o l l o w t h e f r o n t , a r e c o n s t r i c t e d i n t o a s m a l l e r a n d s m a l l e r v o l u m e a s t h e r a d i u s d e c r e a s e s . The f o c u s i n g e f f e c t s o f t h e i m p l o s i o n s t a r t t o be s i g n i f i c a n t o n l y a f t e r t h e r a r e f a c t i o n wave h a s a b o u t b e e n f i l l e d i n and t h e p r e s s u r e b e h i n d t h e f r o n t h a s r e a c h e d a c o n s t a n t v a l u e e q u a l t o t h a t o f t h e f r o n t . SMALL CHAMBER ( f i g u r e 5 - 2 ) : The p r e s s u r e d i s t r i -b u t i o n i n t h e s m a l l c hamber i s much s m o o t h e r t h a n t h a t i n - 6 1 -t e d f r o n t I m p l o d i n g d e t o n a t i o n F i g u r e 5-2: P r e s s u r e d i s t r i b u t i o n i n t h e s m a l l chamber. E q u i m o l a r o x y - a c e t y l e n e , i n i t i a l pressure=400 T o r r , - 62 -t h e l a r g e chamber. No s i g n i f i c a n t d i s t u r b a n c e s a r e seen, and t h e r e f l e c t e d shock wave, g e n e r a t e d a t t h e c e n t e r o f c o l l a p s e , i s w e l l d e v e l o p e d . I t i s n o t p e r t u r b e d by any se c o n d a r y shock wave as i n t h e l a r g e chamber and shows a v e r y pronounced decay as i t moves outwards. The p r e s s u r e a t t h e c e n t e r was measured t o be a f a c t o r o f 15 above t h e c o r r e s p o n d i n g C.J. v a l u e of a p l a n e d e t o n a t i o n . S i m i l a r p r e s s u r e r e c o r d s were o b t a i n e d f o r o t h e r i n i -t i a l p r e s s u r e s . 5-3 COMPARISON WITH THE THEORY: In o r d e r t o compare t h e s e measurements w i t h t h e t h e o r y , t h e p r e s s u r e b e h i n d t h e f r o n t was n o r m a l i z e d by t h e C.J. p r e s s u r e o f a p l a n e s e l f - s u p p o r t e d d e t o n a t i o n and p l o t t e d as a f u n c t i o n o f t h e r e d u c e d r a d i u s , f , ( f i g u r e 5-3). The e r r o r b a r s i n t h e r a d i u s v a r i a b l e r e p r e s e n t t h e j i t t e r i n t h e i m p l o s i o n p o i n t o f t h e f r o n t . Our n u m e r i c a l s o l u t i o n o f t h e C.C.W. model i s shown as a s o l i d l i n e i n f i g u r e 5-3. The d a t a p o i n t s f i t t h i s c u r v e v e r y w e l l e x c e p t f o r v a l u e s o f f l a r g e r t h a n 0.5 . These p o i n t s were o b t a i n e d i n t h e l a r g e chamber and i n d i c a t e t h a t t h e f r o n t does n o t s t a r t as a C.J. d e t o n a t i o n a t r=R^ ( f = l ) . T h i s i m p l i e s t h a t t h e f r o n t i s v e r y much p e r t u r b e d by t u r n i n g around t h e c e n t e r p l a t e and c o n f i r m t h e a s s u m p t i o n t h a t t h e p e r t u r b a t i o n s P i and P 2 o f f i g u r e 5-1 o r i g i n a t e i n t h e c h a n n e l c o n n e c t i n g t h e two s i d e s o f t h e chamber. F i g u r e 5-3: V a r i a t i o n o f t h e d e t o n a t i o n p r e s s u r e w i t h r a d i u s . P r e s s u r e r e d u c e d t o t h e C.J. p r e s s u r e , and f r a c t i o n a l r a d i u s . - 64 -The dashed l i n e i n f i g u r e 5-3 i s Lee's / l / t h e o r e t i -c a l c u r v e f o r t h e C.C.W. model c a l c u l a t i o n s . T h i s c u r v e was t a k e n from r e f e r e n c e 1. I t i s o b v i o u s t h a t our d a t a p o i n t s f i t t h e s o l i d c u r v e b e t t e r t h a n t h e o t h e r . However, t h e s e two c u r v e s s h o u l d be t h e same s i n c e t h e y r e p r e s e n t t h e s o l u t i o n o f t h e same s e t o f e q u a t i o n s o f a n o n - d i m e n s i o n a l model. We made s u r e t h a t o ur t h e o r e t i c a l r e s u l t s were n o t i n e r r o r by r e w r i t i n g t h e program used i n t h e n u m e r i c a l s o l u t i o n o f e q u a t i o n s (2-35) and (2 - 3 8 ) , and o b t a i n e d c o n s i s -t a n t r e s u l t s u s i n g two d i f f e r e n t s o l u t i o n methods. The range o f g 2 used i n t h e c a l c u l a t i o n s a l s o i n c l u d e d t h e v a l u e used by Lee. T h e r e f o r e we f e e l t h a t our s o l u t i o n i s not i n e r r o r and the d i s c r e p a n c y remains u n e x p l a i n e d . W i t h t h e s t i p u l a t i o n t h a t our t h e o r e t i c a l c u r v e i s c o r r e c t , we can say t h a t t h e p r e s s u r e a t t h e d e t o n a t i o n f r o n t obeys t h e C.C.W. model v e r y c l o s e l y . S i n c e t h e f o c u s i n g e f f e c t f o r t h e p r e s s u r e i s a c c u r a t e l y d e s c r i b e d by th e C.C.W. model f o r t h e l a r g e and s m a l l chambers, we con-c l u d e t h a t t h e p r e s s u r e b u i l t - u p i s i n d e e d dependent on t h e d i m e n s i o n l e s s r a d i u s and not on the a b s o l u t e v a l u e o f t h e r a d i u s . - 65 -CHAPTER 6 SPECTRUM OF IMPLODING DETONATIONS In t h e smear camera s t u d y o f the i m p l o s i o n ( c h a p t e r 4 ) , we n o t i c e d a d i s t i n c t d i f f e r e n c e i n t h e l u m i n o s i t y f o r d i f -f e r e n t c o m p o s i t i o n s o f t h e d e t o n a t i n g gas m i x t u r e . T h i s r e m a r k a b l e d i f f e r e n c e i n b r i g h t n e s s must be a s s o c i a t e d w i t h a s i g n i f i c a n t d i f f e r e n c e i n t h e spectrum w h i c h f o l l o w s from changes i n t h e - r e a c t i o n p r o d u c t s o f t h e d e t o n a t i o n . I t was t h e r e f o r e d e c i d e d t o t a k e t i m e " i n t e g r a t e d but space r e s o l v e d s p e c t r a o f t h e d i s c h a r g e i n o r d e r t o d e t e r m i n e t h e r e a c t i o n p r o d u c t s r e s p o n s i b l e f o r t h e o b s e r v e d l u m i n o s i t y changes. 6-1 EXPERIMENTAL SET-UP: The s m a l l chamber w i t h t h e q u a r t z window was used f o r t h e s p e c t r o s c o p i c s t u d i e s . A q u a r t z window i s e s s e n t i a l a t t h i s p o i n t s i n c e l u c i t e i s n o t t r a n s p a r e n t t o w a v e l e n g t h s o s h o r t e r t h a n 4200 A. T h i s window had t o be changed p e r i o -d i c a l l y as i t c r a c k e d and g o t c o a t e d w i t h c a r b o n and w i t h some m e t a l l i c d e p o s i t , p r o b a b l y b r a s s s t r i p p e d from t h e i g n i -t i o n e l e c t r o d e s , t h e wedges, o r t h e window h o l d e r . The s p e c t r o g r a p h used was a H i l g e r medium q u a r t z p r i s m o o s p e c t r o g r a p h h a v i n g a d i s p e r s i o n o f about 36 A/mm a t 4000 A and an f number o f 8. A d i a m e t e r o f t h e chamber was imaged Only i n r i c h m i x t u r e s . - 6 6 -o n t o t h e s l i t o f t h e s p e c t r o g r a p h . Space r e s o l v e d but t i m e i n t e g r a t e d s p e c t r a were o b t a i n e d t h i s way. Kodak I-F spec-t r o g r a p h ^ p l a t e s were used and d e v e l o p e d i n D-19 a c c o r d i n g t o t h e s p e c i f i c a t i o n s . About 2 t o 5 superimposed s h o t s were r e q u i r e d t o o b t a i n w e l l exposed p l a t e s . 6-2 DISCUSSION OF THE SPECTRA: The spectrum o f an e q u i m o l a r o x y - a c e t y l e n e i m p l o d i n g d e t o n a t i o n i s shown i n f i g u r e 6-1. T h i s p l a t e was t a k e n w i t h o u t a f o c u s i n g l e n s between t h e chamber and t h e s l i t o f the s p e c t r o g r a p h , hence t h e s p a c i a l dependence o f t h e spectrum i s n o t o b s e r v e d h e r e . Other t y p i c a l s p e c t r a , t a k e n w i t h t h e f o c u s i n g l e n s , a r e shown i n f i g u r e 6-2. The s p e c t r a i n t h i s f i g u r e a r e a r r a n g e d i n o r d e r o f i n c r e a s i n g a c e t y l e n e concen-t r a t i o n . As e x p e c t e d , t h e spectrum o f t h e d e t o n a t i o n i s v e r y s e n s i t i v e t o t h e gas c o m p o s i t i o n . The a l m o s t pure OH band spectrum o f s t o i c h i o m e t r i c and l e a n m i x t u r e s ( p l a t e s A & B) changes t o a s t r o n g c a r b o n r a d i c a l s ( C 2 , CH, CN) band s p e c t r u m i n r i c h m i x t u r e s ( p l a t e D). I n v e r y r i c h m i x t u r e s , o n l y a low t e m p e r a t u r e c a r b o n continuum appears ( p l a t e F ) . The t e m p e r a t u r e measurements o f c h a p t e r 7 a r e o b t a i n e d o from t h e CN 3883 A band system w h i c h appears o n l y w e a k l y i n p l a t e D. I n an attempt t o i n c r e a s e t h e i n t e n s i t y of t h i s s ystem, a s m a l l p e r c e n t a g e o f n i t r o g e n was added t o t h e gas m i x t u r e ( p l a t e s C & E) . The spectrum o f t h e s e two p l a t e s show a v e r y marked d e c r e a s e i n i n t e n s i t y of t h e C 2 and CH - 67 -A l - 3 9 4 4 , CN-4216,CH-4315, *• A (A) CN-3590, :N-3383 , X (A) A l - 3 0 9 3 , A l - 3 0 8 2 , OH-3064, | CH-3157, CH-3145, Cu-3274, Cu-3248, F i g u r e 5-1: E n l a r g e d spectrum o f an i m p l o d i n g d e t o n a t i o n i n e q u i m o l a r o x y - a c e t y l e n e . ( N o f o c u s i n g l e n s ) I I OH-3064A system. I 1 C N - V i o l e t system. I — — l C 2-Swan 0system. I 1 CH-4300A system. I 1 CN-Red system. F i g u r e 6-2: S p e c t r a o f i m p l o d i n g d e t o n a t i o n s f o r v a r i o u s gas c o m p o s i t i o n s . - 69 -band system w h i l e t h e CN becomes the most i n t e n s e f e a t u r e . T h i s w i l l a l l o w us t o j u s t i f y some o f t h e a s s u m p t i o n s made i n • t h e t e m p e r a t u r e measurements. B e s i d e s t h e m o l e c u l a r bands, a w e l l marked continuum appears a t t h e c e n t e r o f i m p l o s i o n . T h i s continuum and t h e e x t e n s i o n o f t h e band.systems on t h e a x i s o f t h e chamber, suggest a f a i r l y h i g h t e m p e r a t u r e a t t h e f o c u s of t h e i m p l o -s i o n . Two c o n t i n u a can be seen i n p l a t e D ( I i and i 2 ) . These c o r r e s p o n d t o t h e two s h o t s used i n t h e e x p osure of t h e p l a t e ; t h e two c o l l a p s e s d i d not o c c u r a t t h e same p o s i t i o n a l o n g t h e s l i t and r e c o r d e d as two d i s t i n c t c o n t i n u a . P e r s i s t e n t a t o m i c l i n e s o f v a r i o u s elements were i d e n -t i f i e d as L i , Na, Ca, A l , and Cu. The Ca, Cu, and Na l i n e s were always p r e s e n t . The o t h e r l i n e s appeared o n l y i n t h e f i r s t few s p e c t r a t a k e n t h r o u g h a newly p o l i s h e d window and can t h e r e f o r e be a t t r i b u t e d t o r e s i d u e s o f t h e p o l i s h i n g com-pound l e f t on t h e window. Some d e t a i l s of t h e s p e c t r a , l i k e o t h e bands around 6300 and 3300 A ( p l a t e C ) , were not i d e n t i f i e d . 6-3 RICH AND LEAN MIXTURES: The g r e a t d i f f e r e n c e i n t h e e m i s s i o n s p e c t r a of r i c h -and l e a n m i x t u r e s can be e x p l a i n e d u s i n g t h e n e t r e a c t i o n f o r e q u i m o l a r c o n c e n t r a t i o n : C 2 H 2 + 0 2 2 CO + H 2 F o r r i c h m i x t u r e s , a s l i g h t e x c e s s a c e t y l e n e i s p r e s e n t - 70 -and decomposes r e a d i l y t o CH and C 2, t h u s s t r o n g bands of t h e s e r a d i c a l s a r e e m i t t e d . When n i t r o g e n i s p r e s e n t , i t r e a c t s w i t h t h e l e f t o v e r c a r b o n t o produce CN and t h e r e f o r e s t r o n g CN bands a r e e m i t t e d . I n l e a n m i x t u r e s , on t h e o t h e r hand, oxygen i s i n e x c e s s f o r t h e above r e a c t i o n and t h e r e f o r e some of t h e hydrogen w i l l be o x i d i z e d t o form OH and H 20 . T h i s r e a c t i o n i s f a v o u r e d o v e r o v e r t h e f o r m a t i o n o f C 0 2 s i n c e t h e o x i d i z a t i o n o f c a r b o n monoxide i s a slow r e a c t i o n . Thus i n l e a n m i x t u r e s , OH bands appear as t h e predominant s p e c t r a l f e a t u r e ( p l a t e s B & D). T h i s predominance o f e i t h e r OH o r C 2 and CH bands a l s o s o l v e s t h e q u e s t i o n o f t h e l u m i n o s i t y v a r i a t i o n o b s e r v e d on t h e smear p h o t o g r a p h s . S i n c e normal g l a s s l e n s e s were used t o f o c u s t h e s l i t of t h e smear camera onto t h e chamber, t h e u l t r a v i o l e t OH r a d i a t i o n i s not r e c o r d e d on t h e f i l m . Thus t h e l u m i n o s i t y of d e t o n a t i o n s i n l e a n mix-t u r e s appears v e r y weak on t h e f i l m compared t o t h a t o f d e t -o n a t i o n s i n r i c h m i x t u r e s , w h i c h r a d i a t e m a i n l y i n t h e v i s i -b l e range of t h e spectrum. The above o b s e r v a t i o n s seem t o be i n good agreement w i t h p r e v i o u s i n v e s t i g a t i o n s p a r t i c u l a r l y t h a t o f F a i r b a i r n and Gaydon /24/ and t h a t o f Gaydon /25/. The t a b l e s o f P e a r s e and Gaydon /26/ were used f o r most o f t h e i d e n t i f i c a t i o n o f the bands. * o G l a s s i s not t r a n s p a r e n t f o r w a v e l e n g t h s below ^ 3800 A. - 71 -CHAPTER 7 TEMPERATURE MEASUREMENTS The l a r g e i n c r e a s e i n l u m i n o s i t y a t t h e c e n t e r o f c o l l a p s e o b s e r v e d i n t h e photographs o f t h e i m p l o s i o n and th e p r e s e n c e o f a continuum a t t h e f o c u s o f i m p l o s i o n i n t h e t i m e - i n t e g r a t e d s p e c t r a , were i n t e r p r e t e d as i n d i c a t i v e o f h i g h p r e s s u r e s and t e m p e r a t u r e s . The v e r y h i g h p r e s s u r e i n c r e a s e was i n d e e d v e r i f i e d by t h e measurements o f c h a p t e r 5, t h u s i t remains t o o b t a i n t h e t e m p e r a t u r e f i e l d t o v e r i -f y t h e i n t e r p r e t a t i o n . The d i a g n o s t i c t e c h n i q u e s used t o measure t h e tempe-r a t u r e o f a plasma a r e c e n t e r e d on t h e a n a l y s i s of t h e spec-trum, e i t h e r i n e m i s s i o n o r i n a b s o r p t i o n . The g r e a t advan-t a g e o f t h e s e methods i s t h a t t h e y do not d i s t u r b t h e plasma under s t u d y . They have, on t h e o t h e r hand, some s i g n i f i c a n t draw-backs. The a n a l y s i s o f the d a t a r e q u i r e s a s s u m p t i o n s about t h e s t a t e o f t h e plasma w h i c h a r e o f t e n n o t met by t h e e x p e r i m e n t a l c o n d i t i o n s . Thermal e q u i l i b r i u m i s t h e most c o n t r o v e r s i a l a s s u m p t i o n s i n c e i t may be h a r d t o a s c e r t a i n t h e v a l i d i t y o f t h e e q u i l i b r i u m c r i t e r i a i n a t r a n s i e n t p l a s -ma. The t e m p e r a t u r e measurements o f t h i s c h a p t e r a r e based o on t h e a n a l y s i s o f t h e 3883 A band system o f t h e CN m o l e c u l e . The anomalous r e s u l t s a r e e x p l a i n e d by a non-t h e r m a l p o p u l a -- 72 -t i o n o f t h e v i b r a t i o n a l l e v e l s o f t h e m o l e c u l e . 7-1 THEORY OF MEASUREMENTS: When v i e w e d w i t h a l o w d i s p e r s i o n s p e c t r o g r a p h , m o l e -c u l a r b a n d s a p p e a r l i k e c o n t i n u u m r a d i a t i o n . T h i s c o n t i n u u m i s a c t u a l l y c omposed o f o v e r l a p p i n g , n o n - r e s o l v e d r o t a t i o n a l l i n e s and t h e r e f o r e some i n f o r m a t i o n a b o u t t h e t e m p e r a t u r e o f t h e e m i t t e r s c a n be o b t a i n e d f r o m t h e s h a p e o f t h e m o l e -c u l a r b a n d /27, 28, 29/. The i n t e n s i t y c o n t r i b u t i o n a t w a v e l e n g t h X o f a l i n e a t w a v e l e n g t h X^ and o f t o t a l i n t e n s i t y P^, i s g i v e n b y : H i(X) « P ^ ^ ) f(X-X i) (7-1) w h e r e f (X-X^) i s t h e l i n e s p r e a d f u n c t i o n w h i c h i s a c o n v o -l u t i o n o f t h e i n s t r u m e n t f u n c t i o n a n d o f t h e o r i g i n a l l i n e p r o f i l e . H e n c e : H(X) = I P i ( X i ) f (X-Xi) (7-2) i i s t h e t o t a l i n t e n s i t y a t X on t h e p l a t e o f t h e s p e c t r o -g r a p h o r t h e s l i t o f t h e m o n o c h r o m a t o r . N o t e t h a t t h e p r o -p o r t i o n a l i t y c o n s t a n t o f e q u a t i o n (7-1) h a s b e e n s e t t o 1 i n e q u a t i o n (7-2) s i n c e o n l y r e l a t i v e i n t e n s i t i e s a r e r e q u i -r e d . A h a l f w i d t h AX^ c a n a l w a y s be d e f i n e d by means o f t h e l i n e s p r e a d f u n c t i o n f (X-X^) . I f we t a k e a w a v e l e n g t h i n -t e r v a l AX , c e n t e r e d on X , s u c h t h a t AX /AX < l / 3 , t h e t o t a l s' o s I -o b s e r v e d i n t e n s i t y i n t h i s i n t e r v a l i s g i v e n b y : H(X ) = T P. (X.) AX g(X.-X ) (7-3) where g(A.-A ) i s t h e t o t a l s l i t f u n c t i o n i o •A +?AA -, o s g(A.-A ) = -AAs f ( X - X ± ) dA (7-4) A - 7 A A o s The w a v e l e n g t h i n t e r v a l , AA g, can e i t h e r be t h e w i d t h of t h e e x i t s l i t o f t h e monochromator o r t h e s l i t - w i d t h of the m i c r o d e n s i t o m e t e r used t o scan t h e s p e c t r o g r a p h i c p l a t e s . By i n s e r t i n g t h e v a l u e s o f P^, w h i c h can be c a l c u l a t e d i n the c a s e of the CN bands, Watson e t a l /29/ were a b l e t o f i n d t h e o r e t i c a l i n t e n s i t y p r o f i l e s o f t h e band s y s t e m . f o r pure CN r a d i a t i o n i n an o p t i c a l l y t h i n plasma. They found t h a t t h e s l o p e o f t h e l o g a r i t h m i c i n t e n s i t y c u r v e o f t h e o o 3883 A band system a t 3810 A i s a s i m p l e f u n c t i o n o f t h e t e m p e r a t u r e , f i g u r e 7-1, independent o f t h e s l i t f u n c t i o n used i n t h e c a l c u l a t i o n s . I t i s i n t e r e s t i n g t o note t h a t i f t h i s c u r v e i s p l o t t e d on l o g a r i t h m i c s c a l e s , f i g u r e 7-2, th e r e l a t i o n t u r n s out t o be l i n e a r . T h i s f a c t w i l l be used t o o b t a i n a c c u r a t e e x t r a p o l a t i o n s o f t h e d a t a g i v e n by Watson e t a l i n r e f e r e n c e 29. B e f o r e a p p l y i n g t h e s l o p e c r i t e r i o n t o d e t e r m i n e t h e t e m p e r a t u r e o f t h e plasma, t h e u n d e r l y i n g a s s u m p t i o n s have t o be examined i n t h e l i g h t o f t h e e x p e r i m e n t a l s e t - u p . The r e l a t i o n shown i n f i g u r e 7-1 i s v a l i d o n l y f o r pure CN r a d i a t i o n ; any a p p r e c i a b l e c o n t r i b u t i o n from a background continuum o r from a n o t h e r band system w i l l a l t e r t h e r e s u l t s i n an u n p r e d i c t a b l e way u n l e s s t h e e x a c t amount and shape - 74 -2000 3000 4000 5000 6000 Temperature (°K) 4 i|.tttj-tHf+ :H#i1+y|{iiitEfl±^ ± 3 -u 1 ijjj jr. ! " i~ ~M I iffi 'igure 7-2: P l o t o f Watson's W TUri d a t a on l o g - l o g is; s c a l e s . I S ± fx., xrit 2.5 : falErji l^ i^T: E 2 -EEE! Eitlti ii-H •ttrM++t : 1.5 : n fitiiit fljTffj i J J J J 1J ,::E 3. +fcj M ~,—t: _-i4r.