Detonation Properties of Ozone

Detonation Properties of Ozone S. A. HARPER, Radio Corp. of America, Lancaster, Pa.

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 10, 2017 | http://pubs.acs.org Publication Date: January 1, 1959 | doi: 10.1021/ba-1959-0021.ch005

W. E. GORDON, Arthur D. Little, Inc., Cambridge, Mass.

High concentrations of ozone can explode in a most violent a n d , usually, unexpected way. The initial ozone pressure affects detonation properties. A notable feature of the ozone system is the wide range of detonation properties in the detonatable region of composition, compared to the hydrogen -oxygen system.

T h e d e c o m p o s i t i o n of ozone h a s b e e n of g r e a t i n t e r e s t t o those c o n c e r n e d w i t h c o m b u s t i o n , because of t h e a p p a r e n t s i m p l i c i t y of t h e r e a c t i o n a n d t h e f a c t t h a t t h e r e is o n l y one p r o d u c t gas, o x y g e n . L e w i s a n d v o n E l b e {13) d e v e l o p e d a t h e o r y of flame p r o p a g a t i o n i n o z o n e - o x y g e n m i x t u r e s o n t h e basis of t h e i r b u r n i n g v e l o c i t y s t u d i e s . T h e y (12) d e r i v e d h i g h - t e m p e r a t u r e specific h e a t v a l u e s f o r o x y g e n f r o m their explosion data. Preparation

and

Analysis

of O z o n e - O x y g e n

Mixtures

C o n c e n t r a t e d ozone w a s p r e p a r e d b y a m e t h o d s i m i l a r t o t h a t of K a r r e r a n d W u l f (9). A s c h e m a t i c d i a g r a m of t h e a p p a r a t u s is s h o w n i n F i g u r e 1. A s t r e a m of o z o n i z e d o x y g e n f r o m a S i e m e n s - t y p e o z o n i z e r ( a b o u t 3 m o l e % ozone) w a s c o n d e n s e d i n t h e t r a p . T h e l o w e r p a r t of t h e t r a p w a s encased i n a c o p p e r s h e a t h t o reduce t e m p e r a t u r e g r a d i e n t s . A h e a t e r c o i l w a s w o u n d o n t h e s u r f a c e of t h e c o p p e r . T e m p e r a t u r e at t h e base of t h e t r a p w a s i n d i c a t e d b y a c o p p e r - c o n s t a n t a n c o u p l e i n s e r t e d in a t h e r m o c o u p l e w e l l . T h e t h e r m o c o u p l e w a s a t t a c h e d to a r e c o r d i n g p o t e n t i o m e t e r . W h e n a sufficient q u a n t i t y of t h e l i q u i d m i x t u r e h a d c o l l e c t e d in A, t h e o z o n i z e r s t r e a m w a s s h u t off. T h e ozone c o n t e n t of t h e l i q u i d w a s t h e n e n r i c h e d by e v a p o r a t i n g t h e o x y g e n , by o p e n i n g ( s l i g h t l y ) t h e v a l v e t o t h e v a c u u m p u m p . ( T h e p u m p was p r o t e c t e d f r o m ozone by a s o d a - l i m e tube.) W h e n t h e o x y g e n h a d been r e m o v e d , t h e p u m p w a s s h u t off, a n d t h e s t o p c o c k to t h e e v a c u a t e d storage t a n k , D, w a s o p e n e d . T h e h e a t e r w a s t h e n t u r n e d on a n d t h e t e m p e r a t u r e r a i s e d s l o w l y , c a u s i n g t h e ozone to b o i l a n d collect in D. ( T h e l i q u i d - a i r l e v e l in t h e D e w a r w a s b e l o w t h e b o t t o m of t h e t r a p d u r i n g t h i s o p e r a t i o n . A nice c o n t r o l of t e m p e r a t u r e w a s possible.) The p r e s s u r e w a s f o l l o w e d on a stainless steel B o u r d o n gage. A c c u r a t e p r e s s u r e m e a s u r e m e n t s were m a d e on a m e r c u r y m a n o m e t e r p r o t e c t e d by a s u l f u r i c a c i d buffer manometer. F o r a n a l y s i s , t h e ozone m i x t u r e w a s a d m i t t e d i n t o t h e e v a c u a t e d a n a l y s i s b u l b , Β ( F i g u r e 1 ) , to a p r e s s u r e of 10 to 50 m m . of m e r c u r y . T h e gas w a s d i l u t e d w i t h o x y g e n to a p r e s s u r e of 1 a t m . , a n d b u b b l e d t h r o u g h a p o t a s s i u m i o d i d e s o l u t i o n in J. T h e l i b e r a t e d i o d i n e w a s t i t r a t e d w i t h s o d i u m t h i o s u l f a t e . F r e s h l y p r e p a r e d ozone w a s f o u n d to be 9 5 % p u r e . (Oxygen made u p the r e m a i n d e r of the gas.) A f t e r s t a n d i n g f o r 1 d a y in t h e storage flask, t h e c o n c e n t r a t i o n of ozone d r o p p e d to a b o u t 8 0 % , a n d a f t e r a b o u t 1 week to 5 0 % . 28

