T h e s is s u b m itte d f o r th e d e g re e o f
D o cto r o f P h ilo so p h y
■by
Malcolm K enneth M cIntosh
D epartm ent o f P h y s ic s School o f G en eral S tu d ie s A u s tr a lia n N a tio n a l U n iv e r s ity C an b e rra A.C.T.
Candidate:-. Malcolm Kenneth McIntosh
Supervisors: R.J. Stalker 3 . Sc., M.Eng.3c., Ph.D,
R.J. Sandeman B.Sc., M.Sc., Ph.D.
The contents of this thesis, except where indicated in the acknowledgements or by a reference, are entirely my own work.
* TABLK 0 ? COKTESTS
Pa^e No.
1. I n tr o d u c t i o n 1 *
2. T h e o r e t i c a l Models 6»
2.1 Chem ical Models 6.
2 .1 .1 Thermodynamic P r o p e r t i e s 6,
2 .1 .2 R e a c tio n K in e tic s 8»
2 .2 Plow C a l c u la tio n s 12.
3. Shock Tunnel C a l i b r a t i o n s 19»
3.1 The A.N.U. F re e P i s t o n Shock T unnels 19«
3 .2 P re v io u s Work i n th e A.N.U. Shock Tunnels 22.
3 .3 F o rm atio n o f t h e N ozzle R e s e rv o ir 24.
3 .3 .1 R a d ia tiv e Energy D is s ip a tio n 25.
3 .3 .2 V iscous E f f e c t s 26.
3 .3 .3 Chem ical N o n e q u ilib riu m 28.
4
3 .3 .4 R e s u lts 29.
3 .4 N ozzle Flow 31.
3.4*1 Chem ical N o n e q u ilib riu m 32.
3 .4 .2 V isco u s E f f e c t s 36.
3.4 * 3 U se fu l T e st Time 38.
3 .4 .4 ‘ R e s u lts 43.
3.4*5 Flows i n Carbon D io x id e - N itro g e n M ix tu re s 44.
3 .4 .6 Flows i n Argon 48.
4 . Sim ple Model Flows 51«
4 .1 Wedges, Cones and S pheres 53.
4 .1 .1 Y/edge Flow 53.
4 .1 . 2 Cone Flow 55.
4 . 1 . 3 H em isphere - C y lin d e r Flow 56.
5. Model Flows w ith Chem ical N o n eq u ilib riu m 6 1 .
5.1 The F la re d -H e m is p h e re -C y lin d e r 6 1 .
5 .2 Model Flows i n T .3 6 2 ,
6 . C o n clu sio n s 6 7 .
Acknowledgements 6 9 .
Appendix A L i s t o f P u b li c a tio n s 70.
Appendix B E x p e rim en ta l T echniques 72.
R e fe re n c e s 80.
f-£ables
1. C h a r a c t e r i s t i c s o f th e AHU F ree P is to n Shock T u n n els. 2 . O p e ra tin g C o n d itio n s i n Shock Tunnel T .1 .
F ig u re s
1. D ir e c t E n try F l i g h t C o r r id o r s .
2. H y p erso n ic F l i g h t S im u la tio n F a c i l i t y Summary. 3. M o le c u la r K in e tic Energy i n H ypersonic F l i g h t . 4 . F re e P is to n Shock Tunnel Y/ave Diagram.’
5. I n i t i a l Shock Wave V e l o c i t i e s i n T .1 . 6. I n i t i a l Shock Wave V e l o c i t i e s i n T .2 . 7. I n i t i a l Shock Y/ave V e l o c i t i e s i n T .3 . 8 . R a d ia tiv e R e la x a tio n i n Argon i n T .2 .
9 . R a d ia tiv e R e la x a tio n i n Argon a t C o n d itio n s Comparable to A ir i n T .2 . 10. V iscous E f f e c t s i n a R e f le c te d Shock -Tunnel.
«
11. S p e c ie s C o n c e n tra tio n s b eh in d an I n c id e n t Shock Y/ave i n A ir. 12. P r e s s u r e i n th e N ozzle R e s e rv o ir i n T .2 .
13. T em perature i n th e N ozzle R e s e rv o ir in T .2 .
14* S p e c ie s C o n c e n tra tio n s i n th e N ozzle R e s e rv o ir in A ir i n T .2 . 15. S p e c ie s C o n c e n tra tio n s i n th e N ozzle R e se rv o ir i n 5 N^, 50$ C02
16. S p e c ie s C o n c e n tra tio n s i n th e N ozzle R e se rv o ir i n Carbon D io x id e i n T .2 . 17* S p e c ie s C o n c e n tra tio n s i n th e N ozzle R e se rv o ir i n Argon i n T .2 .
18. S p e c ie s C o n c e n tra tio n s i n a N ozzle Expansion i n A ir i n T .2 . 19. S p e c ie s C o n c e n tra tio n s i n a N ozzle Expansion i n N itro g e n i n T .2 .
20. S p e c ie s C o n c e n tra tio n s i n a N ozzle Expansion i n 50$ N^, 5 C02 i n T .2 . 21. S p e c ie s C o n c e n tra tio n s i n a N ozzle Expansion i n Argon i n T .2 .
%
22. A x ial P i t o t P r e s s u r e Survey i n T .1 . 23. R a d ia l P i t o t P r e s s u r e Survey In T .1 . 24. P i t o t P r e s s u r e i n T .3 .
26. Free Stream Velocity in Air in T.2.
27
. Free Stream Velocity in Nitrogen in T.2.28. Free Stream Velocity in Carlton Dioxide in T.2.
29
. Free Stream Species Concentrations in T.1.30. Free Stream Species Concentrations in Air in T.2.
31
. Free Stream Species Concentrations in Nitrogen in T.2.32. Test Time in T.2 with Large Nozzle Throa/t.
33. Test Time in T.2 with Small Nozzle Throat
34* Time Resolved Wedge Shock Angles in T.1.
35. Y/edge Shock Angles in T.1.
36
. Shock /angles on a 25° Wedge in Air in T.2.37* Shock Angles on a 35° Wed ge in Air in T.2. with Small Nozzle Area Ratio.
38. Shock Angles on a 35° Wedge in Air in T.2. with Lgrge Nozzle Area Ratio.
39» Shock Angles on a 35° Wedge in Nitrogen in T.2. with Large Nozzle Area
.Ratio.
40. Wedge Shock Angles in Carbon Dioxide in T.2.
41. Shock Angles on a 35° Wedge in Carbon Dioxide in T.2.
42. Cone Shock /ingles in T.2.
43» Shock Stand-off Distance on a Hemisphere in Air in T.2.
44» Shock Stand-off Distance on a Hemisphere in Carbon Dioxide in T.2.
45* Species Concentrations behind the Shock Wave on a Hemisphere in Air
46
. Species Concentrations behind the Shock Wave on a Hemisphere in Nitrogen 47* Shock Stand-off Distance on a Hemisphere in Air in T.3.48. Stream Tube Cross-Sectional Areas behind the Shock Waves on a Wedge in T.3.
49« Shock Wave Angles on a Wedge in Air in T.3.
50. ' Shock Wave Angles on a Y/edge in Nitrogen in T.3.
51. Schlieren Photograph of Wedge Flow in T. 3*
52. Schlieren Photograph of Flow over a Flared Hemisphere Cylinder.
53. Interpretation of Flow over a Flared Hemisphere Cylinder.
56
. Streak Photographs of Incident and Reflected Shock Waves.57* ' Streak Photographs of Free Stream Gas Flow, 58. Framing Photograph of Shock Wave on Wedge. 59* Spark Tracer Technique.
60. Streak Photographs of Spark Tracer.
61
. Magnetohydrodynamic Technique.62. Magnetic Field Properties for the Magnetohydrodynamic Technique.
63
. Flow over the Magnetohydrodynamic Probes.£4. Oscilloscope Traces from the Magnetohydrodynamic Technique.
65
. Pitot Pressure Probe.66. Pressure Transducer Converter Circuit.
67
. Free Stream Pitot Pressure Traces.68* Pitot Pressure behind an Oblique Shock Wave.
69
. ' Pitot Pressure in the Nozzle Boundary Layer.70. The Single or Double Pass Schlieren System. 71. Schlieren Photographs in T.2.
B ss magnetic field c S3 specific heat
C S3 " j£I
|iT* d S3 distance
E = electric field
F S3 force
h SS enthalpy
0 S3 current density
P S3 pressure
q S3 charge
u S3 velocity
V S3 voltage
R 33 Resistance
Re S3
p \X X .