--.r^  tJSEjti T ~T-!--r-H- •*+•:+) TH-: ~I i J—1 {_ j+t .-;-'+; zatilifi -i-f-i —H-i-rrf^  m l i t - : , I f f THT TiTi Eff •l-tii :E i E* i_t i .-rt i ' ; i i - 4 El+Eiil -mm 11ii:tirt m hi] ] 1 ni --L—it iW :I;T ! 1 —r—j j—-t™ 11 ±i±!±iJH iritLui jkni; W ^ .9 ^ !i , i! t •ttSff EH iff; . i 1 i Sff" l 1 ! M i l ! i < 11 ni H : i 1 ; 1 i Mil i i O f O .8.-! J4EE -EH:; -n ' i - " .— iffi E S Eff -j-t—t-'EEfE^  E?EE?E§: ESEE-5=fE i—1 J X .7 -< EE'?! "-4 ilzHt;; EE Ef I S E E : ;tixrnq±r - - -E p i 1 i-h 4+;--- 1 •" -fiE rrb ; i : -H-ri-rEH-tfjfri-H-. Jr:.-.-j: x M- r. O :T f nnEirr" IE:"-". ~ iH::: jr= E :;EI :-:-;:. ; :\ -;Lv;.r;:-:.:. 1 - 1 5 ? rn . #§E EE; s •n;: - =E — E; . : :• • . . :r.:^ :::-.:- T aEEi iff!iii! fji E: fffi ffE Efi: f—r- - r;': E! :ifEffE Effffii E-.4 '-t :p +rfjiiu E; xdit n EE IE r:: H-r-i-.-n . -r-^ r-T,- ± .3 1 3 M : i i E E:H: ±Lrx ~ - : EnEJ1 Lj..-i^ .. .2.5 1111 11 M •E =f3i - .:. • . E : : • : : : ^;:E:I i i i 1 i:^\:r;;iiE;E;i ,- <2J : 111 Ei -E. S S "E"±:*: IE:: -f-^-EE&ff 4-—^ fff-rE 4 5 6 7 8 9 1 0 . 1 5 20 25 30 Temperature (°K x K ) - 3 ) - 75 -o f t h e s e c o n t r i b u t i o n s a r e known so t h a t t h e y can be e l i m i -n a t e d from t h e i n t e n s i t y c u r v e . In o r d e r t o a v o i d t h e s e c o m p l i c a t e d and o f t e n i m p o s s i b l e c o r r e c t i o n s , a s l i g h t l y r i c h gas m i x t u r e w i t h a s m a l l p e r c e n t a g e o f a i r was. used. I n t h i s c a s e , t h e spectrum ( p l a t e E i n f i g u r e 6-2) i s a l m o s t p u r e l y CN and t h e continuum i s c o m p l e t e l y s u p r e s s e d e x c e p t v e r y c l o s e t o t h e c e n t e r o f i m p l o s i o n . The CH bands w h i c h a r e t h e c l o s e s t system t o t h e r e g i o n o f i n t e r e s t a r e v e r y o weak and i n f a c t do n o t e x t e n d beyond 387 2 A i n t h e low wave-l e n g t h r e g i o n . C o n t r i b u t i o n s from a t o m i c l i n e s have no e f -f e c t on t h e s l o p e . e v e n i f some were p r e s e n t , w h i c h i s n o t t h e c a s e . A n o t h e r a s s u m p t i o n i s , of c o u r s e , t h e r m a l e q u i l i b r i u m . S i n c e t h e r o t a t i o n a l l i n e s o f d i f f e r e n t v i b r a t i o n a l s t a t e s a r e superimposed t o g i v e t h e s l o p e o f t h e t a i l of t h e CN band system, b o t h r o t a t i o n a l and v i b r a t i o n a l e q u i l i b r i u m a r e assumed. I t i s o n l y under t h e s e c o n d i t i o n s t h a t t h e r e l a t i v e i n t e n s i t i e s o f t h e l i n e s , P . ( X . ) , can be c a l c u l a t e d . 1 x R o t a t i o n a l e q u i l i b r i u m i s u s u a l l y e s t a b l i s h e d w i t h i n a few c o l l i s i o n s /30, 31/ and t h e r e f o r e i s a v e r y f a s t p r o c e s s . V i b r a t i o n a l e q u i l i b r i u m , on t h e o t h e r hand, has a l o n g r e l a x -— a t i o n -time-which-depends on t h e t e m p e r a t u r e , t h e p r e s s u r e and t h e t y p e o f m o l e c u l e s p r e s e n t i n t h e gas. Greene and T o e n n i e s / 3 1 / quote v a l u e s o f 14-42 ysec f o r t h e r e l a x a t i o n t i m e o f t h e CN v i b r a t i o n a l s t a t e s i n t h e t e m p e r a t u r e range o f 9550 t o 6000 °K a t an u n s p e c i f i e d p r e s s u r e . T h i s v e r y - 76 -l o n g r e l a x a t i o n t i m e m i g h t c a u s e some p r o b l e m s w h i c h w i l l be d i s c u s s e d l a t e r i n t h e l i g h t o f t h e e x p e r i m e n t a l d a t a . The c a l c u l a t i o n s o f t h e b a nd s l o p e / 2 9 / w e r e d o n e f o r a n o p t i c a l l y t h i n p l a s m a w h e r e t h e e m i s s i o n o f t h e b a n d i s much s m a l l e r t h a n t h e e m i s s i o n o f a b l a c k - b o d y a t t h e same t e m p e r a t u r e . I f f o r a g i v e n s p e c t r a l f e a t u r e , t h e e m i s s i o n l e v e l i s c l o s e t o t h a t o f t h e b l a c k - b o d y , t h e s h a p e o f t h i s l i n e o r b a n d w i l l be d i s t o r t e d by a b s o r p t i o n , t h e w i n g s a n d t a i l s b e i n g l e s s a b s o r b e d t h a n t h e p e a k s . No d i r e c t m easu-r e m e n t s o f t h e o p t i c a l t h i c k n e s s o f t h e p l a s m a was made. An i n d i r e c t e v i d e n c e showed, h o w e v e r , t h a t t h e p l a s m a i s p r a c t i c a l l y o p t i c a l l y t h i n e v e n f o r t h e s t r o n g l y e m i t t e d b a n d s . T h i s e v i d e n c e s h a l l become c l e a r a s t h e r e s u l t s a r e d i s c u s s e d l a t e r i n t h i s c h a p t e r . 7-2 TIME INTEGRATED TEMPERATURE: S p e c t r o g r a p h i c p l a t e s s i m i l a r t o t h o s e i n t h e p r e v i o u s c h a p t e r c a n be u s e d t o o b t a i n s p a c e r e s o l v e d b u t t i m e i n t e -g r a t e d t e m p e r a t u r e s . The c a l c u l a t i o n s o f W a t s o n e t a l w e r e done f o r G a u s s i a n a n d u n i f o r m l i n e s p r e a d f u n c t i o n s h a v i n g a n e q u i v a l e n t w i d t h o o f 1-6 A. " T h i s r e q u i r e m e n t i s e a s i l y met e x p e r i m e n t a l l y by u s i n g t h e s m a l l q u a r t z s p e c t r o g r a p h d e s c r i b e d i n t h e p r e v i o u s c h a p t e r . The l i n e s p r e a d f u n c t i o n was d e t e r m i n e d e x p e r i m e n -t a l l y f r o m t h e w i d t h o f an i r o n l i n e t a k e n w i t h v a r i o u s s l i t o w i d t h . F i g u r e 7-3a shows a t y p i c a l p r o f i l e o f t h e 3865.5 A - 77 -- 6 - 3 0 . 3 6 X (A) -*-o F i g u r e 7-3a: P r o f i l e o f t h e 3865.5 A Fe l i n e t a k e n w i t h a 25 y s l i t w i d t h and scanned w i t h a 7 y s l i t . i i i i r 5 10 15 20 25 S p e c t r o g r a p h s l i t - w i d t h (y) o F i g u r e 7-3b: Maximum i n t e n s i t y and h a l f - w i d t h o f t h e Fe 3865.5 A l i n e as a f u n c t i o n o f t h e s l i t w i d t h o f t h e s p e c t r o g r a p h . - 78 -i r o n l i n e c h o s e n f o r t h i s p u r p o s e . The r e l e v a n t d a t a c a n be f o u n d o n t h e f i g u r e . The v a r i a t i o n o f t h e w i d t h and p e a k i n t e n s i t y o f t h e l i n e a r e shown i n f i g u r e 7-3b. The o d i s p e r s i o n o f t h e s p e c t r o g r a p h i s 31.5 A/mm i n t h i s r e g i o n h e n c e , t h e e f f e c t i v e s l i t w i d t h c a n be f o u n d f r o m f i g u r e 7-3b. We u s e d a s l i t o f 25 y w h i c h c o r r e s p o n d s t o a n e f f e c t i v e w i d t h o o f 3 A. T h i s s l i t w i d t h i s i n t h e m i d d l e o f t h e r a n g e u s e d by W a t s o n e t a l and t h e r e f o r e s h o u l d be s a t i s f a c t o r y . S i n c e s p e c t r o g r a p h i c p l a t e s a r e n o n - l i n e a r r e c o r d s o f w a v e l e n g t h and i n t e n s i t y , t h e y must be c a l i b r a t e d . The wave-l e n g t h c a l i b r a t i o n was d o n e by t a k i n g a p h o t o g r a p h o f t h e s p e c t r u m o f a n i r o n a r c . W i t h t h e h e l p o f t h e i d e n t i f i c a t i o n o f t h e i r o n l i n e s , t h e d i s t a n c e a x i s o n t h e p l a t e c a n be c o n -v e r t e d , t o a w a v e l e n g t h s c a l e . T h i s c a l i b r a t i o n d o e s n o t n e e d t o be done f o r e a c h p l a t e s i n c e i t d e p e n d s on t h e s p e c -t r o g r a p h a n d n o t o n t h e p l a t e . The i n t e n s i t y c a l i b r a t i o n , o n t h e o t h e r h a n d , n e e d s t o be done f o r e a c h p l a t e a s t h e r e s p o n s e o f t h e e m u l s i o n m i g h t v a r y f r o m p l a t e t o p l a t e . T h i s c a l i b r a t i o n was done i n a s t a n d a r d way u s i n g a t u n g s -t e n f i l a m e n t lamp and a 7 - s t e p n e u t r a l d e n s i t y f i l t e r ( H i l -g e r F 1 2 7 3 ) . The f i l a m e n t o f t h e lamp was f o c u s e d by a q u a r t z l e n s o n t o t h e e n t r a n c e s l i t o f t h e s p e c t r o g r a p h . The s t e p f i l t e r was t h e n p l a c e d i n f r o n t o f t h e s l i t a n d a p l a t e e x -p o s e d f o r a f e w s e c o n d s t o o b t a i n t h e p r o p e r d e n s i t y v a r i a -t i o n s o n t h e e m u l s i o n . U s i n g t h e known t r a n s m i s s i o n o f t h e v a r i o u s s t e p s o f t h e f i l t e r , a n d m e a s u r i n g t h e c o r r e s p o n d i n g - 79 -e m u l s i o n d e n s i t y , a p l o t o f t h e p l a t e d e n s i t y v e r s u s r e l a t i v e i n t e n s i t y can be o b t a i n e d (H&D c a l i b r a t i o n c u r v e ) . T h i s c a l i b r a t i o n c u r v e can t h e n be used t o c o n v e r t d e n s i t y r e c o r d s t o r e l a t i v e i n t e n s i t y p l o t s . The p l a t e s were t a k e n w i t h t h e s l i t o f t h e s p e c t r o -graph f o c u s e d a l o n g a d i a m e t e r o f t h e chamber. F i g u r e 7-4 shows a t y p i c a l p l a t e from w h i c h t h e t i m e averaged tempera-t u r e o f t h e d i s c h a r g e can be o b t a i n e d . The two s e t s o f c a -l i b r a t i o n s t e p s were produced w i t h t h e s t e p f i l t e r i n con-j u c t i o n w i t h a n e u t r a l d e n s i t y f i l t e r ( d e n s i t y = 0 . 4 ) . A m i -c r o d e n s i t o m e t e r , w i t h i t s s l i t w i d t h and h e i g h t s e t a t 15 u and 500 u r e s p e c t i v e l y , was used t o o b t a i n t h e c a l i b r a t i o n c u r v e o f t h e e m u l s i o n . The p l a t e was t h e n scanned a t v a r i o u s r a d i a l p o s i t i o n s w i t h t h e same s e n s i t i v i t y and s l i t on t h e s c a n n i n g d e v i c e . The s l i t s e t t i n g s gave an e f f e c t i v e wave-o l e n g t h r e s o l u t i o n o f 0.5 A and a s p a c i a l r e s o l u t i o n of ap-p r o x i m a t e l y 8 mm a l o n g t h e d i a m e t e r o f t h e chamber. The m i c r o d e n s i t o m e t e r t r a c e s were hand averaged t o smooth out t h e e f f e c t s o f t h e g r a i n i n e s s o f t h e p l a t e , t h e n t h e s e ave-r a g e d d e n s i t y t r a c e s were c o n v e r t e d i n t o r e l a t i v e i n t e n s i t y p l o t s on a l o g a r i t h m i c s c a l e making use of t h e c a l i b r a t i o n "curve o f t h e e m u l s i o n s e n s i t i v i t y . "The t e m p e r a t u r e was t h e n o d e t e r m i n e d from t h e s l o p e o f t h i s c u r v e a t 3810 A. 7-3 SPACE-TIME RESOLVED MEASUREMENTS: The t i m e v a r i a t i o n o f t h e i n t e n s i t y o f t h e CN band s y s -80 -CN-4216, CN-3883, * A, (A) CN-3590, C a l i b r a t i o n s t e p s 2.5 cm C e n t e r o f chamber 2.5 cm *• C a l i b r a t i o n s t e p s w i t h 0.4 N.D. f i l t e r . F i g u r e 7-4: T y p i c a l p l a t e o f the CN v i o l e t system used i n t h e temperature measurements. P l a t e exposed w i t h 2 s h o t s Rogowski c o i l ;» , \ > \ ', i v i v ; , \, \ • » , P M T r i g g e r i n p u t . Chamber Monochromator O s c i l l o s c o p e F i g u r e 7-5: E x p e r i m e n t a l set-up f o r the time r e s o l v e d tempe-r a t u r e measurements. P M = P h o t o m u l t i p l i e r . - 81 -tern was observed w i t h a monochromator-photomultiplier a r r a n -gement. From these r e c o r d s , i t was p o s s i b l e to o b t a i n the time h i s t o r y of the temperature. F i g u r e 7-5 shows a sk e t c h of the experimental set-up. The monochromator i s J a r r e l l Ash 1/4 meter g r a t i n g i n s t r u -ct o went (bl a z e d a t 3000 A) w i t h a d i s p e r s i o n of 33 A/mm and with 100 y entrance and e x i t s l i t s which gave a l i n e spread f u n c t i o n s i m i l a r to those used by Watson e t a l . In order to o b t a i n s p a c i a l r e s o l u t i o n , the c e n t e r p a r t of the entrance s l i t of the monochromator (250 y) was focused 1:1 onto the chamber. The remaining l e n g t h of the s l i t was masked o f f to prevent s t r a y l i g h t from i n t e r f e r i n g with the r e c o r d s . The chamber was mounted on a t r a c k and c o u l d be moved by means of a threaded bar. T h i s enabled the image of the s l i t t o be p o s i t i o n e d anywhere along the diameter of the chamber. The p h o t o m u l t i p l i e r i s a 931A RCA tube. I t s S-4 spec-o t r a l response peaks a t about 4 000 A and t h e r e f o r e i t s sen-s i t i v i t y should not change a p p r e c i a b l y over the range of o wavelength i n v e s t i g a t e d (3790 to 3830 A). The l i n e a r i t y of the p h o t o m u l t i p l i e r was t e s t e d e x p e r i m e n t a l l y by means of a l i g h t p u l s e of about 5 ysec d u r a t i o n . T h i s p u l s e was pro-e d u c e d w i t h the h e l p of the smear camera and of a sun-gun. The l i g h t i n t e n s i t y was v a r i e d by p l a c i n g n e u t r a l d e n s i t y f i l t e r s i n f r o n t of the p h o t o m u l t i p l i e r . The p l o t of the p h o t o m u l t i p l i e r output v o l t a g e v e r s u s i n t e n s i t y was found to be l i n e a r i n the range of v o l t a g e s observed d u r i n g the - 82 -measurements o f t h e CN band i n t e n s i t y . The c o a x i a l c a b l e between t h e p h o t o m u l t i p l i e r and t h e o s c i l l o s c o p e was t e r m i -n a t e d by i t s c h a r a c t e r i s t i c impedance t o p r e v e n t r e f l e c t i o n s i n t h e c a b l e w h i c h c o u l d a l t e r s i g n i f i c a n t l y t h e shape o f t h e s i g n a l . The 545-A T e k t r o n i x o s c i l l o s c o p e was t r i g g e r e d by t h e p u l s e from a Rogowski c o i l p l a c e d around t h e d i s c h a r g e i g n i -t i o n l e a d s . The sweep o f t h e t r a c e was d e l a y e d i n t e r n a l l y so t h a t t h e s i g n a l c o u l d be d i s p l a y e d on a c o n v e n i e n t t i m e s c a l e . The measurements were r e p e a t e d a t l e a s t f o u r t i m e s a t each o f t h e f i v e w a v e l e n g t h s o b s e r v e d (3790, 3800, 3810, o 3820, and 3830 A) i n an a t t e m p t t o average o u t t h e i r r e p r o -d u c i b i l i t y i n t r o d u c e d by t h e j i t t e r i n t h e c o l l a p s e p o i n t . The measurements were t a k e n a t n i n e r a d i a l p o s i t i o n s on b o t h s i d e s o f t h e chamber. I n v i e w o f t h e g r e a t e r s e n s i t i v i t y o f t h e p h o t o m u l t i p l i e r compared t o t h e s p e c t r o g r a p h i c p l a t e s , a much s m a l l e r i n i t i a l p r e s s u r e c o u l d be used. S u f f i c i e n t i n t e n s i t y was o b t a i n e d w i t h an i n i t i a l p r e s s u r e o f 200 T o r r ( 8 0 C 2 H 2 + 7 5 O 2 + 5 A i r ) . A t t h i s low p r e s s u r e , t h e q u a r t z window d i d n o t c r a c k and needed o n l y t o be p o l i s h e d from t i m e t o t i m e . Some t y p i c a l o s c i l l o g r a m s a r e shown i n f i g u r e 7-6. The t r a c e s were t a k e n on T r i - X f i l m t o t r a n s f e r them e a s i l y o n t o g r a p h pa p e r . From t h e shape o f t h e t r a c e s , i t was p o s s i b l e t o e l i m i n a t e t h e r e c o r d s o f g r o s s l y e c c e n t r i c s h o t s . T h i s - 83 -t -> (2 y s e c / d i v ) > • H \ > C) r=22.5 mm t -*• (5 y s e c / d i v ) F i g u r e 7-6: T y p i c a l i n t e n s i t y v a r i a t i o n s o f t h e CN band a t o 3790 A a t t h r e e r a d i a l p o s i t i o n s . - 84 -was s p e c i a l l y i m p o r t a n t a t or c l o s e t o t h e c e n t e r where t h e i n t e n s i t y depends a g r e a t d e a l on t h e e x a c t p o s i t i o n of t h e c o l l a p s e p o i n t . The r e l a t i v e i n t e n s i t i e s o b s e r v e d a t a g i v e n t i m e and r a d i a l p o s i t i o n were p l o t t e d on s e m i - l o g a -r i t h m i c paper v e r s u s w a v e l e n g t h . The b e s t f i t s t r a i g h t l i n e t h r o u g h t h e p o i n t s was found and t h e t e m p e r a t u r e d e t e r m i n e d from t h e s l o p e o f t h e l i n e and o f t h e graph o f f i g u r e 7-2. • A f t e r h a v i n g o b t a i n e d a few t e m p e r a t u r e s by hand c a l c u l a -t i o n s and r e d u c t i o n , t h e IBM-360 computer was used. The s l o p e and s t a n d a r d d e v i a t i o n were o b t a i n e d by t h e l e a s t s q uare f i t method. 7-4 RESULTS: The t i m e averaged t e m p e r a t u r e from t h e s p e c t r o g r a p h i c p l a t e s was found t o be 8500 °K (±10%). Even though s l i g h t l y h i g h e r v a l u e s were o b t a i n e d on t h e a x i s o f t h e chamber, i t -was not p o s s i b l e t o f i n d a r e a l l y s i g n i f i c a n t r a d i a l depen-dence o f t h e t e m p e r a t u r e as a l l measured v a l u e s were t h e same w i t h i n t h e e r r o r bounds. The t e m p e r a t u r e f i e l d d i s t r i b u t i o n o b t a i n e d from t h e p h o t o m u l t i p l i e r measurements i s d i s p l a y e d i n a t h r e e dimen-s i o n a l - p l o t - i n f i g u r e 7-7 .— -The heavy l i n e s i n t h e r - t p l a n e ( l i n e s I and E ) show t h e p a t h o f t h e i m p l o d i n g d e t o n a t i o n and t h e r e f l e c t e d shock wave r e s p e c t i v e l y . Two o f t h e s e c u r v e s a r e shown i n d e t a i l i n f i g u r e 7-8 . The s i z e of t h e e r r o r b a r s r e p r e s e n t s t h e root-mean-square e r r o r p o s s i b l e i n t h e f i t t i n g o f a s t r a i g h t l i n e t h r o u g h t h e d a t a p o i n t s . The -. 85 -T.(°K) t (ysec) R e f l e c t e d shock; I - I m p l o d i n g d e t o n a t i o n . F i g u r e 7-7: Temperature p r o f i l e s i n t h e chamber. - 86 -Time (ysec) -»-0 1 2 3 Time (ysec) F i g u r e 7-8: Temperature p r o f i l e s a t R=0 and R=10 mm. e x c e l l e n t agreement of t h e two s e t s o f p o i n t s , c o r r e s p o n -d i n g t o t h e two r u n s made a t each r a d i a l p o s i t i o n s , shows t h e v e r y good r e p r o d u c i b i l i t y o f t h e measurements. 