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Piezoprobe measurements in pulsed discharges Ardila, Ricardo 1970

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PIEZOPROBE MEASUREMENTS IN PULSED DISCHARGES by R i c a r d o A r d i l a L i e . C. F i s i c a s , U n i v e r s i d a d de M a d r i d , 1967 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n t h e Department of PHYSICS We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1970 In presenting th i s thes i s in pa r t i a l f u l f i lment o f the requirements fo r an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make i t f r ee l y ava i l ab le for reference and study. I fur ther agree tha permission for extensive copying of th i s thes is for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th i s thes i s f o r f i nanc ia l gain sha l l not be allowed without my wr i t ten permiss ion. Depa rtment The Univers i ty of B r i t i s h Columbia Vancouver 8, Canada i i ABSTRACT P i e z o p r o b e s of d e s i g n P h i l l i p s - C u r z o n 1 mm i n d i a m e t e r have been c a l i b r a t e d i n the p r e s s u r e range 0.2 t o 35 atm . S t e p p r e s s u r e p u l s e s f o r the c a l i -b r a t i o n were produced w i t h plane shock waves i n the range 0 . 2 - 1 atm , and w i t h p l a n e d e t o n a t i o n s i n A c e t y l e n e - O x y g e n i n the range 2 - 3 5 atm . The c a l i b r a t e d probes were used t o measure the s p a c e - t i m e p r e s s u r e p r o f i l e s i n I) c o n c e n t r i c d e t o n a t i o n s II) r a d i a t i o n f r o n t s b e h i n d windows and I I I ) p r e s s u r e waves i n d u c e d by an i n t e n s e l i g h t s o u r c e . The measurements s u p p o r t e d e x i s t i n g models of the dynamics of th e s e p u l s e d d i s c h a r g e s . i i i • TABLE OF CONTENTS A b s t r a c t I I n t r o d u c t i o n I - l D e s i g n of the probes I I C a l i b r a t i o n I I - l C a l i b r a t i o n of the probes a t low p r e s s u r e s I I - 2 C a l i b r a t i o n w i t h p l a n e d e t o n a t i o n s I I I P r e s s u r e p r o f i l e s of a c o n c e n t r i c d e t o n a t i o n I I I - l I n t r o d u c t i o n I I I - 2 A p p a r a t u s I I I - 3 R e s u l t s I I I - 4 C o n c l u s i o n s IV R a d i a t i o n f r o n t s b e h i n d windows IV- 1 I n t r o d u c t i o n IV-2 A p p a r a t u s IV-3 E x p e r i m e n t a l R e s u l t s IV-4 Comparison w i t h t h e o r y V Shock waves i n d u c e d by i n t e n s e l i g h t s o u r c e VI C o n c l u s i o n s A Appendix i v LIST OF ILLUSTRATIONS F i g u r e 1 P i e z o p r o b e 2 D e t a i l of probe 3a Probe assembly 3b Probe assembly 4 Probe c a l i b r a t i o n a t low p r e s s u r e s 5 Smear photograph of p l a n e d e t o n a t i o n 6 E x p e r i m e n t a l s e t - u p f o r c a l i b r a t i o n 7 Probe c a l i b r a t i o n a t h i g h p r e s s u r e s 8a D e t o n a t i o n chamber 8b C e n t e r p l a t e i n s m a l l d e t o n a t i o n chamber 9 P r e s s u r e a t the d e t o n a t i o n f r o n t vs. r a d i u s f o r i n i t i a l p r e s s u r e s of 500, 400, 300 T o r r 10 P r e s s u r e d i s t r i b u t i o n i n l a r g e d e t o n a t i o n chamber 11 P r e s s u r e d i s t r i b u t i o n i n s m a l l d e t o n a t i o n chamber 12 P r e s s u r e a t the d e t o n a t i o n f r o n t v s . r a d i u s ' f o r i n i t i a l p r e s s u r e s of 300, 400, 500 T o r r 13 V a r i a t i o n of d e t o n a t i o n p r e s s u r e w i t h r a d i u s f o r a c y l i n d r i c a l i m p l o d i n g d e t o n a t i o n wave i n e q u i m o l a r A c e t y l e n e - O x y g e n m i x t u r e 14 E x p e r i m e n t a l s e t - u p f o r the s t u d y of r a d i a t i o n f r o n t s i n Oxygen 15a L i g h t p u l s e from Bogen s o u r c e 15b Probe s i g n a l E x p e r i m e n t a l p r e s s u r e p r o f i l e s i n Oxygen a t 80 T o r r E x p e r i m e n t a l p r e s s u r e p r o f i l e s i n Oxygen a t 760 T o r r T h e o r e t i c a l p r e s s u r e p r o f i l e s i n Oxygen a t 0.1 Atm E x p e r i m e n t a l s e t - u p f o r the p r o d u c t i o n of shock f r o n t s i n Argon w i t h the Bogen s o u r c e H i g h speed photograph o f the d i s c h a r g e of the l i g h t s o u r c e i n Argon H i g h speed photograph o f the d i s c h a r g e o f the l i g h t s o u r c e i n Argon x - t diagram of the d i s c h a r g e of the Bogen s o u r c e i n Argon P r e s s u r e p r o f i l e b e h i n d the r a d i a t i o n f r o n t Shock tube S e t - u p f o r probe c a l i b r a t i o n Probe s i g n a l v i ACKNOWLEDGMENTS I w i s h t o thank Dr. B. A h l b o r n f o r h i s gui d a n c e and encouragement t h r o u g h o u t the p r e p a r a t i o n of t h i s t h e s i s . I would a l s o l i k e t o thank Dr. F. Cur z o n and Dr. M. P h i l l i p s f o r h e l p i n c o n s t r u c t i n g the p i e z o -probes . I want t o e x p r e s s my a p p r e c i a t i o n f o r the many f r u i t f u l d i s c u s s i o n s h e l d w i t h members of the Plasma P h y s i c s group , i n p a r t i c u l a r w i t h Mr. J . S t r a c h a n and Mr. J . P. Hun i . I am g r a t e f u l t o Mr. Huni f o r v e r y h e l p f u l s u g g e s t i o n s c o n c e r n i n g C h a p t e r I I I . F i n a l l y , I w i s h t o acknowledge s t i m u l a t i n g d i s c u s s i o n s h e l d w i t h Dr. R. C. C r o s s . -1-INTRODUCTION I t i s i m p o r t a n t f o r the u n d e r s t a n d i n g of p u l s e d d i s c h a r g e s and wave p r o p a g a t i o n phenomena i n gases t o know the p r e s s u r e as a f u n c t i o n of space and time . The magnitude and v a r i a t i o n of the p r e s s u r e may i n p r i n c i p l e be d e r i v e d from t i m e - r e s o l v e d s p e c t r o s c o p i c measurements of t e m p e r a t u r e and d e n s i t y , p r o v i d e d the c o m p o s i t i o n and s t a t e of e q u i l i b r i u m of the gas i s known. W i t h the i n t r o d u c t i o n of p i e z o e l e c t r i c t r a n s d u c e r s d i r e c t p r e s s u r e measurements have become p o s s i b l e . These measurements do not r e q u i r e a s s u m p t i o n s about the com-p o s i t i o n and e q u i l i b r i u m o f the plasma , but r e l y heav-i l y on a p r e c i s e c a l i b r a t i o