Reynolds Number = V-j^~ •* mass fraction
X S3
X S3 distance
s
S3 order function or boundary layer thickness S3 ratio of specific heatsS3 density
= oblique shock angle to free stream
S3 wedge angle to free stream
p S3 viscosity
% S3 shock wave - boundary layer interaction parameter
Subscripts
f S3 t of formation
at constant volume stagnation conditions
• S in c e World War I I , th e shock tu n n e l has keen dev elo p ed as a v e r s a t i l e and in e x p e n s iv e means o f i n v e s t i g a t i n g high speed gas flo w s . A v e ry l a r g e p a r t o f th e work i n t h i s f i e l d has "been con cern ed w ith b o d ie s moving i n a i r and, s p e c i f i c a l l y , v/ith v e h ic le s r e - e n t e r i n g th e E a r t h ’ s
atm osphere a f t e r f l i g h t s i n s p a c e 0 F ig u r e 1 i s a v e l o c i t y - a l t i t u d e c h a r t showing a v a r i e t y o f d i r e c t - e n t r y f l i g h t c o r r i d o r s . Almost a l l work has c o n c e n tra te d on t h e manned r e - e n t r y c o r r i d o r a t speeds below 8 k m /se c. I f th e speed i s g iv e n b y ^ 2 x s t a g n a tio n e n th alp y , t h i s c o rre sp o n d s t o
11
a s ta g n a tio n e n th a lp y o f 3 .2 x 10 erg/gm . 11
This v a lu e ( 3 .2 x 10 erg/gm ) i s , by a com bination o f t e c h n i c a l and in c e n t i v e l i m i t s , ab o u t th e h ig h e s t o b ta in a b le i n c o n v e n tio n a lly
d r iv e n shock t u n n e l s . F ig u re 2 i s a summary o f c u r r e n t te c h n iq u e s f o r la b o r a t o r y s im u la tio n o f r e - e n t r y ty p e flow s» Techniques which g iv e
s ta g n a t i o n e n th a l p ie s i n a i r i n ex cess o f 3 .2 x 10 erg/gm a re th e a r c - h e a te d d r i v e r , 4m agnetohydrodynam ic au g m en tatio n o f th e flow energy o f a c o n v e n tio n a l shock tu n n e l and th e f r e e p i s t o n d r i v e r . The t e s t gas produced by th e f i r s t two o f th e s e te c h n iq u e s i s o f te n co n tam in ated w ith m e ta l l i c m a t e r i a l th ro u g h e r o s io n o f th e e n e rg y -s u p p ly in g e l e c t r o d e s , making i t u n s u i ta b l e f o r s tu d ie s o f flo w i n Ma tm o s p h e ric M gases» The f r e e - p i s t o n d r i v e r , on which th e work i n t h i s stu d y i s b a s e d , i s a r e l a t i v e l y new te c h n iq u e which has b een
d ev elo p ed to y i e l d t o t a l t e s t flo w e n th a l p ie s as high as th o s e e n c o u n te re d d u rin g e n tr y to p l a n e t a r y atm ospheres a f t e r deep space o r i n t e r - p l a n e t a i y
I
voyages •
The u n iq u e a b i l i t y o f th e f r e e p is to n shock tu n n e l to p ro d u c e c le a n t e s t gas a t v e ry h ig h e n th a lp y l e v e l s i s p a r t i c u l a r l y im p o r ta n t i n s t u d i e s o f e n tr y to atm o sp h eres c o n s i s t i n g o f gases o th e r th a n a ir » D ir e c t e n try sp eed s on i n t e r - p l a n e t a r y m issio n s a re h ig h (s e e f i g u r e 1) b e c a u se th e v e h ic le m ust e sc a p e th e E a r t h 's g r a v i t a t i o n a l fie ld ", th e
s tu d y to in c lu d e t e s t g a se s o f s i m i l a r com position to th e atm ospheres o f Mars and Venus, th e E a r t h ’ s c l o s e s t n e ig h b o u rs.
Also in c lu d e d on f ig u r e 2 a re perform ance l e v e l s used i n a v a r i e t y o f in d i v i d u a l e x p e r im e n ta l s tu d ie s ( th e numbers co rresp o n d t o r e f e r e n c e s l i s t e d on th e page f o llo w in g th e f i g u r e ) . These are r e p r e s e n t a t i v e o f an
e x te n s iv e l i t e r a t u r e su rv e y and i n d i c a t e th a t any work done w ith tu n n e l r e s e r v o i r te m p e ra tu re s shove 8000°K w i l l be a u s e f u l a d d itio n t o p r e s e n t
v' know ledge.
The m ost i n t e r e s t i n g f e a t u r e o f very high sp eed r e - e n t r y ty p e flo w s i s t h a t th e k i n e t i c energy o f th e gas m olecules p a s s in g o v e r th e body i s com parable t o th e fo rm a tio n energy of chem ical bon d s. F ig u re 3
shows th e k i n e t i c en erg y p e r m o lecu le o f ambient a i r as a f u n c tio n o f t h e f l i g h t v e l o c i t y . Also shown on th e en erg y s c a le are r e a c t i o n e n e r g ie s
(n o t to be co n fu sed w ith r e a c t i o n a c t i v a t i o n energy, th e r e a c t i o n energy i s th e n e t energy y i e l d f o r th e r e a c t i o n ) f o r a v a r ie t y o f r e a c t i o n s w hich
o c c u r i n th e ’’a tm o s p h e ric ” g a s e s . (N ote t h a t r e a c tio n e n e r g ie s a r e a d d i t i v e , so t h a t i t ta k e s 32.35 eV to form two 0 io n s from one 0^ m o le c u le .; As th e m o le c u les have a M axw ell-B oltzm an v e l o c i t y d i s t r i b u t i o n i n m ost o f th e
E a r t h 's r e - e n t r y f l i g h t c o r r i d o r , th e energy o f sane m o lecu les i s much
h ig h e r th a n th e mean v a lu e shov/n i n f i g u r e 3» so th a t some i o n i s a t i o n o c cu rs below 8 km /sec f l i g h t v e l o c i t y (a s evidenced by the com m unications b la c k o u t d u rin g r e - e n t r y ) , b u t d i s s o c i a t i o n a c c o u n ts f o r most o f th e i n t e r n a l en erg y
/ i n c r e a s e i n th e gas as i t i s h e a le d by th e passage o f th e body» Above 8 k m /se c, i o n i s a t i o n h as a s i g n i f i c a n t e f f e c t on th e energy balance*,
A lthough a r e a c t i o n may b e e n e r g e tic a lly f e a s i b l e , th e fo rm a tio n
\
o f p ro d u c ts i s a f u n c tio n o f th e fre q u e n c y w ith which r e a c t a n t p a r t i c l e s c o l l i d e and th e p r o b a b i l i t y o f a c o l l i s i o n y ie ld in g th e r e a c tio n p r o d u c ts . The fo rm er i s a f u n c tio n o f th e number o f p a r t i c l e s and t h e i r v e lo c i ty d i s t r i b u t i o n and th e l a t t e r i s a f u n c tio n o f th e energy o f th e c o l l i s i o n ,
which is also a function of the velocity distribution» The number of product particles depends upon the time the gas spends in the environment, which is a function of the gas velocity and the dimensions of the region.
Prom these considerations, it is apparent that, for laboratory simulation of the chemical changes which occur in re-entry flora, the free stream velocity and density of the gas, as well as the body size should be reproduced» The last of these is often impractical, but useful results may be obtained using smaller sized models0
Othei flo.v properties such as Mach number and total pressure, which are important if the aerodynamic forces on the body are to be simulated, need not be reproduced if only the chemical properties are to be examined, provided that the Mach number is high enough for the flow to be considered hypersonic.
As described above, the free stream velocity is directly related to the stagnation enthalpy» The density is related less directly to the stagnation or nozzle reservoir pressure. The free piston shock tunnel, es
shown in figure 2, has the capability of producing high values of both of these properties.