7-5 DISCUSSION OF THE RESULTS: The t e m p e r a t u r e b e h i n d a s t e a d y p l a n e d e t o n a t i o n has been c a l c u l a t e d by J o u g u e t t o be 5570 °K i n t h e c a s e o f e q u i m o l a r o x y - a c e t y l e n e d e t o n a t i o n . T h i s v a l u e r e p r e s e n t s an upper l i m i t as i t was o b t a i n e d f o r a l o s s l e s s i n f i n i t e d e t o n a t i o n . R a d i a t i o n l o s s e s as w e l l as boundary e f f e c t s would t e n d t o l o w e r t h i s v a l u e . Thus, comparing our expe-r i m e n t a l r e s u l t s w i t h t h e v a l u e c a l c u l a t e d by J o u g u e t , i t appears t h a t t h e measurements d i d not y i e l d e q u i l i b r i u m t e m p e r a t u r e s . We have r a t h e r o b t a i n e d some combined average p o p u l a t i o n t e m p e r a t u r e o f t h e r o t a t i o n a l and v i b r a t i o n a l s t a t e s o f t h e CN m o l e c u l e . As mentioned p r e v i o u s l y , t h e p o p u l a t i o n t e m p e r a t u r e o f t h e r o t a t i o n a l s t a t e s i s p r a c t i c a l l y i d e n t i c a l t o t h e t r u e gas t e m p e r a t u r e s i n c e t h e r o t a t i o n a l r e l a x a t i o n t i m e i s v e r y s h o r t (of t h e o r d e r o f a few t e n s t o hundreds n a n o s e c o n d s ) . P a r k i n s o n e t a l /32/ r e p o r t e d good a g r e e -ment between t h e r o t a t i o n a l t e m p e r a t u r e o f t h e CN m o l e c u l e s i n a shock h e a t e d plasma and t h e c a l c u l a t e d k i n e t i c temp-- - e r a t u r e . A l s o , D. F i s s e l and H. M e i s l / 3 3 / measured t i m e i n t e g r a t e d r o t a t i o n a l t e m p e r a t u r e s o f two r a d i c a l s (CN and OH) i n t h e chamber. They used f i r s t a r i c h and t h e n a l e a n - 88 -gas m i x t u r e t o o b t a i n t h e CN and t h e OH bands r e s p e c t i v e l y . A 3/4 meter g r a t i n g s p e c t r o g r a p h (SPEX) was used t o r e c o r d w e l l r e s o l v e d CN and OH bands. They a p p l i e d t h e a n a l y s i s o f P a r k i n s o n /32/ t o t h e CN band and t h e i s o - i n t e n s i t y method o f J . Hopkins /34/ t o t h e OH band and found t i m e averaged t e m p e r a t u r e s o f 3100 and 3400 °K r e s p e c t i v e l y w i t h an. e s t i m a t e d e r r o r o f ±20% i n each c a s e . A g a i n , no s i g n i f i c a n t r a d i a l dependence was o b s e r v e d . These v a l u e s a r e much l o w e r t h a n t h e one o b t a i n e d from t h e s l o p e c r i t e -r i o n and, i n v i e w o f J o u g u e t ' s c a l c u l a t e d t e m p e r a t u r e , t h e s e r o t a t i o n a l t e m p e r a t u r e s appear t o be more r e p r e s e n t a t i v e o f t h e r e a l a verage t e m p e r a t u r e o f t h e gas. NON-THERMAL POPULATION: The v e r y l a r g e d i s c r e p a n c y between t h e r o t a t i o n a l and t h e ' s l o p e ' t e m p e r a t u r e s , can be e x p l a i n e d by assuming a n o n - t h e r m a l p o p u l a t i o n o f t h e CN o v i b r a t i o n a l s t a t e s . The 3883 A band system i s composed o f f i v e bands c o r r e s p o n d i n g t o d i f f e r e n t v i b r a t i o n a l t r a n s i t t i o n s . I f we assume t h a t t h e r o t a t i o n a l s t a t e s a r e i n e q u i -l i b r i u m w i t h i n each v i b r a t i o n a l l e v e l , t h e i n t e n s i t i e s of th e r o t a t i o n a l l i n e s i n each band have a d e f i n i t e f u n c t i o n a l dependence on t h e w a v e l e n g t h . T h i s dependence i s shown i n - f i g u r e 7-9 /28, 35/. The s l o p e o f t h e t a i l o f t h e band i s seen t o d e c r e a s e m o n o t o n i c a l l y w i t h t h e d i s t a n c e from t h e head o f t h e band. Hence, i f t h e bands f u r t h e s t from t h e o o b s e r v a t i o n p o i n t (3810 A) a r e s t r o n g e r t h a n f o r e q u i l i b r i u m , t h e s l o p e a t t h a t p o i n t w i l l be s m a l l e r t h a n f o r e q u i l i b r i u m . - 89 -P-branch Head o f t h e band F i g u r e 7-9: I n t e n s i t y o f t h e r o t a t i o n a l l i n e s o f t h e P and R branches i n a r o t a t i o n a l band as f u n c t i o n o f wave-l e n g t h . The r o t a t i o n a l quantum number J i n c r e a s e s i n t h e d i r e c t i o n o f t h e a r r o w s . T h e r e f o r e a h i g h e r t e m p e r a t u r e i s o b t a i n e d from t h e s l o p e c r i t e r i o n . T h i s n o n - t h e r m a l p o p u l a t i o n o f t h e v i b r a t i o n a l s t a t e s , w h i c h can e x p l a i n our r e s u l t s , c o r r e s p o n d s t o a low p o p u l a t i o n t e m p e r a t u r e o f t h e v i b r a t i o n a l s t a t e s o f t h e CN m o l e c u l e . T h i s c o n c l u s i o n s u p p o r t s t h e f r o z e n v i b r a t i o n a l s t a t e a s s u m p t i o n made sometimes t o c a l c u l a t e t h e d e t o n a t i o n p a r a m e t e r s e x a c t l y /36/. I t i s b e l i e v e d t h a t t h e c h e m i c a l r e a c t i o n i s r e s p o n s i b l e f o r t h i s anomalous v i b r a t i o n a l e x c i t a t i o n . However, t h e r e a c t i o n s w h i c h produce t h e r a -d i c a l s a r e not c o m p l e t e l y u n d e r s t o o d a t p r e s e n t . INTERPRETATION OF THE TIME-RESOLVED MEASUREMENTS: In t h e l i g h t o f t h e above d i s c u s s i o n , t h e ti m e r e s o l v e d t e m p e r a t u r e measurements can now be i n t e r p r e t e d i n t h e f o l -l o w i n g way. A t l a r g e r a d i i , t h e measured t e m p e r a t u r e i s - 90 -v e r y h i g h a t t h e f r o n t and c o r r e s p o n d s t o a v e r y low v i b r a -t i o n a l t e m p e r a t u r e due t o t h e anomalous e x c i t a t i o n o f t h e r e a c t i o n p r o d u c t s . B e h i n d t h e d e t o n a t i o n f r o n t , a decay c o r r e s p o n d i n g t o v i b r a t i o n a l r e l a x a t i o n i s o b s e r v e d . The t e m p e r a t u r e and p r e s s u r e dependence o f t h e r e l a x a t i o n t i m e can be seen from t h e decay o f t h e t e m p e r a t u r e a t v a r i o u s r a d i a l p o s i t i o n s . I t becomes s h o r t e r towards t h e c e n t e r . C l o s e t o t h e a x i s o f t h e chamber, the d e t o n a t i o n i s v e r y much o v e r - d r i v e n and behaves more l i k e a s t r o n g shock wave tha n a d e t o n a t i o n . The t e m p e r a t u r e s p i k e a t t h e f r o n t ( c h a r a c -t e r i s t i c o f t h e c h e m i c a l r e a c t i o n ) t e n d s t o d i s a p p e a r as t h e e f f e c t s o f t h e c h e m i c a l r e a c t i o n become s e c o n d a r y . At t h e p o i n t o f c o l l a p s e , t h e t e m p e r a t u r e i s too h i g h t o be measured by t h e s l o p e c r i t e r i o n . The s l o p e a t t h a t p o i n t i s o f t h e o r d e r o f 10~k and t h e e r r o r o f f i t about 1 0 - 3 . I t i s t h e r e f o r e i m p o s s i b l e t o g i v e an e s t i m a t e o f t h e tem-p e r a t u r e . A l o w e r l i m i t would be 25,000 °K, t h i s c o r r e s -ponds t o t h e l o w e r l i m i t o f t h e e r r o r b a r . T h i s h i g h temp-e r a t u r e i s f o l l o w e d by a v e r y f a s t decay which i s produced by t h e e x p a n s i o n wave g e n e r a t e d a t t h e c e n t e r o f c o l l a p s e . As seen i n the p r e s s u r e measurements, f i g u r e 5-2, t h e s t r e n g t h o f t h e r e f l e c t e d shock wave decays v e r y r a p i d l y . T h i s i s w e l l c o n f i r m e d by t h e t e m p e r a t u r e measurements h e r e . C l o s e t o t h e c e n t e r , t h e r e f l e c t e d shock produces a s i g n i f i c a n t temp-e r a t u r e r i s e , w h i c h r a p i d l y decays s i n c e t h i s f r o n t i s f o l l o w e d by a r a r e f a c t i o n wave. As t h e shock moves ou t w a r d s , the - 91 -c o r r e s p o n d i n g t e m p e r a t u r e s t e p becomes s m a l l e r and e v e n t u a l l y becomes n e g a t i v e . T h i s unexpected b e h a v i o u r can be e x p l a i n e d by t h e f a c t t h a t t h e v i b r a t i o n a l r e l a x a t i o n t i m e i s q u i t e l o n g i n t h e r e a c t i o n p r o d u c t s . Thus e q u i l i b r i u m has n o t been r e a c h e d when the r e f l e c t e d f r o n t a r r i v e s . T h i s pure shock wave p a s s i n g t h r o u g h a n o n - e q u i l i b r i u m gas t e n d s t o ' t h e r m a l i z e ' t h e gas t o t h e e q u i l i b r i u m s t a t e c o m p a t i b l e w i t h t h e s t r e n g t h o f t h e shock wave. Hence t h e measured t e m p e r a t u r e i s s m a l l e r b e h i n d t h e r e f l e c t e d f r o n t t h a n ahead o f i t s i n c e the c r i t e r i o n used t o o b t a i n t h e t e m p e r a t u r e g i v e s h i g h v a l u e s f o r t h e t y p e o f n o n - e q u i l i b r i u m t h o u g h t t o be p r e s e n t i n t h e r e a c t i o n p r o d u c t s . We can t h e r e f o r e assume t h a t t h e f i n a l e q u i l i b r i u m t e m p e r a t u r e i n t h e chamber i s c l o s e t o 5000 °K ( f i g u r e 7-7). 7-6 DISCUSSION OF SOME OTHER ASSUMPTIONS: Hayi n g c o n s i d e r e d n o n - e q u i l i b r i u m e f f e c t s , we can now l o o k a t t h e o t h e r a s s u m p t i o n s : o p t i c a l t h i c k n e s s and back-ground r a d i a t i o n . The ' s l o p e ' c r i t e r i o n was d e v e l o p e d f o r an OPTICALLY THIN PLASMA. T h i s means t h a t t h e band e m i s s i o n l e v e l must be much l e s s t h a n t h e b l a c k - b o d y r a d i a t i o n a t t h e same temp-o e r a t u r e . The i n t e n s i t y o f t h e t a i l o f t h e CN band a t 3810 A i s a l m o s t an o r d e r o f magnitude l o w e r t h a n t h a t o f t h e head o o f t h e band system a t 388 3 A. S i n c e no n o t i c e a b l e a b s o r p -t i o n e f f e c t s can be d e t e c t e d a t t h e head o f t h e band ( i e : - 92 -f l a t t e n i n g o f t h e peak i n t e n s i t y ) , i t i s most r e a s o n a o l e t o o assume t h a t t h e plasma i s o p t i c a l l y t h i n a t 3810 A. The e f f e c t s o f a BACKGROUND CONTINUUM would be t o i n -c r e a s e t h e measured t e m p e r a t u r e . T h i s can be seen from t h e f o l l o w i n g s i m p l e a n a l y s i s . I t i s u n l i k e l y t h a t any back-ground i n t e n s i t y , I D , would v a r y v e r y much over t h e c o n s i -£ 5 O d e r e d w a v e l e n g t h i n t e r v a l (A 2-AI=40 A ) , t h e r e f o r e , t h e s l o p e between Xi and A 2 i s : S l o p e = A = l o g ( I A i + I B ) - l o g ( I X 2 + l B ) X l - X 2 w h i c h may be w r i t t e n a s : 1 . 1 X l + 1 B A = A y l o g ± The g r e a t e r 1^, t h e c l o s e r t o u n i t y i s t h e r a t i o o f t h e i n t e n s i t i e s . T h i s means a s m a l l e r s l o p e and t h e r e f o r e a h i g h e r t e m p e r a t u r e . On t h e s p e c t r o g r a p h i c p l a t e s , a con-tinuum i s seen and i t s i n t e n s i t y i n c r e a s e s towards t h e c e n t e r . I f t h e continuum were t o i n t e r f e r e w i t h t h e measu-rements, t h e t e m p e r a t u r e s h o u l d r i s e c o n s i s t e n t l y w i t h d e c r e a s i n g r a d i u s . T h i s i s o b v i o u s l y n o t o b s e r v e d . T here-f o r e , we can-assume t h a t t h e i n t e n s i t y o f t h e background -emission i s t o o low t o i n t e r f e r e w i t h t h e measurements and -t h a t I can be n e g l e c t e d compared w i t h I , and I. t o •D A 1 A 2 good a c c u r a c y . - 9 3 -S i n c e t h e ' s l o p e ' t e m p e r a t u r e measures some und e t e r m i n e d c o m b i n a t i o n o f t h e r o t a t i o n a l and v i b r a t i o n a l e x c i t a t i o n t e m p e r a t u r e , and does n o t r e p r e s e n t t h e t r u e k i n e t i c gas temp e r a t u r e , i t i s p o i n t l e s s t o compare t h e measured t e m p e r a t u r e s w i t h t h e t h e o r e t i c a l c u r v e o f f i g u r e 2-6. We can say, how-e v e r , t h a t t h e t e m p e r a t u r e tends t o i n c r e a s e a t the c e n t e r of i m p l o s i o n and t h a t t h i s v e r y sharp t e m p e r a t u r e i n c r e a s e i s f o l l o w e d by a f a s t decay. These o b s e r v a t i o n s a r e i n q u a l i t a t i v e agreement w i t h t h e e x p e c t e d b e h a v i o u r o f t h e gas t e m p e r a t u r e i n t h e i m p l o d i n g d e t o n a t i o n . The t e m p e r a t u r e measurements of D. E. R o b e r t s /69/ a t the c e n t e r of a s p h e r i c a l i m p l o s i o n suggest a low f i n a l t e m p e r a t u r e (about 5500 °K),, However, the f i n a l r a d i u s of i m p l o s i o n a c h e i v e d i n h i s case seems t o be much l a r g e r t h a n o u r s . We would t h e r e f o r e e x p e c t h i g h e r t e m p e r a t u r e as shown by our lower l i m i t of 25.000 °K and the measurements of B e l o k o n ' e t a l /66/. APPLICATIONS The f i r s t p a r t o f t h i s t h e s i s was devo t e d t o the s t u d y o f IMPLOSIONS. The f o c u s i n g e f f e c t s p r e d i c t e d by the t h e o r y were i n v e s t i g a t e d i n i m p l o d i n g d e t o n a t i o n s . We b e l e i v e t o have added weight t o the C.C.W. model by Our measurements o f the c o l l a p s e c u r v e , the p r e s s u r e f i e l d and the te m p e r a t u r e d i s t r i b u t i o n i n the chamber, even though the l a t t e r measure-ments were not v e r y c o n c l u s i v e . The second p a r t of t h i s t h e s i s i s devoted t o p e r t i c u l a r a p p l i c a t i o n s o f DETONATIONS and some d e t a i l s of the d e t o n a t i o n p r o c e s s e s which we found o r c o n f i r m e d i n the c o u r s e of the s t u d y . The two a p p l i c a t i o n s p r e s e n t e d a r e the development of a c y l i n d r i c a l i m p l o d i n g d e t o n a t i o n d r i v e r f o r a p r e s s u r e d r i v e n shock tube and t h e c a l i b r a t i o n of p i e z o e l e c t r i c p r e s s u r e probes by making use o f p l a n e d e t o n a t i o n s . The o t h e r p o i n t s w h i c h c o n f i r m p r e v i o u s o b s e r v a t i o n s a r e : 1 ) boundary l a y e r e f f e c t s on the v e l o c i t y o f p l a n e d e t o n a t i o n s , 2) d e t o n a t i o n s p i n , 3} the von Neumann s p i k e i n p l a n e d e t o n a t i o n s and 4) the r a r e f a c t i o n wave b e h i n d a p l a n e d e t o n a t i o n . - 95 -CHAPTER 8 AN IMPLODING DETONATION DRIVER T h i s c h a p t e r d e s c r i b e s a d e v i c e w h i c h makes use o f im-p l o d i n g d e t o n a t i o n s t o produce shock waves o f h i g h Mach num-b e r s . The main p o i n t of t h i s c h a p t e r i s t o show t h a t the h i g h p r e s s u r e gas a t t h e c e n t e r o f an i m p l o d i n g d e t o n a t i o n can be us e d , w i t h s e v e r a l a d v a n t a g e s , as a d r i v e r gas i n a p r e s s u r e d r i v e n shock tube. S i n c e t h e s e r e s u l t s a re s t r i c t l y e m p i r i c a l , shock t h e o r y s h a l l n o t be d i s c u s s e d f u r t h e r t h a n what has been p r e s e n t e d i n t h e t h e o r y c h a p t e r ( c h a p t e r 2 ) . F o r an i n t r o d u c t i o n t o t h e shock t h e o r y , t h e r e a d e r i s r e f e r r e d t o any t e x t on gas dynamics /13,15/ o r t o more s p e c i a l i z e d p u b l i c a t i o n s /10,7O,37/. I t i s n e c e s s a r y , however, t o i n t r o d u c e some shock tube t e r m i n o l o g y . 8-1 TERMINOLOGY: A p r e s s u r e d r i v e n shock tube c o n s i s t s o f a h i g h p r e s s u r e d r i v e r s e c t i o n and a low p r e s s u r e t e s t s e c t i o n w h i c h a r e i n i t i a l l y s e p a r a t e d by a membrane (or d i a p h r a g m ) . P a r a m e t e r s i n t h e d r i v e r and t e s t s e c t i o n s a r e l a b e l e d w i t h t h e i n -d i c e s 4 and 1 r e s p e c t i v e l y , see f i g u r e 8-1. When t h e membrane i s p u n c t u r e d , e i t h e r by means o f a p l u n g e r o r by o v e r p r e s s u r e , a shock wave p r o p a g a t e s i n t o t h e t e s t gas w i t h a v e l o c i t y V . The shock wave i s d e s c r i b e d - 96 -I n i t i a l l y Membrane a) D r i v e r s e c t i o n b) T e s t s e c t i o n A f t e r t h e diaphram b u r s t s 2 : V Shock wave F i g u r e 8-1: S k e t c h o f a p r e s s u r e d r i v e n shock tube, most c o n v e n i e n t l y by i t s Mach number, M , w h i c h i s t h e speed of t h e wave d i v i d e d by t h e speed o f sound i n t h e t e s t g a s ; M =V / a i . The dependence o f the Mach number on t h e i n i t i a l s s pa r a m e t e r s can be s i m p l i f i e d t o t h e form: M c « f i ( f - ^ ) f i (!•*-) s a i P i (8-1) where f i and f 2 a r e m o n o t o n i c a l l y i n c r e a s i n g f u n c t i o n s . 'In r e c e n t y e a r s , e f f o r t s have been made t o produce s t r o n g shock waves f r e e o f e l e c t r i c and mag n e t i c f i e l d s . T h i s i s a c h i e v e d i n p r e s s u r e d r i v e n shock t u b e s by i n c r e a s i n g b o t h t h e d r i v e r p r e s s u r e and i t s t e m p e r a t u r e . T h i s can be a c c o m p l i s h e d by means o f an e l e c t r i c d i s c h a r g e o r a combus-t i o n p r o c e s s /38/ or by making use of e x p l o s i v e c h a r g e s i n v a r i o u s g e o m e t r i c c o n f i g u r a t i o n s . Some o f the most r e c e n t developments i n shock tube t e c h n o l o g y can be found i n r e f . 3 9 . - 97 -The work of I. I. G l a s s and J . C. P o i n s s o t /40/ i s of s p e c i a l i n t e r e s t here s i n c e t h e i r d r i v e r makes use of the i m p l o s i o n c o n c e p t . I n t h i s c h a p t e r , a new, cheap but e f f i c i e n t d r i v e r i s d e s c r i b e d / 4 1/ and some o f i t s p e r f o r m a n c e s i n v e s t i g a t e d . I t makes use o f t h e h i g h p r e s s u r e and t e m p e r a t u r e gas o b t a i n e d a t t h e c e n t e r o f an i m p l o d i n g d e t o n a t i o n . We were a b l e t o o b t a i n Mach 14 i n argon a t one T o r r i n i t i a l p r e s s u r e . Much h i g h e r Mach numbers seem t o be e a s i l y f e a s i b l e w i t h a s i m i l a r d e v i c e o f l a r g e r d i m e n s i o n s . 8-2 EXPERIMENTAL SET-UP: The d r i v e r c o n s i s t s o f t h e l a r g e d e t o n a t i o n chamber f i t t e d w i t h a s p e c i a l l y d e s i g n e d f r o n t p l a t e t o adapt t h e shock tube. T h i s p l a t e i s made o f b r a s s r a t h e r t h a n l u c i t e s i n c e o p t i c a l o b s e r v a t i o n s a r e not n e c e s s a r y i n t h e d r i v e r . - The h i g h e r s t r e n g t h o f b r a s s a l l o w s us t o use h i g h e r i n i t i a l p r e s s u r e s i n t h e chamber t h a n were p o s s i b l e w i t h t h e l u c i t e f r o n t p l a t e . A 1.4 cm h o l e was bored o u t o f t h e c e n t e r o f t h e p l a t e , a t h i n diaphragm o f m y l a r o r 0.002" b r a s s s h i m s t o c k was used t o i s o l a t e t h e two systems. A l e v e r mechanism was -—mounted on t h e p l a t e to-change e a s i l y t h e membrane and t o clamp i t f i r m l y p r o v i d i n g a vacuum s e a l f o r t h e chamber and t h e t u b e . A s k e t c h o f t h e a p p a r a t u s i s shown i n f i g u r e 8-2; more d e t a i l s may be found i n appendix A. The shock tube i s c o n s t r u c t e d o f 2.5 cm d i a m e t e r p y r e x F i g u r e 8-2: S k e t c h o f a shock tube u s i n g t h e d e t o n a t i o n chamber as a d r i v e r . - 99 -tube s e c t i o n s . A tapered brass s e c t i o n was used to match the hole at the center of the f r o n t p l a t e to the diameter of the tube. F a i r l y heavy br a c i n g of the chamber was found necessary to prevent the pyrex tube from breaking due to the r e c o i l of the d r i v e r s e c t i o n . 