Superorbital entry heat transfer including atomic line radiation and massive blowing

In P a r t i a l F1dfiPlment of t h e Requirements Par t h e Degree of

Aeronautical Engineer

C a l i f o r n i a I n s t i % u t e o f Technology Pasadena, C a l i f o r n i a

June, 1968

The author expresses his appreciation to D r , Mi%eh Thonas, Dr, Bill Rigdon, and *ofessor Lester Lees for their enlightening

&seuasions and t h w ~ h t f u % . ~ o m e n t s which have had a significant influence on the development and scope of this paper,

This resemch WEIS sponsored by the NASA LaaagPey Reaemch

Center mder Contract go, Hug-7757 and by $he Douglas Aircrafk Company Independent Wesemch md Development _Promm, e n t i t l e d

Wansf er (80301-010 39113 ) ,

At s u p e r o r b i t & reentry veboeities radiative heating is the dominmt mode of heat t r a n s f e r Lo the stagnation region of b l u n t reentry vehicles, The radiative heat transfer rate at the w a l l is detemined by the tenperatwe profile %hsrough t h e shock layer which depends on the net radiative $ransport through both %he d s e o u s inner region adjacen$ Lo the w a l l m d the outer region vhere eon~eetion and radiati-re trmsport processes dsniinate $he enera transfer, \$hen a%omsi.c line %ransitions are included a very small s c a l e 1enp"bh for radiant enerm t r m s ~ o r t is intraduced which r e s d t s in characteristic changes in the shock layer f l o w . The inclusion of atomic line transi- Lions necessitates eonsideration 09 self-absosagstion of radiant enera and results in the e o q l i n g sf radiant energr trmsport m d c o n ~ ~ e c t i o n a d eonduetion transport processes even f o r relatively s m d l vehicle nos e r a d f i

.

In the fomdation o f this problem no restrictions a r e placed on ^%he v a r i a t i o n of %he a b s o q " s i g coefficient ~f the m e d i u w i t h wavelength. 11s cn illustrative e x m p l e the e f f e c t s of nose r a f i m , w a l l refiectidty, and massive blowing have 'been coraputed for t h e shock Sayer f l o w f i e l d o f a s@erfed$y blunted vehicle a% 50,008 feet per second md 280,888 foot altitude in air,

Abstract

Table o f Contents

List sf Figures List O$ Symbols

TITLE

11. D i f f e r e n t i e l Equations: Application to the Pomssd Stagnakion Region of a S p h e r i c d I y Blunted Vehicle

I V mied Solutions f o r Atmospheric E n t q : Va = 50,000 f p s , h = 200,000 E%

References

Appendix A

-

^Gas Properties Table %

Figures

1 Coordina%e SysLen and Shock Layer Flow F i e l d ( schemati e )

2 Shock brer Flov F i e l d for 1 , 0 foot Eose Radius With go Blowing

3 Shack Layer Plow Field for 2,5 foot Nose Radius With No Blowing

4

Shock Laxer PIOW F i e l d for L O , O foot Nose Radius With No Blowing

5 ^{Shock Layer Flow} F i e l d for 15,O f o o t Nose Radius WiLh No Blowing

6 Variation of NeL fiiasion and Owe-Sided F l u e s Across Shock Layer With No Blowing

FP I Spectral _Wadiat i o n I n s i d e a ~ t Xiorma$ t o Wa11 f gar

1-0 foot Nose Radius With No Blowing

8 S p e c t r a l Radiria,%ion Incident _Nsmal Lo _'Wall for 10,0 foot Nose Radius 'With No Blowing

9 In%egra%ed V * -+- F for Sbock-Layer Radia%fon Traveling

~ o w a r d t h e wall , o ) ~ a ~ u e t t e d

o

, U em from the

$0 Heat W a n ~ f e r Rates &S a Function of Hose Radius With Ms Blowing

11 Reduction in Radiative Flux to ;t-Jall h e to Radia%ive and Csnvecti%be Coupling

12 Composition o f Badiative Heat FLUX at $he Wall as a fine$ion sf Hose Radius

13 Shock Layer Tmperatwe Bofiles Showing $he E f f e c t o f Wall R e f S e e t i v i t y

181 Uncoupled Flow F i e l d Solution f o r lOs0 foes$ Rose Radius W i t h Blowing

PAGE

23

24

2 5

26

27

28

29

30

31

32

33

3

4

3 5

1 5 ^Shock h y e r Flaw Field for 1 - 0 foot Hose Radius With Blowing

3-7

^{Varia%ion of Wet mission and} One-$i&ed F l u e s

Across Shock Layer Wf%h Blowing

18 Spec$r& Contribdtion t o t h e Radf a t i s e Kea%

Wansfer Rate for 10,O foot Hose Eadius

19 Absorp&io~ Coefficient sf A i r a% %b, atm W e s a m e

and 1SfBQO"M

PAGE

37

spectral in%ensity o f black body specific he&

racik.ia%ive f l u vector

r&iative flux In posi$ive $-direction radiative f l a in negea-$ive p-direction alt f eUde

