i

I[

• "i_ _.

, ONTAMINATION DUE TO BACKFLOW FROM CONTROL

HOTO_ EXHAUST Final Report (Lockheed

"i _ _issiles and Space Co.) 39 p HC A03/HF A01 Unclas-.: _ CSCL 22B G3/16 5572_

,j ,

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;! _ '

-. _ I III III II I IIIII II ;

1977004149

https://ntrs.nasa.gov/search.jsp?R=19770004149 2018-05-26T08:18:56+00:00Z

!i!IJ "_ LMSC-HREC TR D568000 ._

" ' (/;./z /!} , ltslilll &-Sllilci ¢oltill.liny, ln¢.

Ii HUNTSVILLEliESEARCH& ENGINEERINGCENTER

, ,i, ¢.mliltrltis itelillirch Pirk "i

,,. 4800 Bradford Drive.i:"i; G" Huntlsvllle. Alabama

!; .,,

,i, ,i !1

i i 'T .., i

i! ,.

_: /_ SPACE SHUTTLE CONTAMINATION

,i _ DUE TO BACKFLOW FROM ,>!! CONTROL MOTOR .!',, ,--> EXHAUST .

i.i ,:,1:

,_ _i: FINAL REPORT

v,>

!: October 1976

t .._ Contract NAS8-31440

_ iil

• !. Prepared for National Aeronautici and Space Administr

•::: s.J. Robert,o. ;_' .<_j? ,S.T.K. Chan ',', ,_;;;t

" A.L. Lee t- -- _,_!>:I",<,"-- , C!. £_iD '_

i: -- APPROVED:

_,. B. Hobson Shirley, Su t_',. Engineering Sciences Section

:Ls. Ar'r or /Resident Director

It'

#". ' t

I,

1977004149-TSA03

, °

' _' LMSC-HREC TR D_O0

.!_:_i i!

:• FOR EWOR D ,_

This document is the final report for Contract lxlAS8-31440, "Space i

:7 Shuttle Contamination Due to BacMlow from Control Motor Exhaust." The

contract was initiated on 10 April 1975 as a 10-month effcrt to develop ana-

_ lyrical techniques for predicting the back-scattering of out gas contamination

due to outgassing from an orbiting spacecraft. The contract was later ex- -

_ tended an additional eight months to perform analyticaL-studies of molecular--

; _ scattering due to the vernier and flash evaporator plumes _mpinging on the

Space Shuttle Orbiter wings.

The results of the first 10-month effort were documented in an Interim•

_ Report. _ The results of the remaining 8-month effort are documente_i_ !

ii this final report.r

_ The study was performed by personnel of the Lockheed Missiles &

Space Company, Inc., Huntsville Research & Engineering Center, for the

.... Space Sciences Laboratory" of NASA-MarshaU Space Flight Center. The

NASA Technical Monitor is Dr. R. J. Naumann. The interest of Dr. Naumann

in these studies has been greatly appreciated.

*Robcrtson, S. J., "Space Self-Contamination Due to Back-Scattering ofOutgas Products," LMSC-HREC TR D496676, Lockheed Missiles & SpaceCompany, Inc., Huntsville, Ala., January 1976.

ii

LOCKHEED-HUNTSVILLE RESEARCH & ENGINEERING CENTER

1977004149-TSA04

iii

LOCKHEED-HUNTSVILLE RE5EARCH & ENGINEERING CENTER

,/

,- '%

1977004149-TSA05

LMSC-HREC TR D568000 ',

I'

: "_ k INTRODUCTION AND SUMMARY "

i :ii2_ The studies reported in this document are concerned with aspects of _ :-- the overal_problem generally referred to as spacecraft contamination. The

I :::_ Space Shuttle orbiter and accompanying Spacelab payloads are the particular

l _ spacecraft with which these studles are concerned. The following two _pecific: I _

;_ _ problems were add.res_ed. The first concerned the scattering of moleculesf_ from the vernier engines and flash evaporator nozzle after impingement on

_,, the orbiter _.'-ing surfaces. The scattered molecules may pass before the

i ..... field of view of optical instruments, tb,lspossibly obscuring observations.

ii _ This problem was considered in a previous study reported in Ref. 1. This

ii} _ previous study, however, was somewhat simplified in that collis_ons between ;

4i the scattered molecules and the plume flow f_eld were not considered. The't i i'j;

::.! . _ purpose of the present study was _o specifically consider the effect of these

_ collisions. The results of the study show that the effect of the collisions is

_i:_ri , to reduce the predicted column densities due to vernier engine firings by

";,i up to 90% depending on the location and orientation of the vernier engine and

..... direction of the line of sight (LOS).ii

!/:, i i The second problem dealt with in these studies concerned the backflow

of molecules out of the flash evaporator nozzle plume flow field due to

i i! , _ intermolecular collisions in the plume. A method was formulated for dealing.!, , !

_ . with this problem and results were obtained which compared surpri._mgl_

; i' well with experiment data. More reliable testing is needed to judge the accu-

_ racy of the theoretical results.'!i

: Detailed results of these studies are given in the following sections.