8-3 PERFORMANCE OF THE SHOCK TUBE: The shock wave i n the tube was photographed w i t h the smear camera by foc u s i n g the s l i t of the camera along the a x i s of the tube. An o b s t a c l e 1.8 cm i n diameter was i n s e r -ted at a p o s i t i o n 84 cm from the membrane to block o f f the center p o r t i o n of the tube. The shock wave r e f l e c t e d from t h i s o b s t r u c t i o n probes the gas flow behind the i n c i d e n t shock and allows to deduce the p o s i t i o n of the contact sur-face between the shock heated gas and the d r i v e r gas. Figures 8-3a and 8~3b show two smear photographs of a shock wave i n argon seeded w i t h 14% acetylene to make the shock f r o n t and shock-heated r e g i o n luminous. The d r i v e r gas was i n t h i s case a 2:3 mixture of acetylene and oxygen at an i n i t i a l pressure of 600 Torr. A mylar diaphragm was used i n t h i s and a l l subsequent runs. Figure 8-4 i s a smear t r a c e of a shock wave in.pure argon. There the f r o n t does not record on the photograph and only the contact surface shows up. The performances of the tube were i n v e s t i g a t e d under many d i f f e r e n t gas combinations and the Mach number was measured as a f u n c t i o n of the pressure r a t i o P 5 / P 1 . - 100 -a) F i g u r e 3-3: Smear photographs o f a shock wave (Markers=5 cm a p a r t , sweep-31.25 y s e c / d i v ) a) Test gas pressure=15 T o r r (6 Ar •!• 1 C 2 K 2 ) b) D r i v e r gas pressure=600 T o r r (2 C 2 H 2 + 2 O,) b) Te s t gas pressure=4.8 T o r r (6 Ar •'- 1 C ?H 2) D r i v e r gas pressure=600 T o r r ( 2 C 2 I I 2 + 2 0 2) F i g u r e 8-4: Smear camera photograph of a shock wave. Markers=5 cm a p a r t Sweep=31.25 s e c / d i v T e s t gas, A r , 3.2 T o r r D r i v e r gas, 2 C 2H 2 + 2 0 2 , 600 T o r r . X - 1 0 1 -F i g u r e 8-5 shows hov; M v a r i e s when Ps i s k e p t c o n s t a n t a t 600 T o r r ( 2 C 2 H 2 + 3 0 2 ) , w h i l e P i i s v a r i e d f r o m 0.2 t o 15 T o r r ( 6 A r + l C 2 H 2 ) . T h e s e m e a s u r e m e n t s w e r e t a k e n f r o m smear c a m e r a t r a c e s a t a p o s i t i o n 8 0-84 cm d o w n s t r e a m o f t h e membrane. The r e s u l t s o f O e r t e l / 3 9 / a n d N e t t / 4 2 / o b t a i n e d i n t y p i -c a l s h o c k t u b e s w e r e a d d e d i n f i g u r e 8-5 t o g i v e a compa-r a i s o n c r i t e r i a f o r t h e p e r f o r m a n c e o f o u r s h o c k t u b e . The r e s u l t s o f f i g u r e 8-6 a r e u s u a l l y h a r d t o o b t a i n i n t h i s Mach number r a n g e i n c o n v e n t i o n a l s h o c k t u b e s . I t shows how t h e Mach number v a r i e s when P i i s k e p t c o n s t a n t (8 T o r r A i r ) , w h i l e P 5 S i s v a r i e d f r o m 200 t o 700 T o r r ( C 2 H 2 + 0 2 ) . The m e a s u r e m e n t s m a r k e d a s c i r c l e s w e r e o b t a i n e d f r o m two p h o -t o m u l t i p l i e r s p l a c e d 15 cm f r o m t h e membrane and e x a c t l y 3.45 cm a p a r t . The c r o s s e s a r e d a t a p o i n t s o b t a i n e d f r o m smear t r a c e s a t a d i s t a n c e 10-20 cm f r o m t h e d i a p h r a m . F r o m f i g u r e s 8-5 and 8-6, i t i s c l e a r t h a t t h e Mach number, M , i s more s e n s i t i v e t o a n i n c r e a s e o f P, t h a n a d e c r e a s e s 0 o f P j . ' H i g h e r i n i t i a l p r e s s u r e s i n t h e d r i v e r c h amber w e r e n o t p o s s i b l e a n d t h e c u r v e o f f i g u r e 8-6 c o u l d n o t be e x t e n d e t o h i g h e r p r e s s u r e s f o r s a f e t y r e a s o n s . W o r k i n g w i t h a n i n i t i a l p r e s s u r e o f a r o u n d 700 T o r r , t h e 3/8" b r a s s f r o n t ..plate d e v e l o p e d a - b u l g e o f a l m o s t 1 cm a t t h e c e n t e r . A- c o m p a r i s o n b e t w e e n t h e p e r f o r m a n c e s o f t h e s h o c k t u b e w i t h m y l a r and b r a s s d i a p h r a g m s i s g i v e n i n f i g u r e 8-7. A d r a s t i c r e d u c t i o n o f t h e s h o c k s p e e d i s o b s e r v e d when b r a s s membranes a r e u s e d , s p e c i a l l y a t l o w p r e s s u r e s d o w n s t r e a m . *Ps i s u s e d t o d e n o t e t h e p r e s s u r e i n t h e d r i v e r . F i g u r e 8-5: Mach number v e r s u s p r e s s u r e r a t i o 18 16 14 12 u cu Xi s c 8 5 o 50 100 500 1000 5000 P r e s s u r e r a t i o = Chamber f i l l i n g p r e s s u r e / T e s t gas p r e s s u r e - 103 -10 20 40 60 100 P r e s s u r e r a t i o F i g u r e 8-6: Mach number v e r s u s p r e s s u r e r a t i o . T e s t gas pressure=8 T o r r ( A i r ) D r i v e r g a s , C 2 H 6 + 0 2 , p r e s s u r e v a r i a b l e from 200 t o 7 00 T o r r . & Data from t h e p h o t o m u l t i p l i e r s 4. Data from t h e smear photographs Mach number - frOT -- 1 0 5 -A p o s s i b l e e x p l a n a t i o n of t h i s e f f e c t i s g i v e n i n the next s e c t i o n . 8-4 COMMENTS ON THE RESULTS: SHOCK-HEATED REGION: The l e n g t h o f the shock h e a t e d r e g i o n 3 d , i n an i d e a l shock tube i s g i v e n by: d=x/ , where x i s the p o s i t i o n of the shock wave a l o n g the tube and the d e n s i t y r a t i o a c r o s s the f r o n t . In a r e a l shock t u b e , how-e v e r , the shock-heated r e g i o n l e n g t h , d^, i s much l e s s than f o r the i d e a l c a s e . T h i s r e d u c t i o n i s due m a i n l y t o t h r e e e f f e c t s " . 1) r e a l gas e f f e c t s w hich i n c r e a s e the d e n s i t y r a t i o , 2) m i x i n g o c c u r s a t the c o n t a c t s u r f a c e between the d r i v e r gas and the shock heated gas, t h i s i s s p e c i a l l y i m p o r t a n t a t the i n i t i a l phase of the shock f r o n t f o r m a t i o n , 3) boundary l a y e r e f f e c t s . The m i x i n g e f f e c t i v e l y r e d u c e s the l e n g t h x, and the boundary l a y e r e f f e c t s tend t o reduce the growth o f the s h o c k - h e a t e d r e g i o n as the wave p r o p a g a t e s /71/. I n f i g u r e 8-3a (15 T o r r t e s t gas p r e s s u r e ) , t h e shock-h e a t e d r e g i o n i s d =5.5 cm when t h e f r o n t r e a c h e s t h e r e f l e c -r t o r ( p l a c e d a t 84 cm downstream). T a k i n g t h e d e n s i t y r a t i o as a p p r o x i m a t e l y 4, d=21 cm a t t h e same p o s i t i o n . Hence o n l y 25% o f t h e t o t a l t e s t gas can be found i n t h e s h o c k - h e a t e d r e g i o n . I f we e x t r a p o l a t e back i n t i m e and space t h e c o n t a c t s u r f a c e and t h e shock f r o n t i n f i g u r e 8-3a, t h e f r o n t seems t o d e t a c h from t h e d r i v e r gas about 35 cm b e f o r e t h e r e f l e c t o r t h a t i s about 50 cm downstream. • Hence, i n t h e f i r s t 50 cm of t h e t u b e , m i x i n g between d r i v e r and s h o c k - h e a t e d gas i s - 106 -predominent and i t . i s n o t a f t e r t h a t p o i n t t h a t t h e f r o n t d e t a c h e s from t h e d r i v e r gas. I f we t a k e x=35 cm t h e n d=8.5 cm, t h e r e f o r e o n l y 65% o f t h e t e s t gas i n t h a t r e g i o n i s found i n t h e s h o c k - h e a t e d r e g i o n . T h i s 35% l o s s i s due t o t h e boundary l a y e r e f f e c t s and p r o b a b l y f u r t h e r m i x i n g a t t h e c o n t a c t s u r f a c e . In f i g u r e 8-3b (4.8 T o r r t e s t gas i n i t i a l p r e s s u r e ) , o n l y 15% o f t h e t o t a l t e s t gas i s i n t h e s h o c k - h e a t e d r e g i o n and 60% o f t h e t e s t gas a f t e r t h e shock f r o n t d e t a c h e d from t h e c o n t a c t s u r f a c e . These v e r y h i g h p e r c e n t a g e l o s s e s can be e a s i l y e x p l a i n e d by t h e f a c t t h a t t h e p r e s s u r e i n t h e d r i v e r i s not u n i f o r m a c r o s s t h e tube and t h a t t h e boundary l a y e r e f f e c t s a r e q u i t e l a r g e due t o t h e s m a l l s i z e o f t h e t u b e . THE RUPTURE OF THE MEMBRANE: The p r e s s u r e p r o f i l e s i n t h e d e t o n a t i o n chamber have shown a smooth i n c r e a s e o f t h e p r e s s u r e as t h e f r o n t c o l l a p s e s t o t h e c e n t e r . A v e r y l a r g e p r e s s u r e s p i k e d e v e l o p s on t h e a x i s o f i m p l o s i o n and sub-s e q u e n t l y decays v e r y r a p i d l y as t h e gas expands back i n r a d i a l d i r e c t i o n f o l l o w i n g t h e f o r m a t i o n o f a r e f l e c t e d shock wave. The p r e s e n c e o f a b r e a k a b l e diaphragm a t t h e " c e n t e r p r o v i d e s a p r e s s u r e r e l e a s e w h i c h would g r e a t l y i n -f l u e n c e t h e development o f t h e p r e s s u r e b u i l d - u p i n t h e chamber. When m y l a r i s used, i t i s b e l i e v e d t h a t t h e h e a t i n g o f t h e m a t e r i a l by t h e a b s o r p t i o n o f r a d i a t i o n and t h e h i g h - 107 -p r e s s u r e d e v e l o p e d (60-80 atm a t r=0.7 cm f o r P 5=600 T o r r ) combine t o break o f f t h e membrane c l e a n l y a t t h e r i m o f t h e h o l e as soon as t h e i m p l o d i n g d e t o n a t i o n has r e a c h e d t h i s p o i n t . T h i s v i e w i s v e r y s t r o n g l y s u p p o r t e d by t h e f a c t t h a t m y l a r d i s k s , h a r d l y d i s t o r t e d , have been found a few f e e t from t h e chamber when the d r i v e r was f i r e d i n t o open a i r w i t h o u t a shock t u b e , f i g u r e 8-8. The e a r l y o p e n i n g of t h e membrane a l l o w s t h e d r i v e r gas t o be f r e e l y i n j e c t e d i n t h e tube s t a r t i n g from t h e w a l l . I n t h i s c a s e , t h e v e r y h i g h p r e s s u r e b u i l d - u p a t t h e f o c u s o f t h e i m p l o s i o n i s p r o b a b l y e l i m i n a t e d p r e v e n t i n g t h e . f o r m a t i o n o f t h e s t r o n g o u t - g o i n g r e f l e c t e d shock wave i n t h e d e t o n a t i o n chamber. The p o i n t a t w h i c h t h e f r o n t d e t a c h e s from t h e d r i v e r gas depends on how much m i x i n g t a k e s p l a c e between t h e d r i v e r and t h e downstream ga s e s . A l t h o u g h t h i s e f f e c t was not t h r o u g h l y i n v e s t i g a t e d , i t was found t h a t t h e r e i s more m i x i n g a t lower downstream p r e s s u r e s . T h i s i s due t o t h e f a c t t h a t t h e d r i v e r gas e s c a p e s , a t a h i g h e r v e l o c i t y i n l o w e r p r e s s u r e s t h a n i n h i g h e r p r e s s u r e s . T h i s r e d u c e s t h e e f f e c t i v e d r i v i n g p r e s s u r e and t h e l e n g t h o f t h e shock-h e a t e d r e g i o n , hence d e c r e a s i n g t h e e f f i c i e n c y o f t h e d r i v e r . B r a s s diaphragms, on t h e o t h e r hand, seem t o behave v e r y d i f f e r e n t l y . F i g u r e 8-9 shows t h r e e b r a s s diaphragms (0.004" t h i c k ) o b t a i n e d by u s i n g d i f f e r e n t d r i v e r p r e s s u r e s , membrane-a c o n t a i n e d t h e i m p l o s i o n i n an i n i t i a l p r e s s u r e o f 3 00 T o r r , however, a s h a r p n i p p l e was formed a t t h e - 108 -F i g u r e 8-8: Open s h u t t e r photograph o f the d r i v e r f i r e d i n open a i r . (500 T o r r , C 2H 2+0 2) a) a F i g u r e 8-9: Br a s s membranes (0.004") a) D r i v e r gas=C 2H 2+0 2,300 T o r r b) D r i v e r gas=C 2H 2+0 2,400 T o r r .* c ) D r i v e r gas=C 2H 2+0 2,600 T o r r c) F i g u r e 8-10: One of t h e ' s t r a n g e ' smear photographs o b t a i n e d w i t h b r a s s membranes. D r i v e r : 6 0 0 T o r r (C 2H 2+0 2) T e s t gas:4 T o r r (6Ar+C 2H 2) Markers=5 cm a p a r t Sweep=31.25 y s e c / d i v . t x - 109 -c e n t e r w h e r e t h e p r e s s u r e s p i k e d e v e l o p e d . A t P =400 T o r r , t h e c e n t e r p a r t o f t h e membrane i s t o r n o f f a n d r a d i a l c r a c k s a p p e a r (membrane-b, f i g u r e 8-9). A t P =600 T o r r , t h e w h o l e membrane i s p u n c h e d o u t e x c e p t f o r some p a r t s o n t h e r i m . (membrane-c, f i g u r e 8-9). A l t h o u g h t h e s e membranes a r e t w i c e a s t h i c k as t h o s e a c t u a l l y u s e d d u r i n g t h e i n v e s t i g a -t i o n o f t h e t u b e p e r f o r m a n c e s , t h e t h i n n e r membranes a r e e x p e c t e d t o show t h e same b e h a v i o u r . The p r e s s u r e d e v e l o p e d a t t h e r i m o f t h e h o l e , a t t h e c e n t e r o f t h e f r o n t p l a t e o f t h e c h a m b e r , i s n o t s u f f i c i e n t t o t e a r t h e b r a s s . I t i s n o t u n t i l t h e p r e s s u r e s p i k e i s f u l l y d e v e l o p e d t h a t t h e b r a s s s p l i t s a t t h e c e n t e r and o p e n s up i n two o r more p e t a l s . T h e s e p e t a l s a r e t h e n t o r n o f f by t h e g a s f l o w i n g i n t o t h e t u b e . T h i s d i a p h r a g m o p e n i n g m e c h a n i s m h a s two i m p o r t a n t i m p l i c a t i o n s . F i r s t l y , t h e d r i v e r g a s i s now i n j e c t e d a s a g a s j e t on t h e a x i s o f t h e s h o c k t u b e i n s t e a d o f e n t e r i n g t h e t u b e f r o m t h e r i m . T h i s means s u b s t a n t i a l l y more r a d i a l d i f f u s i o n and m i x i n g b e f o r e t h e d r i v e r g a s becomes p l a n e a n d t h e s h o c k wave s e p a r a t e s f r o m t h e c o n t a c t s u r f a c e . The s e c o n d i m p l i c a t i o n h a s t o do w i t h t h e b e h a v i o u r o f t h e d r i v e r g a s i n t h e chamber i t s e l f . S i n c e t h e p r e s s u r e b u i l d - u p h a s t o o c c u r b e f o r e t h e b r a s s membrane o p e n s , t h e s t r o n g r e f l e c t e d s h o c k wave, w h i c h we o b s e r v e i n t h e d e t o n a t i o n c h amber " ( f i g u r e 5-1) , m u s t be f o r m e d i n t h e d r i v e r . T h u s a g r e a t p a r t o f t h e p r e s s u r e r e l e a s e o c c u r s i n r a d i a l d i r e c t i o n i n t h e c hamber h e n c e r e d u c i n g t h e e f f e c t i v e n e s s o f t h e d r i v e r . - 110 -We a l s o know t h a t a second i m p l o s i o n f o l l o w s t h e r e f l e c t e d f r o n t i n t h e d r i v e r chamber ( f i g u r e 4-9). T h e r e f o r e , when t h i s second i m p l o s i o n r e a c h e s t h e c e n t e r , a second shock wave i s g e n e r a t e d i n t h e shock tube s i n c e t h e diaphragm i s f u l l y open a t t h a t t i m e . T h i s second shock wave c a t c h e s up w i t h t h e f i r s t one and r e i n f o r c e s i t t o produce a s i n g l e s t r o n g e r shock wave. The q u a l i t a t i v e e x p l a n a t i o n s j u s t g i v e n can e x p l a i n t h e many " s t r a n g e " smears w h i c h were o b t a i n e u s i n g b r a s s membrane. One o f t h e s e smear ph o t o g r a p h s i s shown i n f i g u r e 8-10. W i t h t h e h e l p o f t h e above c o n s i d e r a t i o n s , a p l a u s i b l e e x p l a n a t i o n o f f i g u r e 8-7 can now be g i v e n : The p o s i t i o n a t w h i c h t h e second shock wave c a t c h e s up w i t h t h e f i r s t one depends on t h e v e l o c i t y o f t h e l a t t e r wave hence on t h e down-s t r e a m p r e s s u r e s i n c e t h e t i m e between t h e f i r s t and second i m p l o s i o n i n t h e d r i v e r i s c o n s t a n t . . The v e l o c i t y measure-ments were done a t 80 cm from t h e diaphragm, t h u s , t h e v a l u e s , o b t a i n e d a t h i g h p r e s s u r e s a r e v a l i d f o r t h e shock wave r e s u l t i n g form t h e i n t e r a c t i o n o f t h e two f r o n t s , whereas th e Mach numbers o b t a i n e d a t low p r e s s u r e s a p p l y o n l y t o the f i r s t f r o n t s i n c e t h e second shock has not caught up w i t h t h e f i r s t a t t h e p o s i t i o n t h e measurements were t a k e n . Temperature e f f e c t s , w h i c h have n o t been mentioned so f a r a l s o c o n t r i b u t e t o t h e e f f e c t i v e n e s s o f t h e d r i v e r . A l t h o u g h t h e d r i v e r gas m i x t u r e has a low i n i t i a l sound speed (320 m/sec), t h e r i s e i n t e m p e r a t u r e due t o t h e - I l l -d e t o n a t i o n and t h e f o c u s i n g e f f e c t s o f t h e i m p l o s i o n , combine t o r a i s e t h e speed o f sound t o v a l u e s w h i c h a r e v e r y h a r d t o a t t a i n i n s t a n d a r d p r e s s u r e d r i v e n shock t u b e s . ' 8-5 SUMMARY: Our shock t u b e has p erformances comparable w i t h t h o s e o f much l a r g e r a p p a r a t u s . S t i l l h i g h e r Mach numbers seem t o be q u i t e f e a s i b l e s i n c e t h e p r e s s u r e b u i l d - u p i n t h e c y l i n d r i c a l d e t o n a t i o n chamber depends o n l y on t h e d i m e n s i o n l e s s p arameter r/R^. Much h i g h e r e f f e c t i v e d r i v e r p r e s s u r e s can be o b t a i n e d by d e c r e a s i n g t h i s r a t i o o v e r t h e a r e a o f t h e t u b e . H i g h e r p r e s s u r e s can a l s o . b e o b t a i n e d by i n c r e a s i n g t h e i n i t i a l p r e s s u r e i n t h e chamber. To a c h i e v e t h i s , a s t r o n g e r and l a r g e r chamber s h o u l d be used. The d e v i c e i s s i m p l e and i n e x p e n s i v e t o assemble and can be o p e r a t e d w i t h o n l y s h o r t i n t e r v a l s between s h o t s , f u r t h e r -more, t h e c h e m i c a l energy used i s cheap and r e a d i l y a v a i l a b l e . One'of t h e g r e a t e s t advantage of t h i s d e v i c e i s t h a t o n l y a t h i n membrane s u f f i c e s t o i s o l a t e t h e d r i v e r from t h e t e s t s e c t i o n , t h i s a l l o w s t h e membrane t o b u r s t p r a c t i c a l l y w i t h o u t j i t t e r and g i v e e x c e l l e n t t i m i n g p o s s i b i l i t i e s . - 112 -CHAPTER 9 APPLICATION AND PROPERTIES OF PLANE DETONATIONS A c a l i b r a t e d p r e s s u r e probe was needed f o r t h e p r e s s u r e measurements i n t h e d e t o n a t i o n chamber. We had a t our d i s -p o s a l p i e z o e l e c t r i c p r e s s u r e probes ( d e s c r i b e d i n a p p e n d i x E) c a l i b r a t e d i n the range o f 0.1 t o 0.7 atmospheres /43,44/. However, t h e p r e s s u r e s i n t h e d e t o n a t i o n chamber a r e i n t h e range o f 10 t o 100 atmospheres;hence i t was n e c e s s a r y t o e x t e n d t h e range o f c a l i b r a t i o n t o as h i g h p r e s s u r e s as p o s s i b l e . T h i s was done by making use o f p l a n e d e t o n a t i o n s . C a l i b r a t i o n p r e s s u r e s o f up t o 3 0 atmospheres were o b t a i n e d . T h i s work i s t o appear i n p r i n t s h o r t l y /4 5/. In t h e c o u r s e o f t h i s c a l i b r a t i o n some i n t e r e s t i n g o b s e r v a t i o n s were o b t a i n e d p e r t a i n i n g t o t h e p r o p a g a t i o n o f p l a n e d e t o n a t i o n s . These a r e r e p o r t e d b r i e f l y i n t h i s c h a p t e r . 