o 6 Flows i n Argon

In document Nonequilibrium effects in shock tunnels (Page 57-89)

References 97 and 99 consider the reflected shock-boundary layer

3.4 o 6 Flows i n Argon

As a f i r s t a p p ro x im a tio n and t o fin d lim i t in g v a lu e s , i t was

«

assumed t h a t r a d i a t i o n l o s s e s i n argon co u ld be n e g le c te d ( s e e s e c t i o n 3»3«1)<> N ozzle r e s e r v o i r c o n d itio n s were c a l c u l a t e d u sin g th e method d e s c r ib e d i n

s e c tio n 2 .2 and n o z z le ex p an sio n s were c a lc u la te d w ith th e assum ption t h a t th e gas was i n therm odynam ic eq uilibrium «, A ty p ic a l p l o t o f s p e c ie s

c o n c e n tr a tio n s i n a n o z z le i s g iv e n i n f ig u r e 21,

Flows i n a rg o n d i f f e r from flo w s in th e o th e r a tm o sp h eric g a se s (oxygen, n itr o g e n and carbon d io x id e ) i n two a s p e c ts . F i r s t l y , b e in g monatom ic, argon l o s e s no en ergy t o d i s s o c i a t i o n and i s g e n e r a lly much

h o t t e r ( f i g u r e 13) and has h ig h e r l e v e l s o f io n is a tio n th a n th e o th e r g a s e s . F o r exam ple, i n th e n o z z le r e s e r v o i r , th e c a lc u la tio n s i n d i c a t e t h a t a

s i g n i f i c a n t q u a n tiy o f energy i s ab so rb ed by second i o n i z a t i o n o f th e argon atom ( f i g u r e 17)» S eco n d ly , th e v e ry r a p id reco m b in atio n r e a c tio n s

(ap p ro x im ated h e re by th e a ssu m p tio n of eq u ilib riu m ) m a in ta in th e high te m p e ra tu re s and i o n i z a t i o n l e v e l s i n th e no zzle expansion by r e l e a s i n g th e fo rm a tio n en erg y o f th e i o n s . T his p ro cess i s l im it e d by th e number o f io n s i n th e r e s e r v o i r , and when reco m b in atio n i s c o m p le te, th e te m p e ra tu re d ro p s r a p i d l y as th e ex p an sio n c o n tin u e s w ith th e argon b eh av in g as a

monatomic p e r f e c t gas«

E x p e rim en ta l t e s t s w ith argon t e s t gas i n d ic a te d t h a t h is s im p le ' d e s c r i p t i o n i s in a d e q u a te .

The m agnetohydrodynam ic v e l o c i t y measurement te c h n iq u e o u tp u t ( f i g u r e

64

) gave a p o s i t i v e ( o r n e g a ti v e , depending on th e m ag n etic f i e l d d i r e c t i o n ) v o lta g e d u r in g th e f i r s t

70

m icro sec a f t e r shock r e f l e c t i o n o n ly , and th e n dropped to z e ro i n a m anner e x a c tly s i m i l a r to t h a t o f a i r a f t e r th e o n s e t o f h eliu m d r i v e r gas c o n ta m in a tio n . The f i r s t 80 m ic ro se c i s shown i n s e c tio n 3 . 4«3 to h e a p p ro x im a te ly th e d u r a tio n o f th e c o n t a c t s u r f a c e i n t e r a c t i o n s . In t h i s c a s e , th e 70 m icro sec may he c o n s id e re d as th e tim e f o r th e r e f l e c t e d shock to re a c h th e c o n ta c t s u r f a c e and f o r an e x p a n sio n wave to r e t u r n to th e end w a ll ,

The s p a rk t r a c e r te c h n iq u e showed hig h v e l o c i t i e s to

250

m ic ro s e c , which i n d i c a t e d t h a t th e d e c r e a s e i n th e m agnetohydrodynam ic p ro b e o u tp u t

«

wan n o t due to a d e c r e a s e i n v e l o c i t y , h u t to a d e c re a s e i n th e c o n d u c tiv ity o f th e gaSo

The p i t o t p ro b e gave r e s u l t s s i m i l a r to th e MED p ro b e , e x c e p t t h a t th e d u r a tio n o f th e p e rio d b e f o r e th e d e c re a se was s h o r t e r

(50

in ic ro s e c , t y p i c a l l y ) . Also th e o u tp u t in c r e a s e d a f t e r 150 m ic ro sec and th e n d e c re a se d s la w ly . The l e v e l a f t e r 150 m icrosec was com parable t o t h a t o f p u re d r i v e r gas f lo w 0

S c h lie r e n p h o to g rap h y o f th e shock wave on a tw o -d im en sio n a l wedge o f 35° h a l f a n g le (s e e s e c t i o n s

4

«1.1 and 4 ,2 f o r te c h n iq u e s ) gave sh o ck -to -w ed g e a n g le s which v a r ie d i n an a p p a r e n tly random fa s h io n d u r in g th e f i r s t 200 m ic ro s e c ,