intensity of r a d i a t i o n total % h e m a eondue%ivity

Pinew spectral absorption c o e f f i c i e n t P1anck me= absorg%ion coefficient presswe

heat Lrwsfer sate a% m11

A dT/dy

distance from boar cenkerlina R e p o l d s Ember

b&g nose r d i u s

l i n e sf sight path lcngLh tmperatme

velsei%y pmallel Lo body veloci%y noma1 to body

freestre= velocity a o t ~ n e e n o r m 1 to bow

Y distance norm1 to body

T rsdiakion-convection coupling pmmeter

8 angle be%ween y mi% vector and l i n e of sight path LJ viscosity

P density

Q Stefan-Wltzmann constan%

w wve nmber

Subscripts

ta spectral

For atmospheric cn%ry veloei$fes above escape speed thema1 radiakion signifieanm%ly alters the _flaw field about b1mt enLry bodies. The predominant effect of the radiance sf the hot gas eap is the d.n%ro&uetion of ent"na1py gradients in the outer shqck layer, Thus, when radiative transfer is important, the flow field can no.$ be sepwated i n t o the usual isoenergetir i n v i s e i d ou%er shoek lwer and a non-adiabatic viscous boundug layer, This effect has bean %rested by others using either the gray gas approximation"' or polynomial expres- sions for the velocity and eoncentration p r o f i l e s and n m a r i e a l ia%e- pation over &equeneg of radiation'2'. It is now ^well knom that use of the g a y gas approximtisn in radiative transfer c8leulations for high-taperaewe air results in serious error, Also the difficulties associated with inlegrati~ over frequency while also integrating .$;he

eonsemak ion equations are obvious ( ~ o s h i zaki and Wilson were limited to abou% 28 frequency p o i n t s ) .

As a rasul% of these difficulties

maw

approxba%e tecBBniques b v e been developed to solve rdiative _gssmmic problens (31

9P+1961

In general the accmscy o f t h e vmious so1uLlons is u&n

f ligb% ewerbents have been made above 36,080 fps (EASA~ s WoJect PIRE) where couplianrp i s ra%;\zar weak, I n lieu o f e w e r b e n data f o r

shoek layer tempera%ures of approximate^ $5,00O0K and Pwge physical s%xe, more exact ce%.lcdakfons r a l s f n f n g complete spectral detail with as few flow field approxba%ions as possfble are required, I n pm%icu- lar atmfc l i n e e d s s i s n nust be included since, clue t o t h e very large

values of absorption coefficient at the center of these lenes, an e*remely ma11 scale lengkh for t h e radiant e n e r a transport is introduced,

I n j e c t i o n into %he b ~ u d a q layer is unavoidable i n t h e flight regime considered here since the heat transfer rates eweotm$ered

-

^on

the order of 10 3 vatts/cm2

-

will necessitate either ablative heat

shields o r transpiration esoXim for thermal protection, Pngection ^of foreign gas greatly eomplica&es the analysis proeedwe because $he absorption coefficient of %he gas-sir mixtwe, on which $he radiative transport processes critically depend, is a strong fuwc%isn of _{t h e}

species _present and %heir concentrations, However, the first order effects of injection on the sheek layer $ 1 field s%ruetme ~ can be dekemined by considering air as the injec$ed gas, and this approach will be used here,

In the present investigakion of these phenmena t h e p r h a ~ mphasis has been on r e t s f n i ~ as eomplete spectral d e k a i l as posefble, thereby m&ing f u l l use of existing knowledge of radiative mechanisms, The shock layer flow i s considered to be in local chemical and t h s m o -

ie equilbbrim f o r the entry conditions chosen, _The e n e r a

equation is satis%fer% by using a n ftera%lve techiqua axid _assming one- dbensisnality of the radiation field, Molecular heat conduction and viscous monaentw transpofi are retained across t h e en%ire shock layer,

The solutions sb-abained reveal $he de%ails of the shock layer flaw field s t r u c k w e and rdiakive transport processes as well as _Lhe convective a d radiative heat transfer rates,

11. DIPFEWEliTIU EQUATIONG: APPEICATIBB TO TEE FORWmD STAGHATIOM REGION OF A

SPEmICGLY BLUmD VEHICLE

Consider t h e shoe% layer B 1 m field about the forward stagna- tion point of ⁸ blunt body shorn schematically in Figwe 1, In order Lo =count f o r radiative t r a n s p o r t ^of enerm %he edfre shock layer m w t be considered,

For ~ - 8 a a a ~ - s t a t e , axismetric flaw $ha t h i n shock layer equations are the following (1)

