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A high performance diaphragm shock tube with an imploding detonation driver. Redfern, Paul Joseph 1971

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A HIGH PERFORMANCE DIAPHRAGM SHOCK.TUBE w i t h an IMPLODING DETONATION DRIVER b y P a u l J . R e d f e r n . Sc. ( E . E . ) , U n i v e r s i t y o f A l b e r t a , 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT 0 THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the department of 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 t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA Au g u s t , 1971 In present ing th i s thes i s in p a r t i a l f u l f i lmen t of the requirements fo r an advanced degree at the Un iver s i t y of B r i t i s h Columbia, I agree that the L ib ra ry sha l l make i t f r e e l y ava i l ab le for reference and study. I fu r ther agree that permission for extens ive copying of th i s thes i s fo r s cho la r l y purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or pub l i ca t i on of th i s thes i s f o r f i nanc i a l gain sha l l not be allowed without my wr i t ten permiss ion. Department of / AyG/C S> The Un ivers i ty o f B r i t i s h Columbia Vancouver 8, Canada i i ABSTRACT The p e r f o r m a n c e o f a d i aphragm shock t u b e w i t h 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 i s t h e o r e t i c a l l y and e x p e r i m e n t a l l y i n v e s t i g a t e d . S t r o n g shock waves a r e p r o d u c e d by a d r i v e r i n w h i c h a d e t o n a t i o n i s f o r c e d to i m p l o d e to t h e apex o f a c o n i c a l c h a n n e l . In t h i s geomet ry , t h e a r e a c o n v e r g e n c e e x p e r i e n c e d by the i m p l o d i n g f r o n t e l e v a t e s the d r i v e r gas t e m p e r a t u r e and p r e s s u r e above t h e u s u a l Chapman-Jouguet v a l u e s , t h e r e b y i n c r e a s i n g the s t r e n g t h o f t h e t e s t s h o c k . T h e o r e t i c a l l y , t h e r e l a t i o n s h i p between t e s t shock s t r e n g t h , f i l l i n g p r e s s u r e , and a r e a r e d u c t i o n i n a c o n i c a l c h a n n e l i s s t u d i e d . E x p e r i m e n -t a l l y , t h e i m p o r t a n c e o f t h e g e o m e t r i c p a r a m e t e r s - s l a n t a n g l e , c h a n n e l w i d t h and c h a n n e l c o n v e r g e n c e - i s i n v e s t i g a t e d . The p e r f o r m a n c e o f t h e c o n i c a l i m p l o s i o n d r i v e r compares w e l l w i t h t h a t o f o t h e r membrane shock t u b e s . F o r i n s t a n c e , f o r o x y - a c e t y l e n e d e t o n a t i o n s , d r i v i n g i n t o a r g o n o f 5 T o r r , a Mach number g r e a t e r t han 13 may be r e a c h e d f o r a d r i v e r to t e s t gas p r e s s u r e r a t i o o f 100. The same Mach number a v a i l a b l e f rom a Chapman-Jouguet d e t o n a t i o n d r i v e r o c c u r s o n l y above a p r e s s u r e r a t i o o f 200. F o r c o l d h y d r o g e n and c o n s t a n t vo lume o x y - h y d r o g e n c o m b u s t i o n , p r e s -6 4-s u r e r a t i o s o f 10 and 2 X 10 r e s p e c t i v e l y a r e r e q u i r e d to p r o d u c e Mach 1 3 . D e s i g n c r i t e r i a f o r a l a r g e a r e a r e d u c t i o n d r i v i n g f a c i l i t y a r e a l s o g i v e n . i i i TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i i i L I ST OF FIGURES v ACKNOWLEDGEMENTS v i i CHAPTER 1 I n t r o d u c t i o n _ • 1 1-1 O p e r a t i o n o f a membrane shock tube 1- 2 Summary o f the t h e s i s ' ^ CHAPTER 2 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 t h r o u g h an a r e a c o n v e r g e n c e * * 8 8 2- 1 P l a n e d e t o n a t i o n s 2-2 The C.C.W. mode l o f an i m p l o d i n g d e t o n a t i o n ^ o r . 2-3 C h a n n e l a'£ f i n i t e , w i d t h " CHAPTER 3 T h e o r e t i c a l d e s c r i p t i o n o f i m p l o s i o n d r i v e n shock waves • . . , . . , . . . . . . . . » . . . . . . • • • • • • » 27 3-1 R e f l e c t e d shock d e t o n a t i o n d r i v e r 29 CHAPTER 4 P l a n e d e t o n a t i o n d r i v e r - an e x p e r i m e n t a l s t u d y o f p e r f o r m a n c e and d i aphragm o p e n i n g 35 4-1 E x p e r i m e n t a l s e t - u p 35 4 -2 R e f l e c t e d shock 3 8 4 - 3 T e s t shock 3 8 CHAPTER 5 Imp lod ing d e t o n a t i o n d r i v e r • • * ^ 5 - 1 E x p e r i m e n t a l s e t - u p 45 5-2 R e l a t i v e p e r f o r m a n c e o f cones o f d i f f e r e n t s l a n t ^ 8 5-3 Wid th o f t he c h a n n e l ^ 9 CO 5-4 C o n v e r g i n g w i d t h d r i v e r CO 5-5 S t r u c t u r e o f t he i m p l o d i n g f r o n t n e a r t h e apex i v CHAPTER 6 Su rvey o f some d e t o n a t i o n d r i v i n g t e c h n i q u e s 56 6-1 P o t e n t i a l Mach numbers o f 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 s 58 CHAPTER 7 C o n c l u s i o n s and s u g g e s t i o n s f o r f u t u r e work 62 BIBLIOGRAPHY ,. 64 APPENDIX A Wave i n t e r a c t i o n d e s c r i p t i o n o f weak d i aphragm 66 d r i v e r APPENDIX B D e t a i l e d d e s c r i p t i o n o f t h e e x p e r i m e n t a l a p p a r a t u s 70 L I ST OF 'F IGURES Page 1-1 S i m p l e p r e s s u r e d r i v e n shock t u b e 2 1-2 C y l i n d r i c a l d e t o n a t i o n d r i v e r 4 1- 3 C o n i c a l c h a n n e l i m p l o s i o n d r i v e r 5 2- 1 P l a n e d i s c o n t i n u i t y v i e w e d f rom l a b . f r a s " i o 2-2 C o - o r d i n a t e sy s tem 14 2-3 F r o n t v i ew o f c o n i c a l c o l l a p s e - showing f l o w d e s c r i b e d by c h a r a c t e r i s t i c e q u a t i o n 17 2-4 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 21 2-5 P r e s s 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 22 2-6 F r o n t 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 23 2 -7 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 24 2- 8 I m p l o s i o n n e a r apex ' 25 3 - 1A x - t d i a g r a m o f z e r o d e l a y d i aphragm o p e n i n g 28 3- 1B x - t d i a g r am o f d e l a y e d o p e n i n g o f d i aphragm 28 4 - 1 F u l l s c a l e s e c t i o n o f d i aphragm c lamp and shock tube 36 4 - 2 Smear camera and d e l a y s e t - u p 37 4-3 Smear pho tog raphs o f t h e d e t o n a t i o n , t e s t , and r e f l e c t e d shock waves 39 4 - 4 Smear p h o t o g r a p h o f the two luminous r e g i o n s i n t h e t e s t s e c t i o n 40 4 -5 Smear pho tog raph o f the t e s t shock w i t h a r e f l e c t o r 12 cm. f rom the d i aphragm , 40 4 - 6 Mach number v e r s u s p r e s s u r e r a t i o ( p l a n e d r i v e r ) 42 5- 1 S c h e m a t i c o f t he c o n i c a l d r i v i n g chamber 46 5-2 P h o t o g r a p h o f the 0 = 1 5 ° d r i v e r 47 5-3 Smear pho tog raph o f t he t e s t shock f o r t he 0 = 40 47 cone v i Page 5-4 Mach number v e r s u s s l a n t a n g l e 50 5-5 Mach number v e r s u s p r e s s u r e r a t i o ( <f) - 15 d r i v e r ) 51 5-6 S c h e m a t i c o f t he c o n i c a l d r i v e r r e p l i c a and image c o n v e r t e r p h o t o g r a p h s n e a r t h e apex 53 5- 7 Image c o n v e r t e r s e t - u p 54 6- 1 The d r i v e r used by C o a t e s and Gaydon 56 6-2 Compar i s on o f some d e t o n a t i o n d r i v e r s 57 6-3 Mach number v e r s u s p r e s s u r e r a t i o and d i a m e t e r r a t i o ( c o n i c a l d r i v e r ) 60 6-4 Mach number v e r s u s p r e s s u r e r a t i o and d i a m e t e r r a t i o ( s p h e r i c a l d r i v e r ) 61 A - l C o m p a r i s o n o f t h e two d i aphragm o p e n i n g d e l a y s f o r a C . J . and o v e r d r i v e n d e t o n a t i o n d r i v e r 67 A - 2 C o m p a r i s o n o f t h e two d i aphragm o p e n i n g d e l a y s f o r a shock wave i n t h e d r i v e r . 68 B - l F u l l s c a l e s e c t i o n o f t h e c o n i c a l d r i v e r 72 B-2 G e n e r a l l a y - o u t 75 B-3 H i gh v o l t a g e c i r c u i t f o r i g n i t i n g t h e d e t o n a t i o n 76 v i i ACKNOWLEDGEMENTS I w o u l d l i k e t o take t h i s o p p o r t u n i t y to s i n c e r e l y thank -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 , f o r h i s i n v a l u a b l e and e n t h u s i a s t i c g u i d a n c e . t h rough the c o u r s e o f t h i s work . A l s o , I am d e e p l y i n d e p t e d to Dr , J , - ? , H u n i , whose p r e v i o u s e x p e r i e n c e i n t h i s f i e l d s i m p l i f i e d the e x p e r i m e n t a l a s p e c t s o f t h i s work c o n s i d e r a b l y , I wou ld a l s o l i k e to than!; the members o f the P l a s m a P h y s i c s group f o r t h e i r e x p r e s s e d i n t e r e s t i n t h i s - p r o j e c t . In p a r t i c u l a r , I wou ld l i k e to thank Mr, J , S t r a c h a n f o r h i s c o n t r i b u t i o n s to C h a p t e r T h r e e . The c o o p e r a t i v e a s s i s t a n c e o f 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 acknow-l e d g e d . I w o u l d e s p e c i a l l y l i k e 'to thank Mr, D. H a i n e s f o r h i s a s s i s t a n c e i n the machine shop . My thanks a l s o t o Mr, T), S i e b e r g f o r m a i n t a i n i n g the e l e c t r o n i c s c f the e x p e r i m e n t . INTRODUCTION D u r i n g the p a s t s e v e r a l d e c a d e s , the shock tube has become an Impor -t a n t r e s e a r c h t o o l i n t he s t u d y o f h i g h t e m p e r a t u r e gases and h i g h v e l o -c i t y gas f l o w s . T h i s i s p a r t l y due to the f a c t t h a t shock waves can be e a s i l y and i n e x p e n s i v e l y p r o d u c e d f rom a v a r i e t y o f d e v i c e s . F u r t h e r m o r e , the p l a s m a p r o d u c e d by shock waves can be d e s c r i b e d w i t h r a t h e r l i t t l e m a t h e m a t i c a l e f f o r t . In p l a sma p h y s i c s , t h e o r i e s d e s c r i b i n g c o l . l . i s i o n a l and c o l l i s i o n l e s s h e a t i n g , r e l a x a t i o n , and a t t a i n m e n t o f l o c a l t h e r m a l e q u a l i b r i u m , have been t e s t e d and d e v e l o p e d i n c o n n e c t i o n w i t h shock wave r e s e a r c h . The shock tube a l s o has a p p l i c a t i o n s r a n g i n g f rom h i g h v e l o c i t y gas dynamic s i m u l a t i o n - o f i n t e r e s t i n ae rodynamic s and the space p rog ram - t o l a s e r t o p i c s . 2nd resesr .cn i n T)v power g e n e r a t i o n . Even r e s e a r c h i n s u c h s e e m i n g l y u n r e l a t e d f i e l d s as p h y s i c a l c h e m i s t r y ( h i g h t e m p e r a t u r e r e a c -t i o n k i n e t i c s ) has b e n e f i t t e d f rom work w i t h shock waves . In t h i s t h e s i s we e x p e r i m e n t a l l y and t h e o r e t i c a l l y i n v e s t i g a t e the o p e r a t i o n o f / a s i m p l e , b u t u n i q u e d e v i c e c a p a b l e o f p r o d u c i n g s t r o n g shock waves . To f u l l y e x p l a i n t h i s d r i v e r s y s t e m , t h e o p e r a t i o n o f a s i m p l e p r e s s u r e d r i v e a shock tube must be o u t l i n e d . 1-1 OPERATION OF A PRESSURE DRIVE'-? MEMIRANE SHOCK TUBE B a s i c a l l y , a p r e s s u r e d r i v e n shock tube i s a l o n g tube s e p a r a t e d by a d iaphragm i n t o 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 , ( f i g , 1 - 1 ) . - 2 -D r i v e r s i d e T e s t sect.'ton h i g h p r e s s u r e Di r i p h rj.^H low piresstire • S h o c k ' F r o n t Figur -3 1-1 Simple pressure driven shock tube. The d iaphragm i s b r o k e n by an o v e r p r e s s u r e i n the d r i v e r g a s , o r by some s u i t a b l e m e c h a n i c a l o r e l e c t r i c a l means. T h i s sudden o p e n i n g o f the d i sphragm causes the d r i v e r gas t o expand w i t h h i g h v e l o c i t y i n t o the low p r e s s u r e t e s t gas . The l e a d i n g edge o f the a c c e l e r a t e d d r i v e r g a s , r e f e r -r e d t o as the c o n t a c t s u r f a c e , a c t s as a p i s t o n w h i c h pushes an e v e r i n -c r e a s i n g t h i c k n e s s o f t e s t gas ahead o f i t . T h i s a c c u m u l a t e d t e s t gas i s a c c e l e r a t e d and a d i a b a t i c a l l y c o m p r e s s e d , t h e r e b y b e i n g h e a t e d to a h i g h t e m p e r a t u r e . The l e a d i n g edge o f t h i s s l u g o f heated, t e s t g a s , c a l l e d the shock f r o n t , moves t h r o u g h the u n d i s t u r b e d gas a t s u p e r s o n i c v e l o c i t y . Much a t t e n t i o n i n shock tube p h y s i c s has been d e v o t e d t o o b t a i n i n g the s t r o n g e s t p o s s i b l e shock waves i n the t e s t ga s . To a c h i e v e t h i s , i t i s n e c e s s a r y t h a t the p r e s s u r e and t e m p e r a t u r e ( s p e e d o f sound) o f the d r i v e r gas be r a i s e d t o a maximum, F o r t h i s r e a s o n v a r i o u s methods have been u s e d t o h e a t the d r i v e r gas . These methods range f rom s l ow e x t e r n a l h e a t i n g to use o f e x p l o s i v e 9 charges /•!?