measurement of momentum transfer coefficients … paper 3701 measurement of momentum transfer...
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Technical Paper 3701
Measurement of Momentum Transfer
Coefficients for H2, N2, CO, and CO2 Incident
Upon Spacecraft Surfaces
Steven R. Cook and Mark A. Hoffbauer
November 1997
https://ntrs.nasa.gov/search.jsp?R=19980003332 2018-07-17T07:44:16+00:00Z
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Technical Paper 3701
Measurement of Momentum Transfer Coefficients for H2, N2,
CO, and CO2 Incident Upon Spacecraft Surfaces
Steven R. Cook and Mark A. Hoffbauer
Los Alamos National Laboratory
National Aeronautics
and Space Administration
Lyndon B Johnson Space Center
Houston, Texas 77058-4406
November 1997
Available from:
NASA Center for AeroSpace Information
800 Elkridge Landing Road
Linthicum Heights, MD 21090-2934Price Code: A17
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161Price Code: A10
Contents
Abstract
1 Background
2 Tile Momentmn Accommodation Coefficients
3 The Reduced Force Coefficients
4 The Nocilla Gas-Surface Interaction Model
5 Experimental Results
6 Conclusions
5
5
6
7
8
10
11
List of Figures
1 The data for 2590 m/s
2 The data for 2590 m/s
3 The data for 2590 m/s
1 The data for 2590 m/s
5 The data for 1870 m/s
6 The data for 18711 m/s
7 The data for 1870 m/s
8 The data for 1870 m/s
9 The data for 1870 m/s
10 The data for 1870 m/s
11 The data for 1870 m/s
12 The data for 1870 m/s
13 The data for 1670 m/s
1,1 The data for 1670 m/s
15 The data tor 1670 m/s
16 The data tbr 1670 ln/S
17 The data tbr 4620 m/s
18 The data for ,1620 m/s
19 The data for 46211 m/s
20 The data for 462/) m/s
21 The data for 3180 in/s
22 The data for 3180 m/s
23 The data for 3180 in/s
2.1 Tile data for 3180 m/s
25 The data tor 3200 m/s
26 The data for 3200 m/s
27 'File data for 3200 m/s
28 The data for 3200 nl/s
29 "I'll(, data for 28411 m/s
30 The data for 2840 m/s
31 The data tbr 28.10 m/s
H2 incident upon the solar panel ................. 13
tt2 incMent upon SiO2-coated Kapton .............. 1.1
H2 incident upon Kapton ..................... 15
[I2 incident upon Z-9%coated aluminum ............ 16
N2 incident upon the solar panel ................. 17
N_ incident upon SiO2-coated Kapton .............. 18
N2 incident upon Kapton ..................... 19
N2 incident upon Z-93-coated ahuninum ............ 20
CO incident upon the solar panel ................ 21
('O incident upon SiO2-coated t(apton ............. 22
CO incident upon Kapton .................... 23
CO incident upon Z-93-coated aluminum ............ 2,1
CO2 inc, ident upon the solar panel ................ 25
CO2 incident upon SiO2-coated Kat)ton ............. 26
CO2 incident upon Kapton .................... 27
CO2 incident upon Z-93-coated alunfinum ........... 28
H2 incident upon the solar panel ................. 29
H2 incident upon SiO2-coated Kapton .............. 30
H2 incident upon Kapton ..................... 31
H2 incident upon Z-93-coated aluminum ............ 32
N2 incident ut)on tile solar panel ................. 33
N2 incident upon SiO2-coated Kapton .............. 3-1
N9 incident upon Kapton ..................... 35
N:_ incident upon Z-93-coated alunfiImm ............ 36
CO incident upon the solar panel ................ 37
CO incidenl upon SiO2-coated Kapton ............. 38
(IO incident upon Kapton .................... 39
(!0 incident upon Z-93-coated aluminunl ............ ,10
('()2 incident upon the solar panel ................ 41
("()2 incident upon Si()2-coated Kapton ............. .12
(_O2 incident upon Kapton .................... -13
32 The data for 2840 m/s CO2 incident upon Z-93-coated aluminum ........... 44
33 The angular distribution functions for 2590 m/s H 2 incident upon the solar panel. 45
34 The angular distribution functions for 2590 m/s H2 incident upon SiO2-coated Kapton. 46
35 The angular distribution functions for 25911 m/s H2 incident upon Kapton ...... 47
36 The angular distribution flmctions tbr 2590 m/s H2 incident upon Z-93-coated alu-minum ............................................ 48
37 The ang_ular distribution f\mctions for 1870 m/s N2 incident upon the solar panel. 49
38 The ang-ular distribution functions for 1870 m/s N2 incident upon SiO2-coated Kapton. 50
39 The angular distribution functions for 1870 m/s N2 incident upon Kapton ...... 51
40 The angular distribution functions for 1870 m/s N2 incident upon Z-93-coated ahl-minum ............................................ 52
41 The angular distribution functions for 18711 m/s CO incident upon the solar panel.. 53
42 The an_flar distribution functions for 1870 m/s CO incident upon SiO2-coated Kapton. 54
43 The angular distribution functions for 1870 m/s CO incident upon Kapton ...... 55
44 The angular distribution functions for 1870 m/s CO incident upon Z-93-coated alu-minum ............................................ 56
45 The anglflar distribution fllnctions for 1670 m/s (!O2 incident upon the solar panel. 57
46 The angular distribution functions for 1670 m/s CO2 incident upon SiO2-coated
Kapton ............................................ 58
47 The angular distribution functions for 1670 m/s CO2 incident upon Kapton ...... 59
48 The angular distribution functions for 1670 m/s CO2 incident upon Z-93-coated
aluminum ........................................... 60
49 The angular distribution functions for 4620 m/s H2 incident upon the solar panel. 61
50 The angular distribution functions for 4620 m/s H2 incident upon SiO2-coated Kapton. 62
51 The angular distribution functions for 4620 m/s H2 incident upon Kapton ...... 63
52 The angxllar distribution functions for 4620 m/s H2 incident upon Z-93-coated alu-minum ............................................ 64
53 The angular distribution functions for 3180 m/s N2 incident upon the solar panel. 65
54 The angular distribution functions for 3180 m/s N2 incident upon SiO2-coated Kapton. 66
55 The angaflar distribution functions for 3180 m/s N2 incident upon Kapton ...... 67
56 The angular distribution functions for 3180 m/s N2 incident upon Z-93-coated alu-minum ............................................ 68
57 The ang_flar distribution functions for 3200 m/s CO incident upon the solar panel. 69
58 The ang_flar distribution functions for 3200 m/s CO incident upon SiO2-(:oated Kapton. 71}
59 The angular distribution functions for 3200 m/s CO incident upon Kapton ...... 71
60 The angular distribution functions for 3200 m/s CO incident upon Z-93-coated alu-minum ............................................ 72
61 The angular distribution functions for 284/) m/s CO2 incident upon the solar panel. 73
62 The angular distribution fimctions for 2840 m/s CO2 incident upon SiO_-coatedKapton ............................................ 74
63 The angular distribution functions for 2840 m/s CO2 incident upon Kapton ...... 75
64 The angular distribution functions for 2840 m/s CO2 incident _93-coated Munfinum. 76
List of Tables
1 2590 m/s H2 incident upon the solar panel ........................ 13
2 2590 m/s H2 incident upon SiO2-coated Kapton ..................... 14
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
3O
31
32
33
34
35
36
37
38
39
4O
,11
42
,13
44
,15
.16
,17
48
49
5O
2590
2590
1870
187O
187O
1870
1870
1870
1870
1870
1670
1670
1670
1670
4620
4620
4620
4620
3180
3180
3180
3180
3200
3200
3200
3200
2840
2840
2840
284O
The
The
The
The
The
The
The
The
The
The
The
The
The
_l'he
The
The
The
The
m/s H2 incident upon Kapton ............................ 15
m/s t12 incident ut)on Z-93-coated aluininnm ................... 16
m/s N2 incident upon the solar panel ........................ 17
m/s N2 incident upon SiO2-(:oated Kapton ..................... 18
m/s N2 incident ut)on Kapton ............................ 19
m/s N2 incident upon Z-93-coated alumimun ................... 2(1
m/s CO incident upon the solar panel ....................... 21
m/s CO incident upon SiO2-coated Kapton .................... 22
m/s CO incident upon Kapton ........................... 23
m/s CO incident upon Z-93-coated almninum ................... 24
m/s (',O2 incident upon the solar t)anel ....................... 25
m/s ('02 incident upon SiO2-coated Kapton .................... 26
m/s (:()2 incident upon Kapton ........................... 27
m/s (702 incident upon Z-93-c, oated alunfinum .................. 28
m/s 1t2 incident upon the solar palm ........................ 2.(1
m/s |I2 incident upon SiO2-coated Kat)ton ..................... 30
m/s tI2 incident upon Kapton ............................ 31
m/s 1t2 incident ut)on Z-9:{-coated alunfinum ................... 32
m/s N.) incident Ul)On tile solar panel ........................ 33
m/s N,) incident upon SiO2-coated Kapton ..................... 31
m/s N2 incident ut)on Kapton ............................ 35