OZONE CHEMISTRY AND TECHNOLOGY Advances in Chemistry; American Chemical Society: Washington, DC, 1959.


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G O R D O N - D E T O N A T I O N PROPERTIES

S O L U T I O N ^

Figure 1.

Apparatus for preparation of gaseous mixtures of ozone and oxygen A. B. C. D.

Ozone condenser Ozone analysis bulb Mixing flask Ozone gas storage flask

O z o n e - o x y g e n m i x t u r e s of t h e d e s i r e d c o n c e n t r a t i o n w e r e m a d e u p i n t h e m i x i n g flask, C , a n d a n a l y z e d j u s t b e f o r e use. T h e m i x t u r e w a s finally t r a n s f e r r e d f r o m t h e m i x i n g flask t o t h e d e t o n a t i o n t u b e . Detonation

Apparatus

Detonation T u b e . T h e d e t o n a t i o n t u b e a s s e m b l y is s h o w n i n F i g u r e 2. T h e d e t o n a t i o n t u b e p r o p e r w a s of stainless steel, 2.54 c m . i n i n s i d e d i a m e t e r a n d 4.9 m e t e r s l o n g . F o u r p i e z o e l e c t r i c gages were s p a c e d a l o n g t h e t u b e a t i n t e r v a l s . A t t a c h e d b y a s t a n d a r d p i p e u n i o n t o t h e f r o n t of t h e d e t o n a t i o n t u b e w a s a n " i n i t i a t o r " s e c t i o n of e q u a l d i a m e t e r a n d 1.9 m e t e r s l o n g . F o r e x p e r i m e n t s w i t h r i c h ozone m i x t u r e s , w h i c h w o u l d i g n i t e b y a s p a r k a n d d e v e l o p a d e t o n a t i o n w a v e , t h e whole tube, i n c l u d i n g the i n i t i a t o r section, was filled w i t h the ozone-oxygen m i x t u r e . F o r experiments w i t h more dilute m i x t u r e s , where detonation w o u l d not b u i l d u p , i t was n e c e s s a r y t o s t a r t t h e d e t o n a t i o n w i t h a s t r o n g s h o c k w a v e . I n order to produce the shock, a cellophane d i a p h r a g m was clamped i n the pipe u n i o n , a n d the initiator section w a s filled w i t h a s t o i c h i o m e t r i c m i x t u r e of h y d r o g e n a n d o x y g e n ( k n a l l g a s ) . T h e knallgas detonated w h e n i t was ignited b y a spark, p r o d u c i n g a powerful shock w a v e . D e t o n a t i o n s t a r t e d i m m e d i a t e l y w h e n t h e s h o c k w a v e a d v a n c e d i n t o t h e ozone mixture. SPARK

DIAPHRAGM

GAUGES Figure 2.

Detonation tube


A D V A N C E S IN CHEMISTRY SERIES

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Piezoelectric Gages. T h e gage c o n s t r u c t i o n ( F i g u r e 3 ) w a s s i m i l a r t o t h a t u s e d previously b y Gordon (7). T h e c r y s t a l element consisted of a s a n d w i c h of four t o u r m a l i n e disks m o u n t e d o n a steel s h a n k . ( C r y s t a l e l e m e n t s of t h i s t y p e a r e a v a i l a b l e f r o m C r y s t a l R e s e a r c h , Inc., 40 C o n c o r d L a n e , Cambridge, Mass.) T h i s element, supported b y a n axial shaft, was held i n a 6-inch length of ^ - i n c h diameter brass tube (standard % - i n c h p i p e ) . T h e u p p e r edge o f t h e e l e m e n t w a s a b o u t 1 m m . b e l o w t h e r i m o f t h e t u b e . T h e t u b e w a s filled u n d e r v a c u u m w i t h a w a r m m i x t u r e of m e d i c i n a l m i n e r a l o i l a n d p e t r o l e u m j e l l y , w h i c h set i n t o a soft g e l o n c o o l i n g . T h e gage u n i t w a s f a s t e n e d b y a t h r e a d e d j o i n t i n t h e w a l l of t h e d e t o n a t i o n t u b e , w i t h t h e r i m of t h e gage t u b e flush w i t h t h e i n s i d e o f t h e d e t o n a t i o n t u b e .