In a new facility, such as the free piston shock tunnel, it is essential to obtain a, thorough understanding of the experimental
performance and, if possible, to develop a theoretical model before simulation experiments are made on vehicle models*
I
Three types of calibration can be considered for a very high enthalpy shook tunnel: "wind tunnel", "shock tunnel" and "chemical". Wind tunnel calibrations are those conducted in continuous, "blow-down" or other facilities in which the reservoir properties may be regarded as steady or only slowly and predictably varying. They concentrate on flow in the nozzle aid the determination of such properties as pitot pressure and heat transfer at many positions in the nozzle flow. Their aim is to
d e term in e th e u n ifo r m ity o f th e flow and th e e f f e c t s of th e v is c o u s
b o u n d ary l a y e r on th e n o z z le w a lls , as w e ll as t o fin d a c c u r a te , a b s o lu t e v a lu e s f o r th e flow p r o p e r t i e s a t th e n o z z le e x i t . Shock tu n n e l c a l i b r a t i o n s
a re made to a s s e s s th e e f f e c t s on flo w a t th e n o zzle e x i t o f th e l a r g e a m p litu d e , s h o r t d u r a tio n t r a n s i e n t s (sh o ck w aves), which g e n e r a te h ig h e n th a lp y gas i n th e n o z z le r e s e r v o i r . They r e q u ir e tim e - r e s o lv in g
m easurem ents o f , f o r exam ple, th e p r e s s u r e a id lu m in o s ity o f th e gas as i t form s t h e n o z z le r e s e r v o i r a id o f wind tu n n e l ty p e m easurem ents i n th e n o z z le flo w . They have as t h e i r p rim a ry fu n c tio n th e d e te r m in a tio n o f a
'•useful'* t e s t tim e d u rin g which th e flo w i s s te a d y and th e p r o p e r t i e s o f th e t e s t flo w a re known. A h ig h e n th a lp y shock tu n n e l has an added c o m p lic a tio n i n t h a t th e t e s t gas changes i t s n a tu r e and hence i t s w ind- and s h o c k - tu n n e l p r o p e r t i e s as a r e s u l t o f r e a c tio n s among i t s chem ical c o n s t i t u e n t s . Such changes 4i n th e n a tu r e o f th e t e s t gas sh o u ld be accounted f o r i n a ch em ical c a l i b r a t i o n as th e y p la y an im p o r ta n t p a r t i n th e s im u la tio n o f r e - e n t r y model flo w s .
A number o f wind- and s h o c k - tu n n e l c a l i b r a t i o n m easurem ents had b een made on th e A u s tr a lia n N a tio n a l U n iv e r s ity (A.N.TJ.) f r e e p i s t o n shock
tu n n e ls p r i o r to th e commencement o f t h i s s tu d y . A rev iew i s g iv e n i n
c h a p te r 3. The f i r s t aim o f t h i s s tu d y was to extend th o s e c a l i b r a t i o n s and to c h e m ic a lly c a l i b r a t e th e tu n n e l s . Many te c h n iq u e s commonly used t o
c a l i b r a t e shock tu n n e ls f o r aerodynam ic s tu d ie s g iv e l i t t l e o r no in f o r m a tio n on th e chem ical p r o p e r t i e s o f th e t e s t g a s . Hence, th e developm ent o f new te c h n iq u e s , th e a d a p ta tio n o f o ld te c h n iq u e s to th e h ig h e n th a lp y
en v iro n m en t, and th e developm ent o f an ad eq u ate t h e o r e t i c a l model w ere a l l r e q u ir e d .
To a s s i s t i n th e c a l i b r a t i o n s and as a f i r s t s te p to th e i n v e s t i g a t i o n o f flow s o v er models o f r e - e n t r y v e h i c l e s , a number o f sim p le model flo w s
w ere examined. The co m b in atio n o f low f r e e stre am d e n s ity and sm a ll model s i z e was su ch t h a t t h e r e were no o b s e rv a b le e f f e c t s o f chem ical r e a c t i o n s
i n “th e model flov7s and th e t e s t gas c o u ld be c o n s id e re d , f o r p r a c t i c a l p u rp o s e s , as a p e r f e c t g a s . The n o z z le r e s e r v o i r p r o p e r ti e s shown i n f i g u r e 2 i n d i c a t e t h a t th e f r e e p i s t o n shock tu n n e ls a r e th e most l i k e l y to p ro d u c e model flo w s w ith ch em ical non e q u ilib riu m . Tunnels w ith lo w e r e n th a lp y l e v e l s th a n t h e f r e e p i s t o n m achines have been used t o i n v e s t i g a t e v i b r a t i o n a l r e l a x a t i o n o v e r m odels, b u t th e a u th o r has seen no r e f e r e n c e t o a h y p e rs o n ic tu n n e l c a p a b le o f p ro d u c in g ch am ica lly r e a c t i n g model flo w s 0
E a rly i n 1970 a new, l a r g e , f r e e p is to n shock tu n n e l bn own as T .3 became o p e r a tiv e a t th e A . N . U . C a l i b r a t i n g ex p erim en ts and c a l c u l a t i o n s i n d i c a t e d t h a t model flo w s w ith ch em ical non e q u ilib riu m c o u ld be e f f e c t i v e l y s t u d ie d i n t h i s tu n n e l . The r e s u l t s o f a p r e lim in a ry s tu d y o f c h em ical n o n e q u ilib riu m i n v e ry h ig h e n th a lp y model flow s form th e f i n a l c h a p te r o f
t h i s t h e s i s and th e y a r e b e lie v e d t o be th e f i r s t o f t h e i r k in d .
[image:14.562.24.549.293.820.2]2 . * TKSORETICAL HÖDELS
2 .1 C hem ical P r o p e r t i e s o f G ases
As i n d i c a t e d i n c h a p t e r 1, i n v e s t i g a t i o n s o f h ig h e n th a lp y g as flo w s s h o u ld c o n s i d e r th e e f f e c t s o f c h e m ic a l r e a c t i o n s w ith in t h e f lo w in g t e s t g a s . T h ese a r e e x p e c te d t o o c c u r as th e g a s i s h e a te d by t h e r a p i d c o n v e r s io n o f l a r g e q u a n t i t i e s o f k i n e t i c e n erg y to th e rm a l e n e rg y d u r i n g c o m p re s s io n , f o r ex am p le, on a body n o s e . The r e v e r s e p r o c e s s o c c u r s d u r i n g e x ira n sio n , f o r ex am p le, i n a body wake«»
F o r t h e c o n d i t i o n s e x p e r ie n c e d i n th e f l i g h t c o r r i d o r s o f f i g u r e 1, an d u n le s s e x tre m e s o f d e n s i t y a r e e n c o u n te r e d , a g as may b e c o n s id e r e d a s a m ix tu r e o f r e a c t i n g c h e m ic a l s p e c i e s , each o f w hich b e h a v e s as a p e r f e c t gas ( r e f s . 1 8 ,4 4 )« A d e s c r i p t i o n o f t h e c h e m ic a l p r o p e r t i e s o f
a g a s r e q u i r e s t h e s p e c i f i c a t i o n o f two s e t s o f p r o p e r t i e s : n am ely , o f
t h e e q u i l i b r i u m therm odynam ic p r o p e r t i e s o f 'e a c h o f th e c o n s t i t u e n t c h e m ic a l €
s p e c i e s and o f t h e k i n e t i c s o f t h e r e a c t i o n s among th e s p e c i e s .
2,1. 1 Thermodynamic P r o p e r t i e s
The therm odynam ic p r o p e r t i e s o f c h e m ic a l s p e c ie s a r e d e te r m in e d e x p e r i m e n t a lly fro m s p e c t r o s c o p i c o b s e r v a ti o n s o f t h e c h a r a c t e r i s t i c
f r e q u e n c i e s o f e l e c tr o m a g n e ti c r a d i a t i o n e m itte d a n d /o r a b s o rb e d by p a r t i c l e s (ato m s o r m o le c u le s ) o f t h e s p e c i e s . From th e o b se rv e d f r e q u e n c i e s , t h e e n e rg y l e v e l s t r u c t u r e o f th e p a r t i c l e can b e deduced ( r e f s . 1 , 2 ) . Two s e t s o f t a b l e s o f e n e rg y l e v e l s w ere u s e d i n t h i s s tu d y ( r e f s . 2 , 3 ) and th e y w ere fo u n d t o b e a d e q u a te f o r t h e s p e c i e s and c o n d i tio n s e n c o u n te r e d i n t h e f r e e p i s t o n sh o ck t u n n e l s .