9-1 HIGH PRESSURE CALIBRATION OF A PIEZOELECTRIC PROBE: METHOD OF CALIBRATION: The p r e s s u r e b e h i n d a C.J. d e t o n a t i o n i s g i v e n ap-p r o x i m a t e l y by e q u a t i o n (2-16) with, t h e a s s u m p t i o n t h a t M?>>1. I f t h i s a s s u m p t i o n i s not made, one has: 113 P i v g 2 + i ; g 2 + i o r . P 2 = i±4^ x P l w h e r e 3 o = ^ = ^ ( 9 " 2 ) g 2 + i a i P i i s d e f i n e d a s t h e d e n s i t y p e r u n i t p r e s s u r e , t h u s 8 0 i s a c o n s t a n t w h i c h c a n be c a l c u l a t e d f r o m t h e d e n s i t y o f t h e g a s . The e f f e c t i v e a d i a b a t i c e x p o n e n t , g 2 , i s t a k e n t o be 1.25±0.05. The r a n g e ±0.05 i n c l u d e s t h e v a r i a t i o n s e x p e c t e d i n a d e t o n a t i o n / 4 6 / . T h i s 4% r a n g e i n t h e c o n s t a n t c o r -r e s p o n d s t o a 2% u n c e r t a i n t y i n t h e p r e s s u r e r a t i o s i n c e t h e e f f e c t i v e a d i a b a t i c c o n s t a n t a p p e a r s o n l y a s ( g 2 + l ) i n e q u a t i o n ( 9 - 1 ) . F o r l a r g e p r e s s u r e r a t i o s , one n e e d s h i g h g a s d e n s i t i e s a n d f a s t d e t o n a t i o n s p e e d s . I t a p p e a r s , f r o m t h e d a t a g i v e n i n K h i t r i n / 8 / . t h a t an e q u i m o l a r o x y - a c e t y l e n e m i x t u r e i s t h e m o s t s u i t a b l e c h o i c e f o r t h i s p u r p o s e . The o n l y o t h e r g a s w i t h a h i g h e r p r e s s u r e r a t i o i s o x y - c y a n o g e n , h o w e v e r , t h e p r o b l e m s i n v o l v e d i n h a n d l i n g t h i s p o i s o n o u s g a s do n o t w a r r a n t i t s u s e . CALIBRATION OF THE PROBE: The c a l i b r a t i o n o f t h e p i e z o e l e c t r i c p r e s s u r e p r o b e was p e r f o r m e d i n a 110 cm l o n g , 2.5 cm d i a m e t e r p y r e x t u b e c l o s e d a t b o t h e n d s . Two b r a s s e l e c t r o d e s w e r e p l a c e d a t one e n d o f t h e t u b e t o s p a r k i g n i t e t h e g a s . The p r o b e was p l a c e d f l u s h w i t h t h e w a l l o f t h e t u b e p e r p e n d i c u l a r - 114 -t o i t s a x i s a t a p o s i t i o n 90 cm from t h e i g n i t i o n end. The o u t p u t o f the probe was f e d d i r e c t l y t o a. 545-A o s c i l l o s c o p e ( T e k t r o n i x ) u s i n g a t y p e W p l u g - i n u n i t ( T e k t r o n i x ) . The speed of t h e d e t o n a t i o n was o b t a i n e d from smear camera photographs as w e l l as t h e t i m e i n t e r v a l between t h e i g n i t i o n and t h e p r e s s u r e p u l s e a r r i v a l , t a k i n g i n t o account t h e d e l a y t i m e o f t h e probe. The v a l u e s o b t a i n e d from t h e s e two methods agr e e w i t h i n t h e e x p e r i m e n t a l and r e p r o d u c i b i l i t y e r r o r s w h i c h have a combined e f f e c t o f l e s s t h a n one p e r - c e n t . A t y p i c a l smear camera r e c o r d and p i e z o e l e c t r i c p r e s s u r e probe t r a c e a r e shown i n f i g u r e 9-1. The p e r f e c t s t r a i g h t l i n e f o l l o w e d by t h e f r o n t on t h e smear i n d i c a t e s t h a t t h e d e t -o n a t i o n i s in d e e d a s e l f s u p p o r t i n g d e t o n a t i o n o f t h e C . J . t y p e /15/. The p r e s s u r e r e c o r d shows a sharp r i s e o f l e s s t h a n one m i c r o s e c o n d and a smooth, slow decay c o r r e s p o n d i n g t o t h e r a r e f a c t i o n wave f o l l o w i n g i t . The r a r e f a c t i o n wave i s d i s c u s s e d below. The s m a l l s t e p a t t h e b e g i n n i n g o f t h e t r a c e o f t h e probe i s i d e n t i f i e d as an o v e r - s h o o t o f t h e probe. The t r u e v o l t a g e o u t p u t i s t a k e n t o be t h e v a l u e j u s t b e h i n d t h i s o v e r - s h o o t . A p l o t of t h e d e t o n a t i o n v e l o c i t y v e r s u s t h e i n i t i a l p r e s s u r e i s shown i n f i g u r e 9-2. T h i s c u r v e appears t o agree v e r y w e l l w i t h t h e o b s e r v a t i o n s made p r e v i o u s l y by Di x o n /8/ f o r v a r i o u s gas m i x t u r e s . The f i n a l p r e s s u r e i s t h e n c a l c u l a t e d u s i n g t h i s f u n c t i o n , U i ( P i ) , and t h e c o n s t a n t 6o=H.8 10~ 6sec 2m"" 2 f o r C 2H 2+0 2. The r e s u l t s a r e p l o t t e d - 115 -Smear photograph Pi = 300 T o r r (C 2H 2+0 2) Sweep=40 y s e c / d i v . Markers=5 and 1 cm. D e t o n a t i o n tube D e t o n a t i o n f r o n t J V P r e s s u r e probe I g n i t i o n T y p i c a l p r e s s u r e r e c o r d V=0.5 V o l t / d i v t=10 y s e c / d i v V F i g u r e 9-1: P r e s s u r e probe c a l i b r a t i o n s e t - u p . - 116 -2. 84 o d) w e 2. 76 o QJ O . UJ C 0 • H -P 2. 68 (C o 4 J (U Q 2. 60 100 200 300 I n i t i a l p r e s s u r e , P i ( T o r r ) 400 500 F i g u r e 9-2: V e l o c i t y o f a p l a n e d e t o n a t i o n v e r s u s p r e s s u r e . ( x D a t a o b t a i n e d i n t h e d e t o n a t i o n chamber ) F i g u r e 9-3: P r e s s u r e r a t i o ( P 2 / P i ) and f i n a l p r e s s u r e ( P 2 ) v e r s u s i n i t i a l p r e s s u r e ( P i ) f o r a p l a n e d e t o n a t i o n . - 117 -i n f i g u r e 9-3. The c a l i b r a t i o n c u r v e o f t h e p r e s s u r e probe can now be found-by p l o t t i n g t h e o u t p u t o f t h e probe v e r s u s t h e C.J. p r e s s u r e . The c a l i b r a t i o n p o i n t s were f i r s t p l o t t e d on l o g - l o g paper t o check t h e l i n e a r i t y o f t h e r e s -ponse of t h e p r o b e , f i g u r e 9-4. The s e n s i t i v i t y o f t h e gauge was t h e n found by p l o t t i n g t h e d a t a p o i n t s on l i n e a r s c a l e s , f i g u r e 9-5. The p r e s s u r e gauge was found t o be l i n e a r i n t h e range o f c a l i b r a t i o n and t o have a s e n s i t i v i t y o f 70 u v o l t s / T o r r . 9-2 PROPAGATION AND PROPERTIES OF PLANE DETONATIONS: BOUNDARY LAYER EFFECTS: I n t h e t h e o r y c h a p t e r , we found t h a t t h e speed o f a C.J. d e t o n a t i o n , V , s h o u l d be i n d e p e n d e n t o f t h e i n i t i a l s p r e s s u r e , P i ; however, i n t h e d e r i v a t i o n o f t h i s r e s u l t , we n e g l e c t e d c o n f i n e m e n t e f f e c t s by assuming a l o s s l e s s i n f i n i t e p l a n e wave. I n t h i s s e c t i o n , we a t t e m p t t o a c c o u n t f o r t h e o b s e r v e d dependence o f V on P i ( f i g u r e 9-2) by making use o f t h e t h e o r y d e v e l o p e d by Fay /47/. I n h i s p aper, Fay d e t e r m i n e t h e growth o f t h e v i s c o u s boundary l a y e r a t t h e w a l l and i t s e f f e c t s upon t h e f l o w i n t h e r e a c t i o n zone o f t h e d e t o n a t i o n . For a p l a n e wave p r o p a g a t i n g i n a t u b e , a f r a c t i o n a l d e c r e a s e i n v e l o c i t y ' was found t o have t h e f o l l o w i n g form: - 118 -0 5 10 15 20 F i n a l p r e s s u r e ( x i o 3 T o r r ) F i g u r e 9-5: V o l t a g e o u t p u t o f t h e probe v . s . p r e s s u r e s t e p . ( C a l i b r a t i o n c u r v e , s e n s i t i v i t y = 7 0 y V o l t s / T o r r ) - 1 1 9 -V Vs 6 * ( 9 - 3 ) ,—— OC .-v 0 d where d i s t h e tube d i a m e t e r , VQ i s t h e speed of t h e d e t -o n a t i o n w i t h no boundary e f f e c t s ( i e : d-><») and 6* i s t h e d i s p l a c e m e n t t h i c k n e s s , r e l a t e d t o t h e boundary l a y e r ' t h i c k n e s s and w h i c h i s g i v e n by / 4 7 / : 6* « fi°.8X ( V I 0 / P I V S ) ( 9 - 4 ) 6 i s t h e r e a c t i o n zone t h i c k n e s s , y 0 t h e v i s c o s i t y o f t h e gas, V t h e speed o f t h e f r o n t and px t h e i n i t i a l d e n s i t y . T h i s r e l a t i o n i s based on t h e e x p e r i m e n t a l r e s u l t s o f Gooderum /4 8/. We w i l l show l a t e r t h a t t h e r e a c t i o n zone o f a d e t o n a t i o n v a r i e s i n v e r s e l y w i t h t h e p r e s s u r e , i e : 6 o c l / P i . F u r t h e r more, we have pi<*Pi and f i n a l l y i f y 0 i s t a k e n t o be i n d e p e n d e n t o f t h e p r e s s u r e , e q u a t i o n ( 9 - 3 ) can be w r i t t e n a s : v n - v P i * ( - ) x v 0 , 2 = C o n s t a n t = C ( 9 - 5 ) V S s Hence p l o t t i n g 1/PjV^* 2 v e r s u s V , we s h o u l d o b t a i n a s t r a i g h t l i n e o f s l o p e -1/CVQ and V g i n t e r c e p t V^. Such a p l o t i s shown i n f i g u r e 9-6. The r e s u l t i n g c u r v e i s not a s t r a i g h t l i n e , however, f o r l a r g e r v a l u e s o f V , t h a t i s f o r h i g h e r i n i t i a l p r e s s u r e s , t h e c u r v e o f f i g u r e 9-6 t e n d t o a good s t r a i g h t l i n e w i t h an i n t e r c e p t on t h e V s a x i s o f 2 . 9 6 Km/sec, T h i s v e l o c i t y e s t i m a t e f o r a l o s s l e s s d e t o n a t i o n i n oxy-a c e t y l e n e gas compares v e r y w e l l w i t h t h e v a l u e q u o t e d i n 2.80 2.85 2.90 2.95 P l a n e d e t o n a t i o n v e l o c i t y , V (Km/sec). F i g u r e 9-6: P l o t o f 1/PiV 0- 2 v e r s u s V t o check on Fay's boundary l a y e r t h e o r y . - 121 -K h i t r i n /8/ f o r t h e same gas (2.961 Km/sec). V a r i a t i o n s i n the d e t o n a t i o n speed were a l s o o b s e r v e d i n . t h e d e t o n a t i o n chamber. The v a l u e s o b t a i n e d i n t h e chamber a r e p l o t t e d i n f i g u r e 9-2. The d e t o n a t i o n v e l o c i t y i n t h e chamber i s about 3% lower t h a n t h e c o r r e s p o n d i n g speed i n t h e tub e . T h i s d i s c r e p e n c y i s a t t r i b u t e d t o t h e boundary l a y e r w hich s h o u l d have more pronounced e f f e c t s i n t h e chamber s i n c e t h e r a t i o of t h e d e t o n a t i o n f r o n t t o th e c o n t a c t l i n e between t h e f r o n t and t h e c o n t a i n e r i s s m a l l e r i n t h e chamber t h a n i n t h e tube (0.6 v.s 1.3 cm). F u r t h e r r e f i n e m e n t s on the c a l c u l a t i o n of the d e t o n a t i o n speed have been made by v a r i o u s a u t h o r s . A b r i e f summary o f the s e developments i s g i v e n i n W i l l i a m s ' book /36/. More r e c e n t l y , A. B e n o i t a t UTIAS / l l / , made complex and a c c u r a t e c a l c u l a t i o n s of the C.J. s t a t e of a d e t o n a t i o n and found a d e f i n i t e dependence of the s t a t e on t h e i n i t i a l p r e s s u r e . DETONATION SPIN: L a r g e a m p l i t u d e f l u c t u a t i o n s i n t h e probe o u t p u t were o b s e r v e d i n low p r e s s u r e d e t o n a t i o n s (Pj<20 T o r r ) . These were i n t e r p r e t e d as t h e r e s u l t o f d e t o n a t i o n s p i n , l a t e r t h i s was c o n f i r m e d by smear -photographs. F i g u r e 9-7 shows s p i n n i n g d e t o n a t i o n s i n o x y - a c e t y l e n e m i x t u r e s a t s e v e r a l i n i t i a l p r e s s u r e s . The s p i n shows up v e r y d i s t i n c t i v e l y when t h e p r e s s u r e f l u c t u a t i o n s a r e compared w i t h t h e smear t r a c e s . D e t o n a t i o n s p i n , w h i c h c o r r e s p o n d s t o t h e h e l i c a l - 122 -10 ysec t k 45.5 ysec P i =7 T o r r 20 m V . J 45.5 ysec 10 ysec 50 mV 10 ysec Pi=10 T o r r 45.5 ysec F i g u r e 9-7: D e t o n a t i o n s p i n ; P r e s s u r e r e c o r d s and smear photographs. Pi=15 T o r r m o t i o n o f a d e t o n a t i o n h e a d i n t h e f r o n t , h a s b e e n e x t e n s i -76,7,9,11,49,73/. T h e r e f o r e we s h a l l n o t e x p a n d on i t a n d r e f e r t h e i n t e r e s t e d r e a d e r t o t h e l i t e r a t u r e . The a p p e a r -a n c e o f s p i n a t l o w i n i t i a l p r e s s u r e s makes t h i s r a n g e u n u s a b l e f o r t h e c a l i b r a t i o n o f the' p r o b e s i n c e t h e e q u i -l i b r i u m p r e s s u r e i s n o t r e a c h e d b e h i n d t h e f r o n t . RAREFACTION WAVE: One o f t h e b o u n d a r y c o n d i t i o n s w h i c h h a v e t o be s a t i s -f i e d a t t h e c l o s e d e n d o f t h e t u b e i s z e r o mass v e l o c i t y . T h i s means t h a t a r a r e f a c t i o n wave must f o l l o w t h e d e t o n a t i o n f r o n t s i n c e i t i m p a r t s a d i r e c t e d . m o t i o n t o t h e g a s . The t h e o r e t i c a l d i s t r i b u t i o n o f p r e s s u r e , mass v e l o c i t y a n d d e n s i t y i n s u c h a r a r e f a c t i o n wave, h a v e b e e n p r e d i c t e d b y T a y l o r / 5 0 / a n d h a v e b e e n v e r i f i e d e x p e r i m e n t a l l y i n a number o f e x p e r i m e n t s / 5 1 , 5 2 , 5 3 / . When t h e d e t o n a t i o n r e a c h e s t h e e n d o f t h e t u b e , a s h o c k wave i s r e f l e c t e d b a c k i n t o t h e r a r e f a c t i o n wave. F i g u r e 9-8 shows a smear p h t o g r a p h o f a d e t o n a t i o n a n d r e f l e c t e d s h o c k wave i n a 30 cm l o n g , 2.5 cm d i a m e t e r t u b e a t an i n i t i a l p r e s s u r e o f 200 T o r r i n C 2 H 2 + 0 2 . The v e l o c i t y o f t h e r e f l e c t e d wave i s n o t c o n s t a n t a n d c a n be p r e d i c t e d f r o m t h e e q u a t i o n / 5 5 / : v e l y i n v e s t i g a t e d b o t h e x p e r i m e n t a l l y a n d t h e o r e t i c a l l y V ( x j ) = V ( x 0 ) + 8V 9 P i d P j + 9 V 3 U i dUi ) (9-6) - 124 -t 25 ysec I g n i t i o n 5 cm P e r t u r b a t i o n F i g u r e 9-8: D e t o n a t i o n and r e f l e c t e d shock wave. - 125 -and the knowledge of the p a r t i a l d e r i v a t i v e s . J . D. Strachan /54,55/, f o l l o w e d an a n a l y s i s s i m i l a r to t h a t of C h i s n e l l /56/ Ohyama /57/ and Whitham /20/ to show t h a t these d e r i v a t i v e s can be e v a l u a t e d to f i r s t order and t h a t e q u a t i o n (9-6) can be reduced t o : V ( x i ) = V ( x 0 ) + Ui (xi) + f ( P i , V , U i , P i ) dpi x=x 0 + X i h(pi.,V,Ui ,Pi) dPi (9-7) / X = X o where f - — and h= TTT- . , 0 N, 3Ui 3Pi (9-8) The c o n d i t i o n s ahead of the r e f l e c t e d f r o n t are known from the C.J. c o n d i t i o n s and the r a r e f a c t i o n wave eq u a t i o n s . Thus from a measurement of the i n i t i a l v e l o c i t y of the r e f l e c t e d shock wave, the speed of the wave can be c a l c u l a t e d f o r any p o s i t i o n i n s i d e the r a r e f a c t i o n wave by u s i n g equation (9-7). F i g u r e 9-9 shows the p r e d i c t e d shock speed ( s o l i d l i n e ) and the experimental v a l u e s obtained from smear photographs. These r e s u l t s are p l o t t e d a g a i n s t the f r a c t i o n a l d i s t a n c e through the r a r e f a c t i o n wave, x. There i s - e x c e l l e n t agreement up to x=0.3. Beyond t h i s p o i n t , the e xperimental p o i n t s f a l l below the t h e o r e t i c a l curve. -At the c o r r e s p o n d i n g p l a c e on the smear photographs ( f i g u r e 9-8), a s m a l l d i s t u r b a n c e i s seen t o reach the r e f l e c t e d f r o n t . T h i s d i s t u r b a n c e seems to o r i g i n a t e from the i g n i t i o n - 1 2 6 -F i g u r e 9-9: V e l o c i t y o f r e f l e c t e d shock wave, V , v e r s u s f r a c t i o n a l d i s t a n c e i n the r a r e f a c t i o n wave, x o , O - E x p e r i m e n t a l d a t a from two smears. 1,1 1 1 - T h e o r e t i c a l c u r v e . - 127 -e n d o f t h e t u b e . I t i s p r o b a b l y a weak s h o c k wave a r i s i n g f r o m t h e r e f l e c t i o n ' o f t h e s h o c k wave o r d e t o n a t i o n wave g e n e r a t e d b a c k w a r d s by t h e i g n i t i o n s p a r k ( f i g u r e 9 - 8 ) . T h i s , s h o r t a n a l y s i s i s a g o o d e x p e r i m e n t a l c h e c k on S t r a c h a n ' s a n a l y s i s o f t h e p e n e t r a t i o n o f s h o c k waves i n n o n - u n i f o r m f l o w f i e l d s . THE VON NEUMANN S P I K E : As m e n t i o n e d i n c h a p t e r 2, a d e t o n a t i o n i s e s s e n t i a l l y a s h o c k wave i m m e d i a t e l y f o l l o w e d by a r e a c t i o n z o n e . T h i s z o n e i s c h a r a c t e r i z e d by a d e c r e a s e i n p r e s s u r e f r o m t h e s h o c k wave p r e s s u r e , P , t o t h e C . J . p r e s s u r e , P ^ T . F r o m S O i J e q u a t i o n ( 2 - 1 5 ) , P % 2 P r , T s i n c e t h e e n e r g y i n p u t , Q, i s S C u e q u a l t o z e r o f o r a s h o c k wave. T h i s p r e s s u r e o v e r s h o o t i s c a l l e d t h e v o n Neumann s p i k e . U s i n g a s i m p l e m o d e l , t h e w i d t h o f t h e r e a c t i o n z o n e i s g i v e n by 6«NX, w h e r e N i s t h e number o f c o l l i s i o n s r e q u i r e d f o r c o m p l e t i o n o f t h e c h e m i c a l r e a c t i o n a n d A t h e mean f r e e p a t h i n t h e g a s . I n a g i v e n g a s m i x t u r e , N s h o u l d n o t d e p e n d on t h e i n i t i a l p r e s s u r e o f t h e g a s . A l s o , f r o m e l e m e n t a r y K i n e t i c t h e o r y , 6 0 C l / n and n a P , w h e r e n i s t h e p a r t i c l e number d e n s i t y a n d P t h e p r e s s u r e . Hence we e x p e c t t h e r e a c t i o n z o n e t h i c k n e s s t o be i n v e r s e l y d e p e n d e n t on t h e p r e s s u r e , i e : 6«1/P. T h e r e i s g o o d e x p e r i m e n t a l e v i d e n c e t h a t t h i s r e l a t i o n i s i n d e e d a g o o d a p p r o x i m a t i o n / 5 3 , 5 8 / . I t i s u n f o r t u n a t e t h a t a t l o w i n i t i a l p r e s s u r e s t h e d e t o n a t i o n p r o p a g a t e s i n a s p i n n i n g - 128 -mode, making i t i m p o s s i b l e t o d i s t i n g u i s h between p r e s s u r e v a r i a t i o n s due t o t h e s p i n and t h e r e a c t i o n zone. However, a- sharp p r e s s u r e s p i k e i s r e c o r d e d on some p r e s s u r e t r a c e s a t v e r y low i n i t i a l gas p r e s s u r e s ( f i g u r e 9-10a). I f t h i s p r e s s u r e s p i k e i s i d e n t i f i e d as t h e von Neumann s p i k e , t h e w i d t h o f t h e r e a c t i o n zone c o r r e s p o n d i n g t o t h i s 2 usee p r e s s u r e p u l s e i s about 5 mm s i n c e t h e wave t r a v e l s a t a p p r o x i m a t e l y 3 mm/usec and t h e probe i s 1 mm i n d i a m e t e r . S c a l i n g t h i s w i d t h w i t h t h e p r e s s u r e , t h e r e a c t i o n zone t h i c k n e s s i s about 50 y a t a t m o s p h e r i c p r e s s u r e . T h i s v a l u e can a l s o be o b t a i n e d i n a n o t h e r way. At s l i g h l y more e l e v a t e d i n i t i a l p r e s s u r e s (below 50 T o r r ) , some s o r t o f s p i k e i s always o b s e r v e d a t t h e b e g i n n i n g o f t h e p r e s s u r e r e c o r d s ( f i g u r e 9-10b). These become s m a l l e r w i t h i n c r e a s i n g i n i t i a l p r e s s u r e s and f i n a l l y d i s a p p e a r c o m p l e t e l y a t p r e s s u r e s above 50 T o r r ( f i g u r e 9-10c), where o n l y t h e s m a l l o v e r s h o o t o f t h e probe i s seen. I t can be shown, from t h e s i z e o f t h e probe and t h e speed o f t h e d e t o n a t i o n wave, t h a t a r e a c t i o n zone o f l e s s t h a n 1 mm would not r e c o r d s i n c e t h e p r e s s u r e p u l s e would pass over t h e end o f t h e probe i n a t i m e s h o r t e r t h a n t h e r i s e - t i m e o f t h e gauge. T h e r e f o r e a t P =50 T o r r , t h e r e a c t i o n zone t h i c k n e s s i s about 1 mm o r l e s s , t h i s c o r r e s p o n d s t o about 60 y or l e s s a t a t m o s p h e r i c p r e s s u r e . - 129 -a) I n i t i a l pressure=7 T o r r S c a l e s : V e r t i c a l = 1 0 raV/div H o r i z o n t a l = 1 0 y s e c / d i v b) I n i t i a l p ressure=25 T o r r S c a l e s : V e r t i c a l = 5 0 mV/div H o r i z o n t a l = 1 0 y s e c / d i v c) I n i t i a l pressure=50 T o r r S c a l e s : V e r t i c a l = 1 0 0 mV/div H o r i z o n t a l = 1 0 y s e c / d i v F i g u r e 9-10: P r e s s u r e r e c o r d s o f low p r e s s u r e d e t o n a t i o n s t a k e n w i t h a p i e z o e l e c t r i c p r e s s u r e gauge. D e t o n a t i o n gas = C 2 H 2 + 0 2. Leaf 129 repeated i n page numbering. - 123;-..