60ntfnuity

asg

a

^u

l a a~

+

+

pvc

--

= u

22

+ P ( ~ ) +

+

^(rlt

---I - ^v

^{e F}

Puep

I G

P 3~ ax 33-

where -+ F is t h e radiative flux vec$or, The coupling be%;ween the radia-

t i v e enerw %rawsport and t h e okher processes is evidenced by the inclusion of $he net radiative energy loss per unit v o l w a , V * -+ F , in

t h e energy equation, The evaluation _of this t e r m is considered in Seetion 111,

These aquakisns can be reduced t o ordinary d i f f e r e n t i a l

equatisns valid near the stagnation s%remPine by noting tb&L t o firs%

order in x

The continuity equakion then becomes

S u b s t i t u t i n g Eq,

5

in the momentm and snerm e q a t i o n aria neglecting terms of order x yields the f o l l m i n g :

Msmen%m and Con%inui%y

T d

p

-

"""

-

^d"%

P

w

^d~

( A , , - * f

(7)

where, after Referenee 1, %p/ax, has been replaced by its value i m e d i - a t e l y behind a spherical shock nem the sLagnatisn s t r e m l i n e ,

The boundmy conditions on Eqs

.

^{6 and -re at y -. O}

DV "" PWVW

1 a(ov)

m - s

P

Qf

" ^"

^TW

where 6, the shock s$md-off d i s t m e e , i s t o be deternine& e o m t h e solu%ion,

For cases i n which blowing i s absan% i n t a p a % i o e of E q s , 6 and 7 i s started at t h e d l by assming values f o r $he convsc-$;fve heat trwsfer rate an& shew stress and continues away from t h e wall

~ % i l %be shock ^{( Q V} - - O P m ~ w ) i s ~ e a c k l e a ~ "6"8b~lkl.$. V ~ ~ $ U B B %he B B ~ % m f e s i o n as a f m e t i o n o f p v a r e uses i n t h e s o l u t i o n of t h e enerm equa%ion to obtain soku%ion C W V ~ B f o r the tempera%me. Boundary eon- d i t i o n s on T and -a at the shock are matches by repea%ed adgustment of

$he esnvec"$ivs heat transfer rats and shew at "$e ^wall,

m e n mssive blowing i s considered some modificstfon t o this procadme is required, I n % e g r d s01utions 0-2 both t h e rnmanem and e n e r a equations can be e a s i l y obtainede For i n s t a n c e , t h e solukion of the e n e r a aquation i s

where

This _equation shows %hat small errors in %he ehsfea of ~ ( o ) cause the computed v d u e of ~ ( y ) t o depmt e w o n e n t i a l y from the correct v d u e of

&(y) I n regions where p v is greater than zero, Since pvc /A is of the P

order o f P Lo 1 0 for the case considered here, the error grows very fast. The situation i a m a c t l y _%he a m @ when %he momsntu equation is considered, In general the requirment that both o f these equations be in%egrated simUtaneous1y means %ha% v s y i n g initial v&ues of $ha convective he& transfer rate and t h e she= streso a$ the wall is not a practical way t o satis* boundmy conditions imposed 8% %be shock, I n order to overcone this difficulty, nmerical integra%ion fs started at pv = 0 (i,e,, away from the w a l l ) and proceeds in both d i r e c t i o n s , m i l e this procedwe eibhinakes the n m e r i c a l integra%ion instability i n the b;lbom region, it r e q d r e s that fom i n i t i a l V ~ U C S be f%era%ed upon ( ~ ( p v =

o ) ,

^{u ( p v} = 01, d ~ / d y ( p v = 0 ) and the shew stress at pv = 0 ) and $ha% %he boundaq conditions on T and u be m&ched at both t h e w d l and the shock, The addition of two more initial values quad-- r u p l e ~ the complexity of the i t e r a t i o n procedwe required since there a r e now s i d e e n deriva%ives sf the end v d u e s i n s t e a of fom as when integration is s t a r l e d a% the w a l l ,

In order to evduake the net raaiant energy emission, B * + P ,

the s c t u d shock layer g e m e t v is replacad by a plane pwalPe1 layer, i n f i n i t e in extent, w i t h properties vmying only in t h e y-arection, The net emission from this layer is then given by

where F denotes the f l u of r&iant enera in the y-afrection, _This approxiaatien is in accord with the _resvlts of who computed t h e f l u x in the x-direction employing the gray gas assaption but _not the plane pwallel shoek

lwer

approxhatfon, E i s reaul$s indfca$e that %he contssibu%ion ^$0 V * + P f i g s a n t h e x-dirsctfon flux 2s smll, B e

plane pmalLel shock layer approx-tion is mare valid when a$omic l i n e s and d t r ~ v i o l e t photsionizatfon eontinurn are include8 since t h a t p& of %he radiation s p e ~ % r m behaves i s % . an opaque mmner (except new the bomdmlss) and o d g radiation from newby poin%s is hportane, Splitting the _flux into p o s i t i v e and negea;$ive y-cmponen%a reslnlts i n

F(Y

1

= ^~'(y)