n t e c h n i q u e and p r o p e r a p p l i -c a t i o n o f the probes . In t h i s t h e s i s a new c a l i b r a t i o n t e c h n i q u e was a p p l i e d , i n which s t e p p r e s s u r e p u l s e s o f known s t r e n g t h were o b t a i n e d w i t h p l a n e d e t o n a t i o n s . The probes were the n a p p l i e d t o i n v e s t i g a t e the p r e s s u r e p r o f i l e s o f o v e r d r i v e n c o n c e n t r i c d e t o n a t i o n s , the f o r m a t i o n of r a d i a t i o n - i n d u c e d p r e s s u r e waves , and the head-on c o l -l i s i o n o f two shock waves . -2-CHAPTER I DESIGN OF THE PROBES I t i s n e c e s s a r y f o r the u n d e r s t a n d i n g o f t h i s t h e s i s t o know the b a s i c d e s i g n of the p i e z o p r o b e s . T h e r e f o r e , a s h o r t d e s c r i p t i o n i s g i v e n here ; more d e t a i l s about the probes may be o b t a i n e d from P h i l l i p s ( 1969 ) ( Ref. 1 ) The probes use the p i e z o - e l e c t r i c e f f e c t : i f a f o r c e i s a p p l i e d t o two o p p o s i t e s u r f a c e s of a c e r t a i n group of i o n i c c r y s t a l s , the m a t e r i a l w i l l be p o l a r -i z e d . The p o l a r i z a t i o n produces a s u r f a c e charge on two o p p o s i t e s i d e s of the c r y s t a l . T h i s charge i s p r o p o r t i o n a l t o the a p p l i e d s t r e s s w i t h i n p r o p e r l i m i t s , and i t can be measured w i t h a h i g h impedance v o l t m e t e r . E s s e n t i a l l y , the probes c o n s i s t of a p i e z o c r y s t a l C ( PZT-4 ) of 0.2 mm t h i c k n e s s which i s mounted between c y l i n d r i c a l q u a r t z r o d s R^ , R^ of 1 mm d i a m e t e r and about 10 cm i n l e n g t h . The ends o f the q u a r t z r o d s a r e c a r e f u l l y ground and a t t a c h e d t o the c r y s t a l ( F i g . 1 ) Fig. 1 Piezoprobe -3-The unknown p r e s s u r e p u l s e p i s a p p l i e d t o the s u r f a c e of the p r e s s u r e t r a n s d u c e r , , and a r r i v e s a t the c r y s t a l C a f t e r a time 1,/c, , where c i s 1 1 ' 1 the speed of sound i n q u a r t z . The p u l s e produces a m e c h a n i c a l s t r e s s i n the p i e z o c r y s t a l , so t h a t a v o l t a g e d i f f e r e n c e i s i n d u c e d between the f a c e s and S , w h i c h can be measured w i t h an o s c i l l o s c o p e . The 2 p r e s s u r e p u l s e a f t e r p a s s i n g t h r o u g h the p i e z o e l e c t r i c element e n t e r s the r e f l e c t i o n d e l a y r o d , R , and 2 t r a v e l s t o the end of i t i n a time 1 /c . I t i s t h e n 2 1 r e f l e c t e d and p asses a g a i n t h r o u g h the c r y s t a l p r o d u c i n g a second s i g n a l . The time d i f f e r e n c e between i n c i d e n t and r e f l e c t e d p u l s e s i s t h e n r = 21 /c and s i n c e the 2 1 two s i g n a l s i n t e r f e r e , the r e a d i n g time of the probe i s l i m i t e d t o r . We a r e assuming t h a t t h e r e a r e no r e f l e c t i o n s a t the c o n t a c t s u r f a c e between the c r y s t a l and the q u a r t z b a r s . These can o n l y be a v o i d e d i f the a c o u s t i c a l impedances match e x a c t l y . Even i f t h i s i s so , the b o n d i n g agent may cause p a r t i a l r e f l e c t i o n s w hich c o u l d d i s t o r t the s i g n a l under o b s e r v a t i o n . Jones ( Ref. 2 ) has shown t h a t f o r a t y p i c a l epoxy r e s i n , i f d £~ 0.06r , where d i s the t h i c k n e s s of the l a y e r of g l u e and r t h e r a d i u s o f the r o d s , the t r a n s m i s s i o n r e a c h e s 99%. -4-We are also neglecting dispersion of the sound pulse i n the quartz rods \ i t can be shown that i f O^rA — 0.1 , where X i s the smallest wavelength ' m m present in the pressure pulse spectrum , the pulse 1/2 w i l l propagate undistorted with speed ( E/Q ) , rod , and E the Young's modulus .(Ref. 2) This type of probes has a number of features which make i t useful for measurements taken in pulsed e l e c t r i c a l connections can be removed out of the region occupied by the plasma . In t h i s manner , the e f f e c t of thermally-induced stresses can be avoided , and the c i r c u i t r y can be shielded against electromagnetic f i e l d s associated with production of the plasmas . In cases where i t i s d i f f i c u l t to exclude the f i e l d s completely , the measurement of the pressure can be delayed a c o u s t i c a l l y u n t i l a f t e r the electromagnetic f i e l d s have decayed , by choosing a suitable length 1^ for the pressure transducer . Good s p a t i a l resolution can be achieved with a rod of s u f f i c i e n t l y small diam-eter , s a c r i f i c i n g some of the s e n s i t i v i t y of the probe. The observation time r can be of any desired duration , according to the length of the rear rod. where the mass density of the material of the discharges the s e n s i t i v e element and the associated -5-The p i e z o e l e c t r i c wafer should be of the same diam-eter as the quartz rods to match acoustic impedances . However , as the thickness of the c r y s t a l disks i s only 0.2 mm , i t i s d i f f i c u l t to cut them to the ri g h t diam-eter and shape . The ends of the acoustic l i n e next to the p i e z o e l e c t r i c substance are coated with a thin layer of s i l v e r paint , and leads which make e l e c t r i c a l contact with the sides of the PZT-4 disk take the si g n a l to an oscilloscope . The c r y s t a l i s glued to the quartz bars with epoxy r e s i n ( F i g . 2 ) . Quartz i s used because i t i s an insulator and has a high melting point . In order to avoid d i s t o r t i o n of the s i g n a l , the probes must be c a r e f u l l y mounted to allow free motion of the surface of the pressure transducer ( Figs. 3a , 3b ) . F i n a l l y , in evaluating the signals one must keep in mind that piezoprobes with short rise-time may show an overshoot of the si g n a l . The magnitude of t h i s overshoot depends on the length of the pressure transducer , 1^  ( Ref. 3 ) . For our probes , i t i s less than 10% . - b -Fig. 2 Detail of Probe S QUARTZ • PZT-4 Sf L VER PAINT EPOXY RESIN brass case Fig. 3 b glass jacket reflection delay rodR2 n  crystal C transducer R1 -7-CHAPTER I I I I - l CALIBRATION OF THE PROBES AT LOW PRESSURES I t i s a w e l l known c a l i b r a t i o n t e c h n i q u e t o i n s e r t the p i e z o p r o b e f l u s h w i t h the w a l l s o f a membrane shock tube and measure the re s p o n s e o f the probe as f u n c t i o n o f i n i t i a l p r e s s u r e and shock f r o n t v e l o c i t y . Knowing th e s e two v a l u e s , the p r e s s u r e jump can be c a l c u l a t e d . T h i s method was used i n t h i s work t o o b t a i n a c a l i b r a t i o n of the probes i n the low p r e s s u r e range. ( 100 T o r r ^ p ^ 4 0 0 T o r r ) and the r e s u l t s a r e shown i n F i g . 