/, Of the p o s s i b l e h e a t i n g methods , the two most commonly used a re e l e c t r i c a l d i s c h a r g e , /18/,/35/, and i n t e r n a l c o m b u s t i o n . T h e r e a re two main types o f combus t i on d r i v e n t u b e s . One t ype h e a t s the d r i v e r gas by means o f a f l a m e , /]6/,/30/, The o t h e r t ype makes use o f a d e t o n a t i o n p r o c e s s , /20/,/24/j/29/,/25/, D e t o n a t i o n d r i v e r s have r e c e i v e d c o n s i d e r a b l e a t t e n a t i o n s i n c e t h e y - 3 -p r o v i d e a f a i r l y i n e x p e n s i v e method o f g e n e r a t i n g shock waves o f moderate t o h i g h Mach numbers . W h i l e t h e y do n o t i n genera l , p r o d u c e the e x t r e m e l y h i g h Mach numbers o f some d e v i c e s wh i ch employ s o l i d e x p l o s i v e s / 1 6 / , and e l e c t r o m a g n e t i c a c c e l e r a t i o n /32/, they do have c e r t a i n c h a r a c t e r i s t i c s a s s o c i a t e d w i t h a " h i g h p e r f o r m a n c e " f a c i l i t y . * D e t o n a t i o n d r i v e n shock tubes can meet the f o l l o w i n g s p e c i f i c a t i o n s : 1. Low c o s t i n c o n s t r u c t i o n and o p e r a t i o n . 2. Moderate t o h i g h Mach numbers o f good r e p r o d u c e a b i l i t y . 3. Gas f l o w w h i c h i s f r e e c f m a g n e t i c f i e l d s . 4. Low j i t t e r i n t r i g g e r t o o b s e r v a t i o n t i m e . 5. S m a l l d i f f e r e n c e i n f i l l i n g p r e s s u r e between d r i v e r and t e s t s e c t i o n s , -6. H i g h s h o t t o s h o t r e p e t i t i o n f r e q u e n c y , 7. In l a r g e d e v i c e s the p r e s e n c e o f a r a r e f a c t i o n wave b e h i n d One o f the most s e v e r e drawbacks o f d e t o n a t i o n d r i v e r s i s c l e a n l i n e s s . In c e r t a i n a p p l i c a t i o n s , p a r t i c u l a r l y s p e c t r o s c o p i c , the n a t u r e o f the r e a c -t i o n p r o d u c t s w o u l d r e q u i r e t h a t the a p p a r a t u s be c l e a n e d b e f o r e each s h o t , The s t a n d a r d d e t o n a t i o n d r i v i n g f a c i l i t y i s s i m i l a r t o o u r s c h e m a t i c i l l u s t r a t i o n o f a s i m p l e shock t u b e , ( f i g , 1 -1 ) , In the d r i v e r s e c t i o n , the d e t o n a t i o n i s i g n i t e d a t the c l o s e d e n d . A p l a n e Chapman-Jouguet d e -t o n a t i o n wave t h e n p r o p a g a t e s t h r o u g h the unburn t gas and s t r i k e s the d i a -phragm, w h i c h i s t hen r u p t u r e d by the sudden i n c r e a s e i n p r e s s u r e o r m e l t e d by the i n c r e a s e i n t e m p e r a t u r e . Some i m p o r t a n t f e a t u r e s o f t h i s t y p e o f d r i v e r a r e : 1, B e h i n d the d e t o n a t i o n f ront , t h e r e i s a f l o w o f gas o r dynamic An e x c e l l e n t c r i t i q u e o f the v a r i o u s d r i v i n g methods i s g i v e n by War ren and H a r r i s , / 2 8 / . -4-p r e s s u r e w h i c h w i l l , a s s i s t i n the d i aphragm r u p t u r e and. sub sequen t a c c e l e r a t i o n o f d r i v e r gas i n t o the t e s t s e c t i o n , 2, The d e t o n a t i o n f r o n t i s p l a n e ; t h e r e f o r e , i m p l y i n g u n i f o r m o p e n i n g o f the d i a p h r a g m , thus m i n i m i z i n g t u r b u l e n t f l o w i n the shock t u b e , R e c e n t l y , i n t h i s l a b o r a t o r y ' , U u n i /lA/} has d e v e l o p e d a t e c h n i q u e wh i ch shows c o n s i d e r a b l e promise, i n i n c r e a s i n g the shock s t r e n g t h o f d e t o -n a t i o n d r i v e r s . In t h i s d r i v e r , a d e t o n a t i o n was made t o i m p l o d e s y m m e t r i -c a l l y t o the. a x i 3 o f a c y l i n d e r , where the d i aphragm and shock tube were l o c a t e d , ( f i g , 1-2). , F i g u r e 1-2 C y l i n d r i c a l d e t o n a t i o n d r i v e r , I m p l o d i n g f r o n t In t h i s geomet ry , the a rea r e d u c t i o n e x p e r i e n c e d by the c o l l a p s i n g f r o n t causes the d e t o n a t i o n to become o v e r d r i v e n . " S i n c e the p res sure , and t e m p e r a t u r e b e h i n d an o v e r d r i v e n d e t o n a t i o n are l a r g e r than b e h i n d a C . J , d e t o n a t i o n , • t h i s d r i v e r i s e x p e c t e d to p r o d u c e s t r o n g e r s h o c k s . T h i s d r i -v e r has the un ique f e a t u r e t h a t the p i - e d i c t e d shock s t r e n g t h i n c r e a s e s mono t o n i c a l l y w i t h the r a t i o o f d r i v e r t o shock tube d i a m e t e r (/?/»')•> The c y -l i n d r i c a l d r i v e r , however , does n o t have the m e n t i o n e d d e s i r a b l e f e a t u r e s o f a p l a n e C . J , d r i v e r . The o b j e c t o f t h i s t h e s i s i s to i n v e s t i g a t e the p e r f o r m a n c e of. a d r i -v e r wh i ch combines the advan tages o f b o t h n l a n e and c y l i n d r i c a l g e o m e t r i e s . The term " o v e r d r i v e n " w i l l be e x p l a i n e d i n some d e t a i l i n C h a p t e r Two. H e r e , o v e r d r i v e n can be assumed to mean o f g r e a t e r Mach. number than o r -d i n a r y d e t o n a t i o n s . Da/e C SttMteon F i g u r e 1-3 C o n i c a l d e t o n a t i o n snock wave d r i v e r . Imploding d e t o n a t i o n f r o n t i n d i c a t e d by arrows. I.n the p r o p o s e d d e s i g n , the d e t o n a t i o n i m p l o d e s to the apex o f a c o n i c a l -c h a n n e l , ( f i g , 1 - 3 ) , where the membrane and shock tube a rc l o c a t e d , In t h i s d r i v e r , as i n the." c y l i n d r i c a l , the d e t o n a t i o n f r o n t e x p e r i e n c e s an a r e a r e d u c t i o n , and t h e r e f o r e becomes o v e r d r i v e n . M o r e o v e r , a component o f dynamic p r e s s u r e a l o n g the shock tube' a x i s i n p r o v i d e d . The aim o f t h i s t h e s i s i s f i r s t l y t o e s t a b l i s h i f such a c o n i c a l d r i v e r -can i n f a c t p r o d u c e s t r o n g e r shocks than any known d e t o n a t i o n d r i v e r , - wh i ch was found t o be the c a s e , - a n d s e c o n d l y t o o p t i m i s e the d e s i g n so t h a t a l a r g e h i g h p e r f o r m a n c e d r i v e r can be b u i l t . To o p t i m i z e t h i s d r i v i n g t e c h -n i q u e , a number a p a r a m e t e r s must be c o n s i d e r e d . These w i l l be o u t l i n e d b e l o w . Two i m p o r t a n t p a r a m e t e r s common t o a l l d e t o n a t i o n d r i v e r s a r e the c h o i c e o f d e t o n a t i o n m i x t u r e (C + 0 , 2H^ 4- 0^ , 4 H 2 + 0^ , e t c ) , and the c h o i c e o f d e t o n a t i o n and t e s t gas f i l l i n g p r e s s u r e s . The use o f an i m p l o s i o n d r i v e r , however.. i " t ~ o r h : c " 3 " r ~ t h e ~ w a y * a b l e nsrr.r'1"* t - ~ r a t i o o f d r i v e r t o shock tube d i a m e t e r , s i n c e t h i s r a t i o d e t e r m i n e s the e x t e n t t o w h i c h the d e t o n a t i o n •is o v e r d r i v e n . To e n a b l e one to make s u i t a b l e c h o i c e s o f the above t h r e e p a r a m e t e r s ( d e t o n a t i o n m i x t u r e , f i l l i n g p r e s s u r e s , and d i a m e t e r r a t i o ) , a n u -a n t i t a t i v e mode l o f the i m p l o s i o n d r i v i n g t e c h n i q u e i s d e r i v e d and p a r t i a l l y t e s t e d , However, the use o f a c o n i c a l d r i v e r i n t r o d u c e s two a d d i t i o n a l v a r i -a b l e s n o t a c c o u n t e d f o r i n the m o d e l . These a re the s l a n t a n g l e 0 and the w i d t h o f the c h a n n e l W, ( f i g . 1 -3 ) , The i n f l u e n c e o f t h e s e v a r i a b l e s i s s t u -d i e d e x p e r i m e n t a l l y . 1-2 SUMMARY OF THE THESIS ' As seen a b o v e , a d iaphragm shod ' , tube has e s s e n t i a l l y t h r e e p a r t s : the d r i v e r s i d e , the membrane, and the t e s t s e c t i o n , The. f u n c t i o n o f each o f t he se must be u n d e r s t o o d i n d e t a i l i f the h i g h e s t p e r f o r m a n c e i s t o be o b -t a i n e d , In C h a p t e r Two, a b r i e f summary o f s t a n d a r d d e t o n a t i o n t h e o r y i s f i r s t -g i v e n , ( S e c t i o n 2 - 1 ) , p r o v i d i n g the b a s i s f o r a t h e o r e t i c a l mode l o f the c o n i c a l i m p l o s i o n . T h i s mode l i s d e r i v e d i n a g e n e r a l fo rm and i n c l u d e s L e e ' s / 6 / mode l f o r 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 as a s p e c i a l c a s e . The r e s u l t s o f t h i s c h a p t e r e n a b l e us t o p r e d i c t the thermodynamic s t a t e o f the d r i v e r gas n e a r the d i aphragm. In C h a p t e r T h r e e we d e r i v e the t h e o r y w h i c h r e l a t e s the s t r e n g t h o f the t e s t whock t o the s t a t e o f the d r i v e r gas . The r e s u l t s o f C h a p t e r s Two and T h r e e p r o v i d e a q uan t i t a t i ve s un de r s t an d i n g o f the o p e r a t i o n o f an I m p l o s i o n d r i v e r . I t t u r n s out t h a t the p r e d i c t e d s t r e n g t h o f the t e s t shock i s s e n -s i t i v e t o the membrane o p e n i n g d e l a y . Two ext reme ca se s a re e n v i s a g e d ; d e -l a y e d o p e n i n g and i n s t a n t a n e o u s o p e n i n g , and models a re d e r i v e d f o r e a c h , ( S e c t i o n 3 - 1 , and Append i x A ) , To. c l a r i f y w h i c h o f the two models a p p l i e s , an a u x i l i a r y shock wave e x p e r i m e n t i s p e r f o r m e d , ( C h a p t e r F o u r ) , showing t h a t the d i aphragm opens w i t h d e l a y , . C h a p t e r s Two, T h r e e , and Four l a y the ground work f o r u n d e r s t a n d i n g the o p e r a t i o n o f a c o n i c a l d r i v e r , w h i c h i s i n v e s t i g a t e d i n C h a p t e r F i v e . Here we e x p e r i m e n t a l l y d e t e r m i n e the i m p o r t a n c e o f < s l a n t a n g l e , c h a n n e l w i d t h , and c h a n n e l c o n v e r g e n c e , A compar i s on w i t h the p e r f o r m a n c e o f o t h e r shock tubes i s g i v e n i n Chap -t e r S i x , where we a l s o p r e s e n t some p r e d i c t e d Mach numbers w h i c h may s e r v e as gu i de l i n e s f o r the c o n s t r u c t i o n o f a l a r g e i m p l o s i o n . d r i v e r . A d e t a i l e d d e s c r i p t i o n o f the e x p e r i m e n t a l a p p a r a t u s i s g i v e n i n Appen -d i x B. . . The g e n e r a l model o f i m p l o d i n g d e t o n a t i o n s and t h e membrane o p e n i n g mode l s a r e c o n s i d e r e d the o r i g i n a l t h e o r e t i c a l c o n t r i b u t i o n s o f t h i s t h e s i s . The e x -p e r i m e n t a l ' i n v e s t i g a t i o n s a r e b e l i e v e d to be the f i r s t known s t u d y o f t h e i inpor t ance o f d r i v e r geometry i n 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 s . -8-CHAPTER TWO PROPAGATION O F A DETONATION THROUGH AN AREA CONVERGENCE The p r o p o s e d h i g h p e r f o r m a n c e membrane shock tube makes use o f an o v e r -d r i v e n d e t o n a t i o n t o i n c r e a s e the t e m p e r a t u r e and. p r e s s u r e o f the d r i v e r g a 3 . An o v e r d r i v e n , d e t o n a t i o n can be p r o d u c e d by l e t t i n g a .p lane d e t o n a t i o n p r o -paga te t h r o u g h a c h a n n e l o f c o n v e r g i n g c r o s s s e c t i o n , and t h i s mot i on i s now s t u d i e d In d e t a i l . The c h a n n e l has the geometry o f a cone o f a r b i t r a r y s l a n t ang le 0 ( f i g . 