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UBC Theses and Dissertations

Electrical power generation from standing shock waves Pearson, John Beverly 1979

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ELECTRICAL POWER GENERATION FROM STANDING SHOCK WAVES by JOHN BEVERLY PEARSON B . S c , Queen's U n i v e r s i t y , 1976 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department o f Phys i cs ) We accept t h i s t h e s i s as conforming to the r e q u i r e d s tandard THE UNIVERSITY OF BRITISH COLUMBIA December 1979 (c)John Beve r l y Pearson , 1979 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Phy s i c s  The University of Brit ish Columbia 2 0 7 5 Wesbrook Place Vancouver, Canada V6T 1W5 Date December 31, 1979 i i ABSTRACT S t a n d i n g s h o c k waves i n a s u p e r s o n i c f l o w f i e l d p r o d u c e d e n s i t y g r a d i e n t s a c r o s s w h i c h an e l e c t r i c a l p o t e n t i a l i s e s t a b l i s h e d . I f e l e c t r o d e s a r e mounted u p s t r e a m and d o w n s t r e a m o f t h e s t a n d i n g s h o c k , an e l e c t r i c a l c u r r e n t c a n be e x t r a c t e d . The e l e c t r i c a l power o u t p u t by s u c h a s y s t e m ( c a l l e d a bow s h o c k g e n e r a t o r ) h a s been m e a s u r e d . To p r o d u c e t h e s u p e r s o n i c f l o w an o v e r d r i v e n d e t o n a t i o n s h o c k t u b e , c a p a b l e o f p r o d u c i n g Mach 12 s h o c k s i n 5 T o r r a r g o n , was c o n s t r u c t e d and u s e d as a s h o r t d u r a t i o n s u p e r s o n i c w i n d t u n n e l . The open c i r c u i t v o l t a g e o f a s i n g l e bow s h o c k g e n e r a t o r w i t h a 2 cm e l e c t r o d e s e p a r a t i o n was m e a s u r e d t o be 0.95 V, and t h e maximum power o u t p u t t o 53 mW. By r e d u c i n g t h e e l e c t r o d e s e p a r a t i o n t o 1 cm t h e maximum power o u t p u t was i n c r e a s e d t o 90 mW, w h i l e t h e open c i r c u i t v o l t a g e r e m a i n e d u n c h a n g e d . I t was f o u n d t h a t when two bow s h o c k g e n e r a t o r s a r e mounted s i d e by s i d e i n t h e f l o w a p a r a l l e l c o n n e c t i o n o f t h e i r o u t p u t s p r o d u c e d a s m a l l i n c r e a s e i n c u r r e n t . However no i n c r e a s e i n o u t p u t v o l t a g e was o b s e r v e d when t h e g e n e r a t o r s were c o n n e c t e d i n s e r i e s . I t was a l s o f o u n d t h a t when an o b l i q u e s h o c k and i t s r e f l e c t i o n f r o m t h e w a l l were c o n n e c t e d t o g e t h e r i n s e r i e s , t h e o u t p u t v o l t a g e was l e s s t h a n t h a t o f t h e o b l i q u e s h o c k a l o n e . However t h i s was l i k e l y due t o a s h o r t c i r c u i t p a t h b e t w e e n t h e e l e c t r o d e s t h r o u g h t h e b o u n d a r y l a y e r . Some o f t h e m e a s u r e m e n t s were i n c o n c l u s i v e due t o an i n s u f f i c i e n t l y l o n g t e s t t i m e . A p r e l i m i n a r y a n a l y s i s was i i i done on a system i n which a set of bow shock ge n e r a t o r s i s used as a topping system f o r a c o n v e n t i o n a l e l e c t r i c a l g e n e r a t i o n system. I t was shown that the bow shock ge n e r a t o r s must be operated at very low Mach numbers i f they are to be e f f i c i e n t i n t h i s a p p l i c a t i o n . i v TABLE OF CONTENTS A b s t r a c t i i T a b l e Of C o n t e n t s i v L i s t Of T a b l e s v i i L i s t Of F i g u r e s v i i i A c k n o w l e d g e m e n t s x i 1. INTRODUCTION 1 1.1 P r i n c i p l e Of The Bow Shock G e n e r a t o r 1 2. PRODUCTION OF A SUITABLE TEST FLOW WITH AN OVERDRIVEN DETONATION SHOCK TUBE 6 2.1 S u p e r s o n i c F l o w B e h i n d A Shock Wave 7 2.2 The R e q u i r e m e n t Of I o n i z a t i o n I n c r e a s e A c r o s s The S t a n d i n g S h o c k 11 2.3 The D i a p h r a g m Shock Tube 15 2.4 O v e r d r i v e n D e t o n a t i o n Shock Tube 20 2.5 Summary 23 3. CONSTRUCTION AND DEVELOPMENT OF THE SHOCK TUBE 24 3.1 C o n s t r u c t i o n Of The Shock Tube 24 3.1.1 The F a c i l i t y 24 3.1.2 D r i v e r S e c t i o n 26 3.1.3 I g n i t i o n S y s t e m 29 3.1.4 S h o c k Tube 29 3.1.5 Pumping And F i l l i n g S y s t e m s 30 3.1.6 T e s t S e c t i o n 31 3.1.7 Pressure Probe Flanges 34 3.2 Measurements 35 3.2.1 Dependence Of The Shock Speed On The F i l l Gas Pressures 36 3.2.2 Dependence Of The Shock Speed On P o s i t i o n ... 39 3.2.3 The X-T Diagram For The Shock Front 43 3.2.4 Smear Camera Measurements 43 3.2.5 Test Time 48 3.3 Summary 49 4. CONSTRUCTION OF GENERATOR TEST SYSTEMS 51 4.1 P a r a l l e l Shock Generators 51 4.2 R e f l e c t e d Shock Generators 55 4.3 P r o v i s i o n s For Generator Connections And Power Measurement 58 5. EXPERIMENTS 59 5.1 I n d i v i d u a l Shock Generator Experiments 61 5.2 S e r i e s Connected Shock Generators 70 5.3 P a r a l l e l Connected Shock Generator 72 5.4 R e f l e c t e d Oblique Shock Generator 74 6. INTERPRETATION OF RESULTS 7 9 6.1 Summary Of R e s u l t s 79 6.2 Shock Angle 81 6.3 Open C i r c u i t Voltage 83 6.4 I n t e r n a l R e s i s t a n c e 88 6.5 Bottom Shock 91 6.6 S e r i e s Connection 92 v i 6.7 P a r a l l e l Connection 93 6.8 Reflected Oblique Shock 94 7. EFFECTIVENESS AND SYSTEM ANALYSIS 97 8. CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK 107 8.1 Summary And Conclusions 107 8.2 Suggestions For Future Work 110 Bibliography 112 Appendix A. Calculation Of The Thermodynamic State Behind An Ionizing Shock 114 Appendix B. Available Energy Loss In Bow Shock Generators And Mixing 116 B.l Incident Flow Parameters 116 B.2 Standing Shock Jump 117 B.3 Energy Extracted By The Generator 117 B.4 Available Energy L o s s l n Generator 120 B.5 Available Energy Loss In Mixing 121 v i i L I S T OF T A B L E S T a b l e I 88 v i i i LIST OF FIGURES FIGURE PAGE .1.1 A r e p r e s e n t a t i o n of the s t r u c t u r e of an i o n i z i n g shock f r o n t 2 1.2 The two geometries used t o i n v e s t i g a t e m u l t i p l e shock connections 4 2.1 The flow across a shock f r o n t 8 2.2 The l o c a l Mach number of the shock heated gas as a f u n c t i o n of the shock Mach number (M^) 10 2.3 F r a c t i o n a l i o n i z a t i o n of a gas with an i o n i z a t i o n (a) as a f u n c t i o n of temperature.... 12 2.4 Temperature (T^) and degree of i o n i z a t i o n ( c ^ ) i n the flow behind a shock wave i n argon. The f i g u r e s on the graphs are the i n i t i a l pressure ahead of the shocks 14 2.5 The diaphragm shock tube 16 2.6 The r e l a t i o n s h i p between diaphragm pressure r a t i o (p^/p.) and Mach number (M^) shown f o r a v a r i e t y o f sound speed r a t i o s (a^/a^) 18 2.7 An a x i a l s e c t i o n of the shock tube d r i v e r (schematic). 21 2.8 A smear camera photograph of one s e c t o r of a c y l i n d r i c a l imploding detonation. 22 3.1 Schematic diagram of the shock tube system 25 3.2 Cross s e c t i o n o f the d r i v e r 27 3.3 D e t a i l of the acetate diaphragm 28 3.4 The t e s t s e c t i o n w i t h removable l i d s 32 3.5 Cross s e c t i o n of the t e s t s e c t i o n 33 3.6 The pressure probe flange 34 3.7 The shock speed measured f o r va r i o u s f i l l gas pressures 37 3.8 A t y p i c a l smear camera photograph 38 3.9 A t y p i c a l p a i r . o f pressure s i g n a l s used f o r shock r . • ' . speed measurements 40 i x F I G U R E : P A G E 3 . 1 0 S h o c k s p e e d a s a f u n c t i o n o f d i s t a n c e f r o m t h e d i a p h r a g m . T h e m a g n i t u d e o f t h e p r e s s u r e p r o b e s i g n a l i m m e d i a t e l y b e h i n d t h e s h o c k ( V ) i s s h o w n . T h e d o t t e d l i n e i s t h e t h e o r e t i c a l v a l u e o f V c a l c u l a t e d f r o m t h e s h o c k s p e e d . R e p r e s e n t a t i v e p r e s s u r e p r o b e s i g n a l s f r o m t h r e e l o c a t i o n s a l o n g t h e t u b e a r e a l s o s h o w n . 41 3 . 1 1 T h e X - T d i a g r a m f o r t h e s h o c k w a v e 44 3 . 1 2 T h e a p p a r a t u s u s e d t o c h e c k t h e i n t e r p r e t a t i o n o f t h e s m e a r c a m e r a p h o t o g r a p h s . . . . 45 3 . 1 3 A t y p i c a l s m e a r c a m e r a p h o t o g r a p h u s e d t o c h e c k t h a t t h e f i r s t f a i n t l u m i n o s i t y w a s t h e s h o c k 46 3 . 1 4 P h o t o d e n s i t o m e t e r r e c o r d s o f t w o s m e a r c a m e r a p h o t o g r a p h s f o r i d e n t i c a l i n i t i a l c o n d i t i o n s . . . . 47 3 . 1 5 T e s t t i m e a s a f u n c t i o n o f p o s i t r o n i n t h e s h o c k t u b e 50 4 . 1 S c h e m a t i c d i a g r a m ( c r o s s s e c t i o n ) o f p a r a l l e l s h o c k g e n e r a t o r s , 52 4 . 2 A c r o s s s e c t i o n o f t h e p a r a l l e l s t a n d i n g s h o c k g e n e r a t i n g s y s t e m . 53 4 . 3 S c h e m a t i c d i a g r a m o f t h e r e f l e c t e d s h o c k r.-: • :"4 c o n f i g u r a t i o n 56 4 . 4 A c r o s s s e c t i o n o f t h e r e f l e c t e d s h o c k g e n e r a t o r s y s t e m 57 5 . 1 S i n g l e s t a n d i n g s h o c k g e n e r a t o r s t r e t c h i n g a c r o s s t h e w h o l e t u b e . 61 5 . 2 S i n g l e s h o c k g e n e r a t o r r e s u l t s 63 5 . 3 S m e a r c a m e r a p h o t o g r a p h o f t h e s l u g o f t e s t g a s t a k e n 9 0 c m . f r o n t h e d i a p h r a g m 64 5 . 4 V-I c h a r a c t e r i s t i c f o r t w o i n d i v i d u a l g e n e r a t o r s 65 5 . 5 P o w e r o u t p u t v s c u r r e n t f o r t w o i n d i v i d u a l g e n e r a t o r s . . 66 5 . 6 C o n f i g u r a t i o n a n d e l e c t r o d e n u m b e r s f o r t h e t w o w e d g e b o w s h o c k g e n e r a t o r e x p e r i m e n t s . 67 5 . 7 Two w e d g e o p e n c i r c u i t v o l t a g e ( a c r o s s 1009.) a n d f r a m i n g c a m e r a p i c t u r e s 68 5 . 8 Two o f t h e c o n f i g u r a t i o n s t h a t w e r e t r i e d w h i l e a t t e m p t i n g t o i m p r o v e t h e b o t t o n s h o c k s i g n a l 69 X FIGURE PAGE 5.9 The s e r i e s connec t ion exper iments 71 5.10 Loading o f the genera tors used f o r the p a r a l l e l connec t ion exper iments 73 5.11 Output o f s i n g l e genera tor compared to output o f p a r a l l e l connec t ion o f both g e n e r a t o r s . . . . . . . . . 74 5.12 A comparison o f the r e s u l t s o f the r e f l e c t e d shock ; - . o r . s e r i e s a d d i t i o n s i g n a l and the e a r l y s i n g l e shock exper iments 76 5.13 The r e f l e c t e d ob l i que shock vo l t age 78 6.1 Obl ique shock 82 6.2 The model used f o r the shock s t r u c t u r e . . . . . . . 86 6.3 S e r i e s connected shocks . 93 6.4 A comparison of the r e f l e c t e d shock experiment and the f l o o r mounted wedge experiment 95 7.1 An example o f a combined bow shock and conven t i ona l t u r b i n e genera t ion system. . 98 7.2 A comparison o f the a v a i l a b l e energy l o s t from one gram o f hot i npu t gas (AA) i n both the c o o l i n g p rocesses (bow shock genera tor and mix ing) as a f u n c t i o n o f the Mach number at which the genera tor i s run (M ) . . . . . . . . 103 7.3 Energy e x t r a c t e d (e) and e f f e c t i v e n e s s o f a bow shock genera tor as a f u n c t i o n o f Mach number (M^) 104 7.4 A v a i l a b l e energy f low i n the shock genera tor p l u s conven t iona l generator system compared to tha t i n the mix ing p l us conven t i ona l genera tor system 105 B . l Bow shock generator reg ions 118 B.2 The mix ing process 123 x i ACKNOWLEDGEMENTS I would l i k e to express my thanks to my s u p e r v i s o r , Dr. B. Ahlborn, f o r suggesting t h i s p r o j e c t and f o r h i s he l p and encouragement throughout the work. I would a l s o l i k e to thank Dr. F. Curzon f o r h i s h e l p f u l d i s c u s s i o n s and h i s suggestions during the completion of t h i s work. Also a l l the members of the Plasma P h y s i c s Group, f a c u l t y members and students a l i k e , were always w i l l i n g to d i s c u s s problems and o f f e r encouragement. A. Cheuck has been very good at d e s i g n i n g and b u i l d i n g e l e c t r o n i c equipment f o r the shock tube and f o r d i a g n o s t i c s . His w i l l i n g n e s s to provide prompt a t t e n t i o n i n the r e p a i r or adjustment of any equipment was most a p p r e c i a t e d . I a l s o wish to thank the members of the main machine shop, p a r t i c u l a r l y Mr. P. Hass and Mr. 0. C h r i s t i a n s e n , f o r the machining of the shock tube and the d r i v e r s e c t i o n and Mr. C. Sedger of the student shop f o r h i s a s s i s t a n c e and suggestions throughout the p r o j e c t . F i n a l l y I wish to thank my w i f e , J anet, f o r her a s s i s t a n c e i n the p r e p a r a t i o n of t h i s r e p o r t . 1 CHAPTER 1 . INTRODUCTION 1.1 P R I N C I P L E OF THE BOW SHOCK GENERATOR The e x i s t e n c e o f s p a c e c h a r g e l a y e r s a n d e l e c t r i c f i e l d s i n s i d e i o n i z i n g s h o c k f r o n t s h a s b e e n known f o r some t i m e and a number o f e x p e r i m e n t s h a v e m e a s u r e d t h e v o l t a g e a c r o s s a 1 2 f r e e r u n n i n g s h o c k » . I n a f r e e r u n n i n g s h o c k t h e m o v i n g s p a c e c h a r g e l a y e r 3 a l s o h a s a m a g n e t i c f i e l d a s s o c i a t e d w i t h i t . An u n d e r s t a n d i n g o f t h e s e f e a t u r e s o f s h o c k f r o n t s i s i m p o r t a n t t o a v a r i e t y o f f i e l d s i n c l u d i n g l a s e r f u s i o n e x p e r i m e n t s , 4 s t e l l a r f o r m a t i o n , and d i r e c t e n e r g y c o n v e r s i o n . The v o l t a g e a c r o s s t h e s h o c k a r i s e s b e c a u s e o f t h e s t r o n g p r e s s u r e and i o n i z a t i o n g r a d i e n t s i n t h e s h o c k f r o n t . D r i v e n b y t h e s e g r a d i e n t s t h e e l e c t r o n s b e h i n d t h e s h o c k d i f f u s e f o r w a r d away f r o m t h e r e g i o n o f h i g h c o n c e n t r a t i o n . B e c a u s e t h e i o n s h a v e a much l o w e r m o b i l i t y , t h e y r e m a i n more o r l e s s f i x e d and a c h a r g e s e p a r a t i o n d e v e l o p s . An e q u i l i b r i u m i s r e a c h e d when t h e e l e c t r i c f i e l d i n d u c e d b y t h e c h a r g e s e p a r a t i o n b a l a n c e s t h e g r a d i e n t t e r m d r i v i n g t h e d i f f u s i o n . T h i s e l e c t r i c f i e l d embedded i n t h e s h o c k f r o n t r e s u l t s i n a p o t e n t i a l d i f f e r e n c e a c r o s s t h e s h o c k . A r e p r e s e n t a t i o n o f t h e v a r i a t i o n o f t h e s e q u a n t i t i e s a c r o s s a s h o c k f r o n t i s shown i n F i g u r e 1.1 4„ . , SHOCK PROPAGATING TO THE LEFT e ( n r n e ) where p = pressure of the gas p = density of the gas _ rr n.= ion number density 1 n = electron number density e E = e l e c t r i c f i e l d V V = voltage or p o t e n t i a l F i g u r e 1.1 A r e p r e s e n t a t i o n o f t h e s t r u c t u r e o f an i o n i z i n g s h o c k f r o n t I n o r d e r t o make m e a s u r e m e n t s o f t h e e l e c t r o m a g n e t i c e f f e c t s more e a s i l y a s h o c k f r o n t w h i c h i s s t a t i o n a r y i n t h e l a b f r a m e w o u l d be d e s i r a b l e . S u c h a s h o c k may be g e n e r a t e d b y d i r e c t i n g a s u p e r s o n i c g a s f l o w o n t o a f i x e d o b s t a c l e t o c r e a t e a s t a n d i n g bow s h o c k . The v o l t a g e a c r o s s t h e s h o c k c a n e a s i l y be m e a s u r e d by p l a c i n g one e l e c t r o d e on e a c h s i d e o f t h e s t a n d i n g s h o c k . F u r t h e r m o r e , i f t h e s e e l e c t r o d e s a r e c o n n e c t e d t o a l o a d t h e p o t e n t i a l a c r o s s t h e s h o c k c a n be made t o d r i v e a c u r r e n t t h r o u g h t h e l o a d . I n t h i s way a s t a n d i n g s h o c k c a n be u s e d t o e x t r a c t e l e c t r i c a l e n e r g y d i r e c t l y f r o m a f l o w o f h o t g a s . S u c h a d e v i c e i s t e r m e d a "bow s h o c k g e n e r a t o r " 5 . The v o l t a g e o u t p u t o f a bow s h o c k g e n e r a t o r h a s 3 been measured**»° and was found to be t y p i c a l l y about 1 v o l t . These p a r t i c u l a r measurements a l s o i n d i c a t e d a short c i r c u i t c u r r e n t of approximately 100mA. A bow shock generator can i n p r i n c i p l e operate i n a temperature regime w e l l above the range of c o n v e n t i o n a l thermodynamic engines such as t u r b i n e s . T h i s i s a temperature regime where to date o n l y Magnetohydrodynamic machines have been proposed f o r d i r e c t energy c o n v e r s i o n . In order to make the bow shock generator a p r a c t i c a l d e v i c e f o r the d i r e c t c o n v e r s i o n of e l e c t r i c a l power one would l i k e to in c r e a s e the output v o l t a g e or c u r r e n t . The aim of t h i s t h e s i s was to see i f t h i s c ould be done by connecting together the outputs from more than one shock gen e r a t o r . Connections between shocks were i n v e s t i g a t e d i n two b a s i c geometries (see Fig u r e 1.2): (1) connections between s e v e r a l shocks which stood s i d e by s i d e i n the flow (both s e r i e s and p a r a l l e l e l e c t r i c a l connections) (2) a connection of s e v e r a l shocks formed by one shock and i t s s u c c e s s i v e r e f l e c t i o n from the w a l l s ( s e r i e s e l e c t r i c a l c o n n e c t i o n ) . 0 Another important aim of t h i s work was to d e f i n e a u s e f u l f i g u r e of merit f o r the bow shock generators so that t h e i r performance i n these t e s t s could be compared to that of other systems. To c r e a t e a standing bow shock s u i t a b l e f o r use i n the t e s t s o u t l i n e d above one must have an i n c i d e n t flow which a) M u l t i p l e s t a n d i n g s h o c k s a r r a n g e d p h y s i c a l l y i n p a r a l l e l a c r o s s t h e f l o w b ) M u l t i p l e s t a n d i n g s h o c k s f o r m e d b y r e f l e c t i o n s f r o m t h e w a l l s 4 F i g u r e 1.2 The two g e o m e t r i e s u s e d t o i n v e s t i g a t e m u l t i p l e s h o c k c o n n e c t i o n s m e e t s a number o f r e q u i r e m e n t s . T hese may be s u m m a r i z e d as f o l l o w s : 1) The f l o w must c o n s i s t o f g a s i n a w e l l d e f i n e d t h e r m o d y n a m i c s t a t e . 2) The f l o w must be s u p e r s o n i c . 3) The d u r a t i o n o f t h e f l o w must be a t l e a s t 10 m i c r o s e c o n d s t o a l l o w t i m e f o r m e a s u r e m e n t s t o be made. 4) The f l o w s h o u l d show an i n c r e a s e o f i o n i z a t i o n on p a s s i n g t h r o u g h t h e s t a n d i n g s h o c k . 