-CHAPTER 10 CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK 10-1 CYLINDRICAL IMPLOSIONS: One o f the aims o f t h i s t h e s i s was t o v e r i f y e x p e r i -m e n t a l l y t h e p r e d i c t i o n s o f th e C.C.W. model f o r i m p l o d i n g d e t o n a t i o n s . To t h i s end, a p r e l i m i n a r y i n v e s t i g a t i o n o f the i m p l o s i o n p r o p e r t i e s o f t h e d e t o n a t i o n was c a r r i e d o u t w i t h an image c o n v e r t e r camera. T h i s s u r v e y showed t h a t we were a b l e t o produce v e r y s t a b l e and e x t r e m e l y r e p r o d u -c i b l e i m p l o d i n g d e t o n a t i o n s . A h i g h r e s o l u t i o n smear camera, was t h e n b u i l t and used t o o b t a i n a c c u r a t e measurements o f the i m p l o s i o n p a t h o f th e d e t o n a t i o n f r o n t . The e x c e l l e n t f i t between t h e d a t a and t h e t h e o r e t i c a l c u r v e showed t h a t t h e speed o f t h e wave can be v e r y v / e l l p r e d i c t e d by t h e model c a l c u l a t i o n s . We a l s o r e p r o d u c e d t h e p r e s s u r e measurements of Lee e t a l / l / . The f o c u s i n g e f f e c t s o f the i m p l o s i o n on the d e t o n a t i o n f r o n t p r e s s u r e were c o n f i r m e d t o obey v e r y c l o s e l y t h e t h e o r e t i c a l c u r v e . An att e m p t a t me a s u r i n g t h e gas t e m p e r a t u r e was i m p a i r e d because t h e r e a c t i o n p r o d u c t s b e h i n d t h e d e t o n a t i o n f r o n t a r e not i n t h e r m a l e q u i l i b r i u m . I t was t h e r e f o r e i m p o s s i b l e t o o b t a i n v e r y s i g n i f i c a n t r e s u l t s . One o f t h e c o n c l u s i o n s drawn from t h e s e measure-ments was t h a t t h e plasma i s o p t i c a l l y t h i n even f o r t h e most i n t e n s e s p e c t r a l f e a t u r e s . T h i s c o n c l u s i o n c a s t s some doubts - 130 -o n t h e v a l i d i t y o f t h e two c o l o r m e t h o d u s e d by K n y s t a u t a s and L e e /59/ t o o b t a i n a t e m p e r a t u r e e s t i m a t e o f a b o u t 200xl0 3 °K a t t h e c e n t e r o f i m p l o s i o n . The h i g h l y t r a n s i e n t n a t u r e o f t h e i m p l o s i o n p o i n t makes i t v e r y d i f f i c u l t t o m e a s u r e t e m p e r a t u r e s , h o w e v e r , t h i s v e r y f a c t m i g h t p r o v e o f i n t e r e s t ' t o s t u d y t h e e x i s t e n c e o f m o l e c u l e s u n d e r t h e e x t r e m e c o n d i t i o n s e x i s t i n g a t t h e c e n t e r o f c o l l a p s e . 10-2 A P P L I C A T I O N S : The s e c o n d o b j e c t o f t h e t h e s i s was t o show t h e f e a s i -b i l i t y o f u s i n g t h e i m p l o d i n g d e t o n a t i o n a s a d r i v e r s e c t i o n f o r a p r e s s u r e d r i v e n s h o c k t u b e . We b e l i e v e t o h a v e shown t h a t s u c h a d e v i c e c a n i n d e e d be u s e d t o p r o d u c e f a s t s h o c k w a v e s . H o w e v e r , t h e h i g h l y n o n - u n i f o r m p r e s s u r e d i s t r i b u t i o n o f t h e d r i v e r g a s seems t o c r e a t e v e r y l a r g e l o s s e s o f s h o c k h e a t e d g a s , r e d u c i n g t h e l e n g t h o f u s a b l e p l a s m a b e h i n d t h e s h o c k f r o n t . The m o s t p r o m i s i n g a s p e c t o f t h i s s h o c k t u b e i s t h e p o s s i b i l i t y o f o b t a i n i n g h i g h Mach numbers i n f a i r l y h i g h t e s t g a s p r e s s u r e s by i n c r e a s i n g t h e s i z e a n d i n i t i a l p r e s s u r e i n t h e d r i v e r c h a m b e r . I t seems q u i t e f e a s i b l e t o d e s i g n a n d b u i l d a d r i v e r s e c t i o n o f s t i l l m o d e r a t e s i z e ( a b o u t 1 m i n d i a m e t e r ) a n d c a p a b l e o f w i t h s t a n d i n g 10 atm i n i t i a l p r e s s u r e w h i c h w o u l d g e n e r a t e 50 t o 100 M . J o u l e s and a minimum d r i v i n g p r e s s u r e o f 10 3 atm o v e r t h e s e c t i o n o f a 2" s h o c k t u b e . B e f o r e b u i l d i n g s u c h -a d e v i c e , a t h o r o u g h s t u d y o f t h e s h o c k f o r m a t i o n and t h e e f f e c t s o f t h e g e o m e t r i c a l f a c t o r s s h o u l d be done t o o p t i m i z e t h e p e r f o r m a n c e s o f t h e shock t u b e . S p e c i a l e f f o r t s s h o u l d be made t o t r y t o re d u c e t h e m i x i n g o f t h e d r i v e r and t e s t gases i n t h e i n i t i a l phase o f shock f o r m a t i o n . The c a l i b r a t i o n o f t h e p i e z o e l e c t r i c p r e s s u r e probe by means o f p l a n e d e t o n a t i o n s p r o v e d t o be . a v e r y r e l i a b l e and easy method. The s e t - u p used i n t h e c a l i b r a t i o n a l s o a l l o w e d us t o o b t a i n some v a l u a b l e i n f o r m a t i o n s on t h e p r o -p e r t i e s o f p l a n e d e t o n a t i o n s i n e q u i m o l a r o x y - a c e t y l e n e . We found t h a t Fay's a c c o u n t o f t h e e f f e c t s o f a l a m i n a r boundary l a y e r on t h e d e t o n a t i o n speed, was q u i t e s a t i s f a c -t o r y a t h i g h i n i t i a l p r e s s u r e s (>200 T o r r ) b u t f a i l e d t o e x p l a i n t h e l a r g e r v e l o c i t y d e c r e a s e a t lo w e r p r e s s u r e s . We a l s o were a b l e t o o b t a i n a r e l a t i v e l y a c c u r a t e measurement of t h e von Neumann s p i k e l e n g t h (50 u a t 1 a t m . i n i t i a l p r e s s u r e ). The shock wave r e f l e c t e d o f f t h e end o f t h e c a l i b r a t i o n tube a l l o w e d us t o make a r e l i a b l e e x p e r i m e n t a l v e r i f i c a t i o n of t h e t h e o r y o f shock p r o p a g a t i o n i n non-u n i f o r m r e g i o n s d e v e l o p e d by J . D. S t r a c h a n . The e x i s t e n c e o f d e t o n a t i o n s p i n i n low p r e s s u r e d e t o n a t i o n s (<20 T o r r ) was de m o n s t r a t e d by smear photographs and p r e s s u r e r e c o r d s . - 132 -BIBLIOGRAPHY 1. J . H. L e e a n d B. H. K. L e e , P h y s . o f F l u i d s , 8 _ , 2148 (1965) 2. A. L. F u l l e r a n d R. A. G r o s s , P h y s . F l u i d s , 1 1 , 534 (1968) 3. M. B e r t h e l o t a n d P. V i e i l l e , Ann. de C h i m i e e t de P h y s i q u e , [ 5 ] , 2 8, 289 (1883) 4. E. M a l l a r d a n d H. L. L e C h a t e l i e r , A nn. d e s M i n e s , [ 8 ] , 4_, 274 (1883) 5. S. S. P e n n e r and B. P. M u l l i n s , E x p l o s i o n s , D e t o n a t i o n s ,  F l a m m a b i l i t y a n d I g n i t i o n , P e r g a m o n P r e s s (1959) 6. I a . B. Z e l d o v i c h a n d A. S. K o m p a n e e t s , T h e o r y o f D e t o n a t i o n , A c a d e m i c P r e s s (1960) 7. B. L e w i s a n d G. v o n E l b e , C o m b u s t i o n , F l a m e s a n d E x p l o s i o n s  o f g a s e s , A c a d e m i c P r e s s , 2nd E d . (1961) 8. L. N. K h i t r i n , The P h y s i c s o f C o m b u s t i o n a n d E x p l o s i o n , I s r a e l P r o g r a m f o r S c i e n t i f i c T r a n s l a t i o n s , J e r u s a l e m (1962) 9. A. S. S o k o i i k , S e l f - I g n i t i o n , F l a m e and D e t o n a t i o n i n G a s e s , I s r a e l P r o g r a m f o r S c i e n t i f i c T r a n s l a t i o n s , J e r u s a l e m (1963) 10. A. G. Gaydon and I . R. H u r l e , The S h o c k Tube i n High-Tempe- r a t u r e C h e m i c a l P h y s i c s , Chapman a n d H a l l , L o n d o n (1963) 11. F. A. W i l l i a m s , C o m b u s t i o n T h e o r y , A d d i s o n - W e s l e y (1965) 12. J . H. L e e , R. K n y s t a u t a s a n d G. G. B a c h , T h e o r y o f E x p l o s i o n s , AFOSR S c i e n t i f i c R e p o r t , MERL R e p o r t 69-10 (Nov. 1969) 13. J . A. O w c z a r e k , F u n d a m e n t a l s o f Gas D y n a m i c s , I n t e r n a t i o n a l T e x t b o o k Company (1964) 14. Y. B. Z e l d o v i c h , . N . A . C . A . , T.M. 1261 (1940) 15. L. D. L a n d a u a n d E. M. L i f s h i t z , F l u i d M e c h a n i c s , P e r g a m o n P r e s s (1959) 16. B. A h l b o r n a nd M. S a l v a t , Z. N a t u r f o r s c h u n g , 2 2 a , 260 (1967) 17. B. A h l b o r n a n d W. Z u z a k , Can. J . P h y s . , 47, 1709 (1969) 18. W. C h e s t e r , P h i l . Mag., 45_, 1293 (1954) 19. R. F. C h i s n e l l , P r o c . Roy. S o c . ( L o n d o n ) , A 2 2 3 , 350 (1955) - 133 -20. G.-B. W h i t h a m , - J . F l u i d Mech.., 4_, 337 (1958) 21. J . A. F a y , P h y s . F l u i d s , 2 , 283 (1959) 22. J . H. L e e , R. K n y s t a u t a s a n d G. G. B a c h , T h e o r y o f E x p l o s i o n s , AFOSR 69-3090 TR, M e r l R e p o r t 69-10 (Nov. 1 9 6 9 ) , C h a p t e r I 23. B. A h l b o r n a n d J . - P . H u n i , A I A A , 7, 1191 (1969) 24. A. R. F a i r b a i r n a n d A. G. G a y d o n , R o y . S o c . L o n d o n , A 2 3 9 , 4 6 4 ( 1 9 5 7 ) 25. A. G. Gaydon a n d I . R. H u r l e , The S h o c k Tube i n H i g h - T e m p e r a - t u r e C h e m i c a l P h y s i c s , - Chapman and H a l l , L o n d o n ( 1 9 6 3 ) , Chap. X I I I 26. R. W. B. P e a r s e and A. G. G a y d o n , The I d e n t i f i c a t i o n o f  M o l e c u l a r S p e c t r a , Chapman and H a l l , L o n d o n ( 1 9 6 3 ) , 3 r d E d . 27. J . A. S m i t , P h y s i c a X I I , 683 (1946) 28. M. M. S m i t - M i e s s e n a n d J . L. S p i e r , P h y s i c a I X , 193 (1942) 29. R. W a t s o n , W. G. P l a n e t a n d C. C. P i t t s , A p p l i e d O p t i c s , 7_, 1941 (1968) 30. J . N. B r a d l e y , S h o c k Waves i n C h e m i s t r y a nd P h y s i c s , J o h n W i l e y & Sons (New Y o r k ) ( 1 9 6 2 ) , C h a p t e r V l " 31. E. F. G r e e n e a nd J . P. T o e n h i e s , C h e m i c a l R e a c t i o n s i n S h o c k Waves, E d w a r d A r n o l d (London) ( 1 9 6 4 ) , T a b l e 7-7 32. W. H. P a r k i n s o n a n d R. W. N i c h o l l s , C an. J . P h y s . 38 , 715 (1960) 33. D. F i s s e l a n d H. M e i s l , U n d e r g r a d u a t e l a b o r a t o r y r e p o r t ( P r i v a t e c o m m u n i c a t i o n ) 34. G. H. D i e k e a nd H. M. C r o s s w h i t e , J o h n s H o p k i n s U n i v e r s i t y r e p o r t , C F - 7 9 0 , JHB-3-A (1948) 35. W. J e v o n s , R e p o r t on B a n d - S p e c t r a o f D i a t o m i c M o l e c u l e s , The P h y s i c a l S o c i e t y (London) (1932) 36. F. A. W i l l i a m s , C o m b u s t i o n T h e o r y , ' A d d i s o n - W e s l e y ( 1 9 6 5 ) , Chap.6 37. Y a . B. Z e l ' d o v i c h a n d Yu. P. R a i s e r , P h y s i c s o f S h o c k Waves  a n d H i g h - T e m p e r a t u r e H y d r o d y n a m i c P h e n o m e n a , A c a d e m i c P r e s s (1966) 38. H. O e r t e l , S t r o s s r o h r e , S p r i n g e r - V e r l a g ( B e r l i n ) 1966 39. P r o c e e d i n g s o f t h e S e v e n t h I n t e r n a t i o n a l S h o c k Tube Symposium, U n i v e r s i t y o f T o r o n t o P r e s s (1969) 40. I. I. G l a s s a n d J. C. P o i n s s o t , " I m p l o s i o n d r i v e n S h o c k T u b e " , p a p e r i n t h e r e f . 39 - 134 -42. H. N e t t , I P P 3/43 (1966) 43. M. G. R. P h i l l i p s , P h . D. T h e s i s , 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 (1969) 44. R. A r d i l a , MSc. T h e s i s , 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 (1970) 45. J . - P . H u n i , R. A r d i l a a n d B. A h l b o r n , Rev. S c . I n s t . ( J u n e 1970) 46. J . B. P e a r s o n a n d R. C. F e l l i n g e r , T h e r m o d y n a m i c P r o p e r t i e s  o f C o m b u s t i o n G a s e s , The Iowa U n i v e r s i t y P r e s s , Ames (1965) 47. J . A. F a y , P h y s . F l u i d s , 2 _ , 283 (1959) 48. P. B. Gooderum, NACA T e c h . N o t e 4243 (1958) 49. J . A. F a y , J . Chem. P h y s . 20_, 942 (1952) 50. G. I . T a y l o r , P r o c . Roy. S o c . ( L o n d o n ) , A 2 0 0 , 234 (1950) 51. S. P a t t e r s o n , R e s e a r c h ( L o n d o n ) , 3_, 99 (1950) 52. W. E. G o r d o n , 3 r d Symposium o n C o m b u s t i o n , F l a m e s a nd E x p l o s i o n Phenomena (194 9) 53. G. B. K i s t i a k o w s k y a n d P. H. K y d d , J . Chem. P h y s . 23,271 (1955) 54. J . D. S t r a c h a n , M. S c . T h e s i s , 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 (1969) 55. J . D. S t r a c h a n , J . - P . H u n i a nd B. A h l b o r n , J . F l u i d Mech. ( i n p r e s s ) 56. R. F. C h i s n e l l , P r o c . Roy. S o c . ( L o n d o n ) , A 2 3 2 , 350 (1955) 57. N. Ohyama, P r o g , o f T h e o r e t i c a l P h y s . 215 , ,251 (1961) 58. G. B. K i s t i a k o w s k y a n d P. H. K y d d , J . Chem. P h y s . 22,1940 (1954) a n d J . Chem. Phys.. 2_5, 824 (1956) .59. R. K n y s t a u s t a s , B. H. K. L e e , and J . H. S. L e e , P h y s . F l u i d s , 1 2 , S u p p l e m e n t 1,1-165, May 1969 60. S. G l a s s t o n e a n d D. L e w i s , E l e m e n t s o f P h y s i c a l C h e m i s t r y , D. V a n N o s t r a n d Comp, I n c . 2nd. E d . (1960) Chap. 3 6 1 . G. G u d e r l e y ^ u f t f a r h t f o r s e h u n g , 1 9 , 3 0 2 ( 1 9 4 2 ) 6 2 . R. B. P a y n e , J . F l u i d M e c h., 2, 1 8 5 ( 1 9 5 7 ) 6 3 . Y a . B. Z e l ' d o v i c h , J E T P , 3j3, 5 5 0 ( 1 9 5 9 ) - 135 -64. R. L. Welsh, J . F l u i d Mech., 29, 61 (1967) 65. R. W. P e r r y and A. K a n t r o w i t z , J . App. Phys., 22, 878 (1951) 66. V. A. B e l o k o n , A. I . P e t r u k i n and V. A. P r o s k u r y a k o v , JETP, 21, 33 (1965) 67. D. B e r n s t e i n and R. C. G o e t t e l m a n , Rev. S c i . I n s t r u m . , 37, 1373 (1966) 68. J . Wadsworth and F. E. S t o k e s , J . S c i . I n s t r u m . , 39,439(1962) 69. D. E. R o b e r t s , UTIAS T e c h n i c a l Note No. 140 ( S e p t . 1969) 70. I . I . G l a s s , W M a r t i n and G. N. P a t t e r s o n , UTIAS R e p o r t No. 2 (Nov. 1953) 7 1 . A Roshko, Phys. F l u i d s , 3_, 835 (1960) 72;; A . B e n o i t , UTIAS T e c h n i c a l Notes No. 85 (Nov' 64) , 102 (Dec'66), 104 (Dec'66), 128 (Aug'68) .. . --73. -B. V. V o i t s e k h o v s k i i , V. V. M i t r o f a n o v and M. E. T o p c h i a n , T w e l f t h (1968) Symposium ( I n t e r n a t i o n a l ) on Combustion, The Combustion I n s t i t u t e , 829 (1969) -A. K. Macpherson, Same as above, 839 74. D. H. Edwards, Same as r e f . 73, 819 Leaf 135 repeated i n page numbering. - 135 -APPENDIX A The d e t o n a t i o n chambers The d e t a i l e d c o n s t r u c t i o n of the d e t o n a t i o n cham-b e r s and of the a t t a c h m e n t s i s g i v e n h e r e . THE LARGE CHAMBER: A f u l l s c a l e s e c t i o n of the l a r g e chamber i s shown i n f i g u r e A - l . I n t h i s chamber the c e n t e r p l a t e i s sup-p o r t e d by the s p a r k gap and s i x wedges. The i n t a k e and e v a c u a t i o n p o r t s a r e s i t u a t e d on the r i m of the chamber th r o u g h the aluminum r i n g as can be seen from f i g u r e A-3. The s p a r k gap has been s i m p l i f i e d i n f i g u r e A - l and i s t h e r e f o r e shown i n more d e t a i l s i n f i g u r e A-2. The vacuum s e a l between the b r a s s and the p o l y e t h y l e n e i n s u -l a t i o n i s a c h i e v e d by h a v i n g the p a r t s f i t v e r y t i g h t l y t o g e t h e r . The e x t r a s h o u l d e r , S 2 , i n s i d e the r e t u r n e l e c -t r o d e was found n e c e s s a r y t o p r e v e n t the i n s u l a t i o n from b r e a k i n g a t the f i r s t s h o u l d e r , S]_. The f r o n t p l a t e used i n the p r e s s u r e measurements i s shown i n f i g u r e A-3. Two p a r t i a l s e c t i o n s of the p l a t e a r e i n c l u d e d t o show a b o l t and a probe p o r t . S i n c e t h i s p l a t e i s made up of a one i n c h and a h a l f i n c h p l a t e s - g l u e d - t o g e t h e r , the f o u r b o l t s were used t o g i v e e x t r a s t r e n g t h t o the j o i n t . F i g u r e A - l : S e c t i o n of the l a r g e chamber. S- s p a r k gap, W- wedges, D- d e f l e c t i o n p l a t e , F- f r o n t p l a t e , B- back p l a t e , C- i g n i t i o n c a p a c i t o r . ' / / / ' 11 I / I f ' t / i //"/ / f / f f / f f 7 7 ,. L JO / 7/7/^ / R e t u r n e l e c t r o d e C e n t e r e l e c t r o d e 1 2 e v e n l y spaced screws Spacers 0ZZ3 mirximiij. — 7 1 s i P o l y e t h y l e n e i n s u l a t i o n \ L u c i t e back p l a t e / / / / 4 F i g u r e A-2: Blow-up view of the s p a r k gap - 138 -B) C ) F i g u r e A-3; F r o n t p l a t e used i n the p r e s s u r e measurements, A) Photograph of the equipment, B) s e c t i o n of one o f the f o u r r e e n f o r c e m e n t b o l t s , C) s e c t i o n of one o f the p r e s s u r e probe p o r t s . F i g u r e A - 4 : Section of the shock tube a t t a c h m e n t s AI Photograph of the chamber w i t h the p l a t e . « • a r d s o l d e r j o i n t . - 1 4 0 -F i g u r e A-4 shows the d e t a i l s of the f r o n t p l a t e and l e v e r mechanism used t o adapt the shock tube. THE SMALL CHAMBER: A v i e w of the back of the s m a l l chamber i s shown i n f i g u r e A-5. Twelve wedges were used i n t h i s chamber as the s p a r k gap does not p r o v i d e a c e n t r a l s u p p o r t . F i g u r e A-6 shows the s e c t i o n A-A' of the chamber. In t h i s f i g u r e we can see the i g n i t i o n s e t - u p which makes use of a c e n t r a l e l e c t r o d e , a r e t u r n bar and two of the 12 screws used t o f a s t e n the c e n t e r p l a t e t o the back p l a t e . The i n t a k e , I , and e v a c u a t i o n p o r t s , E, are s i t u a t e d a t the back of the chamber as can be seen i n f i g u r e A-5. The q u a r t z window h o l d e r used i n most of the op-t i c a l o b s e r v a t i o n s i s shown i n f i g u r e A-7. One of the l u c i t e i n s e r t s used i n the p r e s s u r e measurements c l o s e t o the c e n t e r of i m p l o s i o n i s shown i n f i g u r e A-8. F i g u r e A-5: Back view o f the s m a l l chamber, I - I n t a k e p o r t ? E- E v a c u a t i o n p o r t F i g u r e A-6: S e c t i o n A-A' o f t h e s m a l l chamber. - 143 -Q u a r t z Window F i g u r e A-7: S e c t i o n of the q u a r t z window h o l d e r . F i g u r e A-8: S e c t i o n of one of the l u c i t e i n s e r t s used i n the p r e s s u r e measurements c l o s e t o the c e n t e r o f i m p l o s i o n . T h i s i n s e r t r e p l a c e s the q u a r t z window of f i g u r e A-7. - 144 -APPENDIX B G e n e r a l l a y - o u t and t r i g g e r i n g c i r c u i t . F i g u r e B - l shows the g e n e r a l l a y - o u t of the ap-p a r a t u s . The m i x i n g tank i s a 4" d i a m e t e r , 18" l o n g c y l i n d e r . F o r s a f e t y measures i t was i n c l o s e d i n an open ended dou b l e l a y e r c y l i n d e r of heavy w i r e mesh (1/4" mesh, 1/8" w i r e ) . The 0-4 atm p r e s s u r e gauge i s used t o m o n i t o r the p r e s s u r e i n the m i x i n g t a n k , w h i l e the o t h e r gauge m o n i t o r s the f i l l i n g p r e s s u r e i n the d e t o n a t i o n chamber. F i g u r e B-2 shows the c i r c u i t diagram of the i g n i t i o n system. A l t h o u g h the c i r c u i t and power s u p p l y were c a p a b l e of h a n d l i n g 20 kV, o n l y 15 kV were used as t h i s v o l t a g e was found t o g i v e enough i g n i t i o n energy t o s e t o f f the d e t o n a t i o n . - 145 -F i g u r e B - l : G e n e r a l l a y - o u t of the a p p a r a t u s . — ® — : V a l v e s . - 146 -S p 2 S p 3 6 T 2 .