1 -3 ) . The d e r i v a t i o n f o l l o w s the app roach o f C h e s t e r / l l / , C h i s n e l /.12/, and Witham / 1 3 / , ( C . C . W . ) , and i n c l u d e s the Lee / 6 / mode l f o r c y l i n d r i c a l g e o -metry when ^ = 90 , The mode l d e s c r i b e s the p r o p e r t i e s o f s t a t e , p r e s s u r e , d e n s i t y , e n t h a l p y , and p a r t i c l e v e l o c i t y b e h i n d the 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 the i n i t i a l c o n d i t i o n s and the a r e a th rough the gas f l o w s . D i r -e c t l y b e h i n d the f r o n t , t he se v a r i a b l e s a re o b t a i n e d u s i n g the s t a n d a r d 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 o f mass , momentum and ene rgy - Rank ine Hugo -n i o t r e l a t i o n s - w i t h an energy s o u r c e t e r m . Some d i s t a n c e b e h i n d the f r o n t , the v a r i a b l e s a re o b t a i n e d from the c o n s e r v a t i o n e q u a t i o n s i n a p a r t i c u l a r d i f f e r e n t i a l form, ( c h a r a c t e r i s t i c s ) , u s i n g the Rank ine H u g o n i o t r e l a t i o n s as boundary v a l u e s and the Chapman-Jouguet v e l o c i t y as. an i n i t i a l c o n d i t i o n , 2-1 PLANE DETONATIONS The combus t i on o f e x p l o s i v e gas m i x t u r e s can take p l a c e i n two d i s t i n c t manner s , u s u a l l y dependent on the n a t u r e o f the gases and on the m i x t u r e . One form of combus t i on i s t h rough the p r o p a g a t i o n o f an o r d i n a r y f l ame f r o n t . T h i s i s a r e l a t i v e l y s l ow e v e n t , the v e l o c i t y o f w h i c h depends on. many c h e -m i c a l p r o c e s s e s i n v o l v i n g a c t i v a t i o n e n e r g i e s , r a t e o f r a d i c a l d i f f u s i o n , and h e a t t r a n s f e r . B u r n i n g v e l o c i t i e s f o r o x y - a c e t y l e n e m i x t u r e s a re about 10 m e t e r s / s e c , S t r o n g p r e s s u r e d i s c o n t i n u i t i e s w h i c h smooth out t y p i c a l l y w i t h the s p e e d o f sound do n o t d e v e l o p i n f l a m e s . I f , however , the c o n d i t i o n s b e h i n d a f l ame a r e such t h a t the e x p a n s i o n o f h e a t e d gas can cause gas movements w h i c h i n c r e a s e the f r o n t v e l o c i t y , the n a t u r e o f p r o p a g a t i o n can change d r a s t i c a l l y , becoming e x t r e m e l y v i o l e n t . T h i s phenomenon i s known as d e t o n a t i o n and can p r o p a g a t e a t v e l o c i t i e s g r e a t e r than 3 k m , / s e c . Many e x t e n s i v e and w e l l documented a c c o u n t s o f d e t o n a t i o n s can be f o u n d i n r e -f e r e n c e s /I/ t o / 5 / . S e l f - s u p p o r t e d d e t o n a t i o n s , t r a v e l at 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 and have a l a r g e p r e s s u r e jump a c r o s s the f r o n t . The v e l o c i t y o f p r o g a g a t i o n i s dependent on the r e a c t i o n ene r gy o f the gas m i x t u r e , b u t v e r y i n s e n s i t i v e t o i n i t i a l p r e s s u r e - e x c e p t f o r a c r i t i c a l p r e s s u r e be l ow w h i c h o n l y a f l ame can e x i s t . U n l i k e a f l a m e , 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 do n o t i n f l u e n c e a d e t o n a t i o n / 2 / , / 3 / . These p r o p e r t i e s c l o s e l y l i n k a d e t o n a t i o n t o the p r o p a g a t i o n o f a shock wave, A d e t o n a -t i o n may be though t o f as a shock wave f o l l o w e d by a c h e m i c a l r e a c t i o n , The pa s s a ge o f the shock i n s t a n t a n e o u s l y h e a t s ( i n a thermodynamic s en se ) the gas m i x t u r e above i t s i g n i t i o n t e m p e r a t u r e , whereby the c h e m i c a l r e a c t i o n p r o c e e d s and r e l e a s e s e n e r g y . T h i s e n e r g y i n t u r n p r o v i d e s , t h r o u g h the e x p a n s i o n o f h o t g a s , the mechanism to push t h e . s h o c k . Thus the v e l o c i t y o f p r o p a g a t i o n i s d e t e r m i n e d by the d i f f e r e n c e between the c h e m i c a l e n e r g y r e -l e a s e d p e r u n i t mass and the ene rgy a b s o r b e d p e r u n i t mass due t o shock h e a t i n g . These two p r o c e s s e s have n e a r l y the same dependence on i n i t i a l pres-s u r e , and as a r e s u l t , p r e s s u r e d o e s . n o t g r e a t l y i n f l u e n c e v e l o c i t y . T h i s i s i n c o n t r a s t t o the p r o p a g a t i o n o f a shock wave i n a n o n - c o m b u s t i b l e g a s , where an e x t e r n a l s o u r c e o f ene r gy must be s u p p l i e d ' . I n t h i s c a s e , the s p e e d of the shock i s d e t e r m i n e d by the i n i t i a l t e s t gas p r e s s u r e , and by the. d r i -v i n g mechanism,. T h e r e f o r e , a c o n t i n u o u s range o f v e l o c i t i e s . i s p o s s i b l e , The u n i q u e n e s s o f the f r o n t v e l o c i t y and the. s t a t e o f the .gas b e h i n d the f r o n t i i i p l a n e s e l f - s u s t a i n e d d e t o n a t i o n s has been s t u d i e d i n g r e a t d e t a i l , -10-/ , ! / t o 151, He re i t 13 s u f f i c i e n t t o say t h i s un ique s t a t e o f the r e a c t i o n p r o d u c t s i s g i v e n by the C , J , c o n d i t i o n , w h i c h c o r r e s p o n d s t o the l o w e s t p o s s i b l e f r o n t v e l o c i t y c o m p a t i b l e w i t h the c o n s e r v a t i o n e q u a t i o n s . In p h y s i c a l t e r m s , the C . J , s t a t e i s e q u i v a l e n t t o the s i t u a t i o n where the f r o n t p r o p a g a t e s at the speed o f .sound r e l a t i v e to the. r e a c t i o n p r o d u c t s . The s t a n d a r d q u a n t i t a t i v e d e s c r i p t i o n o f p l a n e d e t o n a t i o n s w h i c h nox^ f o l l o w s , i s i n c l u d e d , s i n c e i t forms the b a s i s f o r the C.C.W, mode l o f the c o n i c a l c o l l a p s e . To a p p l y the c o n s e r v a t i o n e q u a t i o n , we c o n s i d e r a frame o f r e f e r e n c e w h i c h i s s t a t i o n a r y i n the l a b o r a t o r y . We w i l l c o n s i d e r the d e t o n a t i o n s as a p l a n e d i s c o n t i n u i t y w h i c h i n c l u d e s an ene r gy s o u r c e , F i g u r e 2-1 P l a n e d i s c o n t i n u i t y v i e w e d from L a b , f r ame. Assuming one d i m e n s i o n a l f l o w , we can e x p r e s s the c o n s e r v a t i o n e q u a -t i o n s as f o l l o w s : Mass : f>Vn - fZ {V,z - UJ 2.1 2 2. M o m e n t ™ , : /> + ^ Vn = + fL ( V,, - U, ) 2 . 2 h,+ Q + i V,l* ht * ir(vl2.-u2f . 2.3 The' s u b s c r i p t : (.1) denotes the i n i t i a l s t a t e ; and (2) t he s t a t e b e -h i n d the d e t o n a t i o n . The symbol s p, U, /) , r e p r e s e n t p r e s s u r e , d e n s i t y , * 1/ gas v e l o c i t y , and e n t h a l p y , r e s p e c t i v e l y , V/& I s the v e l o c i t y o f p r o p a g a -t i o n o f the f r o n t , and Q i s the c h e m i c a l ene r gy re l ea sed , p e r u n i t mass . We a l s o r e q u i r e a knowledge o f the e n t h a l p y as a f u n c t i o n o f the p r e s s u r e and. d e n s i t y . T h i s i s p r o v i d e d by the e q u a t i o n o f s t a t e : In the l a b frame o f r e f e r e n c e . y i s the r a t i o o f s p e c i f i c h e a t s f o r an i d e a l ga s . F o r a r e a l g a s , an e f f e c t i v e a d i a b a t i c exponent 0 can be d e f i n e d i n terms o f e n t h a l p y ( A h l -bo rn and S a l v a t / 7 / ) , i n w h i c h case g assumes a f u n c t i o n a l dependence on p r e s s u r e and t e m p e r a t u r e . T h e n : h - frr • % We now have f o u r e q u a t i o n s and f i v e unknowns: S/^ j j pj ^ and L/^«For the t ime b e i n g , we w i l l l e a v e the s y s tem u n d e r d e t e r m i n e d and s o l v e the s y s t e m g e n e r a l l y , l e a v i n g the d e t o n a t i o n f r o n t v e l o c i t y as a p a r a m e t e r . The s o l u t i o n o f 2.1 to 2,4 can then be e x p r e s s e d as ( A h l b o r n /33 / ) : r - XK> ti +- AJ ) 2.5 V , 2 ft ?2 -1 LL. 2.6 2,7 * I' 'A f HI !• rt ITT I 2,9 tii ~ 0( Sz ~ 3, nj) h, £ = • 2 (K+I)<?-2.?±LJ^L$J_ 2.IO 2 .11 C * i s the s p e e d o f sound i n the unburnt gas and i s the >fach number o f the f r o n t . These o p p r e s s i o n s can be s i m p l i f i e d c o n s i d e r a b l y w i t h the s t r o n g 2 shock a p p r o x i m a t i o n when " * 3 ^ 1 . In o x y - a c e t y l e n e d e t o n a t i o n s , t h i s i s q u i t e v a l i d s i n c e the Mach number i s a t l e a s t e i g h t . Then e q n s . 2 .10 , 2 . 8 , 2.9 become r e s p e c t i v e l y : a = o 7 = • • • • C o n s e q u e n t l y , e q n s . 2 . 5 , 2 . 6 , and 2.7 r e d u c e t o : = J L - A + f , - ^ / - ^ 1 v.. I L THT J f 2 „ 1 2 2 0 1 3 12 2 ' tlA J J fi- J b f i i p<~ St We w i l l now impose the C . J . c o n d i t i o n w h i c h demands t h a t VJ^ be a minimum. T h i s o c c u r s when A£ i s i d e n t i c a l l y z e r o . Then e q n s , 2 , 1 2 , 2 . 1 3 , 2,14 can be w r i t t e n a s : Ui, _ J 2 . 1 5 fi_ _ _Jl_ . ~ 2 . 1 6 3.- 3, M?a 2 0 1 7 P, ?2+l When = 0 we have the v e l o c i t y o f a C . J , d e t o n a t i o n : V i 2 ~ V c ^ - Z 2(tf-l) Qj 2 . 1 8 With the d e f i n i t i o n o f the sound speed 2,11 and e q n s . 2,15 and 2 . 1 6 , can be w r i t t e n as : - 5a w 2 . 1 9 •2 -9i + , Vl2 The p h y s i c a l s i g n i f i c a n c e o f the C J . c o n d i t i o n can be seen f rom e q n s . 2.19 and 2 . 1 5 , w h i c h r e s u l t i n : 2.20 _ „ = U~ -4- C~ 1 2 VC T T h a t i s , a C J , d e t o n a t i o n p r o p a g a t e s at. the s p e e d o f sound r e l a t i v e t o the r e a c t i o n p r o d u c t s . 2-2 TOE C.C.W. NODEL OF AM IMPLODING DETONATION A f t e r s u m m a r i z i n g some p a r t s o f s t a n d a r d d e t o n a t i o n t h e o r y , we t u r n t o the main t o p i c o f t h i s c h a p t e r : . .Trie deve lopement o f a mode l f o r an i m -p l o d i n g d e t o n a t i o n and o u t l i n e the C C N . p r o c e d u r e . The e s s e n t i a l p o i n t o f t h i s d e s c r i p t i o n i s to use the jump c o n d i t i o n s 2 , 1 2 , 2 . 1 3 , . 2 , 1 4 , at the f r o n t as boundary v a l u e s f o r the f l o w b e h i n d the f r o n t , L e e , / 6 / , a p p l i e d t h i s p r o c e d u r e t o i m p l o d i n g c y l i n d r i c a l , d e t o n a t i o n s * In t h i s t h e s i s , t h i s p r o c e d u r e i s a p p l i e d to a c o n i c a l c h a n n e l o f c o n s t a n t w i d t h , ( f i g , 1 -3 ) . S i n c e the s l a n t a n g l e 0 i s l e f t v a r i a b l e , ou r r e s u l t i n c l u d e s L e e ' s r e -r e s u l t (when ), p r o v i d i n g a c o n v e n i e n t check on o u r c a l c u l a -t i o n s . • F o r s i m p l i c i t y , we w i l l der ive, the mode l f o r a c h a n n e l o f i n f i n t e s i -ma l w i d t h . We w i l l t h e n e x p r e s s the s o l u t i o n s i n a g e n e r a l f o rm t h a t w i l l a l l o w us t o make c o r r e c t i o n s f o r f i n i t e w i d t h . T h i s w i l l be d i s c u s s e d a t the end. o f t h i s c h a p t e r . F o r the i m p l o s i o n o f a d e t o n a t i o n to the apex o f a c o n i c a l c h a n n e l , one wants t o know the f r o n t v e l o c i t y , 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 the f r o n t as a f u n c t i o n o f the c o - o r d i n a t e s o f the moving f r o n t . The c o n --14-s e r v a t l o n e q u a t i o n s f o r a gas f l o w w i t h no ene r gy s o u r c e o r s i n k terms may be w r i t t e n as : Mass : Momentum: E n e r g y : at f Mr f cl* € i s the i n t e r n a l energy and j=> , U , and.P a re as d e f i n e d p r e v i o u s l y , We w i l l now d e f i n e ou r c o - o r d i n a t e s y s tem i n the f o l l o w i n g manner: 2.20 2.21 2.22 F i f ru re 2-2 C o - o r d i n a t e " """" s y s t e m . Here any p o i n t on the s u r f a c e o f the cone can be e x p r e s s e d i n terms o f i t s c y -l i n d r i c a l c o - o r d i n a t e s ( , 6? , 5? ) . We w i l l assume t h a t the d e t o n a t i o n i m -p l o d e s s y m m e t r i c a l l y f rom the o u t e r base o f r a d i u s B 0 a l o n g the s u r f a c e to the apex, i n wh i ch case a l l & dependance can be n e g l e c t e d . W i t h the e q u a t i o n o f s t a t e 2,A and the d e f i n i t i o n of sound speed 2.11 eqn s . 2.20, 2,21, 2.22 r e -duce t o : if + £_uy + ? 2r 5 ? lJ£ + u^M*. +. L IE + <5 + . i . a P - o 2.23 2.24 -15-h£ + U r * P + u**£ - c2(\i ^ , < L f + U z - \ £ ) = o 2-25 At }r o? ^ h r * The s u b s c i p t s t and ? r e p r e s e n t the r a d i a l and a x i a l components o f v e l o c i t y We a l s o know t h a t the d e t o n a t i o n must p r o p a g a t e i n the nar row c h a n n e l . P r o -v i d i n g i t does so i n a smooth , c o n t i n u o u s manner , we a l s o have the e q u a t i o n o f f l o w i n the c h a n n e l : / U ( = ur/s>h (f) - U 2 / c o S $ 2.26 We w i l l now d e f i n e a new v a r i a b l e S , the s l a n t h e i g h t , as the d i s t a n c e t o any p o i n t on the s u r f a c e measured f rom the apex-(see f i g . 2-2) Tn terms o f ^ and i? the s l a n t h e i g h t can be e x p r e s s e d a s : . W i t h the a i d o f e q n . 2,26 and the d e f i n i t i o n o f s l a n t h e i g h t , e q n s . 2,23 2 .24 , 2,25 s i m p l i f y to t d L 4. p cild. -f LA ±JL -f- Jc_ri - U • *t ^ ^ 5 S i t as" f a s -A t a s V U dS 1 ^ , 2 o 28 2.29 t Here ^ i s u n d e r s t o o d as b e i n g i n the 5 d i r e c t i o n , Mow we w i l l mod i f y t h e s e e q u a t i o n s a c c o r d i n g to the e x p r e s s i o n : [c*X e 9 n ( 2 . 2 7 ) - r e f n.(2. 29) t C f X € f „ . ( 2 . 2 f j j Whereby we o b t a i n the f o l l o w i n g e q u a t i o n : H + (.u tc) H tc ?Cj% r ( u t c ) ^ ] + c f £ £ = _ 0 S i n c e fi\ , the a r e a th rough wh i ch the gas f l o w s , i s p r o p o r t i o n a l t o 5 , the above e q u a t i o n can be w r i t t e n a s : le + ^^c)l£ ± c f [ ^ +(u±c)]Lf] + r-%Z ff = 0 2.30 T h i s e q u a t i o n d e s c r i b e s the f l o w a l o n g the c o n t o u r l i n e s J^jf •= ^l- t -+ -c a l l e d the C and C c h a r a c t e r i s t i c s . E x p r e s s i n g e q n . 2,30 i n c h a r a c t e r -i s t i c f o r m : d P + c e ciM. -r ?uc-2 — = O 2 o 3 1 oUr y UT (u±c)A o(t Where the l a s t t e rm has been changed f rom a s p a c i a l t o a t ime d e r i v a t i v e a c -c o r d i n g t o : E q u a t i o n 2,31 may now be w r i t t e n i n i n c r e m e n t a l r a t h e r than d i f f e r e n t i a l f o r m : *Ucs SA r, 2.32 %-pt cf %u+ s—rj - o Witham / 1 3 / has shown t h a t the p o s i t i v e c h a r a c t e r i s t i c s p l a y the ma jo r r o l e i n d e t e r m i n i n g the f u t u r e mot i on o f a s h o c k , w h i l e the n e g a t i v e c h a r a c -t e r i s t i c s p r o p a g a t e r e f l e c t e d d i s t u r b a n c e s back i n t o the r e s u l t i n g f l o w , T h e r e f o r e , a t o r i m m e d i a t e l y b e h i n d the d e t o n a t i o n f r o n t , e q n . 