-

~ - ( y ) ( 9

1

In Eq, 10 8 is $ha angle between a line sf sight pa%k fron the edge sf the Payer to the y-sta%ion an& the _y-seetor along _{t h e} stagnation s t ~ e ~ l i n e (see Figme 1). I is the specLsa1 i n t e n s i t y of r a & % a l i o n at

@

y t r a v e l i n g i n the ⁸ d i r e c t i o n and is given by integration of t h e Wbert-Bouguer l a w for a nsn-scattering medim

where a denotes distance slow the l i n e o f sight path,

The bomdav conditions on ^Eq, 11 depend on the optical proper- ties sf the m P 1 , T h e e E i m P t i w w d 1 conditions are considered hers, The usual condition b p o s e d is $ha% %be mB1 is perfectly transpwent.

This b p L i e s t h a t

I ~ ( o , B ) = 0 f o r all w and 0 '8 5 n / 2 (l2a>

The o%her two limiting eases a r e a perfectu black w a l l o r a perfectly reflecting w a l l . The radiative b o r n d a y conditions f o r these two eases w e as f 0110~s ;;:

black wall

l o ( 0 , 8 ) = B ~ ( T ~ ) ^{f o r all w and O 2 8 c n / 2}

ref l e e t i n g w a l l

I ( 0 , 8 ) = 1 ~ ( 0 , n - 6 ) f o r a l l w a n d 0 f3 312

W

- -

^(3-2e

1

Eqs, P2a, b, e set t h e i n i t i a l conditions f o r t h e intensity of radiation leaving t h e wall. The bomdasy csndi%fons for the radiation t r a v e l i n g Loward the w d b are usually set by t h e conditions of a trans- pmen% shock and no mission from the breestrem &he& of t h e shock.

Bowever, it should be recognized that some Braetion of %ha r a d i a t i o n

L h s b leaves the shock Payer will be absorbed by the freestrem thus raising its temperatme and increasing i t s emission, A quantitative esLima%e sf this effect has y e t to be made and the a s s m p l i o n of no emission from the F r e e s t p e a .%rill be re%ained for hi^ investigation.

The boundary condition for the radiation traveling toward t h e wall i s Lhus

I ~ ( S , B ) = 0 f o r all o and r / 2 8 - c n

.

⁽¹³⁾

These equations permit t h e evduation sf the net emission from an elmental unit volme of gas, provided the temperature profile is

hewn, Since the temperature depends on the value of the net emission, which i n t u n depends on $he %emperra$ure profile across the entire shock layer, an iterative technique is mployed in this invesliga%ion, Assmad tabular vdues of the net m i s s i o n as the fiiammction of p v are used in the solution of the conservakion equations $0 obtain solution cmves for the t a p e r h u e . The first set of these v d u e a i s obtained 'by empuking

B + F $OF t h e -coupled kemperature profile, i,e,, t h e solution of the conserva%ion equations wi%h V + P ^f 0 , With the temperature profile

computed, E q s ,

8,

9 , 1 0 , and 11 are used with the appropriate boundmy conditions a% $he w i p l l to c o m p t e new values for %he net emission, Eq. 11 is solved using second-order Rugge-Ku%$a for the most p&,

However, d e n %he Intensity at any frequency becmes close to the black- body value, the s s p p t o t i c form of Eq, 11

is used, The use of this ~ s ~ p t o t i ~ egression for the intensity allows l u g e integration intervals to be used, tmically about ^1/100th the shock layer thicitness, rather than intervals of the order l / k o

required P s r integration stability if t h e f u l l equa%ion were retained, The intensity for eight different s%a& d i r e c t i o n s $bough t h e Payer is found by integration along each path; f l u e s are t h e n delemined by Gaussim quadratwe. This cycle is repeated u n t i l t h e input and output net emission curves converge,

EV, TYPICAL SOLUTION6 FOR ATMOSPHmIG Y Vm = 50,000 i p s , h

--

^{200,000 ft}

me method8 described in Sec"$Ions II and III have been used t o obtain sslu%fons for atmospheric e a Q q at 50,000 f e e t per second and

200,000 feet altitude with a m11 $emperatwe o f 2000°K, The air prop- erties used are described in the Appendix, $aPsnspod of r d i a n t energy by a%omic l i n e transitions _{i a} included, In the following discussion sf the resdLs obtained pmtfcular atten$ioir% is paid t e a the _effect of the inclusion of a%omie line radla%ion,

Flow F i e l d Solutions

The effec$s of radiwt _enerm transpork on the shock _1ayer stmctme f o r mrious nose rdif and a tranapmant w d 2 are shorn in F i w e s 2, 3 , h-, and 4 , b i s s f s n of t h e m d radiation results in s eoa%-$inuak deerewe i n temperaewe as the gas B l o w s towwd the wall,

ma

sharp decline i n temperatme near $he shock i s due to the b d l d up of intensity in the vacum a L r a v i s l a t speekrm to the black bow limit, T h i s oecms a v e q s d l distance behind t h e shock wave due to the lmge v a u e s of the ku for t h e atomic l i n e s . The lmrr tempcaratma throughout the shock Payer r e s d t s in higher density and a earresponding deerease

in %he shock s$and-off distance, Shear s%ress _a% the WE&% i s increased and t h e velo~itg b o m d a q layer thickness decreased due to the coupling of radia%ion and cog%vec%ion enerm transport modes,

m e r a i a n t e n e r a trwsport Is shorn i n Figme

4

f o r a 10 foot nose radius, The net emission at the shock is _only slfghtLy lwgea than

the Lranspwent emission into 271 steradians, i , e , , 2

kp

( T s ) ^aTs

'.