4 . T h i s c a l i -b r a t i o n method i s q u i t e a s t a n d a r d p r o c e d u r e ( B l i c h l (4) , P h i l l i p s (1) ) . F o r c o m p l e t e n e s s , however , some d e t a i l s a r e g i v e n i n the A p p e d i x . A s e v e r e drawback of the shock tube c a l i b r a t i o n i s the f a c t t h a t o n l y r a t h e r low p r e s s u r e s o f the o r d e r o f 1 Atm can be o b t a i n e d . F o r some a p p l i c a -t i o n s i t i s d e s i r a b l e t o c a l i b r a t e the probes a t much h i g h e r p r e s s u r e s ; s i n c e e x t r a p o l a t i o n from the c a l i b r a t e d range t o about 50 Atm would l e a d t o i n t o l e r a b l e e r r o r s , a new method of p r o d u c i n g t e s t p u l s e s of up t o 35 Atm w i t h p l a n e d e t o n a t i o n s was s u c c e s s f u l l y a p p l i e d . I1-2 CALIBRATION WITH PLANE DETONATIONS The d e t o n a t i o n wave was produced i n a 110 cm l o n g , -8-2.5 cm diameter pyrex tube closed at both ends . A 15 KV , 1.6 uF spark discharge was used to i g n i t e the detonation gas . The tube was f i r s t evacuated and then f i l l e d with a mixture of Oxygen and Acet-ylene which was prepared i n a separate mixing cham-ber . The probe was mounted fl u s h with the walls of the tube , perpendicular to i t s axis , at a position 90 cm from the i g n i t i o n end . ( Fi g . 6 ) The speed of the detonation , V , was obtained 1 from smear photographs ( F i g . 5 ) ( Ref. 5 ) and from the time i n t e r v a l between the i g n i t i o n and the a r r i v a l of the pressure pulse at the observation point . These measurements indicated that the detonation i s indeed a Chapman-Jouget detonation . The amplitude of the pressure jump i s then given by 1 -> * (1) 1 + r / 2 where p^ , , are the pressure and density ahead of the front , and y i s the s p e c i f i c heat r a t i o of the 2 reaction products taken as 1.25 +_ 0.05 . This includes a l l the values of y i n the range of pressures and tem-2 peratures expected in the detonation wave . ( Ref. 6 ) The uncertainty i n the value of y corresponds to a maximum 2% error i n the pressure r a t i o . -9-With Po ~ ) i e q u a t i o n ( 1 ) can be put as x + V 2 2 1 + r J P l 1 + ^ 2 The o u t p u t of the probe i s p l o t t e d a g a i n s t p r e s s u r e i n F i g . 7 . We found a l i n e a r r e l a t i o n s h i p , the s e n s i t i v i t y of t h i s probe b e i n g 1 4 . 3 Torr/mV +_ 5% . In the n e x t c h a p t e r s we w i l l d i s c u s s t h r e e e x p e r -iments i n which the probes have s u c c e s s f u l l y been em-p l o y e d . Sm ear Photograph of plane detonation i i 5 cm "1 1SKV Fig. 6 T 1 Tube Probe Experimental Set-up for Calibration -13-CHAPTER I I I PRESSURE PROFILES OF A CONCENTRIC DETONATION I I I - l INTRODUCTION C o n c e n t r i c d e t o n a t i o n s have been s t u d i e d t h e o r e t -i c a l l y by C h e s t e r (7) , C h i s n e l l (8) , Whitham (9) , Lee (10) , and the t h e o r y of these waves i s so f a r advanced t h a t the d i s t r i b u t i o n s of p r e s s u r e , d e n s i t y and v e l o c i t y can be n u m e r i c a l l y p r e d i c t e d . The f i r s t e x p e r i m e n t a l check of t h i s t h e o r y was a t t e m p t e d by Lee . He measured the p r e s s u r e w i t h t r a n s d u c e r s o f 3.2 mm d i a m e t e r . The probes o f P h i l l i p s have a supe-r i o r s p a t i a l r e s o l u t i o n and are r e l i a b l y p u l s e - t e s t e d up t o the r e q u i r e d range . We t h e r e f o r e s e t out t o r e p e a t Lee's measurements i n t h i s l a b o r a t o r y . The r e s u l t s were a l s o e x p e c t e d t o be o f g r e a t v a l u e t o J . P. Huni , who has s t u d i e d the dynamics and thermodynamics of the con-c e n t r i c d e t o n a t i o n s w i t h smear camera and s p e c t r o s c o p i c methods ( Ref. 11 ). I I 1 - 2 APPARATUS The c o n c e n t r i c d e t o n a t i o n i s i g n i t e d i n a c y l i n d r i c a l d e t o n a t i o n chamber i n d i c a t e d i n F i g . 8a ( Ref. 11 ) . For o p e r a t i o n the chamber i s e v a c u a t e d and then f i l l e d t o the Fig.. Ba Detonation -14-Chamber Fig. 8b Center Plate in Small Detonation Chamber -15 -d e s i r e d p r e s s u r e ( 300 , 400 , 500 T o r r ) w i t h an e q u i -molar m i x t u r e of A c e t y l e n e and Oxygen p r e v i o u s l y p r e -pared i n a s e p a r a t e m i x i n g chamber . The gas i s then c o n c e n t r i c a l l y i g n i t e d by the s p a r k gap S on the i g n i -t i o n s i d e of the chamber , I t forms an e x p l o s i o n f r o n t t h a t i s t u r n e d around the b a k e l i t e c e n t r a l p l a t e D t o form the c o n c e n t r i c i m p l o d i n g f r o n t i n the o b s e r v a t i o n s i d e of the chamber . At l a r g e r a d i i , the f r o n t behaves l i k e a p l a n e d e t o n a t i o n , o b e y i n g the Chapman-Jouget c o n d i t i o n s . Ten h o l e s t o i n s e r t the probes a t d i f f e r e n t r a d i i were made i n the f r o n t p l a t e F . The p r e s s u r e was r e c o r d e d a t 1 o n l y one p o s i t i o n a t a time , r e l y i n g on the good r e p r o -d u c i b i l i t y of the d i s c h a r g e t o get the f u l l p r e s s u r e d i s -t r i b u t i o n . The o t h e r p o r t s were f i t t e d w i t h s p e c i a l l y made b r a s s p l u g s . I I 1 - 3 RESULTS In a f i r s t s t u d y , the peak v a l u e s of the p r e s s u r e a m p l i t u d e of the d e t o n a t i o n wave were measured a t d i f f e r e n t r a d i a l p o s i t i o n s f o r s e v e r a l f i l l i n g p r e s s u r e s . F i g . 