2.32 w i l l be u s e d , k e e p i n g o n l y the p o s i t i v e . c h a r a c t e r i s t i c . E q u a t i o n 2,32 governs the f l o w i n a ' r e g i o n c o n t a i n i n g no d i s c o n t i n u i t i e s and no h e a t s o u r c e s . T h e r e f o r e , we w i l l have t o s p e c i f y the r e g i o n o f f l o w t o w h i c h we want t o a p p l y t h i s e q u a t i o n . (See f i g . 2 - 3 . ) F o r the case o f a c o n i c a l d e t o n a t i o n , t h i s r e g i o n l i e s o u t s i d e the r e g i o n o f the d i s c o n t i n u i t y f r o n t ( i e . S 7 ) .. The e q u a t i o n s w h i c h p r e d i c t the f l o w p a r a m e t e r s a c r o s s the d i s c o n t i n u i t y i n terms o f I t s >fach number a re ' g iven by the jump c o n d i t i o n s , 2 , 1 2 , 2 . 1 3 , 2 .14, T h u s , on s u b s t i t u t i n g t he se r e l a t i o n s i n t o 2 . 3 2 , and i n t e g r a t i n g the i n c r e a s e i n Mach number, the r e s u l t i n g v a r i a -t i o n i n the f l ow q u a n t i t i e s can be r e l a t e d to the deg ree o f a r e a r e d u c t i o n e x -p e r i e n c e d by the i m p l o d i n g f r o n t , - 1 7 -F low f i e l d d e s c r i b e d by c h a r a c t e r i s t i c e q u a t i o n F i g u r e 2-3 F r o n t v iew o f c o n i c a l c o l l a n s e . S i n c e eqn . 2.32 w i l l be i n t e g r a t e d n u m e r i c a l l y , we w i l l e x p r e s s the f i n a l r e s u l t s i n a more g e n e r a l fo rm by i n t r o d u c i n g the f o l l o w i n g d i m e n -s i o n l e s s v a r i a b l e s : 5 = s / s %Z1 2.33 -18-§p i s the f r o n t v e l o c i t y and ^ i a the s l a n t h e i g h t n o r m a l i z e d to the p o s i t i o n o f t he f r o n t . The l i m i t p l a c e d on the d i m e n s i o n l e s s s l a n t (^ — 1 ) i m p l i e s t h a t a l l p o i n t s i n the r e a c t i o n p r o d u c t s a r e i n c l u d e d and a l l p o i n t s i n the unburn t gas a re e x c l u d e d . The p a r a m e t e r s d i r e c t l y b e h i n d the f r o n t a re o b t a i n e d f o r ^ " ^ . In terms o f t h e s e v a r i a b l e s , e q u a t i o n 2.32 b e -comes , k e e p i n g o n l y the p o s i t i v e c h a r a c t e r i s t i c : In terms o f t he se v a r i a b l e s , the jump c o n d i t i o n s 2 , 1 2 , 2 . 1 3 , 2 , 1 4 , can be w r i t t e n a s : - 9i + ! _ 2.35 3* + I * * if" s i f l ~ ' 2 j ' ' * 2.36 J 2 J'2. * "771 ~ ~ * J ' 1 2 Here oC represents departures from the C . J . c o n d i t i o n (0-<<*jf,°^,-0) . E l i m i -nating and /Ifrom 3.34 and 2 .35 , we have the equation r e l a t i n g <<- to & . The c o n s t a n t of i n t e g r a t i o n can be o b t a i n e d f rom the s t a t e o f the. f r o n t a t l a r g e S where we e x p e c t the v a r i a b l e s t o behave v e r y much l i k e a p l a n e C..T. d e t o n a t i o n . In t h i s ca se we can put ° C - O &t A ~ ^ / "* ^O • The r e s u l t s can be e x p r e s s e d i n more c o n v e n i e n t fo rm by n o r m a l i z i n g the - 1 9 -f l ow q u a n t i t i e s t o t h e i r C . J , v a l u e s , These r educed q u a n t i t i e s are g i v e n b y : ? ~ " "fey. " * " °C 2.38 ucr. VV.KJ. fl-^* p-P . Jk£_ . _ J _ _ The t e m p e r a t u r e b e h i n d the f r o n t can be o b t a i n e d f rom the e q u a t i o n s t a t e : Pi XL _ 2 • • 1ft2 i s the mean m o l e c u l a r w e i g h t o f the r e a c t i o n p r o d u c t s , ' Icrrp.al ining the t e m p e r a t u r e to i t s C . J , v a l u e , we o b t a i n : T - ~ — 2,42 ' 1 - 9 ^ The v a l u e o f ^ ••-s v e r y much In q u e s t i o n and i s p r o b a b l y no t c o n s t a n t o v e r the whole f l o w f i e l d due to i t s dependence rn t e m p e r a t u r e and p r e s s u r e , F o r C . J , d e t o n a t i o n s i n e q u i m o l a r oxy-a.ee t y l e n e m i x t u r e s 6 Hun i / IA/ has used the measured v a l u e s of v e l o c i t y (2 ,73 t o 2.96 k m . / s e c , ) rnd the b e s t e s t i m a t e o f Q (7.72 X 1 0 6 J / k g ) / 1 5 / to determne the v a l u e o f y 2 V e q n . 2,18) to be 1,235 _ . 015 . However , we sha.11 see t h a t w i t h the e x c e p t i o n o f t e m p e r a t u r e , the f l ow q u a n t i t i e s are n o t e x t r e m e l y dependent on the exact, v a l u e o f • The v a r i a b l e . oC can h e . f o u n d PS a f u n c t i o n of.'A by s o l v i n g e q n ; 2 . 3 7 , The f l o w q u a n t i t i e s can t h e n be s p e c i f i e d .as a f u n c t i o n o f A by s u b s t i t u -t i n g <?C i n eqns , 2,38 to 2 ,42 , E q u a t i o n 2,37 has been i n t e g r a t e d as a f u n c -t i o n o f a r e a on the computer and the p l o t s o f p , P , V , ~f v e r s u s A a re shown i n f i g u r e s 2 -4 , 5 , 6 , 7 , By e x p r e s s i n g the gas p a r a m e t e r s as a f u n c t i o n o f A r a t h e r than 5 , the q u a n t i t i e s a re i n a more g e n e r a l form and c o r r e c -t i o n s f o r c h a n n e l w i d t h can be made, . F o r an i n f i n i t e s i m a l l y w ide c h a n n e l , we can m e r e l y r e p l a c e A by 5 i n e q u a t i o n 2.37 .and f i g u r e ? 2 - 4 , 5 , 6 , 7 , w h e r e : -~ s F o r c y l i n d r i c a l c o l l a p s e $ ~ P and e q n . 2.37 i s i d e n t i c a l to Lee s r e -s u l t / 6 / , As the s l a n t h e i g h t o f the i m p l o d i n g f r o n t becomes s m a l l , °£ & ^Sn* ly As oC a p p r o a c h e s - ^ ' t h e f r o n t v e l o c i t y , p a r t i c l e v e l o c i t y , t e m p e r a t u r e , xv and p r e s s u r e become unbounded. The d e n s i t y p on the o t h e r h a n d , a p p r o a c h e s , . , . . , . , . , „ . „ . . c J?iL- ... 3*+r- , , ^ - *f 3 • •' • s h o c k . -21--23--24-2-3 CHANNEL•OF FINITE WIDTH In a d a p t i n g the model to a c h a n n e l o f f i n i t e w i d t h , we w i l l assume t h a t the f l o w i s q u a s i one. d i m e n s i o n a l ; t h a t i s , a i l the q u a n t i t i e s a r e a v e r a g e d o v e r the c r o s s s e c t i o n o f the c h a n n e l and a re f u n c t i o n s o f S and ~t~ o n l y , ( h y d r a u l i c a p p r o x i m a t i o n ) . Near the apex o f c o l l a p s e , however , the f o l l o w i n g s h o u l d h a p p e n : the ma jo r e f f e c t s h o u l d be t h a t Sf w i l l n o t be u n i q u e l y d e f i n e d a c r o s s t he o c h a n n e l w i d t h , w i t h the s l a n t h e i g h t n e a r the o u t e r w a l l ( Sp ) b e i n g l a r g e r c « than t h a t n e a r the i n n e r ( ~>/T ) . I m p l o d i n g f r o n t / _ F i g u r e 2-8 , 3>-Imp losi.cn near apex, In o r d e r to account f o r t h i s , we w i l l assume t h a t the f r o n t rema ins o r i -e n t e d n o r m a l t o the w a l l s of the c h a n n e l . W i t h t h i s a s s u m p t i o n , the ave rage v a l u e o f the f l ow q u a n t i t i e s a c r o s s the. c h a n n e l pan be g i v e n by the known t a r e a th rough wh i ch the gas f l o w s . T h i s i n t u r n can be s p e c i f i e d by any v a l u e ro . . . . . . o f s l a n t h e i g h t we choose (eg . V.) ,. F o r .a channe l o f c o n s t a n t w i d t h W " the a r e a through w h i c h the gas f l o w s i s g i v e n b y : A = ^ k. _ S / - *> _ S / - f cot <j> 2 . 4 3 ~ *o ~ s.- t <•<.* <t> sc^ T h i s e x p r e s s i o n can t h e n be u s e d w i t h the p l o t s o f j> , P , V $ 7~»' v e r -sus r\ t o r e l a t e t he se v a r i a b l e s to 5^ . A l t h o u g h the a s s u m p t i o n s • i n the a -bove may be v i o l a t e d v e r y n e a r the apex , t h i s a p p r e a c h s h o u l d be somewhat more r e f i n e d than assuming \A/S 0 , F o r cones of l a r g e 0 , e q u a t i o n 2,4.3 s h o u l d be a c l o s e a p p r o x i m a t i o n even as $f ~® 0 , F o r cones o f s m a l l $ t h i s w i l l p r o b a b l y ' n o t be s o . A f t e r the d e t o n a t i o n f r o n t has p a s s e d the t i p o f the i n n e r c o n e , a s e m i - q u ant j - 2 6 -. ' tat ive d e s c r i p t i o n can be made by assuming the shape o f the f r o n t i s t e n -d i n g to a s e c t o r o f a s p h e r e (A n c o n s t ' S ) • E q u a t i o n 2,37 w i l l then t ake the f o r m : -F (oc) £<<• + 2 - 0 where 2 The c o n s t a n t o f i n t e g r a t i o n can be o b t a i n e d from the p r e d i c t e d s t a t e o f the d e t o n a t i o n a t S, = 0» CHAPTER THREE THEORETICAL DESCRIPTION op IMPLOSION DRIVEN SHOCK WAVES H a v i n g gone t o g r e a t d e t a i l i n p r e d i c t i n g the thermodynamic s t a t e o f the d e t o n a t i o n gas a t t he apex o f a c o n i c a l i m p l o s i o n , we^  w i l l now e x p l a i n how t h i s r e l a t e s to t h e s t r e n g t h o f t he shock w a v e - i n t h e t e s t s e c t i o n . In t h i s c h a p t e r we p r e s e n t a mode l w h i c h q u a n t i t a t i v e l y d e s c r i b e s t h i s . The model d e a l s w i t h the s p e c i a l t ype o f d r i v e r i n w h i c h a shock o r d e t o n a t i o n wave imp inge s upon the d i aph ragm. I t i s t h i s wave w h i c h h e a t s the d r i v e r gas and b r e a k s the d i aphragm. B e f o r e p r e s e n t i n g t h i s t h e o r y , we w i l l g i v e a b r i e f d i s c u s s i o n o f the two p o s s i b l e d i aphragm o p e n i n g p r o c e s s e s w h i c h may p o s s i b l y a p p l y t o d e t o n a t i o n d r i v e r s . I n p r i n c i p l e , t h e r e must b e - a d e l a y t ime between the a r r i v a l o f the p r i m a r y wave and the r u p t u r e o f the membrane. In d e t o n a t i o n d r i v e r s , however , t h i s d e l a y t ime may be r e l a t i v e l y s h o r t , s i n c e d iaphragms c a p a b l e 5 o f w i t h s t a n d i n g a s m a l l p r e s s u r e d i f f e r e n c e a c r o s s them may be u s e d . Depend ing on t h i s d e l a y t ime two p o s s i b i l i t i e s a r i s e . I f "XQ i s f a i r l y l o n g , a r e -f l e c t e d shock wave w i l l p r o p a g a t e f rom the unopened d iaphragm back i n t o the b u r n t d r i v e r g a s . I f ^ o i s v e r y c l o s e to z e r o , t h i s r e f l e c t e d shock may n o t d e v e l o p o r may be. q u i c k l y " e a t e n away" by the e x p a n s i o n x^ave from the low p r e s s u r e t e s t s e c t i o n . These two p o s s i b i l i t i e s a re shown i n x - t d iagrams i n f i g u r e 3 -1 . The numbers I n d i c a t e the v a r i o u s s t a t e s o f the ga se s . The n o t a t i o n (r.ty) , u sed by S t r a c h a n ' 3 4 / , i n d i c a t e s t he s u r -f a c e s s e p a r a t i n g v a r i o u s f l o w r e g i m e s . B e h i n d the d e t o n a t i o n f r o n t O-,?^ t h e r e i s a f l o w o f momentum o r 2 dynamic p r e s s u r e ( ) . If f p i s v e r y c l o s e to ~ e r o , t h i s momentum s h o u l d be t r a n s f e r e d d i r e c t l y to the c o n t a c t s u r f a c e and s h o u l d a s s i s t t h i 3 s u r f a c e l n d r i v i n g the shock wave. I f i s somewhat l o n g e r , the d iaphragm w i l l impede o r s t o p the mot i on o f gas b e h i n d s u r f a c e O - i ^ r e s u l t i n g i n the -23-shock heated:-t e s t qas • reac t i o n i i ^ . p r o d u c t s i l l l l und i s turbed t e s t gas ~ < l , 6 > Diaphragm X co l d d r i v e r gas F i g , 3-13 X - t Diagram of Delayed Open i ng of Membrane A J f o r m a t i o n o f a r e f l e c t e d shock wave. However , the m o t i o n o f gas b e h i n d s u r f a c e ^ 1 , 2 ^ w i l l , i n b e i n g s t o p p e d , i n c r e a s e the t e m p e r a t u r e i n Reg i on 3, thus i n d i r e c t l y c o n t r i b u t i n g to the s t r e n g t h o f the t e s t s h o c k . F o r d e t o n a t i o n d r i v e r s , these two p o s s i b i l i t i e s have been q u a l i t a t i v e l y m e n t i o n e d by Coates and Gaydon / 2 0 7 . E x p e r i m e n t a l l y we f o u n d , ( C h a p t e r F o u r ) , t h a t a shock wave was r e f l e - c t e d back i n t o the d r i v e r gas . T h e r e f o r e , the t h e o r y f o r t h i s p o s s i b i l i t y i s p r e s e n t e d i n t h i s c h a p t e r , and f o r com-p l e t e n e s s , the o t h e r p o s s i b i l i t y i s g i v e n i n A p p e n d i x A. 3-1 REFLECTED SHOCK DETONATION DRIVER • In t he x - f d i a g r a m s , ( f i g . 3-IB) , the f o l l o w i n g r e l a t i o n s h o l d a c r o s s the v a r i o u s s u r f a c e s . S u r f a c e ^1 ,6^ i s the d i aphragm f o r w h i c h we have the known p r e s s u r e , and a l s o f o r w h i c h the p a r t i c l e v e l o c i t y on e i t h e r s i d e i s z e r o : The d e t o n a t i o n ^ 1 , 2 ^ may o r may n o t be i n an o v e r d r i v e n s t a t e . From e q u a t i o n s 2 , 1 3 , 2 ,14 , 2 , 1 2 , we h a v e : 3.1 BL P, 3 . 3 3 . 