1-1

' ?

lOCKHEED. HUNTSVILLE RESEARCH & ENGINEERING CENTER ._

1977004149-TSA06

_, [, !4Ii +,"

_: !:_ :. I_MSC-HREC TR D_68000---. ,It _iilf_ ,,,

ii 2. MOLECULAR SCATTERING FROM ORBITER WING '

The analytical metho&_mployed tn.-this-e_u_y is based on. the.BGK m_l_ Ii! first described by Bhatnagar et al (Ref. I). The application in the present

!i analysis is similar to a previous application described in Ref. 2. The BGK ,:

!! model kinetic equation for this applic,a.j_.QnAJL._

_i 8f l ; '_ v. --_ = _,(M - fl) (z.l)

i. ,j... 8r

• Ii!i

:_: _ii i where fl is the di, stribution function for. the molecules flowing from the jet

ii under consideration, We assume that the molecules flow. f_om the jet l_ca-:. !:

!; ' tion to the o_bi_er wing stu_£ace where Ltr_flects _ccording te a Lamber.fish

il " (cosine law) directional distribution, Some of the reflected motecules then

ii : travel from the surface to the LOS for which column densities are being

! ;: computed. Enroute from the wing surface to the LOS, collisions occur withi.

the jet plume flow field and the-ambient atmosphere. The collision processes

_, _! are such that the molecules are either overwhelmingly scattered in the dLrec-

• " tion of the jet flow or the ambient flow, depending on whether the cotlisions

are with the jet flow field or the ambient atmosphere. The collided molecules

are thus primarily deflected away from the LOS and may be regarded as lost.

The quantiAy M in Eq. (2.1), which accounts for the further travels of these

•/ ' deflected molecules, may therefore be set to zero. The quanti_y P is the

total collision frequency which includes both collisions with the jet plume

and the ambient atmosphere. The total coL1islonfreqt_ency P may be ex-

pressed as the sum of the two separate collision rates:

--ull+ fiZ Iz.z)

1

2-1

#tOCKHI:ED-HUNTSVltLERESEARCH & ENGINEERINGCENTER

977004 49-TSA07

L_-PIREC TR D568000

., ,_ wh_r._-Vll is thc collisiOa rate with tlm jetph_mo, ar.d PIZ is tltocollision

rate-with .the--a_t_u_t armor he_.__e.L_.__l_aL_ainn. rates a re g4.vcn by!.

, _, (Raf. Z).:i

i

i 11",.oz3 "11 ,,-

!, I, I•. and i_

' ' !I9: i',

_ .... u1_. = 1. 0Z'3 n z uz o-t2.. - IZ. 4) _,}

!i • _i

i! ,:_ where m 1 is the jet p].ume mass flow rate pe_ unit area at a point in the flow ill

::;_ , _ field, m 1 is the molecular mass of the molecules in tl_e jet plume, all t.s the •i' cross section for collisionsbetween jet molecules reflected f_om the wing

'_'" i_, _, and moLer._es in the plurn_oav field, n Z is the number density of molecules:!

in the ambient atmosphere, uz is the ambient flow velocity and _IZ is the _ !• . cross section for collisions between jet molecules reflected from the wing

and molecules in the ambient atmosphere, i

i

!i Integrating Eq. (2.I) for the distributionfunction at a point in the LOS _:i_ yield s

I z ,,]! r: :

• _ (T._')=fl1_',rw)exp - -- v(_.) d_' (z._)" rw

• _ _ _-_

, where rw is a point on the wing surface and fl (v,"w) is the distribution

I_ function of thc reflected molecules at the wing surface. The function of

Z_Z ,:,

1977004 ] 49-TSA08

_' LMSC.,H_EC TR D568000

"!_:, i'I 1_',_'w)_ _- ..... ml _,sp " Zk T (Z.61:,i w'I: :

i where n w is a unit vector normal to the wing surface, ej. w is a-uni&vecto¢

_, in the direction from the jet to the point r w on the wd.ng surface, k is

,_ , : Boltzmann' s constant and T w is the temperature of th_ wing surface, The!i I local number density, n, is found by integrating Eq. (2.5)over v,ll velocities?

i; and directions from the wing su-rface to the point on the LOS. Af.t_r the velo-i'

i{ . . cities are integrated out, the remaining expression is:

li n(_')= 1 j rw', eJ'Wzw' er-w!! " _8_rmkTw -.A r

•L Ii ml1 • exp - P (r') dr' dA (2.7)_FF

'

,, where e is a unit vector in the direction from the point r on the LOS toi* r-w

_: the point rw on the wing surface, r is the distance from r t_r w and A is

: wing surface area. Equation (2,7) is integrated numerically.

:: The columr_ density N is obtained by numerically integrating the num-

L ber density n along the LOS from the prime measuring point (PMP) out to:. a point where the density has diminished to small values.

• i_. The orbiter geometry is represented in this analysis as a triangular

! shaped wing defined by the location o£ the three vertex points. In all the

; : results presented in this document, the three vertices are: (760, 110, 376),

! (1_00, 110, 296) and (1500, 480, 296) where (x,y,z) are the coordinates of the

f!. _ three points in inches according to the Shuttle orbiter vehicle coordinatei'

system. In the numerical analysis, the wing is divided into elementary J

2-3

, #i['- LOCKHLED. HUNTSVILLE RESEARCH a ENGINEERING CENTE.Rr

F #

. / . . . t. .-..,,d..... ,s,_* ................

'"' ' 1977004149-TSA09

ii ....