(-RQ -^ \AAA R, -OTJW c 2 SPx R 5 V -H.V. 5 1 -5 2 " R ± -R 2 *~ Rg — ^4 ~ R 5 " R 6 -C l -C 2 " T l " T 2 --SPi sp2 SP3 Micro-ammeter, O-lOO micro-amps * ,- Sorensen power s u p p l y , 20kV, S o l e n o i d d i s c o n n e c t i n g the H, S o l e n o i d t o s h o r t the bank. C h a r g i n g r e s i s t o r = 166 k a . Dump r e s i s t o r = 33 k a . Meter r e s i s t a n c e = 2 0 0 Ma P o t e n t i a l d i v i d e r =• 175 Mo. B l e e d e r r e s i s t a n c e f o r C 2 = 30mA. V. when f i r i n g 1 . 5 k a B i a s r e s i s t o r = 540 Ma Main c a p a c i t o r f o r i g n i t i o n of d e t o n a t i o n = 1.6 [ i f , 20 kV, C a p a c i t o r f o r t r i g g e r s p a r k = 0.005 u f , 30 kV. P u l s e s t e p - u p t r a n s f o r m e r 300 t o 10,000 V. I s o l a t i o n t r a n s f o r m e r 1:1. - Secondary s p a r k gap t o d i s c h a r g e C 2. - T r i g g e r s p a r k gap f o r i g n i t i o n . - Spark gap of the chamber. F i g u r e B-2: C i r c u i t diagram of the i g n i t i o n system. - 147 -APPENDIX C The smear camera The camera d e s c r i b e d here o p e r a t e s on the w e l l -known p r i n c i p l e of the smear camera ( a l s o c a l l e d s t r e a k camera) which a l l o w s f o r c o n t i n u o u s time r e c o r d of o n e - d i m e n s i o n a l luminous e v e n t s . The c o n v e n t i o n a l s t r e a k camera c o n s i s t s of a s l i t , a l e n s , a r o t a t i n g p l a n e m i r r o r and a r e c o r d i n g s u r f a c e , u s u a l l y a f i l m . The s l i t i s imaged on the f i l m v i a the l e n s and the m i r r o r . As the m i r r o r r o t a t e s , the image sweeps a c r o s s the f i l m w i t h a speed of 2 c j r , where ui i s the a n g u l a r speed of the m i r r o r and r the m i r r o r - t o - f i l m d i s t a n c e . In a n o t h e r smear camera d e s i g n , the s l i t and f i l m , p l a c e d s i d e by s i d e , a r e i n the f o c a l p l a n e of the l e n s . The l i g h t from the s l i t emerges from the l e n s as a p a r a l l e l beam which i s then r e f l e c t e d back t h r o u g h the same l e n s and f o c u s s e d on the f i l m . The image speed i s then 2cjf, where f i s the f o c a l l e n g t h of the l e n s . •--In the p r e s e n t camera d e s i g n ( f i g u r e C - l ) , the l e n s and p l a n e m i r r o r a r e r e p l a c e d by a f r o n t - s i l v e r e d s p h e r i c a l m i r r o r t h u s e l i m i n a t i n g the l a r g e and e x p e n s i v e l e n s needed t o o b t a i n a camera of s m a l l f-number. An e l e c t r o n i c c i r c u i t , m o n i t o r i n g the r o t o r speed, - 1 4 8 -F i g u r e C - l : G e n e r a l l a y - o u t of the camera. - 149 -g i v e s c o n v e n i e n t t r i g g e r i n g f a c i l i t i e s . The camera can be d e s c r i b e d i n f i v e p a r t s : 1) Top assembly 2) Body of the camera 3) R o t o r and motor 4) Rotor-motor assembly 5 ) The e l e c t r o n i c s . 1) TOP ASSEMBLY: The t o p assembly s e r v e s as s l i t and f i l m h o l d e r and p r o v i d e s the a d j u s t m e n t s n e c e s s a r y f o r p r o p e r f o c u s i n g . The assembly, a 6" x 6" x 8" b o t t o m l e s s box made of 1/4" aluminum p l a t e s , f i t s i n s i d e the camera body. A t r a c k and l o c k i n g mechanism h o l d s the assembly i n p o s i t i o n and a l l o w s f o r the up and down motion needed f o r f o c u s i n g . A 7 cm long' s l i t of v a r i a b l e w i d t h i s mounted on a s e p a r a t e p l a t e a t t a c h e d t o the assembly by f o u r t h r e a d e d b a r s (B) p e r m i t t i n g t o move the s l i t r e l a t i v e t o the m i r r o r and f i l m . A s m a l l f r o n t - s i l v e r e d m i r r o r (M) d e f l e c t s the l i g h t from the s l i t down t o the r o t o r . The m i r r o r i s e p o x i e d on a 1/2" b r a s s bar mounted i n s i d e the box. In o r d e r t o m i n i m i z e s p h e r i c a l a b e r r a t i o n e f f e c t s , the m i r r o r i s p l a c e d as c l o s e as p o s s i b l e t o the a x i s of the camera but w i t h o u t i n t e r f e r i n g w i t h the image on the f i l m . The p r e s e n t camera has a maximum a n g l e of 7° between the - 150 -i n c i d e n t and r e f l e c t e d beams. The r e f l e c t o r i s mounted w i t h a c e r t a i n degree of freedom i n o r d e r t o c e n t e r the beam on the r o t o r and t o make the s l i t image on the f i l m e x a c t l y p e r p e n d i c u l a r t o the time a x i s of the camera. The 1/2" w i d t h and 3" l e n g t h of the m i r r o r i s d i c t a t e d by i t s p o s i t i o n r e l a t i v e t o the s l i t and the a c c e p t a n c e a n g l e of the s p h e r i c a l m i r r o r . L i g h t b a f f l e s a r e p l a c e d a t the e n t r a n c e h o l e of the assembly t o p r e v e n t a l l s t r a y l i g h t from e n t e r i n g the camera. The b a f f l e s a r e a d j u s t e d so t h a t the l i g h t from the s l i t c o v e r s e x a c t l y the whole s p h e r i c a l m i r r o r . The t o p of the assembly i s such t h a t i t accomodates a . s t a n d a r d o s c i l l o s c o p e camera f i l m - h o l d e r . 2) BODY OF THE CAMERA: The body of the camera i s a l i g h t - t i g h t box open a t both ends. I t i s made of 1/2" plywood; i t has an i n s i d e s e c t i o n of 6" x 6" and i s 29" l o n g . I t s e r v e s as a j u n c -t i o n between the t o p and r o t o r - m o t o r a s s e m b l i e s . 3) ROTOR AND MOTOR: A) The r o t o r : ( F i g u r e s C-2, C-3, and C-4 ) The r o t o r i s made from a 4" s o l i d c y l i n d e r of aluminum 4 1/2" l o n g . Two s o f t s t e e l s h a f t s a r e f i t t e d on the c y l i n d e r . The m i r r o r i s sunk i n t o the r o t o r deep enough t o have the r e f l e c t i n g s u r f a c e on the a x i s of r o t a t i o n . - 151 -F i g u r e C-4: R o t o r , s e c t i o n B-B' - 1 5 3 -T h i s g i v e s a pure r o t a t i o n a l m otion t o the m i r r o r r a t h e r than a c o m b i n a t i o n of r o t a t i o n and t r a n s l a t i o n which would r e s u l t i f the m i r r o r were mounted o f f a x i s . When the r o t o r has been machined and the b a l l b e a r i n g s f i t t e d on the s h a f t s , the m i r r o r i s e p o x i e d i n p l a c e . The r o t o r i s then b a l a n c e d s t a t i c a l l y b e f o r e i t i s i n s e r t e d i n the assembly. B) The motor: The motor i s a s m a l l s t a n d a r d power t o o l motor from the S t a n l e y Company. The s h a f t of the motor i s t e r m i n a t e d by a 1/4" c h u c k - t y p e f i t t i n g . 4) ROTOR-MOTOR ASSEMBLY: The r o t o r and motor a r e mounted c o a x i a l l y on a 5" x 2" aluminum U beam a p p r o x i m a t e l y 18" l o n g ( f i g u r e C -5). A r u b b e r mounted c o u p l i n g i s used between the r o t o r and the motor. When the assembly was com p l e t e d and a l l the moving p a r t s mounted on i t , i t was g i v e n t o a s p e c i a l i z e d l o c a l company t o be d y n a m i c a l l y b a l a n c e d * . 5 ) THE ELECTRONICS: The speed of the motor i s c o n t r o l l e d by a s t a n d a r d v a r i a c i n s e r i e s w i t h a s w i t c h . * T h i s was done by Dynamic E n g i n e e r i n g Co. L t d , 1219 R i c h a r d s S t r e e t , V a n c o u v e r . MOTOR ROTOR PICK-UP HEAD. O O O O o o o 1 RUBBER MOUNTED COUPLING FLYWHEEL F i g u r e C-5: Rotor-motor assembly - 155 -On the o u t s i d e of the r o t o r - m o t o r assembly a s m a l l f l y w h e e l i s mounted on the a x i s of the r o t o r . A m a g n e t i z e d r a z o r - b l a d e i s i n s e r t e d on the r i m of the f l y w h e e l . A magnetic p i c k - u p head m o n i t o r s the r o t a t i o n of the r o t o r . The head i s mounted on a p l a t e which i s f r e e t o r o t a t e about the a x i s , t h u s , the p u l s e from the r a z o r - b l a d e can be p i c k e d up a t any p o i n t on the r e v o l u t i o n . The p u l s e s from the p i c k - u p head are f e d t h r o u g h a s a t u r a t e d a m p l i f i e r t o produce c l e a n square p u l s e s . These p u l s e s a r e then used t o t r i g g e r a d e l a y u n i t w h i c h , i n t u r n , g i v e s out p u l s e s a t a f i x e d but v a r i a b l e time a f t e r h a v i n g been t r i g g e r e d . The d e l a y i s c o n t r o l l e d by a h i g h p r e c i s i o n t e n - t u r n p o t e n t i o m e t e r . The d e l a y e d and the u n d e l a y e d p u l s e s are f e d t o a one-shot c o i n c i d e n c e gate so t h a t when the p e r i o d of the r o t o r i s e q u a l t o the d e l a y t i m e , a s i n g l e t r i g g e r p u l s e i s g i v e n o u t . Thus, by c o n t r o l l i n g the d e l a y t i m e , one c o n t r o l s the speed of the r o t o r a t which the t r i g g e r p u l s e i s g i v e n o u t . The d e l a y time between the time a t which the m i r r o r comes i n t o p o s i t i o n a t the b e g i n n i n g of the f i l m and the t r i g g e r p u l s e i s c o n t r o l l e d by the p o s i t i o n of the p i c k - u p head. The more " l e a d " the head has on the m i r r o r , the l o n g e r the d e l a y . For most a p p l i c a t i o n s a 15° l e a d was used. T h i s g i v e s a l a r g e d e l a y time between the t r i g g e r p u l s e and the b e g i n n i n g of the smear and a l l o w s one t o use a n o t h e r d e l a y u n i t f o r proper t i m i n g . T h i s t i m i n g . - 156 -method was found t o be more c o n v e n i e n t than t o a d j u s t the p o s i t i o n of the magnetic head. A s o l e n o i d - o p e r a t e d s w i t c h was added, i n p a r a l l e l w i t h the manual s w i t c h of the motor. The c i r c u i t which a c t i v a t e s the r e l a y , not o n l y a l l o w s t o s t a r t the camera v i a a p u s h - b u t t o n , but a l s o s w i t c h e s o f f the motor when the t r i g g e r p u l s e i s g i v e n o u t . The time r e s p o n s e of the r e l a y i s slow enough (15 msec) t o a l l o w f o r the event under s t u d y t o t a k e p l a c e b e f o r e the motor i s a c t u a l l y s w i t c h e d o f f . SWEEP SPEED CALIBRATION: A c a l i b r a t i o n c u r v e of the sweep speed v e r s u s the p o t e n t i o m e t e r s e t t i n g was o b t a i n e d t o an a b s o l u t e a c c u r a c y o f 0.5% and a r e l a t i v e a c c u r a c y of 0.05%. T h i s was a c h i e v e d by m o n i t o r i n g the p e r i o d of r e v o l u t i o n of the r o t o r a t the time the t r i g g e r p u l s e i s g i v e n o u t . A 545-A T e k t r o n i x o s c i l l o s c o p e i n c o n j u n c t i o n w i t h a type 781-A Dumont time mark g e n e r a t o r was used t o measure the p e r i o d t o f o u r s i g n i f i c a n t f i g u r e s . The r e p r o d u c i b i l i t y of the camera e l e c t r o n i c s was f o u n d t o be about 0.05%. The sweep speed was c a l c u l a t e d from the p e r i o d and the f i l m to m i r r o r d i s t a n c e ( L ) . I t i s t h r o u g h t h i s d i s t a n c e t h a t the 0.5% e r r o r i s i n t r o d u c e d s i n c e L i s known o n l y t o w i t h i n 0.5 cm f o r a t o t a l d i s t a n c e of 91 cm. The c a l i b r a t i o n was p e r i o -d i c a l l y c h e c k e d , no n o t i c e a b l e d r i f t was o b s e r v e d . - 157 -SMEAR CAMERA DATA: ' The m i r r o r : R a d i u s of c u r v a t u r e : 91 cm ( - 0.5 cm) D i a m e t e r : 3.050 i n c h e s T h i c k n e s s : 3/8 i n c h e s The motor: S t a n l e y Company, type H14, model A, 115 v o l t s , 2.5 amps, r a t e d f o r 27,000 rpm. Top speed of the motor w i t h the r o t o r : 13,500 rpm. W r i t i n g speed: , C o n t i n u o u s l y v a r i a b l e from 2.5 t o 0.22 mm/u.sec. O b s e r v a t i o n t i m e : From 36 t o 405 |j.sec R e s o l u t i o n : 10 m i c r o n s on the f i l m f o r an i n f i n i t e l y narrow s l i t and p e r f e c t e m u l s i o n . - 158 -APPENDIX D D - l : C a l i b r a t i o n o f the space a x i s : In o r d e r t o o b t a i n good s p a c i a l r e s o l u t i o n , an a c c u r a t e c a l i b r a t i o n was n e c e s s a r y . On the smears t a k e n of the whole chamber, the c a l i b r a t i o n marks were made on the f r o n t p l a t e of the chamber and t h e r e f o r e , d i r e c t c a l i b r a t i o n was p o s s i b l e . W ith the e n t r a n c e o p t i c s used t o image the o b j e c t onto the s l i t of the camera, the a v e r -age m a g n i f i c a t i o n * a c r o s s the f a c e was found t o be 0.444 w i t h a p o s s i b l e e r r o r of 0.003 and a random v a r i a t i o n of 0.008 a c r o s s the f a c e . These e r r o r s are m a i n l y due t o the a c c u r a c y w i t h which the markers were p l a c e d (0.2 mm). The c a l i b r a t i o n of the smears t a k e n t h r o u g h the q u a r t z window had t o be done s e p a r a t e l y and more a c c u r a t e l y . T h i s was a c h i e v e d by p l a c i n g an a c c u r a t e l y known c i r c l e p a t t e r n on the window i n s i d e the chamber where the s l i t was f o c u s e d . . The p a t t e r n was then photographed by i l l u -m i n a t i n g i t w i t h a sun-gun and r o t a t i n g the m i r r o r of the camera s l o w l y f o r a few seconds w i t h the same s e t t i n g of the e n t r a n c e o p t i c s used t o take the smears. The l i n e p a t t e r n of the photograph was then measured w i t h a t r a v -e l i n g m i c r o s c o p e ; the p e r c e n t d e v i a t i o n from the average * The m a g n i f i c a t i o n i s d e f i n e d as the d i s t a n c e 6x on the f i l m which c o r r e s p o n d s t o Ay — 1 cm on the chamber. - 1 5 9 -m a g n i f i c a t i o n was then p l o t t e d v e r s u s the d i s t a n c e from the c e n t e r of the s l i t as i n f i g u r e D - l . F i g u r e D - l : M a g n i f i c a t i o n v a r i a t i o n s a l o n g the s l i t . The two s e t s of p o i n t s r e p r e s e n t the two m a g n i f i -c a t i o n s used i n the measurements d i s c u s s e d i n c h a p t e r 4. I t can be shown t h a t t h e s e v a r i a t i o n s from the average m a g n i f i c a t i o n do not a f f e c t the shape of the smear t r a c e s a p p r e c i a b l y when o n l y the c e n t r a l 2 cm of the smears a r e used as i t i s the c a s e i n c h a p t e r 4. The m a g n i f i c a t i o n M, can be w r i t t e n a s : M = — = 1 ( 1 + f ( x ) ) ( D - l ) A X where M i s the average m a g n i f i c a t i o n a c r o s s the f i l m and f ( x ) the d e v i a t i o n from M as a f u n c t i o n of the p o s i t i o n on the s l i t image. The v a l u e *y' c o r r e s p o n d i n g t o a d i s t a n c e 'x' on the f i l m can be o b t a i n e d by i n t e g r a t i n g e q u a t i o n ( D - l ) : - 160 -px y = M ( x + E ( x ) ) ; E ( x ) = f(x') dx' . (D-2) J o The c o r r e c t i o n E ( x ) can e a s i l y be e s t i m a t e d by a p p r o x i -m a t i n g f ( x ) by the dashed l i n e i n f i g u r e D - l . C o n s i d e r i n g the f u l l s l i t w i d t h , i e : 2 cm, f ( x ) can be w r i t t e n as: f ( x ) = 0.01 ( 1 - x ) (D-3) hence E ( x ) = 0.01 ( x. - x 2 / 2 ) (D-4) E q u a t i o n (D-4) has a maximum a t x = 1 where E ( x ) = 0.005. I f o n l y the f i r s t c e n t i m e t e r i s c o n s i d e r e d , e q u a t i o n s (D-3) and (D-4) become: f ' ( x ) = 0.003 ( 1 - 2x ) (D-3') and E ' ( x ) = 0.003 ( x - x 2 ) (D-4* ) and the maximum v a l u e of E ' ( x ) o c c u r s a t x = 1/2, where E ' ( x ) = 0.0008 . T h i s e r r o r i s l e s s t h a n one p a r t i n a thousand and can be n e g l e c t e d compared w i t h the u n c e r -t a i n t y of measurements on the smears. Thus o n l y an a c c u r a t e v a l u e of M over the c e n t r a l 2 cm of the f i l m i s r e q u i r e d f o r c a l i b r a t i o n . T h i s i s e a s i l y o b t a i n e d s i n c e M i s the r a t i o of two f a i r l y l a r g e q u a n t i t i e s w hich can be measured q u i t e a c c u r a t e l y . I t must be emphasized here t h a t a c c u r a t e measurements ar e o n l y p o s s i b l e when the a l i g n m e n t of the camera and the e n t r a n c e o p t i c s i s done v e r y c a r e f u l l y as by u s i n g a s m a l l gas l a s e r . - 161 -D-2 : O f f - a x i s e f f e c t s : The a l i g n m e n t was done i n such a way as t o make the o p t i c a l a x i s of the camera and f o c u s i n g l e n s e s c o i n c i d