2 -30-In the above y0 represents departures of the detonation from i t s C.J. sta t e . In terms of the dimensionless v a r i a b l e cC , i t i s equivalent to: p = 1 + $2 <• For a plane C.J. detonation j3 — 1 . This applies to a d r i v e r with no area convergence before the diaphragm. This type of d r i v e r i s i n v e s t i -gated i n Chapter Four. For overdriven detonations i < < 2 . This ap-l i e s to our co n i c a l d r i v e r (Chapter Five) and Huni's d r i v e r . For a shock wave J3= 2 which applies to the d r i v e r used by Glass et a l / l 9 / . Surface ^2,3^ i s the r e f l e c t e d shock wave. S e t t i n g Q - 0 i n eqns. 2.12, 2,13, 2.14, y i e l d s : / J . - I - 33 + 292 M l 3 3.4 2 3,5 — — ^ i IIITI i W i n n II unrig ,m 3.6 Here we have assumed that the r e f l e c t e d shock propagates without any change i n front area." For a cone, those equations are expected to be only a good, approximation close to the diaphragm. As the r e f l e c t e d shock pro-pagates back up the co n i c a l channel, the in c r e a s i n g area of the front w i l l reduce the pressure and sound speed behind i t . I f a detonation i s r e f l e c t e d from a plane s t a t i o n a r y surface C/j i s zero. Since i t i s r e f l e c t e d from a diaphragm, we w i l l leave i t as a para-meter to be determined from measurements of and » ^4,5^ i s the contact surface separating the expanding d r i v e r gas from the shock heated test gas. For t h i s surface we have: -31-S u r f a c e ^ 5 , 6 ^ i s the shock f r o n t In the, t e s t gas . A g a i n s e t t i n g Q~ 0 i n e q n s , 2 , 1 2 , 2 , 1 3 , 2 , 1 3 , one o b t a i n s : 3 . 7 3.8 S u r f a c e (>3 th) i n some way r e p r e s e n t s the b u r s t i n g o f the d i aphragm. Reg i on (.3,$ i s a r a r e f a c t i o n wave. F o r i s e n t r o p i c f l o w the p a r -t i c l e v e l o c i t y i m p a r t e d by t h i s c o n t i n u o u s u n s t e a d y e x p a n s i o n f rom t o PA i s g i v e n by / l / : — , n \ h"1 ~i assuming <^ = Jq. . T h i s r e l a t i o n i s e x a c t f o r u n i f o r m f l o w , w h i c h f o r a c o n i c a l d r i v e r w i l l o n l y a p p l y the i n s t a n t the d iaphragm b r e a k s . A t a l a -t e r t ime when the r a r e f a c t i o n head has t r a v e l l e d some d i s t a n c e up the c o n i -c a l c h a n n e l , the f l o w w i l l be n o n - u n i f o r m c o n v e r g e n t . T h i s i s ana logous t o n o z z l e f l o w and i t has been shown by A l p h a r and Wh i te / 2 1 / and R e s l e r e t a l / 2 2 / , p r o v i d i n g the f l ow I s n ' t t u r b u l e n t , t h a t the p a r t i c l e v e l o c i t y i m -p a r t e d by such an e x p a n s i o n i s s l i g h t l y g r e a t e r than p r e d i c t e d by eqn , 3 ,9 . We a l s o , however , have m e n t i o n e d t h a t the r e f l e c t e d shock w i l l decay as i t p r o p a g a t e s away f r om the d i a p h r a g m , thus r e d u c i n g Pg and C3 . We w i l l n e -g l e c t these two e f f e c t s s i n c e they a re d i f f i c u l t t o t r e a t e x a c t l y , and f u r -t h e r m o r e , w i l l have a tendency to compensate each o t h e r . The v a l u e o f i n e q n , 3.9 can be o b t a i n e d from the r e l a t i o n : -32-With the aid of eqns, 3 . 2 , 3 . 3 , 3.A, 3.6, C-onan now be expressed as: C r 2 c, /? The value of P^"/P% i n c r i n ' - ' » 9 c a n • , e obtained using the i d e n t i t y : & = Pi EL PI P± / V With the aid of eqns. 3,8, 3 .4 , and 3 . 2 , r e c a l l i n g that P^.a Pg , we can express t h i s • r a t i o as: a p6f(%+o(<h+o(2%yh)(i+- i7/?J J 3 1 X The v e l o c i t y of the tes t shock can then be obtained from eqns, 3,7 and 3 , 9 , noting that U^.' U<: Where and *4-/p are given by eqns, 3.1.0 and 3 .11 . The above expressions can be s i m p l i f i e d considerably with the strong shock a p p r o x i m a t i o n , tf >> i . T h i s i s . q u i t e . - v a l i d - f o r ht% and t'ig^, which are t y p i c a l l y greater than eight but cannot be made for /"^^which i s almost always between two and unity. With this approximation eqn, 3.12 reduces to: ; Vk- {u3 + j ^ f i 3 : 3 Where C 3 and Pfy/p can now be e x p r e s s e d as : The value of L/j and j can be obtained from a knowledge of V^^ using eqns, 3.5 and 3.1 For the case when (j^- 0 ve can express M^^-^ > -33-Then the v e l o c i t y o f the t e s t shock i s c o m p l e t e l y s p e c i f i e d by V^^"^ — P P(> and ]d(oC) . I f we t ake the ext reme case where co , it can be 6 seen t h a t : v/ — > . c T h e r e f o r e , f o r a t h e o r e t i c a l l y I n f i n i t e f i l l i n g p r e s s u r e r a t i o , the p r e -d i c t e d shock v e l o c i t y s t i l l rema ins f i n i t e . T h i s i s i n t e r e s t i n g t o com-p a r e w i t h the p r e d i c t e d shock v e l o c i t y g i v e n by the s i t u a t i o n where the r a t i o o f d r i v e r t o shock tube d i a m e t e r s I s i n f i n i t e . F o r t h i s the p r e s s u r e r a t i o ^4-/p a l s o app roaches z e r o s i n c e the p r e d i c t e d p r e s s u r e i s unboun-ded a t the apex o f I m p l o s i o n . However , the f r o n t v e l o c i t y approaches i n -f i n i t y , (much more s l o w l y than p r e s s u r e ) , at the apex. C o n s e q u e n t l y , the sound speed o f the d r i v e r gas i n c r e a s e s w i t h o u t b o u n d s , i m p l y i n g an i n f i n -i t e t e s t shock v e l o c i t y . The above d i s c u s s i o n i s h y p o t h e t i c a l , b u t i t does p r o v i d e an i n t u i t i v e u n d e r s t a n d i n g o f the p r o d u c t i o n o f 3hock waves f rom I m p l o d i n g d e t o n a t i o n s . The f i r s t o r d e r e f f e c t i s the i n c r e a s e d p r e s s u r e o f the d r i v e r g a 3 . However , the i n c r e a s e i n shock v e l o c i t y a v a i l a b l e f rom t h i s has an u p p e r l i m i t ( about a o n e - f o l d i n c r e a s e f o r ^ /p i n i t i a l l y e q u a l t o . 0 1 , see f i g s . 6.3 and 6 , 4 ) , The s e c o n d o r d e r e f f e c t i s the i n c r e a s e i n d e -t o n a t i o n f r o n t v e l o c i t y . A o n e - f o l d i n c r e a s e due e n t i r e l y t o t h i s e f f e c t , u n f o r t u n a t e l y , o c c u r s o n l y above a d i a m e t e r r a t i o ..of about 500, I f the i m -p l o d i n g d e t o n a t i o n i s s p h e r i c a l , t h i s same i n c r e a s e i s a c h i e v e d f o r a r a t i o o f about 30. - . ' In d e r i v i n g the above e x p r e s s i o n s we have assumed t h a t the i n i t i a l f l ow i n the shock tube i s one d i m e n s i o n a l . The d e s c r i p t i o n c o m p l e t e l y n e g l e c t s t u r b u l e n t f l o w as w e l l as m i x i n g d r i v e r and t e s t gas a t the c o n t a c t zone , T u r b u l e n c e i m p l i e s a l o s s o f momentum to the w a l l s o f the shock tube as w e l l as i n the g e n e r a t i o n o f h e a t . F o r t h i s r e a s o n v e l o c i t i e s p r e d i c t e d s h o u l d be maximum v a l u e s . S i n c e t u r b u l e n c e w i l l be d i r e c t l y r e l a t e d to the d iaphragm -34-o p e n i n g p r o c e s s , t h i s a s s u m p t i o n w i l l be more o r l e s s c r i t i c a l , d e p e n -d i n g on the geometry o f the d r i v e r . F o r a p l a n e d r i v e r , t h i s a s s u m p t i o n s h o u l d be more v a l i d than f o r a c y l i n d r i c a l . -35-aiAFTER FOUR PLANE DETONATION DRIVER AN EXPERIMENTAL STUDY OF PERFORMANCE AND DIAPHRAGM OPENING In Chapter Three, the inodel p r e d i c t i n g _ the ' v e l o c i t y of the te s t shock was derived with a knowledge that the diaphragm ruptures with a time delay. In t h i s chapter,.we present, the experimental v e r i f i c a t i o n of t h i s . In such an experiment i t i s e s s e n t i a l to observe the d r i v e r s e c t i o n as w e l l as the tes t s e c t i o n . Since c o n i c a l or c y l i n d r i c a l d r i -vers are not p r a c t i c a l f o r side-on observation, a plane d r i v e r was em-ployed. The shock v e l o c i t i e s produced by th i s plane driver'provide a convenient test of the v a l i d i t y of the theory and also provide data to compare with the experimental r e s u l t s of the c o n i c a l d r i v e r discussed i n Chapter Five. 4-1 EXPERIMENTAL SET-UP The d r i v e r s ection and shock tube were constructed of 2,54 cm, i , d . pyrex tube s e c t i o n s , ( f i g . 4-1). Two l u c i t e discs of the same bore as the shock tube were used to clamp the diaphragm which was .033 mm, thick mylar. On each side of the diaphragm there was an 0 r i n g s e a l to pro-vide a vacuum. The diaphragm was clamped between the discs by means of two screws which were designed to be turned by hand f o r easy diaphragm replacement. In the d r i v e r , the detonation mixture was i g n i t e d by means of an e l e c -t r i c a l discharge, The spark gap was at the f a r end from the diaphragm and was a conventional T tube type with a backst-rap. For th i s reason the d r i -ver was made extra long (1,2 m.) and the capacitor discharged at minimum voltage (12 KV.), to ensure that at the diaphragm the datonationwas not influenced by the discharge (See f i g . 4-2). r i r Jl r-Pr Figure 4-1 Ll i i 0 F u l l scale section of .'diaphragm clamp and shock tuDe. I co I -3 7 -V e l o c i t y measurements were t aken on b o t h s i d e s o f the d i aphragm by means o f a smear camera. A d e t a i l e d d e s c r i p t i o n o f the camera o p t i c s and e l e c t r o n i c s i s g i v e n by H u n i / 1 4 / , Trie s l i t o f the camera was f o c u s e d a -l o n g the a x i s o f the tube v i a two f : 5 a c h r o m a t i c l e n s e s o f f o c a l l e n g t h 38 cm. T h i s g i ve s a c o n t i n u o u s s p a c e - t i m e r e c o r d o f the l u m i n o s i t y on b o t h s i d e s o f the d iaphragm e x c e p t f o r a f o u r c e n t i m e t e r r e g i o n on e i t h e r s i d e consumed by the c l amp ing d e v i c e . The d i s c h a r g e was t r i g g e r e d by a p u l s e f rom the t r i g g e r d e l a y u n i t o f the smear camera. The camera and d e l a y s e t up a re r e p r e s e n t e d s c h e m a t i c a l l y i n f i g u r e 4 - 2 , The d e t o n a t i o n gas was 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 300 T o r r , The t e s t gas was a r gon s e e d e d w i t h f i v e p e r c e n t (by p r e s s u r e ) a c e t y l e n e . A c e t y l e n e was added to make the shock more l u m i n o u s . The t e s t gas p r e s s u r e was v a r i a b l e f rom 300 down t o l e s s t han 1 T o r r , Most smear pho tog raphs were taken on p o l a r o i d 3000 A.S.A.. f i l m . Smear camera F i g u r e -4-2 Camera and d e l a y s e t - u p , - 3 8 -4-2 THE REFLECTED SHOCK For mylar diaphragms i t was found that a shock wave was reflected from the diaphragm back into the driver gas. Velocity measurements were taken from over 35 photographs covering the entire range of test gas pressure. It was interesting that the velocity of the reflected shock did not seem to change as the i n i t i a l pressure ratio across the diaphragm was varied. This indicates that the diaphragm alone withstands the impact of the incident de-tonation. In Chapter Three, the value of in eqn. 3.17 was l e f t as a parameter. Using the measured values of Vp3(1.16 km./sec.), and ^£(2.86 km./sec.) in eqns, 3.1 and 3.5 the value of can be determined. It can be seen ( f i g . 4-3) that the reflected shock speeds up as i t enters the rarefaction wave behind the detonation. This i s known from Strachan et al /34/, Velocity measurements were made by extrapolating V^jback to the diaphragm. The value of the particle velocity U^ is exactly zero i f the detonation i s reflected from a plane solid wall. Assuming /.23, the particle velocity behind the reflected shock was found to be: U 3 = -.11 + .05 km./sec. ( 9 = 1.23) U 3 .= -.05 + .05 km./sec. ($ =1.19) U 3 = -.006'7- .05 km./sec. ( <? = 1.15) 3 -U 3 = -.22 + .05 km../sec. (<^ 3 = <J 2 = 1.4} i d e a l d i a t o m i c gas) Within the experimental error, this indicates that the membrane behaves like a so l i d reflector, 4-3 . TEST SHOCK Smear photographs were taken of the luminosity in the test section of the shock tube. The photographs reveal two luminosities leaving the diaphragm location, ( f i g . 4-4), Since i t was not clear that the leading luminosity was -39- 1 cm t F i g u r e 4-3 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 , t e s t , and r e f l e c t e d s h o c k waves. M a r k e r s 1 cm. a p a r t . Sweep s p e e d = 20.80 m i c r o s e c o n d s / c m . D r i v e r gas e q u i m o l a r o x y - a c e t y l e n e (300 T o r r ) . T e s t gas a r g o n _ A_=100 T o r r _B_=12 T o r r C=2 T o r r The diaphragm clamp obscures the region X i to X -40-F i g a r e 4-4 Smear photograph of the two luminous r e g i o n s i n the t e s t s e c t i o n . D r i v e r gas e q u i n i o l a r oxy-a c e t y l e n e (300 T o r r ) . T e s t gas argon (9 T o r r ) Sweep speed = 25.63 usee /cm. Markers 1 cm. a p a r t F i g u r e 4-5 Smear photographs of the t e s t shock w i t h a r e f l e c t o r 12 cm. from the diaphragm. D r i v e r gas e q u i m o l a r o x y - a c e t y -l e n e (300 T o r r ) . T e s t gas argon A = 3 T o r r . B • 300 T o r r . ( i n v i s a b l e shock f r o n t ) . Markers 1 cm. a p a r t . Sweep speed = 15.21 usec/cm. 1 cm . - I k-B -41-fcbe shock f r o n t , a b r a s s r e f l e c t o r was p l a c e d t w e l v e c e n t i m e t e r s f rom the d i aphragm. I t was found t h a t f o r a rgon p r e s s u r e s above 200 T o r r , an i n v i -s i b l e shock f r o n t p r e c e d e s the l e a d i n g s u r f a c e on the smear , ( f i g . 