CONDUCTOR. Figure 3.

Piezoelectric g a g e

Calibration. C a l i b r a t i o n b y three independent methods gave good agreement. T h e first c a l i b r a t i o n w a s m a d e b y t h e m a n u f a c t u r e r o f t h e c r y s t a l elements, b y measuring t h e electric charge p r o d u c e d w h e n t h e pressure o n t h e element w a s suddenly r e d u c e d . A s i m i l a r " s t a t i c " c a l i b r a t i o n w a s m a d e o n t h e c o m p l e t e gage u n i t s . T h e t h i r d m e t h o d of c a l i b r a t i o n w a s m o r e s i g n i f i c a n t f o r t h e d e t o n a t i o n w a v e m e a s u r e m e n t s . T h e gages w e r e m o u n t e d i n p o s i t i o n i n t h e d e t o n a t i o n t u b e . T h e i n i t i a t o r s e c t i o n of t h e t u b e w a s filled w i t h k n a l l g a s a n d t h e gage s e c t i o n w i t h a i r . U p o n d e t o n a t i o n of t h e k n a l l g a s , a s h o c k w a v e w a s p r o d u c e d i n t h e gage s e c t i o n . T h e s h o c k w a v e h a d a c o n t o u r s i m i l a r t o t h a t o f t h e ozone d e t o n a t i o n w a v e . Therefore, t h e s a m e d y n a m i c c h a r a c t e r i s t i c s of t h e gages were b r o u g h t i n t o p l a y b y t h e s h o c k w a v e as b y t h e d e t o n a t i o n w a v e . F o r t h e c a l i b r a t i o n , t h e pressure i n t h e shock wave was c o m p u t e d f r o m t h e veloc i t y t h r o u g h t h e H u g o n i o t r e l a t i o n . T h e v e l o c i t y ( a n d p r e s s u r e ) of t h e s h o c k w a v e p r o d u c e d i n t h i s w a y d e c a y s r a p i d l y as t h e w a v e progresses d o w n t h e t u b e . T h e


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PROPERTIES


i n s t a n t a n e o u s v e l o c i t y o f t h e w a v e a t e a c h gage w a s c o m p u t e d b y a n e m p i r i c a l f o r m u l a f r o m t h e a v e r a g e v e l o c i t i e s m e a s u r e d i n t h e t h r e e i n t e r v a l s b e t w e e n t h e gage (8). Recording System. A s c h e m a t i c d i a g r a m of t h e r e c o r d i n g s y s t e m i s s h o w n i n F i g u r e 4. T h e a m p l i f i e d s i g n a l s f r o m t h e c r y s t a l s — t h e f o u r gages w e r e c o n n e c t e d i n p a r a l l e l — w e r e i m p r e s s e d o n t h e h o r i z o n t a l - d e f l e c t i o n p l a t e s of t h e c a t h o d e - r a y t u b e . T h e screen of t h e t u b e w a s p h o t o g r a p h e d w i t h a r o t a t i n g - d r u m c a m e r a . T h e d r u m r a n a t a u n i f o r m speed a n d , t h e r e f o r e , t h e t i m e base w a s l i n e a r . T i m e c a l i b r a t i o n w a s o b t a i n e d b y m e a n s o f a flashing n e o n " c r a t e r " t u b e ( S y l v a n i a , T y p e R 1 1 3 0 B ) w h i c h w a s a c t i v a t e d b y a 1000-cycle t u n i n g - f o r k o s c i l l a t o r . T h e c r a t e r t u b e w a s i n t h e

CAMERA

/

/

Figure 4.