''i I,MSC-IA{EC 'I:R D_6HODO

i

.i! :_i triangles of the same sli_pa a_t the _grati_n carried, out-.Qver, tA_indt,vtdu_l-i;i

il elements by assutnl_g a linear vaCiation of tl_e inte.g_ The location of th_

_.i : PMP was taken to be (1107, 0, 507). The locations of both the Nos. 4 and 6iI vernier engines were taken to be (1565, 134, 459), with the No. 4 ,Jirocted tn

_ the -Z direction and the No. 6 directed in the +Y dir-cctton. The temperature J

o£ the wing surface T w was assumed to be 300K. The flash cvaper&tor nozzle

{ was taken to be located at (1504, 126, 291), which is slightly below and to therear of the wing trailing edge, and directed in the +Y direction.

g i

Number densities and column densities were computed along LOB-s

from the PMP in the +Z direction and in a direction 60 deg from the +Z axis

i : and 30 deg from the +Y axis tn the YZ plane. In the vehicle coordinate-.system,

the +X axis points in the aftdirection, the +Y ax_s points in the starboard dl.

rection and the +Z axis points directly overhead. Results were obtained for

the Nos. 4 and 6 vernier, engines and the latest considered location of the flash

evaporator.

Shown in Figs. 2-I through 2-8 are computed number densities along a

, LOS in the +Z direction during firing of the No. 6 vernier e_gine at a_n orbit

altitude of 400 kin. The results shown in Fig. 2-1 are the total density, n,

: ':i: the contribution due to direct flow from the jet, nd, and the contribution due

i" to scattering from the wing, n s. These results include attenuation effects

due to collisionswith both the jet plume flow fieldand the &mblent atmosphere.

The direct flow portion nd is seen_to be the primary contribution ove_ the

_: bulk of the LOS. Recall that this portion is attenuated only by collisionswithi,

the ambient atmosphere. The scattered portion ns, on the other hand, is

' attenuated by collisions with both the jet plume and the ambient atmosphere,

': thus resulting in a relatively rapid decrease in density along the LOS. The

same results are shown again in Fig. Z-la with the additional shadowing of the

cargo bay doors and fuselage. The contribution due to direct flow from the

jet, nd, is not reduced while the contribution duc to the scattering off the

: .... wing, ns, is greatly reduced, especially for the portion of the LOS near the _ 1

LOCKHEED. HUNTSVILLE RESEARCH & ENGINEERING CENTER

1977004149-TSA10

.: i.

,. LMSC-HREC TR D56B000

• .i ' ' Idll ................................................................................

,i th

',: I,OS _ Z di rortion!,

o 1010 No.6 Vernier

"-. _ _. 2_ +Y direct_.onaft location

o gl

n 400 km altitude

t

i,

109 _

108 ........... 1................................................0 10 Z0 30 411 50 60 70

Distance Along LOS (m)

Fig. Z-I - Computed Number Densities Along a Line-of-Slight ConsideringCollisions with the Jet Plume Flow Field and the Ambient

Atmosphere '-_,

t2-5

_' LOCKHEED. HUNTSVILLE RESEARCH & ENGINEERING CENTER

f I

1977004149-TSA11

"tU

il LMSC-H_F.;G TR D56_00Q

, i0 II ...........................................................................

iF.

5,

!

i il I i

i

_° ,I0IO _._ , ' , 1

_.- .............. Iii i = i

- .%i

,. ! _ ..... ._ ...... ...

: f _ _.

.....k .......:..................\

_ ' i ii i X , ................

....... , , , ,, , , ,,,,,,, ,, ,, i i

0 I0 Z0 30 40 50 60 70

I Distance Along LOS(m)

ii Fig. Z-la - Computed Number Densities Along a LLne of Sight Consideringr. Collisions with the Jet Plume Field and Ambient Atmosphere

and Shading Effects of Orbiter Geometry

|...

:i

i-

/ LOCKHEED. HUNTSVILL_ RESEARCH & ENGINEERING CENTER

1977004149-TSA12

J.

_ _ LMSC-HREC TR D558000 1• " !i m

i' ii PMP, The result i_ a r-odt_eed n_nb_.¢ d_n_£1_,, At tie--location near the!:

" i_ PMAu.fhe sh_dnwing of the- cargo bay door_ _.nd fu,a_a.go roduce_ the number-.

i density t_ lo_a tha_-o_o-thtrd of the ortgtna-I valu_!

I; The uamo re_tt_ are _hown lh Fig. 2=2 but without including any alton.uatlon o_foct_i(the_o 'tsub0crIpi,d_moto, _oro molecular collisions}, Th_

L cltroct flow contribution, ndo, is aeon to not be chftaged appreciably, but the• scattered contribution is incroanod substantially. Vtguro _==2a shows the

i same romdt.s but including the shadowing _ffocts of shuttle geometry. The._ " i scattL_redcontrlbtttlonis soon to be reduced drastically within I0 m of

the PMI a.

The same results are again shown in Fig, Z-3 but this time considering

:,IiI_ collisions only with the jet plume flow flold (the ttnattsubscri@t denotes noatmospheric collisions). Con'tparlng these results with Fig, 2-I shows that

I atmospheric collisions_t_n orbit altitudeof 400 km are not significantcom-

.... _ pared to collisions with the jet plume flow field. Figure 2.3a shows the

addltioi_l effects of shading, The scattered amount is reduced by more thanlan order of magnitude.

I The relative effects of considering collisions are also illustratedin

Fig. Z-4 in which the portion scattered from the wing is shown without

'_ collisions (nso), with collisionswith the jet plume flow fieldonly (nana) and:" with colli_ionswith both the jet phmle flow fieldand ambient atmosphere (ns).