m/s N2 incident upon Z-93-coated ahmfinum ................... 36
in/s CO incident ui)on the solar l)anel ....................... 37
m/s (IO incident upon SiO:_-coate(t Kapton .................... 38
m/s (IO incident ut)on Kapton ........................... 39
in/s ('O incident ut)on Z-93-coated ahmfinmn ................... 10
nl/s C()2 incident upon the solar panel ....................... 41
m/s CO2 incident upon Si()2-coated Kat)ton .................... 42
nl/s CO2 incident Ul)On Kapton ........................... 43
nl/s (102 incident Ul)On Z-93-coated ahuninmn .................. ,1.1
Nocilla model t)arameters for 2590 m/s I12 incident ut)on the solar t)anel ..... 45
Nocilla
Nocilla
Nocilla
Nocilla
Nocilla
Nocilla
Nocilla
Nocilla
Nocilla
Nocilla
Nocilla
Nocilla
Nocilla
No(:illa
Nocilla
Nocilla
Nocilla
model t)arameters for 2590 Ill/S H2 incident upon Si()2-coated Kat)ton.. ,16
model parameters tbr 2590 m/s H2 incident upon Kapton ......... 47
model parameters for 2590 m/s It2 incident upon Z-93-(:oated alunlinunl 48
model t)arameters for 1870 m/s N2 incident upon the solar panel ..... 19
model t)arameters for 1870 m/s N2 incident upon SiO2-coate(t Kapton.. 50
model t)arameters for 1870 in/s N2 incident upon Kaploll ......... 51
model parameters tor 1870 m/s N2 inc, ident nt)on Z-93-coate(t aluminum. 52
model t)arameters for 1870 m/s CO incident upon tile solar t)anel .... 53
model l)arameters for 1870 m/s (IO incident upon SiO2-coated Kat)ton. 5-1
nlodel paranleters for 1870 m/s CO incident upon Kat)ton ........ 55
model parameters for 1870 m/s ('O inci(lent ut)on Z-93-coated aluminmn. 56
model l)arametel's fox' 1670 m/s ('()2 incident upon the solar panel .... 57
model parameters for 1670 m/s (I()2 incident upon SiO2-eoated Kat)ton. 58
model 1)arameters for 1670 m/s (102 inci(lent Ul)on Kat)ton ........ 59
model t)aramcters for 1670 m/s (102 incident upon Z-93-(:oated ahmlinum. 60
mo(lel t)aramelers for 4620 m/s It,2 incident ut)on the solar panel ..... 61
too(tel t)arameters for ,162() m/s tt2 incidenl ut)on Si()2-coaled Kat)lon.. 62
3
51 The Nocillamodel52 Tile Nocillamodel53 TheNocilla model
54 The Nocilla model
55 Tile Nocilla model
56 Tlle Nocilla model
57 The Nocilla model
58 The Nocilla model
59 The Nocilla model
60 Tile Nocilla model
61 Tile Nocilla model
62 Tile Nocilla model
63 Tile Nocilla model
64
65
66
67
parameters for 4620 m
parameters for 4620 m
parameters for 3180 In
parameters for 3180 in
paranleters for 3180 m
parameters for 3180 m
parameters for 3200 m
parameters tor 3200 m
/s H2 ilmident upon Kapton ......... 63
/s H2 incident upon Z-93-coated aluminum. 64
/s N2 incident upon the solar panel ..... 65
/s N2 incident upon SiO2-coated Kapton. , 66
/s N_ incident upon Kapton ......... 67
/s N2 incident upon Z-93-coated ahlminmn. 68
/s CO incident upon the solax" panel .... 69
/s CO incident upon SiO2-coated Kapton. 70
parameters fox" 3200 m/s CO incident upon Kapton ........ 71
paralneters for 3200 m/s CO incident upon Z-93-coated almninum. 72
tmrameters tor 2840 m/s CO2 incident upon the solm" panel .... 73
parameters for 28,10 m/s CO2 incident upon SiO2-coated Kapton. 74
parameters for 28,I0 m/s CO2 incident upon Kapton ........ 75
The Nocilla model parameters fox" 2840 m/s CO2 incident upon Z-93-coated aluminum. 76
Colnparison of the Reduced Force CoetIicient measurements fox" 1870 m/s N,_ incident
upon the solar panel made with the carrier gases H2 and He .............. 77
Comparison of the Reduced l%rce Coefficient measurements for 1870 m/s CO inci-
dent upon the solar panel made with the carrier gases H2 and He ........... 77
(lomparison of the Reduced Force Coefficient measurements for 1670 m/s (?02 inci-
dent upon the solar panel made with the carrier gases H_ and Ile ........... 77
4
Abstract
Measurements of monlentunl trans[er coetlicients were made for gas-surface interactions between
the Space Shuttle reaction (:ontrol jet tflume gases and the solar palml array materials to be used
on the International Space Station. Actual conditions were simulated using a supersonic nozzle
source to produce bealns of the gases with approximately the same average velocities as the gases
have in the Shuttle t)lumes. Samples of the actual solar panel materials were inounted on a
torsion balance that was used to measure the force exerted on the surfaces by the molecular
beams. Measurements were made with It2, N2, CO, and (I()2 incident upon the solar array
material, Kapton, SiO2-coatcd Kat)ton, an(t Z-93-coated A1. The measurements showed that
molecules scatter [rom the sm'faees more specularly as the angle of inciden(:e increases an(t that
the scattering behavior has a strong dependence upon both the incident gas and velocity. These
results show that tot some teetmical surfaces the simple assumption of diffuse scattering with
colnplete thermal accoxninodation is entirely inadequate. It is clear that additional measuremems
are required to produce models that more accurately describe the gas-surface interactions
encountered in raretied flow regimes.
1 Background
This I)roject was motivated by the need to ac<:urately model the forces exerted on the large solar
panel arrays to be used on the International Space Station by gases emitted from the reaction
control .jets on the Space Shuttle. This effort has been one of the largest ever undertaken to
measure and dmraeterize momentmn transferred to sm'faces by incident gases. The experimental
effort has resulted in the most comt)rehensive and accurate measurements ever made in this fieht.
I;sing this data it. is now possible to construct a limited number of accurate empirical models of
forces exerted on spacecraft surfaces by incident gases in rarefied flow regimes. The high accuracv
of these measurements also makes it, possible to obtain an mlderstanding of fllndamenta]
microscopic gas-surface interaction properties. The results of these experiments show that. even
fl'om technical surfaces, molecules scatter more speeularly as the angle of incidence increases, and
that the scattering has a strong dependence 1lt)Oll both the incident gas and velocity.
Theoretical advances were made in addition to the experimental contributions. _lYaditionally, the
momentum accommodation coefficients have been used to analyze the lnonlentllln transferred to
surfaces by incident gases in rarefied flow regimes, ttowever, the momentum accommodation
coefficients contain sing_flarities that render them unusable for a large mlmber of gas-surface
interactions, including those that are of specific interesl to NASA under im_estigation al LANI_.
Therefore, a new formalism was developed based upon two momentum transfer l)arameters <:alled
the reduced force coefficients. We have shown that tile nlacroscopic average momentunl
transferred to a surfa<:e bv incident lnolecules in raretied flow regimes can be completely
characterized using the reduced force coefficients. These coefficients can also 1)e used t<>
determined the magnitude and directioll of the flux-weighte<t average velocity of the scattered
ulole(;llles.
In the past. a kn(>wledge of the energy accommodation coefficient was required to determine the
flux-weighted average translational energy of the scattered molecules. Aeem'ate measurements of
energy a<:cOlninodation coefficients are difficult, however, and would introduce an additional
sour<:e of ml<:ertainty. A forinula was derived using the reduced force coefficients that acenrately
approximatesthe flux-weightedaveragetranslationalenergyof thescatteredmolecules,therebyeliminatingthe needto measureenergyacconmlodationcoefficients.This breakthroughmakesitpossibleto uniquelydeterminethe adjustableparametersin tile Nocillagas-surfaceinteractionmodelsolelyfrom measurementsof the momentumtransferredto surfacesby incidentgases.
Thisproject,to (latehasresultedin onePh.D.dissertationandsix refereedpublications[1, '2,3, 4, 5, 6, 7]. Fouradditionalmanuscriptsarenearcompletionandwill besubmittedtoPhysicalReviewE.The apparatushasbeenextensivelyimprovedandis nowfully operational.Inaddition,manynewandexcitingresultshavebeenrecentlyobtainedandwill bepublishedinfuture articles.
lRecently,a differentiallypumpedtime-of-flightsystemwasaddedto theapparatusthat will allowaccuratemeasurementsof thevelocitydistribution functionsof moleculesscatteredfrom surfaces.This systemwasdesignedsothat.during time-of-flightmeasulvments,the torsionbalancecanbeusedto simultaneouslymeasurethe Inomentumtransferredto thesurfaceby the incidentgas.This experimentalcapabilitywill makeit possibleto compareapproximatevelocitydistributionfunctionsof tile scatteredmoleculesconstructedfl'omthe nmcroscopicaveragetransferofmomentumandenergyto the surfacest)y the incidentgases,suchasthe Nocillamodel,with theactualmeasuredvelocitydistribution functionsof tile scatteredmolecules.