5) T h e r e s h o u l d be no e l e c t r i c a l c u r r e n t s p r e s e n t i n t h e i n i t i a l f l o w . T h i s t h e s i s i s d i v i d e d i n t o two m a i n p a r t s . The f i r s t p a r t ( C h a p t e r s 1 t o 4) d e a l s w i t h t h e t h e o r y , c o n s t r u c t i o n , and t e s t i n g o f a d e v i c e w h i c h g e n e r a t e s a s u i t a b l e s u p e r s o n i c f l o w f i e l d w h i l e t h e s e c o n d p a r t ( C h a p t e r s 4 t o 8) d e a l s w i t h 5 the i n v e s t i g a t i o n s and a n a l y s i s of the bow shock g e n e r a t o r s . In Chapter 2 a method of gen e r a t i n g a s u i t a b l e flow using an imploding d e t o n a t i o n shock tube i s developed. Chapter 3 d e s c r i b e s the c o n s t r u c t i o n and p r e l i m i n a r y t e s t i n g of the shock tube. The design and c o n s t r u c t i o n of the generator systems i s o u t l i n e d i n Chapter 4 . Chapter 5 d e s c r i b e s the experiments i n which s e v e r a l generators were connected t o g e t h e r . The r e s u l t s from these experiments are inc l u d e d i n t h i s chapter along with those from some t e s t s on i n d i v i d u a l shock g e n e r a t o r s . A l l of these r e s u l t s are summarized i n Chapter 6 and an attempt i s made to i n t e r p r e t some of them t h e o r e t i c a l l y . In Chapter 7 a u s e f u l f i g u r e of merit ( the e f f e c t i v e n e s s ) i s d e f i n e d f o r the generators and a t y p i c a l value i s quoted. In a d d i t i o n a comparison i s made between the performance of a h y b r i d bow shock g e n e r a t o r / c o n v e n t i o n a l t u r b i n e g e n e r a t i o n system and that of a s t r i c t l y c o n v e n t i o n a l system. Chapter 8 c o n t a i n s a summary of the o r i g i n a l c o n t r i b u t i o n s made by the author, as w e l l as the c o n c l u s i o n s and suggestions f o r f u r t h e r work. 6 CHAPTER 2 . PRODUCTION OF A S U I T A B L E T E S T FLOW WITH AN  OVERDRIVEN DETONATION SHOCK TUBE The e x p e r i m e n t o u t l i n e d i n C h a p t e r 1 r e q u i r e s a s u p e r s o n i c f l o w o f g a s t h a t i s i n a w e l l d e f i n e d t h e r m o d y n a m i c s t a t e . When an o b s t a c l e i s i n s e r t e d i n t o t h e f l o w s o t h a t a s t a n d i n g s h o c k i s c r e a t e d t h e i o n i z a t i o n i n t h e f l o w m u s t i n c r e a s e s i g n i f i c a n t l y a c r o s s t h e s h o c k . The f l o w m u s t a l s o be f r e e o f l a r g e e l e c t r i c a l c u r r e n t s . One o f t h e s i m p l e s t ways o f g e n e r a t i n g a s u i t a b l e t e s t f l o w w o u l d be t o u s e t h e f l o w b e h i n d a s h o c k wave i n a r g o n . The t h e r m o d y n a m i c s t a t e o f a g a s b e h i n d a s h o c k i s w e l l d e f i n e d and a r g o n i s o n e o f t h e s i m p l e s t and b e s t u n d e r s t o o d g a s e s . I f t h e s h o c k wave i s made s t r o n g e n o u g h t h e f l o w b e h i n d i t c a n become s u p e r s o n i c i n t h e l a b f r a m e . I n t h i s way a s h o c k t u b e c a n be u s e d a s a s h o r t d u r a t i o n s u p e r s o n i c w i n d t u n n e l . The s u p e r s o n i c f l o w o f a r g o n a t a n y p o i n t i n s u c h a w i n d t u n n e l l a s t s f r o m t h e t i m e t h e s h o c k wave a r r i v e s u n t i l t h e t i m e t h e c o n t a c t s u r f a c e a r r i v e s . The Mach number f o r t h e f l o w b e h i n d t h e s h o c k f r o n t d e p e n d s on t h e s t r e n g t h o f t h e s h o c k , and c a n be o b t a i n e d f r o m t h e R a n k i n e - H u g o n i o t c o n s e r v a t i o n e q u a t i o n s w h i c h a p p l y t o g a s f l o w i n g t h r o u g h t h e s h o c k f r o n t . 7 2.1 SUPERSONIC FLOW BEHIND A SHOCK WAVE The c o n s e r v a t i o n e q u a t i o n s f o r t h e f l o w a c r o s s a s h o c k f r o n t may be w r i t t e n i n t h e f r a m e o f r e f e r e n c e o f t h e s h o c k a s ^ : P l V - P 2 U 2 ' (2.1) momentum: p : + p ^ » 2 = p 2 + p ^ ' 2 (2.2) energy: + • 2 = ^ + Hu^2 ( 2. 3) where t h e p r i m e s i n d i c a t e t h a t t h e q u a n t i t i e s a r e m e a s u r e d i n t h e s h o c k f r o n t f r a m e and t h e v a r i a b l e s a r e d e f i n e d as shown i n F i g u r e 2.1. An e q u i v a l e n t r e p r e s e n t a t i o n o f t h e s h o c k i n t h e l a b fra m e i s a l s o shown i n F i g u r e 2.1. The e q u a t i o n o f s t a t e f o r t h e g a s i s i n i t i a l l y t a k e n t o be t h a t f o r a s i m p l e i d e a l g a s ^ ( c o n s t a n t s p e c i f i c h e a t , no i o n i z a t i o n , m o n a t omic) h = Y P (2.4) Y+l P 3 where y i - s fche a d i a b a t i c e x p o n e n t e q u a l t o c / c . I f t h e P v 8 S H O C K F R A M E OF R E F E R E N C E L A B F R A M E OF R E F E R E N C E p p h 2 )2 2 R Pr hi P P h a„ 2 / 2 2 2 p p h s u' 2 u 2  Ws u,= where W = shock speed and u 0 = W - u „ s 2 s 2 u = l o c a l gas v e l o c i t y = Ws T = l o c a l gas temperature p = gas p ressu re p = gas d e n s i t y a = l o c a l sound speed F i g u r e 2 . 1 The f l o w a c r o s s a s h o c k f r o n t s h o c k p r o p a g a t e s i n t o s t a t i o n a r y g a s t h e i n i t i a l v e l o c i t y i n g t h e s h o c k f r a m e , u , i s e q u a l t o t h e s h o c k s p e e d W . U s i n g 1 s t h e i n i t i a l c o n d i t i o n s i n t h e s t a t i o n a r y g a s t h e f o u r e q u a t i o n s ( 2 . 1 ) t h r o u g h ( 2 . 4 ) may be s o l v e d k e e p i n g (u '=W ) 1 s t h e s h o c k s p e e d a s t h e f r e e p a r a m e t e r . I f t h i s s h o c k s p e e d i s n o r m a l i z e d t o t h e s o u n d v e l o c i t y i n t h e g a s a h e a d o f t h e s h o c k by d e f i n i n g t h e Mach number (M 1 ) ( 2 . 5 ) • t h e n t h e w e l l known s h o c k r e l a t i o n s a r e f o u n d . 9 P2 = CT+1)M1 = u ' Pl •2+(y-l)M1 2YM1 -(Y-1) Y+l (2.6) (2.7) \ = (2YM12-(Y-D)(2+(Y-1)M12) ( 2 . 8 ) T 2 2 1 (Y + l) \ A f i g u r e o f m e r i t f o r t h e f l o w g e n e r a t e d b e h i n d a s h o c k wave i s p r o v i d e d by t h e l o c a l Mach number M =u / a . T h i s i s 2 2 2 t h e Mach number o f t h e f l o w i n t h e l a b f r a m e . M i s r e l a t e d 2 t o t h e Mach number o f t h e s h o c k f r o n t (M =W /a , s e e F i g u r e 1 s 1 2.1) by t h e f o l l o w i n g e x p r e s s i o n , w h i c h may be o b t a i n e d by s u i t a b l e c o m b i n a t i o n s o f t h e ab o v e r e s u l t s ' . M^ =-U 2 = 2CM 1 2 - r ) (2.9) a 2 (2YM12-Y-1)3I(2+(Y-1)M12)}2 T h i s f u n c t i o n i s p l o t t e d i n F i g u r e 2.2. I t s h o u l d be n o t e d t h a t M h a s an up p e r bound w h i c h i s p r a c t i c a l l y r e a c h e d w i t h s h o c k s p e e d s (Mj) o f a b o u t Mach 10. From e q u a t i o n 2.9 t h e upper l i m i t f o r M 2 may be s e e n t o be 10 « I 1 1 I l_ 1.0 2.0 5.0 10 20 50 M<| >-Figure 2.2 The l o c a l Mach number of the shock heated gas (M2) as a f u n c t i o n of the shock Mach number (M ) . M. 2max = H m ( M 2 ) YCY-I) (2.10) For an i d e a l monatomic gas with y=1.67 the highest Mach number which may be achieved i n the flow behind a shock i s M2=1.35. If the gas i s i o n i z e d by i t s passage through the shock wave Y i s no longer a constant and, i n f a c t , i t becomes somewhat 11 s m a l l e r . I n t h i s c a s e t h e h i g h e s t a v a i l a b l e Mach number w o u l d be s l i g h t l y h i g h e r ( 1 . 6 3 ) . 2 . 2 THE REQUIREMENT OF I O N I Z A T I O N I N C R E A S E ACROSS THE STANDING  SHOCK W h i l e i t i s p o s s i b l e t o g e n e r a t e a s u p e r s o n i c f l o w w i t h a s h o c k w a v e , f o r t h e p u r p o s e o f t h e s e e x p e r i m e n t s t h e f l o w m u s t a l s o s a t i s f y a n o t h e r r e q u i r e m e n t , t h a t o f s h o w i n g an i n c r e a s e i n i o n i z a t i o n on p a s s i n g t h r o u g h a s t a n d i n g s h o c k . S i n c e i t i s n o t p o s s i b l e t o p r o d u c e h i g h Mach number f l o w s , a s t a n d i n g s h o c k ( c r e a t e d b y i n s e r t i n g an o b s t a c l e i n t o t h e f l o w ) w i l l be r e l a t i v e l y w e a k . T h i s means t h a t t h e j ump i n t h e t e m p e r a t u r e o f t h e f l o w a c r o s s t h e s t a n d i n g s h o c k w i l l be f a i r l y s m a l l . The v a r i a t i o n o f t h e d e g r e e o f i o n i z a t i o n , a, w i t h t e m p e r a t u r e and p r e s s u r e i s shown f o r a g a s w i t h an i o n i z a t i o n e n e r g y o f 15 eV i n F i g u r e 2 . 3 8 . F rom t h i s d a t a i t c a n be s e e n t h a t t h e m o s t r a p i d c h a n g e o f i o n i z a t i o n w i t h t e m p e r a t u r e i s o b t a i n e d i f o i s i n t h e r a n g e 5 - 9 5 % . I n t h i s p a r t i a l l y i o n i z e d r e g i m e t h e d e g r e e o f i o n i z a t i o n i s v e r y s e n s i t i v e t o t e m p e r a t u r e and t h u s e v e n a weak s t a n d i n g s h o c k w i l l i n c r e a s e t h e i o n i z a t i o n s u b s t a n t i a l l y . I f a s h o c k t u b e i s t o be u s e d t o p r o d u c e t h e s u p e r s o n i c f l o w f o r t h e study of bow shock g e n e r a t o r s i t i s t h e r e f o r e i m p o r t a n t t h a t t h e i n c i d e n t s h o c k be o f s u f f i c i e n t l y h i g h Mach number t o p r o d u c e p a r t i a l i o n i z a t i o n i n t h e a r g o n b e h i n d i t . When i o n i z a t i o n b e c o m e s s i g n i f i c a n t t h e c a l c u l a t i o n o f oC 4 0 0 0 6000 8000 10000 12000 14000 16000 18000 T E M P E R A T U R E (°K) F i g u r e 2.3 F r a c t i o n a l i o n i z a t i o n (a) of a gas with an i o n i z a t i o n energy of 15 eV as a f u n c t i o n of temperature. 13 t h e t h e r m o d y n a m i c p a r a m e t e r s b e h i n d t h e s h o c k f r o n t b e c o m e s 9 somewha t more c o m p l i c a t e d . I n a p a r t i a l l y i o n i z e d g a s y i s no l o n g e r a c o n s t a n t i n d e p e n d e n t o f t h e p r e s s u r e a n d t e m p e r a t u r e and t h e e q u a t i o n o f s t a t e ( 2 . 4 ) i s no l o n g e r a p p l i c a b l e . F u r t h e r m o r e t h e c o e f f i c i e n t y c a n n o t s e r v e t o r e p r e s e n t b o t h t h e s p e c i f i c h e a t r a t i o , c ^ / c v , and t h e e n t h a l p y c o e f f i c i e n t . T h e r e f o r e f o r u s e i n t h e e q u a t i o n o f 9 s t a t e t h e new e n t h a l p y c o e f f i c i e n t , g , i s d e f i n e d . W i t h t h i s c o e f f i c i e n t , w h i c h i s a f u n c t i o n o f t h e t h e r m o d y n a m i c v a r i a b l e s , t h e e q u a t i o n o f s t a t e may be w r i t t e n a s h = g P = g(h,p) P ( 2 . 1 1 ) g-1 p g ( n , p ) - l p | I f t h e f u n c t i o n g ( h , p ) i s known f r o m t h e r m o d y n a m i c d a t a , t h e t h r e e c o n s e r v a t i o n e q u a t i o n s , ( 2 . 1 ) t h r o u g h ( 2 . 3 ) , and t h e new e q u a t i o n o f s t a t e , ( 2 . 1 1 ) , may be s o l v e d b y a n i t e r a t i v e m e t h o d l e a v i n g t h e Mach number a s a p a r a m e t e r . D e t a i l s o f t h i s m e t h o d a r e d e s c r i b e d i n A p p e n d i x A . I n t h i s way t h e t h e r m o d y n a m i c v a r i a b l e s b e h i n d p a r t i a l l y i o n i z i n g s h o c k f r o n t s may be c a l c u l a t e d . Of t h e s e v a r i a b l e s t h e t e m p e r a t u r e and t h e d e g r e e o f i o n i z a t i o n a r e o f t h e m o s t i m m e d i a t e i n t e r e s t . F i g u r e 2 . 4 1 0 s h o w s t h e t e m p e r a t u r e and d e g r e e o f i o n i z a t i o n b e h i n d a s h o c k wave p r o p a g a t i n g i n t o a r g o n a s a f u n c t i o n o f Mach n u m b e r . The v a l u e s a r e shown f o r a number o f i n i t i a l a r g o n p r e s s u r e s . An e x a m i n a t i o n o f t h e g r a p h s h o w s t h a t i f 14 F i g u r e i n the graphs 2.4 Temperature ( T 2 ) and degree flow behind a shock wave i n argon, are the i n i t i a l p r e s s u r e ahead of o f i o n i z a t i o n ( a 2 ) The f i g u r e s on the the shocks. 15 t h e r e i s t o be s i g n i f i c a n t i o n i z a t i o n i n t h e f l o w b e h i n d t h e s h o c k t h e n t h e s h o c k s p e e d m u s t be a t l e a s t Mach 1 1 . I f a n o b s t a c l e i s i n s e r t e d i n t o t h e f l o w b e h i n d a Mach 11 s h o c k wave a s t a n d i n g s h o c k w i l l be c r e a t e d and t h e i o n i z a t i o n i n t h e f l o w w i l l be s i g n i f i c a n t l y i n c r e a s e d a c r o s s t h e s h o c k . 2 . 3 THE DIAPHRAGM SHOCK TUBE I n o r d e r t o s a t i s f y t h e r e q u i r e m e n t s f o r t h e t e s t f l o w , a s h o c k t u b e c a p a b l e o f p r o d u c i n g a Mach 11 s h o c k i s n e e d e d . To s e e w h a t f e a t u r e s a r e n e c e s s a r y f o r a s h o c k t u b e t o p r o d u c e s u c h h i g h Mach n u m b e r s t h e o p e r a t i o n o f a c o n v e n t i o n a l d i a p h r a g m s h o c k t u b e i s f i r s t d i s c u s s e d . F o r t h e p u r p o s e s o f t h i s s e c t i o n Y=g i s a s s u m e d t o be c o n s t a n t . F i g u r e 2 . 5 s h o w s a d i a g r a m o f a d i a p h r a g m s h o c k t u b e . The d r i v e r s e c t i o n on t h e l e f t i s f i l l e d w i t h a h i g h p r e s s u r e g a s w h i l e t h e l o w p r e s s u r e s e c t i o n o n t h e r i g h t i s f i l l e d w i t h t h e t e s t g a s . A d i a p h r a g m s e p a r a t e s t h e two s e c t i o n s . When t h i s d i a p h r a g m i s c a u s e d t o b u r s t , a s h o c k wave t r a v e l s down t h e s h o c k t u b e i n t o t h e t e s t g a s w h i l e a r a r e f a c t i o n wave moves b a c k i n t o t h e d r i v e r . T h e s e f e a t u r e s a r e shown i n t h e . X - T d i a g r a m a b o v e t h e s h o c k t u b e . A t some t i m e , T , a f t e r t h e d i a p h r a g m h a s o p e n e d one w o u l d f i n d a v e l o c i t y and p r e s s u r e d i s t r i b u t i o n i n t h e s h o c k t u b e s i m i l a r t o t h a t shown a t t h e b o t t o m o f F i g u r e 2 . 5 . The s p e e d o f t h e s h o c k may be r e l a t e d t o t h e i n i t i a l c o n d i t i o n s i n t h e h i g h and l o w p r e s s u r e s e c t i o n s i n t h e X X PRESSURE PROFILE AT TIME F i g u r e 2.5 The diaphragm shock tube 17 f o l l o w i n g way. The i n i t i a l c o n d i t i o n s i n t h e l o w p r e s s u r e s e c t i o n , r e g i o n 1, may be r e l a t e d t o t h o s e i n r e g i o n 2 by t h e s h o c k r e l a t i o n s w i t h t h e Mach number, M^, a s a p a r a m e t e r . I f i t i s assumed t h a t t h e p r e s s u r e and v e l o c i t y a r e c o n s t a n t a c r o s s t h e c o n t a c t s u r f a c e , t h e c o n d i t i o n s i n r e g i o n 2 c a n be r e l a t e d t o t h o s e i n r e g i o n 3. F i n a l l y , t o r e l a t e r e g i o n 3 t o t h e i n i t i a l c o n d i t i o n s i n t h e h i g h p r e s s u r e s e c t i o n , r e g i o n 4, t h e r a r e f a c t i o n wave i s assumed t o be i s e n t r o p i c . I n t h i s way t h e i n i t i a l c o n d i t i o n s i n t h e l o w p r e s s u r e s e c t i o n have been r e l a t e d t o t h o s e i n t h e h i g h p r e s s u r e s e c t i o n w i t h t h e Mach number (M^) as a p a r a m e t e r . The i n i t i a l p r e s s u r e r a t i o a c r o s s t h e d i a p h r a g m P^/Pj t h a t i s needed t o o b t a i n a s h o c k o f Mach number M c a n t h e r e f o r e be e x p r e s s e d as The d i a p h r a g m p r e s s u r e r a t i o i s p l o t t e d as a f u n c t i o n o f Mach number f o r s e v e r a l sound s p e e d r a t i o s a ^ a j i n Fi g u r e 2.6. An e x a m i n a t i o n o f t h e e q u a t i o n (2.12) o r t h e g r a p h shows t h a t i n o r d e r t o a c h i e v e h i g h Mach number s h o c k s , a h i g h d i a p h r a g m a r e n e e d e d . The i n i t i a l f i l l p r e s s u r e o f a r g o n on t h e l o w p r e s s u r e s i d e o f t h e d i a p h r a g m was 5 T o r r . T h i s v a l u e was c h o s e n t o o b t a i n h i g h d i a p h r a g m p r e s s u r e r a t i o s b u t s t i l l m a i n t a i n a (2.12) p r e s s u r e r a t i o , P 4 / P j , and a h i g h sound s p e e d r a t i o , a^/a 1' .Figure 2.6 The r e l a t i o n s h i p between, diaphragm pre s sure r a t i o (P^/p j ) a n d Mach number (M ) shown f o r a v a r i e t y o f sound speed r a t i o s ( a . / a . ) 19 s u b s t a n t i a l d e n s i t y i n t h e g a s b e h i n d t h e s h o c k . The p r e s s u r e r e q u i r e d i n t h e d r i v e r s e c t i o n t o g e n e r a t e a Mach 11 s h o c k c a n be c a l c u l a t e d f r o m t h e s e i n i t i a l c o n d i t i o n s a n d e q u a t i o n (2.12). F o r a p p r o x i m a t e c a l c u l a t i o n s t h e g r a p h i n F i g u r e ( 2 . 6 ) may be u s e d . I f h e l i u m i s u s e d a s a d r i v e r g a s t h e p r e s s u r e i n t h e d r i v e r w o u l d h a v e t o be 2000 a t m o s p h e r e s . T h i s was j u d g e d t o be t o o l a r g e a p r e s s u r e t o be h a n d l e d i n a n y r e a s o n a b l y s i z e d e x p e r i m e n t . By u s i n g a g a s w i t h a h i g h e r s o u n d s p e e d , s u c h a s h y d r o g e n , t h e d r i v e r p r e s s u r e c o u l d be r e d u c e d t o 65 a t m o s p h e r e s . H o w e v e r t h e u s e o f h i g h p r e s s u r e h y d r o g e n was c o n s i d e r e d t o be t o o d a n g e r o u s b e c a u s e we do n o t h a v e t h e f a c i l i t i e s t o h a n d l e h i g h p r e s s u r e h y d r o g e n s a f e l y . H i g h M a c h number s h o c k s may a l s o be g e n e r a t e d b y i n c r e a s i n g t h e s o u n d s p e e d i n t h e d r i v e r g a s t h r o u g h h e a t i n g . The e l e c t r o t h e r m a l s h o c k t u b e i s o n e d e v i c e w h i c h u s e s t h i s p r i n c i p l e . U n f o r t u n a t e l y i t i s known ^ t h a t e l e c t r i c a l s i g n a l s may be p i c k e d up a l m o s t a n y w h e r e i n an e l e c t r o t h e r m a l s h o c k t u b e . T h e s e s i g n a l s w o u l d make t h e d e t e c t i o n and i n t e r p r e t a t i o n o f bow s h o c k g e n e r a t o r s i g n a l s e x c e e d i n g l y d i f f i c u l t . T h e r e f o r e t h i s t y p e o f s h o c k t u b e was i m m e d i a t e l y r u l e d o u t . A n o t h e r means o f h e a t i n g t h e d r i v e r g a s i s t o f i l l t h e d r i v i n g s e c t i o n w i t h a c o m b u s t i b l e m i x t u r e o f g a s e s and t o i g n i t e t h e m i x t u r e s . A f t e r t h e r e a c t i o n i s c o m p l e t e t h e d r i v e r w i l l be f i l l e d w i t h h i g h p r e s s u r e , h i g h t e m p e r a t u r e g a s . 20 2.4 OVERDRIVEN DETONATION SHOCK TUBE 13 I t has been demonstrated i n t h i s l a b that a simple and e f f e c t i v e shock tube, capable of producing high Mach number shock waves, can be b u i l t with an 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 . In t h i s d e v i c e the combustible mixture of d r i v e r gases i s heated and r a i s e d to a high pressure by a d e t o n a t i o n wave. The d r i v e r s e c t i o n f o r such a shock tube has a s p e c i a l geometry as shown i n F i g u r e ( 2 . 7 ) . A d e t o n a t i o n wave i s i n i t i a t e d at one end of the chamber with a strong spark and propagates up to the midplane of the d r i v e r as a Chapman-Jouget d e t o n a t i o n . Beyond t h i s p o i n t the wave i s force d i n t o a converging channel and i t becomes an 13 14 o v e r d r i v e n , or strong , d e t o n a t i o n . The diaphragm b u r s t s s h o r t l y a f t e r the de t o n a t i o n has been r e f l e c t e d from i t and a shock wave i s d r i v e n i n t o the low pressure gas. The main advantage of the 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 i s that the pressure and temperature behind an o v e r d r i v e n d e t o n a t i o n are higher**' than those those a v a i l a b l e with other combustion pro c e s s e s . T h i s makes such a d r i v e r very a t t r a c t i v e f o r producing high Mach number shocks. While i t i s r e l a t i v e l y easy to produce a shock of speed Mach 11 i n an o v e r d r i v e n d e t o n a t i o n shock tube the flow of argon behind the shock may not be completely uniform. There are s e v e r a l p o t e n t i a l causes of unsteadiness i n t h i s flow. A de t o n a t i o n wave i s , i n g e n e r a l , followed by a centred r a r e f a c t i o n wave where the pressure i s decreased. While the 21 INLET AXIS Figu r e 2.7 An a x i a l secton of the shock tube d r i v e r (schematic). area convergence i n the d r i v e r s e c t i o n helps to " f i l l i n " some of t h i s decrease the pressure i n the d r i v e r w i l l not be completely uniform when the diaphragm b u r s t s . In a d d i t i o n , s t u d i e s of imploding d e t o n a t i o n have shown that the gas behind the r e f l e c t e d d e t o n a t i o n i s not at r e s t . F i g u r e (2.8) shows a smear camera photograph of a s e c t o r of a c y l i n r i c a l imploding d e t o n a t i o n * 6 . I t can be seen t h a t the p a r t i c l e paths behind the r e f l e c t e d d e t o n a t i o n move away from the a x i s . The f a c t t h a t both the pressure and the gas v e l o c i t y i n the d r i v e r s e c t i o n w i l l be nonuniform when the diaphragm ruptures may intr o d u c e d i s t u r b a n c e s i n t o the flow behind the shock. These d i s t u r b a n c e s w i l l be i n the form of compression or r a r e f a c t i o n 22 REFLECTED SHOCK IMPLODING DETONATION CO +10 4-0 r ad i u s (cm) H 0 F i g u r e 2.8 A smear camera photograph of one s e c t o r of a c y l i n d r i c a l imploding detonation 23 w a v e s w h i c h p r o p a g a t e down t h e s h o c k t u b e . T h e y w i l l f i r s t i n f l u e n c e t h e p r e s s u r e and v e l o c i t y o f t h e s l u g o f t e s t g a s and somewha t l a t e r t h e y w i l l a f f e c t t h e s p e e d o f t h e s h o c k f r o n t i t s e l f . 2 . 