',i Again, collisionswith the ambient atmosphere are shown to not b_ significant

'. _ at 400 km altitude, but collisions with the jet plume flow field are shown to0.. :,

: : greatly reduce the computed densities. Figure Z-4a shows the effects of

i shading. The reduction of number densltlcs is most drastic in th_-veglon,

i within Z0 meters of the laMP.I

: The effect of altitude on densities along the LOS is shown in Fig. 2-5.

The densities in this figure are the total number densities including direct

"' flow and scattered from the wing with collisions wi*.h both the jet plume flow

: Z-7

!_. LOCKHEED- HUNTSVILL_ RESEAHCH & £NGINEEr41NGCENTER

: :-::--_.-i:-::==:-,-+.........-::"-:- :......................'..........................................................." 1977004 i'"49--TSA13

-_ II0

' ,._,,lolO

III

"!?109 - 1,08 œ�direction

-- No. 6 Vernier+Y direction

aft location

400 km altitude

' : LMSC-HREC TR D568000 .....

_ , 1011 _-._[

It' 108i-.- 0 10 20 30 40 50 60 70

m I Distance Along LOS (m)

_" Fig. 2-2a - Computed Number Densities Along a Line of Sight Considering• Collisions with Neither the Jet Ph,me Field Nor the AmbientAtmosphere but Including the Shading Effects of Orbiter Geometry

2-9

: .r..

: 13 LOCKHEED-HUNTSVILLE RESEARCH & ENGINEERING CENTER_:I;

1977004149-TSB01

L:, i!, lo8 I I I I I.... _I

il _: 0 10 20 30 40 50 60 70

Distance Along LOS (rn)

Fig. 2-3 - Computed Number Densities Along a Line-of-Sight ConsideringCollisio_s with the Jet Plume Flow Field Only

_. 2-10

_2 - ' LOCKHEED. HUNTSV|LLE RESEARCH & ENGINEERING CENTER t

, , J

• ,_gi

I ' I

!i +. i,_

i! L_ISC-HREC TR D568000

i.. _ i011 ,m

++ I ,i i. ++

it

i

I

," ,j

--, \N

:: u \_+,,,,I

. n s

Z 109 _"-++

/ \I

_. 10 8 •p, G I0 20 30 40 50 60 70

Distance Along LOS (m)

Fig. 2-3a - Computer Number Densities Along a Line of Sight ConsideringCollisions with the ..t Plume Flow Field Only and Shading iEffects of Orbiter Geometry i

" Z-ll

- LOCKHEED . HUNTSVILLE RESEARCH & ENGINEERING CENTER •% "

k

• t' ......

_-,,_ .++- ....................................................................................... in

+I977004 +I49-TS B03

los _ ..... _l 1 I I .t ........... L_0 l0 20 30 40 50 60 70

Distancc Along LOS (rn)

Fig. 2-4 - Computed Number Densities Along a Line-of-Sight for MoleculesScattered Off the Wing

2-12!

LOCKHEED. HUNTSVILLE RESEARCH & ENGtNEEIRING CENTER

i "

+ :t !I,MH(:.- I IR E(', T I_, I)5680t)0

4

,._. ; m I i Iu_ __ J/

,; r i ii f _! • _!.! • -!

F

:i

" /_ _1( \

r:: _

: .- (,1

°,...I

12._ _!-

+ N

", E __ Z

/

_4L,_,, _ ...

,. t t i .........

0 10 20 30 40 50 60 70

I Distance Along LOS (m)

Fig. 2-4a - Computed Number Densities Along a Line of Sight for MoleculesScattered Off the Wing with Consido+ration of Orbiter GeometryShad hag s

2-13

t LOCKHEED. HUNTSVILLE RESEARCH & ENGINEERING CENTER

I i

LMSC-HREC TR D568000 ,_d

• lO I! .... -..........................

" l, r

t_1

. LOS �„�direction

v

No. 6 Vernier1 _ 1.0! |�direction

,, aft Iocatlol_

0 :

400 km altitude

', 300

i _ 'I z

LO- -- : .

-- 200 ,: :

1 :

, lo_ ! ____ I I_ 1 ....o lo zo 30 40 so 60 70

Distance Along LOS (m)

Fig. 2-5 - Computed Number Densities Along a Line-of-Sight for Various, Orbit Altitudes

2-14

b

LOCKHEED. HUNTSVILLE RESEARCH & ENGINEERING CENTER,.,"

1977004149-TSB06

!i ! i_!I , 3

: ' r LMSC-HREC TR D5_8000

r! '"

.,ii :i!i _elxt ahct a_bion_ attnosphege, The ambien_ atmosp_l_er¢ is seen to-be_come

a sLgnlILaa_t _ctor at a].titud_s be.low 30_-km,. The _ffacts af--shadtng are

i; {! show_ h_ Fig. Z-Sa. R ts seen that t_e nambee dei_st_i_sare r_tuczM.to:i

!_I ailp_roxima_ly haLf-of their..orlglrm.l w_laaes in. the _-eg£on wl_Mn ZOrn Of

!i i: the PM]_, The _u_aber densities ara-_ot affected much lsy the shactlng in

ii ' the region fartb_ away from the P_P. '

• !!AdditionaL-res,,i_sare shown in Fig. 2-6 for the No. 6 ve_r_er engine• Ii

"I: along a LOS in the YZ plane,60 deg from the +Z axis and-these results i_nclude

i I collislorts with the jet l_lume and ambient atmosphene 30 deg from the +Y axis. _

In this case the density iftcreases along the LO_ out to about 15 m befor_e

! diminishing. The increase is-due to pene/ration of the LOS Lnto the denser

regions-of the plume. Figure Z-6a shows the effectsof shading. The

; scattered-part is again seen to be cut down •within I0 m of the PMP.