In addition,an improvedtorsionbalancehasbeenfabricatedthat canbeusedto measureboththe momentmntransfercoefficientsand theabsoluteflux densitiesof themolecularbeams.Thisnewtorsionbalancewill simplit}"theexperimentalprocedures,reducethe timetakento completea setof measurements,andincreasethe accuracyof the results.Accuracyis increasedmainlydueto eliminatingtheuseof massspectrometersto measurethepercentageof eachgasspeciesin themolecularbeams.
2 The Momentum Accommodation Coefllcients
The tangential cr and normal or' momentum accommodation coefficients can be expressed as [8]
-gi sin Oi - _._ sin 0_cr = , (1)
_i sin Oi
° r = '_'7i cos Oi -- Ts cos 0s_ ;' (2)
T'i cos Oi v/rrkT/2m
where ,77.,is the magnitude of the flux-weighted average (hereafter referred to as average) velocity,, 0
is the angle between the average velocity and the surface normal, the subscripts i and s represent
the incident and scattered molecules respectively, k is Boltzmann's constant, T is the temperature
of the scattering surface, and m is the mass of the individual gas molecules. The quantity
v/rrkT/2m is the average velocity of the scattered molecules assmning diffuse scattering from the
surface with complete thermal accomnlodation [8].
For many applications the tangential molnentuln accommodation coefficient has a removable
singularity at an angle of incidence Oi nornml to the surface and is well behaved. However, for
applications where 0., is not equal to zero at normal angles of incidence, the tangential coefficient
would diverge. Problems with the singularity in the normal momentum accommodation
coefficient result in divergent behavior for essentially every application involving a directed gas
flow. In addition, the angleof incidenceat whichtile sinKnlarityoccursis a flmctionof theaveragevelocityof the incidentmoleculesandthe temperatureof the scatteringsurface.For ttl("gas-surfaceinteractionsconsideredin this report, the angleof incidenceat whichthe singularityoccurredrangedfrom55_ to 85_. Thedivergentbehaviorcausedt)5,this singularitymadeitnearlyimt)ossit)leto useth(' normal(:oefiicient.
Toover(:omethis singaflarityproblem, Knuth [9] (teiined a norinal momentum transfer coefficient
that elinfinates the fml(:tional det)endenee of the singadarity upon the average veh)city of the
incident mole(:ules an(t lhe surfa(:e tenq)erature. However, the eoetlicient diverges at large angles
of incidence for all non sI)ecular scattering t)rocesses. Therefore, a new formalism was develot)ed
that (:ompletely eliminated the prot)lems (:ause(t t)y singularities.
3 The Reduced Force Coefficients
The definitions of the reduced force <:oetfieients were arrived at by considering the force exerle(t
on a surface by an incident molecular beam. The singulm'ity t)roblems were eliminated by defining
the coefficients with denominators that are independent of the incident flow direction. The
tangential ft and normal .f_ reduce(t force coeflieients are defined as
f,, _ F_,_+_,_ (4)
where _ is the magnitude of the average momentum, and the subscripts t and t_ are the tangential
and norinal components, respectively. The redu(:ed force coefficients can also be written as
where F is the nmgufitu(te of the for(:e exerted on the surface t)y the inci(tcnI gas, and Ni is 1he
total incident ihLx. Thus, the eoeiticicnt s can 1)e (let,ermined fi'om measurements of ['}, F_, 5,},
and "5i. Equations (3) and (4) can be u_d to express the magnitude and direction of the a_'erage
velocity of the st'at tered molecules as
"5._=-5i _(ft - sin Oi )'_ + (.fr_ -cos O_)2 (;)
( sin O_ - ft _0_ = tan ' kf-_ "'c_s:'O// " (8)
Spherical polar (:()ordinates are use(t to define the directions of the average velocities of the
incident and scattered molecules. The polar angle is measm'ed fl'om the surface normal, the
azimuthal angle is 18() _ for the average veh)('ity of the incident nlole(:ules and is assumed t() be 0 _
for the a_erage velocity of the scattered molecules, and the scattering surface is in the l)lane
define(t t)y the polar angle of 9(F.
A new parameter tt, called the scalar momentum accommodation coetiicient is introduced and
defined as
It-- (.q)
The quantity Pd is the magnitude of tile average monmntum of the scattered molecules assuming
diffuse scattering and is given by' v/rrkTm/2. The scalar momentum accommodation coefficient
ranges between zero for specular scattering and one for diffuse _attering with complete thermal
accommodation and is well defined for all angles of incidence.
For applications where differences between the average energies associated with the internal-state
distribution functions of the incident and scattered molecules can be neglected, the energy
accommodation coefficient e can be written as [8, 10]
= v7- la, (10)D
where _.,2 is the average of the velocity squared, and 41,'Tim is the average of the velocity squared
of the scattered molecules assuming diffuse scattering. A knowledge of the reduced force
coefficients is not sufficient to determine the energ__y accomnlodation coefficient using Eq. (10).
Additional information is required to determine v_. The simple assumption of equating vr2t._with v-7
can result in errors as large as 60_:.. A more accurate approximation for u"7__ can be nmde with an
energy accommodation coefficient e' based on the average velocities of the incident and scattered
molecules. The coefficient is defined as
= _2 _ rr/,:7/2m,,) • (11)
From a knowledge of the reduced force coefficients and the velocity distribution function of the
molecular beam, the coefficient e_ can be calculated. The uncertainty associated with the
approximation of equating e' with e has 1)een shown to be less than 4-1_ for gas-surface
interactions where the average energy of the incident molecules is large comt)ared to/,'T [1]. With""7-
this appi'oximation, ui_ can be written as
(_2)
m
The quantity v/2 can be determined from a knowledge of the velocity, distribution function of the
incident molecules. The average translational energy of the scattered molecules can be obtained
using Eq. (12).
4 The Nocilla Gas-Surface Interaction Model
']?he Nocilla gas-surface interaction inodel assumes that the velocity distrit)ution function of the
scattered molecules can be approximated using a drifting Maxwellian (tistribution fimction with
most probable velocity U defined as [11]
N (v) = ,, exp 2a-T ]' (la)
where n and T, are the number density and temperature of the scattered molecules, respectively.
The adjustable parameters in the Nocilla model are n, T,, and U. The most probable velocity of
the scattered molecules is assumed to lie in the plane formed by the surface normal an(l the
average velocity of die incident molecules. Equations (14)-(17), obtained by integrating Eq. (13),
can be used to determine the four Nocilla model paranleters:
where
T._sin 0_ = g_"sin 0,,.
,,_A<,'_+,/_(_+a') _7r_cos O_ = ,S' c a_ + v/-ffAE
t,(2+ s")_,:'_++v(}+ s")a,_c_ = 5,2 ( a_ + V/-_AE '
(1.1)
(15)
(16)
(17)
s - (as)
A = N cos Ou, (19)
E = 1 4-erfA. (20)
and 0, is t.he angle t)etween the surface nornlal_ is the flux density of the scatt.ered niolecules,
and the most. probable velocity U. IMng Eqs. (15), (16) and (17) it can t)e shown thai
5'sinO,, (c "_+ x/_,AE)tail 0,s = ' (21 )
A_. "2 + v_ (½ +a2) E'
'S'" 0'2(c A2 x/'_AE)('G sin 0,,)2 (, Slll u) -_-- (22)AE"
_lb determine S and 0,,, Eqs. (21) and (22) can be evaluated iteratively. Then Eq. (15) is used to
deterinine U, and E(I. (18) is used to obtain T,.
\Vhen t.he scattering angle 0,, is equal t.o zero, Eq. (15) implies 0,, Inust equal zero or 18W. l_br
this sl)ecial case, ,q can 1)e (teternlined fronl an equation obtained bv confl)ining Eqs. (21) and
(22), given t)y
,,_ a (_ _'_± v_SE ') (2:_)
W] lel'e
E'= 1:1: eft& (21)
_(5t,,:2 )a = (e+,_'_)_-'_+ v,_ +,_" s_' (25)The phis sign is used if 0u equals zero while the minus sign is used if 0,, equals 180 _. Once ,_,'is
known, U can be evaluated iteratively using Eq. (16). t_br all cases, after 0u, U, and N have been
determined, n cmi be obtained fixmi Eq. (14) 1)y equating the incident and exit fhLx-densities.
The angular dist.ribution function I is (tefine(t l)y letting I (0, O) dt_ ret)resent the fraction of qb,
t.hat scalAers into the differential solid angle dtl about the direction define(t by 0 and 0. where 0 is
the spherical coordinate azimuthal angle. [;sing the Nocilla model to approximate the angular
distribution function of tile scattered molecules Rives
where
and
(-) (,- S 2
I (o, = - cos o (2 s)
O =14- fl2 -1- v/'_p (3 + p2) (l + erfp) e p2, (27)
fl = S (sin 0 cos 0 sin 0,, + cos 0 cos Oct). (28)
Tile angular distribution fimction can also be thought of as representing the probability that a
molecule with incident velocity vi scatters into the solid angle d{/about the direction defined by' 0
and 0- Once the Nocilla model parameters have been determined, Eq. (26) can be used to
approximate the angular distribution ftmction of the scattered molecules.