The e n e rg y l e v e l s t r u c t u r e o f a p a r t i c l e can b e u s e d t o c a l c u l a t e «
i t s therm odynam ic p r o j^ e r ti e s i n s e v e r a l w ays: ( i ) S im ple m odels o f th e b e h a v io u r o f th e p a r t i c l e s u c h a s t h e " r i g i d r o t a t o r ” and t h e "h arm o n ic o s c i l l a t o r " u s e t h e e n e rg y l e v e l s d i r e c t l y ( r e f s . 4>5»52) . They a r e l i m i t e d
i n a c c u ra c y by th e num ber o f energy l e v e l s in c lu d e d i n each c a l c u l a t i o n ( t h e tim e ta k e n f o r a c a l c u l a t i o n i s p r o p o r tio n a l to th e number o f e n erg y l e v e l s c o n s id e r e d ) more o f ta n th a n by in a d e q u a c ie s o f th e models» S in c e th e number o f en erg y l e v e l s r e q u ir e d f o r an a c c u ra te n u m e ric a l d e s c r i p t i o n in c r e a s e s w ith i n c r e a s i n g te m p e ra tu re , such models a re u s u a ll y u sed a t low te m p e ra tu re s o n ly (below 5000°K i n t h i s w ork), ( i i ) A quantum m ech an ical d e s c r i p t i o n o f th e p a r t i c l e can be o b ta in e d by u sin g th e energy l e v e l s t r u c t u r e
it
and a s u i t a b l e e l e c t r o n i c p o t e n t i a l en erg y fu n c tio n w ith th e S c h rö d in g e r Wave E q u a tio n ( r e f . 4)» b u t th e tim e ta k e n f o r such c a l c u l a t i o n s p r e v e n ts t h e i r u se i n c a l c u l a t i o n s o f complex g as flo w s, ( i i i ) The energy l e v e l s can b e u sed to d e te rm in e th e e q u ilib r iu m p a r t i t i o n i n g o f energy w ith in th e p a r t i c l e , w hich i s d e s c r ib e d m a th e m a tic a lly by ''p a r t i t i o n f u n c tio n s " ( r e f s . 5 ,1 8 ) . T his m ethod i s a l s o to o in v o lv e d to be in c lu d e d i n complex g as flo w c a l c u l a t i o n s . However, i t can b e u sed t o g iv e thermodynamic p r o p e r t i e s w ith h ig h a c c u ra c y and s e v e r a l s e t s o f ta b u la te d p r o p e r tie s so d e r iv e d were u sed i n t h i s s tu d y ( r e f s » 6 to 1 0 ). Economic u se of th e t a b u l a t e d d a t a r e q u ir e d t h a t th e y f i r s t b e f i t t e d w ith polynom ial f u n c tio n s o f te m p e ra tu re ; th e n each su b se q u e n t c a l c u l a t i o n o f thermodynamic p r o p e r tie s r e q u ir e d o n ly th e e v a lu a tio n o f th e p o ly n o m ia ls . Two polynom ial forms a re i n common u s e ; one ev o lv ed a t th e C o rn e ll A e ro n a u tic a l L a b o ra to rie s ( r e f s . 44»54) and th e o th e r recommended by JAITAF ( r e f . 9)« Both g iv e e r r o r s of a p p ro x im a te ly j f o a
L u rin g th e c o u rs e o f t h i s s tu d y , energy l e v e l d a t a and p o ly n o m ial c o e f f i c i e n t s from " l e a s t s q u a re s " f i t s t o ta b u la te d d a t a were c o l l e c t e d f o r 26 s p e o ie s : COg, Kg, Og, CO, NO, CN, C, 0 , H, A, He, Kg, 0+, C0+ , N0+, C+ , N+ , A+, He+ , C + + , 0 + + , N++, A++, He**, e " , Cg.
Thermodynamic p r o p e r t i e s f o r each o f th e above s p e c ie s were
d e te rm in e d u s in g m ethods ( i ) and ( i i i ) d e s c rib e d above, and u s in g t a b u l a t e d therm odynam ic d a t a from a t l e a s t two s o u r c e s . Agreement betw een r e s u l t s
u s in g th e d i f f e r e n t m ethods and d a ta s o u rc e s 'was w ith in 5/^ o v e r th e te m p e ra tu re ra n g e s s p e c i f i e d by th e d a ta so u rces»
To ch eck th e a cc u ra cy o f th e above s p e c i f i c a t i o n s o f therm odynam ic p r o p e r t i e s o f s p e c ie s f u r t h e r , g ro s s e q u ilib riu m thermodynamic p r o p e r t i e s
( e n th a lp y , e n tro p y and d e n s it y as f u n c tio n s of te m p e ratu re and p r e s s u r e )
w ere c a l c u l a t e d f o r a number o f common g ases and gas m ix tu res* C o m p ariso n w ith p u b lis h e d t a b l e s ( r e f s . 11 to 16) gave agreem ent w ith in 5p»
2 .1 .2 “R ea c tio n K i n e tic s
At th e h ig h te m p e ra tu re s u sed i n th is stu d y , r e a c t i o n s among th e c h em ica l s p e c ie s form ed i n a gas a re commonly in v e s t ig a te d by m o n ito r in g th e a p p earan ce o r d is a p p e a ra n c e o f s p e c ie s follo w in g a r a p id " s w itc h in g "
o f th e gas from an i n i t i a l n o n - r e a c t in g s t a t e to a r e a c t i n g s t a t e ( r e f s . 17, 110) . S w itc h in g may be a c h ie v e d by a shock wave ( r e f . 21) o r a f l a s h o f e le c tro m a g n e tic r a d i a t i o n ( f l a s h - p h o t o l y s i s ) ( r e f . 19)« A le s s t r a n s i e n t s i t u a t i o n i s p o s s ib le i n a flo w - d is c h a r g e sy stem ( r e f o 2 0 ). A h ig h -to -lo w te m p e ra tu re " sw itc h "
may b e o b ta in e d by a, sudden ex p an sio n o f th e g a s . O p tic a l and mass s p e c tro m e te rs 4
a r e th e most commonly u sed m o n ito rin g sy stem s.
I n h e a te d a i r below 8000°K, th e dominant r e a c tio n s a re ( r e f . 23 to 2 7 ,5 2 ) :
(1 ) H2 + M 2N + M
(2 ) °2 + M 20 + M
(3 ) NO + M __s . N + 0 + M
(4 ) n2 + 0 — Sv NO + N
(5 ) °2 + N ----i*. NO + 0
(6 ) K2 + °2 —^ 2N0
(7 ) N ■f i0 N0+ + e~
Above 8000°K, io n s su ch as N„+ ,
%
q u a n t i t i e s and t h e i r fo rm a tio n r e a c t i o n s e .g . N + M N+ + e~ + M
where M = a t h i r d body
N+ and 0+ a p p ea r i n s i g n i f i c a n t
and io n exchange r e a c t i o n s
e .g . K* t 0 ^ H + 0+
become s i g n i f i c a n t . At s t i l l h ig h e r te m p e ra tu re s o f a p p ro x im a te ly
0
15000°K, and for the densities typical of this study, douhly charged species,
++ ++
IT and 0 , are formed and the small quantity of argon in the air becomes
partially ionised.
Rate constants for these reactions have been determined by many
workers and the work has been reviewed on many occasions. Several review
papers were U3ed in this study (refs. 23 to 30). It was noted that almost all work has been done at temperatures below 6000°K and extrapolation to
15000°K was used for this study,, For each reaction, the results in the review papers were compared to ensure the best possible accuracy.
For reactions (l) to (7) above, the rate constants were found
to have an accuracy of + 10$. For some of the ion exchange reactions,
errors in the rate constants of 2 orders of magnitude were probable. However, the effects of such errors in the ionization reaction rates on the flow properties were small because the species involved only appeared
*
in appreciable concentrations in the hot, high density nozzle reservoir and at the very beginning of the nozzle expansion, where they were very
close to equilibrium. Before conditions in the nozzle expansion became
favourable for nonequilibrium, their numbers had become negligible. Recombination reactions are more complicated than dissociation and ionization reactions because the species need not recombine to form molecules or atoms in the ground state, but may form species in excited
stateso This is most important where the excited level is metastable and
/
decay to the ground state is very slow (LASER action has been achieved in carbon dioxide in a shock tunnel by this process), or for vibrational levels in diatomic and triatomic molecules where the relaxation time is comparable to the characteristic flow time (e.g., the time for the gas to flow over a
body or through a shock heated slug of gas). In most applications,
recombination to states other than the ground state is ignored and the recombination rate is taken to be an average value computed through the forward rate and the equilibrium constant (which includes contributions
from v i b r a t i o n a l arid o t h e r l e v e l s b e c a u se i t i s c a lc u la te d from th e e q u ilib r iu m therm odynam ic p r o p e r t i e s o f th e s p e c ie s in v o lv e d i n th e r e a c t i o n ) .
The r e a c t i o n sy stem f o r a i r d e s c r ib e d above (no e x c ite d s t a t e s a r e c o n s id e re d i n th e r e a c t i o n r a t e s ) has g iv en good agreem ent vrith e x p e rim e n ts h e re (d e s c r ib e d i n su b se q u e n t c h a p te r s ) and elsev/here» T his may b e due to th e r a t e s b e in g d e term in e d from ex p erim en ts s i m i l a r to th o s e
used t o v e r i f y them , r a t h e r th a n to th e in s i g n i f i c a n c e o f re c o m b in a tio n t o e x c it e d s t a t e s »
Some v/orkers have in c lu d e d e x c ite d s t a t e s i n t h e i r c a l c u l a t i o n s » F o r exam ple, r e f e r e n c e 25 l i s t s r e a c t i o n s in v o lv in g a s i n g l e v i b r a t i o n a l l e v e l each f o r and NO and r e f e r e n c e 52 in c lu d e s a c ru d e model f o r c o u p lin g th e d i s s o c i a t i o n r a t e o f d ia to m ic m olecules to th e c a l c u l a t e d s t a t e o f v i b r a t i o n a l e x c it a tio n * C o n s id e ra tio n o f e x c ite d s t a t e s i s common
4
i n ch em ical shock tu b e s t u d i e s su ch as th o s e review ed i n r e f e r e n c e s 20, 21 and 110» G e n e ra lly th e s e w ere made a t v e ry much lo w e r te m p e ra tu re s th a n w ere ach iev ed i n th e f r e e p i s t o n shock tu n n e ls , and used g a se s o t h e r th a n th e '‘atm o sp h eric" c o n s t i t u e n t s c o n s id e re d h e re . The te c h n iq u e s w ere u sed i n th e d e te r m in a tio n o f th e carbon d io x id e r e a c ti o n system d e s c r ib e d l a t e r i n t h i s s e c t i o n .