4 - 5 ) . Below 200 T o r r , the r e f l e c t o r r e v e a l e d t h a t the l e a d i n g l u m i n o s i t y was the shock f r o n t o r u o s c p a r a t e d shock f r o n t and c o n t a c t s u r f a c e . The t r a i l i n g s u r f a c e i s b e l i e v e d to be p a r t i c l e s o f d i aphragm. I t s v e l o c i t y i s low and v e r y i n s e n s i t i v e to changes i n a rgon f i l l i n g p r e s s u r e . At low a rgon p r e s -s u r e s , i t s s e p a r a t i o n f rom the l e a d i n g f r o n t I n c r e a s e s c o n s i d e r a b l y . F i g . 4-4 shows the s t r e a k y n a t u r e o f t h i s r e g i o n . F i g . 4-6 summar izes the e x p e r i m e n t a l r e s u l t s . The d o t s r e p r e s e n t t h e l e a d i n g f r o n t w h i l e the t r i a n g l e s r e p r e s e n t the t r a i l i n g l u m i n o s i t y , The s o l i d l i n e i s the v e l o c i t y o f the shock f r o n t p r e d i c t e d by eqn* 3 .13 , T h i s . e q u a t i o n was s o l v e d i t e r a t i v e l y on the computer , t a k i n g i n t o a c c o u n t r e a l gas e f f e c t s i n a r gon ( A h l b o m and S a l v a t / 7 / ) , The. measured v a l u e o f was u s e d i n o b t a i n i n g the t h e o r e t i c a l curve~. I t can be seen t h a t the v e l o c i t y o f the shock f r o n t i s about 20% l e s s than p r e d i c t e d . The v a r i a t i o n o f v e l o c i t y w i t h r e s p e c t t o p r e s s u r e behaves v e r y much as p r e d i c t e d . The t ime d e l a y o f the d iaphragm o p e n i n g was f o u n d by e x t r a p o l a t i n g the I i n c i d e n t d e t o n a t i o n , r e f l e c t e d s h o c k , and the two shock tube l u m i n o s i t i e s t o the l o c a t i o n o f the d i aphragm. The average d e l a y was about 'YQ- 17 Y s e c , » t a ^ e n ' f rom o v e r 30 p h o t o g r a p h s c o v e r i n g the argon p r e s s u r e r ange , T h e r e was c o n -s i d e r a b l e j i t t e r i n t h i s d e l a y , b u t o v e r the range o f p r e s s u r e s u sed i t was a lways between 14 and 2 1 ^ s e c , The d e l a y a p p e a r e d to be about 10% l e s s f o r v e r y low argon p r e s s u r e s , ( s e v e r a l T o r r ) than f o r the h i g h , (•'W00 T o r r ) . T h i s d i f f e r e n c e i n d e l a y t ime may n o t n e c e s s a r i l y mean t h a t the d i aphragm b u r s t s w i t h 10% l e s s d e l a y , s i n c e we have no knowledge o f how the shock, f r o n t a c c e l e r a t e s i n the r e g i o n o b s c u r e d by the d i aphragm c lamp. -43-P u r i n g t h i s d e l a y t i m e , t h e r m a l l o s s e s w i l l r e d u c e t h e sound speed o f the gas b e h i n d the r e f l e c t e d s h o c k . An o r d e r o f magn i tude e s t i m a t e o f t he r a d i a t i v e l o s s e s , ( a s suming the gas r a d i a t e s as a b l a c k b o d y ) , y i e l d e d a 10% r e d u c t i o n i n sound s p e e d . T h i s c a l c u l a t i o n was too c rude t o be o f any r e a l q u a n t i t a t i v e v a l u e , b u t i t may i n d i c a t e t h a t r a d i a t i v e l o s s e s c o u l d p a r t l y e x p l a i n the l ower than p r e d i c t e d v e l o c i t i e s . -44-CIIAPTER FIVE ' .IMPLODING DETONATION DRIVER So f a r we have t h e o r e t i c a l l y s t u d i e d the i n c r e a s e o f p r e s s u r e and sound s p e e d 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 and have d e v e l o p e d a model to p r e d i c t the v e l o c i t y o f the t e s t shock as a f u n c t i o n o f t h i s . I t rema ins to show e x -p e r i m e n t a l l y t h a t shock waves can i n d e e d be g e n e r a t e d w i t h such a d r i v e r , wh i ch a re s t r o n g e r than p l a n e d e t o n a t i o n d r i v e n shock waves . F u r t h e r m o r e , we want t o d e t e r m i n e e x p e r i m e n t a l l y the cone a n g l e 0 w h i c h w i l l y i e l d the s t r o n g e s t p o s s i b l e s h o c k s . I t was shown i n C h a p t e r Two t h a t the s t a t e o f an i m p l o d i n g d e t o n a t i o n n e a r the apex o f a cone i s a p p r o x i m a t e l y the same as n e a r the a x i s o f a c y l i n -d e r . However , t h e r e s h o u l d be some b a s i c d i f f e r e n c e s between a c o n i c a l d r i v e r and a c y l i n d r i c a l . These w i l l be r e i t e r a t e d b e l o w . W h i l e b o t h g e o m e t r i e s have the same magn i tude o f dynamic p r e s s u r e b e h i n d 2 the i m p l o d i n g f r o n t , a cone has a component j>2 ^ 2 a l o n g the tube a x i s , . I f the diaphrcigm b u r s t e a s i l y , t h i s component w i l l c o n t r i b u t e to the speed o f the c o n t a c t s u r f a c e . I f i n s t e a d a shock i s r e f l e c t e d f rom the d i a p h r a g m , t h i s dynamic p r e s s u r e s h o u l d a s s i s t i n the d i aphragm r u p t u r e . F u r t h e r m o r e , f o r a c o n e , the i m p l o d i n g f r o n t more c l o s e l y r e p r e s e n t s a p l a n e d e t o n a t i o n i n s h a p e , p a r t i c u l a r l y f o r s m a l l 0 ; t h e r e f o r e , the d i aphragm o p e n i n g p r o c e s s s h o u l d be more u n i f o r m , thus r e d u c i n g t u r b u l e n t f l o w . A f t e r the d i aphragm has r u p -t u r e d , the geometry o f the d r i v e r w i l l a l s o i n f l u e n c e the manner i n w h i c h the h e a t e d d r i v e r gas i s a c c e l e r a t e d down the shock t u b e . In a c y l i n d r i c a l d r i v e r the r a r e f a c t i o n head w i l l p r o p a g a t e r a d i a l l y ou tward f rom the d i aphragm l o c a -t i o n . The gas v e l o c i t y i m p a r t e d by t h i s e x p a n s i o n w i l l i n i t i a l l y be i n the r a d i a l d i r e c t i o n . A c o n i c a l d r i v e r , t h e r e f o r e , s h o u l d a c c e l e r a t e the d r i v e r gas down the shock tube i n a more d i r e c t manner. To i n v e s t i g a t e these q u a l i t a t i v e a r gument s , d r i v i n g chambers o f d i f f e r e n t s l a n t a n g l e s were b u i l t and t e s t e d . A g a i n , as w i t h the p l a n e d r i v e r , o u r i n t e n t i o n was n o t t o b u i l d a f i n a l v e r s i o n o f a p r a c t i c a l d r i v e r o f s t r o n g * shocks, , bu t r a t h e r to u n d e r s t a n d the f u n d a m e n t a l a s p e c t s o f t h e o p e r a t i o n o f such a dev ice- . S i n c e t h i s r e q u i r e d a c e r t a i n amount o f t r i a l and e r r o r p r o ™ c e d u r e , the d r i v e r s were b u i l t s m a l l f o r ea sy c o n t s t r u c t l o n and low c o s t . S i m i l a r l y , the shock tube was o f a s m a l l d i a m e t e r to e n s u r e t h a t a t the d i a -phragm, the d e t o n a t i o n wou ld be o v e r d r i v e n . 5-1 EXPERIMENTAL SET -UP ' A ma jo r p rob lem i n p r o d u c i n g an i m p l o d i n g d e t o n a t i o n l i e s i n the f a c t t h a t the d e t o n a t i o n must be p r o d u c e d u n i f o r m l y a t the base o f the c o n i c a l c h a n n e l . The method u sed was the s o - c a l l e d % * d e f l e c t i o n p l a t e t e c h n i q u e " , used by L e e /(>/ and Html / 1 4 / f o r c y l i n d r i ' c a l l y i m p l o d i n g d e t o n a t i o n s . T h i s c o n s i s t e d o f i g n i t i n g the d e t o n a t i o n a t the c e n t r e p o i n t o f the f l a t ba se o f the c o n e , thus p r o d u c i n g a c y l i n d r i c a l l y e x p l o d i n g wave, ( f i g . 5 - 1 ) . Upon r e a c h i n g the o u t e r ba se r a d i u s , the d e t o n a t i o n i s t u r n e d th rough a na r row c h a n n e l and f o r c e d t o imp lode to the apex o f the cone. In f i g u r e 5 - 1 , the t a p e r e d p a r t s o f the i n n e r and o u t e r chamber were d e s i g n e d to be r e p l a c e a b l e . Matched s e t s o f i n n e r and o u t e r cones were ma-c h i n e d f rom l a m i n a t e d l a y e r s o f l u c i t e f o r the f o l l o w i n g h a l f a n g l e s a t the apex : 9 0 , 80 , 70, 6 0 , 5 0 , 4 0 , 30 , and 15 d e g r e e s . A l l i n n e r cones h a d a base d i a m e t e r o f 10.40 c m . , and the d e f l e c t i o n c h a n n e l was ,17 cm. w i d e , The s p a c i n g between i n n e r and o u t e r c o n e s , measured p e r p e n d i c u l a r t o the s l a n t , was k e p t c o n s t a n t a t ,67 ~ . 0 4 cm, f o r a l l matched s e t s . The shock tube was a s i n g l e p i e c e o f l u c i t e t u b i n g 1,27 cm. i n s i d e d i a -m e t e r . A b r a s s r e f l e c t o r was p l a c e d i n the tube a p p r o x i m a t e l y one m e t e r f rom the d iaphragm to p r o d u c e a r e f l e c t e d s h o c k . A l l shock v e l o c i t y measurements were t aken w i t h a smear camera whose s l i t was f o c u s s e d a l o n g the tube a x i s v i a two l e n s e s . Due t o the s m a l l d i a m e t e r o f -47-F i g u r e 5-2 * ~ X F i g u r e 5-3 Smear photograph of the t e s t shook for tne ^ = 40 cone. R e f l e c t o r 1 meter from the diaphragm D r i v e r gas e q u i m o l a r o x y - a c e t y l e n e (550 T o r r ) T e s t gas argon (4 p a r t s ) a c e t y l e i e (1 p a r t ) a t 6 T o r r . Markers 1 cm. a p a r t . Sv/eep speed = 27.53 usec/cm. the t u b e , the shock was n o t e a s i l y d e t e c t e d . T h e r e f o r e , the s l i t w i d t h o f the camera was k e p t l a r g e and 10,000 A . S . A , p o l a r o i d f i l m was u s e d . F o r a l l measurements , the d r i v e r gas was 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 and the chamber was f i l l e d to 550 T o r r i n i t i a l p r e s s u r e , The t e s t gas was f o u r p a r t s a rgon mixed w i t h one p a r t a c e t y l e n e , n e c e s s a r y to make the t e s t shock d e t e c t a b l e . M y l a r d iaphragms (.033 mm. t h i c k ) , were u sed t h r o u g h o u t . The d e t o n a t i o n was t r i g g e r e d f rom the smear camera e l e c t r o n i c s i n an i d e n t i c a l manner as i n C h a p t e r F o u r . 5-2 RELATIVE PERFORMANCE OF THE CONES OF DIFFERENT SLANT Shock v e l o c i t y measurements were made f o r a l l the m a t c h i n g s e t s o f i n n e r and o u t e r c o n e s . F o r t h e s e measurements , the t e s t gas p r e s s u r e was 6 T o r r . I t was f o u n d t h a t the Mach number i n c r e a s e d m o n o t o n i c a l l y as the h a l f ang l e a t the apex d e c r e a s e d , ( f i g . 5 - 4 ) . Improvement i n approach o f 50% was o b s e r v e d o v e r a c y l i n d r i c a l d r i v e r . I t i s p o s s i b l e , b e c a u s e o f f i n i t e W, t h a t some o f the improvement c o u l d be due t o the f a c t t h a t the d e t o n a t i o n i s more o v e r d r i v e n i n t he more t a p e r e d c o n e s . We can q u a n t i t a t i v e l y e s t i m a t e the magn i tude o f t h i s e f f e c t by assuming t h a t the s t a t e o f the d e t o n a t i o n a t the apex c o r r e s p o n d s t o the v a l u e a c h i e v e d when bp , ( eqn . 2 . 4 3 ) , i s g i v e n by r / s i n y) , where r i s the r a d i u s o f the shock t u b e . The c o r r e s p o n d i n g d i f f e r e n c e i n Cg and can then be c a l c u l a t e d and r e l a t e d t o the shock v e l o c i t y u s i n g e q n , 3 .13 . In t h i s c a l c u l a t i o n , we have assumed a shock i s r e f l e c t e d f rom the d i aphragm as f ound f o r i d e n t i c a l d iaphragms i n C h a p t e r F o u r . . The r e s u l t o f t h i s c a l -c u l a t i o n i s shown as the s o l i d l i n e i n f i g . 5 -4 , We have a d j u s t e d the a b -s o l u t e v a l u e o f t h i s c u r v e to the e x p e r i m e n t a l Mach number o f the $5 = 15 cone , s i n c e in. t h i s g raph we a r e m a i n l y c o n c e r n e d w i t h r e l a t i v e Mach numbers . The a b s o l u t e v a l u e can be o b t a i n e d f rom f i g . 5-5 i n w h i c h the 0 - 15 d r i ~ v e r i s compared w i t h t h e o r y , I t can be s e e n t h a t the f i n i t e w i d t h e f f e c t i s q u i t e s m a l l , i n d i c a t i n g t h a t the improvement i s m o s t l y due to the q u a l i -t a t i v e r e a s o n s s t a t e d . The measurements a l s o r e v e a l t h a t the a t t e n a t i o n o f the shock was much l e s s f o r the more t a p e r e d cones . W i t h the c y l i n d r i c a l d r i v e r , a t t e n a t i o n o f the shock v e l o c i t y became n o t i c e a b l e above an argon p r e s s u r e o f 30 T o r r , Comparable a t t e n a t i o n w i t h the = 15 d r i v e r took p l a c e o n l y above 60 T o r r . In f i g . 