5 Experimental Results
The experimental results were obtained from measurements of the forces exerted on surfaces by
molecular t)eams of the gases using a torsion balance. The torsion balance apparatus used to
measure the forces, along with the techniques used to measure the flux-densities and velocity
distribution functions of the moleeulm" beams are described elsewhere[l, 2]. The average velocities
of the molecular beams ranged fi'om 1670 m/s for CO2 to 4620 m/s for H2. The total uncertainty
in tile reduced force coefficient measurements is estimated to be less than 4-1@){.
Measurements of the reduced force coefficients for N2, CO, and CO2 incident upon the solar
panel, SiO2-coated Kapton, and Kapton showed that these gas-surface interactions have many
similarities. Scamfing electron microscope measurements revealed that the solar panel,
SiO2-coated Kapton, and Kapton had similar surface roughness and were smooth on a scale of
less than 1 inn. while the Z-93-coated ahmfinum surface was rough on a 100 #m scale. This
contrast in surface roughness could account for the significant differences between the way thefour gases scattered from Z-93-coated aluminum and the other three surfaces.
Figures 1 32 are plots of the reduced force coefficients, -iT,s/Ti, Os, and t t as a flmction of the angle
of incidence Oi for the various gas-surface interactions, while Tables 1-32 contain all actual
experimental data. The gases N2, CO, and CO2 can be seen to scatter from Z-93-coated
alunfinum diffusely with ahnost complete thermal acconlmodation by noting that 0_ is close to
zero and t t is close to one at all angles of incidence. H2 can be seen to scatter froin Z-93-coated
alunfinum diffusely by noting that Os is (;lose to zero ['or all angles of incidence. However, fl varieswidely over the range of angles of incidence.
For the gases incident upon the solar panel, SiO2-coated Kapton, and Kapton gr and 0_ increase
as the angle of incidence inex_ases, consistent with the scattering becoming more specular. For
large angles of incidence, the scattering angles for CO2 are larger than for N2 and CO, and the
scattering angles for N2 and CO are larger thml for H2. ]'his effect can be explained by" noting
that tile mass of H2 is significantly smaller than the mass of N2 and CO, and the masses of N2
and CO axe smaller than the mass of CO_ and that a given force perpendicular to the direction of
motion wouM deltect H2 more than N2 and (IO. and would deflect N._ and CO more than CO2.
10
Thus,for largeanglesof incidencewherethe scatteringbecomesmorespecular,it. is reasonabletoassumethat the largerepulsiveforceexertedon themoleculesby thesurfacewill deflect[12morethan N2and(70, andwill deflect,N2andCO morethanC()2.
In Figs.33 61,polarplotsof theangulardistributionfunctionsof the scatteredmoleculesareshownfor the variousgas-surfaceinteractions.The Nocillamodelparmnetersareshownin Tahles33 64andwereobtainedfor the gas-surfaceinteractionsusingthepreviouslyoutlinedprocedure.Negativevaluesfor 0,, imply that 0,, is 180 _'. Equation (26) was t hell used to calculate the
angular distribution functions. In these figures, the origin can be thought of as the impingement
point of the molecular beam, the vertical axis is perpendicular to the scattering surface, and the
horizontal axis is defined by the projection of U onto the plane of the scaltering surface. I:igln'es
33 64 show the intersection of the plane formed by the average velocity of the incident molecules
and the surface normal with the three-dimensional angular distribution functions. The distance
from the origin to a point on a lobe times dt_ represents the pl'obahility that a molecule wilh the
indicated average velocity scatters from the surface into a differential solid angle dft about the
direction defined 1V 0 and 0. These distances are defined by the tick marks on the horizontal and
vertical axis. The portion of the horizontal axis to the right of the vertical axis corresponds to
0 = 0, and the portion to the left of the vertical axis corresponds to 0 = 18(F. The polar angle is
given along the circular axis of the graphs.
The general trend that the scattering t)ecomes more specular with increasing angles of incidence
for gases scattering from the solar panel, SiO2-coated Kapton, and Kapton can b(' inferred fl'om
Figs. 33 64. As the angle of incidence increases, the lobes become much larger 1)ecmlsc of the way
in which the angular distribution function is normalized according to the equation
I (0, 0) d[_ = 1. (2.9)
This hehavior has flm(lamental physical significance. As the angle of incidence increases, the size
of the lobes also increases, meaning fewer partMes scatter out. of the plane formed by the average
velocity of the incident molecules and the surface normal. This effect is lnore t)ronounced for N2.
(:(), and C()2 than for }t2 and for the larger incidenl velocities.
The figmres show that scattering from Z-93-coated aluminum is nearly diffuse for all angles of
incidence. This result was observed for all gases incident upon Z-93-coated aluminum and at all
incident velocities. Nearly diffuse scattering is most likely due to the extremely rough surface
mol3)holog.v of Z-93-coated aluininmn.
Tables 65 67 compare nleasurenlents of the reduced force coefficients for N2. ('O. and ('02 inade
with the carrier gases tt_ and tie. The data agree io within the uncertainty of the lneasuwments
for all angles of incidence except 85 _. AI this angle of incidence aligmnent of the sample with the
molecular beam is extremely critical. A minor misalignment could result in a kaction of the beam
nlissing the sample. The large discrepancy at the angle of incidence of 85 '_ could be due to this
effect.
6 Conclusions
,kt. Ile!.v formalisin has been use(t to analyze the average momentunl transferred to sm'faces 1)v
ineidenl gases. This new tbrmalism eliminates the singularity problems associated with the
11
momentumaccommodationcoefficientsandcanbeusedto uniquelydeterminethe Nocillagas-surfaceinteractionmodelparameters.The formalismeliminatesthe needto measureenergyacconmlodationcoefficients,therebyreducingthe numberof experimentallydeterminedparametersrequiredto obtain th0Nocillamodelparameters.
Tile resultsdiscussedin this report showthat moleculesscatterfrom technicalsurfacesmorespecularlyastheangleof incidenceincreases,andthat thescatteringhasa strongdependenceuponboth theincidentgasandvelocity.The_ resultsshowthat for sometechnicalsurfacesthesimpleassumptionof diflk_sescatteringwith completethermalaccommodationisentirelyinadequate.
References
[1] S. R. Cook, Ph.D. thesis, The University of Texas at Austin, 1995.
[2] S. R. Cook, M. A. Hoffbauer, J. B. Cross, H. Wellenstein, and M. Fink, Hey. Sci. Instmm.
67, 1781 (1996).
[3] S. R. ('ook and M. A. tIoffbauer, Phys. Rex,. E 55, R3828 (1997).
[4] S. R. Cook, J. B. Cross, and M. A. Hofi%auer, in Ra_'efied Ga._ Dynamics 19, edited by J.
Harvey and G. Lord (Oxford ITniversity Press, Oxford, 1995), Vol. '2, pp. 967 973.
[5] S. R. Cook and M. A. Hoffbauer, in RaTv.fied Gas Dynamics 20, edited by C. Shen (Peking
University Press. Beijing, 1997), pp. -m_ 4_..
[6] S. R. Cook and M. A. Hoffbauer, J. of Spacecraft and Rockets 34, 379 (1997).
[7] S. R. Cook an(t M. A. Hoffbauer, J. of Vac. Sci. and Tech. A 15, 1 (1997).
[8] S. A. Schaaf, in Encyclopedia of Physics, edited by S. F]/igge and C. Truesdell
(Springer-Verlag, Berlin, 1963), No. 2, pp. 591 624.
[9] E. L. Knuth, AIAA Journal 18, 602 (1980).
[10] Dynamics of Cas-5"uffacc Intcvactio't_s, edited by C. T. Rettner and M. N. R. Ashfold (The
Royal Society of Chemistry, (lambridge, 1991).
[11] S. Nocilla, in Rarefied Cas Dynamics, edited by J. A. Laurmann (Academic Press, New York,
1.()63), Vol. 1, pp. 327-346.
12
_0
c-
O
OO(Doi,=.
0U_
"0
0
"0
CK
1.5
1.0
0.5
0.0
75
60
.-. 45Or)
30
"0v
_ 15
! • ! • ! ! ! !
I
(a)
• ! , t , I , I i | i
! ! • ! , ! !
(c)
/m _lf
m--
(b)
I , I
1 • I
(d)
i • i • i • i •
/m _m__ram/ \i
I i I m I i I *
I • I I I
/
I i I * I , l * l , I , m I , I * I m I
0 15 30 45 60 75 90 0 15 30 45 60
O,(degrees) oi (degrees)
Figure 1: The data for 2590 m/s 1t2 incident upon the solar panel.
1.0
0.8
0.6
0.4 -_ i
0.2
0.0
1.0
0.8
0.4
0.2
, ' , 0.075 90
Table 1:2590 m/s [I2 incident upon the solar panel
0i (dcgTees) f, f,, W_/T.'i T., (m/s) 0s (degrees) t' (' c"7 (m/s) 2
0 0 1.59 (1.586 1520 0 0.88_ 0.91_ 5.02x 1() (_
25 0.317 1.48 0.587 1520 10.3 (/.886 0.916 5.02× 10 (_
50 0.612 1.28 0.656 1700 13.6 0.738 0.796 5.25× 10 (;
75 0.750 0.85J 0.633 1640 19.9 0.788 0.839 5.17× 1()_
85 0.619 0.539 0.588 1520 39.8 0.883 0.915 5.03x 10 _i
1;3
1.5
¢/J
¢-.ID
O_" 1.0
00
0I,--
0LL 0.5"O
0
0.0
75
6O
...-. 45(/)
3O
"0v
_' 15
I " I '
-O
J"e_ (a)
I • I • I . I i | i | i I
I I " I • I I I I
./fai
jm" (c)
I , i , I • i • I • I . I
0 15 30 45 60 75 90
O,(degrees)
I " I • I " ! ' I
III j/
11
!