\

\

Recording system

field of t h e c a m e r a a n d w a s p h o t o g r a p h e d c a t h o d e - r a y screen.

simultaneously w i t h

the trace

on the

Oscillograph Records. T h e f o u r p i e z o e l e c t r i c gages w e r e u s e d t o o b t a i n t h e v e l o c i t y as w e l l as t h e p r e s s u r e of t h e d e t o n a t i o n w a v e . B y reading from the record t h e t i m e of a r r i v a l of t h e d e t o n a t i o n f r o n t a t successive gages, t h e a v e r a g e speed of t h e f r o n t i n t h e i n t e r v a l b e t w e e n gages w a s o b t a i n e d . F i g u r e 5 shows t y p i c a l r e c o r d s f o r t h r e e different c o n c e n t r a t i o n s of ozone. T h e m i d d l e r e c o r d ( f o r 1 7 . 3 % ozone) i s t y p i c a l of a n o n s p i n n i n g d e t o n a t i o n . T h e v i b r a tions i n t h e other t w o records are associated w i t h spin. T o measure pressure, a n enlarged t r a c i n g of t h e record was m a d e a n d a s m o o t h median line d r a w n t h r o u g h t h e vibrations. T h e intersection of this median line w i t h t h e rise l i n e ( n o t v i s i b l e i n F i g u r e 5 because of l o w i n t e n s i t y ) w a s t a k e n as t h e d e t o n a t i o n pressure.




32

Figure

5.

Oscillograph

records for various mixtures

ozone-oxygen

A. 10.5% ozone B. 1 7 . 3 % ozone C. 7 7 % ozone

Calculated Detonation Properties T h e c a l c u l a t e d C h a p m a n - J o u g e t d e t o n a t i o n p r o p e r t i e s f o r ozone a r e g i v e n i n T a b l e I . T h e m e t h o d s of c a l c u l a t i o n a r e d e s c r i b e d i n s e v e r a l p l a c e s — f o r e x a m p l e , b y L e w i s a n d v o n E l b e (11). T a b l e I.

Ozone, Mole % 100 80.0 80.0 75.0 70.0 64.0 45.4 36.8 25.0 17.3 10.5 9.2

Theoretical Detonation Properties of O z o n e - O x y g e n Mixtures Initial Pressure, Atm. 0.100 0.147 0.100 0.132 0.132 0.175 0.172 0.138

Detonation Temp. ° K . 4018 3555 3545 3426 3291 3123 2533 2218 1733 1373 1019 945

Product Dissociation, % 5.45 3.29 3.54 2.90 2.35 1.71 0.38 0.11

Detonation Pressure Ratio 29.48 25.75 25.46 24.54 23.52 22.24 17.50 14.88 10.98 8.26 5.77 5.28

Detonation Velocity, M./Sec. 1836 1781 1771 1755 1736 1710 1577 1481 1302 1144 964 921

T h e i n i t i a l p r e s s u r e of t h e ozone m i x t u r e affects t h e d e t o n a t i o n p r o p e r t i e s t h r o u g h t h e i n f l u e n c e o f p r e s s u r e o n t h e degree of d i s s o c i a t i o n of t h e p r o d u c t g a s e s — i n t h i s case j u s t o x y g e n . T h e r e f o r e i n i t i a l p r e s s u r e v a l u e s w e r e c h o s e n f o r c a l c u l a t i o n s i n T a b l e I t o c o r r e s p o n d t o c o n d i t i o n s i n t h e e x p e r i m e n t s . F o r l o w ozone c o n c e n t r a t i o n s ,



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d i s s o c i a t i o n is n e g l i g i b l e (because of t h e l o w d e t o n a t i o n t e m p e r a t u r e ) , a n d , t h e r e f o r e , t h e d e t o n a t i o n p r o p e r t i e s are i n d e p e n d e n t of p r e s s u r e . A n o t a b l e f e a t u r e of t h e ozone s y s t e m is t h e w i d e range of t h e d e t o n a t i o n p r o p erties i n t h e d e t o n a t a b l e r e g i o n of c o m p o s i t i o n , as c o m p a r e d , f o r e x a m p l e , w i t h t h e h y d r o g e n - o x y g e n s y s t e m . F o r t h i s r e a s o n , t h e ozone s y s t e m p r o v i d e s a g o o d test of t h e Chapman-Jouget theory. Detonation Velocity. T h e d e t o n a t i o n w a v e i n ozone m i x t u r e s , i n c o m m o n w i t h a l l s y s t e m s , reaches a s t e a d y s t a t e o n l y a f t e r t r a v e l i n g s o m e d i s t a n c e i n t h e t u b e , i r r e s p e c t i v e of t h e m e a n s of i n i t i a t i o n , w h e t h e r b y s p a r k o r s h o c k w a v e . I n t h e b e g i n n i n g , t h e w a v e is u s u a l l y " o v e r i n i t i a t e d " (14), h a v i n g b o t h a h i g h e r p r e s s u r e a n d v e l o c i t y t h a n i n the steady state. F o r the shock-wave initiated m i x t u r e s (below 6 0 % ozone), t h e degree of o v e r i n i t i a t i o n c o u l d be r e d u c e d b y p u t t i n g a buffer zone of a i r a h e a d of the knallgas m i x t u r e i n the i n i t i a t o r section. T h e shock wave was t h e r e b y attenuated before i t r e a c h e d t h e ozone m i x t u r e . W h e n t h e a v e r a g e v e l o c i t i e s i n t h e l a s t t w o gage i n t e r v a l s a g r e e d w i t h i n 1 % o r b e t t e r , i t w a s a s s u m e d t h a t a s t e a d y s t a t e h a d been reached.