A s t h e f l u travebiw toxwd the wall, F

-

i" builds up, the net emission f a l l s r a p i u g due %s self absorption, The efiremely large value of V * + F at

%he shock (about 250,000 waLts/cm 3 ) produces t h e steep declines in tem-

perature at the shock wave evidenced in t h e flow field aolu%isns, Since the temperatwe decreases con%inuoualy as t h e gas flows toward the bo43-, F- does not increwe monolsnieally _{w i t h} increasing distance from the shock* The absorption spike close Lo t h e wall is due entirely to ab- sorption of t h e F- flux in the boundary barer, Because of the small L h i c h e s s sf the _bomdary layer, however, the reduetion of t h e radiative heat transfer rate at the w a l l is _sml%, For large nose radii the eon- version of r d i a t i v e to eonveetive _enerw in the boundary Sayer has a

significant effect on $he ssnveetive heat Lransfer r a k e ,

Figmes 7 and 8 present the spectral radiakion incident- normal to the w a l l for nose radii of" 1 and 1 6 feet, respectively, The centers of" the vbeum ultraviolet lines _are seen to be strongly self-absorbed while the wings contrfbute s i g n f f i c a n t u to %he flux at t h e w a l l , The

infrared and visible lines, t h w g h no% self-reversed, w e somewhat self-absorbed at the lmger nose radius,

Figme 9 shows %he contribution to t h e net emission from %he flux in the negaLive ;y-direction at a position O , 1 1 c m f r m the w a l l for

$he PO foot nose radius, A t %his position the a a l m i i e Pines have already been self-reversed and the dominmt mode of radiant energy t r a n s p o r t is d t r a v i o l e L merged-Sine and photoionization continurn absorption,

Heat Wansfer Rates

The dependence of the radiative and convective hea%ing rakes on nose radius wikhout b l m f n g i s ahom in F i g w e 10, The dashed lines indicate the ucoupled heating rates, obtained by ignoring the radiation tern In the enerw equation. There are two conpensating e f f e c t s tending to pertmb the convective heat transfer rate; the reduced enthalpy

po%entid due Lo radiazive cooling tends to decrease $he convective heaking rate, while radiant anera absorption in the boundary layer tends to increase it, m e n atmic lines are eonsidereel t h e latter

effect domf nates _except at small nose r&ii where boundary layer abserp- t i o n i s smll. Eowever, if atomic line radiation is neglcctedthaae

effects tend to cancel as shorn i n Referenee 2 ,

As discussed pre?f~iously, t h e radiative flux a% the wall i s

reduced due to radiative cooling, shock layer absorption, and b o u n d a ~ l ~ a r absorption; boaaaadmy layer absorption i s relatively unimportant except when large blowing rates are considered, These mechanisms pro- vide subs$antial reductions _{i n} the radiative flux to the s w f a e e ss

shorn in F i g w e $1, Were the reduction in radiative heat transfer _rate

i s correla%ed with .g, t h e ratio of total weoup%ed energy l o s s

$0 the to%a41 available freestrem enerm, The inclusion of atmic lines is seen to enhance the reduction in radiative heating t b o u g h the mechanism o f increased tempera%ura drop -edfa%ew behind the shock

of the heat transfer rates obtained for all cases in- vestigated is given in Table 1,

A s s h w n in Figwe 10 the rebeliative heat transfer does no% in- crease mono$oniealFky with increasing nose r d i u s , Radiative heating is

m a x i m w for apprsxhate1y an II foot nose radius at the f l i g h t eondi-

% i o n s eonsidered here, Figme 12 shows t h a t t h i s r e s u l t is due $0 a deerease I n the F l u from %he strong lines and ul%raviolet portion sf

r e a c h i n g t h e wall. This e f f e c t can be $raced to t h e lower tmperatwe at %he edge of the boundary Payer with increasing radius due to s a d i a t b e cooling,