5-5 we have compared the 0 = .15 d r i v e r w i t h t h e o r y , I t can be s e e n t h a t the d i s c r e p a n c y between t h e o r y and. e x p e r i m e n t i s g r e a t e r than f o r the p l a n e d r i v e r . The r e a s o n f o r t h i s i s b e l i e v e d to be due to w a l l l o s -ses and boundary l a y e r e f f e c t s , s i n c e the t u b e " d i a m e t e r was o n l y h a l f t h a t o f the p l a n e d r i v e r . A l s o f o r the p l a n e d r i v e r , we were a b l e t o use the mea-s u r e d v a l u e o f the r e f l e c t e d shock, s p e e d r a t h e r than the c a l c u l a t e d . T h i s d i f f e r e n c e i n ^ s s m a H » however , the c a l c u l a t i o n o f the t e s t shock v e -l o c i t y i s q u i t e s e n s i t i v e to i t . 5-3 WIDTH OF THE CHANNEL In compar ing the p e r f o r m a n c e o f d r i v e r s o f d i f f e r e n t $ , the w i d t h o f the c h a n n e l was k e p t c o n s t a n t , T h e r e f o r e , t h e r e was no r e a s o n t o b e l i e v e t h a t the a r b i t r a r i l y chosen w i d t h w o u l d p r o d u c e optimum r e s u l t s . T h e o r e t i -c a l l y , the degree to w h i c h the d e t o n a t i o n i s o v e r d r i v e n depends s l i g h t l y on the c h a n n e l w i d t h , P r a c t i c a l l y , the c h a n n e l s h o u l d be w ide enough to l i m i t w a l l l o s s e s and to p r o v i d e a s u f f i c i e n t volume o f h e a t e d gas t o d r i v e the s h o c k . On the o t h e r h a n d , the c h a n n e l s h o u l d be n a r r o w enough t o f a c i l i t a t e u n i f o r m i g n i t i o n a t the cone b a s e . To i n v e s t i g a t e the i n f l u e n c e o f c h a n n e l w i d t h , two l u c i t e s p a c e r s were mach ined to f i t between the chamber back and o u t e r cone . These s p a c e r s p r o -v i d e d two a d d i t i o n a l c h a n n e l w i d t h s o f ,96 and 1.46 cm, f o r the *ft * 60 • cone . V e l o c i t y measurements r e v e a l e d t h a t the T-'ach-numbers p r o d u c e d by the -50-13 J2 M 11 10 F i g u r e 5-4 Mach number v e r s u s s l a n t a n g l e T e s t gas p r e s s u r e 6 T o r r . D r i v e r g a s . p r e s s u r e 550 T o r r finite W correc tion © <4 © © © @ W^67crn. © © '90° W° 70c 60° 50° 40° 30° 75 .22 20' n 56 I 72 8 & 2 [ 8 l _ _J 1 i L .01 .02 Figure 5-5 Mach number of the + cu~~, - r i v e , gas pressure T.l??* ^ i l ^ e r THEORY EXPERIMENT t h r e e d i f f e r e n t w i d t h s were w i t h i n the s t a n d a r d d e v i a t i o n , ( f i g . 5 - 4 ) . T h e r e f o r e , w i t h i n r e a s o n a b l e l i m i t s , the w i d t h o f the c h a n n e l does n o t seem i m p o r t a n t . In d e s i g n i n g a l a r g e d r i v e r , the above r e s u l t s w o u l d p r o b a b l y be more m e a n i n g f u l i f the w i d t h s were s c a l e d up i n p r o p o r t i o n t o the d r i v e r d i m e n s i o n s , 5-4 CONVERGING WIDTH DRIVER W h i l e the a c t u a l w i d t h o f the c h a n n e l does n o t appear t o be i m p o r t a n t , one s h o u l d e x p e c t a c o n v e r g i n g w i d t h t o i n f l u e n c e the shock s t r e n g t h . From e q u a t i o n 2,37 we see t h a t the degree t o w h i c h the d e t o n a t i o n i s o v e r d r i v e n the c h a n n e l d e c r e a s e s as the f r o n t n e a r s the d i a p h r a g m , we s h o u l d e x p e c t more o ve r c omp re s s i on . t ier cone . The w i d t h o f the c h a n n e l a t the t i p o f the i n n e r cone was a p p r o x i -ma te l y ,56 cm. F o r an a r gon p r e s s u r e o f 12 T o r r , a Mach number o f 1 0 . 5 1 - , 2 2 was o b t a i n e d , compared to 9 , 9 4 - 1 6 f o r the 30 matched p a i r ( a v e r a g e d o v e r 8 s h o t s f o r e a c h ) . A c o n v e r g i n g w i d t h c h a n n e l thus appear s v e r y w o r t h o f c o n -s i d e r a t i o n i n d e s i g n i n g a l a r g e d r i v e r , s i n c e i t r e d u c e s the r e q u i r e m e n t o f the l a r g e ba se r a d i u s n e c e s s a r y f o r r e a s o n a b l e o v e r c o m p r e s s i o n , 5-5 STRUCTURE OF THE IMPLODING FRONT NEAR THE APEX In the d e f l e c t i o n p l a t e t e c h n i q u e o f p r o d u c i n g c o n i c a l l y i m p l o d i n g d e -t o n a t i o n s , c e r t a i n q u e s t i o n s a r i s e . Some o f the more i m p o r t a n t o f t he se may b e ; What i s the s t r u c t u r e c f the i m p l o d i n g f r o n t i n the c h a n n e l and what t ake s p l a c e a t the apex o f c o l l a p s e ? S i n c e p h o t o g r a p h i c I n f o r m a t i o n w o u l d be d i f f i c u l t t o o b t a i n i n the d r i -ve i - , the I m p l o s i o n was s i m u l a t e d i n a p l a n e r e p l i c a o f the d r i v e r . In t h i s • r e p l i c a , a p l a n e d e t o n a t i o n was made to p r o p a g a t e i n a c h a n n e l o f r e c t a n g u l a r c r o s s - s e c t i o n o f u n i f o r m w i d t h (2^5 cm,) and depth (.63 cm, ) , , ( f i g , 5-6),, s c a l e s as C o n s e q u e n t l y , i f the w i d t h o f To i n v e s t i g a t e t h i s , we p a i r e d the o o - 30 o u t e r cone w i t h a 25 i n -I n t e r f r a m e d e l a y 2 j i s e c . E x t e r n a l d e l a y " 90 p.,sec. Exposure time 500 nanosec. F i g u r e 5-6 Schematic o f the c o n i c a l d r i v e r r e p l i c a and image c o n v e r t e r p h o t o g r a p h s a t the apex f o r (f = 55°. D e t o n a t i o n gas e q a i m o l a r o x y - a c e t y l e n e (300 T o r r ) , 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 i n t h i s geometry i s o n l y a p p r o x i m a t e l y s i -m i l a r t o t h a t i n the c o n i c a l d r i v e r s i n c e the f r o n t does n o t e x p e r i e n c e an a r e a r e d u c t i o n . The chamber f r o n t p l a t e was c o n s t r u c t e d o f 1.27 cm, t h i c k l u c i t e and the back p l a t e o f .63 cm. t h i c k a luminum, A vacuum s e a l was p r o v i d e d by a ga sket c u t f rom a s h e e t o f r u b b e r to f i t a round the p e r i m e t e r o f the cham-b e r . The l u c i t e i n s e r t s were r e p l a c e a b l e . P h o t o g r a p h s o f the d e t o n a t i o n f r o n t were taken w i t h a T..R.W. image c o n v e r t e r camera , (model 1 - D ) 4 f i t t e d w i t h a s u b m i c r o s e c o n d 5 frame p l u g -i n u n i t (model 2 6 - B ) , A T.R.W. t r i g g e r d e l a y g e n e r a t o r , (model 4 6 - A ) , was used t o o b t a i n p r o p e r t i m i n g . Rogowski c o i l F i g u r e 5-7 Image c o n v e r t e r s e t - u p . P h o t o g r a p h s o f the f r o n t a t the apex o f c o l l a p s e a re shown i n f i g , 5 -6 . I t can be seen t h a t the d e t o n a t i o n f r o n t i s o r i e n t e d p e r p e n d i c u l a r t o the channe l w a l l s . H ie p r o c e s s was f o u n d to be r e p r c d u c e a b l e w i t h i n a s e v e r a l m i l l i m e t e r j i t t e r , when the chamber was n o t l e a k i n g . I t wa s , how-e v e r , d i f f i c u l t t o get the two c o n v e r g i n g f r o n t s t o meet p r e c i s e l y a t the apex , s i n c e s ymmet r i c c o n s t r u c t i o n o f the a p p a r a t u s was much more d i f f i c u l t i n t h i s chamber. •55-SUMMARY OF RESULTS The e x p e r i m e n t a l r e s u l t s o f t h i s c h a p t e r r e v e a l t h a t : 1. The s t r e n g t h o f the t e s t shock i n c r e a s e s r o ' n c t o n i c a . l l y as (f) i s r e d u c e d , 2, O v e r d r i v i n g the d e t o n a t i o n i n c r e a s e s the shock v e l o c i t y . T h i s i s s u p p o r t e d by two f a c t s ; the c o n v e r g i n g w i d t h p r o d u c e d h i g h e r Mach numbers , and the y) = 15 d r i v e r p r o d u c e d s t r o n g e r shock s than the p l a n e d r i v e r (shown i n n e x t c h a p t e r ) . 3. C h a n n e l w i d t h i s n o t a c r i t i c a l p a r a m e t e r . 4, The f r o n t i s o r i e n t e d n o r m a l to the c h a n n e l w a l l s . CHAPTER S IX SURVEY OF SOKE DETONATION DRIVING TECHNIQUES H a v i n g s t u d i e d the o p e r a t i o n o f ou r d e t o n a t i o n d r i v e r s , i t i s i n t e r -e s t i n g to compare the p e r f o r m a n c e w i t h o t h e r combus t i on and d e t o n a t i o n shock wave g e n e r a t o r s , A f undamenta l p a r a m e t e r o f a d r i v i n g f a c i l i t y i s the range o f o b t a i n a b l e Mach numbers. F i g u r e 6-2 summar izes t he e x p e r i -m e n t a l Mach numbers o f some d e t o n a t i o n d r i v e r s . We have i n c l u d e d H u n i ' s / 1 4 / and o u r r e s u l t s as w e l l as some f rom d e t o n a t i o n d r i v e r s u sed by Lee / 2 9 / , and Coates and Gaydon / 2 0 / , The d a t a o f Nagamatsu e t a l / 3 0 / , wa3 i n c l u d e d as a compar i s on between d e t o n a t i o n and c o n s t a n t volume combus t i on o f an o x y - h y d r o g e n p l u s h e l i u m m i x t u r e , w h i c h they u sed to d r i v e shock s i n -t o a i r . The d r i v e r s used by Lee and Coa te s w i l l r e q u i r e a b r i e f e x p l a n a t i o n , Lee used a p l a n e d r i v e r w i t h the same t e s t and d e t o n a t i o n gas t h a t was u sed i n o u r work . However, he i g n i t e d the d e t o n a t i o n a t the d i a p h r a g m , i n w h i c h case t h e r e wou ld be l i t t l e o r no c o n t r i b u t i n g dynamic p r e s s u r e b e h i n d the f r o n t . The d r i v e r used by Coates and Gaydon u s e d a 3H£ + 0 2 d e t o n a t i o n mix-t u r e and a rgon as a t e s t gas . The d e t o n a t i o n s t a g e was p r e c e d e d by a h i g h p r e s s u r e c o l d hydrogen s e c t i o n , ( f i g . 6 - 1 ) . #1 c o l d H. d e t o n a t i o n m i x t u r e Argon F i g u r e 6-1 The d r i v e r used by Coa tes and Gaydon Shock waves i n the t e s t s e c t i o n were p r o d u c e d by two d i f f e r e n t methods. In the f i r s t o r p r i m a r y d e t o n a t i o n method, the d e t o n a t i o n m i x t u r e was i g n i t e d i r e c t l y f rom the shock p r o d u c e d by the b r e a k i n g o f d i aphragm #1. W i t h t h i s i n d u c t i o n method, i t i s p o s s i b l e t o o v e r d r i v e the d e t o n a t i o n i f the hydrogen -58-p r e s s u r e i s much g r e a t e r than the p r e s s u r e o f the d e t o n a t i o n m i x t u r e . They r e p o r t e d t h a t a t t e m p t s t o use o v e r d r i v e n d e t o n a t i o n s were u n s u c c e s s f u l b e -cause o f wave i n t e r a c t i o n s due t o f i n i t e b r e a k i n g t imes o f the s e c o n d d i a -phragm. In the s e c o n d , o r r e t o n a t i o n method , the shock p r o d u c e d by the r u p t u r e o f d iaphragm ill was s u f f i c i e n t l y weak s o t h a t the d e t o n a t i o n m i x t u r e w o u l d n o t i g n i t e u n t i l t h i s shock was r e f l e c t e d f rom d iaphragm #2, T h i s method p r o -duced the s t r o n g e s t shocks i n the t e s t s e c t i o n , T h i s d r i v i n g method seems t o be v e r y e f f e c t i v e , b u t i t does have a drawback i n t h a t the p r e s s u r e o f the d e t o n a t i o n m i x t u r e must be q u i t e low ( < 200 T o r r ) , s i n c e h i g h e r p r e s s u r e s w o u l d r e q u i r e e x t r e m e l y l a r g e c o l d h y d r o g e n p r e s s u r e s ; ( 3* 10 a t m o s p h e r e s ) . The a c t u a l p e r f o r m a n c e o f t h i s d e v i c e i s a m a t t e r o f i n t e r p r e t a t i o n , so i n f i g . 