11
(b)
_m _n ---n
I • I • I • I I I a I I I
I I I I I I
_11 111
(d)
I t I t I , I , I , I • I
0 15 30 45 60 75 90
O,(degrees)
Figure "2: The data for 2590 m/s I-I2 incident upon SiO2-coated Kapton.
1.0
0.8
0.6
C:l*...
0.4 --_ t
0.2
0.0
1.0
0.8
0.4
0.2
0.0
Table 2:2590 m/s H2 incident llpon SiO2-coated Kapton
0 0 1.52 0.520 1350 0
25 0.307 1.48 0.585 1510 11.4
50 0.584 1.26 (/.645 1670 16.4
75 0.733 0.893 0.676 1750 20.1
85 (I.656 0.653 0.660 1710 31.0
1.03 1.02 4.82× 10 6
0.891 0.920 5.02×106
0.761 0.816 5.22× l0 G
0.696 0.760 5.32x10 _
0.129 0.18. 5.27×10 _
t4
..... . , • , 1.0
1.5
c-
.D
0
1.00
0
0
0LL"0 0.5
0
"0
n'-0.0
75
60
..-. 45O9
30"0v
_" 15
(a)
I ' I " I " !
ill
....---- III _11J
jB
(c)
I I I . I I i i i I
0 15 30 45 60 75 90
0i (degrees)
f..J \mJ •
(b)
0.8
0.6
0.4 -._ i
0.2
I , ! , | , I , I ' ' " ' 00.
I ' I " I ' I ' I I !
1.0
0.8
0.6
0.4
0.2
' ' ' ' ' ' ' 0.015 30 45 60 75 90
ei (degrees)
(d)
I , I
0
Figure 3: The data for 2590 m/s H2 incident ut)on Kapton.
Table 3:2590 m/s tt2 inciden! upon Kapton
o_(d_g-,.,_e_) f_ f,, _/_ ,__._(,,/_) O_(d_.g,.e_._) t' _' '_'_(m/_)_
0 0 1.54 0.540 1400 0
25 0.340 1.51 0.606 157/) 7.8/)
50 0.625 1.28 0.657 1700 12..1
75 1/.826 0.907 1}.663 1720 12.2
85 0.833 0.635 /1.571 1480 16.6
0.986 1).990 -1.88× 10(;
0.8,15 0.885 5.118x 10(;
0.735 0.79,1 5.26×10 G
0.721 0.78,1 5.28;_< I(F_
0,920 0.9,12 4.!)7× l()_;
15
1.5oo
r-ID
1.00
0
(3
0IJ_•"o 0.5
0
rr0.0
75
60
.-.. 45cf}
30
"13v
_' 15
! " ! ' I ! • ! , !
• _I --I--_t
/(a)
I • i i I i i • I , I . I
I " I ' I " I ' I ' I
(c)
• _m -_m
i • i . i " I , I i I m I
0 15 30 45 60 75 90
O,(degrees)
, . , • , • , • , 1.0
/m_ I
i _____._---I -- \
(b)
I m I i I _ I L I , I
! I " I ' ! I ' I '
-= /
(d)
l . I , I • l • I • i I I
0 15 30 45 60 75 90
O,(degrees)
0.8
0.6
0.2
' 0.0!
1.0
0.8
0.6
0.4
0.2
0.4 ~._ m
Figure 4: The data for 2590 m/s H2 incident upon Z-93-coated aluminum.
0.0
Table 4:2590 m/s H2 incident upon Z-93-coated aluminum
Oi (degrees) St St, T's/'gi '_L'_s(in/s) Os (degrees) t* e' v"7 (m/s) 2
0
25
50
75
85
0 1.53 0.535 1380 0
0.388 1.46 0.551 1430 3.59
0.745 1.26 0.613 1590 1.96
1.02 0.839 0.582 15111 -5.02
1.06 0.594 0.511 1320 -7.25
0.998 0.999 4.87× 106
0.963 0.973 4.91×106
0.830 0.873 5.11x106
0.897 0.925 5.01×106
1.05 1.03 4.80× 10[;
16
-- , ...... 1.0
1.5(/1
c"(1)
o_
0°_
::I::m 1.000
0
0LL•"o 0.5
0
rr0.0
75
60
45(/)
oIm 30
v
_ 15
0
.\
(a)
i • i • i • i • i I l
//
(c)
i i | i | i I • | , I i I
0 15 30 45 60 75 90
(degrees)
(b)
1.0
0.8
0.6\
0.4
0.2
(d)
, . , , , . ' . ' .... 00.0 15 30 45 60 75 90
(degrees)
[:igure 5: The data for 1870 m/s N2 incident upon the solar pane].
"t::
Table 5:1870 m/s N2 in(:ident upon tile solar panel
Oi (degrees) f, .[,, T._/,_i T8 0n/s) 08 (degrees) t' (' _ (m/s) 2
0
25
50
75
85
0 1.26 0.262 .191 0
0.362 1.17 (}.274 513 12.8
0.628 0.949 0.;}35 629 24.3
0.67. () 0.581 0.431 808 41.7
0.522 0.340 0.537 1010 61.9
0.920 0.96!) -1.487, 105
0.905 0.963 1.69>< 105
0.828 0.924 5.94× l0 s
0.71).(-) 0.847 8.37> 10r,
0.577 0.7,10 1.187,I0(;
17
1.5
GOt--CD
1.00
0¢D0
0I.t.._ 0.5
¢.)-1
CDcc
0.0
75
6O
.--. 45O9
3OCD
v
_' 15
0
(a)
i . i i I i i A i _ I , I
! I l I ' I ' l ' !
./
(c)
i . ! , I . ! I . i . J
0 15 30 45 60 75 90
O_(degrees)
_J"
/
(b)
I , i L I , I _ I . ! • I
! • i . ! • I • i • I !
=\
(d)
I _ l • I • i i i i l , I
0 15 30 45 60 75 90
O_(degrees)
0.8
0.6
0.4 -_ i
0.2
0.0
1.0
0.8
0.4
0.2
0.0
Figure 6: Tile data for 1870 m/s N2 incident upon SiO2-coated Kapton.
Table 6:1870 m/s N2 incident tlpon SiO2-coated Kapton
Oi (degrees) It jr,, vs/v_ v8 (../_) o.,(degrees) # _' _,_(m/s?0 0 1.25 0.247 46,1 0
9 "25 0.350 1.16 0.-6_ 501 15.8
50 0.602 0.945 0.344 645 28.5
75 0.658 0.603 0.462 865 41.9
85 0.578 0.412 0.530 993 52.1
0.938 0.977 4.23x105
0.913 0.966 4.57x105
0.818 0.918 6.13×105
0.671 0.819 9.29× 10r)
0.586 0.748 1.15× 106
18
I " i • I " I • ! I l I i ' i • i " , " I ' I 1.0
1.5
o_¢-
(..)
1.00
0(1)EO
u_-_ 0.5
O
"ID
rr0.0
75
6O
,._, 45if)tD
3OtD
"Ov
_ 15
O_
"-O
_m _m
"\.
m/ (a)
| , I i I i i I I I I • I
I I I I l i I
_.jm
(c)
I , I i I i I , I • I i I
0 15 30 45 60 75 90
0i (degrees)
/m _m --m
._...m/m /
0.8
0.6
0.4 -._ m
0.2
(b)
l m I m I , I , I , i , i 00.
i ' I • I ' i I I I
1.0
0.8
m_m_
kI _m --m
0.6
0.4
0.2
(d)
.... , . , . , .... 00.0 15 30 45 60 75 90
0i (degrees)
"l:::
Figure 7: The data for1870 m/s N2 incident upon Kapton.
Table 7:1870 m/s N2 incident upon Kapton
Oi (degTees) ft f, V.,/Vi T._On/s) O_ (degrees) t' _' e-_"(m/s) 2
0 0 1.25 0.2-18 465 0
25 0.366 1.19 (3.288 5,1(t 11.3
50 0,638 0.959 0.3,11 639 22.1
75 0.7,10 0.60.9 (t.417 781 32.8
85 0.722 0.40:_ 0.418 78,1 40.9
0.937 0.977 ,1.25× l0 s
0.888 0.95.1 ,1.96x10 r'
O.821 0.920 6.07 × 105
0.727 0.860 7.98× 1()5
0.725 0.858 8.02× 10r,
19
1.5¢J0
,4,...*¢-
,mO
fi51.0
00
0
0Ii•"o 0.5
0
"0
rr0.0
75
60
.-.. 45ca0
lm 30
"0v
15
I • i • I I • i • I
0_
/'\./ "\
/ (a)
I . i i I i I i I , I , I
I ! ! I I • i • I
(c)
i / xI
I , ! • I
l . I i , i , I i I i I
0 15 3o 45 6o 75 9o
(degrees)
I
I
m-
, • , • , • , 1.0
(b)
• __---m ------I --m
i • i I m I m I , I
| • l • I • I . I • I
(d)
--m _m ---__---m /I
i . m • I m I , I m I
15 30 45 60 75 90
(degrees)
0.8
0.6
0.4 -_: m
0.2
0.0
1.0
0.8
0.4
0.2
0.0
Figure 8: The data for 1870 m/s N2 incident upon Z-93-coated aluminun_.