5 SUMMARY I t s h o u l d be p o s s i b l e t o m e e t m o s t o f t h e r e q u i r e m e n t s f o r t h e t e s t f l o w o u t l i n e d i n t h e i n t r o d u c t i o n ( C h a p t e r 1) by u s i n g t h e f l o w b e h i n d a Mach 11 s h o c k wave i n a r g o n . T h i s f l o w w i l l be s u p e r s o n i c and i t i s p o s s i b l e t o c r e a t e a s t a n d i n g s h o c k i n w h i c h t h e d e g r e e o f i o n i z a t i o n o f t h e f l o w i s i n c r e a s e d ( f r o m a p p r o x i m a t e l y 2 .7% t o 5%) . By u s i n g a s h o c k t u b e w i t h a n 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 a s h o c k o f s p e e d Mach 11 may be o b t a i n e d . The o n l y s h o r t c o m i n g o f t h i s d e v i c e i s t h a t f l o w b e h i n d s h o c k s g e n e r a t e d i n t h i s m a n n e r may show some u n s t e a d y f e a t u r e s . T h i s t y p e o f s h o c k t u b e was s e l e c t e d h o w e v e r b e c a u s e i t s o p e r a t i o n was f r e e f r o m l a r g e e l e c t r i c a l c u r r e n t s and i t s d e s i g n was s i m p l e . 24 CHAPTER 3. CONSTRUCTION AND DEVELOPMENT OF THE SHOCK TUBE  3.1 CONSTRUCTION OF THE SHOCK TUBE 3.1.1 The F a c i l i t y In the previous chapter i t was pointed out that a shock tube with a hot d r i v e r gas was r e q u i r e d i n order to study the e x t r a c t i o n of e l e c t r i c a l power from standing shock waves. Using the experience with d e t o n a t i o n shock tubes acquired i n 1 ^ t h i s l a b i t was decided to c o n s t r u c t such a d e v i c e . A schematic diagram of the e n t i r e system i s shown i n Fig u r e 3.1. The main f e a t u r e s of t h i s new f a c i l i t y are that i t has a square c r o s s s e c t i o n with an area of one square inch and an o v e r a l l l e n g t h of approximately two metres. The shock tube was b u i l t i n s e c t i o n s so that a s h o r t t e s t s e c t i o n could be i n s e r t e d i n t o the tube at a v a r i e t y of d i s t a n c e s from the diaphragm. The d r i v e r s e c t i o n i s of the imploding d e t o n a t i o n type, using oxy-acetylene as the d r i v e r gas. An ac e t a t e diaphragm separates the d r i v e r s e c t i o n from the shock tube. 25 TO PUMP 1 SHOCK TUBE AIR INLET MIXING /^~N PRESSURE \ ) - A C E T Y L E N E - O X Y G E N p [Xj AIR INLET MIXING CHAMBER 1 DUMP . T A N K VACUUM VALVE id PUMP 2 DIGITAL GAUGE T T / I / \ ARGON [Xi—1><3—tXj—0*3" S N S AIR INLET S = SOLENOID VALVE N= NEEDLE VALVE = CONTROL F i g u r e 3 . 1 S c h e m a t i c d i a g r a m o f t h e s h o c k t u b e s y s t e m . 26 3 . 1 . 2 D r i v e r S e c t i o n The m a i n b o d y o f t h e d r i v e r c o n s i s t e d o f two a l u m i n u m c o n e s , t h e f i r s t a s t h e d i v e r g e n t s e c t i o n and t h e s e c o n d a s t h e c o n v e r g e n t ( i m p l o d i n g ) s e c t i o n ( s e e F i g u r e 3 . 2 ) . The c o n e s w e r e c a s t f r o m B 135 a l u m i n u m and t h e n m a c h i n e d . T h e y w e r e m a t e d a t t h e i r b a s e s b y a m a c h i n e d a l u m i n u m r i n g t o w h i c h t h e y w e r e h e l d w i t h f l a n g e s . The r i n g a l s o p r o v i d e d f o r f i l l i n g and p u m p i n g o u t t h e d r i v e r t h r o u g h two h o l e s on o p p o s i t e s i d e s . The t o t a l v o l u m e o f t h e d r i v e r was a p p r o x i m a t e l y f o u r l i t r e s . A t t h e b a c k end o f t h e d r i v e r a s p a r k i g n i t e r h o u s e d i n l u c i t e was b o l t e d t o t h e f i r s t a l u m i n u m c o n e . A s p a r k b e t w e e n t h e s e two e l e c t r o d e s i n i t i a t e d t h e d e t o n a t i o n i n t h e d r i v e r g a s . A t t h e f r o n t end o f t h e d r i v e r a b r a s s r o u n d t o s q u a r e t r a n s i t i o n p i e c e (one i n c h l o n g ) was b o l t e d t o t h e s e c o n d a l u m i n u m c o n e . T h i s s e r v e d t o m a t c h t h e r o u n d g e o m e t r y o f t h e d r i v e r s e c t i o n t o t h e s q u a r e c r o s s s e c t i o n o f t h e s h o c k t u b e i t s e l f . T h r o u g h o u t t h e d r i v e r s e c t i o n O - r i n g s w e r e u s e d a s v a c u u m s e a l s . The e n t i r e d r i v e r s e c t i o n was f a s t e n e d w i t h s t e e l s t r a p s and b o l t s t o i t s own t a b l e w h i c h was l o a d e d w i t h 70 Kg o f c o n c r e t e , t o d e c r e a s e t h e r e c o i l . The a c e t a t e d i a p h r a g m was m o u n t e d b e t w e e n two O - r i n g s ; one on t h e f a c e o f t h e b r a s s t r a n s i t i o n p i e c e and t h e o t h e r on a r e p l a c e a b l e l u c i t e f l a n g e . B o t h t h e d i a p h r a g m and f l a n g e w e r e h e l d i n p l a c e b y t h e f o u r b o l t s w h i c h b o l t e d t h e f i r s t l e n g t h o f s h o c k t u b e t o t h e d r i v e r ( s e e F i g u r e 3 . 3 ) . The 27 inches F i g u r e 3.2 Cross s e c t i o n of the d r i v e r 28 F i g u r e 3 . 3 D e t a i l of the acetate diaphragm 29 l u c i t e f l a n g e needed replacement o c c a s i o n a l l y because of e r o s i o n caused by the b u r s t i n g of the diaphragm. 3.1.3 I g n i t i o n System The d e t o n a t i o n mixture i n the d r i v e r s e c t i o n was i g n i t e d by a spark between two e l e c t r o d e s . These e l e c t r o d e s were mounted i n a s h o r t l u c i t e tube at the end of the d r i v e r o p p o s i t e the diaphragm as shown i n Fig u r e 3.2. Energy f o r the spark was s t o r e d i n a 1.6yf c a p a c i t o r which was charged to 11 KV (approximately 100J) . A t r i g g e r a b l e spark gap between the c a p a c i t o r and the e l e c t r o d e s allowed the shock tube to be f i r e d . T h i s system i s shown s c h e m a t i c a l l y i n F i g u r e $.1. 3.1.4 Shock Tube The shock tube i t s e l f was b u i l t i n three i n t e r c h a n g e a b l e l e n g t h s , which were 50, 75, and 100 cm. l o n g . Flanges and O-ring s e a l s at the end of each s e c t i o n allowed them to be connected together. Each s e c t i o n was made of l u c i t e i n a box c o n s t r u c t i o n with w a l l s about one h a l f inch t h i c k . The s e c t i o n s were glued together with machine screws every two and one h a l f inches f o r support. To make the system r i g i d the whole shock tube was mounted on a le n g t h of aluminum channel. I t was supported above the channel on stands which allowed easy access to a l l s i d e s of the tube. A dump tank of about one l i t r e volume was connected 30 t o t h e l a s t s e c t i o n o f t h e s h o c k t u b e . P e r i o d i c c l e a n i n g o f t h e s h o c k t u b e was d o n e b y d i s m a n t l i n g t h e s e c t i o n s and c l e a n i n g e a c h o n e w i t h a r e c t a n g u l a r s w a b . A f e l t c l o t h s o a k e d i n B r a s s o was m o u n t e d on t h e swab t o p o l i s h t h e t u b e w a l l s . 3 . 1 . 5 P u m p i n g And F i l l i n g S y s t e m s The o x y - a c e t y l e n e w i t h w h i c h t h e d r i v e r was f i l l e d was p r e m i x e d i n a m i x i n g c h a m b e r w h i c h h e l d e n o u g h g a s f o r s e v e r a l s h o t s . T h i s c h a m b e r , w h i c h s t o o d a d j a c e n t t o t h e d r i v e r s e c t i o n , was c y l i n d r i c a l i n s h a p e and was e n c l o s e d i n a w i r e mesh s c r e e n f o r s a f e t y . The b o t t o m o f t h e m i x i n g c h a m b e r was s o l d e r e d t o t h e m i x i n g c h a m b e r w i t h s o f t s o l d e r so t h a t i f t h e m i x t u r e a c c i d e n t a l l y i g n i t e d t h e b o t t o m w o u l d f a i l f i r s t . The o x y - a c e t y l e n e was m i x e d two p a r t s o x y g e n t o o n e p a r t a c e t y l e n e b y p r e s s u r e . The p r e s s u r e s w e r e m o n i t o r e d on t h e m i x i n g c h a m b e r p r e s s u r e g a u g e a s e a c h g a s was a d d e d . S i n c e t h e m i x i n g c h a m b e r was b u i l t a s a v a c u u m t a n k , t h e t o t a l f i l l p r e s s u r e n e v e r e x c e e d e d o n e a t m o s p h e r e . A f t e r a l l o w i n g some t i m e f o r m i x i n g , t h e d r i v e r was f i l l e d t o t h e c h o s e n p r e s s u r e ( f r o m 100 t o 300 T o r r ) a s shown b y t h e d r i v e r p r e s s u r e g a u g e . B e f o r e a s h o t was f i r e d i s o l a t i o n v a l v e s a t t h e i n l e t and o u t l e t p o r t s o f t h e d r i v e r w e r e c l o s e d t o p r o t e c t a l l g a u g e s and t u b i n g . A f t e r a s h o t t h e d r i v e r was pumped o u t t h r o u g h a p o r t o p p o s i t e t h e f i l l i n g p o r t . The s h o c k t u b e c o u l d be e i t h e r f i l l e d o r pumped o u t 31 t h r o u g h a p o r t i n t h e dump t a n k . The f i l l i n g o f t h e t u b e w i t h t h e t e s t g a s ( a r g o n i n t h i s c a s e ) was c o n t r o l l e d b y a s e t p o i n t p r e s s u r e g a u g e and a s o l e n o i d v a l v e . T h i s a l l o w e d t h e t u b e t o be a u t o m a t i c a l l y f i l l e d t o an a c c u r a t e l y known p r e s s u r e . D u r i n g a s h o t t h e p r e s s u r e g a u g e was p r o t e c t e d w i t h an i s o l a t i o n v a l v e . A r o t a r y pump was o n c e a g a i n u s e d t o pump o u t t h e t u b e a f t e r e a c h s h o t . 3 . 1 . 6 T e s t S e c t i o n I n o r d e r t o make t h e b e s t u s e o f t h e s h o c k t u b e a s h o r t t e s t s e c t i o n was c o n s t r u c t e d a s shown i n F i g u r e 3 . 4 and F i g u r e 3 . 5 . I t c o u l d be b o l t e d b e t w e e n a n y two s e c t i o n s o f t h e s h o c k t u b e and t h u s m o u n t e d a t a v a r i e t y o f d i s t a n c e s f r o m t h e d i a p h r a g m . By u s i n g a t e s t s e c t i o n m o d e l s s u c h a s bow s h o c k g e n e r a t o r s o r i n s t r u m e n t a t i o n c o u l d be m o u n t e d i n t h e t u b e w i t h o u t a l t e r i n g t h e s h o c k t u b e s e c t i o n s t h e m s e l v e s . The t e s t s e c t i o n had two r e m o v e a b l e l i d s ( one t o p and one b o t t o m ) a s shown i n F i g u r e 3 . 4 on w h i c h t h e m o d e l s o r i n s t r u m e n t a t i o n c o u l d be m o u n t e d . The l i d s w e r e o f s i m p l e d e s i g n and new o n e s c o u l d q u i c k l y be m a c h i n e d i f r e p l a c e m e n t s o r e x t r a s w e r e n e e d e d . The t e s t s e c t i o n was b u i l t f r o m t h r e e q u a r t e r i n c h l u c i t e w i t h O - r i n g s t o s e a l t h e l i d s . The l i d s w e r e c l a m p e d t o g e t h e r f r o m t h e o u t s i d e so t h a t w i t h t h e O - r i n g s f u l l y c o m p r e s s e d t h e i n s i d e f a c e s o f t h e l i d s w e r e f l u s h w i t h t h e t u b e w a l l s ( s e e F i g u r e 3 . 5 ) . F i g u r e 3.4 The t e s t s e c t i o n with removable l i d s 33 F i g u r e 3 . 5 Cross s e c t i o n of the t e s t s e c t i o n 3 4 3 . 1 . 7 P r e s s u r e P r o b e F l a n g e s T w o f l a n g e s , e a c h o n e i n c h t h i c k , w e r e m a c h i n e d t o a c c o m o d a t e p i e z o - e l e c t r i c p r e s s u r e p r o b e s ( s e e F i g u r e 3 . 6 ) . THREADED HOLE F i g u r e 3 . 6 T h e p r e s s u r e p r o b e f l a n g e T h e s e f l a n g e s c o u l d t h e n b e c l a m p e d b e t w e e n a n y o f t h e s e c t i o n s o f t h e t u b e a n d u s e d f o r t r i g g e r i n g o t h e r a p p a r a t u s o r i n a p a i r a t e a c h e n d o f t h e t e s t s e c t i o n t o m o n i t o r s h o c k s p e e d . T h e p i e z o p r o b e s u s e d i n t h i s e x p e r i m e n t w e r e 35 m a n u f a c t u r e d by C e l e s c o T r a n s d u c e r P r o d u c t s I n c . and were t y p e LD25. They had a s e n s i t i v i t y o f a b o u t . 1 5 V / p s i . W i t h t h e s e p r o b e s a c h e c k was k e p t on t h e r e p r o d u c i b i l i t y o f t h e s h o c k s p e e d t h r o u g h o u t t h e bow s h o c k g e n e r a t o r t e s t e x p e r i m e n t s . F o r t h e measurement o f s h o c k v e l o c i t i e s t h e p i e z o p r o b e o u t p u t s were f i r s t b u f f e r e d t h r o u g h a h i g h i n p u t i m p e d a n c e b u f f e r a m p l i f i e r and t h e n u s e d t o t r i g g e r a s t a r t / s t o p d i g i t a l m i c r o s e c o n d c o u n t e r . 3.2 MEASUREMENTS A number o f p r e l i m i n a r y e x p e r i m e n t s were made on t h e s h o c k t u b e b e f o r e t h e e x p e r i m e n t s w i t h t h e bow s h o c k g e n e r a t o r were u n d e r t a k e n . The a i m o f t h e s e e x p e r i m e n t s was t o i n v e s t i g a t e t h e p e r f o r m a n c e o f t h e s h o c k t u b e and t o i n v e s t i g a t e some o f t h e p r o p e r t i e s o f t h e s l u g o f s h o c k c o m p r e s s e d a r g o n w h i c h t r a v e l s down t h e t u b e . The s t e a d i n e s s o f t h i s f l o w b e h i n d t h e s h o c k was o f p a r t i c u l a r i n t e r e s t . T h r o u g h o u t t h e e x p e r i m e n t s a d r i v e r g a s m i x t u r e o f one p a r t a c e t y l e n e t o two p a r t s o x y g e n b y p r e s s u r e was u s e d . The g a s use d i n t h e l o w p r e s s u r e s e c t i o n o f t h e s h o c k t u b e was a l w a y s a r g o n . 36 3 . 2 . 1 . D e p e n d e n c e Of The S h o c k S p e e d On The F i l l Gas P r e s s u r e s The f i r s t s e t o f e x p e r i m e n t s e x p l o r e d t h e r a n g e o f Mach n u m b e r s t h a t w e r e a v a i l a b l e w i t h : t h e s h o c k t u b e . The s h o c k f r o n t s p e e d was m e a s u r e d a t a d i s t a n c e o f a b o u t one m e t r e f r o m t h e d i a p h r a g m f o r a n u m b e r o f d i f f e r e n t f i l l gas p r e s s u r e s . B o t h t h e d r i v e r p r e s s u r e and t h e s h o c k t u b e p r e s s u r e w e r e v a r i e d . The r e s u l t s a r e s u m m a r i z e d i n F i g u r e 3 . 7 w h i c h shows t h e Mach number m e a s u r e d f o r e a c h c o m b i n a t i o n o f f i l l gas p r e s s u r e s . In t h e c a s e o f t h e d r i v e r s e c t i o n , t h e p r e s s u r e when t h e d i a p h r a g m b u r s t s , w i l l , o f c o u r s e , be much h i g h e r t h a n t h e d r i v e r f i l l gas p r e s s u r e . The p r e s s u r e i s i n c r e a s e d o n c e b e h i n d t h e d e t o n a t i o n wave and o n c e a g a i n when t h e d e t o n a t i o n 1 7 i s r e f l e c t e d a t t h e d i a p h r a g m end o f t h e d r i v e r . No a t t e m p t was made t o m e a s u r e t h i s p r e s s u r e i n t h e s e e x p e r i m e n t s b u t t h e r e s u l t s f r o m o t h e r e x p e r i m e n t s done i n t h i s l a b ^ i n d i c a t e t h a t i t i s o f t h e o r d e r o f 100 a t m o s p h e r e s . In t h e s e e x p e r i m e n t s t h e s p e e d o f t h e s h o c k was m e a s u r e d w i t h a s m e a r o r s t r e a k c a m e r a . I n t h i s t e c h n i q u e t h e a x i s o f t h e c s h o c k t u b e i s i m a g e d o n t o t h e s l i t o f t h e s m e a r c a m e r a w i t h a l e n s . The smea r c a m e r a r e c o r d s a p o s i t i o n v e r s u s t i m e h i s t o r y r d f t h e l u m i n o s i t y b y s w e e p i n g t h e i m a g e o f t h e s l i t a c r o s s t h e f i l m . Two m a r k e r s , s p a c e d - a n a c c u r a t e d i s t a n c e a p a r t , w e r e p l a c e d on t h e s h o c k t u b e w a l l w i t h i n t h e f i e l d o f v i e w o f t h e s m e a r c a m e r a . By m e a s u r i n g t h e t r a n s i t t i m e f o r t h e s h o c k b e t w e e n t h e m a r k e r s on t h e p h o t o g r a p h t h e s h o c k 3 7 5.2 h DRIVER F I L L P R E S S U R E IN TORR • = 3 0 0 • = 2 5 0 O = 2 0 0 • =150 15 112.5 M A C H NUMBER I 10 7.5 J L JL mim J L 5 10 SHOCK T U B E F ILL P R E S S U R E ( T O R R ) Figure- 3 . 7 The shock speed measured f o r v a r i o u s f i l l gas pre s s u r e s 38 s p e e d was c a l c u l a t e d . A t y p i c a l smear camera p h o t o g r a p h i s shown i n F i g u r e 3.8. A few o f t h e v a l u e s i n c l u d e d i n t h i s | - — 6 4 m m »| SPEED= M A C H 9.0 ±.1 F i g u r e 3.8 A t y p i c a l smear camera p h o t o g r a p h d a t a were n o t a c t u a l l y done w i t h a smear camera b u t r a t h e r b y m e a s u r i n g t h e t r a n s i t t i m e f o r t h e s h o c k b e t w e e n two p r e s s u r e p r o b e s a s d e s c r i b e d i n t h e n e x t s e c t i o n . The r e s u l t s o f t h e s e i n v e s t i g a t i o n s show, t h a t i n t h i s 39 s h o c k t u b e , t h e Mach number o f t h e s h o c k c a n e a s i l y be v a r i e d o v e r a f a i r l y w i d e r a n g e f r o m Mach 6 t o Mach 1 2 . 5 . I t c a n be s e e n t h a t t h e d e s i g n c r i t e r i o n o f a Mach 10 t o 11 s h o c k p r o p a g a t i n g i n t o 5 T o r r a r g o n was r e a d i l y a c h i e v e d . 3 . 2 . 2 D e p e n d e n c e O f The S h o c k S p e e d On P o s i t i o n Once t h e d e p e n d e n c e o f t h e s h o c k s p e e d on t h e f i l l g a s p r e s s u r e h a d b e e n e s t a b l i s h e d a t o n e p o s i t i o n i n t h e t u b e t h e v a r i a t i o n o f s h o c k s p e e d a l o n g t h e t u b e was i n v e s t i g a t e d . T h i s was d o n e b y m e a s u r i n g t h e s h o c k s p e e d a t a number o f s t a t i o n s a l o n g t h e t u b e . T h e s e t e s t s w e r e a l l c a r r i e d o u t w i t h a d r i v e r f i l l p r e s s u r e o f 200 T o r r and a s h o c k t u b e f i l l p r e s s u r e o f 5 T o r r . To m e a s u r e t h e s h o c k s p e e d two o f t h e p i e z o - e l e c t r i c p r e s s u r e p r o b e s w e r e m o u n t e d a known d i s t a n c e a p a r t i n one o f t h e l i d s o f t h e t e s t s e c t i o n . The o u t p u t s f r o m t h e p r e s s u r e p r o b e s w e r e p u t t h r o u g h a h i g h i n p u t i m p e d a n c e b u f f e r a m p l i f i e r and d i s p l a y e d on a d u a l t r a c e o s c i l l o s c o p e . A t h i r d p r e s s u r e p r o b e m o u n t e d i m m e d i a t e l y a h e a d o f t h e t e s t s e c t i o n was u s e d t o t r i g g e r t h e s c o p e . F rom t h e t i m e i n t e r v a l b e t w e e n t h e r i s i n g e d g e s o f t h e two s i g n a l s and t h e known d i s t a n c e b e t w e e n t h e p r o b e s t h e s h o c k s p e e d was c a l c u l a t e d . A t y p i c a l e x a m p l e o f t h e two p r e s s u r e s i g n a l s i s shown i n F i g u r e 3 . 9 . The s h o c k s p e e d was m e a s u r e d a t a v a r i e t y o f d i s t a n c e s f r o m t h e d i a p h r a g m by l o c a t i n g t h e t e s t s e c t i o n b e t w e e n d i f f e r e n t s e c t i o n s o f t h e s h o c k t u b e . The r e s u l t s f r o m t h e s e 40 1.0 V/div P R O B E S E P A R A T I O N = 1 0 2 m m S P E E D = M A C H 11.3 F i g u r e 3.9 A t y p i c a l p a i r of pressure s i g n a l s used f o r shock speed measurement experiments are shown i n Fig u r e 3.10 as a p l o t of shock speed versus d i s t a n c e from the diaphragm. Each data p o i n t i s an average from s e v e r a l shots done at that d i s t a n c e . The v a r i a t i o n of the speed at any p o i n t from shot to shot was q u i t e s m a l l , except at a d i s t a n c e of 65 cm. from the diaphragm, where there was as much as a 20 per cent v a r i a t i o n . F i g u r e 3.10 a l s o shows t y p i c a l pressure s i g n a l s from s e v e r a l of the s t a t i o n s along the tube. These were obtained with one of the probes i n the t e s t s e c t i o n using a long time s c a l e . I t was found that the type LD25 probes were best s u i t e d f o r measuring the time of a r r i v a l of shocks or 41 *|3 c/> O > 5 0 <>N 100 ^ 150 DISTANCE F R O M D I A P H R A G M " "(cm) • 1 1 I —1—f—1—1— —\—1—1' 1 i i IH-i i I I I I I P I 1 1 I I I I l i l t * 2 V / d i v 1V/d iv ALL 5 /d i v IVAl iv F i g u r e 3.10 Shock speed as a f u n c t i o n o f d i s t a n c e from the diaphragm. The magnitude o f the p r e s s u r e probe s i g n a l i m m e d i a t e l y b e h i n d the shock (V) i s shown. The d o t t e d l i n e i s the t h e o r e t i c a l v a l u e o f V c a l c u l a t e d from the shock speed. R e p r e s e n t a t i v e p r e s s u r e probe s i g n a l s from t h r e e l o c a t i o n s a l o n g the tube are a l s o shown 42 observing strong pressure g r a d i e n t s i n the flow. D i s t r i b u t e d r a r e f a c t i o n waves or short regions o f constant pressure were hard to i d e n t i f y because of the r i n g i n g of the probe s i g n a l . The pressure s t e p a c r o s s the shock f r o n t was f a i r l y w e l l d e f i n e d however, and t h i s jump, i n v o l t s , i s shown f o r s e v e r a l s t a t i o n s along the tube i n Fig u r e 3.10. T h i s g i v e s an i n d i c a t i o n of the r e l a t i v e s t r e n g t h of the shock as a f u n c t i o n of the d i s t a n c e from the diaphragm. The r e s u l t s show one ra t h e r i n t e r e s t i n g f e a t u r e . A s l i g h t i n c r e a s e i n shock speed i s observed about 65 cm. from the diaphragm. A f t e r t h i s the shock decays f a i r l y u n i f o r m l y f o r the next metre. T h i s i n c r e a s e d speed i s c o n s i s t e n t with the pressure t r a c e shown from the previous s t a t i o n as shown i n Figu r e 3.10. I t appears that due to some unsteadiness i n the d r i v e r a compression wave i s emitted from the d r i v e r some 30 microseconds a f t e r the shock has been launched. T h i s compression wave catches up to and r e i n f o r c e s the shock about 65 cm. from the diaphragm accounting f o r the increased speed measured i n t h a t r e g i o n . I f i n some shots the compression wave were to cat c h the shock j u s t before 65 cm. and i n other shots not u n t i l j u s t a f t e r 65 cm. there should be a l a r g e shot to shot v a r i a t i o n i n the measured speed. T h i s l a r g e s c a t t e r i n v e l o c i t i e s was indeed observed at a d i s t a n c e of 65 cm. from the diaphragm. 