The influence of wall reflectivity is shorn in F i g w e 13, The kernperatwe profile for %he PO foot nose radius shock lqyer _{w i t h} a totally r e f l e c t i n g wall (wall is p e r f e c t l y r e f l e c t i n g at all wave lengths) is compared to %ha% of a traospment wall, The to%all'y ra- fleeting wall is $%%a limit ease and ilPus%ra%es the m u h m e f f e c t due to wall reflectivity, The erithalpy potential across the boundary layer

i s increased due Lo absorption of $he r e f l e e t e d f1m and t h e eenveetlve heat LransEer r a t e i s increased, Since a u o s t half of the radiant enerm ineiden* on the w a l l i s v a e u ~ - u ~ % r ~ v i o P e t 3 for whieh all materi- a l s are n e w l y black, the Lotally reflecting xa91 does no% represent any r e d s u ~ f a c e . O f more practical concern is %he affect of totally

black walls, Calculation of the net r a d i a n t emission a s s m i n g a t o t a l l y black w a l l results i n values iaenticaab ( x i t h i n the accuracy sf t h e ca$- culations) Lo those obtained for tranepwent walls, T h i s r e s u l t i s not s w p r i s i n g since the radiative P 1 n emikted f r o m t h e cold -wall i s much less khan %he f l u x from the high temperature shock l a y e r , 1% can be concluded $hen t h a t %he raBia%ive boundary conclitions a t t h e wall have a negligible e f f e e L on the gas cap radia%ive transfer and the t r a n s p a - ent wall a s s u p t i o n is sufficient for eonputing the flow field s o l u t i o n ,

Strong blming sslutisns are especially important 8% high entry velscities because radiative heating will induce massive ablation sf the vehiele surface, Thus, it is imperative to understand %he affects of

l a r g e blmiw rates on the shock layer flow field strucLure and the attendant changes fn radiative and eonveetive hea% transfer rates, I d e d l y , of eowse, one w o a d _Like to csrm out this investigation using radiative and transporx properties for %he blown gas nixture which correspond to the complex molecu%ea present in the a b l a t i o n proaucts of most %beat s h i e l d material,

The blowing rate used in %he present study corresponds Lo _wha%

would be a classical shear 1 w e r ( p v

W W ^9-Vm >> 1) solu%ion if raaia%ive coupling were neglected, T h i s is ilPus"h;r%ed f n P i g w e

14

which shows the temperature and tangential velocity profiles obtained by integrating the conservation squations with V + F s e t to zero, The

region Prom the wall Lo a'oou% y ₌ 0 0 , 9 em has t h e properties of constant non-zero shear (as also f m n d in Reference

7 )

and temperawre; %he region of _maBm shear is displaced from the wall by the s m e mount,

sen

r a a a n t enerw $ransport is included strong reabsorption by tihe cooler i n j e c t a d gas r e s d t s in the flow fields shorn in

F i w e s 15 and 16 f o r 1 foot and LO foot nose r a d i i , respectively, For the 90 foot case eonveclive heat transfer is increased from zero

(fox- the uncouple& profile) $0 135 wa%ts/cm and 2 the radiative heating reauced _about ~ 8 % to k322 w&t%s/cm 2

.

^{If the b l o m gas} were emposed of abla%ion products including complex molecules which have sus%an%fally

bmger absorption coefficients t h a n air, the conversion of radiative $0

convective e n e r u would be enhanced and %he radiative h e a t i n g f w t h e r reduced ^,

The radiative energy t r a n s p o r t f o r this case i s s%ao~m in

P i g m e 17, It is seen that there is a n e t absorption s f r a d i a n t enerm through the injected gas r e g i o n causing F- to decrease significantly from its maximw value at y/6 approximately equal %o one-half, A corn- pmison sf t h e integral sf the f l u inefden% on t h e wall as s fmction of w

f o r %he blowing and no-blowing ten-boot nose radius eases is shobrn i n F i g w e

18,

It is evident from these curves $hat the reduckion in t h e r a d i a t i v e heat transfer to the w a x 1 for the blowing case is due to

absorption o f radia%isn in t h e merged ultraviolet lines and photoioniza- tion eoai%$inum by the _{b l m n} gas,

Toe stagnation-pain% shock-%eyer equations have been solved using detailed s p e e t r d caleula%isn ^{s f} t h e r d i a t i v e - c o n v e c t i v e

soupling. Atonic lines are included in t h e description of _{t h e absorp-} tion c o e f f i c i e n t and their spectrd structure i s retained twoughout

%he c a l e d a t i o n prscedme, The so1utions obtained indieate Lh& the inclusion of atomic lines efianees t h e rarsbiative cooling effect

resulting in decreased radiative flux a t ^the w a l l , Hmever, s l i g h % l y 5ncreased absorption in the bomdary Payer causes t h e convective he&%

transfer ra%es to increase above the _nomind value that qmuld be obtained if radiant e n e r a ZransporL were neglected,

The solutions obtained w i t h strong blowing indieate %ha$ r a d i - an% enerm transport can s&rongly modify t h e flow f i e l d strue%we 191

"$he b%okm gas region through absorption in the ul%saviole% p o r t i o n o f

the speetrm, S i g n i f i c a n t reductions in &he r a d i a t i v e heat transfer ra%e ocew due t o t h i s absorption,

me affect of r s d f d i v e boundary cond%tlon~ a$ the &;pa11 _on

shock $apes sdructme wss considered and f m n d to be s m d l f o r rara_bistic e n t q body properties,

Bowe, J, T, and Viegas, J, R e , a'601utisne of the Ionized Radia%ing Shoe$ hyerg Ineluding Reabsorption and Foreign Species EfPec$s, and Stagna%ion Region Hea% Transfer

MA

^TR

R-159 (1963) .