Table 8:1870 m/s N2 incident upon Z-93-coated alunfinum
0 i (de.l_l'ees) It f,, g,/_i t', (m/s) O_ (degrees) # e' v"_"(m/s) 2
0
25
50
75
85
0 1.21 0.211 3q5 0
0.408 1.12 0.218 409 3.82
0.747 0.889 0.247 463 4.45
0.962 0.506 0._4_ 464 0.851
0.987 0.308 0.221 414 2.34
0.984 0.994 3.68× 105
0.975 0.991 3.78×105
0.939 0.977 4.23x105
0.938 0.977 4.23 × 10"_'
0.971 0.990 3.82×105
20
1.5Or)
E
O0--
1.00
0
0
0I.L-o 0.5
0
n"0.0
75
6O
.-. 45
3O
_'_ 15
_m \
O \
\-
(a)
i I I i I ' u • I
/f
(c)
I , I a i I l m I * n , I
0 15 30 45 60 75 90
0 i (degrees)
(b)
n , I • , • , . , , , . , 0.0
! ' u ' I ' i ' u • i • I
1.0
0.8
m_m_
\0.6
0.4
0.2
(d)
i . , . , , , , I , ' . ' 00.
0 15 30 45 60 75 90
8i (degrees)
3=
Figure 9: The data for 1870 m/s (!O incident upon the solar panel.
Table 9:1870 m/s ('() incident upon the solar panel
0,: (d,_aT_es) f, .f,, Ts/Ti ,.", (m/s) 0s (deg,'ces) /i " "_ ('"/,_7
0 0 1.26 0.260 488 0
25 0.366 1.18 0.279 524 11.7
50 0.634 0.948 0.333 621 23,,1
75 0.688 0.577 0.123 7.03 ,11.2
85 0.530 0.338 0.530 .0.(_;_ 61.7
0.922 0.970 4.46X 10'_,
0.898 0.959 1.80× l()'_'
0.832 0.925 5.89× 1()r'
0.719 0.855 8.15×10 r,
0.586 0.74.9 1.15×10 (;
21
1.5¢0
c-Ill
o_
O
m 1.00
0
0
0U_•"o 0.5
0
n"0.0
75
6O
..-.. 450
c:m 3o"0
_' 15
I • i , ! • ! • ! • !
Q__D
\
(a)
I , t . I " I , I a i _ I
I ! ' I " I ! " ! ' I
./
(c)
I • i " ' ' I , I , I , I
0 15 30 45 60 75 90
0i (degrees)
, • , • , • , • , • , 1.0
m
• ____.--m _m"
/
(b)
| I i , i i I • i i I
I • ! • i • i I I I
• _m _m
(d)
I , I I i * I , I , I
0 15 30 45 6o 7s 9o
(degrees)
0.8
0.6
0.4 -_: m
0.2
0.0
1.0
0.8
0.4
0.2
0.0
Figure 10: The data for 1870 m/s CO incident upon SiO2-coated Kat>ton.
Table 10:1870 m/s CO incident upon SiO2-coa,ted Kapton
Oi (degTees) ft fr, -#_/'5i "_s (m/s) Os (degrees) tt (' v-7_2 (m/s) 2
0 0 1.25 0.249 :167 0
25 0.352 1.16 0.265 497 15.4
50 0.611 0.944 0.339 635 27.2
75 0.666 0.596 0.451 845 41.7
85 0.589 0.406 0.517 970 51.9
0.936 0.976 4.26×105
0.916 0.968 ,1.54×10 r'
0.824 0.921 6.02× 105
0.685 0.829 8.96×10 _
0.602 0.762 1.11×106
'2'2
, . ....... . , . , . , . , , . , 1.0
1.5q)
c-a)
°_
0
1.00
0
0
0LL
O.G
0cI
23
rr0.0
75
60
,,-., 45
30
"0v
15
O_11
"\.
(a)
I * I _ I i I • I • I • I
I I I " I " I I I
(c)
I I I I I • I • I • I , l
0 15 30 45 60 75 90
(degrees)
_111 --II
/I j
i1_ IIj
(b)
0.8
0.6
0.4 ~_ i
0.2
' ' ' ' ' ' ' ' " ' ' ' 00.
I I I I I " I " I
1.0
0.8
0.6
0.4
II _11 ___.__
_11 roll
0.2
(d)
I , I , I , I • , • ' " ' 00.0 15 30 45 60 75 90
0i (degrees)
Figure 11: The data for 1870 Ill/,"; (IO incident upon Kapton.
Table 11:1870 m/s CO incident upon Kapton
0i (degTees) .f, .f,, T._/Ti T.s (m/s) 0_ (degrees) t' " _ (m/s) 2
0 0 1.26 0.259 486 0
25 0.371 1.19 0.290 514 10.3) -50 0.6,11 0.956 0.337 633 21.
0._4o 0.603 0.409 766 32.675 " _-
85 0.728 0.400 0.412 772 -10.6
0.923 0.,971 4.4,1 × l(}r'
(1.885 0.953 5.00× l0 s
0.826 0.922 5..(t9× 10r'
0.737 0.867 7.76× 10'_'
0.733 0.86,1 7.84× lOr'
23
1.5
_0.O..d
c-ID
Oo_
1.00
00
0ii._ 0.5
0
n"0.0
75
60
._. 45¢/)
0
o_ 30
v
_ 15
I I I I I I " I
O_
_o _o._/..,.......n _u
./ °\
J(a)
• •
I • t • n • | a I . I , I
I u I I • u • I ' u
(c)
._...n .---------------- m• / _m --m
m • n . i . I * I , I , I
0 15 30 45 60 75 90
O, (degrees)
, • , • , • , 1.0
• __ • ___--m -m"-m
(b)
I . I , I , I I m i I
l I " ! " I I | | ' I
• n _m ----___--m_m
(d)
I . I • I I I • l l I
0 15 30 45 60 75 90
0, (degrees)
0.8
0.6
_o
0.4 --_o
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
"l=:
Figm'c 12: Tile data for 1870 m/s CO incident upon Z-93-coated alunfinum.
Table 12:1870 m/s CO incident upon Z-93-coated aluminum
Oi (degrees) ft fi, Ts/Ti '_s (m/s) 0._(degrees) # e' t,-_s2 (m/s) 2
0
25
50
75
85
0 1.22 0.215 404 0
0.409 1.13 0.221 414 3.52
0.746 0.890 0.248 466 4.65
0.963 0.507 0.248 465 0.687
0.991 0.309 0.222 416 1.45
0.978 0.992 3.74× 105
0.971 0.990 3.83x105
0.937 0.976 4.25x105
0.938 0.977 4.24×105
0.970 0.98!) 3.84x105
24
1.5(D
c-
.m
O
1.00
0
0u_._ 0.5
"00
0.0
75
60
..-. 45
_ 30
V
_'_ 15
0
(a)
/
(c)
I • I , I • I . ! , I , I
0 15 30 45 60 75 90
(degrees)
(b)
I , I , I , , • , • J • , 0.0
I " I " ! " I " , I I
1.0
• 0.8
\0.6
0.4
0.2
' . ' , ' ........ 0.00 15 30 45 60 75 90
ei (degrees)
3:::
Figure 13: The data for 1670 m/s CO2 incident upon the solar panel.
Table 13:1670 nl/s (',02 incident upon the solar panel
Oi (degTees) ft f,, Ws/"Yi Ta (m/s) 0,, (de_rees) tt ,:' _ (m/s) 2
0 (l 1.21 0.213 355 0
25 0.381 1.13 0.227 37.9 10.5
50 0.66 ] (/. 891 0.269 449 22.9
75 0.734 0.519 0.348 582 41.7
85 0.562 0.288 0.478 799 65.2
0.957 0.986 2.60>< 10s
0.93.9 0.979 2.77×10 r'
0.888 0.958 3.33× 10r'
0.792 0.907 ,1.6.1× 10s
0.634 0.796 7.52×10 s
25
1.5
or)E:(_
°n
0°_
::I:=1.0
o0
0
0Im"0 0.5
0
"0(3
rr"0.0
75
6O
..-. 4500
(_
(:_ 3O
....... 1.0
(a)
I • l , I , I • I , I • l
! I I I " I ' I " I
m
./
(c)
I I • I • I • I • I
15 30 45 60 75 90
0 i (degrees)
• _____--m _m
(b)
0.8
0.6
/
0.2
............. 00.I I I I I I I
1.0
0.8
\
0.6
0.4
0.2
m ---____..._ m
(d)
............. 00.0 15 30 45 60 75 90
ei (degrees)
Figm'e 14: The data for 1670 m/s CO2 incident upon SiO2-coated Kapton.