6 - 2 , we have g raphed the Mach number as a f u n c t i o n o f the t e s t to d e t o n a t i o n gas p r e s s u r e r a t i o ( b roken c u r v e ) , and a l s o the t e s t t o c o l d h y -drogen r a t i o ( s o l i d l i n e ) , 6-1 POTENTIAL MACH NUMBERS OF IMPLODING DETONATION DRIVERS From the t h e o r y o f C h a p t e r s Two and T h r e e , we are a b l e t o p r e d i c t t he Mach numbers o b t a i n a b l e from o v e r d r i v e n d e t o n a t i o n s , S i n c e the deg ree t o wh i ch the d e t o n a t i o n i s o v e r d r i v e n s c a l e s as the r a t i o o f d r i v e r t o shock tube d i a m e t e r , t h i s r a t i o i s an i m p o r t a n t c o n s i d e r a t i o n f o r the d e s i g n o f a l a r g e d r i v e r . In f i g u r e s 6-3 and 6-4 we have i n c l u d e d some p r e d i c t e d Mach numbers f o r v a r i o u s r a t i o s o f d r i v e r t o tube d i a m e t e r . Our e x p e r i m e n t a l r e -s u l t s i n d i c a t e t h a t these p r e d i c t e d Mach numbers a re p r o b a b l y about 20 to 40% too h i g h , depend ing on the shock tube d i a m e t e r . The graphs were o b t a i n e d f rom i t e r a t i v e s o l u t i o n s o f e q u a t i o n 3 ,13 , u s i n g the computer . The d r i v e r gas was assumed to be e q u i l m o l a r o x y - a e e t y l e n e , and the t e s t gas a r g o n . R e a l gas e f f e c t s i n argon / 7 / , were a c c o u n t e d f o r t o make the p r e d i c t i o n s as r e a l -i s t i c as p o s s i b l e . In each c a s e the o v e r c o m p r e s s i o n o f the d r i v e r gas was a s -sumed t o be the v a l u e p r e d i c t e d the i n s t a n t t h e f r o n t has c o n v e r g e d to t h e r a d - 5 9 -of the shock tube only. This should be the most conservative estimate of the degree to which the detonation i s overdriven. The predictions f o r both c o n i c a l channel ( i n f i n i t e s i m a l width) and hemispherical geometries -are included. The hemispherical or s p h e r i c a l sec-tor appears much more desirable, providing a method of uniform i g n i t i o n can be employed. The p o s s i b i l i t y of using a plane large diameter d r i v e r with a very gradual area reduction should d e f i n i t e l y be considered. In t h i s geo-metry, the area through which the gas flows i s quadratic with respect to the dr i v e r diameter. Providing that large gradients do not develop across the fr o n t , t h i s geometry i s e s s e n t i a l l y the same as a s p h e r i c a l sector. The predicted performance of a converging width c o n i c a l d r i v e r w i l l l i e between these extremes. ^ 0 " Figure 6 - 4 Mach number versus pressure r a t i o and diameter r a t i o f o r a spherical d r i v e r . -62-CHAFTER SEVEN . CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK The object of this thesis was to determine the f e a s i b i l i t y of produ-cing shock waves from overdriven detonations and i n v e s t i g a t e the impor-tance of d r i v e r geometry. We believe to have shown that overdriven deto-nations, as predicted, can be made to produce stronger shock waves than plane C.J, detonations. However, i f an implosion technique i s used to overdrive the detonation, i t was found that the geometry of the d r i v e r i s of major importance. Rather than state that a s p e c i f i c geometry i s d e f i n i t e l y optimum, we w i l l form some general conclusions. Our r e s u l t s i n d i c a t e that i t i s very important that the detonation front be as plane as possible as i t nears the diaphragm, and also the d r i v e r geometry be such that the gas v e l o c i t y imparted by the r a r e f a c t i o n wave i s i n the a x i a l d i r e c t i o n . This was de-duced, since the c o n i c a l geometry used i n th i s work i s more s a t i s f a c t o r y than c y l i n d r i c a l . I t i s obvious that a sector of a sphere would be the most desirable geometry of a l l , however, uniform i g n i t i o n of a detonation i n t h i s geometry w i l l not be without t e c h n i c a l d i f f i c u l t i e s , I f i t i s found that s p h e r i c a l geometry cannot be used, i t i s ray opinion that plane geometry with a very gradual area reduction would be optimum. I t seems quite f e a s i b l e to design and b u i l d a plane area reduction or s p h e r i c a l sector d r i v e r capable of producing Mach 50, For a 2.5 cm, shock tube diameter, this should be achieved by a 1 meter diameter d r i v e r f i l l e d to about 10 atmospheres i n i t i a l pressure (fox 1 Torr in. argon) . The only obvious l i m i t a t i o n of implosion drivers i s that they are re-s t r i c t e d to small diameter shock tubes. Class and Poinssot /31/ have re-ported that exploding a layer of PETH explosive at the stirface of a 20,3 cm, diameter hemisphere has produced Mach 95 i n a i r at 1 Torr, However, since -63-they used an 8 mm. diameter shock tube, the high Mach number was a v a i l a b l e only at the expense of tube diameter. SUGGESTIONS FOR FURTHER WORK In our i n v e s t i g a t i o n , our primary concern was Mach number. Another very important consideration i s shock attenuation. While detonation d r i -vers produce higher i n i t i a l Mach numbers than t h e i r combustion counterparts, constant volume, and constant pressure combustion, the presence of the rare-f a c t i o n wave behind the front causes the te s t shock to decay much more rapid-ly / l / , 111 I. In an implosion d r i v e r , the detonation becomes overdriven be-cause the area reduction e s s e n t i a l l y " f i l l s i n " the r a r e f a c t i o n wave. There-fore, i t would be i n t e r e s t i n g to in v e s t i g a t e the attenuation of shocks pro-duced by overdriven detonations. The construction of a large d r i v i n g f a c i l i t y would lead to some i n t e r -e s t i n g experiments concerning i t s operation. Also, i t should be capable of producing Mach numbers (^50), where there i s considerable need f or experi-mental work. -64™ BIBJ.mGRAPHY 1. A.G. Gaydon, B. H u r l e . The Shock Tube i n H i g h Tempera tu re C h e m i c a l P h y s i c s , Chapman Ha l 1 (London 1.963), 2. Y . B , Z e l d o v i c h , A .S , K o m p i n u t s , T h e o r y o f D e t o n a t i o n , A c a d . P r e s s , ( I 9 6 0 ) . 3. Y . B , Z e l d o v i c h , NAGA T . N . 1261, (19AO). 4. L. L a n d a u , L i f s h i t z , F l u i d Me e h , Pergamon P r e s s (1.959), 5. J . H . L e e , R. K n y s t a u t a n , G,G, B a c h , T h e o r y o f E x p l o s i o n s , A.F.o.S.P... S c i e n t i f i c R e p o r t , Her!. R e p o r t 69-10 (Nov, 1969) . 6. J . H . L e e , B.H.K. L e e , Phys.. o f F l u i d s , 8, 2148 , (.1965). 7. B, A h l b o r n , M. S a l v a t , N a t u r f o r s c h u n g 22a , 260 , (1.967). 8. B. A h l b o r n , J . - P . H u n i , J . A p p l . P h y s . 4 0 , 3402, ( 1969 ) , 9. B. A h l b o r n , J . - P . Huni, ' . AIAA J o u r n a l 7, 1.191, (1969 ) . 10. Y . B . Z e l d o v i c h , 3 .V. A y v a z o v , J . P . R . S . , 5735, ( 1 9 6 0 ) . 11. W. 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T r a n s a c t i o n s , 12, 2, ( S e p t . 1 9 6 9 ) . 24. D r e s n e r , J . A p p l . P h y s , , 4 1 , 797, ( 1 9 7 0 ) . -65-25. H . F . W a l d r o n , U T I A S ' R e p o r t 5 0 , (1958), 26. Y . B . Z e l d o v i c h , Y . P . R a i s e r , Acad . P r e s s London (1966 ) . 27 . 1,1, G l a s s , J . G , H a l l , Handbook o f S u p e r s o n i c A e r o d y n a m i c s , s e c t i o n 1.8, Navord r e p o r t 1488, 6, ( 1 9 5 9 ) . 28. W. W a r r e n , G.J. H a r r i s , P r o c . 7 I n t . Shock Tube Symp. 143 , ( 1 9 6 9 ) . 29. B.K.H, ' Lee, AIAA J . V o l , 5 , 4, 791, ( 1967 ) . 30. II. T , Nagaraatsu e t a l , ARS J . 332, ( 1 9 5 9 ) . 31. I.I, G l a s s , J.C. Poinssot, P r o c . 7 I n t . Shook Tube Symp. 343, ( 1970 ) . 32. Gross e t a l , Phy . Rev. L e t 2 5 , 5 7 5 , (.1970). 33. B, A h l b o r n , H. S a l v a t , IPP 3/2 , (1962) , 34. J.D. S t r a c h a n e t a l , J. F l u i d Mech, 4 3 , 3, 478 , ( 1970 ) , 35. M, P h i l l i p s , P h . D. T h e s i s UBC, ( 1965 ) . 36. H. O e r t e l l , Strossrohre, S p r i n g e r - V e r l a g , W i e n - Ma-v Y o r k , ( 1966 ) . APPENDIX A -66-W.AVE INTERACTION D^SCF.IPTTON OF WEAK DIAPHRAGM DRIVE? Xhe x - t d i ag ram i l l u s t r a t i n g t h i s t ype o f d iaphragm o p e n i n g p r o c e s s i s shown i n f i g u r e 3-]. A, T h i s s i t u a t i o n . i s i d e n t i c a l t o the d e l a y e d d i a -phragm o p e n i n g p r o c e s s e x c e p t tha t Reg ion 3 i s no l o n g e r p r e s e n t . E q n s , 3 . 1 , 3 , 2 , 3 .3 , 3 ,5 , and 3,6 remain unchanged. E q n s , 3 .4 , 3 , 5 , and 3.6 a re o m i t t e d , and e q n . 3.9 becomes : u 2 i-p3) *n J U s i n g the f a c t t h a t Pg - PA, , and e q n s . 3,2 and 3.6 we h a v e : From e q n , 3.13 and 3 . 1 , r e c a l l i n g t h a t » we h a v e : C>2 i s - o b t a i n e d from eqn , 3,2 and 3 , 3 , whence : In e q n , A . 3 , we have k e p t o n l y the x component o f p a r t i c l e v e l o c i t y F o r a p l a n e d r i v e r o r a cone, w i t h s m a l l (f) , t h i s s h o u l d p r e s e n t no p r o b l e m s , However, i f we assume t h a t o n l y the x component o f p a r t i c l e v e l o c i t y i s r e t a i n e d f o r a cone o f l a r g e 0 , we must assume t h a t the r a -d i a l component i s e i t h e r , consumed i n t u r b u l e n t ' f l o w , o r t r a n s f o r m e d i n t o h e a t i n the fo rm o f a r e f l e c t e d s h o c k . T h i s p r o b a b l y means t h a t the v a i l - . d i t y o f t h i s model, i s much i n q u e s t i o n when (f) is l a r g e , The above e x p r e s s i o n can a l s o be s i m p l i f i e d c o n s i d e r a b l y w i t h the s t r o n g shock a p p r o x i m a t i o n , Eqn , A ,3 then becomes : and ^ " / / ^ a r e now g i v e n b y : Pz P. 1%+1 f%HJ From t h i s i t can be seen t h a t the Mach number o f the t e s t shock i s , as b e f o r e , a m o n o t o n i e a l l y i n c r e a s i n g f u n c t i o n o f t^/pg s n c i fi • t n e extreme case where ^ ' ° ° » the v e l o c i t y i s g i v e n b y : COMPARISON OF THE TWO DIFFERENT DIAPHRAGM OPENING PROCESSES We have i n c l u d e d some p l o t t e d r e s u l t s o f e q n s , 3.1.3 and A,4 to i l l u s -t r a t e how the i d e a l v e l o c i t y o f the t e s t shock depends on the v a r i o u s p a r a -m e t e r s , The v e l o c i t y p r e d i c t e d by b o t h d i aphragm o p e n i n g p r o c e s s e s are com-p a r e d on each g r a p h . I t i s i n t e r e s t i n g t h a t the d e l a y e d o p e n i n g i s the more f a v o u r a b l e than ' i n s tan t an ions f o r C . J . o r vreak.ly o v e r d r i v e n d e t o n a t i o n s , F o r a s t r o n g l y o v e r d r i v e n d e t o n a t i o n c r a shock wave , the .-ins tantanccus - o p e n i n g i s more f a -v o u r a b l e a t h i g h t e s t gas p r e s s u r e s . At low t e s t gas p r e s s u r e s , both, o p e n i n g p r o c e s s e s p r e d i c t about the same v e l o c i t y . U n t i l a d iaphragm t h a t r u p t u r e s v e r y e a s i l y i s f o u n d , the above c o m p a r i -son i s o n l y o f academic i n t e r e s t . However , s i n c e l i t t l e o r no p r e s s u r e d i f -f e r e n c e i s r e q u i r e d a c r o s s t h e _ d i a p h r a g m , i t seems r e a s o n a b l e t h a t one c o u l d be f o u n d , The compar i son o f t he se two p o s s i b i l i t i e s c o u l d . t h e n be e x p e r i m e n -t a l l y i n v e s t i g a t e d , p r o v i d i n g d e p a r t u r e s f rom i d e a l b e h a v i o u r are s m a l l , o r i d e n t i c a l , f o r b o t h o p e n i n g p r o c e s s e s . SHOCK WAVE (p=2) 3 2 1 3-9^1.66 O 0 A - 2 WEAK DIAPHRAGM REFLECTED SHOCK LOG, P / to 4 6 - 7 0 -APPENPIX B A. d e t a i l e d d e s c r i p t i o n of -the experimental apparatus i s given here, THE CONICAL CHA?-«BER A f u l l scale section of the coni c a l d r i v e r i s shown i n f i g , B - l , In this chamber, the d e f l e c t i o n plate was fastened to the chamber back by means of screws which passed through eight double wedge-shape spacers. The spacers were used to separate the d e f l e c t i o n plate from the chamber back. The wedge shape was chosen to minimize perturbations on the explo-ding wave. The inner cones were fastened to. the d e f l e c t i o n plate by means of two screws, In order to tighten these screws, i t was necessary to have two holes i n the back of the chamber, which, a f t e r attachment of the inner cone, were sealed with vacuum plugs. The back of the chamber and the d e f l e c t ! O i l p.I.cl te were constructed of l u c i t e . The front plate was made of .64 cm. thick brass p l a t e with a 1.27 cm. diameter hole at the centre. The chamber back and front plate wore b o l -ted together with s i x long pieces of threaded rod. The diaphragm was held between the brass front plate, and a l u c i t e d i s c glued to the shock tube. On each side of the diaphragm an 0 r i n g s e a l provided a vacuum. The l u c i t e d i s c was held to the chamber by means of two screws mounted i n the fronti p l a t e . Wing nuts were used to clamp the d i s c . The detonation was i g n i t e d by a spark gap which was discharged a x i a l l y across the centre of the c y l i n d r i c a l back sect i o n , The return path of the current was symmetric to reduce j X B forces, GENERAL LAY-OUT AND TRIGGERING CIRCUIT Fig , B-2 shows the layout of the apparatus. The mixing tank i s a 4 inch diameter IS inch long brass cylinder,. For safety measures, i t was en-, closed i n an open ended double layer c y l i n d e r of heavy wire mesh, (Jg'Wr.h,• }i wire), The 0 to 2 arm. pressure gauge was used f o r the mixing tank; the -71-0 to 1 atm, f o r the chamber, The t r i g g e r i n g c i r c u i t i s shown i n f i g . B -3 , The c i r c u i t and power s u p p l y are c a p a b l e o f h a n d l i n g .2.0 KV, however , i t was n e v e r n e c e s s a r y to use. more than 12 KV to i g n i t e the d e t o n a t i o n . The c i r c u i t was t r i g g e r e d , by a p u l s e f rom a t h y r a t r c n Thedphanus u n i t ; V Section A-A Section B-B Mixing Tank Pump Figure B-2 General l a y - out. <§) valves -76-I 777 j SPI « 5 V& M k f i y - J c ^ 7> '9 rn rh rry rh /77 A - Microammeter„ 0-100 micro-amps. H.V.- Sorenson power s u p p l y , 20KV, 30mA. 51- C h a r g i n g s o l e n o i d . 52- S h o r t i n g s o l e n o i d . R I - C h a r g i n g r e s i s t e r 100 K R2- Dump r e s i s t e r 5 K R3- Meter r e s i s t e r 500 M R4- B i a s r e s i s t e r 300 M C - C a p a c i t o r 1.6 u f , 20KV T - . T r a n s f o r m e r I ; I SPI T r i g g e r can SP2 Spark gap o f chamber F i g u r e B-3 High v o l t a g e c i r c u i t f o r i g n i t i n g t h e d e t o n a t i o n 

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