tool Ο

I

Figure 6.

I ι 1 1 » 1 I ΙΟ 40 60 ÔO O Z O N E C O N C E N T R A T I O N (MOLE P E R C E N T )

I

Detonation velocity of ozone-oxygen mixtures


I I0O


34


The velocity results are given i n T a b l e I I . T h e experimental values (generally s l i g h t l y l o w e r t h a n t h e o r e t i c a l ) a r e also p l o t t e d i n F i g u r e 6 f o r c o m p a r i s o n w i t h t h e t h e o r e t i c a l c u r v e . S u c h a r e s u l t i s also f o u n d f o r h y d r o g e n - o x y g e n m i x t u r e s (15), a n d i s e x p l a i n e d b y t w o f a c t o r s , h e a t losses a n d s p i n effects. B o t h effects a r e greatest i n dilute m i x t u r e s a n d a t l o w pressures. Detonation Pressures. T h e i n t e r p r e t a t i o n of t h e p i e z o e l e c t r i c gage r e c o r d s w a s not u n a m b i g u o u s . I n t h e first place, m a n y of t h e records showed large v i b r a t i o n s , e s p e c i a l l y f o r t h e v e r y l o w ozone c o n c e n t r a t i o n s . T h e s e v i b r a t i o n s a r e k n o w n t o be a s s o c i a t e d w i t h a s p i n n i n g d e t o n a t i o n w a v e . S e c o n d l y , t h e r e c o r d s f o r t h e 17 a n d 2 5 % ozone m i x t u r e s h a d t h e so-called v o n N e u m a n " s p i k e " at t h e wave front. (The sharp pressure p e a k s a r e b a r e l y d i s c e r n i b l e i n t h e r e c o r d f o r t h e d i s c e r n i b l e 1 7 . 3 % m i x t u r e i n F i g u r e 5, b u t t h e y w e r e e v i d e n t i n t h e o r i g i n a l n e g a t i v e . ) A consistent procedure was followed i n measuring t h e records: A m e d i a n line was d r a w n through the oscillograph trace, starting at a point well beyond the wave front, a n d e x t e n d i n g b a c k u p t o w a r d t h e p e a k t o t h e p o i n t w h e r e i t crossed t h e rise l i n e . I n t h i s p r o c e d u r e , t h e c o n t o u r o f t h e e x p a n s i o n w a v e is e x t r a p o l a t e d b a c k t o t h e s h o c k front. T h e value obtained i n this m a n n e r should be closely comparable t o t h e C h a p man-Jouget pressure. B e c a u s e of o v e r i n i t i a t i o n , t h e p r e s s u r e , l i k e t h e v e l o c i t y , u s u a l l y w a s h i g h o n t h e first gage a n d d r o p p e d off a n d l e v e l e d o u t o n gages 3 a n d 4. T h e p r e s s u r e v a l u e s f r o m these l a s t t w o gages a g r e e d w i t h i n e x p e r i m e n t a l e r r o r , t h e a v e r a g e difference between t h e m being about 7 % . I n T a b l e I I I are listed t h e average pressure values

Table III.