0.4 --_ m
Table 14:1670 m/s C()2 incident upon SiO2-coated Kapton
Oi (degrees) ft fr, T's/"Fi _,_ (m/s) 0s (degrees) tt c' v-7 (m/s) 2
0 0 1.19 0.194 324 0
25 0.366 1.lO 0.206 344 16.0
5(1 0.630 ti.889 0.281 469 28.9
75 0.699 0.536 0.385 6,12 44.0
85 0.627 0.350 0.453 757 54.5
0.980 0.994 2.39x105
0.965 0.988 2.53×10 s
0.874 0.951 3.50×105
0.748 0.880 5.35×10 '_
0.664 0.820 6.89×10 '_
26
1.5(D
r"
.m
{jzl:=
1.00
0
OIi
._ 0.5
O
(D
0.0
60
..-. 45tOII1
c_ 3O03
"Ov
_" 15
0
(a)
| I I • I • I , I I , I
./
(c)
I , I , I I I , I , I
0 15 30 45 60 75 90
0i (degrees)
(b)
I _ I
! i
EE_ EE-......._
(d)
0.8
0.6
0.4 -_3 I
0.2
.... ' ' ' ' ' 0.0i I I I I
1.0
_'m _,, 0.8
0.6
0.4
0.2
l , I , I , I , I , I , I 00.
0 15 30 45 60 75 90
0 i (degrees)
Figure 15: The data for 1670 m/s (102 incident upon Kapton.
Tat)le 15:1670 m/s ('O2 incident upon Kal)ton
Oi (degrees) f, f,, vJ-e, r,, (.,/.) o. (deg,._..-,_) /, ,' ,,_ (m/s) _
0 0 1.21 0.210 351 0
25 0.381 1.13 0.232 388 10.3
50 (1.66-1 0.897 0.274 457 21.9
75 0.769 0.511 0.34.1 574 35.0
85 (/.745 0.345 0.360 601 44.2
0.960 0.987 2.572 l0 s
0.933 0.977 2.83× l()r'
0.883 0.955 3.39× 10s
0.797 0.910 4.56× 1(}r)
0.778 0.899 -1.86× 10r,
27
1.5{D
¢--O)
.mO
°m
1.00
(O
0
01.1_•._ 0.5
0
or-0.0
75
60
,-, 45Or)
I:_ 30
"0v
15
0
e_
t_ m _m
.// .\/ (a)I , I , I _ I • I . I • I
• • ____-.-m---------m_m
(b)
(c)
_--m.-------m _m ..-.-mm /
m . i , i • i , i , i , i
0 15 30 45 60 75 90
0i (degrees)
0.8
0.6
0.4 -._ m
0.2
' ' ' ' ' • ' ...... 00.I • l • m , l • !
• _m -------_---mIN
(d)
!
m . i . , . I m I , I , m
0 15 30 45 60 75 90
0i (degrees)
!
1.0
0.8
0.6
0.4
0.2
0.0
Figure 16: The data for 1670 m/s (!02 incident upon Z-93-coated Muminum.
Table 16:1670 m/s CO2 incident upon Z-93-coated alunfinunl
Oi (degrees) f, f,, _8/_i ,'g, (m/s) O_ (degrees) t' e' v-_'_(m/s) 2
0 0 1.18 0.177 295 0
25 0.410 1.08 0.178 297 3.93
50 0.748 0.848 0.206 345 5.07
75 0.957 0.467 0.208 348 2.34
85 0.98,1 0.270 0.184 307 3.85
1.00 1.00 2.22 x 105
0.999 1.00 2.23 x 105
0.964 0.988 2.53× 105
0.962 0.988 2.55×10 r,
0.992 0.998 2.29x105
28
1.560
t-(11
°_
0Zl=
1.00
0(D2O
It.-o 0.5
¢)
"O
0.0
75
60
.-. 45¢/)
0)hi
c:_ 30(1)
2Dv
15
I I
=/ (a)
I , I , I , I • I . I , !
(c)
I
I
I
• _m ___--m --m
(b)
. I _ I , I • I • a . I
! I I I I I
(d)
• _m _m _m
I , ! • I I I . I
0 15 30 45 60 75 90 0 15 30 45 60 75
(degrees) oi (degrees)
F'igure 17: The data for 4620 m/s H2 incident utlon the solar panel.
• i
90
, 1.0
0.8
0.2
0.0
0.6
0.4 --_ m
1.0
0.8
0.6
0.4
0.2
0.0
Table 17: 462(I m/s tt2 incident upon the solar panel
Oi (degl'ees) J) f,, T_/Ti T_ (m/s) O. (degrees) t' ,, ,,'-_z(m/s)_
0 0 1.57 (1.572 2650 0 0.610 0.738 .().32x106
25 0.370 1.48 (/.575 2660 5.25 0.607 0.735 9.36x l()(_
50 0.656 1.23 0.593 2740 10.7 0.580 0.712 .(1.77x 1()(;
75 0.720 0.823 0.616 2850 2;{.5 0.548 0.682 1.03_, 107
85 0.564 0.538 0.624 2800 ,13.8 0.536 0.670 1.05× lO7
29
1.5q)
¢-
¢)°_
_) 1.00
0(1)¢J
0Ii-_ 0.5
¢J
"0
rr0.0
75
60
..-. 45(/1
30"Elv
_" 15
! , . , . , • , • , • , • , 1.0
_0 --II--f t
(a)
I , I , I , I . I • I , I
I I I I I I I
(c)
/
j•l
1tll --II
1
11 ------____.__ 11 J
(b)
0.8
0.6
0.4 -_ t
I • I • I • I • J • I . I
0 15 30 45 60 75 90
8 i (degrees)
0.2
............. 00.
1.0
0.8
0.6
0.4
0.2
I I I I I I " t
(d)
• _-I _I
............. 00.0 15 30 45 60 75 90
0 i (degrees)
-=:
Figure 18: The data for 4620 m/s H2 incident upon SiO2-coated Kapton.
Table 18:4620 m/s H2 incident upon SiO2-coated Kaptonm
Oi (deg_'ees) ft f,, _._1"_ v, (re�s) (degrees) t' _' t'_ (m/s) 2
0
25
50p,,,_
I,')
85
0 1.55 0.552 2550 0
0.343 1.44 0.539 2490 8.54
0.624 1.22 0.594 2750 13.8
0.693 0.828 0.631 2920 25.6
0.624 0.606 0.639 2950 35.7
0.638 0.76:3 8.90>(106
0.658 0.779 8.62×10 G
_'90.ot. 0.711 9.79× 106
0.526 0.661 1.06×107
0.515 0.650 1.08×107
30
1.50o
c-G)O
::1=1.0
00(D0I.,-
0IJ-"o 0.5
0
"0(1)rr
0.0
75
6O
45t,])
o_ 3O
"0v
15
0
• _ --m--.ft
_0_0 ----0--_
(a)
I , I , I , I , I , I I |
! " I ' ! " ! " ! " ! !
(c)
/
I , I , I . I i I i I . I
0 15 30 45 60 75 90
(degrees)
• .______--m_m _m \m
(b)
0.8
m --------_ m
0.6
0.4 -._ m
0.2
i , i • ' • ' , ' , ' , ' 0.0i • I • I • ! " i i i
1.0(d)
0.8
m _m/m 0.6
0.4
0.2
, , , , . i , m , I , L 0.00 15 30 45 60 75 90
(degrees)
Figure 19: The data for 4620 m/s [I2 incident upon t(apton.
Table 19:4620 m/s H2 incident upon Kapton
0,: (degTees) It f, T.,/Ti "5, (m/s) 0._ (degrees) I' (' "_'_(m/s) 2
0
25
50
75
85
0 1.48 0.479 2210 0
0.349 1.38 0.484 2240 8.81
0.655 1.19 0.561 2590 11.4
0.748 0.78,1 0.56. () 2630 22.5
0.69,1 0.517 0.525 2,1;{0 35.1
0.7,13 0.846 7.,18× 10(;
0.737 0.841 7.56× 106
0.627 0.753 9.06×106
0.615 0.7-13 9.24× 106
0.678 0.796 8.3-1× 10[;
31
1.500
r-I1)
O
1.00
0
EO
1.1_
"o 0.5
O
"I3
rr0.0
75
60
_-. 45_0
I:_ 30
"13v
_ 15
I " I • I I I " I • !
i_m Pm
.\.
(a)/I • I I l I | i I . I , I
I " I " I I I I " I
(c)
• _ai _m
_1 --iI • i I I i I , l , I , I
0 15 30 45 60 75 90
0i (degrees)
, • , . , • , • , • , 1.0
_m _m• _u .i \m
(b)
l . m , I , I , l , I , m
I l I I " I • l • m
m" /m_m _m _m
(d)
i . l , l . l , m . i m
0 15 30 45 60 75 90
0i (degrees)
Figlu'e 20: Tile data for 4620 m/s H2 incident upon Z-93-coated aluminum.