R eferen ce 139 g iv e s an e x p e rim e n ta lly d eterm in ed r e a c t i o n r a t e f o r th e " d is s o c ia tiv e - r e c o m b in a tio n " r e a c t i o n :
/
N0+ + e~ N + 0
As can b e seen from f i g u r e 2 (w here *9 co rre sp o n d s to r e f e r e n c e 139) > th e n o z z le r e s e r v o i r c o n d itio n s u sed i n t h i s d e te r m in a tio n a re d i f f e r e n t from th e
t
c o n d itio n s i n th e f r e e p i s t o n shock t u n n e ls . They a r e , however, th e c l o s e s t u sed i n a re c o m b in a tio n r a t e d e te r m in a tio n and i n d i c a t e th e e x t r a p o l a t i o n
r e q u ir e d i n t h i s s tu d y f o r a l l r e a c t i o n r a t e d a ta .
The reaction rate constants for air, determined from the review papers above, were also used for the kinetics of the pure gases, oxygen and
nitrogen, where applicable. The dominant ionization reactions occurring
in oxygen and nitrogen were found to be:
0 + M x — 0+ + e“ + M
N + M N + + e" + M
respectively* The estimated error in the rate constants for these reactions
is + 20$o
Reactions in all "air-type” gases (nitrogen and oxygen mixtures with an inert diluent) can be described using the reaction rates for air shove, but reactions in the other major component of "atmospheric" gases,
carbon dioxide, are not well understood at present* A number of workers have
measured dissociation rates of C02 (refs, 29,30,33,34»35) but the estimated
errors are large (typically 2 orders of magnitude). Estimates of reaction
«
rates for the dissociation of CO^ to C and 0 via CO also have been made from collision theoiy (refs, 31,32) and found to lie within the limits determined
experiment ally •
A reasonable system for carbon dioxide dissociation includes: C02 + M ^ CO + 0 + M
CO + M C + 0 + M C02 + 0 CO + 02 C02 +
c ^
2C0 CO + 0 ^ 02 + cOf these, reaction (a) is the fastest by up to a factor of 100o In a recent paper (ref, 35) > the presence of the Swann bands of the
\
dia.tomic carbon molecule, C 2 , during CO dissociation gave rise to a suggested reaction system involving C^ reactions, which behaved in a similar fashion to the NO "shuffle" reactions in air (reactions 4 2nd 5 above) in that the inteimediate product (C2 in carbon monoxide, NO in air) concentration was
low , "but i t s r e a c t i o n s were r a p id p ro d u c e rs o f o th e r s p e c ie s . The p ro p o sed sy ste m was:
CO + M ^ C + 0 + II C + CO ^ c 2 + 0 0 + CO ^ o2 + C C2 + M ^ 2C + M 0o + M ^ 20 + M
C .
c*-I f c o r r e c t , t h i s mechanism would b e in c lu d e d i m p l i c i t l y i n th e e a r l i e r r a t e d e te r m in a tio n s . I t sh o u ld be n o te d t h a t i s a v e ry s tr o n g r a d i a t o r so t h a t i t c o u ld b e o b se rv e d , b u t b e i n to o sm all a c o n c e n tr a tio n t o a f f e c t th e k i n e t i c s o f th e g a s .
B ecause o f th e c o m p le x itie s o f th e r e a c tio n k i n e t i c s i n a r e a l g a s , th e "Freem an” i d e a l d i s s o c i a t i n g gas ( r e f . 38) i s o f te n u sed to o b ta in an. i n s i g h t in t o th e i n f l u e n c e o f a r e a c t i o n on a flo w sy stem . I t u s e s a s i n g l e i d e a l i s e d r e a c t i o n and an i d e a l i s e d s p e c i f i c a t i o n of th e therm odynam ic
p r o p e r t i e s o f s p e c ie s ( r e f . 3 7 ). I t s main advantage i s t h a t s o l u t i o n s to flo w problem s a r e o f t e n o b ta in a b le i n an a n a l y t i c a l o r s e m i - a n a l y t i c a l
( r e q u i r i n g v e ry l i t t l e n u m e ric a l co m p u tatio n ) form . I t i s m entio n ed h e re b e c a u s e i t was used as a f i r s t a p p ro x im a tio n i n th e i n i t i a l s ta g e s o f t h i s
s tu d y .
2 .2 Flow C a lc u la tio n s
F ig u re 4 i s a tim e - d is ta n c e diagram showing th e waves u sed to g e n e r a te th e n o z z le r e s e r v o i r i n a f r e e p is to n shock tu n n e l (n o te th e d i s c o n t i n u i t y i n th e d i s t a n c e s c a l e ) . F o r th e pu rp o ses o f t h i s s tu d y , th e f r e e p is t o n d r i v e r te c h n iq u e was re g a rd e d as m erely a means o f p ro d u c in g h o t, h ig h p r e s s u r e heliu m to d r iv e an o th e rw is e c o n v e n tio n a l r e f l e c t e d shock tu n n elo (The f r e e p i s to n te c h n iq u e i s an a d a p ta tio n o f th e gun tu n n e l ( r e f . 119) and th e m o tio n s o f th e p is to n and d r i v e r gas a re s u f f i c i e n t l y c o m p lic a te d t o r e q u ir e s tu d y i n t h e i r ov/n r i g h t . F o r th e p u rp o s e s o f t h i s s tu d y , th e p i s t o n com pression r a t i o v.ras k e p t low and th e
[image:21.562.25.545.28.720.2]p i s t o n v e l o c i t y s u b so n ic t o avoid m ost such c o m p lic a tio n s .) Then th e flo w was d iv id e d i n t o th r e e d i s t i n c t re g io n s f o r th e purposes o f n u m e ric a l c a l c u l a t i o n s : th e p ro c e s s e s fo rm in g th e n o z z le r e s e r v o i r , th e n o z z le e x a p n sio n and th e flo w o v e r models«, In a l l th r e e re g io n s th e e f f e c t s o f ch em ical n o n e q u ilib riu m upon th e gas were c o n sid e re d .
The n o z z le r e s e r v o i r was form ed by r e f l e c t i o n from th e end w a ll o f th e shock tu b e o f th e no rm al, i n c i d e n t shock wave g e n e ra te d i n t h e shock tu b e by th e r u p tu r e o f th e diaphragm by h ig h p re s s u re d r i v e r gas ( r e f s . 1 1 0 ,1 1 4 ). Gas p ro c e ss e d by th e i n c i d e n t and r e f l e c t e d shock waves had
h ig h v a lu e s o f te m p e ra tu re and p r e s s u r e and was s t a t i o n a r y i n th e la b o ra /to iy fram e o f reference«,
As th e i n c i d e n t shock wave p ro p a g a te d in to th e u n d is tu rb e d gas i n th e shock tu b e , th e i n t e r f a c e betw een th e t e s t gas and th e d r i v e r gas
( c a l l e d th e c o n ta c t s u r f a c e ) fo llo w e d i t . When th e shock wave was r e f l e c t e d , 4
i t moved i n t o th e gas p ro c e ss e d by th e in c id e n t shock wave and e v e n tu a lly
met th e c o n ta c t s u r f a c e . Depending on th e impedance m is-m atch a t th e i n t e r f a c e , e i t h e r a shock wave o r a r a r e f a c t i o n wave was r e f l e c t e d from th e i n t e r f a c e i n t o th e t e s t g a s, and a shock wave was tr a n s m itte d i n t o th e d r i v e r gas
( 1 0 0 , 1 1 3 , 1 1 6 , 1 1 7 )o Y/hen th e r e f l e c t e d wave from th e c o n ta c t s u r f a c e re a c h e d th e end w a ll, th e .s t e a d y n o z z le r e s e r v o i r c o n d itio n s w ere d is r u p te d and th e u s e f u l " r e f l e c t e d shock" t e s t tim e ended«,
At one (som etim es no) s e t o f i n i t i a l shock tu b e c o n d itio n s f o r a g iv e n s e t o f d r i v e r c o n d itio n s , th e d r i v e r and t e s t g a se s were m atched a c ro s s th e i n t e r f a c e and no wave was r e f l e c t e d from th e i n t e r a c t i o n o f th e r e f l e c t e d shock wave w ith th e c o n ta c t s u r f a c e . This i s r e f e r r e d t o as
" t a i l o r e d i n t e r f a c e " o p e r a tio n ( r e f s . 1 1 3 ,115»118) and i t in c r e a s e d th e u s e f u l t e s t tim e u n t i l a decay i n th e d r i v e r gas p re s s u re re a ch e d th e shock tu b e end w a l l . The decay o r ig i n a te d from th e p ro p a g a tio n o f an ex p an sio n wave i n t o th e d r i v e r gas when th e diaphragm ru p tu r e d .