\

R a d ia tio n l o s s e s as d e s c r ib e d i n s e c tio n 3 .3 .1 a re n o t s u f f i c i e n t to e x p la in th e s e phenomena. A p o s s ib le e x p la n a tio n i s t h a t th e c o n ta c t s u r f a c e i s u n s ta b l e , p a r t i c u l a r l y when i n t e r a c t i n g w ith th e r e f l e c t e d shock wave, A model f o r c o n ta c t s u r f a c e i n s t a b i l i t y o f th e R ay leig h ty p e i s g iv e n i n r e f e r e n c e 98» and flo w s i n argon in th e shock tu n n e ls a t th e c o n d itio n s

in 6his study fitted the conditions required for the instability to he present,,

The effect of the instability is that the contact surface becomes a zone of mixed pockets of helium and argon, which become mixed into all the test gas following the passage of the reflected shock wave through the zone. To detect such non-uniformity requires instruments with very short response

tines, such as the magnetohydrodynamic and pitot pressure probes. Previous

experiments using the stagnation pressure transducer, a stagnation point heat transfer model and a pitot pressure probe (ref. 120) involved response times sufficient only to record average values for the gas, which were reasonably close to values expected from pure gas» With the pitot probe, lov/ values due to helium contamination could be accounted for by ignoring the nozzle boundary layer correction.

The magnetohydrodynamic velocity probe output for argon, measured

between oO and 80 microsec after shock reflection, was compared with similar

results for air measured on the plateau (150 microsec) (see figure

64)*

Calculations predicted velocities for argon between 10 and 20'/0 greater than

for air. The results showed velocities in argon approximately equal to

those in air. This indicated a significant energy loss, which may have

been due to radiation, as explained in section 3» 3*1* At the conditions of this study, a reduction of 10

$

in the test section velocity in argon is equivalent to a reduction of 1270 in the nozzle reservoir temperature,

/

which is not incompatible with radiation losses.

4 o SIMPLE MODEL FLOjVS

I n c h a p te r 3, v a rio u s te c h n iq u e s d esig n ed to c a l i b r a t e th e flo w em erging from th e n o z z le a r e d e s c r ib e d . As a f i n a l c a l i b r a t i o n , flo w s o v er sim p le m odels, f o r which th e f r e e stream c o n d itio n s may be r e l a t e d to th e e x p e rim e n ta l r e s u l t s , vie r e exam ined.

The s im p le s t model would a p p e a r a t f i r s t s i g h t to be a tw o- d im e n sio n a l wedge o f s u f f i c i e n t l y sm all a n g le f o r th e shock wave i t form s i n th e flo w to be a tta c h e d t o th e body n o s e . F o r such a flo w , i f th e g a s i s n o n - r e a c t in g o r i n ch em ical e q u ilib r iu m , th e shock wave i s s t r a i g h t , c o n d itio n s b e h in d th e shock a r e s p a t i a l l y uniform and th e c o n s e r v a tio n e q u a tio n s may b e made q u a s i- o n e - d im e n s io n a l. Two e f f e c t s d e s tr o y t h i s s i m p l i c i t y . F i r s t l y , th e gas form s a v is c o u s boundary l a y e r on t h e wedge s u r f a c e o f a th ic k n e s s a p p ro x im a te ly p r o p o r tio n a l to t h e s q u a re r o o t o f d is ta n c e from th e body n o s e . T his a p p ea rs to th e f r e e stre a m gas a s a

4

cu rv ed s u r f a c e and c u r v a tu r e o f th e shock wave may r e s u l t . S eco n d ly , th e n o z z le flow i s ax isy m m etric and th e wedge i s tw o -d im e n sio n a l„ The e f f e c t s

o f n o z z le flow d iv e rg e n c e have been shown elsew h ere ( r e f . *J0) t o in c lu d e c u r v a tu r e o f th e shock wave b o th p a r a l l e l and tr a n s v e r s e t o th e flo w .

(However, r e f e r e n c e 70 showed t h a t c u r v a tu r e o f th e shock wave t r a n s v e r s e to th e flo w was a.'second o r d e r e f f e c t . I t was c a lc u la te d to b e n e g l i g i b l e a t c o n d itio n s t y p i c a l o f t h i s s tu d y , which im p lie d t h a t S c h lie r e n p h o to g rap h y would g iv e an a c c u r a te p i c t u r e o f th e l o c a t i o n o f th e shock w ave.)

The second o f th e s e problem s can be avoided by u s in g a c o n ic a l m odel« A cone a t z e ro a n g le of a t t a c k has a c o n ic a l shock wave i f i t s

an g le qs l e s s th a n th e detachm ent a n g le , i f th e gas i s n o n - r e a c t in g o r i n e q u ilib riu m and i f th e v is c o u s boundary l a y e r th ic k n e s s i s n e g lig ib le « , At th e c o n d itio n s i n t h i s s tu d y , th e l a s t o f th e s e c o n d itio n s did n o t h o ld ,

A model on which th e boundary l a y e r d isp la ce m e n t th ic k n e s s i s n e g l i g i b l e a t th e c o n d itio n s o f t h i s s tu d y i s a b lu n t body, which has th e shock wave s ta n d in g o f f from th e body n o se and a gas v e l o c i t y o f z ero a t

In document Nonequilibrium effects in shock tunnels (Page 57-89)