43 3 . 2 . 3 The X - T D i a g r a m F o r The S h o c k F r o n t I n a d d i t i o n t o b e i n g u s e d t o m e a s u r e s h o c k v e l o c i t i e s t h e p r e s s u r e p r o b e s w e r e u s e d t o m e a s u r e t h e a b s o l u t e t i m e o f a r r i v a l o f t h e s h o c k a t e a c h s t a t i o n a l o n g t h e t u b e . The a r r i v a l t i m e was m e a s u r e d f r o m t h e t i m e t h e d e t o n a t i n g s p a r k i n t h e d r i v e r s e c t i o n was t r i g g e r e d . T h e s e r e s u l t s a r e shown i n F i g u r e 3 . 1 1 . F rom o t h e r e x p e r i m e n t s i t i s known t h a t t h e d e t o n a t i o n a r r i v e s a t t h e d i a p h r a g m a p p r o x i m a t e l y 250 m i c r o s e c o n d s a f t e r t h e s p a r k . The d e l a y b e f o r e t h e d i a p h r a g m b u r s t s c a n t h e r e f o r e be s e e n t o be o f t h e o r d e r o f 25 m i c r o s e c o n d s . T h e s e r e s u l t s show t h e same e s s e n t i a l f e a t u r e s a s t h e v e l o c i t y m e a s u r e m e n t s . A t a b o u t 65 c m . f r o m t h e d i a p h r a g m t h e r e i s t h e same i n c r e a s e i n s p e e d n o t e d a s i n t h e p r e v i o u s m e a s u r e m e n t s . T h i s i s f o l l o w e d by a f a i r l y u n i f o r m d e c a y i n s h o c k s p e e d f r o m t h i s p o i n t o n w a r d . F o r r e f e r e n c e , t h e t h e o r e t i c a l p o s i t i o n o f t h e c o n t a c t s u r f a c e h a s a l s o b e e n shown i n F i g u r e 3 . 1 1 . The ' p o s i t i o n o f t h e c o n t a c t s u r f a c e was c a l c u l a t e d f r o m t h e c o m p r e s s i o n r a t i o a c r o s s t h e s h o c k a t e a c h p o i n t . 3 . 2 . 4 Smea r C a m e r a M e a s u r e m e n t s The s m e a r c a m e r a p h o t o g r a p h s , f r o m w h i c h t h e v e l o c i t i e s w e r e m e a s u r e d , a l s o y i e l d some i n f o r m a t i o n a b o u t t h e d u r a t i o n and h o m o g e n e i t y o f t h e f l o w b e h i n d t h e s h o c k . The l u m i n o s i t y o f t h e s h o c k f r o n t i t s e l f i s o f t e n v e r y f a i n t , a s c a n be s e e n , 44 iooo h 8 0 0 l-C0 LU 6 0 0 4 0 0 2 0 0 A POSITION OF CONTACT SURFACE FROM THEORY J I I L 5 0 100 150 X ( c m ) 200 F i g u r e 3.11 The X-T diagram f o r the shock wave 45 f o r example, i n Fi g u r e 3.8. I t was necessary t h e r e f o r e to ensure that the f a i n t l u m i n o s i t y i n these photographs was i n f a c t the shock. To check t h a t the shock had been p r o p e r l y i d e n t i f i e d s e v e r a l experiments were done with the arrangement shown i n Fi g u r e 3.12. A pressure probe was mounted in the Fig u r e 3.12 The apparatus used to check the i n t e r p r e t a t i o n of the smear camera photographs centre of the f i e l d of view of the smear camera and i t s p o s i t i o n was marked in the p i c t u r e s by p l a c i n g a black band on 46 t h e s h o c k t u b e . T h e s i g n a l f r o m t h e p r o b e w a s u s e d t o t r i g g e r a n e l e c t r o n i c f l a s h u n i t t h a t w a s f o c u s e d o n t o t h e s l i t o f t h e s m e a r c a m e r a n e a r o n e e n d . F i g u r e 3.13 s h o w s o n e o f t h e s m e a r - S T R E A K S T A R T S 7-9us A F T E R T H E A R R I V A L O E T H E P R E S S U R E F R O N T 7- Bus E L E C T R O N I C D E L A Y C ~ 1 *r-0 5 0 m m D I S T A N C E F i g u r e 3.13 A t y p i c a l s m e a r c a m e r a p h o t o g r a p h u s e d t o c h e c k t h a t t h e f i r s t f a i n t l u m i n o s i t y w a s t h e s h o c k c a m e r a p h o t o g r a p h s t a k e n i n t h i s w a y . T h e s t a r t o f t h e f l a s h g u n s t r e a k , m i n u s a p r e d e t e r m i n e d 7 - 8 m i c r o s e c o n d e l e c t r o n i c d e l a y , m a r k s t h e p o i n t i n t i m e t h a t t h e p r e s s u r e s h o c k a r r i v e s a t t h e p r o b e . T h i s t i m e c a n b e s e e n t o c o r r e s p o n d v e r y w e l l w i t h t h e t i m e o f a r r i v a l o f t h e f a i n t l u m i n o s i t y a t t h e 47 p r e s s u r e p r o b e . An e x a m i n a t i o n o f t h e s m e a r c a m e r a p h o t o g r a p h s showed t h a t t h e l u m i n o s i t y o f t h e - g a s b e h i n d t h e s h o c k was n e i t h e r u n i f o r m n o r c o m p l e t e l y r e p r o d u c i b l e f r o m s h o t t o s h o t . F i g u r e 3 . 1 4 s h o w s two p h o t o d e n s i t o m e t e r t r a c i n g s t h a t w e r e t a k e n f r o m ,1 LUMINOSITY OF SHOT 1 LUMINOSITY OF SHOT 2 TIME 251 3 us SHOCK FRONT END OF LUMINOSITY F i g u r e 3 . 1 4 P h o t o d e n s i t o m e t e r r e c o r d s o f two s m e a r c a m e r a p h o t o g r a p h s f o r i d e n t i c a l i n i t i a l c o n d i t i o n s 48 s m e a r c a m e r a p h o t o g r a p h s o f two s h o t s f i r e d w i t h i d e n t i c a l i n i t i a l c o n d i t i o n s . T h i s s h o t t o s h o t v a r i a t i o n i s p r o b a b l y due t o s m a l l v e l o c i t y v a r i a t i o n s w h i c h t r a n s l a t e i n t o l a r g e r v a r i a t i o n s i n e l e c t r o n i c e x c i t a t i o n i n t h i s t e m p e r a t u r e r e g i o n . D e s p i t e t h i s s h o t t o s h o t v a r i a t i o n e x p e r i m e n t s d o n e l a t e r o n t h e bow s h o c k g e n e r a t o r s s h o w e d how t o i n t e r p r e t t h e s e p h o t o g r a p h s c o n s i s t e n t l y . I t was f o u n d t h a t t h e u s e f u l t e s t f l o w e n d e d a t a t i m e c o r r e s p o n d i n g t o t h e l a s t s h a r p d r o p i n t h e l u m i n o s i t y ( s e e C h a p t e r 5 . 1 ) . F o r a l l t h e s m e a r c a m e r a p h o t o g r a p h s , t h e t o t a l t i m e f r o m t h e a r r i v a l o f t h i s d r o p , was m e a s u r e d t o be f a i r l y c o n s t a n t . 3 . 2 . 5 T e s t T i m e A l l t h e i n f o r m a t i o n f r o m t h e s m e a r c a m e r a p h o t o g r a p h s and p r e s s u r e p r o b e t r a c i n g s was c o m b i n e d t o d e t e r m i n e t h e t e s t t i m e . A t a n y p o i n t i n t h e s h o c k t u b e t h i s t e s t t i m e s t a r t s when t h e s h o c k a r r i v e s and i n t h e o r y w o u l d l a s t u n t i l t h e a r r i v a l o f t h e c o n t a c t s u r f a c e . I n t h e s e e x p e r i m e n t s t h e f l o w b e h i n d t h e s h o c k i s o n l y u s e f u l f o r a s l o n g a s i t i s i o n i z e d and s u p e r s o n i c . On t h e s m e a r c a m e r a p i c t u r e s t h e t e s t t i m e was e s t i m a t e d f r o m t h e d u r a t i o n o f t h e l u m i n o s i t y , a s was d i s c u s s e d i n s e c t i o n 3 . 4 . F r o m t h e p r e s s u r e p r o b e s i g n a l s t h e t e s t t i m e was t a k e n t o be t h e d u r a t i o n o f t h e " c o n s t a n t " p r e s s u r e r e g i o n f o l l o w i n g t h e s h o c k . A t h e o r e t i c a l v a l u e f o r t e s t t i m e , t h e t i m e i n t e r v a l b e t w e e n t h e s h o c k and t h e c o n t a c t s u r f a c e , was 49 al s o c a l c u l a t e d . Using each of these methods an estimate of the t e s t time was made at a number of s t a t i o n s along the tube. The r e s u l t s are shown i n Fig u r e 3.15 as a p l o t of the t e s t time estimated versus p o s i t i o n along the tube. 3.3 SUMMARY Based on the experiments done with the shock tube i t was decided to conduct the bow shock generator t e s t s at a d i s t a n c e of about 90 cm. from the diaphragm. At t h i s p o i n t the v e l o c i t y was r e l a t i v e l y constant from shot to shot and the Mach number was s t i l l q u i t e h i g h . Both the smear camera and pressure probe r e s u l t s i n d i c a t e d t hat there should be, at l e a s t 25 microseconds of t e s t time a f t e r the a r r i v a l of the shock. Some shot to shot v a r i a t i o n of the c o n d i t i o n s i n the flow behind the shock might be expected, however, as i s evidenced by the smear camera photographs. I t might have been p o s s i b l e to achieve a s l i g h t l y longer t e s t time by moving somewhat f u r t h e r from the diaphragm. However, because of d i s c r e p a n c i e s i n the data from the s t a t i o n s t h e r e , i t was decided to t e s t the generators at a p o s i t i o n 90 cm. from the diaphragm. One 75 cm long s e c t i o n of the shock tube was t h e r e f o r e i n t e r p o s e d between the diaphragm and the t e s t s e c t i o n so that the bow shock generators would be l o c a t e d about 90 cm downstream of the diaphragm. 50 60 1 50 40 30 in 3. Ill 2 20 l/J hi 1 1 10 O PRESSURE PROBE • SMEAR CAMERA THEORETICAL MACH 11 g=1.5 1/ 50 100 X (cm) 150 F i g u r e 3.15 T e s t t ime as a f u n c t i o n o f p o s i t i o n i n the shock tube 51 CHAPTER 4 . CONSTRUCTION OF GENERATOR TEST SYSTEMS A s o u t l i n e d i n t h e i n t r o d u c t i o n , two d i f f e r e n t c o n f i g u r a t i o n s had b e e n s u g g e s t e d f o r i n c r e a s i n g t h e c u r r e n t o r v o l t a g e o u t p u t o f bow s h o c k g e n e r a t o r s b y u s i n g s e v e r a l s h o c k s . To t e s t t h e s e c o n c e p t s two d i f f e r e n t g e n e r a t o r s y s t e m s w e r e b u i l t . One s y s t e m was d e s i g n e d t o i n v e s t i g a t e t h e p o w e r e x t r a c t i o n f r o m s e v e r a l s h o c k s w h i c h s t o o d p h y s i c a l l y i n p a r a l l e l a c r o s s t h e f l o w . The o t h e r s y s t e m was d e s i g n e d t o i n v e s t i g a t e t h e powe r e x t r a c t i o n f r o m a number o f s h o c k s f o r m e d b y s u c c e s s i v e r e f l e c t i o n s f r o m t h e w a l l s . I n e a c h c a s e t h e s y s t e m s w e r e b u i l t so t h a t t h e y c o u l d be m o u n t e d on t h e t e s t s e c t i o n l i d s . The w e d g e s and m o u n t i n g s t r u t s f o r t h e g e n e r a t o r s w e r e made t o be a s t h i n a s p o s s i b l e , t o m i n i m i z e t h e o b s t r u c t i o n o f t h e f l o w i n t h e s h o c k t u b e . 4 . 1 P A R A L L E L SHOCK GENERATORS I n t h i s c o n f i g u r a t i o n a number o f s h o c k s , c r e a t e d b y a number o f w e d g e s , s t o o d p h y s i c a l l y i n p a r a l l e l a c r o s s t h e f l o w a s shown s c h e m a t i c a l l y i n f i g u r e 4 . 1 . Two e l e c t r o d e s w e r e m o u n t e d on e a c h w e d g e , w i t h s e p e r a t e e l e c t r i c a l l e a d s , s o t h a t p o w e r c o u l d be e x t r a c t e d f r o m e a c h s h o c k s e p e r a t e l y . The o u t p u t s f r o m t h e g e n e r a t o r s c o u l d t h e n 52 STANDING SHOCK SUPERSONIC GAS FLOW > *m. - ELECTRODES F i g u r e 4 . 1 S c h e m a t i c d i a g r a m ( c r o s s s e c t i o n ) o f t h e p a r a l l e l s h o c k g e n e r a t o r s be c o n n e c t e d e l e c t r i c a l l y i n p a r a l l e l o r i n s e r i e s a s d e s i r e d f o r t e s t i n g . So t h a t t h e e l e c t r o d e s w o u l d n o t be i n f l u e n c e d by t h e p o t e n t i a l e l s e w h e r e i n t h e p l a s m a t h e r e s t o f t h e w e d g e , o r i t s s u r f a c e a t l e a s t , h a d t o be made o f i n s u l a t i n g m a t e r i a l . Due t o t h e s p a c e l i m i t a t i o n s i n t h e s h o c k t u b e , o n l y two s t a n d i n g s h o c k s , c r e a t e d b y two w e d g e s w e r e i n v e s t i g a t e d . F i g u r e 4 . 2 shows a d r a w i n g o f t h e g e n e r a t o r s y s t e m u s e d t o t e s t p a r a l l e l and s e r i e s c o n n e c t i o n s o f p a r a l l e l s t a n d i n g s h o c k s . The m a i n b o d y o f t h e wedge was b u i l t o f a n i n s u l a t i n g m a t e r i a l . The i n s u l a t o r was r e q u i r e d t o w i t h s t a n d h i g h t e m p e r a t u r e s , be m a c h i n e a b l e , and h a v e g o o d m e c h a n i c a l s t r e n g t h . The a s y m m e t r i c s h a p e o f t h e w e d g e s u s e d i n t h i s p a r t o f t h e e x p e r i m e n t m e a n t t h a t t h e n o s e s o f t h e w e d g e s e x p e r i e n c e d c o n s i d e r a b l e b e n d i n g moments and t h u s m e c h a n i c a l s t r e n g t h was c r u c i a l . A number o f i n s u l a t o r s w e r e t r i e d f o r F i g u r e 4.2 A c r o s s s e c t i o n o f t h e p a r a l l e l s t a n d i n g s h o c k g e n e r a t i n g s y s t e m . 54 t h i s p u r p o s e , b u t a p h e n o l i c r e s i n b o a r d was f o u n d t o be m o s t s a t i s f a c t o r y . M a c h i n e a b l e c e r a m i c s w e r e a l s o c o n s i d e r e d , b u t t h e y w e r e j u d g e d t o be t o o b r i t t l e and weak f o r t h i s a p p l i c a t i o n . I n p r a c t i c e i t was f o u n d n e c e s s a r y t o r e i n f o r c e t h e u p p e r wedge w i t h a s t e e l s p l i n e a s shown i n f i g u r e 4 . 2 . A number o f m a t e r i a l s w e r e t r i e d f o r u s e i n e l e c t r o d e s , b u t s t e e l was f o u n d t o be m o s t p r a c t i c a l i n t e r m s o f d u r a b i l i t y . S t e e l was t h e r e f o r e u s e d a s an e l e c t r o d e m a t e r i a l t h r o u g h o u t . The t o p ( f r o n t ) e l e c t r o d e s on t h e t i p o f b o t h w e d g e s w e r e s u b j e c t e d t o s u c h d a m a g e , p r o b a b l y due t o d e b r i s f r o m t h e r u p t u r e d m e m b r a n e , t h a t i t was f o u n d n e c e s s a r y t o h e a t t r e a t ( c a s e h a r d e n ) them a f t e r m a c h i n i n g . A f t e r h e a t t r e a t i n g t h e e l e c t r o d e s w e r e g l u e d , w i t h e p o x y , i n t o s l o t s m i l l e d i n t h e w e d g e . The b o t t o m e l e c t r o d e o n t h e u p p e r wedge m u s t be c o m p l e t e l y i n f r o n t o f t h e s t a n d i n g s h o c k p r o d u c e d b y t h e l o w e r w e d g e , o t h e r w i s e t h e e l e c t r o d e w i l l s h o r t o u t t h e p o t e n t i a l a c r o s s t h e l o w e r s h o c k . S i n c e t h e wedge a n g l e was q u i t e s m a l l ( 1 2 ° ) i t was v e r y d i f f i c u l t t o s q u e e z e i n two e l e c t r o d e s and t h e i r l e a d s r i g h t a t t h e t i p o f t h e wedge and s t i l l r e t a i n s u f f i c i e n t m e c h a n i c a l s t r e n g t h . The b o t t o m e l e c t r o d e o f t h e u p p e r wedge was t h e r e f o r e r e m o v e d a b o u t o n e h a l f i n c h f r o m t h e t i p and t h e w h o l e u p p e r wedge moved f o r w a r d t o k e e p t h e e l e c t r o d e c l e a r o f t h e l o w e r s h o c k ( s e e f i g u r e 4 . 2 ) . S t a g g e r i n g t h e w e d g e s l i k e t h i s made d e s i g n and c o n s t r u c t i o n e a s i e r b u t i t d i d s h o r t e n t h e t e s t t i m e s l i g h t l y 55 s i n c e b o t h w e d g e s w e r e n o t a l w a y s i n t h e s u p e r s o n i c f l o w a t t h e same t i m e . I n t h e f i r s t e x p e r i m e n t s t h e w e d g e s w e r e m o u n t e d w i t h s m a l l m a c h i n e s c r e w s t h r o u g h t h e w a l l s o f t h e t e s t s e c t i o n . H o w e v e r b e c a u s e t h e w e d g e s w e r e t h i n , t h e y t e n d e d t o f r a c t u r e a r o u n d t h e m o u n t i n g h o l e s . I n l a t e r e x p e r i m e n t s t h e w e d g e s w e r e t h e r e f o r e m o u n t e d on s u p p o r t s t r u t s f r o m t h e t o p and b o t t o m l i d s ( s e e f i g u r e 4 . 2 ) . T h e s e s u p p o r t s t r u t s w e r e a l s o b u i l t f r o m p h e n o l i c r e s i n b o a r d . M o u n t i n g t h e w e d g e s on s t r u t s f r o m t h e l i d s was n o t o n l y f o u n d t o be s t r o n g e r , b u t a l s o mean t t h a t t h e w e d g e s c o u l d e a s i l y be r e m o v e d f o r c l e a n i n g b e t w e e n s h o t s . F u r t h e r m o r e , t h e e l e c t r i c a l c o n n e c t i o n s t o e a c h e l e c t r o d e w e r e e a s i l y made b y r u n n i n g a w i r e t h r o u g h t h e b o d y o f t h e w e d g e , t h r o u g h t h e c e n t r e o f t h e s t r u t , and o u t v i a a c o n n e c t o r i n t h e l i d . 4 . 2 R E F L E C T E D SHOCK GENERATORS I n t h i s c o n f i g u r a t i o n s e v e r a l s t a n d i n g s h o c k s w e r e c r e a t e d b y s u c c e s s i v e r e f l e c t i o n s o f one s h o c k f r o m t h e w a l l s , a s shown s c h e m a t i c a l l y i n f i g u r e 4 . 3 . By u s i n g a number o f e l e c t r o d e s m o u n t e d on t h e w a l l and on t h e w e d g e , t h e o u t p u t f r o m e a c h s h o c k c o u l d be m e a s u r e d s e p a r a t e l y o r t h e o u t p u t s c o u l d be c o n n e c t e d i n s e r i e s . T h e r e w e r e no p r o v i s i o n s f o r p a r a l l e l c o n n e c t i o n s . F o r t h e f l o w c o n d i t i o n s i n t h e s h o c k t u b e t h e s t a n d i n g s h o c k was o n l y r e f l e c t e d f r o m t h e w a l l o n c e b e f o r e i t became 56 F i g u r e 4.3 S c h e m a t i c d i a g r a m o f t h e r e f l e c t e d s h o c k c o n f i g u r a t i o n v e r y weak. A f t e r t h i s p o i n t t h e f l o w was n e a r l y s o n i c . F i g u r e 4.4 shows a d r a w i n g o f t h e g e n e r a t o r s y s t e m used t o i n v e s t i g a t e t h e power o u t p u t o f a s t a n d i n g s h o c k and i t s f i r s t r e f l e c t i o n f r o m t h e w a l l . The c o n s t r u c t i o n o f t h i s s y s t e m was c o n s i d e r a b l y s i m p l e r t h a n t h e m u l t i p l e wedge s y s t e m . The s y m m e t r i c s h a p e o f t h e wedge meant t h a t t h e wedge was n o t s u b j e c t t o undue b e n d i n g s t r e s s and d i d n o t need a s t e e l r e i n f o r c i n g s p l i n e . The c o n s t r u c t i o n m a t e r i a l s were s i m i l a r t o t h o s e u s e d i n t h e m u l t i p l e wedge e x p e r i m e n t s . The e l e c t r o d e s were a l l made f r o m s t e e l , w h i l e t h e body o f t h e wedge and t h e s u p p o r t s t r u t were made f r o m p h e n o l i c b o a r d . E l e c t r i c a l c o n n e c t i o n s were o n c e a g a i n made w i t h a w i r e l e d t h r o u g h t h e b o d y o f t h e wedge and o u t t h r o u g h t h e s u p p o r t s t r u t t o t h e l i d . 57 F i g u r e 4.4 A c ros s s e c t i o n o f the r e f l e c t e d shock genera tor system 58 4.3 P R O V I S I O N S FOR GENERATOR CONNECTIONS AND POWER MEASUREMENT F o r t h e e x p e r i m e n t s o n e i t h e r c o n f i g u r a t i o n a p a t c h p a n e l was m o u n t e d i m m e d i a t e l y o u t s i d e t h e t e s t s e c t i o n so t h a t l e a d s f r o m t h e e l e c t r o d e s c o u l d be c o n n e c t e d t o g e t h e r i n a n y c o m b i n a t i o n . T h i s a l l o w e d t h e g e n e r a t o r s t o be r u n i n d i v i d u a l l y o r c o n n e c t e d t o g e t h e r i n s e r i e s o r i n p a r a l l e l . The p a n e l a l s o had p l u g - i n s f o r r e s i s t o r s s o t h a t e a c h g e n e r a t o r o r c o m b i n a t i o n c o u l d be l o a d e d a s d e s i r e d . The o u t p u t o f t h e g e n e r a t o r i n t o t h e l o a d was f o u n d b y m e a s u r i n g t h e v o l t a g e a c r o s s a c c u r a t e l y known l o a d r e s i s t o r s . D i f f e r e n t i a l a m p l i f i e r s a n d a d u a l beam o s c i l l o s c o p e w e r e u s e d f o r a l l o u t p u t v o l t a g e m e a s u r e m e n t s . 59 CHAPTER 5 . E X P E R I M E N T S B a s e d on t h e t e s t s d o n e on t h e s h o c k t u b e ( s e e c h a p t e r 3) i t was d e c i d e d t o c o n d u c t t h e bow s h o c k g e n e r a t o r t e s t s w i t h t h e t e s t s e c t i o n l o c a t e d 75 c m . f r o m t h e d i a p h r a g m . T h i s m e a n t t h a t t h e g e n e r a t o r s t h e m s e l v e s w e r e a b o u t 90 c m . f r o m t h e d i a p h r a g m . The s h o c k t u b e was o p e r a t e d w i t h a n o x y - a c e t y l e n e f i l l p r e s s u r e o f 250 T o r r and an a r g o n f i l l p r e s s u r e o f 5 T o r r . T h i s g a v e a n i n c i d e n t s h o c k a t a s p e e d o f 3 . 6 m m / m i c r o s e c o n d ( Mach 1 1 . 