9 shows the r e s u l t s . I t i s seen t h a t the f i n a l p r e s s u r e r a t i o s c a l e s w i t h i n 5% as the f i l l i n g p r e s s u r e s , s i n c e from the measurements one f i n d s the average r a t i o of the f i n a l p r e s s u r e s P 5 0 c / P 3 0 0 w h i l e the f i l l i n g = 1.30 P 400 P 300 Aim 10 1 1 1 • r 20mm 40 60 rQ *. r Fig. 9 Pressure at the Detonation Front vs. Radius for Initial Pressures of 500,400, 300 (Torr) -17-p r e s s u r e r a t i o g i v e s a t h e o r e t i c a l v a l u e 500/300 _ 1.25 400/300 T h i s b e h a v i o r i s e x p e c t e d and i t i s a l s o a n i c e c o n f i r -m a t ion of the l i n e a r i t y of the probe i n t h i s p r e s s u r e range . F u r t h e r , i t can be n o t i c e d t h a t the s i g n a l s o b t a i n e d a t i n i t i a l p r e s s u r e s of 400 and 500 T o r r 70 mm away from the c e n t e r are l a r g e r t h a n n e i g h b o r v a l u e s . T h i s i s due t o i r r e g u l a r i t i e s i n the f r o n t / which i s d i s t o r t e d when t u r n i n g around the edge of the c e n t e r p l a t e , a l t h o u g h i t s t a b i l i z e s l a t e r . The p r e s s u r e d i s t r i b u t i o n as a f u n c t i o n of r a d i a l p o s i t i o n and time i s shown i n F i g . 10 , f o r an i n i t i a l p r e s s u r e o f 400 T o r r . The measurements are ta k e n a t v a l u e s of r between 13 and 70 mm ; a t t=0 the d e t o n a t i o n f r o n t appears a t r=70 mm and moves toward the c e n t e r of the chamber . The p r e s s u r e f i r s t f a l l s o f f b e h i n d the f r o n t , but then s t a r t s t o r i s e a g a i n . T h i s b e h a v i o r i s b a r e l y n o t i c e a b l e i n the p r o f i l e s t a k e n a t r = 70 mm; however , the sec o n d a r y maximum becomes s t e e p e r i n the f o l l o w i n g p r o f i l e s u n t i l i t l o o k s l i k e a s e c o n d a r y d i s c o n t i n u i t y f r o n t . I t t r a v e l s a t the same v e l o c i t y as the d e t o n a t i o n f r o n t . We can n o t i c e t h a t i n the p r o f i l e s t a k e n a t l a r g e v a l u e s of r the p r e s s u r e b e h i n d the f r o n t decays r a p i d l y , w h i l e the p r o f i l e s t a k e n c l o s e r t o the c e n t e r show a p l a t e a u b e h i n d the f r o n t . T h i s i s e x p e c t e d , and i s due p Pressure distribution in large detonation chamber -19-t o the f a c t t h a t the c o n v e r g i n g f l o w of gas tends t o f i l l i n the r a r e f a c t i o n wave which f o l l o w s the d e t o n a t i o n f r o n t . ( Ref. 11 ) . A s m a l l e r chamber was d e s i g n e d and c o n s t r u c t e d by J . P. H u n i ( Ref. 11 ) i n which the c e n t e r p l a t e D has smooth and round edges t o m i n i m i z e t u r b u l e n c e e f f e c t s on the gas f l o w around i t ( F i g . 8b ) . We a l s o measured the p r e s s u r e d i s t r i b u t i o n of the d e t o n a t i o n i n t h i s chamber , and the r e s u l t s a r e shown i n F i g s . 11 and 12 . F i g . 11 g i v e s the p r e s s u r e of the d e t o n a t i o n as f u n c t i o n of r a d i u s and time , f o r an i n i t i a l p r e s s u r e of 400 T o r r . The meas-urements are t a k e n f o r v a l u e s of r between 0 and 12 mm | the p r e s s u r e a t the c e n t e r of the chamber r e a c h e s 332 Atm, t o decay t o a v a l u e of 63 Atm a t r = 3 mm . On a l l o f f - a x i s t r a c e s one can c l e a r l y see the i n c o m i n g d e t o n a t i o n wave and t h e subsequent r e f l e c t e d wave , which b r i n g s a c o n s i d -e r a b l e i n c r e a s e i n p r e s s u r e . However , the s e c o n d a r y maximum which f o l l o w s the d e t o n a t i o n f r o n t a t c o n s t a n t d i s t a n c e i n the l a r g e chamber i s not found i n t h i s c a s e . The r - t diagram of the d e t o n a t i o n f r o n t appears i n F i g s . 10 and 11 as a s t r a i g h t l i n e ; smear photographs of the i m p l o s i o n show t h a t the d e t o n a t i o n speeds up s l i g h t -l y towards the c e n t e r ( Ref. 12 ) . T h i s o n l y becomes notice_ a b l e a t v e r y s m a l l r a d i i ; the d i f f e r e n c e between the time -20-^R effected Front Imploding detonation front Fig. 11 Pressure distribution in small -detonation chamber -21-10 J • 1 • Smm 15 <- r Fig. 12 Pressure at the detonation front vs. radius for initial pressures of 3 0 0 , 4 0 0 , 500 Torr -22-f o r l i n e a r i m p l o s i o n and the time a c t u a l l y t a k e n by the d e t o n a t i o n t o r e a c h the c e n t e r of the chamber i s l e s s t han 4% . The r e s u l t s o b t a i n e d i n both chambers are shown i n F i g . 13 . Here , p/p i s p l o t t e d a g a i n s t r / r ; o o p i s the p r e s s u r e a t the d e t o n a t i o n f r o n t a t d i f f e r e n t r a d i a l p o s i t i o n s r ; p i s the Chapman-Jouget p r e s s u r e , o and r i s the r a d i u s of the chamber , a t w h i c h a Chapman-o J o u g e t d e t o n a t i o n i s s e t . The e x p e r i m e n t a l p o i n t s a r e compared w i t h the t h e o r e t i c a l p r o f i l e as g i v e n by Lee ( Ref. 10 ) f o r y = 1.378 . The c h o i c e o f y i s not c r i t i c a l s i n c e t h e r e i s l i t t l e dependence on the a d i a b a t i c exponent. The agreement between the t h e o r e t i c a l c u r v e and e x p e r i m e n t a l p o i n t s i s good , a l t h o u g h a t i n i t i a l p r e s -s u r e s o f 400 and 500 T o r r and l a r g e v a l u e s of r we meas-u r e v a l u e s f o r p/p l a r g e r than e x p e c t e d . o I I 1 - 4 CONCLUSIONS The measurements c o n f i r m e d the l a r g e i n c r e a s e i n p r e s s u r e p r e d i c t e d by t h e o r y f o r o v e r d r i v e n c o n c e n t r i c d e t o n a t i o n s . A s e c o n d a r y p r e s s u r e f r o n t i s d e v e l o p e d i n one of the t e s t chambers , p o s s i b l y due t o a d i s t u r b a n c e i n the -23-f l o w produced by the shape o f the c e n t e r p l a t e . In the i n v e s t i g a t e d range 300 Torrfrp£~500 T o r r the f i n a l p r e s s u r e s a r e l i n e a r l y p r o p o r t i o n a l t o the f i l l i n g p r e s s u r e s . Fig. 13 Variation of Detonation Pressure with Radius for a Cylindrical Imploding Detonation Wave in Equimolar Acetylene-Oxygen