Roshiz&aL, H e and Wilson, K, H e , gJCog%aivective and Radiakfve Heat e a n s f a r Dming Superorbital Entry, ' ' A I M J ,

,

^{V o 1}

^5,

^25-35

⁽¹⁹⁶⁷⁾

^,

Anderson, J r , , J, D,, "'Bsn-gray Radiative Wansfar Effects on the Rsdia%fw SeagnaGion Region Shock b y e r and Etagnation Point Heat Wansfar

,"

NOLYE

67-104 (1967) .

Chapman, G , T , , "Heat eansfer in the 8tagna%ion-Point Eminar Ssmdary Layer with Mass Transfer and Radiant Enerm Kosorp%ion

1 )

Dirling

,

^{Jr ,}

,

^{R B., Rf gdon, $9. S}

,

and Thomas ^q, M a Sd$wnatiog%- Point Heating Ineluding S p e c t r a l Radiative ~ r a n s f e r , "

-

B~rdedSngs of the

1967

Beak %ansfer and Fluid Mechanics Institu%e, Stanford

Chang

,

^{P, and Id, G ,} Vineen%i, '"nvf s ~ i d Radiating Flow Wer a Blunt Body ^,I' Report SWMR No, 278, S t s n f erd, Calif,

,

Stanford University (1946

1

KubsLa, T,, and Pernandez, F , L , , " " ~ m d a r y - ~ a y e r Flows with Large Injec%iorsa and Heat T r a n s f e r

,"

^{A A $ U J ,}

,

^{Vol , 6, 22-28}

^(19681,

Thomas, M e , 9?Phe Spectral Linear Absorption Coefficients o f

Gases--Computer e o g r m SPECS (~189),'"epor% DAC-59135,

Saw%a k*lonica, California

,

^{Douglas AircraBL Coapany,} Inc , (

$966 1

^,

Wbese, W, L ,

,

Smith, M e W,

,

and Glennon, B e M a , "A%omic Wansition Probabilities," Vol, I, Eybogen Twough Neon, Rational Bmeau of

S%a~"edwds, MSmS-IqBS

4 (19661,

Griem, H , R e , MeGsaw-HI11 Book Co,

,

New York (

1964 1,

st ma^, 9, 6,

,

^{and Pyej-tt,} K , D,

,

^{Jr )} 1 P ~ h e o r e $ i ~ 8 b Study of Optical B o p c r l i e s

-

^Photon Absorption Coefficients, Bpaci%ies, and Equa%ions of State sf Light EElemen$s, Including the Effect o f

Lf nes

, "

Report GA-2528, V o l e

I Q

WS'B"/-TR-~~-~P V o L , I

1 ,

General Atomic Division, General wnmics Corporation (99911,

Martinez, M a R e , "Descriptioa of Computer Proarm B187

-

Themochemieal E q u i l i b r i m Bcsperties of Mul%icrnponent Systemsb and Hz89

-

Sta%istieal Themodynmie Prope&ies sf Single Gas Gpeef as ,'"AC-59133, Santa Monica, California, Douglas A i r c r a f t Compaqv, ^IDC,

,

^{( 1967}

1.

13. Cruise, D, R,, "Notes on the Rapid Cora.pu%atisn of Chemical E q u i l f b r i m

,*' -

68, 3799-3802

(1964) .

1 4 Wigdon, W, S,, "'A Computer Code f o r Calculation of Wansport

*opert ies o f High-Temperatwe Gases DAC-$9134 ⁾ Santa Monica $l

California

,

^{Douglas Aircraft Co , ( in prepmat} i o n ) ,

15. Gruszezynski, J , S, and Warren, J r , , W, R e , "Study s f E q u i l i b r i m A i r T o t a l Radiation ,'QaIM J B ⁾ Vole

5,

517-525

(1967).

Appendix A GAS PROPmTEES

The s p e c t r d line= absorption eoefficienk i s of eri$ieal

&porLanee for accmate calculations of the radiadive heat transfer to (8

1

e n t q vehicles. The values use& in this study a r e those of Thomas In that work a complete description of the spectsd absorption coeffi- cient was made including band radiation, photodissociation, photoioniza- tios, photodetacbent

,

^atomic lines, and brebsstrahlung Atomic l i n e s belongiw to md%iplsts were grouped together, since for tnicsab ra-

entry con&itiona he found the spacing be$;ween lines of a particulm multfplet "$ be usually of the s m e order as the line half widths. The f-numbers f o r the ultraviolet lines were taken from NBs'~' and for the visible lines *om ~riem'"). Thomas used the hydrogenie model of

Steward and matt to define lines close to the photoelectric edges.