4 ) . F rom t h i s s p e e d and t h e s h o c k r e l a t i o n s , i n c l u d i n g t h e e f f e c t s o f i o n i z a t i o n ( s e e A p p e n d i x A ) , t h e f o l l o w i n g p a r a m e t e r s w e r e c a l c u l a t e d f o r t h e s u p e r s o n i c f l o w i n t h e t e s t s e c t i o n , d u r i n g t h e t e s t t i m e . p 2 = 1 . 1 5 x l 0 6 2 dynes/cm - 1 Atmosphere p 2 = 5 . 3 x l 0 " 5 gm/cm^ T 2 = 10,300 K h 2 = 6 . 5 x l 01 0 ergs/gm U 2 = 2 . 8 8 x l 05 cm/sec M 2 = 1.58 ne2= 2 . 1 x l 01 6 -3 cm a2 = 6.026 h = 1.51 60 A f l a n g e with a pressure probe i n i t was i n s e r t e d immediately ahead of the t e s t s e c t i o n . By feeding the pressure pulse from the i n c i d e n t shock through a number of v a r i a b l e d e l a y u n i t s , a l l the i n s t r u m e n t a t i o n f o r the t e s t s e c t i o n could be t r i g g e r e d with very l i t t l e j i t t e r . The wedges used i n the generators were a l l machined to have a 12° wedge angle. T h i s allowed comparison of a l l the r e s u l t s from these experiments, as w e l l as a comparison with other work being conducted i n the l a b . The c h o i c e of the wedge angle was governed by two f a c t o r s . The angle must be l a r g e enough to produce a strong standing shock, but not so l a r g e t h a t the shock detaches. I f the shock were to detach, the flow parameters behind i t could no longer be p r e d i c t e d by plane o b l i q u e shock theory. The c o n s t r u c t i o n of the wedges has been d i s c u s s e d i n more d e t a i l i n Chapter 4. It was q u i c k l y found that d e p o s i t s were l e f t on the e l e c t r o d e s a f t e r each shot. The d e p o s i t s appeared to be due, at l e a s t i n p a r t , to hot d e b r i s from the a c e t a t e diaphragm c a r r i e d with the flow. To keep the e l e c t r o d e s u r f a c e s as c l e a n and uncontaminated as p o s s i b l e the wedges and e l e c t r o d e s were removed and sanded with f i n e sandpaper a f t e r each shot. They were then cleaned with methanol and rep l a c e d i n the shock tube which was pumped f o r at l e a s t one h a l f hour before the 61 next shot was f i r e d . A c o n s i s t e n t numbering system has been adopted f o r a l l e l e c t r o d e s i n t h i s chapter. They have been numbered from zero to f i v e and the v o l t a g e measured between any 2 e l e c t r o d e s w i l l always be designated V^^V^-V^. 5.1 INDIVIDUAL SHOCK GENERATOR EXPERIMENTS The f i r s t s e r i e s of experiments measured the output from a s i n g l e standing shock, as shown s c h e m a t i c a l l y i n F i g u r e 5.1. 100JL AA/vV-INCIDENT S H O C K - / F i g u r e 5.1 S i n g l e standing shock generator s t r e t c h i n g across the whole tube The wedge was mounted one quarter inch o f f the f l o o r of the t e s t s e c t i o n so that i t would not be i n the boundary l a y e r . The development and s t a b i l i t y of the standing shock was monitored with a high speed framing camera. T y p i c a l r e s u l t s 62 o f t h e v o l t a g e m e a s u r e d a c r o s s t h e s h o c k and an e x a m p l e o f t h e c a m e r a p i c t u r e s a r e shown i n F i g u r e 5 . 2 . The v o l t a g e was m e a s u r e d w i t h a 100 Ohm l o a d a c r o s s t h e g e n e r a t o r . S i n c e t h e i n t e r n a l r e s i s t a n c e o f t h e g e n e r a t o r was f o u n d t o be o f t h e o r d e r o f a f e w Ohms t h e v o l t a g e m e a s u r e d a c r o s s 100 Ohms r e p r e s e n t s t h e o p e n c i r c u i t v o l t a g e f o r t h e g e n e r a t o r . By u s i n g a r e s i s t o r a s s m a l l a s 100 Ohms s p u r i o u s s i g n a l s due t o h i g h i m p e d e n c e n o i s e s o u r c e s w e r e e l i m i n a t e d . F rom a c o m p a r i s o n o f t h e f r a m i n g c a m e r a p i c t u r e s and t h e v o l t a g e t r a c e i t c a n be s e e n t h a t t h e r e i s a n i n i t i a l t r a n s i e n t s i g n a l a s s o c i a t e d w i t h t h e i n c i d e n t s h o c k . The s t a n d i n g s h o c k i s n o t w e l l e s t a b l i s h e d u n t i l some 10 - 15 m i c r o s e c o n d s a f t e r t h e f i r s t r i s e o f t h e v o l t a g e , and t h e s i g n a l was c o n s i d e r e d t o be s i m p l y a t r a n s i e n t up t o t h i s p o i n t . By t h e t i m e o f t h e f i f t h f r a m i n g c a m e r a p i c t u r e t h e s t a n d i n g s h o c k i s b e g i n n i n g t o l o s e i t s w e l l d e f i n e d e d g e and t h e v o l t a g e b e c o m e s u n s t e a d y , a s shown b y t h e m a r k e d i n c r e a s e i n t h e s i g n a l . I n o t h e r c a s e s i t was o b s e r v e d t h a t t h e v o l t a g e f e l l r a p i d l y t o z e r o a f t e r t h i s p o i n t . The t i m e f r o m t h e a r r i v a l o f t h e s h o c k t o t h e end o f t h e t e s t t i m e c a n be s e e n t o be a b o u t 27 m i c r o s e c o n d s f r o m b o t h t h e f r a m i n g c a m e r a p i c t u r e s and t h e v o l t a g e t r a c e . T h i s c o r r e l a t e s v e r y w e l l w i t h t h e d u r a t i o n o f t h e s t r o n g l u m i n o s i t y i n t h e s m e a r c a m e r a p h o t o g r a p h s ( s e e F i g u r e 5 . 3 ) . T h e s e m e a s u r e m e n t s a l l o w e d t h e t e s t t i m e t o be p r e d i c t e d f r o m t h e s m e a r c a m e r a p h o t o g r a p h s a s was d o n e i n C h a p t e r 3 . 1 2 3 4 5 5 u s/div S H O C K V O L T A G E V 5 1 ( S EE F I G . M ) ( A C R O S S 100 A ) L O C A T I O N O F F R O N T O F W E D G E - S T A N D I N G S H O C K L O S E S W E L L D E F I N E D E D G E ITS - A R R I V A L O F INCIDENT S H O C K F R A M I N G C A M E R A P H O T O G R A P H ( T I M I N G S H O W N A B O V E ) Figure 5.2 S i n g l e Shock Generator Results 64 27ps SHOCK S P E E D M A C H 11.4 F i g u r e 5 . 3 Smear c a m e r a p h o t o g r a p h o f t h e s l u g o f t e s t g a s t a k e n 90 c m . f r o m t h e d i a p h r a g m . I n o r d e r t o i n v e s t i g a t e t h e o u t p u t o f t h e g e n e r a t o r u n d e r l o a d t h e l o a d r e s i s t o r was v a r i e d f r o m s h o t t o s h o t so t h a t a V - I c h a r a c t e r i s t i c c o u l d be p l o t t e d f o r t h e s i n g l e s h o c k . The v o l t a g e s w e r e a l w a y s r e a d f r o m t h e o s c i l l o g r a m s 15 - 20 m i c r o s e c o n d s a f t e r t h e r i s i n g e d g e , when t h e s t a n d i n g s h o c k was w e l l e s t a b l i s h e d . The c h a r a c t e r i s t i c w h i c h i s shown i n F i g u r e 5 . 4 i n d i c a t e s t h e e f f e c t i v e i n t e r n a l r e s i s t a n c e o f t h e g e n e r a t o r i s a b o u t 5 . 5 ± . 5 Ohms. The powe r o u t p u t o f t h e g e n e r a t o r a s a f u n c t i o n o f c u r r e n t i s shown i n F i g u r e 5 . 5 The n e x t s e r i e s o f e x p e r i m e n t s was d o n e w i t h two w e d g e s a s shown i n F i g u r e 5 . 6 . The o u t p u t f r o m e a c h s h o c k was m e a s u r e d s e p a r a t e l y . T y p i c a l o p e n c i r c u i t v o l t a g e s i g n a l s and a f r a m i n g c a m e r a p i c t u r e s e r i e s a r e shown i n F i g u r e 5 . 7 . The 65 1.1 1.0 0.9 cjjioon > 0.8 O ^ELECTRODE SEPARATION =2 cm (SINGLE WEDGE EXPERIMENTS) =>ELECTRODE SEPARATION =1 cm (TOP WEDGE IN 2 WEDGE EXPERIMENTS) < o > 0.6 0.5 u X 0.3 5.5nT 2.8 SI 2.8/1 0.2 0.1 1 ^ I 1.0A1 0.5/1 100 200 CURRENT(mA) 300 F i g u r e 5 .4 V-I c h a r a c t e r i s t i c f o r two i n d i v i d u a l g e n e r a t o r s 100 80 h ELECTRODE SEPARATION • = 1cm O =2cm (SEE RG. 5.4 FOR DETAILS) 60 h CC LU o C L 40 h 20 \-- 0 -100 200 CURRENT (mA) 300 F i g u r e 5.5 Power output vs c u r r e n t f o r two i n d i v i d u a g e n e r a t o r s 67 F i g u r e 5 . 6 C o n f i g u r a t i o n and e l e c t r o d e n u m b e r s f o r t h e two wedge bow s h o c k g e n e r a t o r e x p e r i m e n t s s i g n a l s f r o m t h e t o p s h o c k c o m p a r e d f a v o u r a b l y w i t h t h e p r e v i o u s m e a s u r e m e n t s on a s i n g l e s h o c k . F o r t h e b o t t o m s h o c k h o w e v e r t h e s i g n a l s w e r e c o n s i s t e n t l y o f t h e r e v e r s e p o l a r i t y , o r v e r y s m a l l d u r i n g t h e t i m e t h e f r a m i n g c a m e r a p i c t u r e s showed t h e b o t t o m s h o c k t o be w e l l e s t a b l i s h e d . D e s p i t e t h i s u n e x p e c t e d r e s u l t f o r t h e b o t t o m wedge t h e V - I c h a r a c t e r i s t i c was m e a s u r e d f o r t h e t o p s h o c k b y v a r y i n g t h e l o a d r e s i s t o r f r o m s h o t t o s h o t . The r e s u l t s , shown i n F i g u r e 5 . 4 and F i g u r e 5 . 5 i n d i c a t e d an e f f e c t i v e i n t e r n a l r e s i s t a n c e o f a b o u t 2 . 8 + . 5 Ohms. A t l o w r e s i s t a n c e s i t was a l s o f o u n d t h a t a s m a l l v o l t a g e o f t h e e x p e c t e d p o l a r i t y was g e n e r a t e d b y t h e b o t t o m s h o c k . A number o f a t t e m p t s w e r e made t o i m p r o v e t h e o p e n c i r c u i t s i g n a l f r o m t h e b o t t o m w e d g e . Two o f t h e B O T T O M S H O C K V 13 0 . 5 V / d i v T O P S H O C K V 4 5 5 u s / d i v S H O C K V O L T A G E S ( S E E F I G . 5 .6 F O R E L E C T R O D E N O . ) A R R I V A L O F I N C I D E N T S H O C K FRAMING C A M E R A P H O T O G R A P H ( T I M I N G S H O W N A B O V E ) Figure 5.7 Two wedge open c i r c u i t v o l t a g e (across 100Q) an framing camera p i c t u r e s 69 a) Top wedge moved forward one i n c h and a new. e l e c t r o d e added b) V o l t a g e measured, to a sma l l e l e c t r o d e on the w a l l w i t h the w e d g e s l i n e d up nose to nose F i g u r e 5.8 Two of the c o n f i g u r a t i o n s that were t r i e d while attempting to improve the bottom shock s i g n a l c o n f i g u r a t i o n s that were t r i e d are shown i n Fi g u r e 5 . 8 . In the f i r s t one the top wedge was moved a d i s t a n c e of one inch upstream, and a new e l e c t r o d e added to the underside. In the second case the v o l t a g e was measured from the number 2 e l e c t r o d e to a small e l e c t r o d e mounted i n the w a l l of the t e s t s e c t i o n , ahead of the standing shock. Attempts were a l s o made to improve the s i g n a l by t i l t i n g the nose of the upper wedge down a few degrees. None of these c o n f i g u r a t i o n s was found to produce c o n s i s t e n t l y , a v o l t a g e of the expected p o l a r i t y 70 d u r i n g t h e t i m e t h e s t a n d i n g s h o c k was w e l l e s t a b l i s h e d . 5 . 2 S E R I E S CONNECTED SHOCK GENERATORS To s e e i f t h e v o l t a g e f r o m a s y s t e m o f bow s h o c k g e n e r a t o r s c o u l d be i n c r e a s e d t h e two g e n e r a t o r s w e r e c o n n e c t e d i n s e r i e s b y e x t e r n a l l y s h o r t i n g t h e n e g a t i v e l e a d o f one g e n e r a t o r t o t h e p o s i t i v e l e a d o f t h e o t h e r and m e a s u r i n g t h e v o l t a g e a c r o s s t h e p a i r . A s c h e m a t i c r e p r e s e n t a t i o n o f t h i s e x p e r i m e n t i s shown i n F i g u r e 5 . 9 p a r t B . F o r t h e f i r s t e x p e r i m e n t s w i t h t h e two g e n e r a t o r s c o n n e c t e d i n s e r i e s t h e o u t p u t was m e a s u r e d o p e n c i r c u i t ( a c r o s s l a r g e l o a d r e s i s t a n c e s ) . I n t h e s e e x p e r i m e n t s t h e v o l t a g e m e a s u r e d a c r o s s t h e p a i r o f s h o c k s was n e v e r g r e a t e r t h a n t h a t a c r o s s t h e t o p s h o c k a l o n e . A n o t h e r s e t o f s e r i e s c o n n e c t i o n e x p e r i m e n t s was c a r r i e d o u t w i t h a much l a r g e r l o a d ( s m a l l e r r e s i s t a n c e ) on t h e g e n e r a t o r s . S i n c e a b e t t e r v o l t a g e had b e e n m e a s u r e d a c r o s s t h e b o t t o m s h o c k a l o n e when i t was l o a d e d w i t h 2 . 8 Ohms, i t was h o p e d t h a t t h i s c h a n g e w o u l d i n c r e a s e t h e c o n t r i b u t i o n o f t h e b o t t o m s h o c k t o t h e t o t a l s i g n a l . A s m a l l e r l o a d r e s i s t a n c e s h o u l d a l s o t e n d t o r e d u c e t h e e f f e c t o f p a r a s i t i c l e a k a g e c u r r e n t s t h r o u g h t h e p l a s m a b e t w e e n e l e c t r o d e s 3 and 5 . T y p i c a l r e s u l t s f o r t h e s e e x p e r i m e n t s a r e shown i n F i g u r e 5 . 9 . The v o l t a g e a c r o s s e a c h s h o c k was f i r s t m e a s u r e d s e p a r a t e l y a s shown i n p a r t A . A l o a d r e s i s t o r r o u g h l y 7 1 The s c a l e on a l l three o s c i l l o g r a m s i s 0.5 V / d i v . and 5 u s / d i v . Arrows on the o s c i l l o g r a m s i n d i c a t e the time d u r i n g which both s t a n d i n g shocks are w e l l e s t a b l i s h e d . 5 a) V o l t a g e acros s each shock s e p a r a t e l y 5 b) V o l t a g e acros s bo th shocks i n s e r i e s . 5 c) E f f e c t o f s e r i e s c o n n e c t i o n on the v o l t a g e o f each shock i F i g u r e 5.9 The s e r i e s c o n n e c t i o n exper iments 72 m a t c h e d t o t h e i n t e r n a l i m p e d a n c e o f t h e g e n e r a t o r was u s e d f o r maximum power t r a n s f e r i n t o t h e l o a d . The two g e n e r a t o r s were t h e n c o n n e c t e d i n s e r i e s , k e e p i n g t h e l o a d m a t c h e d as shown i n F i g u r e 5.9 p a r t B. Once a g a i n t h e v o l t a g e m e a s u r e d a c r o s s t h e p a i r o f s h o c k s i n s e r i e s was n o t f o u n d t o be s i g n i f i c a n t l y g r e a t e r t h a n t h e v o l t a g e a c r o s s t h e t o p s h o c k a l o n e . To o b s e r v e t h e e f f e c t o f t h e s e r i e s c o n n e c t i o n on t h e o u t p u t o f e a c h s h o c k , t h e g e n e r a t o r s were c o n n e c t e d as shown i n F i g u r e 5.9 p a r t C. The r e s u l t s show t h a t t h e s i g n a l f r o m t h e t o p s h o c k i s c h a n g e d l i t t l e b y t h e c o n n e c t i o n b u t t h a t t h e s h a p e o f t h e b o t t o m s i g n a l i s q u i t e d i f f e r e n t . The o s c i l l o g r a m a l s o shows t h a t t h e v o l t a g e b e t w e e n e l e c t r o d e s 1 and 3 i s much r e d u c e d d u r i n g t h e t i m e t h e s t a n d i n g s h o c k s a r e w e l l e s t a b l i s h e d . 5.3 PARALLEL CONNECTED SHOCK GENERATOR I f s e v e r a l bow s h o c k g e n e r a t o r s a r e c o n n e c t e d i n p a r a l l e l i t may be p o s s i b l e t o i n c r e a s e t h e c u r r e n t d e l i v e r e d t o a l o a d o v e r t h a t s u p p l i e d by a s i n g l e g e n e r a t o r . I n o r d e r t o t e s t t h i s c o n c e p t an e x p e r i m e n t was d e s i g n e d where t h e two g e n e r a t o r s c o u l d be c o n n e c t e d i n p a r a l l e l . S i n c e t h e v o l t a g e f r o m t h e b o t t o m s h o c k was a l w a y s much s m a l l e r t h a n t h a t f r o m t h e t o p , a s i m p l e p a r a l l e l c o n n e c t i o n o f b o t h g e n e r a t o r s i n t o a s i n g l e m a t c h e d l o a d w o u l d n o t w o r k . I n t h a t c a s e a f r a c t i o n o f t h e power f r o m t h e t o p g e n e r a t o r w o u l d be d i s s i p a t e d i n t h e 73 plasma of the bottom generator i n s t e a d of being d e l i v e r e d to the l o a d . To demonstrate i n c r e a s e d c u r r e n t i n a l o a d , a vo l t a g e d i v i d e r load connected as shown i n Fi g u r e 5.10 was Figu r e 5.10 Loading of the generators used f o r the p a r a l l e l c o nnection experiments used. The output from the top generator was a p p l i e d across both r e s i s t o r s , which were chosen to match the i n t e r n a l r e s i s t a n c e of the top gener a t o r . The v o l t a g e d i v i d e r r a t i o was chosen so that when the bottom generator was connected to the small r e s i s t o r , the power t r a n s f e r to the load was a maximum. By measuring the v o l t a g e across the 1 ohm r e s i s t o r the c u r r e n t d e l i v e r e d to t h i s p a r t of the load could be determined. F i g u r e 5.11 shows a comparison of the v o l t a g e a c r o s s R when o n l y the top generator was connected and then when both ge n e r a t o r s were connected i n p a r a l l e l . While the TOP GENERATOR DIFFERENTIAL SCOPE INPUT * 1 4 74 0.1 V/div 5 )js/div VOLTAGE ACROSS R 2 TOP GENERATOR ONLY 0.1 V/div 5 jjs/div VOLTAGE ACROSS R 2 BOTH GENERATORS IN PARALLEL F i g u r e 5 . 1 1 O u t p u t o f s i n g l e g e n e r a t o r c o m p a r e d t o o u t p u t o f p a r a l l e l c o n n e c t i o n o f b o t h g e n e r a t o r s g e n e r a t o r l o a d i s n o t s e t up t o e x t r a c t maximum t o t a l powe r t h i s e x p e r i m e n t d e m o n s t r a t e s t h a t powe r o u t p u t i s i n c r e a s e d when bow s h o c k g e n e r a t o r s a r e c o n n e c t e d i n p a r a l l e l . 5 . 4 R E F L E C T E D OBLIQUE SHOCK GENERATOR I t may be p o s s i b l e t o i n c r e a s e t h e v o l t a g e o u t p u t o f a s y s t e m o f g e n e r a t o r s and u t i l i z e t h e f l o w more e f f i c i e n t l y b y e x t r a c t i n g powe r f r o m t h e s t a n d i n g o b l i q u e s h o c k and f r o m s u c c e s s i v e r e f l e c t i o n s o f t h i s s h o c k f r o m t h e w a l l s . The v o l t a g e c o u l d be i n c r e a s e d by c o n n e c t i n g t h e o u t p u t f r o m t h e s e s h o c k s t o g e t h e r on s e r i e s . To t e s t t h i s p o s s i b i l i t y a s y s t e m c o n s i s t i n g o f a s i n g l e s t a n d i n g s h o c k and i t s f i r s t r e f l e c t i o n f r o m t h e w a l l was i n v e s t i g a t e d . I n t h e s e e x p e r i m e n t s a s y m m e t r i c wedge w i t h o n e e l e c t r o d e on t h e l e a d i n g e d g e was i J Tr • • 75 u s e d . Two e l e c t r o d e s w e r e m o u n t e d on t h e w a l l one a h e a d o f t h e f i r s t s h o c k p r o d u c e d by t h e wedge and one i n t h e r e g i o n b e h i n d t h e r e f l e c t e d o b l i q u e s h o c k a s shown i n F i g u r e 5 . 1 2 . The d e t a i l s o f t h i s g e n e r a t o r s y s t e m a r e d e s c r i b e d i n C h a p t e r 4 . B e f o r e t h e e x p e r i m e n t s on a s e r i e s c o n n e c t i o n w e r e d o n e t h e f i r s t s h o c k p r o d u c e d by t h e wedge was t e s t e d a s an i n d i v i d u a l s h o c k g e n e r a t o r , w i t h o u t t h e r e f l e c t e d s h o c k . The v o l t a g e was m e a s u r e d o p e n c i r c u i t ( a c r o s s 100 Ohms) b e t w e e n e l e c t r o d e s 4 and 5 ( s e e F i g u r e 5 . 1 2 ) and was f o u n d t o be l . O V i O . l V . T h i s i s i n g o o d a g r e e m e n t w i t h t h e p r e v i o u s r e s u l t s f r o m s i n g l e s h o c k e x p e r i m e n t s . To t e s t t h e c o n c e p t o f c o n n e c t i n g t h e f i r s t s h o c k and i t s r e f l e c t i o n f r o m t h e w a l l t o g e t h e r i n s e r i e s t h e v o l t a g e was m e a s u r e d f r o m e l e c t r o d e 5 t o e l e c t r o d e 2 ( s e e F i g u r e 5 . 1 2 ) . Once a g a i n a 100 Ohm l o a d was u s e d . I t was f o u n d t h a t t h i s v o l t a g e was l e s s t h a n 0 . 1 V , much s m a l l e r t h a n t h a t a c r o s s t h e f i r s t s h o c k a l o n e . F i g u r e 5 . 1 2 s h o w s a t y p i c a l s i g n a l . W h i l e t h i s r e s u l t was somewha t u n e x p e c t e d i t was s i m i l a r t o a r e s u l t o b t a i n e d much e a r l i e r d u r i n g t h e e x p e r i m e n t s on s i n g l e s t a n d i n g s h o c k s . B e f o r e i t was r e c o g n i z e d t h a t i t was i m p o r t a n t t o moun t t h e b o t t o m wedge o u t s i d e t h e b o u n d a r y l a y e r i t h a d b e e n m o u n t e d on t h e f l o o r o f t h e t e s t s e c t i o n a s shown i n F i g u r e 5 . 1 2 . I n t h i s c o n f i g u r a t i o n t h e v o l t a g e a c r o s s t h e s h o c k was m e a s u r e d b e t w e e n an e l e c t r o d e on t h e f r o n t o f t h e wedge and 7 6 100A rVAn a) S e r i e s a d d i t i o n a c r o s s a shock and i t s r e f l e c t i o n . Arrows i n d i c a t e the time d u r i n g which the s t a n d i n g shocks were observed t o be w e l l e s t a b l i s h e d from f r a m i n g camera pho t o g r a p h s . Mo I. 1, 1—1 1 1.0 V/div 5 ps/div I—wv—1 100A b) E a r l / m e a s u r e m e n t o f the v o l t a g e a c r o s s a s i n g l e s t a n d i n g shock F i g u r e 5.12 A comparison o f the r e s u l t s o f the r e f l e c t e d shock s e r i e s a d d i t i o n s i g n a l and the e a r l y s i n g l e shock e x p e r i m e n t s 77 one m o u n t e d on t h e w a l l w e l l a h e a d o f t h e s h o c k . T h i s v o l t a g e , a s shown i n F i g u r e 5 . 