Mixture • Experiment — Theory -25-CHAPTER IV RADIATION FRONTS BEHIND WINDOWS IV-1 INTRODUCTION Pressure measurements with high s p a t i a l and time-resolution can also advantageously be applied to inves-tigate the development of r a d i a t i o n fronts . In an ear-l i e r experiment , Zuzak ( Ref. 13 ) demonstrated that r a d i a t i o n fronts can be produced i n Oxygen behind a L i F window . But while he succeeded i n predicting the time development rather accurately , he was able only to detect q u a l i t a t i v e l y the existence of radiation-induced pressure pulses . His piezoprobes were too i n s e n s i t i v e and too large i n s i z e to make any meaningful p r o f i l e measurements . It was one aim of t h i s thesis to measure the development of the pressure waves induced by absorp-tion of d i s s o c i a t i n g r a d i a t i o n and compare the r e s u l t s with Zuzak's theory. The process by which r a d i a t i o n fronts are formed can be explained as follows •' i f an intense , steady flux of photons i s incident upon an absorbing gas , the photons w i l l cause d i s s o c i a t i o n or i o n i z a t i o n in the test gas i f t h e i r energies are high enough . At a p a r t i c u l a r instant of time , the volume of gas can then be considered -26-as divided i n two regions : one i n which the incident r a d i a t i o n has been absorbed producing i o n i z a t i o n or d i s s o c i a t i o n of almost a l l p a r t i c l e s , and another i n which the r a d i a t i o n has not yet affected the gas . The boundary between these two regions propagates with a c e r t a i n speed which i s a function of the incident flux and the density of absorbing p a r t i c l e s . This boundary constitutes the r a d i a t i o n front . Behind i t , the tem-perature and the number of p a r t i c l e s per unit mass are considerably higher than ahead of the front . The re -s u i t i n g pressure gradient across the r a d i a t i o n front may produce considerable motion of the gas . To estab-l i s h the r a d i a t i o n front i t i s also necessary that the region formed by the dissociated or ionized p a r t i c l e s be transparent to the r a d i a t i o n , and that the extent of the cloud of absorbing p a r t i c l e s be large compared with the mean free path of the r a d i a t i o n . The photon flux does not have to be steady to produce a r a d i a t i o n front : t h i s assumption was introduced to s i m p l i f y the treatment. The d i f f e r e n t types of r a d i a t i o n fronts are studied by Zuzak ( Ref. 13 ) j he also discusses time-varying fluxes , steady r a d i a t i o n fronts are studied in Ref. 14 . Radiation fronts are encountered in i n t e r s t e l l a r space at the edges of HII regions ( clouds of ionized - 2 7 -Hydrogen w h i c h s u r r o u n d h o t young s t a r s ) . The f i r s t i n d i r e c t a c t i o n of a r a d i a t i o n f r o n t i n the l a b o r a t o r y was g i v e n by E l t o n , who n o t i c e d t h a t q u a r t z c o n t a i n e r s of 9 - p i n c h d i s c h a r g e s used t o break e a s i l y , which d i d not happen when g l a s s vessel's were used . He e x p l a i n e d t h i s as due t o t r a n s m i s s i o n of u l t r a v i o l e t r a d i a t i o n from the d i s c h a r g e t h r o u g h the q u a r t z , which d i s s o c i a t e d the Oxygen i n the a i r , i n d u c i n g a shock wave which s h a t t e r e d the q u a r t z v e s s e l . I V - 2 APPARATUS The main r e q u i r e m e n t t o produce r a d i a t i o n f r o n t s i n the l a b o r a t o r y i s an e x t r e m e l y i n t e n s e l i g h t s o u r c e . We used a l i g h t s o u r c e s i m i l a r t o one d e s c r i b e d i n 1 9 6 5 by Bogen e t a l ( r e f . 1 5 ) . A 2 5 JJ.F c a p a c i t o r bank i s charged up t o 2 . 5 KV and d i s c h a r g e d through a 2 . 4 mm d i a m e t e r h o l e d r i l l e d i n a p o l y e t h y l e n e r o d 6 cm l o n g . The c u r r e n t o f the d i s c h a r g e v a p o r i z e s the p o l y e t h y l e n e a t the w a l l s and produces a v e r y hot and dense plasma which e m i t s i n a x i a l d i r e c t i o n b l a c k body r a d i a t i o n of the o r d e r of 1 0 ° K . The l i g h t p u l s e l a s t s about 1 0 u.sec. A diagram of the l i g h t s o u r c e and o f the s e t t i n g of the ex p e r i m e n t i s g i v e n i n F i g . 1 4 . I n o r d e r t o s e p a r a t e the t e s t gas from the l i g h t -28-s o u r c e we a l s o need a window t r a n s p a r e n t t o i o n i z i n g or d i s s o c i a t i n g r a d i a t i o n . We used L i F windows . L i F o t r a n s m i t s r a d i a t i o n above 1050 A . Oxygen was used as t e s t gas j i t has a l a r g e a b s o r p t i o n c r o s s - s e c t i o n f o r d i s s o c i a t i n g photons i n the Schuman-Runge r e g i o n ( 1200-o 1800 A ) , so t h a t p h o t o d i s s o c i a t i o n can be e x p e c t e d i n the t e s t chamber which has s e v e r a l p o r t s t o i n s e r t the p i e z o p r o b e s a t d i f f e r e n t d i s t a n c e s o f f the window . ( F i g . 14 ) IV-3 EXPERIMENTAL RESULTS P r e s s u r e p u l s e s were r e c o r d e d by the probes a f t e r the l i g h t s o u r c e was f i r e d . The a m p l i t u d e o f the s i g n a l s depended on the f i l l i n g p r e s s u r e , p , and became s m a l l e r o than 1 T o r r , the e x p e r i m e n t a l e r r o r o f the probes , a t p = 2 0 T o r r . These p r e s s u r e waves were due t o l i g h t o a b s o r p t i o n f o r the f o l l o w i n g r e a s o n s : i ) I f t h e L i F windows a r e s u b s t i t u t e d by g l a s s windows which c u t down the u l t r a v i o l e t r e g i o n o f the r a d i a t i o n , no d i s s o c i a t i o n t a k e s p l a c e and no p r e s s u r e waves a r e e x p e c t e d . The probes i n f a c t r e c o r d e d no s i g n a l s b e h i n d the g l a s s window . i i ) The a m p l i t u d e of the s i g n a l i s e x p e c t e d t o depend on the i n c i d e n t i n t e n s i t y . S i n c e Carbon i s blown out o f the end of the c a p i l l a r y w i t h each s h o t and i s d e p o s i t e d on -29-the L i F window the t r a n s m i t t e d i n t e n s i t y of each subsequent s h o t w i l l be r e d u c e d i n c o n s e c u t i v e s h o t s . Indeed , the measured p r e s s u r e p u l s e s d e c r e a s e d i n a m p l i t u d e i f the L i F window was not c l e a n e d a f t e r each s h o t . . The development of the p r e s s u r e p u l s e s , f o r d i f f e r e n t f i l l i n g p r e s s u r e s was then a n a l y z e d as f u n c t i o n o f space and time . A t y p i c a l t r a c e of the o u t p u t of the probe a t 80 T o r r i s shown i n F i g . 