I t has b een found elsew h ere t h a t , alth o u g h th e wave r e f l e c t e d from t h e c o n ta c t s u r f a c e u p s e t th e flo w , i t s in f lu e n c e , and t h a t o f th e su b se q u e n t d im in is h in g r e f l e c t i o n s from th e end w all and th e i n t e r f a c e , d ie d o u t, and t h a t t h e r e s u l t i n g s te a d y r e s e r v o i r could be u sed u n t i l th e in f l u e n c e s o f d r i v e r p r e s s u r e decay were f e l t ( r e f s , 44» 1 1 5)* T his i s c a l l e d " e q u ilib r iu m i n t e r f a c e " o p e r a tio n . I t was shown t h a t th e p r o c e s s e s a f t e r th e i n i t i a l shock r e f l e c t i o n were weak, e s p e c i a l l y i f a r a r e f a c t i o n wave was r e f l e c t e d from th e i n t e r f a c e . I f chem ical
n o n e q u ilib riu m was n e g l i g i b l e and th e gas could be c o n sid e re d e i t h e r as n o n - r e a c t i n g o r i n ch em ica l e q u ilib r iu m , ( a t th e high n o z z le r e s e r v o i r te m p e ra tu re s and p r e s s u r e s found i n most shock tu n n e ls and, as w i l l b e shown l a t e r , a t th e c o n d itio n s i n t h i s s tu d y , th e gas was v e ry c lo s e to
e q u ilib r iu m ) th e w eakness o f th e i n t e r a c t i o n s allow ed them t o be ap p ro x im ated by an i s e n t r o p i c e x p a n sio n o r co m p re ssio n . This app ro x im atio n r e q u ir e d t h a t
4
one o f th e s te a d y s t a t e r e s e r v o i r p r o p e r t i e s ( a f t e r th e e f f e c t s o f t h e
c o n ta c t s u r f a c e i n t e r a c t i o n s d ie d o u t and b e fo re th e d r i v e r decay in f l u e n c e s w ere f e l t ) be known e x p e r im e n ta lly to s e t a f i n a l s t a t e f o r th e e x p a n sio n
o r c o m p re ssio n . U s u a lly th e p r e s s u r e i s m easured.
Hence, to c a l c u l a t e p r o p e r t i e s i n th e n o zzle r e s e r v o i r , two shock co m p re ssio n s and an i s e n t r o p i c ex p an sio n o r com pression o f th e t e s t gas w ere c a l c u l a t e d .
To make e s tim a te s and to s e t u p p er end low er l i m i t s , a com puter program was w r i t t e n t o make th e n o z z le r e s e r v o i r c a lc u la tio n s assum ing e i t h e r a n o n - r e a c t in g ( p e r f e c t ) gas o r a gas i n chem ical e q u ilib riu m ( r e f . 39)° Program s p e rfo rm in g a s i m i l a r ran g e o f c a lc u la tio n s were a v a i l a b l e ( r e f s . 4 0 ,4 1 ) b u t th e y u se m ethods o f s p e c if y in g th e chem ical p r o p e r t i e s o f th e gas Y/hich a re n o t as r e a d i l y a d ap te d to u n u su al gas m ix tu res ( p a r t i c u l a r l y th o s e p ro p o se d as p la n e t a r y a tm o sp h e re s).
H i s t o r i c a l l y , c a l c u l a t i o n o f flo w a c ro ss a norm al shock wave w ith c h e m ic a l n o n e q u ilih riu m was one o f th e f i r s t problem s c o n sid e re d i n th e f i e l d o f r e a c t i n g gas flow s* A number o f re fe re n c e s su rv e y th e te c h n iq u e s and t h e i r r e s u l t s ( e . g . , r e f s . 4 3 ,5 2 ) . The method u sed i n t h i s s tu d y
( r e f s . 5 2 ,5 3 ) was s e l e c t e d becau se i t gave a wide c h o ice i n th e s p e c i f i c a t i o n o f th e therm odynam ic and k i n e t i c models used to d e s c r ib e th e t e s t g a s .
I t u se d a m o d ifie d f o u r t h o r d e r E u n g e-K u tta i n t e g r a t i o n scheme ( r e f . 4 5 ) ,
c'-w hich tr)4e a u th o r c la im e d c'-would g iv e convergence and a n u m e ric a l s o l u t i o n i n a r e l a t i v e l y sm a ll number o f s te p s ( s e e s e c tio n
3
*4*5
Tor comments on t h i s a s p e c t o f th e p ro g ram ). C a lc u la tio n s were made o f th e e f f e c t s o f c h em ica l n o n e q u ilib riu m b eh in d th e in c i d e n t shock wave. The program was m o d ifie d t o make s i m i l a r c a l c u l a t i o n s f o r th e r e f l e c t e d shock wave. Acommonly u sed a l t e r n a t i v e to c a l c u l a t i n g chem ical n o n e q u ilih riu m e f f e c t s a c r o s s b o th shock waves i s to assume t h a t th e gas i s n o n - r e a c t iv e a c r o s s th e i n i t i a l shock wave and t h a t i t r e a c t s i n th e n o z z le r e s e r v o i r r e g io n a f t e r th e p a ssa g e o f th e r e f l e c t e d shock wave ( r e f s . 4 2 ,4 3 ) . As i s shown i n s e c t i o n 3 .3 .3 , th e assu m p tio n o f a n o n - r e a c tin g gas b e h in d th e i n c i d e n t shock wave i s i n v a l i d a t th e c o n d itio n s o f t h i s s tu d y .
H ow i n a h y p e rs o n ic n o z z le i s a ls o a w ell s tu d ie d problem ( e . g . r e f s . 4 4 ,4 6 to
50)0
The com puter program ( r e f . 44) u sed in t h i s s tu d y was ch o sen b ecau se o f th e f l e x i b i l i t y i n i t s s p e c i f i c a t i o n s o f n o z z le sh ap eand t e s t gas p r o p e r t i e s (once a g a in w ith th e aim of u s in g gas m ix tu re s s i m i l a r t o p la n e t a r y a tm o s p h e re s ). I t c a l c u l a t e d a q u a si-o n e -d im e n s io n a l e x p an sio n o f a r e a c t i n g gas th ro u g h on a r e a d i s t r i b u t i o n . The a r e a d i s t r i b u t i o n c o u ld b e s p e c i f i e d by up to sev e n p o ly n o m ia ls . F o r sim ple c o n ic a l n o z z le s e x h a u s tin g a t medium R eynolds numbers i n t o an ev ac u a ted dump ta n k , as i n t h i s s tu d y , th e o n e -d im e n sio n al assu m p tio n i s a re a s o n a b le ap p ro x im a tio n . To b y -p a s s th e s a d d le p o in t s i n g u l a r i t y about th e n o z z le t h r o a t , th e program assumed c h em ica l e q u ilib r iu m a t th e t h r o a t and began th e n o n e q u ilib riu m s o lu ti o n as a l i n e a r
»
p ertu rb a tio n o The nonequilibriujm s o lu t io n could be s ta r te d upstream or downstream o f th e n o z z le th roat by t h i s method. The num erical in t e g r a t io n was perfonned by a m od ified Runge-Kutta technique ( r e f . 4 5 ).