Ozone, Mole % 77 77 73 64 64 45.4 36.8 25.0 25.0 17.3 17.3 10.5 10.5 9.2

Initial Pressure, Mm. Hg 110 112 99 133 109 130 105 275 181 399 263 486 321 497

Experimental Detonation Pressures —

Pressure Ratio Obsd. 23.5 22.6 21.3 21.0 20.2 16.2 13.6 10.4 10.2 7.8 8.2 4.2 4.7 4.5

Calcd. 25.0 25.0 24.1 22.2 22.2 17.5 14.9 11.0 11.0 8.3 8.3 5.8 5.8 5.3

Deviation, % -6.0 -9.6 -11.5 -5.4 -9.0 -7.4 -8.7 -5.4 -7.3 -6.0 -0.1 -27.5 -19.0 -15.0

f r o m gages 3 a n d 4 f o r s e v e r a l o z o n e - o x y g e n m i x t u r e s . T h e s e p o i n t s a r e also p l o t t e d i n F i g u r e 7 for comparison w i t h the theoretical curve. T h e e x p e r i m e n t a l pressures a r e g e n e r a l l y s e v e r a l p e r c e n t l o w e r t h a n t h e t h e o r e t i c a l v a l u e s . H o w e v e r , t h e v a r i a t i o n o f p r e s s u r e w i t h ozone c o n c e n t r a t i o n i s c l o s e l y i n a c c o r d w i t h t h e o r y . S i n c e e n e r g y losses w o u l d b e e x p e c t e d t o l o w e r t h e p r e s s u r e b y a p e r c e n t a g e t w o t o t h r e e t i m e s as g r e a t as t h a t f o r t h e v e l o c i t y , p r e s s u r e a n d v e l o c i t y results are m u t u a l l y consistent.

Spin I n e x p e r i m e n t s p r e c e d i n g those o n ozone d e t o n a t i o n s , t h e effect o f s e n d i n g s h o c k w a v e s f r o m a s h o c k t u b e i n t o m i x t u r e s of ozone, n i t r o g e n p e n t o x i d e , a n d o x y g e n w a s i n v e s t i g a t e d . T h e p r e s s u r e r e c o r d s f r o m these e x p e r i m e n t s h a d o s c i l l a t i o n s of v e r y high amplitude, h a r d to explain. O n observing i n a darkened room the propagation o f a s h o c k w a v e i n t o a glass t u b e filled w i t h t h e m i x t u r e , i t w a s n o t i c e d t h a t t h e p i n k



HARPER A N D G O R D O N - D E T O N A T I O N PROPERTIES

Figure 8.

35

Spinning detonation in a mixture of ozone, nitrogen pentoxide, a n d oxygen

flame h a d a " b a n d e d " a p p e a r a n c e . F i g u r e 8 w a s t a k e n w i t h a n o p e n - s h u t t e r c a m e r a . F i g u r e 9 is t h e p r e s s u r e r e c o r d of t h e s h o c k w a v e f r o m a s i m i l a r e x p e r i m e n t . A s p i r a l i n g zone of l u m i n e s c e n c e ( F i g u r e 8 ) w a s first o b s e r v e d i n d e t o n a t i o n s b y C a m p b e l l a n d W o o d h e a d (4), a n d r e f e r r e d t o b y t h e m as " s p i n . " M a n y p h o t o g r a p h i c

Figure 9.