15b ; the shape of the l i g h t p u l s e as f u n c t i o n of time i s shown i n F i g . 15a . The s h o t s were t a k e n i n TRI-X f i l m and d e v e l o p e d i n B19 d e v e l o p e r , so t h a t the n e g a t i v e s c o u l d be e n l a r g e d t o f a c i l i t a t e t r a c i n g . The d i s t a n c e s between the p o i n t s a t which the probes a r e i n s e r t e d a r e s m a l l enough t o a l l o w p l o t t i n g of the p r o f i l e s f o r c o n -s t a n t time a t d i f f e r e n t d i s t a n c e s , x . The 1 mm diam-e t e r p r e s s u r e t r a n s d u c e r o.f the probe i s s u r r o u n d e d by a 1/4" d i a m e t e r g l a s s j a c k e t , w h i c h p r e v e n t s measure-ments a t d i s t a n c e s c l o s e r t o the window than 3.5 mm. F i g . 15c shows the e x p e r i m e n t a l p r e s s u r e p r o f i l e s a t i n t e r v a l s o f 4 usee ^ f t e r the l i g h t s o u r c e i s f i r e d ; / \p r e p r e s e n t s the i n c r e m e n t i n p r e s s u r e due t o the r a -d i a t i o n f r o n t . The speed of p r o p a g a t i o n of the p u l s e i s 330 + 5 m/sec . I t can be seen i n F i g . 15b t h a t the -30-r i s e - t i m e of the probe s i g n a l i s about 3 usee ; t h i s r a t h e r l a r g e v a l u e comes from the t r a n s i t time of the p r e s s u r e p u l s e a c r o s s the f a c e of the probes , s i n c e the measurements were taken w i t h the probes perpen -d i c u l a r t o the a x i s of the chamber . We took some measurements w i t h the p i e z o p r o b e s f a c i n g the p r e s s u r e s i g n a l and the r i s e - t i m e v a l u e i s reduced t o about 1 usee . The a m p l i t u d e of the s i g n a l s o b t a i n e d i n t h i s way i s a l s o s l i g h t l y l a r g e r . T h i s i s q u i t e s u r p r i s i n g , s i n c e i t would i n d i c a t e the e x i s t e n c e of a r a r e f a c t i o n wave which i s not e xpec-t e d f o r a r a d i a t i o n f r o n t t r a v e l l i n g a t s o n i c speed. We took r e a d i n g s of the p r e s s u r e f o r v a l u e s o f x between 0.35 and 22 cm. The p r o f i l e s t a k e n a t 8 ^ x ^ 2 2 cm do not d e p a r t s i g n i f i c a n t l y from the ones found a t c l o s e d i s t a n c e s from the window , and decay v e r y s l o w l y i n a m p l i t u d e . A t y p i c a l p r o f i l e i s shown on the e x t e n d e d s c a l e , ( F i g . 16 ) . The r a d i a t i o n - i n d u c e d p r e s s u r e wave o b v i o u s l y p r o p a g a t e s w i t h v e r y l i t t l e damp-i n g , s i n c e the s o u r c e has been t u r n e d o f f f o r about 600 usee when the p r e s s u r e p u l s e r e a c h e s a p o s i t i o n 20 cm down the t e s t chamber . We found t h a t i n most of the o b s e r v e d p r e s s u r e the z e r o l e v e l ( see F i g . 16 ) -31-F i g . 16 shows the p r o f i l e s t a k e n w i t h an i n i t i a l p r e s s u r e of 760 T o r r f o r 3 . 5f " r xfr : 12 mm . The s i g n a l s f o r 0 ^ x ^ 3 . 5 mm where no measurements were f e a s i b l e , have been e x t r a p o l a t e d from the ones we o b t a i n e d f o r l a r g e v a l u e s of x . The p r o f i l e s c a l c u l a t e d i n 0 f o r 2 an i n i t i a l p r e s s u r e of 76 T o r r and a f l u x i n t e n s i t y 22 -2 -1 of 1.16 x 10" ph.cm sec ( Ref. 13 ) a r e shown i n F i g . 17 . A c c o r d i n g t o t h e s e , the maximum p r e s s u r e i s p = 3.8p w i t h i n 4 usee , 3.3p a t 8 usee and 3.2p o o o a t 16 usee . The r a d i a t i o n i s assumed t o be s w i t c h e d on a t t = 0 , At 16 usee the c o m p r e s s i o n wave i s 8.5 mm away from the window and t r a v e l s a t a v e l o c i t y of 562 m/sec . We o b t a i n e d v e l o c i t i e s of 330 m/sec a t d i s t a n c e s f a r from the L i F window , and f o r an i n i t i a l p r e s s u r e of 760 T o r r . IV-4 COMPARISON WITH THEORY By c o m p a r i s o n between t h e o r y and e x p e r i m e n t we can see t h a t t h e r e i s q u a l i t a t i v e agreement . The p r e s s u r e i n b o t h the t h e o r e t i c a l and e x p e r i m e n t a l p r o f i l e s r a i s e s above the background l e v e l , r e a c h e s a peak v a l u e and the n decays s l o w l y t o some p l a t e a u v a l u e above p ; but o the magnitude of the measured e f f e c t i s much s m a l l e r t h a n e x p e c t e d . T h i s d i s c r e p a n c y i s p r o b a b l y due t o the l a r g e u n c e r t a i n t y f o r the e x p e r i m e n t a l v a l u e s o f the r a d i a t i o n o i n t e n s i t y i n the Schuman-Runge r e g i o n ( 1200-1800 A ) . Zuzak's i n t e n s i t y measurements were o n l y t a k e n above o 2300 A , and F was then o b t a i n e d by e x t r a p o l a t i o n . o The shape of the s i g n a l s and i t s s o n i c p r o p a g a t i o n v e l o c i t y i n d i c a t e t h a t the r a d i a t i o n i s not s t r o n g enough t o i n d u c e a shock wave and o n l y g e n e r a t e s a sound wave. In the ne x t c h a p t e r we s t u d y the type of f l o w produced by the Bogen l i g h t s o u r c e when the L i F window i s removed. light source radiation front i to CO t 3-7 kV Experimental set-up for Fig U the study of radiation fronts • in Oxygen Fig. 15c Experimental pressure profiles in Oxygen at 80 Torr - s e --36--37-CHAPTER V SHOCK WAVES INDUCED BY INTENSE LIGHT SOURCE From our measurements of the development of r a d i a t i o n fronts , i t was concluded that the i n t e n s i t y of the radia -tion of the Bogen source passing through the L i F window was too low to produce fast and strong pressure waves . • If the L i F window i s removed , the complete spectrum of the radiat i o n can f a l l d i r e c t l y into the test gas ( Argon ). At the same time , i t i s possible that some of the poly -ethylene plasma which produces the r a d i a t i o n may now i n t e r -act with the test gas side-on photographs of the discharge of the l i g h t source taken with a high speed framing camera show a bright cloud emerging from the end of the c a p i l l a r y , which spreads out to f i l l the entire cross-section of the tube and then detaches from the l i g h t source and propagates into the test gas . ( Figs. 18a , 18b , 18c ) The time development of th i s phenomenon was studied by Strachan ( Ref. 16 ) with a smear camera , and a schematic of the event i s shown in F i g . 