_ Results for the No. 4 vernier engine are shown in Figs. 2-7, 2-7a, 2-8

• _ and _-8a for the two LOSs. The scattered contril£uki_n_.as.seen in F_g. Z-_

to increase along th_ LOS for about the Rrst 5 m before diminishing. _, 4

When the shading of the orbiter geor_etry is considered, a,sshewn in Figs.

Z-7a and 2-8a, the scattered amount is cut down for the firstI0 m of 4'

the LOS. The number densities alang the LOSs are dominated by the contri- :_

: I bution due to direct flow f_r the first 10 m of the LOS. Dominance is !i

i i then gradually taken over by the scattered flow off the wing.

! ' i

Results for the flash evaporator are shown in Fig. Z-9 for both LOSs. :_

! Only the totaldensity is shown in Fig. Z-9 becattse the jet is located below

• the wing such that there is no scattered contribution along the LOSs being!

considered. As noted in Fig. Z-9, the molecular flow to portions of the LOS

near the spacecraft bod_ are shadowed by the wing. The additional shadings

of the fuselage and cargo bay doors completely eliminate the number densities

on the LOS in the +Z direction. However, the shadings have no effect on the

number densities on the LOS in the +60 deg direction.

2-15.

:: L_OCKH_[D • HUNTSVILLE RF.SEARCH & ENGINEF._ING CENTER

1977004149-TSB07

i .

_.-17

LEK:KH[ED-HUNTSVILLERESEARCH& ENGINEERINGCENTER

=>. _ ...... "" .... " . ,

1977004149-Tfi RR__

| I !.

i ,

.: I.,MB(I-IIItE(; TIi I)661_000 .

II111 .......................... ........-,.....

iii

_ 1010 ,,• i _

U

: _ ...E_,.....i o [ \

. / \°I::1 ,

I. _ f /_. _ 109L _ .....

i'_ / .....

, , , ,,,

i:

• 1i

: /|

.°, 1080 10 ZO 30 40 50 60 70

i DLstance Along LOS (nl)

Fi_.Z-6a - Computed Number Densities for the N_.6 Vernier and LOS 60deg from +Z Ax_s with Orbiter Geometry Shading

Z-18

_" LOCKHfED. HUNTSVILLE RESEARCH & ENGINEERING CENTER¢

'J . h• • fp

1977004149-TSBlO

I i

l08 [..........' _. 0 10 20 30 40 50 60 70

,_: Distance Along LOS (m)

: Fig. Z-7 - Computed Number Densities for the No. 4 V_rnierand LOS Along the +Z Axis

'_" RI,;pRODUGIBILITYOF _'l'IE

•I om_ pgGl_i8 P_ z- _9tOCKttlEO. HUNTSVILLE RESEARCH & ENGINEERING CENTER , #

"7

/ !;' ., . _ , . i

\.

1977004149-TSB11

[,MSC:-Jn_:CTR n_6_ooo

loll,..........

;' , ........ o ,

i , .,,,

_- ,. • , 'lp ...... c

I •"_ , _, \ ........ _ ....

Z, , ,

I • ....... _ _._ .. _

\

[ __ .

• _ ......\

10 8 , ,

0 I0 2,0 30 40 50 60 70

Distance Along LOS (,m)

D'iR, L-Ta - C¢)mput('d Nurnl)er Dmlsities for Ihl, Nt).4 Vernier and LOS Alongthe t Z Axis with OrbEter (;eometry Hhading

;).-L0I#.

LOC,KHf'ED. HUNTSVILLE HESEAHCH & ENGINLLRING CENTI.R

i

1977004149-TSB12

>'._ :.i LMSC -HREC TR D56f1000

I0 II- , ,.

m

10 ........ =

-- m

g o_ \ "\ \

_ Z to? _ __! .........

_ i ..........b

;zt .t' [10 8

0 "_0 2(1 "_0 4O 50 60 70I)iaLance Along I.,()N (J_)

Fi_:.2-8_ - (;c)nlt-)ut,,d Null,her 1)tmMtioa t',)r lho N,_.4 V_,)'nior lind 1,ON 60

dog frt)nl .t-Z Axis with (.)rbitor (_,,,,lt_t.lry bha(ling

lLMSC-HREC TR D568000

f -,. LOS +Z direction

!i _, I

i............. LOS in YZ plane

* -i [ _ iolo!: _ --_ Flash Evaporator.

,-4_ +Y direction

o

400"krn altitude

LOS in +Z direction

W

LOS 60 deg from +Z direction

ii _ ix_ Y Z plane

_'r 2_ 109: i

2 :

P 'i

!' Shadowed by Wing

IB-

m, ,08 I i I i

i! 0 , I0 20 30 40 50 60 70Distance Along LOS (m)

Fig. 2-9 - Computed Number Densities (Total) for the Flash Evaporator2-23

_) LOCKHEED-HUNTSVILLE RESEARCH & ENGINEERING CENTER

", - "..... ".......... 1977004149-TSC01

i " - " 9

,; LMSC-HREC TR D568000

The computed cohunn.dansitLas are shown in Table 2-I for all rases

considered. Three valu.e.s are shown_/_r each case: (I) N h_cl_ effects

o£ colli_iona with both-_he jet plurne and ambient atmosphere, (2) Nna includes

effects of collisions with the jet plume only, and (3) NO includes no collision•i effects. The numbers in parentheses ane-the column densities of each_ase

.... i

when the shading of orbiter geometry is not considered. In all cases, when i ":

the shading is not considered, the collision effects resulted in substantially

_ ; lower computed column densities, as much as 90% lower for the No. 4-vernier

_ engine and LOS in the +Z direction. A r.eduction of 75% is noted for the No.6

vernier engine with LOS in the +Z direction. At this altitude (400 krn),

collision effects with the ambient atmosphere are seen to be relativelyunimpo rtant.