9 4=

Lines from E, N

,

^{0 , and 0} are included,

Thomas has generaged the spectral l i n e m absorption coefficient for air at approximg%%ely 2000 spectral points for Le~peratwes from 2080°K %Po 6 0 ~ ( 3 0 0 ~ ~ and pressme% from 0,603 to 300 atmospheres, The values used in the preseaa$ investigation were sealed aceording to pressme from the values calcdated at P atmosphere, P i g m e $9 shows the values of Bw Thomas obtained st 1 5 , 0 0 0 ° ~ and 1 atmosphere pressure.

The themodynmic properties of air used here are those obtained by Martinez"" from solution aE the chemical equilibrium

(13) equations bg. the method of Cruise

The t r a n s p o r l properties were eslcaa%ed by the _method described f n R e f erenee

14

at the a c t u a l stagnation pressure ( 8

.&6

atmospheres

E q u i l i b r i m eoneentrations of 18 air species were used and t h e effects of charge exchange encounters were considered, The viaeosiLy and

c q u i l i b s i m thermal conductivity were ealeula%ed $0 the second+riEer including the effects sf' LhermP diffusion,

SUltfi4bB:WY OF CASES STCiDIED V

-

^50,000 f t / s e e h = 298,OOC) ft

03

Ty = 2000°1:

10,O Black C 600 5296 5896

-

..

2. Mulurl?crs i n parenthesis refer' t a antrcou?_icc" h6a-k tr .::sfe~

rwtes

.

FIGURE 1 .

COORDINATE SYSTEM AND

SHOCK

LAYER FLOW FIELD

(SCHEMATIC

)

FIGURE 2. S H O C K LAYER

FLOW FIELD FOR 1.0 FOOT NOSE RADIUS

WITH

NO BLOWING

FIGURE 3. SHOCK LAYER FLOW FIELD FOR

2.5

FOOT NOSE RADIUS

WITH NO BLOWING

FIGURE

4 . SHOCK

LAYER FLOW F I E L D FOR 1 0 . 0 FOOT

NOSE

RADI3S WITH

NO

BLOWING

T R A N S P A R E N T

WALL

S ⁼

1 3 . 8 5

cm

F I G U R Z

5 *

SHOCK LAYER FLOW F I E L D F O R 1 5 . 0

FOOT

N O S E R A D I ' J S W I T H NO BLOWING

FIGURE 6. VARIATION OF NET EMISSION AND ONE-SIDED FLUXES

ACROSS

SEOCK

LAYER WITH NO BLOWING

I

E 0

'XI -2 0

;= W Z 6 3 - H H

L) 2

Hcn 23

=r,

F I X R E

9.

INTEGRATED

v*F

FOR SI-IOCK-LAYER RADIATION TRAVXLING TOWARD THE WALL, EVALUATED 0.11 CM

FROM

THE WALL

I

o5

8 6 4

2

I

04 8

h

0 1

6

E 0

\ rn

+-,

4

+.'

1%

-

5

@

2

I

03 8 6

4

2

TRANSPARENT

WALL

1

02

0

5

10 1 5

R N ( f t )

F I G U R E 1 0 . H E A T T R A N S F E R R A T E S A S A F U N C T I O N OF

NOSE

R A D I U S

WIT2 NO BLOWING

FIGURE

1 1 .

REDUCTION IN RADIATIVE FLUX TO WALL

DUE TO RADIATIVE AND CONVECTIVE COUPLING

FIGURE 1

3 .

SHOCK LAYER TEMPERATURE PROFILES SHOWING THE EFFECT OF WALL REFLECTIVITY

FIGUHE 1

4,

UNCOUPLED FLOW

FI&LU

SOLUrI'IOM F O R 1 0 . 0 F O O T NOSE R A D I U S WITH BLOWING

F I G U R E 1 5 , SHOCK

LAYER

FLOW FIELD F O R 1 . 0 F O O T NOSE R A D I U S

WITH BLOWING

FIGURE 16. SHOCK

L A n K FLOW FIELD FOK 10.0

FOOT

NOSE RADIUS WITH BLOWING

TRANSPARENT WALL

FIGURE

17,

V A R I A T I O N O F N E T E M I S S I O N AND O N E - S I D E D

FLUXES

A C R O S S SHOCK LAYER W I T H BLOWING

NO

BLOWIBG

TRANSPARENT WALL

FIGURE

1 8 ,

SPECTRAL CONTRIBUTION TO

'1'HE

RADIATIVE

-HEAT TRANSFER RATE FOR

10.0

FOOT NOSE RADIUS

FIGURE

I

9 ,

ABSORP'I'ION

COEFFICIENT

OF AIR

AT

I

ATN

PRESSURE AND

1

5000 " ^K