Pressure record of spinning detonation in Figure 8




36

i n v e s t i g a t i o n s of t h e p h e n o m e n o n (1-3), h a v e since s h o w n t h a t a h i g h l y l u m i n o u s zone, t r a v e l i n g w i t h t h e w a v e f r o n t , describes a h e l i c a l p a t h n e a r t h e s u r f a c e of t h e t u b e . T h e p i t c h of t h e h e l i x w a s u s u a l l y a b o u t t h r e e t i m e s t h e t u b e d i a m e t e r . C l e a r l y , t h e p r e s s u r e o s c i l l a t i o n s i n F i g u r e 9 a r e associated w i t h t h e s p i n , f o r , w h e n t h e f r e q u e n c y of t h e o s c i l l a t i o n s i s d i v i d e d i n t o t h e s h o c k w a v e v e l o c i t y , t h e " w a v e l e n g t h " so o b t a i n e d is j u s t e q u a l t o t h e p i t c h of t h e h e l i x as m e a s u r e d f r o m t h e p h o t o g r a p h ( F i g u r e 8 ) . S u b s e q u e n t l y , v i b r a t i o n s of t h i s t y p e h a v e been o b s e r v e d i n p r e s sure r e c o r d s f r o m m a n y d e t o n a t i o n s (14)· A t h e o r y f o r s p i n n i n g d e t o n a t i o n h a s been p u t f o r t h b y F a y (6). H e shows t h a t s p i n is a s e l f - e x c i t e d t r a n s v e r s e v i b r a t o r y m o t i o n i n t h e b u r n e d gas, a k i n t o a s t - i n d i n g s o u n d w a v e , b u t w i t h h e l i c a l s y m m e t r y . T h e possible m o d e s of v i b r a t i o n c a n be c a l c u l a t e d f r o m t h e p r o p e r t i e s of t h e gas. T h e f u n d a m e n t a l m o d e a l w a y s h a s a p i t c h equal t o about three tube diameters; higher modes have a n apparent p i t c h smaller t h a n t h i s . S e v e r a l different m o d e s h a v e been o b s e r v e d a n d g o o d c o r r e l a t i o n s a r e f o u n d with F a y ' s theory. T h e o s c i l l o g r a p h r e c o r d s i n F i g u r e 5 i l l u s t r a t e t h e s p i n effects f o u n d i n ozone d e t o n a t i o n s . F o r h i g h ozone c o n c e n t r a t i o n s , t h e r e w a s a h i g h - f r e q u e n c y ( h i g h m o d a l n u m b e r ) , relatively l o w - a m p l i t u d e s p i n ; i n t h e m i d d l e concentration range, there was no s p i n ; a n d a t lower concentrations, a f u n d a m e n t a l spin mode developed, w h i c h i n creased i n a m p l i t u d e as t h e c o n c e n t r a t i o n w a s d r o p p e d . T h e b e h a v i o r of h y d r o g e n m i x t u r e s i s v e r y s i m i l a r t o t h i s (15). M a n y i n t e r e s t i n g questions r e m a i n t o b e a n s w e r e d a b o u t s p i n n i n g d e t o n a t i o n . W h y does s p i n a l w a y s a p p e a r a t l o w c o n c e n t r a t i o n s n e a r t h e d e t o n a t i o n l i m i t ? What d e t e r m i n e s t h e s t a b l e m o d e a n d a m p l i t u d e of t h e s p i n ? W h a t effect, i f a n y , does s p i n h a v e o n t h e s t a b i l i t y of d e t o n a t i o n s ?

Other Features of O z o n e

Detonations

A c c o r d i n g t o t h e t h e o r y a d v a n c e d i n d e p e n d e n t l y b y v o n N e u m a n (16), D o r i n g (5), a n d Z e l d o v i c h (17), t h e d e t o n a t i o n f r o n t is s i m p l y a s h o c k w a v e i n t h e as y e t u n r e a c t e d gas. T h e r e a c t i o n is s t a r t e d b y t h e s u d d e n increase of t e m p e r a t u r e a n d p r e s s u r e a s s o c i a t e d w i t h t h e s h o c k f r o n t , a n d proceeds i n t h e zone w h i c h f o l l o w s i m m e d i a t e l y b e h i n d i t . A s t h e gas reacts, t h e p r e s s u r e d r o p s . A t t h e s o - c a l l e d " C h a p m a n - J o u g e t p l a n e " w h e r e t h e r e a c t i o n is c o m p l e t e , t h e p r e s s u r e h a s d r o p p e d t o a b o u t one h a l f t h e v a l u e a t t h e s h o c k f r o n t . B e y o n d t h i s p o i n t , t h e p r e s s u r e decreased m o r e s l o w l y i n t h e n o r m a l R i e m a n n e x p a n s i o n w a v e (11). U n t i l recently, there has been little experimental evidence to s u p p o r t t h e v o n N e u m a n t h e o r y . H o w e v e r , K i s t i a k o w s k y a n d K y d d (10) h a v e n o w d e t e c t e d a n a r r o w dense r e g i o n a t t h e w a v e f r o n t i n c e r t a i n d e t o n a t i o n s b y x - r a y flash p h o t o g r a p h y , w h i c h a p p e a r s t o b e t h e v o n N e u m a n s p i k e ( h i g h - p r e s s u r e r e a c t i o n zone i n f r o n t of the C h a p m a n - J o u g e t p l a n e ) . T h e pressure records for stoichiometric h y d r o g e n o x y g e n m i x t u r e s d o n o t r e v e a l t h i s h i g h p r e s s u r e r e g i o n (7), b u t a f a i n t h i g h p e a k w a s o b s e r v e d (8) i n c e r t a i n d i l u t e h y d r o g e n m i x t u r e s . r