The reduction of number densities due to geometry shading effects°

is apparent in all vernier cases. The shadings of the cargo bay doors, fuzee-1!

lage and engine pods reduced substantiallythe contribution from the scattered

::i flow to the vicinitywithin I0 m of the PMP, where the number density is

._ i_ highest without the shading. For the flash evaporator the number densities

_ along the LOS are from the direct flow of the plume. The LOS in the +Z I_: direction is completely shaded by the orbiter geometry and consequently the

column density is zero. The LOS in the 60 deg direction is not affected by

the additional shading.

• !i

b i

!

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1977004149-TSC02

'i!

,i' LMSC-HREC TR D568000

L ....

L T v.b/e 2-I- COMPUTED COLUM/W DENSITIES FOR THE NOS. 4 AND 6VERNIER ENGINES AND THE FLASI'IEVAPOB_TOR

I Column Densities (molecules/cm z)

Jet and LOS N N Nna o

" No. 6 Vernier 3.35 x 1013 3.51 x 1013 1.37 x I014

[ LOS +Z Direction (5.14 x 1013 ) (5.41 x 1013 ) (1.99x 1014 )

No. 6 Vernier 3.12 x 1014 3.38 x 1014 5.23 x 1014

i LOS 60 1.eg from (3.25 x 1014 ) (3.51 x 1014 ) (5.64 x 1014 )+ Z Direction

: i ' 1013 1013 1014_ 4 No. 4 Verr_'er 2.43 x 2.56 x 1.57 x

:_ LOS +Z Direction (4.96 x 1013) (5.18 x 1013) (4.17 x I01.-')1 1A_

I No. 4 Vernier 5.95 x 1013 6.20 x 1013 3.82 x 1014LOS 60 deg from (7.81 x 1013 ) (8.10 x 1013 ) (4.90 x 1014 )

+Z DirectionFlash Evapo rater 0.0 0.0 0.0

: I LOS +Z Direction (6.29 x 1012) (7.94 x 1012) (7.94 x 1012)

Flash Evaporator 5.11 x 1013 6.90 x 1013 6.90 x 1013

I LOS 60 deg from (5.11 x 1013 ) (6.90 x 1013 ) (6.90 x 1013 )+Z Direction

N includes molecular scattering from both plume and ambientatmosphere.

N includes molecular scattering from plume only.

I na does not include molecular scattering.N o400 km altitude. Integrated from PMP to 100 m (NR = 10).

f} [ Thenumbersinparenthesesarethe columndensitieswithoutthe effectsof cargo bay doors, fuselage and engine pod interference.

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.fi

i_ IiIi

- i 3. BACKSCATTNR FROM THE FLASH EVAPORATOR PLUMEI

I The mass flow rater_ in the flashevaporator plume _w fieldhas been ,

determined experimentally and is described approximately by the following= 1

empirical equation (Refs. 3 and 4).

_t rn = (cos0)6"z72 (3.1)! r !

• where rn is in gr/cmZ/sec and r is in cm. Tbls.emplrical formula is

- applicable only for direct flow from the nozzle in the forward direction. !

: There will be some backscattering out of the plume in the rear direction as

a result of intermolecular collisions that this formnla does not account for.

The study described in this section is an attempt to formulate a physically

meaningful analytical technique for estimating the magnitude of this back°

"" scarter flux. i:

!,

', We start with the BGK kinetic model equation (Ref. I):|

-_ 8fi v • -_ = v(M -f) (s.z)

: 0r: i_

.A .Awhere v is molecular velocity, r is the position vector, f is the velocity

distribution function, u is the local collision frequency, and M is a local

: : equilibrium distribution function based on an elipsoidal model (Ref. 5):

m m exp - m -V) (3.3)M = n Z_rkT n Z_rkZ s _ "_(Vs

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197700414 -T.QC:.0d

il LMSC-HREC TR D568000_r

i! "

!! ._'i. wher.e n is the local number density, m is the molecular mass, k is the

" Bc_liz, nlann constant, V is the local 3_u_an velocity, v and v are 'molocul.ar; S 11

! ' velocity components along and normal to the streamlAae, and T s and Tn arc __i

temperatures corresponding respectively to the streamlin_ and normal di- '.i

:! Ii rections. Only two temperature components are considered because orifice

_ flow into a vacuum is very similar to spherical source flow expansions (Ref. !i

; i 6). The v_lues of the temperature components serve as an indication of the _

.... directness of the local velocity distribution function. In spherical source I! i• _iflow into a vacuum, it has been shown (Ref. 6) that T tends toward zero.as "

' the distance from the source increases, and T s tends toward a non-zero _4_

asymptotic value. Physically this means that there is some spreac_tn veloci- _

ties at great distances from the source, but the variations are primarily in ;'=

the streamline direction.

i- The plume temperatures were formed by first taking moments on the_,,

BGK equation up through the second moment. This results in four differential

equations in terms of the hydrodynamic quantities: density p, velocity V

and the pressures Ps and Pn:

t_

I d +l dV z.... = 0 (3.4)'.. p ds V ds +s

_, dP P -P

s dV s n = 0 (3.5)ii +ovg; + z s

_" " dPs dV Ps v P

V-d-_- + 3P s _-_+Z--=s -_"(P "Ps ) (3.6)

PV

:" dPn dV + 4 n Pb.. V _ + Pn d"_ _ = _ (p " Pn ) (3.7)

where P = (Ps + 2Pn)/3' 17 is viscosity and s is distance from the source.