1 2 , was o b s e r v e d t o be v e r y s m a l l and o f t h e o p p o s i t e p o l a r i t y t o t h a t e x p e c t e d f r o m t h e o t h e r s i n g l e s t a n d i n g s h o c k e x p e r i m e n t s . I n b o t h e x p e r i m e n t s t h e two e l e c t r o d e s w e r e m o u n t e d one on e a c h s i d e o f t h e s h o c k f r o n t . H o w e v e r t h e y w e r e embedded i n t h e same b o u n d a r y l a y e r and t h e v o l t a g e s w e r e f o u n d t o be much s m a l l e r t h a n t h o s e m e a s u r e d i n o t h e r g e o m e t r i e s . I t t h e r e f o r e a p p e a r s l i k e l y t h a t t h e two e l e c t r o d e s a r e c o n n e c t e d e l e c t r i c a l l y t h r o u g h t h e b o u n d a r y l a y e r w h e r e t h e f l o w i s s u b s o n i c . I n o r d e r t o g a i n f u r t h e r i n s i g h t i n t o t h i s p a r t i c u l a r c o n f i g u r a t i o n o f s h o c k s t h e v o l t a g e a c r o s s t h e r e f l e c t e d s h o c k a l o n e was a l s o m e a s u r e d . The o p e n c i r c u i t (100 Ohms) v o l t a g e was o b t a i n e d b e t w e e n e l e c t r o d e 4 and e l e c t r o d e 2 a s shown i n F i g u r e 5 . 1 3 . I t was f o u n d t o be 0 . 9 V ± 0 . 1 V and t o h a v e o p p o s i t e p o l a r i t y t o t h a t e x p e c t e d f r o m t h e s h o c k v o l t a g e a c r o s s t h e r e f l e c t e d s h o c k . T h i s u n e x p e c t e d s i g n a l i s d i s c u s s e d a l o n g w i t h t h e o t h e r r e s u l t s i n t h e n e x t c h a p t e r . s 78 100A 1.0 V/div F i g u r e 5.13 The r e f l e c t e d o b l i q u e shock v o l t a g e CHAPTER 6. INTERPRETATION OF RESULTS 6.1 SUMMARY OF RESULTS The r e s u l t s d e s c r i b e d i n the previous chapter p a r t l y confirmed our understanding of bow shock generators and were p a r t l y unexpected. When t r y i n g to i n t e r p r e t the r e s u l t s , i t i s important to bear i n mind that the experiments were c a r r i e d out with one p a r t i c u l a r set of supersonic flow c o n d i t i o n s , which may be summarized as f o l l o w s : T = 10,300 K -5 3 Pi = 5.3x10 gm/cm P j = 1.5x10^ dynes/cm ai = 2.7% n = 2 . 1 x l 0 6 cm"3 80 F o r w e d g e s w i t h a n a n g l e 6 = 1 2 ° a s u s e d i n t h e s e e x p e r i m e n t s , t h e s h o c k a n g l e was m e a s u r e d t o be 5 5 ° ± 2 ° . The o b l i q u e s h o c k i n t h e s e e x p e r i m e n t s t h e r e f o r e had a Mach number o f a b o u t 1 . 3 . I n g e n e r a l t h e r e was a c o n s i d e r a b l e s h o t t o s h o t v a r i a t i o n i n t h e o b s e r v e d e l e c t r i c a l s i g n a l s , b o t h i n t h e m a g n i t u d e and t h e s h a p e o f t h e s i g n a l s . The o p e n c i r c u i t v o l t a g e a c r o s s a s i n g l e s t a n d i n g s h o c k c r e a t e d by a wedge was u s u a l l y 0 . 9 5 V ± 0 . 1 V . F o r t h e b o t t o m s h o c k i n t h e two wedge e x p e r i m e n t h o w e v e r , a s m a l l e r l e s s s t e a d y v o l t a g e , w h i c h s o m e t i m e s e v e n s w i t c h e d p o l a r i t y , was 81 m e a s u r e d . When t h e l o a d o n a s i n g l e s h o c k g e n e r a t o r was v a r i e d , t h e o u t p u t v o l t a g e a t maximum power t r a n s f e r was f o u n d t o d e p e n d on t h e e l e c t r o d e s e p a r a t i o n ( d ) . When t h e e l e c t r o d e s w e r e m o u n t e d a t t h e l a r g e s t p r a c t i c a l s e p a r a t i o n (d=2 cm) t h e g e n e r a t o r was f o u n d t o h a v e a maximum power o u t p u t o f 53 mW and an e f f e c t i v e i n t e r n a l r e s i s t a n c e o f a b o u t 5 . 5 ± . 5 Ohms. When t h e d i s t a n c e b e t w e e n t h e e l e c t r o d e s was r e d u c e d t o . d = l cm t h e maximum power o u t p u t i n c r e a s e d t o 90 mW and t h e g e n e r a t o r was f o u n d t o h a v e an e f f e c t i v e i n t e r n a l r e s i s t a n c e o f a b o u t 2 . 8 ± . 5 Ohms. A s e r i e s c o n n e c t i o n o f two s h o c k s t h a t w e r e o n e a b o v e t h e o t h e r i n t h e f l o w d i d n o t p r o d u c e a l a r g e r v o l t a g e t h a n t h a t m e a s u r e d f r o m one o f t h e s h o c k s a l o n e . A p a r a l l e l c o n n e c t i o n o f t h e two s h o c k s d i d h o w e v e r show a s m a l l i n c r e a s e i n o u t p u t c u r r e n t . M e a s u r e m e n t s made o n a s h o c k a n d i t s r e f l e c t i o n f r o m t h e w a l l showed t h e v o l t a g e a c r o s s t h e f i r s t s h o c k t o be i n g o o d a g r e e m e n t w i t h o t h e r s i n g l e s h o c k m e a s u r e m e n t s . The v o l t a g e a c r o s s t h e s h o c k r e f l e c t e d f r o m t h e w a l l h o w e v e r was f o u n d t o be o p p o s i t e i n p o l a r i t y t o t h a t e x p e c t e d . 6 . 2 SHOCK ANGLE The m e a s u r e d s h o c k a n g l e ^ a, ( s e e F i g u r e 6 . 1 ) c a n be c o m p a r e d w i t h t h e v a l u e p r e d i c t e d b y o b l i q u e s h o c k t h e o r y . I n t h i s c a l c u l a t i o n o n e a s s u m e s t h a t t h e f l o w b e h i n d t h e s h o c k i s p a r a l l e l t o t h e wedge s u r f a c e . The i n i t i a l v e l o c i t y o f t h e 82 STANDING SHOCK \ WEDGE F i g u r e 6 . 1 O b l i q u e s h o c k s u p e r s o n i c g a s i s b r o k e n i n t o two c o m p o n e n t s . The v e l o c i t y c o m p o n e n t p a r a l l e l t o t h e s h o c k f r o n t i s u n c h a n g e d a c r o s s t h e s h o c k , w h i l e t h e v e l o c i t y c o m p o n e n t p e r p e n d i c u l a r t o t h e s h o c k f r o n t u n d e r g o e s a j ump a c r o s s t h e s h o c k . The v e l o c i t y j ump f o r t h e p e r p e n d i c u l a r c o m p o n e n t s i s g o v e r n e d by t h e u s u a l s h o c k r e l a t i o n s . I n t h i s way one c a n r e l a t e t h e s h o c k a n g l e , o , t o t h e i n c i d e n t Mach number ( M 2 ) and t h e wedge a n g l e 6. I n t h e c a s e o f p a r t i a l l y i o n i z e d f l o w , t h e n o r m a l s h o c k r e l a t i o n s a r e no l o n g e r a p p l i c a b l e , a s was m e n t i o n e d i n C h a p t e r 2 . A p r o g r a m h a s b e e n w r i t t e n i n t h e l a b h o w e v e r , w h i c h by means o f a n i t e r a t i v e t e c h n i q u e , c a l c u l a t e s t h e f l o w p a r a m e t e r s b e h i n d a n o r m a l s h o c k wave i n p a r t i a l l y i o n i z e d a r g o n ( s e e a p p e n d i x A ) . By a p p l y i n g t h e s e r e s u l t s t o t h e p e r p e n d i c u l a r c o m p o n e n t o f v e l o c i t y a c r o s s t h e o b l i q u e s h o c k , t h e s h o c k a n g l e , o , c a n be f o u n d a s a f u n c t i o n o f M 2 and 6 ( s e e T a b l e 1 , i n S e c t i o n 6 . 3 ) . An o b l i q u e s h o c k p r o g r a m h a s a l s o b e e n w r i t t e n i n t h i s l a b * 8 w h i c h t a b u l a t e s a l l t h e f l o w 83 p a r a m e t e r s b e h i n d t h e o b l i q u e s h o c k , and t h e s h o c k a n g l e f o r g i v e n i n i t i a l c o n d i t i o n s . F o r t h e f l o w c o n d i t i o n s i n t h e s h o c k t u b e , and a wedge a n g l e o f 12 d e g r e e s t h e o b l i q u e s h o c k a n g l e was c a l c u l a t e d t o be 4 6 ° . The m e a s u r e d v a l u e o f t h e a n g l e was 5 5 ° ± 2 ° . T h i s may i n d i c a t e t h a t t h e f l o w b e h i n d t h e i n c i d e n t s h o c k a c t u a l l y had a somewha t l o w e r Mach number t h a n t h a t c a l c u l a t e d f r o m t h e s p e e d o f t h e i n c i d e n t s h o c k . A l t e r n a t i v e l y , s i n c e t h e p r o g r a m d o e s n o t t a k e a c c o u n t o f t h e f i n i t e r e l a x a t i o n r a t e f o r i o n i z a t i o n i n t h e g a s b e h i n d t h e s t a n d i n g s h o c k , t h i s e f f e c t may p r o d u c e a d i f f e r e n t s h o c k a n g l e t h a n t h a t p r e d i c t e d by t h e p r o g r a m . 6 . 3 OPEN C I R C U I T VOLTAGE The o p e n c i r c u i t v o l t a g e a c r o s s t h e s h o c k c a n be d e s c r i b e d w i t h a f a i r l y s i m p l e m o d e l , s t a r t i n g w i t h t h e 19 g e n e r a l i z e d Ohms l a w . I n one d i m e n s i o n w i t h no m a g n e t i c f i e l d s p r e s e n t i t may be s t a t e d a s 84 -'in.e. (e. + e ) + n e. e I — ( 1 ie 10 eo o i o eoj (6.1) = - ( E . - e )grad p - n.(e. + e )eE i o eo' 6 *e i v i o eoJ w h e r e j = current density P e = electron pressure e k l = Q, , H f r i c t i o n c o e f f i c i e n t k l \l= c o l l i s i o n cross section n.,n ,n = ion, electron, and neutral number de n s i t i e s I e o F o r t h e c a s e o f a s t a n d i n g s h o c k t h e r e w i l l be a l a r g e g r a d p g t e r m w h i c h w i l l c a u s e a c h a r g e s e p a r a t i o n b e t w e e n t h e 85 ions and the more mobile e l e c t r o n s . In the open c i r c u i t , steady s t a t e s i t u a t i o n the c u r r e n t w i l l be zero and the g r a d i e n t term w i l l be balanced by an E f i e l d caused by the charge s e p a r a t i o n . Since e . >>e and n =n., the E f i e l d may 10 eo e 1 be w r i t t e n as E = _ g r a d P e = 1 d Cn kT ) e eJ en en dx e dx dx (6.2) The p o t e n t i a l across the shock may be found by i n t e g r a t i n g the E f i e l d from one s i d e of the shock to the oth e r . 2 2 2 (6.3) <(. = j-Edx = k jTed(ln V > + - jc e e 1 1 1 2 For the i n t e g r a t i o n the shock s t r u c t u r e assumed by J a f f r i n was used. A schematic of the shock s t r u c t u r e i s shown i n Figure 6.2. Since the charge s e p a r a t i o n between ions and e l e c t r o n s i s small compared to the atom shock t h i c k n e s s , n 86 THERMAL LAYER -ATOM SHOCK 1 * 6 ® 6 Je (ELECTRON TEMPERATURE) n e n-, (NUMBER DENSITIES) ( POTENTIAL) F i g u r e 6 . 2 The m o d e l u s e d f o r t h e s h o c k s t r u c t u r e may be a s s u m e d t o be c o n s t a n t e v e r y w h e r e e x c e p t i n t h e s h o c k . The e l e c t r o n t e m p e r a t u r e b e g i n s t o r i s e i n t h e t h e r m a l l a y e r a h e a d o f t h e s h o c k b e c a u s e o f t h e h i g h t h e r m a l c o n d u c t i v i t y o f t h e e l e c t r o n s . A c r o s s t h e s h o c k h o w e v e r , T i s a s s u m e d t o be e c o n s t a n t . The i n t e g r a l may t h e r e f o r e be e v a l u a t e d and t h e p o t e n t i a l g i v e n a s : 8 7 ( 6 . 4 ) F i n a l l y , J a f f r i n ' s a n a l y s i s shows t h a t a f t e r t h e s h o c k t h e e l e c t r o n t e m p e r a t u r e r i s e s o n l y a s m a l l amount so t h a t may be a p p r o x i m a t e d by t h e f i n a l e l e c t r o n t e m p e r a t u r e T e2« A s s u m i n g t h a t t h e f l o w i s i n e q u i l i b r i u m b e f o r e and a f t e r t h e t h e r m a l l a y e r , and t h a t t h e i o n i z a t i o n i s f r o z e n t h r o u g h t h e a tom s h o c k , t h e f i n a l r e s u l t f o r t h e p o t e n t i a l i s w i t h t h e t e m p e r a t u r e e x p r e s s e d i n e V , t h e v o l t a g e a c r o s s t h e s h o c k c a n be w r i t t e n a s c a s e o f t h e i n c i d e n t f l o w i n t h e s e e x p e r i m e n t s t h e v o l t a g e p r e d i c t e d by t h i s s i m p l e m o d e l i s a b o u t 0 . 5 V a s c o m p a r e d t o ( 6 . 5 ) ( 6 . 6 ) T h i s v o l t a g e a c r o s s a s t a n d i n g s h o c k may be c a l c u l a t e d , f rom- t h e f l o w s t a t e ; a h e a d o f and b e h i n d t h e s h o c k a s t a b u l a t e d b y t h e o b l i q u e s h o c k c o m p u t e r p r o g r a m ( s e e T a b l e I ) . F o r t h e 88 Wedge angle 6° Shock angle c a l c u l a t e d a0 Shock angle measured a" Shock vo l t age c a l c u l a t e d Shock vo l t age measured 8.9 43 0.36 10.8 45 0.43 12 46.4 55 0.49 0.95 14.1 49.0 0.58 16.8 53 0.70 20.6 61 0.90 T a b l e I C a l c u l a t e d and m e a s u r e d p a r a m e t e r s f o r t h e s h o c k g e n e r a t o r t h e m e a s u r e d v a l u e o f 0 . 9 5 V . The d i s c r e p a n c y may t o a l a r g e e x t e n t be c a u s e d b y t h e p l a s m a s h e a t h s a t t h e e l e c t r o d e s . The b e h a v i o u r o f t h e s e s h e a t h s f o r f l a t p r o b e s i n s u p e r s o n i c f l o w i s c o m p l i c a t e d and h a s n o t b e e n w e l l u n d e r s t o o d so no a t t e m p t was made t o i n c l u d e them i n t h i s m o d e l . 6 . 4 INTERNAL R E S I S T A N C E A s a n e s t i m a t e o f t h e i n t e r n a l r e s i s t a n c e o f t h e g e n e r a t o r s t h e b u l k r e s i s t a n c e o f t h e p l a s m a b e t w e e n t h e e l e c t r o d e s was c a l c u l a t e d . U s i n g t h e g e n e r a l i z e d Ohms l a w ( e q u a t i o n 6 . 1 ) w i t h no m a g n e t i c f i e l d s o r p r e s s u r e g r a d i e n t s , 89 the bulk c o n d u c t i v i t y may be expressed as: j = V i e 6 ' 5 = a, E < 6- 7> J dc n. e. e. +n e. e 1 ie 10 o 10 eo where once again e e Q has been neglected compared to The c o n d u c t i v i t y may thus be expressed as: 'dc 2 e n. I 2 e n. I (6.8) n.e. +n e 4 v7 kTM \ n.Q. +n Q l ie o eo I — eJ I ie o eo The c r o s s s e c t i o n s Q and Q were c a l c u l a t e d from i e eo -13 2 -16 2 Arzimovich to be Q =3.8X10" cm , Q =1.0X10*" cm . Using i e eo the temperature and number d e n s i t i e s ahead of the shock where the c o n d u c t i v i t y i s lowest, a value of a=10.0 mhos/cm was c a l c u l a t e d . T h i s was considered to be onl y an estimate, s i n c e the c r o s s s e c t i o n s a r e o n l y approximate, but i t i s i n l i n e with 21 c o n d u c t i v i t i e s measured by L i n , R e s l e r and Kantrowitz under s i m i l a r c o n d i t i o n s of about 30 mho/cm. The area of the e l e c t r o d e s i n these experiments was about 2 2 cm and f o r the top wedge generator the e l e c t r o d e spacing was about 1 cm. Using the above estimate f o r the c o n d u c t i v i t y , the bulk plasma r e s i s t a n c e of the top generator would be no more than 0.1 Ohm. The measured value of the 90 e f f e c t i v e i n t e r n a l r e s i s t a n c e f o r t h i s generator was about 2.8 Ohms, and the i n t e r n a l r e s i s t a n c e increased by about a f a c t o r of two when the bulk plasma le n g t h was doubled. The d i s c r e p a n c y between measured and c a l c u l a t e d resistamce may be due to the f a c t that i o n i z a t i o n e q u i l i b r i u m had i n f a c t not been reached during the t e s t time. L i n , R e s l e r and K antrowitz, i n t h e i r experiments, noted that i n some cases the c o n d u c t i v i t y was s t i l l r i s i n g at the end of the t e s t time, and t h e r e f o r e f u l l e q u i l i b r i u m c o n d u c t i v i t y had not been reached. T h e i r measured c o n d u c t i v i t i e s f o r these cases were as much as an order of magnitude below the t h e o r e t i c a l v a l u e s . I t may t h e r e f o r e be, that i n the bow shock generator measurements the c o n d u c t i v i t y has not reached i t s maximum e q u i l i b r i u m v a l u e , and thus the bulk r e s i s t a n c e was s t i l l s i g n f i c a n t . An a l t e r n a t i v e e x p l a n a t i o n i s to assume that a s i g n i f i c a n t c o n t r i b u t i o n to the t o t a l r e s i s t a n c c e comes from the thermal, e l e c t r i c a l and flow boundary l a y e r s near the e l e c t r o d e s . I t i s d i f f i c u l t to assess t h e i r i n f l u e n c e q u a n t i t a t i v e l y however, as long as t h e i r exact extent and p h y s i c a l p r o p e r t i e s are net known. From the v a r i a t i o n of output v o l t a g e at maximum power, with d i s t a n c e , i n f o r m a t i o n could a l s o be d e r i v e d about the approximate f i e l d s t r e n g t h i n the c o l d plasmas. 91 6 . 5 BOTTOM SHOCK The b o t t o m s h o c k ' i n t h e two wedge e x p e r i m e n t s was f o u n d t o g i v e a s m a l l u n s t e a d y o p e n c i r c u i t s i g n a l ( b e t w e e n e l e c t r o d e s 1 and 3 i n F i g u r e ( 5 . 6 ) ) , w h i c h s o m e t i m e s e v e n s w i t c h e d p o l a r i t y . S i n c e a g o o d s i g n a l was o b t a i n e d b e t w e e n t h e b o t t o m wedge and an e l e c t r o d e i n t h e t o p l i d o f t h e t e s t s e c t i o n ( e l e c t r o d e s 1 and 2 i n F i g u r e 5 . 6 ) , t h e p r o b l e m c a n be p r e s u m e d t o l i e w i t h t h e t o p w e d g e , o r t h e e l e c t r o d e o n t h e u n d e r s i d e o f t h i s wedge ( e l e c t r o d e 3 ) . The b o u n d a r y l a y e r on t h e u n d e r s i d e o f t h i s wedge w i l l be d i f f e r e n t f r o m t h a t on t h e w a l l . P a r t i c u l a r l y l a t e i n t h e t e s t t i m e , t h e b o u n d a r y l a y e r on t h e w a l l w i l l be t h i c k e r and more d e v e l o p e d . T h i s m i g h t a f f e c t t h e e l e c t r o d e o r t h e p l a s m a s h e a t h i n f r o n t o f t h e e l e c t r o d e on t h e w a l l d i f f e r e n t l y t h a n t h e o n e o n t h e w e d g e . A n o t h e r p o s s i b i l i t y i s t h a t t h e r e was some s p i l l a g e o f h o t p l a s m a a r o u n d t h e e d g e o f t h e w e d g e , f r o m t h e r e g i o n b e h i n d t h e o b l i q u e s h o c k o f t h e t o p w e d g e . S i n c e t h e t i p s o f t h e w e d g e s a r e a l w a y s m i c r o s c o p i c a l l y b l u n t , a s m a l l p o r t i o n o f t h e s t a n d i n g s h o c k w i l l be d e t a c h e d . T h i s may a l l o w some h o t g a s f r o m t h e s t a g n a t i o n p o i n t t o f l o w o u t u n d e r t h e t o p w e d g e . I n some o f t h e f r a m i n g c a m e r a p h o t o g r a p h s , a f a i n t g l o w was n o t i c e d a l o n g t h e b o t t o m o f t h e w e d g e s . T h i s was n o t c o n s i s t e n t l y o b s e r v e d h o w e v e r , and i t was d i f f i c u l t t o t e l l w h e t h e r o r n o t t h e l u m i n o s i t y t r u l y r e p r e s e n t e d h o t g a s f r o m t h e n o s e o f t h e w e d g e . F i n a l l y , i t m i g h t be p o s s i b l e t h a t t h e r e e x i s t e d a p a t K 1 b e t w e e n t h e two e l e c t r o d e s t h r o u g h t h e 9 2 b o u n d a r y l a y e r s w h i c h l i n e t h e v e r t i c a l w a l l s o f t h e s h o c k t u b e . I f t h i s w e r e t h e c a s e , m o v i n g t h e u p p e r e l e c t r o d e f r o m t h e t o p l i d t o t h e m i d d l e wedge w o u l d s i m p l y s h o r t e n t h e l e a k a g e p a t h t h r o u g h t h e b o u n d a r y l a y e r . 6 . 6 S E R I E S CONNECTION I n e x p e r i m e n t s w i t h t h e bow s h o c k g e n e r a t o r s c o n n e c t e d i n s e r i e s t h e o u t p u t v o l t a g e m e a s u r e d a c r o s s b o t h s h o c k s was n e v e r g r e a t e r t h a n t h a t a c r o s s t h e t o p s h o c k a l o n e . Once a g a i n t o t r e a t t h i s p r o b l e m p r o p e r l y t h e e f f e c t s o f t h e s h e a t h s a t t h e e l e c t r o d e s w o u l d h a v e t o be c o n s i d e r e d . A q u a l i t a t i v e a r g u m e n t m i g h t be g i v e n a s f o l l o w s h o w e v e r . B e g i n n i n g a t p o i n t 4 i n F i g u r e 6 . 3 t h e p o t e n t i a l a l o n g t h e d o t t e d l i n e w o u l d d r o p t h r o u g h t h e f i r s t s h o c k , t h e n i t m i g h t v a r y s l i g h t l y f r o m t h e r e t o t h e n e x t s h o c k w h e r e i t w o u l d r i s e a g a i n t o r o u g h l y t h e same v a l u e . The r e s u l t a n t p o t e n t i a l b e t w e e n e l e c t r o d e s 1 and 4 w o u l d be q u i t e s m a l l . When e l e c t r o d e 3 i s s h o r t e d t o e l e c t r o d e 4 i t may be t h a t b o t h e l e c t r o d e s a s s u m e t h e p o t e n t i a l t h a t e l e c t r o d e 4 had b e f o r e t h e c o n n e c t i o n was m a d e . The s h e a t h i n f r o n t o f e l e c t r o d e 3 m i g h t t h e n a d j u s t i t s e l f , i n c r e a s i n g t h e v o l t a g e d r o p a c r o s s t h e s h e a t h s o t h a t a l o n g a p a t h f r o m e l e c t r o d e 4 t o e l e c t r o d e 1 , p a s s i n g t h r o u g h e l e c t r o d e 3 and t h e b o t t o m s h o c k , t h e n e t p o t e n t i a l r i s e i s s m a l l . I t s h o u l d be p o i n t e d o u t t h a t a l t h o u g h t h e r e s u l t s f r o m a s e r i e s c o n n e c t i o n i n t h e p r e s e n t e x p e r i m e n t s a r e d i s c o u r a g i n g , 93 F i g u r e 6.3 S e r i e s c o n n e c t e d s h o c k s t h e p o o r s i g n a l f r o m t h e b o t t o m s h o c k , and t h e v a r i a t i o n i n v o l t a g e s i g n a l s f r o m s h o t t o s h o t , make i t h a r d t o d r a w a f i r m c o n c l u s i o n . 