T h e v o n N e u m a n s p i k e w a s c l e a r l y p r e s e n t i n t h e p r e s s u r e records of 17 a n d 2 5 % ozone m i x t u r e s . T h e v a l u e a t t h e p e a k , w h i c h a c c o r d i n g t o t h e o r y s h o u l d b e a b o u t t w i c e as h i g h as t h e C h a p m a n - J o u g e t p r e s s u r e , w a s o n l y a b o u t 2 5 % h i g h e r t h a n t h e l a t t e r . H o w e v e r , because of t h e p h y s i c a l size of t h e gage a n d t h e l i m i t e d f r e q u e n c y response of t h e a m p l i f i e r s , i t is n o t t o b e e x p e c t e d t h a t a v e r y n a r r o w h i g h - p r e s s u r e r e g i o n w o u l d b e f a i t h f u l l y r e c o r d e d . N e i t h e r t h e r i c h e r n o r t h e w e a k e r ozone m i x t u r e s showed the spike phenomenon. T h e r e a c t i o n zone m a y b e t o o n a r r o w t o b e o b s e r v e d i n t h e richer m i x t u r e s . O n t h e other h a n d , t h e spike m i g h t be obscured i n t h e weak m i x t u r e s b y t h e s p i n effects. A l t e r n a t i v e l y , spinning detonation actually is perhaps a different m o d e of p r o p a g a t i o n f r o m t h e v o n N e u m a n m e c h a n i s m , a n d b o t h i n r i c h a n d weak mixtures where s p i n is present, there is no v o n N e u m a n spike. A n o t h e r f e a t u r e of i n t e r e s t is t h e l o w v a l u e o f t h e c o n c e n t r a t i o n l i m i t f o r d e t o n a -


HARPER A N D


37

t i o n , a b o u t 9 % ozone. T h e e n e r g y of t h i s m i x t u r e is m u c h l o w e r t h a n t h a t of h y d r o g e n - o x y g e n m i x t u r e s a t t h e l i m i t (15). T h e calculated temperature at the shock front ( v o n N e u m a n t h e o r y ) f o r 9 % ozone is o n l y 670° K . T h e c o r r e s p o n d i n g t e m p e r a t u r e i n l i m i t h y d r o g e n m i x t u r e s is a b o u t 1100° K . T h e s e f a c t s m a y b e e x p r e s s e d i n a n o t h e r w a y b y s a y i n g t h a t ozone is m u c h m o r e s e n s i t i v e t o w a r d d e t o n a t i o n t h a n h y d r o g e n oxygen mixtures.


Literature (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17)

Cited

Bone, W. Α., Fraser, R. P., Phil. Trans. Roy. Soc. A 230, 363 (1932). Bone, W. Α., Fraser, R. P., Wheeler, Ibid., A 235, 29 (1935). Campbell, Colin, Finch, A. C., J. Chem. Soc. (London) 1928, 2094. Campbell, Colin, Woodhead, D. W., Ibid., 1926, 192, 3010; 1927, 1572. Doring, Ann. Physik 43, 421 (1943). F a y , J. Α., J. Chem. Phys. 20, 942 (1952). Gordon, J., " T h i r d Symposium on Combustion, Flame and Explosion Phenomena," p. 579, Williams & Wilkins, Baltimore, 1949. Gordon, J., unpublished work. Karrer, S., Wulf, O. R., J. Am. Chem. Soc. 44, 2391 (1922). Kistiakowsky, G. B., K y d d , P. H., J. Chem. Phys. 22, 1940 (1954). Lewis, B., von Elbe, G., "Combustion, Flames and Explosions of Gases," Academic Press, New York, 1951 Lewis, B., von Elbe, G., J. Am. Chem. Soc. 55, 511 (1933) ; 57, 1399 (1935). Lewis, B., von Elbe, G., J. Chem. Phys. 2, 283 (1934). Mooradian, A. J., Gordon, W. E., Ibid., 19, 1166 (1951). Mooradian, A. J., Gordon, W. E., unpublished work. von Neuman, J., OSRD Rept. 549 (1942): Ballistic Research Laboratory File N o . X-122. Zeldovich, V. B., J. Exptl. Theoret. Phys. (U.S.S.R.) 10, 542 (1940).

RECEIVED for review March 27, 1957. Accepted June 19, 1957. Work supported by ONR under contract N7 onr-292, Task Order I. Part of the work for the dissertation submitted by S. A. Harper in partial fulfilment of the requirements for the degree of doctor of philosophy at the University of Missouri.


Detonation Properties of Ozone

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