19 . At a p a r t i c u l a r distance downstream and for Argon pressures over 1 Torr , a f a i n t l y luminous shock wave -38-X Ar — * > I 5cm 1 Q j Fig. 18a 11 ' C Experimental set-up for the production of shock fronts in Ar with the Bogen source -X -X Fig. 18 b Fig. 18 c High Speed Photographs of the Discharge of the Light Source in Argon ; interframe Delay 5usee; Exposure Time 500 nsec -39-Fig. 19 X-t Diagram of the Discharge of the Bogen Light Source in Argon -40-d e t a c h e s from the g e n e r a l f l o w and p r o p a g a t e s ahead of the luminous f r o n t . A c c o r d i n g t o the v a l u e of the p r e s -s u r e i n the r e g i o n O l z X ^ X , two p o s s i b l e e x p l a n a t i o n s e x i s t e d : 2 1) I f p = 2rM± f the f l o w f i e l d would be a b l a s t g + 1 wave , and i t would then be the r e s u l t of d i r e c t i n t e r -a c t i o n between the hydrogen-carbon plasma and the t e s t gas. 2 2) I f p = f the f l o w f i e l d would be a wave p o s s i b l y produced by the a b s o r p t i o n of r a d i a t i o n . The c a l i b r a t e d p i e z o p r o b e s were i n s e r t e d a t d i f -f e r e n t p o s i t i o n s X ; a t d i s t a n c e s w e l l o v er X , the 1 s i g n a l s from the probes l o o k l i k e the ones o b t a i n e d i n the diaphragm shock tube used f o r c a l i b r a t i o n of the - probes a t low p r e s s u r e s . ( I n s e r t b , F i g . 19 ) . At p o i n t s above X^ , the probes r e c o r d b oth the p r e s s u r e jump a t the shock f r o n t and a t the l u m i n o s i t y f r o n t ( I n s e r t a , F i g . 19 ) . The p r e s s u r e b e h i n d the shock f r o n t and the luminous f r o n t was o b s e r v e d t o d e c r e a s e r a p i d l y , i n d i -e a t i n g the p r e s e n c e o f a r a r e f a c t i o n wave b e h i n d the f r o n t . A t p o i n t s between 0 and X^ , the shape and magnitude o f the p r e s s u r e agreed w i t h S t r a c h a n ' s c a l c u l a t i o n s . -41-A t y p i c a l t r a c e of the probe and S t r a c h a n ' s e x p e c t e d v a l u e f o r the p r e s s u r e b e h i n d the f r o n t a r e shown i n F i g . 20 . H i s work s u p p o r t e d by our measurements seemed t o i n d i c a t e t h a t the l i g h t s o u r c e produced a r a d i a t i o n f r o n t t r a v e l l i n g a t the Chapman-Jouget p o i n t . The con -c l u s i o n t h a t the luminous f r o n t i s i s f a c t a r a d i a t i o n f r o n t has r e c e n t l y been d i s p u t e d by R. C. C r o s s on the b a s i s of some q u a l i t a t i v e s p e c t r o s c o p i c measurements , i n which the presence of Hydrogen and Carbon was d e t e c t e d on the luminous f r o n t . ( Ref. 16a ). I t w i l l be i n t e r e s t i n g t o e v a l u a t e the p r e s s u r e measurements when t h e s e new measurements have been c o n c l u d e d . -42-Fig 20 200-Time (microsec) Pressure Profile Behind the Radiation - Piezoprobe Measurements -Calculated by Strachan -43-VI CONCLUSIONS Pi e z o e l e c t r i c probes have been ca l i b r a t e d at high pressures by a new technique using plane detonations , and i t s l i n e a r i t y outside the ca l i b r a t e d region infered by measurements of imploding concentric detonations. The pressure p r o f i l e of these was measured and the re s u l t s agree with expected values . The piezoprobes have also given information about pressure gradients produced i n Oxygen by absorption of d i s s o c i a t i n g r a d i a t i o n . The experimental p r o f i l e s agree q u a l i t a t i v e l y with t h e o r e t i c a l predictions. -44-- BIBLIOGRAPHY M. P h i l l i p s , Ph. D. T h e s i s , Department of P h y s i c s The U n i v e r s i t y of B r i t i s h C olumbia , 1969 I . R. Jones , Aerospace C o r p o r a t i o n R e p o r t TDR-594 (1203-11) TR3 ( 1961 ) D. H. Edwards , L. D a v i e s , T. R. Lawrence The a p p l i c a t i o n of a p i e z o e l e c t r i c b a r gauge t o shock tube s t u d i e s . J o u r n a l of S c i e n t i f i c I n s t r u -ments , 1964 41_ (609-613) K. B l i c h l , Druckmessungen mit p i e z o e l e c t r i s c h e n Sonden an einem l i n e a r e n Z - p i n c h . Z e i t s c h r i f t f l l r N a t u r f o r s c h u n g 19a , 3^ , 1964 J . P. H u n i , R. A r d i l a , B. A h l b o r n C a l i b r a t i o n of P i e z o e l e c t r i c Probe . The Review of S c i e n t i f i c I n s t r u m e n t s ^1 , J u l y 1970 J . D. P e a r s o n , R. C. F e l l i n g e r Thermodynamic P r o p e r t i e s of Combustion Gases . The Iowa S t a t e U n i v e r s i t y P r e s s , 1956 W. C h e s t e r , The Q u a s i C y l i n d r i c a l Shock Tube P h i l o s o p h i c a l Magazine 4j5 , 1954 (1293-1301) R. F. C h i s n e l l . The motion of a shock wave i n a c h a n n e l w i t h a p p l i c a t i o n s t o c y l i n d r i c a l and s p h e r i c a l shock.waves . J o u r n a l o f F l u i d M e c h a n i c s , 2 , 1957 (236-293) G. B. Whitham . On the p r o p a g a t i o n of shock waves t h r o u g h r e g i o n of n o n - u n i f o r m a r e a . J o u r n a l of F l u i d M e c hanics 4 , 1958 (337-359) Lee J . H. and Lee B. H. K. , C y l i n d r i c a l i m p l o d i n g shock waves . The P h y s i c s o f F l u i d s Q , 12 (1965) J . P. H u n i , Ph. D. T h e s i s . Department of P h y s i c s The U n i v e r s i t y of B r i t i s h C olumbia ( To be p u b l i s h e d ) B. A h l b o r n , J . P. Huni . S t a b i l i t y and Space-time measurements of c o n c e n t r i c d e t o n a t i o n s W. Zuzak , Ph. D. T h e s i s , Department o f P h y s i c s The U n i v e r s i t y of B r i t i s h C o l u m b i a , 1963 -45-B. A h l b o r n and W. Zuzak . Steady r a d i a t i o n f r o n t s b e h i n d windows . Can. J . o f P h y s i c s , AT_ , 1969 ( 1709 ) P. Bogen , H. Conrads , D. R u s b l i l d t , Z. P h y s i k 186 , 240 (1965) J . S t r a c h a n , M. Sc. T h e s i s , Department of P h y s i c s The U n i v e r s i t y of B r i t i s h C o lumbia (1969) R. C. C r o s s . P r o p a g a t i o n of shock waves in d u c e d by a h i g h i n t e n s i t y l i g h t s o u r c e , Lab R e p o r t N° 7 Department of P h y s i c s , The U n i v e r s i t y of B r i t i s h C o l u m b i a (1970) I . R. Jones , B e r y l l i u m p r e s s u r e bar h a v i n g sub-m i c r o s e c o n d r i s e - t i m e . The Review of S c i e n t i f i c I n s t r u m e n t s , 37 , (1966) -46-APPENDIX " PROBE CALIBRATION WITH THE SHOCK TUBE To obtain the c a l i b r a t i o n curve at low pressures we used a shock tube designed by P.R. Smy . It i s schemat c = i c a l l y indicated i n F i g . A - l . J Electrodes 1 / Test gas 1 1 / Fig A - / Shock tube Diaphragm The d r i v e r section i s f i l l e d with Helium , which i s heated by the current produced by the discharge of the capacitor C . When the diaphragm breaks a shock front propagates into the test gas . The shock tube i s discussed i n d e t a i l by P h i l l i p s ( Ref. 1 ) Driver gas He Shock Argon DiaphragmProbe 7-HI W^Probe 2 Fig A-2 Set up for probe calibration F_ig. A-2 shows the set-up for the c a l i b r a t i o n . Two probes were located with th e i r measuring ends fl u s h with the walls -47-of the shock tube . In t h i s position the bar experiences a step jump in pressure due to the passing of the shock front . The signal from probe 1 , the triggering probe , was amplified by one channel of a Tektronix Type 1A1 Plug-in unit and then used to trigger time base B of a 545A Oscilloscope . The delayed trigger pulse was then used to trigger time base A which displayed the sig n a l from the test probe ( probe 2 in F i g . A-2 ) . The l i n e a r distance between the probes was 18.8 cm . The test probe, was located at a position downstream the tube i n which i t had been previously found that the shock strength increased l i n e a r l y with i n i t i a l f i l l i n g pressure , for a certain range of pressures. An oscillogram of the sig n a l from the probe i s shown in F i g . A-3 Fig A-3 Probe signal Jones ( Ref. 17 ) constructed a s i m i l a r piezoprobe . He used Beryllium bars of 0.3 cm diameter and PZT-5 . The signals of t h i s probe when placed at the end plate of a diaphragm shock tube are very si m i l a r to the ones we obtained here . He argues that the o s c i l l a t i o n s which occur afte r the i n i t i a l r i s e in the signal are due to r a d i a l -48-o s c i l l a t i o n s of the p i e z o e l e c t r i c d i s k . I t i s s u g g e s t e d t h a t the a m p l i t u d e of t h e s e o s c i l l a t i o n s depends on the pre s e n c e of a i r b u b b l e s i n the cement bond j o i n i n g the p i e z o e l e c t r i c element t o the B e r y l l i u m b a r s . I t may be o b s e r v e d t h a t our probes f o l l o w c l o s e l y the s t e p jump i n p r e s s u r e , w i t h the presence of o s c i l l a t i o n s w hich a r e e x p l a i n e d above . The response of the probe depends v e r y s t r o n g l y on the manner i n which the diaphragm b r e a k s . A c r e a s e i n the shape of an X was made i n them t o f a c i l -i t a t e b u r s t i n g . We found t h a t the s i g n a l s of the probes a p p r o x i m a t e d more c l o s e l y a s t e p when the diaphragm was t o r n i n t o 4 p e t a l s . When the diaphragm d i d n ' t break i n t h i s way , t h e r e were s p u r i o u s b l i p s superimposed t o the e x p e c t e d r e s p o n s e . The a m p l i t u d e of the s i g n a l was a l s o l o w e r i n t h e s e c a s e s , and the r i s e - t i m e c o n s i d e r a b l y l o n g e r . I t was assumed t h a t the d r i v e r gas had not p r o -duced i n t h e s e c a s e s a shock f r o n t , and they were not t a k e n i n acco u n t f o r the c a l i b r a t i o n graph . The p r e s s u r e of the Argon gas i n the t e s t s e c t i o n of the shock tube was v a r i e d from 1 t o 35 T o r r , and the H e l i u m p r e s s u r e i n the d r i v e r s e c t i o n was kept t h r o u g h o u t the c a l i b r a t i o n a t 100 T o r r . The shock speed V can be c a l c u l a t e d e a s i l y s knowing the d i s t a n c e between the probes and the d e l a y t i m e s - 4 9 — i n them . The speed of sound i n Argon a t room te m p e r a t u r e i s 321 m/sec so t h a t the Mach number i s M = V /321 . T h i s s r e s u l t t o g e t h e r w i t h the v a l u e s of the p r e s s u r e i n the Argon gas , p^ , p e r m i t s the c a l c u l a t i o n o f the p r e s s u r e b e h i n d the f r o n t , p 2 The r a t i o Pr>/p., i s g i v e n by ~ 1 £2 2rM 2 - ( y - 1 ) p i y + i T h i s i s t r u e f o r a shock wave p r o p a g a t i n g t h r o u g h a gas w i t h c o n s t a n t s p e c i f i c h e a t s . I t p r e d i c t s the b e h a v i o r of i n e r t monatomic gases e x a c t l y up t o t e m p e r a t u r e s o f the o r d e r o f 8000°K . Above t h i s t e m p e r a t u r e , the e f f e c t s of e l e c t r o n i c e x c i t a t i o n and i o n i z a t i o n b e g i n t o m o d i f y the p r e d i c t e d i d e a l t h e o r e t i c a l v a l u e s . The c o n d i t i o n s i n r e a l m o l e c u l a r gases d e v i a t e r a p i d l y above a few hun-d r e d degrees c e n t i g r a d e due t o the dependence of y on t e m p e r a t u r e . The v a l u e p was c a l c u l a t e d by n u m e r i c a l 2 s o l u t i o n ( Ref. 1 ) of the jump e q u a t i o n s t a k i n g i n a c c o u n t e x c i t a t i o n and i o n i z a t i o n i n the t e s t gas . The graph a m p l i t u d e of the s i g n a l v s . jump i n p r e s -s u r e g i v e s a l i n e a r r e l a t i o n s h i p . F o r p r e s s u r e s above 40 T o r r the a m p l i t u d e of the s i g n a l does not i n c r e a s e l i n e a r l y w i t h p r e s s u r e . T h i s i s not due t o s a t u r a t i o n of the p r o b e s , -50-as was demonstrated by c a l i b r a t i o n at higher pressures , but due to the s p e c i a l c h a r a c t e r i s t i c s of the shock tube. At these pressures the r a r e f a c t i o n wave catches up with the shock front and decreases the strength of the pressure jump. 

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