C a lc u la tio n s o f flow over b o d ies moving at su p erson ic speeds are b a s ic to h y p erso n ics and a wide range o f techniques have been developed f o r
a v a r ie t y o f stup es,, Because a g rea t d ea l o f inform ation on th e chem istry and p h y sic s o f h yp ersonic floyr can be derived by t e s t i n g sim ple models such as wedges, cones and hemispheres ( s e e chapter 4)> only tech n iq u es f o r c a lc u la t in g such flo w s are d is c u s se d here,,
As f i r s t approxim ations and to g iv e lim it in g c o n d itio n s , non r e a c tin g (p e r f e c t g a s) and eq u ilib riu m c o n d itio n s were assumed. For flo w over a wedge under e it h e r o f th e s e c o n d itio n s, th e shock wave i s s t r a ig h t , p ro v id in g th a t th e angle i t p resen ts to the flo w i s l e s s than th e detachment angLe (a s the an gle o f a wedge in c r e a s e s , i t appears to
4
th e flo w to be more l i k e a b lu n t body, u n t i l , at the detachment a n g le , th e shock wave s e p a r a te s from the body n o s e ). P ro p erties o f wedge flo w s were c a lc u la te d by m odifying the normal shock wave equations in th e computer program o f r e f . 39 to in c lu d e momentum con servation normal and tr a n sv e r se to th e shock. This provided an e x tr a equation to accommodate th e extra, v a r ia b le o f shock „angle,,
Flow over a cone a ls o g iv e s a s t r a ig h t shock wave and perm its o f r e a d ily determ ined flo w f i e l d p r o p e r tie s ( r e f s , 62,63)0 A computer program
( r e f . 62) was used to c a lc u la t e d ir e c t io n a l d e r iv a tiv e s to g iv e a f i r s t approxim ation to a cone a t a sm all a n g le o f a tta ck , as w ell as axisym m etric flo w p r o p e r tie s,, A lso, i t could be used in combination ’with a method o f
t
c h a r a c t e r is t ic s program ( r e f . 5 4 ).
The cone flo w program was one o f th ree programs (cone, b lu n t body and method o f c h a r a c t e r is t ic s ) developed at the If A3A Ames L ab oratories fo r n o n -r ea c tin g (p e r f e c t g a s) and chem ical equilibrium c a lc u la tio n s o f flo w
o v e r v e h i c l e s w ith complex a f t e r - b o d i e s „ How n e a r th e body n o se c o u ld be c a l c u l a t e d u s in g th e b l u n t body o r cone pnogratn, depending w h eth er th e n o se was b l u n t o r s h a r p , and co n tin u e d downstream u s in g th e method o f
c h a r a c t e r i s t i c s program . E q u ilib riu m thermodynamic p r o p e r t i e s o f 13 g as m ix tu re s f o r u se w ith th e s e program s were s to r e d as t a b l e s o f s p l i n e - f i t t e d p o ly n o m ia ls , w hich were d e riv e d o r i g i n a l l y u sin g th e method o f r e f e r e n c e 5 2. M o d ific a tio n s to a llo w more g e n e r a l s p e c i f i c a t i o n s co u ld be made sim p ly , b u t w ere u n n e c e s sa ry f o r t h i s s tu d y as p r o p e r t i e s of a l l o f th e m ix tu re s used were in c lu d e d i n th e t a b l e s .
The -Ames b l u n t body program ( r e f s . 54»55) u sed th e in v e r s e method to s o lv e f o r th e body s h a p e , g iv e n th e shock sh ap e . I t allow ed s p e c i f i c a t i o n o f th e shock and body sh ap es by p o ly n o m ials and had an i t e r a t i v e scheme which m o d ifie d th e sh o ck sh ap e c o e f f i c i e n t s u n t i l th e c a lc u la te d body sh ap e a c c u r a te ly m atched th e s p e c i f i e d sh a p e .
«
The m ethod o f c h a r a c t e r i s t i c s program allow ed c a l c u l a t i o n o f embedded shock waves (c o m p ressio n c o m e r o r f l a r e ) , ex p an sio n waves and c o a le s c e d shock w aves. I t was found to b e in a c c u r a te when f l a r e and bow shock waves i n t e r s e c t e d b u t o th e rw is e ad eq u ate f o r a l l th e sh ap es u sed i n t h i s s tu d y .
Model flo w s w ith ch em ical non e q u ilib riu m have been s tu d ie d by many w o rk e rs, b u t, b e c a u se o f th e d i f f i c u l t i e s of c o u p lin g a m u lti-c o m p o n e n t, m u l t i - r e a c t i o n ch em ical system t o an a lr e a d y c o m p licated s e t o f flow
/ e q u a tio n s , and th e v e ry lo n g tim es r e q u ir e d on a high sp eed com puter t o s o lv e th e e q u a tio n s , few c a l c u l a t i o n s have been made. I t i s u n d er th e s e c o n d itio n s t h a t th e "Freeman" gas m entioned i n s e c tio n 2 .1 .2 becomes su ch a v a lu a b le method o f a p p ro x im a tio n ,
N o n e q u ilib riu m b lu n t body c a lc u la tio n s have been made by a number o f m ethods ( r e f s . 52,56 to 5 9 ). The main method used i n t h i s stu d y ( r e f . 52) i s an in v e r s e one w ith th e " C o rn e ll" method o f s p e c if y in g th e ch em ical
p r o p e r t i e s o f th e gas ( s e e s e c tio n 2 . 1 . 1 ) .
Such flo w f i e l d s have b een c a r e f u l l y s tu d ie d and s e v e r a l a p p ro x im a te " s c a lin g " te c h n iq u e s have evolved ( r e f s 0 6 0 ,6 1 ,7 7 ,7 9 ) . One o f th e s e was in c o r p o r a te d i n t o a com puter program ( r e f . 60) and was a v a i l a b l e f o r u se i n t h i s s tu d y . I t r e l i e d on a p r o p e rty common t o th e r e l a x a t i o n zones a lo n g a s tr e a m lin e and behind a normal shock: th e
e n th a lp y rem ain s n e a r ly c o n s ta n t, An an alo g y was e s ta b lis h e d by tr a n s f o r m in g and m apping th e no m a l shock s o l u t i o n o n to th e b lu n t body s tr e a m lin e s „
An a c c u ra c y o f 2$ i n th e shock s t a n d - o f f d is ta n c e compared w ith a f u l l n o n e q u ilib riu m c a l c u l a t i o n i s claim ed by i t s a u th o r s .
N o n eq u ilib riu m r e l a x a t i o n a lo n g a stre am tu b e co u ld b e c a l c u l a t e d from s p e c i f i c a t i o n s o f th e c o n d itio n s a t a p o in t in th e flo w and th e a r e a o r p r e s s u r e d i s t r i b u t i o n a lo n g th e s tre a m tu b e u s in g a v e r s io n o f th e n o z z le flo w com puter program ( r e f . 44)« The a r e a o r p r e s s u re d i s t r i b u t i o n c o u ld b e o b ta in e d e x p e r im e n ta lly , o r from e q u ilib riu m o r p e r f e c t gas c a l c u l a t i o n s u s in g th e methods d e s c r ib e d above.
IT onequilibrium flow o v e r c o n e s, wedges, and o th e r s h a rp -n o se d
b o d ie s have a ls o been s tu d ie d e x te n s iv e ly ( r e f s . 64 to 6 9 ). The d i f f i c u l t i e s i n programming any of th e s e te c h n iq u e s p re v e n te d t h e i r in c l u s i o n i n t h i s work and th e method o f stre a m l i n e r e l a x a t i o n was u sed .
The com puter program s l i s t e d above a r e d e s c rib e d i n d e t a i l ( te c h n iq u e s , in p u t and o u tp u t fo rm ats and sample in p u t decks and o u tp u t l i s t i n g s ) i n r e f e r e n c e 72* D e ta ile d r e s u l t s from th e program s f o r th e shock tu n n e ls T.1 and T. 2 a r e p r e s e n te d i n g r a p h ic a l form i n r e f e r e n c e s 84 and 8 3, r e s p e c t i v e l y .