By manipulating these four differential equations, the following energy

. equation is derived:

3-Z

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1977004149-TSC05

I

I', "' LMSC-I|REC TR D568000

...."_' _i ' 3Ps + 2Pr# _ V _..... -- = constant (3.8)" _1! • P

! Defining Ps = ROTs and l°n = RpT n, a_l of the above equations are reduced to

• _ two differential equations in terms of T s and T n. Thia.pa_r of differentialequations was numerically integrated using the Runge-Kutta technique and the

results curve-fitted to yield:IFor _ < I

• "To- _oo--0.z83 I+0.094_ (3.9)

For _ _>1 I

( T__s = 0.000152 + 0.000800T O

: Tn 0.0003 IZ3 0.0003584

---- _ZTo _ + (3.10)

where T O is the source temperature and

_- s (3.11)_ 0.03088 (0.75)K Re_D

, : _ where K is the exponent in the temperature variation o_ viscosity (1.07 for

water vapor, Ref. 7), Re s"is the throat Reynolds number of the orifice and

D is the orifice diameter. The temperatures given by Eqs. (3.9)and (3.10)

are used in the local distributionfunction given by Eq. {3.3). In deriving Eq.

(3.9),the flow is assumed to be isentropic,while Eq. (3.10)is obtained assum-

ing flow is non-isentroplc far away from the orifice.

The mass flux rh at a point _, which is a far distance away from the

flash evaporator nozzle, is found by operating on the kinetic equation:

3-3

ILOCKHFED. HUNTSVILLE RESEARCH & ENGINEERING CENTIrR

°.,

.... I,MSC-IIREC TR F_('_ nnn

,! I,

!_ ? where i

_ u ) M(v,_') o_ - u Id;_"lla_'l(3.131 i'

v , vr 1 r

.!

The integration path r 1 to r Z is across the plume in the direction out to r. _;

The end points are chosen arbitrarily to cover the significantly dense portionof the plume.

:: 'q

i The integrations in Eqs. (3.1Z) and (3.13) combine to yield a volumetric!,

integral over the significantly dense portion of the plume flow field:

_ = p (7_') I, ) M (_,_') _p - ;(_, vz 1 v(7TM) Id_'qdvdV (3.14) :r _r , !

r i'

The assumption here is that the distance r is large compared to the dimen-

sions of the significantly dense region o£ the plume. The frequency u ('_') is

the local collision frequency for the production of scattered molecules, and

the frequency P (_") in the exponential is the collision frequency for the

attenuation of the scattered beam. Accordingly, the former is given by:

V(_') = kT (_') n (_') (3.15)

+ ZT ) is the local static temperature, and the latter iswhere T "- 1/3 (Ts n_iven by:

(7'" k To n (7'")_- v ) = ...... (3.16)_(T o)

3-4 Ii_'_ t.OCKHEED. HUNTSVILLE RESEARCH & ENGINEERING CENTIR

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1977004149-TSC07

.ii I,MSC-I1REC TR D568000 i,E

• ii

' !i1

_i_ whczc T O ts the sourr-e, or stagnation, tetnperatt_re. The stagnation temp-eratur_ i_ used t_re because it is indicative of the energy of the f_

: _olccules with which the scattered beat_a col_tdo.s.

The localdensityD inE¢I.(3.14)is fotmd by dlvld_ the mass fluxin

i (Eq. (3.I))by the localmean velocityV, assurningthe velocityhas reached

itsthermodynamic limitgivenby:

] 2"/ k To (3.16)vf

¢

I!

where 3/ is the ratio of specific heats (_' = 4/3 for water vapor).

With the above described considerations and after all of the integrations

! are carried out, Eq. (3.14) reduces to the following expression:

l:!i !_ rn =--_ F( _ ) (3.17) :i_i r

_i where _i is the orifice flow rate and F is a dimensionless function of the

ii angle _ formed with the jet axis. The velocity integration was evaluatedi!

_ numerically using the trapezoidal rules, and the volumetric integration was

performed using finite elements (Ref. 8). It was found that the significantly

dense region of the plume for our purposes is contained within 50 cm of the

• orifice location. This permits the representation of the nozzle as a point

:, :: i source at distances comparable to the Space Shuttle Orbiter dimensions.

The results of the integration are given in Fig. 3-I. The only experimental

data to compare this with was obtained in tests in a thermal/vacuum environ-

mental chamber (IRef.9). Multiplying their supersonic nozzle data at _b = 90°

by a factor of three to yield orifice data (Ref. 9, p. 16), we obtain the experl-If,' mental data points shown in Fig. 3-I. The experimental data are higher but

within an order of magnitude of the theoretical curve. Considering the con-

version of supersonic nozzle data to orifice data, and the unknown contri-

I] bution of scattering off test chamber surfaces, the comparison is surprisinglygood.