6.7 P A R A L L E L CONNECTION I n t h e c a s e o f a p a r a l l e l c o n n e c t i o n o f s e v e r a l g e n e r a t o r s i t d o e s a p p e a r t h a t t h e r e may be some o p p o r t u n i t y f o r an i n c r e a s e i n c u r r e n t e x t r a c t i o n . The d i f f e r e n c e i n e f f e c t i v e i n t e r n a l r e s i s t a n c e s b e t w e e n l a r g e and s m a l l s t a n d i n g s h o c k s c o u l d make a number o f s m a l l s h o c k g e n e r a t o r s an a t t r a c t i v e way t o e x t r a c t e n e r g y f r o m a f l o w . 94 6.8 R E F L E C T E D OBL IQUE SHOCK I n t h e e x p e r i m e n t s on t h e r e f l e c t e d s h o c k , t h e a t t e m p t s t o add t h e v o l t a g e s a c r o s s a n o b l i q u e s h o c k a n d i t s r e f l e c t i o n f r o m t h e w a l l g a v e a v e r y s m a l l s i g n a l . A s was p o i n t e d o u t i n C h a p t e r 5 t h e r e was a s i m i l a r i t y b e t w e e n t h i s e x p e r i m e n t and o n e i n w h i c h a wedge and an e l e c t r o d e w e r e m o u n t e d on t h e f l o o r o f t h e t e s t s e c t i o n . The p h y s i c a l s i m i l a r i t y o f t h e f l o w i n b o t h s i t u a t i o n s i s shown i n F i g u r e 6.4. I n b o t h c a s e s t h e two e l e c t r o d e s a r e l o c a t e d c l o s e t o g e t h e r i n t h e b o u n d a r y l a y e r a l o n g t h e w a l l o f t h e t u b e . I f t h e t e m p e r a t u r e i n t h e b o u n d a r y l a y e r i s s u c h t h a t t h e g a s h a s h i g h c o n d u c t i v i t y t h e n t h e two e l e c t r o d e s w i l l be e l e c t r i c a l l y s h o r t e d t h r o u g h t h e b o u n d a r y l a y e r and v e r y l i t t l e v o l t a g e w i l l be m e a s u r e d b e t w e e n t h e m . I n t h e c a s e o f t h e wedge m o u n t e d on t h e f l o o r o f t h e t e s t s e c t i o n , t h e s m a l l v o l t a g e o b s e r v e d was a c t u a l l y o f t h e o p p o s i t e p o l a r i t y t o t h a t e x p e c t e d fr.om t h e v o l t a g e a c r o s s t h e s h o c k . I t may be p o s s i b l e t o e x p l a i n t h i s i n t e r m s o f b o u n d a r y l a y e r s e p a r a t i o n s i n c e t h e s h o c k may c a u s e t h e b o u n d a r y l a y e r t o s e p a r a t e f r o m t h e w a l l u p s t r e a m o f t h e w e d g e . j f t h i s w e r e t o h a p p e n , h o t g a s f r o m b e h i n d t h e s h o c k m i g h t be d r a w n f o r w a r d u n d e r t h e b o u n d a r y l a y e r and b r o u g h t t o r e s t i n a v e r y h o t s t a g n a t i o n s t a t e i m m e d i a t e l y a b o v e t h e e l e c t r o d e w h i c h i s m o u n t e d i n t h e f l o o r . T h i s e l e c t r o d e w o u l d t h e n be h o t t e r t h a n t h e o n e on t h e w e d g e , a n d t h e p o l a r i t y o f t h e v o l t a g e o b s e r v e d b e t w e e n t h e two e l e c t r o d e s w o u l d be t h e 9 5 a) TURNED OVER FOR COMPARISON TO b. F i g u r e 6 . 4 A c o m p a r i s o n o f t h e r e f l e c t e d s h o c k e x p e r i m e n t and t h e f l o o r m o u n t e d wedge e x p e r i m e n t r e v e r s e o f t h a t e x p e c t e d f r o m t h e s h o c k v o l t a g e . An i n t e r p r e t a t i o n o f t h e m e a s u r e d v o l t a g e a c r o s s t h e r e f l e c t e d s h o c k a l o n e c a n a l s o be g i v e n i n t e r m s o f t h e s h o r t c i r c u i t i n g e f f e c t o f t h e b o u n d a r y l a y e r . S i n c e t h e two e l e c t r o d e s o n t h e w a l l a r e s h o r t e d t o g e t h e r b y t h e b o u n d a r y l a y e r t h e v o l t a g e b e t w e e n t h e e l e c t r o d e b e h i n d t h e s h o c k and t h e n o s e o f t h e wedge (V ) w i l l be t h e same a s t h e v o l t a g e 24 b e t w e e n t h e e l e c t r o d e a h e a d o f t h e s h o c k and t h e n o s e o f t h e wedge ( V * 5 4 ) . A p a t h f r o m e l e c t r o d e 2 t o e l e c t r o d e 5 and t h e n t h r o u g h t h e s h o c k t o e l e c t r o d e 4 w o u l d g i v e a s i g n a l o p p o s i t e i n 96 p o l a r i t y to that expected across the reflected shock i t s e l f . The fact that the voltage ( v ^ ) measured in th i s experiment was about the same magnitude as that measured across the f i r s t shock (V ) indicates that in measuring V one most l i k e l y 45 24 simply measures the voltage across the f i r s t shock. Because of the e l e c t r i c a l connection between the electrodes through the boundary layer in these experiments no firm conclusions can be drawn about the f e a s i b i l i t y of series addition of successive shocks. If a longer test time were available i t might be feasible to space two shocks farther apart along the tube so that the electrodes were not shorted through the boundary layer. 97 CHAPTER 7 . E F F E C T I V E N E S S AND SYSTEM A N A L Y S I S One a p p l i c a t i o n f o r bow s h o c k g e n e r a t o r s w o u l d be a s a t o p p i n g s y s t e m a h e a d o f a c o n v e n t i o n a l t u r b i n e g e n e r a t i o n s y s t e m . A c o n v e n t i o n a l t u r b i n e i s l i m i t e d b y t h e r m o - m e c h a n i c a l e f f e c t s t o o p e r a t e w i t h g a s f l o w s a t 2 3 t e m p e r a t u r e s o f a b o u t 1000K o r c o o l e r . I f o n e h a s a f l o w o f g a s w i t h a h i g h s t a g n a t i o n t e m p e r a t u r e , t h e t e m p e r a t u r e m u s t be r e d u c e d b e f o r e t h e f l o w c a n be u s e d i n a t u r b i n e . A s e r i e s o f bow s h o c k g e n e r a t o r s p r o v i d e s a way o f r e d u c i n g t h e s t a g n a t i o n t e m p e r a t u r e b y e x t r a c t i n g e n e r g y f r o m t h e f l o w . A bow s h o c k g e n e r a t o r c a n o p e r a t e a t t h e s e h i g h t e m p e r a t u r e s b e c a u s e i t h a s no m o v i n g p a r t s and c a n t h e r e f o r e be r u n a t t e m p e r a t u r e s g i v e n b y m e t a l l u r g i c a l l i m i t s r a t h e r t h a n t h e r m a l s t r e s s c o n s i d e r a t i o n s . F u r t h e r m o r e i t s h o u l d be r e l a t i v e l y e a s y t o w a t e r c o o l t h e w e d g e s s o t h a t v e r y h o t g a s f l o w s may be u t i l i z e d . A s e r i e s o f bow s h o c k g e n e r a t o r s a c t i n g a h e a d o f t h e c o n v e n t i o n a l t u r b i n e w o u l d a c t a s a t o p p i n g s y s t e m , n o t u n l i k e t h a t p r o p o s e d f o r M . D . H . g e n e r a t o r s . I n t h i s way i t may be p o s s i b l e t o e x t r a c t some e n e r g y f r o m t h e f l o w a t h i g h t e m p e r a t u r e and t h u s i n c r e a s e t h e o v e r a l l e f f i c i e n c y o f t h e s y s t e m . A s c h e m a t i c d i a g r a m f o r s u c h a s y s t e m i s shown i n F i g u r e 7 . 1 . I t i s a s s u m e d t h a t t h e g a s a v a i l a b l e t o t h e s y s t e m i s a t a v e r y h i g h s t a g n a t i o n t e m p e r a t u r e and t h a t t h e 98 ELECTRICAL POWER . * t F i g u r e 7 . 1 An e x a m p l e o f a c o m b i n e d bow s h o c k and c o n v e n t i o n a l t u r b i n e g e n e r a t i o n s y s t e m c o l d e s t r e s e r v o i r t o w h i c h h e a t may u l t i m a t e l y be r e j e c t e d i s a t a t e m p e r a t u r e o f 3 0 0 K . U s i n g t h i s s y s t e m a s an e x a m p l e , a f i g u r e o f m e r i t c a n be c a l c u l a t e d f o r t h e bow s h o c k g e n e r a t o r . To do t h i s t h e c o n c e p t o f a v a i l a b l e e n e r g y i s u s e d . I n a n y f l o w p r o c e s s t h e c h a n g e i n s p e c i f i c a v a i l a b l e e n e r g y o f t h e f l o w c a n be d e f i n e d a s 2 4 2 ( 7 . 1 ) AA = Ah + A(%u ) - - T As = Ah - T As c o c w h e r e AhQ= s p e c i f i c s tagna t i on entha lpy change u = f low v e l o c i t y 99 As = s p e c i f i c entropy change i n the process T c = temperature of the coldest r e s e r v o i r a v a i l a b l e I f i t i s a s s u m e d t h a t t h e bow s h o c k g e n e r a t o r r u n s a d i a b a t i c a l l y , t h e n t h e c h a n g e i n s t a g n a t i o n e n t h a l p y , Ah Q, i s e q u a l t o t h e e l e c t r i c a l e n e r g y e x t r a c t e d b y t h e g e n e r a t o r . The f l o w t h r o u g h t h e s t a n d i n g s h o c k i s h o w e v e r i r r e v e r s i b l e (ASf^O). W h e n e v e r an i r r e v e r s i b l e p r o c e s s t a k e s p l a c e t h e e f f e c t i s t o c o n v e r t a c e r t a i n amoun t o f e n e r g y f r o m a f o r m i n w h i c h i t i s c o m p l e t e l y a v a i l a b l e t o a f o r m i n w h i c h i t i s c o m p l e t e l y u n a v a i l a b l e and c a n no l o n g e r be e x t r a c t e d a s w o r k . The amoun t o f e n e r g y made u n a v a i l a b l e d e p e n d s on t h e e n t r o p y c h a n g e i n t h e p r o c e s s and on t h e t e m p e r a t u r e o f t h e c o l d e s t r e s e r v o i r a t h a n d (T ) t o w h i c h h e a t may be r e j e c t e d t o do w o r k . F o r an i r r e v e r s i b l e p r o c e s s t h e l o s s i n a v a i l a b l e e n e r g y i s g i v e n b y T AS, a s i n d i c a t e d b y t h e p r e s e n c e o f t h i s t e r m i n e q u a t i o n 7 . 1 . I n t h e s y s t e m u s e d a s an e x a m p l e , T c w o u l d be 3 0 0 K . To c a l c u l a t e AS i t i s a s s u m e d t h a t f o r t h e g e n e r a t o r t h e s h o c k i s t h e m a j o r s o u r c e o f e n t r o p y c h a n g e i n t h e f l o w and s o AS c a n be c a l c u l a t e d f r o m s h o c k t h e o r y ( s e e A p p e n d i x B f o r d e t a i l s ) . A s t h e f l o w p a s s e s t h r o u g h t h e g e n e r a t o r e n e r g y i s e x t r a c t e d b u t t h e f l o w s u f f e r s a l o s s i n a v a i l a b l e e n e r g y . One f i g u r e o f m e r i t f o r t h e g e n e r a t o r i s c a l l e d t h e e f f e c t i v e n e s s and i s d e f i n e d a s t h e r a t i o o f t h e e n e r g y 100 e x t r a c t e d f r o m t h e f l o w t o t h e l o s s i n a v a i l a b l e e n e r g y o f t h e f l o w . ( 7 . 2 ) £ = |AWj |AA| w h e r e AW = s p e c i f i c energy e x t r a c t e d from the f low The e f f e c t i v e n e s s c o m p a r e s t h e e n e r g y e x t r a c t e d b y t h e d e v i c e t o t h e e n e r g y e x t r a c t e d by a r e v e r s i b l e d e v i c e o p e r a t i n g b e t w e e n t h e same end c o n d i t i o n s . The e f f e c t i v e n e s s was c a l c u l a t e d and u s e d a s one f i g u r e o f m e r i t f o r t h e o p e r a t i o n o f t h e e x p e r i m e n t a l bow s h o c k g e n e r a t o r s . Once a g a i n T £ was a s s u m e d t o be 300K and t h e e n t r o p y c h a n g e a c r o s s t h e s h o c k was c a l c u l a t e d b a s e d on t h e s t r e n g t h o f t h e o b l i q u e s h o c k . F o r t h e h i g h e s t m e a s u r e d powe r o u t p u t f r o m t h e g e n e r a t o r ( 90mW) t h e e f f e c t i v e n e s s was c a l c u l a t e d t o be a p p r o x i m a t e l y 0 . 2 p e r c e n t . W h i l e t h i s f i g u r e may seem l o w i t m u s t be r e m e m b e r e d t h a t no o t h e r m a c h i n e s , e x c e p t MHD g e n e r a t o r s ( w h i c h h a v e y e t t o o v e r c o m e a number o f s c i e n t i f i c p r o b l e m s ) a r e c a p a b l e o f o p e r a t i n g i n t h i s h i g h t e m p e r a t u r e r e g i o n a t a l l . The o b j e c t o f u s i n g bow s h o c k g e n e r a t o r s a h e a d o f c o n v e n t i o n a l t u r b i n e s i s t o r e d u c e t h e s t a g n a t i o n t e m p e r a t u r e o f t h e f l o w . O t h e r means o f l o w e r i n g t h e s t a g n a t i o n t e m p e r a t u r e m u s t a l s o i n v o l v e 101 a l o s s of a v a i l a b l e energy and do not have the compensating b e n e f i t of energy e x t r a c t i o n . To evaluate the bow shock generator a comparison was made between the l o s s of a v a i l a b l e energy caused by c o o l i n g a hot gas with a bow shock generator and the l o s s i n a v a i l a b l e energy caused by c o o l i n g the gas by the a d d i t i o n of c o l d gas. In each case, one s t a r t s with the hot gas i n i t s s t a g n a t i o n s t a t e ( s t a t i o n a r y ) . The gas may e i t h e r be a c c e l e r a t e d from the s t a g n a t i o n s t a t e to supersonic v e l o c i t i e s i n a Laval noz z l e and then cooled with a bow shock g e n e r a t o r , or a mass of c o l d gas may be added to the hot gas i n the s t a g n a t i o n s t a t e , and the hot gas cooled by thermal c o n d u c t i o n . In each case the gas was cooled to the same end s t a g n a t i o n temperature. The l o s s e s i n the bow shock generator depend on the Mach number at which i t i s operated. Since o n l y one Mach number had been i n v e s t i g a t e d e x p e r i m e n t a l l y a t h e o r e t i c a l c a l c u l a t i o n was done to compare the l o s s e s from both methods of c o o l i n g as a f u n c t i o n of Mach number. The Mach number used throughout these c a l c u l a t i o n s i s the Mach number of the standing shock (equal to the Mach number of the component of the flow p e r p e n d i c u l a r to the standing shock). The c a l c u l a t i o n was based on the flow c o n d i t i o n s used i n the experiments and the v a r i a t i o n i n Mach number would correspond to the use of generators with d i f f e r e n t wedge ang l e s . A model was assumed that allowed a p r e d i c t i o n of the 102 o u t p u t o f t h e g e n e r a t o r a s a f u n c t i o n o f Mach number ( s e e A p p e n d i x B f o r d e t a i l s o f t h e s e c a l c u l a t i o n s ) . A t e a c h M a c h number t h e d r o p i n s t a g n a t i o n t e m p e r a t u r e and t h e l o s s i n a v a i l a b l e e n e r g y c a u s e d b y t h e bow s h o c k g e n e r a t o r was c o m p u t e d . F o r c o m p a r i s o n w i t h m i x i n g , a n amoun t o f c o l d (300K) g a s s u f f i c i e n t t o l o w e r t h e s t a g n a t i o n t e m p e r a t u r e by t h e same amoun t was c o n s i d e r e d t o be a d d e d t o t h e f l o w i n i t s s t a g n a t i o n s t a t e . The l o s s o f a v a i l a b l e e n e r g y t h r o u g h i r r e v e r s i b l e h e a t f l o w f r o m t h e h o t g a s t o t h e c o l d g a s was t h e n c o m p u t e d f o r c o m p a r i s o n ( s e e A p p e n d i x B ) . The r e s u l t s a r e shown i n F i g u r e 7 . 2 a s t h e a v a i l a b l e e n e r g y l o s t f r o m one g r a m o f h o t g a s w h i c h i s p u t t h r o u g h e i t h e r p r o c e s s . The l o s s i n a v a i l a b l e e n e r g y f o r t h e bow s h o c k g e n e r a t o r i s t h e c h a n g e i n a v a i l a b l e e n e r g y f o r t h e f l o w b e y o n d t h e e n e r g y e x t r a c t e d . F o r r e f e r e n c e ^ F i g u r e 7 . 3 shows t h e e n e r g y e x t r a c t e d b y t h e g e n e r a t o r and i t s e f f e c t i v e n e s s a s a f u n c t i o n o f Mach n u m b e r . The a v a i l a b l e e n e r g y f l o w i n s u c h a s y s t e m i s i l l u s t r a t e d s c h e m a t i c a l l y i n F i g u r e 7 . 4 a s s u m i n g p e r f e c t d u c t i n g and p e r f e c t t u r b i n e s . I t c a n be s e e n f r o m t h e e n e r g y b a l a n c e t h a t t h e two p r o c e s s e s w i l l j u s t b r e a k e v e n when t h e e l e c t r i c a l e n e r g y e x t r a c t e d p l u s t h e e n e r g y e x t r a c t e d b y t h e t u r b i n e i n t h e bow s h o c k s y s t e m i s e q u a l t o t h e e n e r g y e x t r a c t e d b y t h e t u r b i n e i n t h e m i x i n g s y s t e m ( A 0 u t b s + A e x = A o u t m ) ' o r a l t e r n a t i v e l y , when t h e a v a i l a b l e e n e r g y l o s s i n t h e bow s h o c k s y s t e m i s e q u a l t o t h e a v a i l a b l e e n e r g y l o s s i n t h e m i x i n g s y s t e m ( A , . =A ) . I f t h e l o s s o f a v a i l a b l e e n e r g y i n c u r r e d l b s Ira 103 F i g u r e 7.2 A comparison o f the a v a i l a b l e energy l o s t from one gram o f hot input gas (AA) i n both the c o o l i n g p roce s se s (bow shock genera to r and mix ing) as a f u n c t i o n o f the Mach number at which the genera to r i s run 104 F i g u r e 7 . 3 Energy e x t r a c t e d (e) and e f f e c t i v e n e s s o f a bow shock genera to r as a f u n c t i o n o f Mach number (M ) 105 ' i n LAVAL NOZZLE 1 A e x BOW SHOCK GENERATOR Aoutbs l A lb s TURBINE Aoutbs 300 K MIXING PROCESS A outm A l m TURBINE Aoutm 300 K One gram of hot gas enters each process A. in ex A., . lbs A outbs lm outm av a i l a b l e energy i n one gram of hot i n l e t gas energy extracted i n bow shock generator a v a i l a b l e energy l o s t i n bow shock generator energy extracted by turbine i n bow shock system av a i l a b l e energy l o s t i n mixing process energy extracted by turbine i n ' m i x i n g p r o c e s s F i g u r e 7.4 A v a i l a b l e energy flow i n the shock generator plus c o n v e n t i o n a l generator system, compared to that i n the mixing plus c o n v e n t i o n a l generator system. by the generator can be made l e s s than that i n c u r r e d by mixing the generator w i l l be the more e f f i c i e n t means of c o o l i n g the flow. As can be seen from F i g u r e 7.2 at low Mach numbers the bow shock generator appears more e f f i c i e n t . T h i s a n a l y s i s has shown that i f a bow shock g e n e r a t i n g 106 system were to be used as a topping system f o r a c o n v e n t i o n a l g e n e r a t i o n p l a n t , i t would have to be run at very low Mach numbers. Mach numbers j u s t g r e a t e r than one are r e l a t i v e l y easy to a c h i e v e . U n f o r t u n a t e l y i n t h i s regime some of the assumptions i n t h i s model break down. I t has been assumed that the shock accounts f o r a l l the l o s s e s i n the bow shock system. At low Mach numbers however, heat l o s s to the w a l l s , and f r i c t i o n i n the d u c t i n g may be important as w e l l . Another problem l i e s with the f a c t that the energy e x t r a c t e d from the flow i n the experiments i s l e s s by a f a c t o r of 300 than that p r e d i c t e d by the model used i n t h i s a n a l y s i s . A more thorough a n a l y s i s , i n c l u d i n g these e f f e c t s would have to be done before one could say that bow shock generators would be v i a b l e i n t h i s p a r t i c u l a r a p p l i c a t i o n . 107 CHAPTER 8 . CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK 8 . 