3. SHOCK TUNNEL CALIBRATIONS
As d e s c r ib e d i n c h a p t e r 1, c a l i b r a t i o n o f th e f r e e p i s t o n sh o c k t u n n e l s i s an e s s e n t i a l p r e li m i n a r y t o t e s t i n g v e h i c le m o d e ls 0 A summary o f t h e sh o ck t u n n e ls and a re v ie w o f p r e v io u s work p re c e d e s d e s c r i p t i o n s o f t h e c a l i b r a t i o n s c o n d u c te d i n t h i s s tu d y . A d e s c r i p t i o n o f th e
e x p e r im e n ta l te c h n iq u e s i s g iv e n i n a p p e n d ix B. 3 d The A.N.U. F re e P i s t o n Shock T u n n els
1 r ' r ' ' ~ r T — 1 T ' T 1 ■ ■ — T ■ ■ r 1 ’■ ,r e r
T hree f r e e p i s t o n sh o ck tu n n e l s w ere u s e d i n t h i s s tu d y . T h e i r p h y s i c a l d im e n sio n s and t y p i c a l o p e r a t i n g c o n d i tio n s a r e g iv e n i n t a b l e s 1
and 2. The t u n n e ls T d and T02 w ere o p e r a b le b e f o r e t h i s s tu d y commenced, b u t To3 was f i r s t a v a i l a b l e f o r u s e e a r l y i n 1970°
The d i s t i n g u i s h i n g f e a t u r e o f t h e f r e e p i s t o n sh o ck tu n n e l i s t h a t i t u s e s th e momentum o f an u n c o n s tr a i n e d p i s t o n t o g e n e r a te h ig h te m p e r a t u r e , h ig h p r e s s u r e d r i v e r g a s ( r e f s . 119, 1 2 0 ), r a t h e r th a n th e m ore d i r e c t and
«
c o n v e n t io n a l m ethods o f e l e c t r i c a l o r c h e m ic a l h e a t in g ( r e f . 114)* B r i e f l y , i t a c h ie v e s t h i s as f o l l o w s 0 The d r i v e r end o f t h e tu n n e l ( u p s tr e a m o f t h e h ig h p r e s s u r e d ia p h ra g m ) c o n s i s t s o f a r e s e r v o i r and a c o m p re ssio n tu b e s e p a r a t e d by a f r e e - s l i d i n g p i s t o n , w hich i s i n i t i a l l y h e ld on a l a u n c h e r
a t th e u p s tre a m end o f th e c o m p re ss io n t u b e . The c o m p re ssio n tu b e i s e v a c u a te d and t h e n f i l l e d w ith h eliu m d r i v e r g as ( p r e s s u r e = 16 p s i a , t y p i c a l l y ) . The r e s e r v o i r i s f i l l e d w ith h ig h p r e s s u r e a i r (700 p s i , t y p i c a l l y ) . The p i s t o n
i s th e n r e l e a s e d and i t i s a c c e l e r a t e d down th e co m p re ssio n tu b e by th e d i f f e r e n c e i n th e p r e s s u r e s on i t s two exp osed f a c e s . At t h e p o i n t w here t h e p r e s s u r e s
on b o th s i d e s o f t h e p i s t o n a r e t h e sam e, th e p i s t o n h a s q u i t e a h ig h v e l o c i t y (3 0 0 f t / s e c , t y p i c a l l y ) and i t c o n t in u e s down th e c o m p re ssio n tu b e u n t i l i t s momentum h as been l o s t i n f u r t h e r c o m p re ss io n o f th e h e liu m . The p r e s s u r e a t t h i s s t a g e (7000 p s i , t y p i c a l l y ) i s j u s t s u f f i c i e n t t o b u r s t th e d ia p h ra g m and c u s h io n th e p i s t o n t o a g e n t l e h a l t a t th e end o f th e c o m p re ss io n t u b e , w h ile t h e c o m p re s s io n - h e a te d h e l i u n a c t s as d r i v e r gas f o r th e sh o ck t u b e .
Each tu n n e l was equipped w ith p r e s s u r e gauges a tta c h e d to th e r e s e r v o i r and th e co m p ressio n tu b e s , which were used t o s e t th e f i r i n g c o n d itio n s f o r a g iv e n diaphragm m a te r ia l and th ic k n e ss* P r e s s u r e s c o u ld be s e t ’w ith an a c c u ra c y o f 1 ;o* This ’was f o r s h o t - t o - s h o t r e p r o d u c i b i l i t y , th e v a lu e o f th e a b o s lu t e p r e s s u r e b e in g unim portant once c o r r e c t f i r i n g c o n d itio n s had been e s ta b lis h e d ,. S t a t i c b u r s tin g p r e s s u r e s were t e s t e d w ith an h y d r a u lic pump f o r a random sam ple o f diaphragms* They were r e p r o d u c ib le w ith in 5i° when d i f f e r e n t b a tc h e s o f m a te r ia l were in v o lv e d and I 70 f o r m a t e r i a l from th e same b a tc h .
The shock tu b e was ev acu ated u s in g a r o ta r y pump to l e s s th a n O0O5 t o r r and th e n f i l l e d w ith t e s t gas u sin g a mercury column as a. p r e s s u r e gauge* A ccuracy was t y p i c a l l y 0.0 2 in Eg i n 1 to 10 i n Hg, o r b e t t e r th a n 2^o. The le a k r a t e ’was such t h a t no o b se rv a b le change i n p r e s s u r e o c c u rre d i n 15 m in u te s , ( th e lo n g e s t checked i n t h i s s tu d y ) , w hich compared fa v o u ra b ly w ith th e 3 m in u tes o r th e r e a b o u ts r e q u ir e d to f i r e th e tu b e a f t e r i s o l a t i n g
th e sh o ck tube*
The i n i t i a l shock sp eed was m easured by re c o r d in g th e tim e , o r tim e s , betw een th e a r r i v a l o f th e shock wave p re s s u re r i s e a t two o r more
p i e z o e l e c t r i c p r e s s u r e tr a n s d u c e r s s e p a r a te d by known d i s t a n c e s . The tr a n s d u c e r s were made from 0*125 i n d ia m e te r , PZT-5A ceram ic c y lin d e r s and were m ounted
f l u s h w ith th e shock tu b e s i d e wall* Each tube had a t le g is t t h r e e p o s i t i o n s a t which th e tr a n s d u c e r s c o u ld be mounted* The tim e was re c o rd e d d i r e c t l y on an o s c il lo s c o p e ( c a l i b r a t e d w ith a T e k tro n ix ty p e 181 Time-Mark G e n e r a to r ) , on a M arconi C o u n te r/F req u e n cy M eter ty p e TP1417A, o r a f t e r p u ls e s h a p in g , on a R acal M icrosecond C hronom eter ty p e 5M5*
x
E xperim ents showed t h a t th e s h o t - t o - s h o t r e p r o d u c i b i l i t y o f th e i n i t i a l shock speed was b e t t e r th a n 2vb*
P r e s s u r e b e h in d th e r e f l e c t e d shock wave was m easured w ith a SLLI ty p e HPZ-1 4 tr a n s d u c e r on T. 1 and T.2 and a K i s t l e r ty p e 6201 t r a n s d u c e r on T*3. The d e v ic e was mounted f l u s h w ith th e s id e w all o f th e shock tu b e ,
a p p ro x im a te ly 0 .7 5 i n from th e n o z z le t h r o a t i n T.1 and T.2 and 1 .5 i n from th e t h r o a t i n T .3 . F o r a c c u r a te and a b s o lu te measurements o f th e p r e s s u r e i n t h i s re g io n , th e tr a n s d u c e r was c o n n ected to a SRI PV 16 No. I0O5O e le c tr o m e te r and th e r e s u l t re c o rd e d on an o s c illo s c o p e . Accuracy i n
d e te rm in in g a v a lu e from th e o s c il lo s c o p e tr a c e s was ab o u t 5i°* F o r m o n ito rin g p u rp o se s o n ly , th e tr a n s d u c e r was sh u n ted by a condenser (0 .1 y u F ),
The n o z z le s l i s t e d i n t a b l e 1 had c o n ic a l p r o f i l e s and, w ith th e e x c e p tio n o f th e n o z z le used on T .1 , u sed th r o a t i n s e r t s c o n s tr u c te d from co m m ercially a v a i l a b l e , tu n g s te n - c a r b id e w ire d i e s , The n o z z le t h r o a t
i n s e r t on T.1 was made o f s t a i n l e s s s t e e l o A n o zzle w ith a p a r a b o lic p r o f i l e wan a ls o a v a i l a b l e f o r u se on T .1 , The n o z zle e x i t - t o - t h r o a t a r e a r a t i o s u sed i n t h i s s tu d y were 560 on T01; 155 o r 5^0 o r 1300 o r 5000 on T .2 ; and 720 on T.3o
. The t e s t s e c t i o n s o f th e tu n n e ls T.1 and T.2 were equipped w ith h ig h q u a l i t y S c h lie r e n windows and v acu u m -tig h t e l e c t r i c a l c o n n e c tio n s and could be used w ith e i t h e r th e shock tu b e o r w ith one o f th e n o z z le s .
The t e s t s e c t i o n and dump ta n k o f each tube ( f o r shock tu n n e l work t h i s re g io n exten d ed to th e n o z z le t h r o a t where a th in "M ylar" diaphragm s e p a r a te d i t from th e sh o ck tu b e ) were evacuated w ith a r o t a r y ty p e pump to a p r e s s u r e o f th e o rd e r o f 0.1 t o r r . I n a d d itio n , T.2 and T.3 had o i l d i f f u s i o n pumps i n s t a l l e d , which e v a c u a te d th e t e s t s e c tio n s to a p r e s s u r e o f a p p ro x im a te ly
0.001 t o r r . /
The t e s t g a s e s , w ith t h e e x c e p tio n o f a i r , which was o b ta in e d
d i r e c t from th e C an b erra atm o sp h ere, w ere s u p p lie d by Commonwealth I n d u s t r i a l Gases L t d . , who s p e c i f i e d 9 9 * 9 9 p u r i t y f o r helium and arg o n , 99*995/* f o r n itr o g e n , 9 9 * 5 Tor oxygen and " b e t t e r th a n 99*0^" Tor carbon d io x id e 0
No s p e c ia l c a r e beyond an o c c a s io n a l washing o u t w ith hexane was ta k e n to keep th e tu n n e ls c le a n .