3-5

;: lOCKHEED.HUNTSVILLERESEARCH& ENGINEERINGCENTER it

, B

] 977004 ] 49-TSC08

il

- " _) .......... =

I .............................. ,

/_ 2.13 cm from orlfi¢o

)_ ............ 1O"3!! " •

i .........

i! ""I:A

I _ 1°-4

i N ...... , ,

%

) -]

' m

, 10-5 .....i

m

-6'I0 A

- _/ 90 ILO 150 18lAnRh" fr_uu l>lun_eAxis 0 {oh'R)

[_'Eg.3-1 - Predicted Far I,'ield Backscattcrm_ for the Flash Evaporator

II(.X';KHIED.HUNTSVILLE RESEARCH & ENGIN_ thiNG CENIER

1977004] 49-TSC09

I -4

I!LMSC-HREC TR D568000

• " il Ba_ed on the result_ obtained b v the present n_odol, an onlplricai

:.. ii formula for the far field back_cattorirtg of the flanh evaporator can be con-

i! _tructed. This empirical formula was found to be

i, :.._ IOn I,L _n_

: i :!I 1.6 cOS: i F(_) = 0.0002x 10 (3.18)

i; i[i

f: with conaputed results shown in Fig. 3-Z. Also shown in the figure are

!! results from the empirical equation for the flash evaporator plume flow

i_ field (_ < 90°) as used in Refs. 3 and 4.

C,

i!

!i ' '

!

m,

I9_

|

3-7

) I,-4lOCKHEED. HUNTSVILLE RESEARCH & [NGINEtRING C,ENII R

"_..... -- ....... 1977004149-TSC1(

!

:. i0 -(>

0 40 60 90 I_0 I_0 IRt) _I0

Ah_|@ {r_ml lqult_,, Axlu, _ (d,,#)

l"i_. 3-Z - F_piri_"_] V_)rn_u]a f_)r the' Plm_' l,'h)w Field and Far FieldBack._cat_,ring for th(, V la,_h EVal)orator

3-8I

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1977004149-TSCll

_ 'I LMBC_HREC TR D568(}00:!

1h

4, CONCLUSIC)NB

Tho two _tudies du_cribod in thi_ roport rooultod in tho d_w_lopmont of

p rat'ti¢'nl analytical techniques for u Htimnting the ront.amh_atttm environment

due to molecular flow from the vornie, r ungineu and flash ¢_vaporator plumes. '_

" It was found that molecular collisions are. an important factor and should be i;

¢.onsidcred in calculations of scattering off the Orbiter wing surfaces. Tha

computed colunm densities were shown to be reduced by as much as 90%,

depending on the jet location and LOS diroctlon, by considt_rlngattentuatlon

of the scattered beam du_ to collisionswith the plume flow field.

An apparently usable analytical technique was d_veloped for estimating

backscatterlng out of the flash evaporator plume flow field. Although the

available experimental data tended to at least partially support the theoretical

results, more reliable data are needed for con_parison.

These stud{es were based on steady state conditions. The actual pulse- I

i like character of the vernier firings and flash evaporator venting will tend

i to reduce the densities from the steady state values,

4-I

!,¢J_KH! [.O•HUNTSVILLE RESEARCH A ENGINLtRING CENTEH

........................................................................................._ n'7"Tnn,4"tao TSC12,__. ..- ... , =..,.,,..,_, _..,-

1,MSC -HI{ _,(.,"" 'l'R I'J_6HOOO

iJ ,,

,- I!|i

; :" I! i

i

! B, REFERENCES!

; t, Bhal:nag_r, P, L,, E, P. Gro_s and M, l_rook, "A Model for Collision• i Proc_sso_ in Gases -I. Small Amplltudv Processes in Charged and" I N¢_ulral One-Con_ponent Systems," Ph_,s. Rev. Vol. 94, No, 3, May 1954,

! p. _II.

) 2. Robertson, S. J., "Spacecraft Self-Contamination Duo to Back-Scattering_ of Outgas Products," LMSC-HREC TR D496676, Lockheed Missiles &_; Space Company, Inc., Huntsville, Ala., January 1976.

t 3. Bareiss, L. E., R. O. Rantanen and E. B. Ress, "Payload/Orbiter Con-i_, taminatlon Control Requirement Study," MCR-74-93, Martin Marietta '/_

Aerospace, Denver, Colo. 24 May 1974.i

" " I: i_ 4. Bareiss, L. E. and E. B. Ress, "Payload/Orbiter Contamination ControlRequirement Study," MCR-75.Z0Z, Martin Marietta Aerospace, Denver,

! Colo., 30 June 1975.

,: 5. Holway, L. H., "Kinetic Theory of Shock Structure Using an E1Epsotdal_' Distribution Function," in Rarefied Gas Dynamics (J. H. de Leeuw, ed.),

_" !: Academic Press, New York, 1966. 1, : : 6. Hamel, B. B. and D. R. Willis, "Kinetic Theory of Source Flow Expansion

with Application to the Free Jet," phys. Fluids, Vol. 9, No. 5, May 1966,

i p.8z9.7. Kennard, E. H., Xinetic Theory_of Gapes, McGraw-Hill, New York, 1938. i4:

I

8. Zienktewicz, O. C., The Finite Element Method in Engineerin_ Science, tMcGraw-Hill, New York, 1971.

9. Visentine, J. T., H.K.F. tChlers, and B. B. Roberts, "Determhaation of

: High Velocity Water Vapor Plume Profile An a Thermal-Vacuum :1" Environment," 7th AIAA/NASA/ASTM/IES Space Simulation Conference, ._

Paper No. 60, LoS Angeles, Callf., November 1973.

; i

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1977004149--I-SC13