1 SUMMARY AND CONCLUSIONS An o v e r d r i v e n d e t o n a t i o n s h o c k t u b e was b u i l t t o p r o d u c e a f l o w s u i t a b l e f o r e x p e r i m e n t s o n powe r e x t r a c t i o n s f r o m s t a n d i n g s h o c k w a v e s . I n m o s t r e s p e c t s t h e s h o c k t u b e met t h e r e q u i r e m e n t s o f t h e s e e x p e r i m e n t s . I t p r o d u c e d a f l o w o f g a s i n a w e l l d e f i n e d t h e r m o d y n a m i c s t a t e t h a t was s u p e r s o n i c and had a d u r a t i o n g r e a t e r t h a n 20 m i c r o s e c o n d s . U n f o r t u n a t e l y t h e f l o w was n o t c o m p l e t e l y c o n s t a n t and u n i f o r m d u r i n g a l l o f t h i s t i m e . By i n s e r t i n g a s u i t a b l e o b s t a c l e i n t o t h e f l o w an o b l i q u e s h o c k c o u l d be c r e a t e d a c r o s s w h i c h t h e i o n i z a t i o n i n t h e f l o w was i n c r e a s e d s i g n i f i c a n t l y . M o s t i m p o r t a n t l y t h e f l o w f i e l d was f r e e o f l a r g e e l e c t r i c a l c u r r e n t s and v o l t a g e s . U s i n g t h i s s h o c k t u b e , a number o f p r e l i m i n a r y e x p e r i m e n t s w e r e c a r r i e d o u t on s i n g l e s t a n d i n g s h o c k s . I t was f o u n d t h a t t h e o p e n c i r c u i t v o l t a g e m e a s u r e d was h i g h e r by a f a c t o r o f two t h a n t h a t c a l c u l a t e d f r o m t h e o r y u s i n g t h e m o d e l o f J a f f r i n . I t i s a p p a r e n t t h a t i t i s n o t s u f f i c i e n t t o c o n s i d e r t h e p o t e n t i a l a c r o s s t h e s h o c k a s t h e o n l y s o u r c e o f v o l t a g e b e t w e e n t h e two e l e c t r o d e s , and t h a t t h e e f f e c t s o f p l a s m a s h e a t h s and f l o w b o u n d a r y l a y e r s a r e i m p o r t a n t a s w e l l . The e f f e c t i v e i n t e r n a l r e s i s t a n c e o f a s h o c k g e n e r a t o r was f o u n d t o d e p e n d on t h e s e p a r a t i o n o f t h e e l e c t r o d e s . The 108 values of r e s i s t a n c e measured were c o n s i d e r a b l y l a r g e r than values p r e d i c t e d from a c a l c u l a t i o n of the bulk c o n d u c t i v i t y of the plasma. Two p o s s i b l e e x p l a n a t i o n s were advanced f o r t h i s . I t could be that the gas i n the shock tube does not reach i t s f u l l e q u i l i b r i u m c o n d u c t i v i t y during the t e s t time. A l t e r n a t i v e l y t h i s e f f e c t may be caused by r e s i s t a n c e s i n the boundary l a y e r s , which vary with the p o s i t i o n s of the e l e c t r o d e s i n the tube. The p r i n c i p l e aim of these experiments was to i n v e s t i g a t e the p o s s i b i l i t y of i n c r e a s i n g the output of bow shock gen e r a t o r s by connecting together more than one g e n e r a t o r . T h i s p o s s i b i l i t y was t e s t e d i n two d i f f e r e n t geometries. In the f i r s t geometry two standing shocks, c r e a t e d by two wedges, stood p h y s i c a l l y i n p a r a l l e l a cross the flow. I t was found that the output v o l t a g e of one of these shocks ( the lower one ) was c o n s i s t e n t l y s m a l l e r than t h a t of the o t h e r , and unless a l a r g e load ( small r e s i s t a n c e ) was connected across t h i s generator the v o l t a g e could even be of the o p p o s i t e p o l a r i t y . In the experiments which attempted to i n c r e a s e the output v o l t a g e by connecting these two shocks together i n s e r i e s , the t o t a l v o l t a g e across both shocks was never observed to be l a r g e r than that across one shock alone. When these two shock ge n e r a t o r s were connected i n p a r a l l e l i t was shown that a small i n c r e a s e i n output c u r r e n t could be o b t a i n e d . In the second geometry, a s e r i e s connection between a 109 standing o b l i q u e shock, and i t s r e f l e c t i o n from the w a l l of the shock tube was i n v e s t i g a t e d . Attempts to add the v o l t a g e s across the two shocks showed the t o t a l v o l t a g e to be very s m a l l . However i t appears as i f the e l e c t r o d e s on each s i d e of the two shocks were shorted together through the boundary l a y e r . T h i s connection through the boundary l a y e r a l s o made i t i mpossible to measure the v o l t a g e across the r e f l e c t e d shock alone, s i n c e the e l e c t r o d e on the w a l l behind the r e f l e c t e d shock was always shorted to the gas ahead of both shocks. A study was a l s o undertaken to d e f i n e a f i g u r e of merit f o r bow shock g e n e r a t o r s , and the use of a f i g u r e c a l l e d the e f f e c t i v e n e s s was proposed. Using the e f f e c t i v e n e s s , a p r e l i m i n a r y a n a l y s i s was made of a hy b r i d bow shock/conventional t u r b i n e g e n e r a t i o n system. I t was shown that i f bow shock generators are to be at a l l p r a c t i c a l i n t h i s a p p l i c a t i o n they must be operated at very low Mach numbers to reduce the l o s s i n a v a i l a b l e energy caused by i r r e v e r s i b i l i t i e s i n the shock. U n f o r t u n a t e l y at low Mach numbers other l o s s e s which are not taken i n t o account i n t h i s model may become important. The experiments with m u l t i p l e shocks were the f i r s t attempts to i n c r e a s e the power output from bow shock gen e r a t o r s by connecting more than one generator together. The proposal of the e f f e c t i v e n e s s as a f i g u r e of m e r i t , and the a n a l y s i s of the performance of bow shock ge n e r a t o r s as a 110 topping system f o r a c o n v e n t i o n a l g e n e r a t i n g p l a n t were a l s o o r i g i n a l c o n t r i b u t i o n s . 8.2 SUGGESTIONS FOR FUTURE WORK There are o b v i o u s l y some f e a t u r e s of these experiments which are not completely understood, and would merit f u r t h e r i n v e s t i g a t i o n . The magnitudes and even the p o l a r i t y of some of the v o l t a g e s measures ac r o s s shocks i n t h i s work cannot be understood i n terms of the shock v o l t a g e a l o n e . No attempt has been made here to t r y to i n c l u d e the e f f e c t s of the plasma sheaths at each e l e c t r o d e , or the e f f e c t s of the flow boundary l a y e r . I f the bow shock generator i s to be more f u l l y understood however, the r e l a t i v e importance of these e f f e c t s must be determined, and some account of them in c l u d e d i n the model. Further experiments might a l s o attempt to determine more p r e c i s e l y the source of the high i n t e r n a l r e s i s t a n c e , s i n c e t h i s w i l l be important i n any attempt to i n c r e a s e the power output of bow shock g e n e r a t o r s . To study p o s s i b l e a p p l i c a t i o n s of bow shock generators i t would be u s e f u l to have a b e t t e r model of the e x t r a c t i o n of e l e c t r i c a l power i n a shock g e n e r a t o r . With such- a model a more d e t a i l e d a n a l y s i s of the h y b r i d g e n e r a t i o n system could be undertaken. At low Mach numbers, where t h i s work i n d i c a t e s they should be run, the assumption that the shock wave accounts f o r most of the l o s s e s i n the flow i s no longer v a l i d , and other l o s s e s must be taken i n t o account. I l l T e s t s on bow s h o c k g e n e r a t o r s s h o u l d a l s o be c o n d u c t e d i n a c o n t i n u o u s f l o w a p p a r a t u s . T h i s w o u l d r e m o v e some o f t h e p r o b l e m s e n c o u n t e r e d w i t h u n s t e a d y f l o w i n t h e s e e x p e r i m e n t s , a s w e l l a s a l l o w i n g m e a s u r e m e n t s i n f l o w s w i t h a w i d e r r a n g e o f Mach n u m b e r s t h a n t h o s e a v a i l a b l e i n a s h o c k t u b e . I n a c o n t i n u o u s f l o w m a c h i n e t h e s h o c k g e n e r a t o r s c o u l d a l s o be moved p h y s i c a l l y f a r t h e r a p a r t s o t h a t t h e y w o u l d n o t be e l e c t r i c a l l y c o n n e c t e d w i t h s h o r t p a t h s i n t h e b o u n d a r y l a y e r s a l o n g t h e w a l l s . A l t e r n a t i v e l y o n e c o u l d t r y t o u s e one o f a number o f m e t h o d s d e v e l o p e d f o r b o u n d a r y l a y e r c o n t r o l t o i n t e r r u p t t h e b o u n d a r y l a y e r b e t w e e n t h e e l e c t r o d e s . 112 BIBLIOGRAPHY 1. Petscheck, H. and Byron, S., Annals of Physics 1, 270-315 (1959). 2. J a f f r i n , M.V., The Physics of F l u i d s 8_, 606-625, (1965). 3. Tidman, D.A. and Burton, L.L., Physics Review L e t t e r s 37, 1397, (1968). 4. Ahlborn, B., Kwan, J . and Pearson, J . , Proceedings of the Twelfth Annual Symposium on Shock Tubes and Waves, Jerusalem, (1979). 5. Ahlborn, B. and Kwan, J . , U.S. Patent #877494, A p p l i e d February 13, 1978. 6. Kwan, J . , Proceedings I.E.E.E. Conference, Monteray, May 1978. 7. Becker, E., Gas Dynamics, Academic Press, New York, (1968). 8. Ahlborn, B., Lecture notes Physics 507, U n i v e r s i t y of B r i t i s h Columbia, (1974). 9. Ahlborn, B., Canadian J o u r n a l of Physics 5_3, 976-979, (1975). 10. R e s l e r , E.L., L i n , S. and Kantrowitz, A., J o u r n a l o f A p p l i e d Physics 2_3, 1390-1399, (1950). 11. Gaydon, A.G. and H u r l e , I.R., The Shock Tube i n High Temperature Chemical P h y s i c s , Chapman and H a l l L t d . , London, (1963). 12. Muntenbruch, H., Physics of F l u i d s Supplement I 12, 1-11, (1969). 13. Redfern, P. and Ahlborn, B., Canadian J o u r n a l of Physics 50_, 1771=1776, (1972) . 14. Courant, R. and F r i e d r i c h s , K-;Or?,"Supersonic Flow- and'-Shock Waves, I n t e r s c i e n c e P u b l i s h e r s , New York, (1948). 15. Ahlborn, B. and Huni, J.P., J o u r n a l of A p p l i e d Physics 40, 3402-3404, (1969). 16. Huni, J.P., Ph.D. Thesis, U n i v e r s i t y of B r i t i s h Columbia, (1970). 17. Redfern, P., M.Sc. Thesis, U n i v e r s i t y of B r i t i s h Columbia, (1971). 18. Kwan, J . , Ph.D. Thesis, U n i v e r s i t y of B r i t i s h Columbia, (to be p u b l i s h e d ) . 19. Wienecke, R., Z e i t s c h Naturforschung 18a, 1151, (1963). 20. Arzimovich, L.A., Elementary Plasma'Physics, B l a i s d e l l P u b l i s h i n g Co., Waltham Mass. (1965). 21. L i n , S.C., R e s l e r , E.L. and Kantrowitz, A., J o u r n a l of A p p l i e d Physics r26_, 95-109, (1955). 113 22. Chapman, A . J . and Wa lker , W . F . , I n t roduc to ry Gas Dynamics, H o l t R inehar t and Winston I n c . , (1971). 23. Lee , J . F . and S e a r s , F .W. , Thermodynamics, Addison Wesley P u b l i s h i n g C o . , Reading M a s s . , (1963) . 24. D r e l l i s h a k , K . S . , Knopp, C F . and Cambel, A . B . , P h y s i c s o f F l u i d s 6_, 1280-1288, (1963) . 25. B o s n j a k o v i c , F . , Sp r i nge , W. and Knoche, K . F . , Z e i t s c h F lugw iss 10, 413-424, (1962) . 114 APPENDIX A CALCULATION OF THE THERMODYNAMIC STATE BEHIND AN IONIZING SHOCK When a gas becomes p a r t i a l l y i o n i z e d the simple equation of s t a t e f o r a c a l o r i c a l l y i d e a l gas i s no longer a p p l i c a b l e . g Instead the enthalpy c o e f f i c i e n t , g, i s d e f i n e d , where g(h,p) i s a f u n c t i o n of the thermodynamic s t a t e of the gas. Using t h i s equation of s t a t e and the c o n s e r v a t i o n equations a c r o s s a shock f r o n t the thermodynamic v a r i a b l e s behind the shock may be found from the i n i t i a l c o n d i t i o n s ahead of the shock and the shock Mach number. However, t h i s c a l c u l a t i o n assumes a knowledge of the enthalpy c o e f f i c i e n t behind the shock, g 2 , which i s i n i t i a l l y unknown. For an e q u i l i b r i u m f i n a l s t a t e , however, g 2 ( h 2 , p 2 ) i s a w e l l d e f i n e d f u n c t i o n of h 2 and p 2 , so that an i t e r a t i v e technique may be 9 used to f i n d the f i n a l s t a t e . T h i s method operated by guessing a value of g 2 and then using i t to c a l c u l a t e the f i n a l s t a t e from the shock r e l a t i o n s and the equation of s t a t e . From the c a l c u l a t e d f i n a l s t a t e a new value of g 2 i s chosen and the process repeats i t s e l f u n t i l the i t e r a t i o n converges. Data f o r g(h,p) may be obtained from thermodynamic c a l c u l a t i o n s using p a r t i t i o n f u n c t i o n s f o r the gas i n qu e s t i o n 25 and the Saha equation To do t h i s i t e r a t i v e c a l c u l a t i o n a computer program has 18 been w r i t t e n i n t h i s l a b by Joe Kwan o. The program t a b u l a t e s a v a r i e t y of thermodynamic v a r i a b l e s behind shock waves i n argon f o r giv e n i n i t i a l c o n d i t i o n s and Mach numbers as high as 115 13. These values were used i n a number of p l a c e s throughout t h i s work. 116 APPENDIX B. AVAILABLE ENERGY LOSS IN BOW SHOCK GENERATORS AND MIXING B . l INCIDENT FLOW PARAMETERS The c a l c u l a t i o n s i n t h i s s e c t i o n were based on the flow i n the shock tube as i t was used i n the experiments. The parameters were c a l c u l a t e d from shock theory a p p l i e d to p a r t i a l l y i o n i z e d argon and based on the observed Mach number (see Appendix A ) . For the flow s t a t e i n the shock tube the c o n d i t i o n s a r e : 6 2 p = 1.15x10 dynes/cm -5 3 p = 5.3x10 gm/cm T = 10,300 K u = 2.88x10^ cm/sec M2= 1.58 h = 6.47xl0 1 0 ergs/gin g = Y = 1.51 ra = p u = 15 gm/sec The corresponding s t a g n a t i o n s t a t e can be obtained from a 2 6 M o l l i e r diagram h Q = 1.06x10'''''' ergs/gm T = 13,000 K o 6 2 p o = 5.4x10 dynes/cm = 5 atm 117 B.2 STANDING SHOCK JUMP The standing shocks i n v e s t i g a t e d were assumed to be weak enough so that Y could be assumed to be constant across the shock. However s i n c e the flow was p a r t i a l l y i o n i z e d the value of Y i n the i n c i d e n t flow (Y=1.51) was used i n place of the low temperature v a l u e . The temperature, p r e s s u r e , and d e n s i t y behind the standing shock were then c a l c u l a t e d as a f u n c t i o n of Mach number from i d e a l shock theory with Y=1.51. B.3 ENERGY EXTRACTED BY THE GENERATOR It was assumed that the V-I c h a r a c t e r i s t i c of the generator was l i n e a r so that the maximum power output could be approximated by V I p = oc SC \ (B. 1) 4 where ^ _ Q p e n c i r c u i t voltage of the generator I = short circuit current of the generator The open c i r c u i t v o l t a g e was p r e d i c t e d by the model expressed i n Chapter s i x 118 oc T 3 i n AT 32 where regions 2 and 3 are as shown i n Figu r e B . l and the INCIDENT SHOCK FLOW F i g u r e B . l Bow shock generator regions temperatures and d e n s i t y r a t i o have been c a l c u l a t e d as shown in the above s e c t i o n . A p r e d i c t i o n has been made of the short c i r c u i t e l e c t r o n c u r r e n t that would flow across the shock i f i t were d i f f u s i o n l i m i t e d . The r e s u l t can be expressed i n the form 119 where 3 . 1 5 x l 0 " 1 2 A(n T ) 2 e eV Amps/cm ^ ^ e V a v g ^ j = shor t c i r c u i t d e n s i t y cu r ren t A (n e T e y )= the change i n e l e c t r o n number d e n s i t y x the temperature product between reg ions 3 and 2 T = some in te rmed ia te temperature i n the shock eVavg r The c u r r e n t p r e d i c t e d from the d i f f u s i o n l i m i t can be shown to be l a r g e r than the f l u x of incoming e l e c t r o n s i n the flow f o r Mach numbers 1.01 or g r e a t e r . Thus f o r a l l but the very weakest shocks the sh o r t c i r c u i t c u r r e n t i s not d i f f u s i o n l i m i t e d . For the o p e r a t i n g c o n d i t i o n s of the shock tube the i n c i d e n t f l u x of e l e c t r o n s corresponded to a c u r r e n t d e n s i t y , 2 of 100 Amps/cm . As an estimate o f the short c i r c u i t c u r r e n t i t was assumed that an e l e c t r o n g r a d i e n t could be maintained i n the shock and a d i f f u s i o n d r i v e n c u r r e n t supported i f o n l y 10 per cent of the incoming e l e c t r o n s c o n t r i b u t e d to the short c i r c u i t c u r r e n t . The short c i r c u i t c u r r e n t was t h e r e f o r e assumed to be 100 Amps over the range of Mach numbers i n v e s t i g a t e d . T h i s was i n f a c t higher by a f a c t o r of 300 than the s h o r t c i r c u i t c u r r e n t measured i n the experiments. The s p e c i f i c energy e x t r a c t e d from the flow at any Mach 120 number i s simply the power p r e d i c t e d by equation (B.l) d i v i d e d by the mass f l u x . e = P m m = 15 gm/sec i n t h i s case Since the flow i s assumed to be a d i a b a t i c the r e d u c t i o n i n s t a g n a t i o n enthalpy i s equal to the energy e x t r a c t e d . Ah = -e o B.4 AVAILABLE ENERGY LOSS IN GENERATOR The change i n a v a i l a b l e energy a c r o s s the shock i s given by (see Chapter 7) AA = Ah - T As o c where T^ = temperature of the col d e s t r e s e r v o i r a v a i l a b l e where Ah" re p r e s e n t s a v a i l a b l e energy e x t r a c t e d i n the form of e l e c t r i c a l power and T cAs represents the l o s s i n a v a i l a b l e energy i n c u r r e d through the i r r e v e r s i b l e nature of the shock. _ (B.2) T As = l o s s of a v a i l a b l e energy c 6 /' The entropy jump i n the shock may be c a l c u l a t e d from the 121 g e n e r a l e n t r o p y c h a n g e i n a n y p r o c e s s p r o c e e d i n g f r o m s t a t e ( T 2 , P 2 ) t o s t a t e ( T 3 , P 3 ) 2 3 . As = c In T 3 - R l n P 3 p — — T P S i n c e t h e s t a n d i n g s h o c k was a s s u m e d t o be weak c ^ and R w e r e t a k e n a s c o n s t a n t a c r o s s t h e s h o c k a l t h o u g h t h e v a l u e s u s e d w e r e t h o s e a t t h e e l e v a t e d t e m p e r a t u r e o f t h e i n c i d e n t f l o w . The t e m p e r a t u r e and p r e s s u r e r a t i o s u s e d w e r e t h o s e p r e v i o u s l y c a l c u l a t e d f o r t h e s t a n d i n g s h o c k jump a s a f u n c t i o n o f Mach n u m b e r . H a v i n g c a l c u l a t e d t h e e n t r o p y i n c r e a s e a s a f u n c t i o n o f Mach n u m b e r , t h e l o s s i n a v a i l a b l e e n e r g y f o r one g r a m o f h o t g a s may be c a l c u l a t e d f r o m e q u a t i o n ( B . 2 ) . T h i s f i g u r e may t h e n be c o m p a r e d t o t h e a v a i l a b l e e n e r g y l o s t when one g r a m o f h o t g a s i s m i x e d w i t h c o l d g a s t o c o o l i t t h e same a m o u n t . B . 5 A V A I L A B L E ENERGY LOSS IN MIX ING F o r c o m p a r i s o n t h e a v a i l a b l e e n e r g y l o s s was c a l c u l a t e d i f t h e f l o w was c o o l e d f r o m t h e s t a g n a t i o n s t a t e t h r o u g h t h e a d d i t i o n o f c o l d g a s . T h i s means t h a t t h e c o l d g a s m u s t a b s o r b a s much e n e r g y f r o m t h e f l o w i n t h e f o r m o f h e a t a s t h e bow s h o c k g e n e r a t o r e x t r a c t e d a s e l e c t r i c a l e n e r g y . I n s t e a d o f b e i n g a c c e l e r a t e d t o s u p e r s o n i c v e l o c i t y i n a L a v a l n o z z l e , t h e f l o w i s i s e n t r o p i c a l l y b r o u g h t t o r e s t so t h a t i t i s i n 122 the s t a g n a t i o n s t a t e , and a mass of c o l d gas, s u f f i c i e n t to achieve the r e q u i r e d c o o l i n g i s added. The a v a i l a b l e energy l o s t from one gram of i n i t i a l l y hot gas can then be c a l c u l a t e d from the i r r e v e r s i b l e heat conduction. An amount of c o l d gas i s assumed to be mixed i n t o one gram of hot gas at s t a g n a t i o n c o n d i t i o n s i n a process i l l u s t r a t e d s c h e m a t i c a l l y i n F i g u r e B.2. Before the c o l d gas can be mixed i t must be compressed to the s t a g n a t i o n p r e s s u r e . I f the compressor i s assumed to be i s e n t r o p i c the work done by the compressor i s W * ra (h»-h ) c c c' The t o t a l change i n a v a i l a b l e energy f o r the system (hot gas plus c o l d gas) from s t a t e 1 to s t a t e 3 i s given by AA ^ = AH - T AS system c = h + H 1 - h - H - T A S o o c = W - T AS c where the v a r i a b l e s are those d e f i n e d i n Figure B.2. I f the compressor i s i s e n t r o p i c the work done on the f l u i d appears t o t a l l y as a v a i l a b l e energy i n the gas and the net r e s u l t of the process i s the l o s s of a v a i l a b l e energy through heat conduction (T AS). Therefore the net change in c a v a i l a b l e energy f o r one gram of hot input gas i s g i v e n by the 123 •ISENTHALPIC — » - 3 13000 K 3 00 K 13000 K 560 K 13000 -£ K COLD GAS COMPRESSED W=m c ( r ! c -h c ) FINAL STATE AFTER HEAT FLOW where AS = entropy change of the system AH = enthalpy change of the system h £ = s p e c i f i c enthalpy of cold gas before compression h 1 = s p e c i f i c enthalpy of cold gas a f t e r compression h Q = s p e c i f i c enthalpy of the hot gas mc = mass of cold gas added W = work done by the compressor c » very smal l F i g u r e B.2 The mixing process l o s s i n a v a i l a b l e energy. AA = T AS = net loss i n s p e c i f i c a v a i l a b l e energy due to mixing For the s t a g n a t i o n s t a t e o u t l i n e d at the beginning of 124 t h i s a p p e n d i x t h e c o l d g a s t o be a d d e d m u s t be i s e n t r o p i c a l l y c o m p r e s s e d t o 5 a t m o s p h e r e s w h i c h r a i s e s i t s t e m p e r a t u r e f r o m 300K t o 5 6 0 K . The mass o f c o m p r e s s e d g a s w h i c h mus t be a d d e d t o one g r a m o f h o t g a s i s d e t e r m i n e d b y t h e amoun t o f h e a t t h a t m u s t be e x t r a c t e d f r o m t h e h o t g a s : (13 f000-e)»13,000 Q = e = m c J c p ( T , 5 atm)dT ( B > 4 ) 560 m c = mass of c o l d gas The i n t e g r a l was a p p r o x i m a t e d n u m e r i c a l l y f r o m t h e d a t a f o r 25 c , . The u p p e r l i m i t may be a p p r o x i m a t e d a s t h e s t a g n a t i o n P t e m p e r a t u r e s i n c e i n a l l c a s e s h e r e t h e amoun t o f c o o l i n g i s s m a l l . The e n t r o p y c h a n g e f o r t h e s y s t e m due t o t h i s h e a t f l o w i s g i v e n b y =13,000 13,000 AS = - Q + / m c C p ( T ' 5 a t m ) dT ( B . 5 ) 560 Once a g a i n t h e i n t e g r a l was a p p r o x i m a t e d f r o m d a t a f o r C p . The l o s s i n s p e c i f i c a v a i l a b l e e n e r g y may t h e n be c a l c u l a t e d f r o m e q u a t i o n B . 3 . A t e a c h o p e r a t i n g Mach number f o r t h e bow s h o c k g e n e r a t o r t h e e n e r g y e x t r a c t e d f r o m one g r a m o f f l o w h a s b e e n c o m p u t e d . I f t h i s same amoun t o f e n e r g y f l o w s i n t o t h e c o l d g a s a s h e a t , t h e a v a i l a b l e e n e r g y l o s t f r o m one g r a m o f h o t g a s i n t h e 125 mixing process may be c a l c u l a t e d from equations (B.4), (B.5), and (B.3). T h i s may then be compared to the a v a i l a b l e energy l o s s f o r the bow shock g e n e r a t o r . 

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