e w i t h t h a t of the chamber, thus the d e t o n a t i o n f r o n t i s viewed o f f a x i s everywhere but a t the c e n t e r of i m p l o s i o n . T h i s i n t r o d u c e s o f f - a x i s e f f e c t s which a r e d i s c u s s e d h e r e . The o f f - a x i s e f f e c t s a r e shown g r a p h i c a l l y i n f i g u r e D-2. The f r o n t ( assumed t o be i n f i n i t e l y t h i n f o r con-v e n i e n c e ) i s a t p o s i t i o n r from the c e n t e r and i s r e p r e -s e n t e d by the l i n e AB. P o i n t A i s f o c u s e d onto A" on the s l i t and seems t o be p o i n t A' from the s l i t . S i m i l a r l y , p o i n t B i s f o c u s e d onto B" a t a d i s t a n c e S from the s l i t 2 r 2 0 5 and ( S + o ) ' from p o i n t A" and appears t o be B'. For our purpose, n^ = n-^  s i n c e b oth media are g a s e s , and n 2 ^ n l * W e c a n e a s i-'-y show t h a t BB' = d - x c o t G i but x = d tan62 and a l s o from S n e l l ' s law n^sinG-^ = n2sin©2 n l or s i n 0 2 = — sin©^ ; t h e r e f o r e BB' = d ( l - t a n 0 2 c o t 9 1 ) = n 2 n i cosG-^ d ( l - — ) . The same r e s u l t a p p l i e s t o AA' but the n2 cos02 n^ COSOJL a n g l e s a r e s l i g h t l y d i f f e r e n t AA' = d ( l - ) . n2 cosO^ These e x p r e s s i o n s can be s i m p l i f i e d by making the s m a l l a n g l e a p p r o x i m a t i o n s i n c e 0 = r/0 , where r £ 20 mm and 0 ^ f = 180 mm hence 0 ^ 0.11 . With t h i s a p p r o x i m a t i o n , AA'= BB' and t h e r e f o r e AB = A'B' . The q u a r t z p l a t e has t h e r e f o r e no e f f e c t s s i n c e the f o c u s i n g a d j u s t m e n t s were F i g u r e D-2: O f f - a x i s e f f e c t s (not to s c a l e ) - 1 6 3 -done w i t h i t i n p l a c e . We s h a l l t h e r e f o r e c o n c e n t r a t e on the e f f e c t s due t o the f i n i t e depth of the f r o n t , i e : AB . S i n c e t ^ 0/20 we can f i n d the v a l u e f o r S by d i f f e r e n -t i a t i n g the l e n s f o r m u l a which g i v e s d l = l /0 dO=M t=S by d e f i n i t i o n of M. We can now g e t S = StanO = S9 f o r s m a l l a n g l e s , 9 = Mr/(I ~ f), b u t - I =(1+M)f t h e r e f o r e , & = ( M ^ t / f ) r . Thus the image of the f r o n t appears t o widen l i n e a r l y w i t h i t s p o s i t i o n and the i m p o r t a n t t h i n g t o note i s t h a t on the smears the image of p o i n t A i s n o t the l e a d i n g edge of the l u m i n o s i t y f r o n t but the t a i l edge. T h i s f a c t i s i m p o r t a n t when we compare the t h e o r e t i c a l c u r v e w i t h the smear t r a c e s . - 164 -APPENDIX E The p i e z o l e c t r i c p r e s s u r e probe The p i e z o e l e c t r i c p r e s s u r e probe used i n the p r e s s u r e measurements was d e s i g n e d by Dr. M . • P h i l l i p s i n the c o u r s e of h i s Ph.D. work here a t the U n i v e r s i t y of B r i t i s h Colum-b i a . I t i s d e s c r i b e d q u i t e e x t e n s i v e l y i n h i s t h e s i s (UBC 1969) and i n R. A r d i l a ' s M.Sc. t h e s i s (UBC 1970). However, p u b l i c a t i o n s of t h i s type do not have wide c i r -c u l a t i o n and t h e r e f o r e f o r c o m p l e t e n e s s I s h a l l g i v e a s h o r t d e s c r i p t i o n of the probe i n t h i s a p p e n d i x . The probe i s of the a c o u s t i c l i n e , o r bar t y p e . A PZT-4 c e r a m i c d i s c of a p p r o x i m a t e l y 2 mm d i a m e t e r and 0.2 mm t h i c k i s p l a c e d between two 1 mm d i a m e t e r q u a r t z r o d s which were p r e v i o u s l y c u t t o a p p r o x i m a t e l y 22 cm and 10 cm l e n g t h f o r the f r o n t and back r o d r e s p e c t i v e l y . The ends of the r o d s were ground f l a t and p e r p e n d i c u l a r t o the r o d ' s a x i s so t h a t good m e c h a n i c a l c o n t a c t was o b t a i n e d between the q u a r t z and the c e r a m i c d i s k . The s i g n a l . .". a c r o s s the c r y s t a l i s tapped i n the f o l l o w i n g way. A f i n e copper w i r e (No. 4 0 ) , s t r i p p e d of i t s i n s u l a t i o n , i s wound (2-3 t u r n s ) on the r o d s c l o s e t o . t h e c e r a m i c element. A c o a t i n g of c o n d u c t i n g s i l v e r p a i n t i s a p p l i e d over the w i r e and the r o d s i n c l u d i n g the end f a c e s . W h i l e the p a i n t i s s t i l l f r e s h , the c r y s t a l i s - 165 -sandwiched f i r m l y between the two r o d s . The p a i n t i s then a l l o w e d to d r y b e f o r e c o v e r i n g the j u n c t i o n w i t h a d r o p of epoxy cement t o add s t r u c t u r a l s t r e n g t h t o the probe. F i g -u r e E - l shows the d e t a i l e d ; c o n s t r u c t i o n of the j u n c t i o n . t The wires a r e then t w i s t e d and the ends s o l d e r e d t o a r t a n d a r d BNC c o n n e c t o r which i s p a r t of the h o u s i n g as5" rably. The f r o n t r o d i s h e l d l o o s e l y i n a s o f t p l a s t i c t u b i n g p r o t e c t e d by a Gorex tube. Other d e t a i l s of the h o u s i n g assembly can e a s i l y be seen from f i g u r e E-2 which shows d e t a i l s of the assembly and from f i g u r e E-3 which shows the a c t u a l probe assembled and d i s a s s e m b l e d . The probes a r e c h a r a c t e r i z e d by a d e l a y t i m e , a - w r i t i n g time and' a r i s e t i m e . The d e l a y time of the probe c o r r e s p o n d s t o the time i t t a k e s f o r the p r e s s u r e p u l s e t o t r a v e l the l e n g t h of the f r o n t r o d . I t can be measured e x p e r i m e n t a l l y or c a l c u l a t e d from the speed of sound i n q u a r t z and the l e n g t h of the r o d . D e l a y t i m e s of the B r a s s tube 0 - r i n g s e a l BNC c o n n e c t o r Set-srew f o r a d j u s t i n g the probe Front q u a r t z r o d B r a s s tube T w i s t e d No. 40 w i r e Corex tube S o f t p l a s t i c tube •PZT-4 c e r a m i c d i s c Back r o d F i g u r e E-2: C o n s t r u c t i o n d e t a i l s of the p r e s s u r e probe h o u s i n g ( From M. P h i l l i p s ' Ph. D. T h e s i s , UBC 1969) - 167 -A) B r a s s c a s i n g Corex j a c k e t J Back r o d I F r o n t r o d PZT-4 element B) F i g u r e E-3: Photographs of the p r e s s u r e probe, A) Assembled and B) d i s a s s e m b l e d . - + H » t 10 ysec F i g u r e E-4: T y p i c a l response of the p r e s s u r e probe to a p r e s s u r e s t e p g e n e r a t e d by a d e t o n a t i o n i n e q u i m o l a r o x y - a c e t y l e n e (P-, = 500 T o r r ) - 168 -o r d e r of 40 jisec a r e t y p i c a l f o r the probes used. The w r i t i n g time i s d i c t a t e d by the l e n g t h of the back r o d . I t can be o b s e r v e d from the t r a c e s and c o r r e s p o n d s to the time taken by the p r e s s u r e p u l s e t o t r a v e l from the c e r a m i c element to the end of the back r o d and back t o the c r y s t a l a f t e r r e f l e c t i o n a t the r e a r of the back r o d . W r i t i n g t i m e s of 30 t o 40 |isec a r e t y p i c a l . The r i s e time i s g i v e n by the e q u a t i o n T = 1.96 V ' ( — ) ( — ) L ^ > r ( E - l ) where T) i s the P o i s s o n ' s r a t i o of the r o d , L and r the l e n g t h and r a d i u s of the r o d r e s p e c t i v e l y , c 0 i s the speed of sound i n q u a r t z . T y p i c a l r i s e t i m e s of 0.8 t o 0.9 jisec were o b s e r v e d ; t h i s v a l u e compares f a i r l y w e l l w i t h the v a l u e c a l c u l a t e d from e q u a t i o n ( E - l ) , r = 0.55 y s e c . The probe s i g n a l s were found t o show a s l i g h t o v e r -shoot as w e l l as some r i n g i n g . The amount of s i g n a l d i s t o r t i o n was found t o v a r y from probe t o probe, some h a v i n g more o v e r - s h o o t than r i n g i n g and v i c e v e r s a . The probe used f o r the measurements of the p r e s s u r e i n the chamber, was chosen f o r i t s r e s p o n s e which showed a compromise between r i s e t i m e , o v e r - s h o o t , s e n s i t i v i t y and w r i t i n g t i m e . A t y p i c a l o s c i l l o g r a m r e c o r d of the probe's r e s p o n s e t o a d e t o n a t i o n wave i s shown i n f i g u r e E-4. - 169 -APPENDIX F The Chapman-Jouguet S t a t e . A l t h o u g h a d i s c u s s i o n of the Chapman-Jouguet s t a t e (C.J.) i s not e s s e n t i a l i n t h i s t h e s i s , t h i s a ppendix i s i n c l u d e d f o r the sake of c o m p l e t e n e s s . In o r d e r t o keep the arguments as s i m p l e as p o s s i b l e , we s h a l l be concerned w i t h a o n e - d i m e n t i o n a l q u a l i -t a t i v e a n a l y s i s of a s t e a d y , s e l f - s u s t a i n e d d e t o n a t i o n i n an i d e a l r e a c t i n g gas. F i r s t we w r i t e down the i n t e g r a l c o n s e r v a t i o n e q u a t i o n s f o r a gas i n i t i a l l y a t r e s t and a comb u s t i o n zone moving w i t h a v e l o c i t y D ( F i g u r e F - l ) : P,U,v,I > U Q , V 0 , 1 0 F i g u r e F - l : A d e t o n a t i o n p r o p a g a t i n g i n a i n i t i a l l y a t r e s t , U G=0. gas Mass: (D-U)/v = D/v Q ( F - l ) Momentum: P + (D-U) 2/v P G + D 2/v o (F-2) Energy: I + (D-U) 2/2 I 0 + D 2/2 (F-3) - 170 -where D, U, v, P, and I a r e the d i s t u r b a n c e v e l o c i t y , the mass v e l o c i t y , the s p e c i f i c volume, the p r e s s u r e , and the e n t h a l p y per u n i t volume i n c l u d i n g c h e m i c a l energy. The z e r o s u b s c r i p t i n d i c a t e s the i n i t i a l c o n d i t i o n s . C ombining e q u a t i o n s ( F - l ) and ( F - 2 ) , we o b t a i n : D 2 = v 2 ( P - P 0 ) / ( v 0 - v ) (F-4) ( D - U ) 2 = v 2 ( P - P 0 ) / ( v 0 - v ) (F-4') From e q u a t i o n s (F-4) and (F-3) we can g e t : 1 ~ X o 8 8 ( v 0 + v ) ( P - P 0 ) / 2 (F-5) or E - E Q = ( v Q - v ) ( P + P Q ) / 2 (F-5') where I=E+Pv, E= i n t e r n a l energy per u n i t mass i n c l u d i n g c h e m i c a l energy. In p r i n c i p l e , the i n t e r n a l energy i s known as a f u n c t i o n of t h r e e parameters f o r a r e a c t i n g gas, i e : E=E(P,v,q), where q i s the degree of c o m p l e t i o n of the c h e m i c a l r e a c t i o n ( 0 =" q =" 1 ). Thus i t i s p o s s i b l e ( a t l e a s t t h e o r e t i c a l l y ) t o p l o t e q u a t i o n (F-5) on a P-v p l a n e . The r e s u l t i n g c u r v e s ( c o r r e s p o n d i n g t o the v a r i o u s v a l u e s of q) a r e c a l l e d the Hugoniot a d i a b a t i c s . E q u a t i o n (F-4) r e p r e s e n t s c h o r d s ( c a l l e d Tode l i n e ) drawn from the i n i t i a l - 171 -s t a t e ( P = P 0 and v=v Q) w i t h a f i x e d s l o p e g i v e n by: -m = - ( P - P 0 ) / ( v - v Q ) = D 2 / v 2 = ( D - U ) 2 / v 2 (F-6) A g r a p h i c a l r e p r e s e n t a t i o n of e q u a t i o n s (F-4) and (F-5) i s g i v e n i n F i g u r e F-2. S i n c e b o t h e q u a t i o n s must be s a t i s f i e d , the p o s s i b l e s t a t e s o f the gas a r e g i v e n by the i n t e r s e c t i o n s of the H u g i n i o t s and the Tode l i n e s . We can t h e r e f o r e d i s t i n g u i s h t h r e e main r e g i o n s a l o n g the a d i a b a t i c s : From A t o B: P < P q and v > v Q , The s l o p e m i s s m a l l and n e g a t i v e y i e l d i n g s m a l l r e a l v a l u e s f o r the p r o p a g a t i o n v e l o c i t y D. T h i s r e g i o n r e p r e s e n t s p r o c e s s e s c o n t r o l l e d by t h e r m a l c o n d u c t i o n and d i f f u s i o n and c o r r e s p o n d s to d e f l a g r a t i o n s . We s h a l l not be c o n c e r n e d w i t h t h i s r e g i o n h e r e . From B t o C: P ^ P Q and v > v Q , m i s p o s i t i v e and D i s i m a g i n a r y . T h i s r e g i o n does not r e p r e s e n t the f i n a l s t a t e s of any r e a l p h y s i c a l p r o c e s s . From C t o G: P ^ P q and v<^v 0, m i s n e g a t i v e and l a r g e i n magnitude, hence D has l a r g e r e a l v a l u e s . T h i s s e c t i o n of the a d i a b a t i c c o r r e s p o n d s t o the p o s s i b l e f i n a l s t a t e s a c h e i v e d i n a d e t o n a t i o n , the f i n a l s t a t e of the r e a c t i o n p r o d u c t s b e h i n d the d e t o n a t i o n f r o n t i s g i v e n by the i n t e r s e c t i o n of the Tode l i n e w i t h the q=l H u g o n i o t . We s h a l l show t h a t t h i s s t a t e can o n l y be the tangency p o i n t between - 172 -F i g u r e F-2: G r a p h i c a l r e p r e s e n t a t i o n of the Tode l i n e s and H u g o n i o t a d i a b a t i c s i n a P-v p l a n e - 173 -t h e s e two c u r v e s . T h i s s t a t e i s c a l l e d the Chapman-Jo'uguet s t a t e ( C . J . ) . E x a m i n i n g the C-G s e c t i o n more c l o s e l y , we see t h a t i n o r d e r f o r the Tode l i n e t o i n t e r s e c t the H u g o n i o t , the s l o p e of the Tode l i n e has t o be s m a l l e r t h a n a c e r t a i n maximum a t t a i n e d v/hen the Tode l i n e i s t a n g e n t t o the a d i a b a t i c . A l s o f o r a l l Tode l i n e s i n t e r s e c t i n g the H u g o n i o t , t h e r e a r e two p o s s i b l e d i f f e r e n t s o l u t i o n s e x c e p t f o r the t a n g e n t c a s e when the two s o l u t i o n s a r e i d e n t i c a l . The lower i n t e r s e c t i o n ( P > P Q ) c o r r e s p o n d s t o weak or under-compressed d e t o n a t i o n s w h i l e the upper i n t e r s e c t i o n (P>]>P0) c o r r e s p o n d s t o o v e r d r i v e n or over-compressed d e t o n a t i o n s . From thermodynamic c o n s i d e r a t i o n s /15/, we know t h a t a t any p o i n t a l o n g the a d i a b a t i c the s l o p e i s g i v e n by: dP/dv = - v 2 C 2 where C i s the speed of sound of the gas i n a s t a t e g i v e n by the p o i n t a t which the d e r i v a t i v e i s e v a l u a t e d . Hence, i n the c a s e of o v e r d r i v e n d e t o n a t i o n s , (D-U), w h i c h i s the speed of the d e t o n a t i o n w i t h r e s p e c t of the r e a c t i o n p r o d u c t s , i s s m a l l e r t h a n the speed of sound i n t h a t gas. I t i s w e l l known t h a t s e l f -s u s t a i n e d d e t o n a t i o n s have t o be f o l l o w e d by a r a r e -- 174 -f a c t i o n wave /14/. T h i s wave wh i c h t r a v e l s a t the speed of sound can c a t c h up w i t h the d e t o n a t i o n f r o n t and weaken i t . T h i s p r o c e s s w i l l c o n t i n u e u n t i l b o t h waves, the r a r e f a c t i o n and d e t o n a t i o n waves, have the same speed. T h i s f i r s t o c c u r s a t the C.J. p o i n t a l o n g the a d i a b a t i c . Thus a s e l f - s u s t a i n e d d e t o n a t i o n s t a r t i n g i n an over-compressed mode w i l l decay and become a s t e a d y d e t o n a t i o n when the C . J . s t a t e i s r e a c h e d . The p o s s i b i l i t y of weak d e t o n a t i o n s can be r u l e d out by c o n s i d e r i n g the mechanism of i g n i t i o n of the c h e m i c a l r e a c t i o n i n a detonat-ion. The s t a t e of the r e a c t i n g gases can f o l l o w two p a t h s a l o n g the Tode l i n e : 1) The s t a t e f o l l o w s the Tode l i n e from the i n i t i a l c o n d i t i o n s up to,.the f i n a l s t a t e as q i n c r e a s e s from 0 t o 1. T h i s mechanism i s un-r e a l i s t i c s i n c e t h e r m a l c o n d u c t i o n i s n e g l i g e a b l e i n a d e t o n a t i o n . In t h i s p i c t u r e , the gases e n t e r i n g the r e a c t i o n zone are s t i l l i n the i n i t i a l s t a t e and under th e s e c o n d i t i o n s the c h e m i c a l r e a c t i o n r a t e i s too s m a l l t o a c c o u n t f o r the h i g h speed of p r o p a g a t i o n of the d e t o n a t i o n . The gas ahead of the r e a c t i o n zone has t o be h e a t e d t o the i g n i t i o n t e m p e r a t u r e b e f o r e the r e a c t i o n r a t e becomes l a r g e - 175 -enough t o y i e l d the l a r g e v e l o c i t i e s o b s e r v e d . 2 ) T h i s l e a d s to the i d e a t h a t the r e a c t i o n zone i s preceeded by a shock wave which h e a t s and compress the m i x t u r e a d i a b a t i c a l l y t o a s t a t e a t w hich spontaneous c o m b u s t i o n can t a k e p l a c e . The shock wave can be c o n s i d e r e d t o o c c u r e x c l u s i v e l y i n the u n r e a c t e d gas s i n c e l i t t l e or no c h e m i c a l r e a c t i o n can t a k e p l a c e o v e r the shock wave t h i c k n e s s . In t h i s p i c t u r e , the s t a t e o f the i n i t i a l gas jumps from P 0 , v 0 t o the i n t e r s e c t i o n of the Tode l i n e w i t h the q=0 a d i a b a t i c . The c h e m i c a l r e a c t i o n t h e n t a k e s p l a c e i n the s h o c k - h e a t e d gas r e l e a s i n g energy and e x p a n d i n g the gas as the t e m p e r a t u r e i n c r e a s e s s t i l l f u r t h e r . I t i s t h i s e x p a n s i o n of the r e a c t i o n p r o d u c t s w h i c h keeps the shock wave i n m o t i o n . T h i s mechanism of i g n i t i o n does not a l l o w f o r the p o s s i b i l i t y of weak d e t o n a t i o n s s i n c e o n l y o v e r d r i v e n d e t o n a t i o n s a r e p o s s i b l e f i n a l s t a t e s o f such a wave s t r u c t u r e . The shock t r a n s i t i o n from o v e r d r i v e n t o undercompressed d e t o n a t i o n i s f o r b i d d e n by shock wave t h e o r y . We have t h e r e f o r e shown t h a t a s t e a d y s e l f -s u s t a i n e d d e t o n a t i o n can o n l y e x i s t i n the C . J . s t a t e . The arguments put f o r w a r d were p u r e l y p h y s i c a l i n n a t u r e . We can a l s o j u s t i f y the above c o n c l u s i o n t h e r m o d y n a m i c a l l y i n the f o l l o w i n g way. - 176 -The e n t r o p y change a l o n g the Hug o n i o t a d i a b a t i c , i s g i v e n by: TdS = dE + Pdv = -i ( (P-P Idv - (v-v )dP ) Hence dS=0 when (P~P 0)dv=(v-v 0)dP„ T h i s c o n d i t i o n c o r r e s p o n d s t o the C . J . p o i n t on the a d i a b a t i c . The e n t r o p y change has t h e r e f o r e a s t a t i o n a r y v a l u e a t the p o i n t of tangency and t h i s v a l u e has been shown t o be a maximum t h e r e f o r e a t h e r m o d y n a m i c a l l y most p r o b a b l e s t a t e . The a n a l y s i s p r e s e n t e d does not r e p r e s e n t the l a t e s t s t a g e of u n d e r s t a n d i n g of the d e t o n a t i o n f r o n t s t r u c t u r e , however, t h i s model s t i l l h o l d s v e r y w e l l i n most c a s e s when o n l y m a c r o s c o p i c s t u d i e s a r e done. A r e c e n t s u r v e y a r t i c l e by D. H. Edwards /74/ g i v e s more r e c e n t v i e w s on the s t r u c t u r e o f the d e t o n a t i o n wave. 

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