0.8
0.6
0.4 -._ m
0.2
0.0
1.0
0.8
0.4
0.2
0.0
]'able 20:4620 m/s H2 incident upon Z-93-coated aluminum
Oi (degrees) St f. Vs/_ i 'L'_s (hi/S) Oa¢ (degrees) # c' v'_2 (m/s) 20
25
50
75
85
0 1.40 0.404 1870 0
0.396 1.28 0.379 1750 3.99
0._8o 1.10 0.461 2130 -2.31
1.04 0.698 0A45 2060 -9.41
1.05 0.465 0.382 1770 -8.85
0.851 0.919 6.24×106
0.886 0.940 5.88× 10 6
0.769 0.865 7.17× 10 6
0.791 0.880 6.90x106
0.882 0.938 5.92× 106
;32
........ . , . , . , . , , , 1.0
1.5ct)
c-
O
:1=0_ 1.000
0
0LL•"o 0.5
0
"0
rr0.0
75
60
,,-, 45q)
£cn 30
"Elv
_" 15
0
0_
• / (a)
I I I • I • I • I . I . I
I ' I " I I 1 I I
ill"i j
//
(c)
I i I * I i I I . I
0 15 30 45 60 75 90
0i (degrees)
(b)
/
0.8
0.6
_ I
0.4 _._ i
0.2
I , I , I , I , I , t . , 0.0
I ' I I | I I I
1.0
• I_i _ 0.8
• 0.6
\0.4
0.2
(d)
I , I i I , | , I , * ' I :0.0
0 15 30 45 60 75 90
(degrees)
3:::
Figzure 21: The data for 3180 m/s N2 incident upon the solar panel.
Table 21:3180 m/s N2 incident upon the _lar panel
O_(deg,rees) .f, .f,, T,/r'i T, (m/s) O_ (degrees) t' (' _ (m/s) 2
0 0 1.28 0.282 896 025 0.400 1.19 0.287 912 4.60
50 0.662 (1.942 0.317 1(}1(} 19.1
75 0.653 0.593 0.,158 1460 43.1
85 0.468 0.371 0.(i00 1910 61.8
0.81;1 0.9:1;1 1.02 × 1()_;
0.807 0.930 1.05× 1()_0.773 0.912 1.24×1() [;
0.614 0.801 2.35×10 (;
0.453 0.64.() 3.88× 10';
33
1.5
00
c-(D
.m
O.u
a=1.0
OO(DOI,=.
OLI_"O 0.5{DO
"O
n-0.0
75
60
..-. 45(D(D(D1,m
c_ 30(D
"Ov
15
0
I I I I I I I
_O
(a)
i . i i I , I i I , I i I
I • I • I • I I I l
/(c)
I , I , I , I , l , I • I
0 15 30 45 60 75 90
0i (degrees)
...... • , 1.0
• _m _m
m//m
(b)
l , , , , . , . , . , , n
I I ' I • I I I I
m_m_
"\
(d)
! 0 !
0 15l • I 0 I , l , m
30 45 60 75 90
0i (degrees)
0.8
0.6
0.4 -_ i
0.2
0.0
1.0
0.8
0.6
Figure 22: Tile data for 3180 m/s N2 incident upon SiO2-coated Kapton.
0.4
0.2
0.0
Table 22:3180 m/s N2 incident upon SiO_-coated Kapton
Oi (degrees) ft f,, -_,,/_i ,'-r, (m/s) 0,_ (degrees) # e' v-7 (,n/s) 2
0
25
5O
75
85
0 1.27 0.273 869 0
0.380 1.16 0.258 820 9.52
0.633 0.937 0.323 1028 24.3
0.613 0.597 0.488 1554 46.2
0.509 0.412 0.585 1862 56.2
0.823 0.938 9.72x105
0.840 0.946 8.89x 10"_
0.766 0.908 1.28x 10 6
0.o19 0.772 2.65x106
0.469 0.666 3.71x106
3,1
, , . , , , . , . , 1.0
1.5
0
1.000
0
01.1_.._ 0.5mo
cc0.0
75
6O
..... 45if}
30
v
15
(a)
I • I • I • | " I • l
/
/(c)
I . I , I , l l , l . l
0 15 30 45 60 75 90
0i (degrees)
i11,/11
• ii_II"
0.8
0.6
%0.4 --_ i
0.2
(b)
, , , , , , , , i , , • | 00.
l " I " I " | I l " l
1.0
0.8
0.6=\
0.4
0.2
(d)
I , I , I , I , I , I , I 0.0
0 15 30 45 60 75 90
Oi(degrees)
Figur(, 2:1: The data for :t180 m/s N2 incident upon t(apt, on.
-r=
Table 2:_: :t180 m/s N2 incident upon Kat)ton
O_ (degn'ees) ft f,, "_',_/"_"i '_2,_ (Ill/S) O_ (dl?gl'ePS) It (! 't'7 ('II/S) 2
0
25
50
T5
85
0 1.22 0.219 698 0
0.:_7.(1 1.12 (1.221 704 11.,1
0.656 1/.918 0,297 9i;_ 21.8
0.656 0.559 0.,1:_1 1;_70 -15.9
0.555 0.:t47 0.512 16:_0 59.5
0.884 0.965 T.02× 10_'
0.881 0.96.1 7.11 × 1(1r)
0.796 0.925 1.11×lO (;
0.641 0.825 2.11 × l()';
0.55:_ 0.748 2.88x 10(;
:_5
1.5if}
c-
0D
O
1.0O0
0
0IJ_•o 0.5
0
"0
n,-0.0
75
60
_,, 45O9{D{DTb.=
c:_ 30
"Ov
_ 15
0
I " I • I • I ' I I
.//
// \.(a)
i . l _ I , I • l i • I
I " I ' ! ' ! ' I ° I ' I
(c)
m_ m
.... <",0 15 30 45 60 75 90
e, (degrees)
, . , • , • , . , • , 1.0
• _m _U ---_-m \i
(b)i • I i m , I , i . i
I " I • I ' ! ! " I • I
• -_-----m _m _i _m
(d)
0.8
0.6
0.4 -_ i
0.2
0.0
1.0
0.8
0.6
I • I i I i I _ I , I , I
0 15 30 45 60 75 90
O,(degrees)
0.4
Figure 24: The data for 3180 m/s N2 incident upon Z-93-coated alunfimnn.
0.2
0.0
Table 24:3180 m/s N2 incident upon Z-93-coated aluminum
Oi (dega'ees) ft f,, _/_i Ts (m/s) 08 (degrees) tt _' v"7 (m/s) 2
0 0 1.17 0.170 539 0
25 0.429 1.06 0.157 499 -2.20
"950 0. i. 8 0.834 0.194 617 -9.33
75 1.00 0.438 0.183 583 -11.6
85 1.01 0.241 0.155 492 -4.48
0.940 0.985 5.05X 105
0.954 0.989 4.62X10 "5
0.912 0.976 5.96X10 .5
(}.925 0.980 5.54× 10'5
0.957 0.989 4.56×105
36
1.5
(D
¢-(1)
0
1.00
0
0L--
0u_-o 0.5(D0
"0
rr0.0
75
6O
..-.. 450g
30
15
0
0
(a)
I * I • I J I i • I i |
I • l • 1 I I I i
//
f/I'
• (C)
I • [ , I i I I * I , I
0 15 30 45 60 75 90
0t (degrees)
I 1 " I I I I I " I
/i __._______- i j
(b)
I I " I ' I I 1 I
\
(d)
0.6
0.4 _l
0.2
1.0
0.8
0.6
0.4
0.2
' ' ' ' ' • ' ' ' ' ' ' ' 00.0 15 30 45 60 75 90
0_ (degrees)
3::
Figalr(, 25: The data for 3200 m/s CO incident upon t,he solar panel.
Table 25:3200 In/s (IO incident upon th(' solar pallel
0
25
50
75
85
0 1.2.(1 0.285 91 ;I 0
O..lO;} 1.1 i) 0.289 .(t26 3.90
0.665 0.945 0.318 1020 18.5
11.661 0.590 (1.,151) 1441) 42.6
0.472 0.365 0.594 1900 62.1
0.809 0.931 1.05xl() {;
0.801 0.i)2. () ].OTx 10 (;
0.771 O./)ll 1.26_:10 _;
0.622 0.808 2.30>_ 10 (;
0.45.(I 0.656 3.85>< 106
37
1.5o0
-b.._C(D
.B
°B
cD 1.0o
0(D0
0LL._ 0.5
"ID(D
n.-0.0
75
6o
._. 45
(D£_) 30
_' 15
0
I • i , ! • i , I • I
(a)
I i I , I , I
I " I " I " I ' I
/
(c)
I , I • I . I , i l I l I
0 15 30 45 60 75 90
(degrees)
l • I • I • ! i I
• _m _m
mm//m
S
(b)
l m I * I i I i I I I i l
i • i • I i i i l
I
0
"\
(d)
i i l m I i I m I , l
15 30 45 60 75 90
(degrees)
Figure 26: Tile data for 3200 m/s CO incident upon SiO2-coated t(apton.
, 1.0
0.8
0.6
0.4 -_ m
0.2
0.0
1.0
0.8
0.4
0.2
0.0
Table 26:3200 m/s CO incident upon SiO2-coated Kapton
Oi (deg-rees) St f,, "ds/"Q ,'Ts(m/s) 08 (degrees) # e' v-'_s2 (m/s) 2
0
25
50
75
85
0 1.27 0.268 857 0
0.380 1.16 0.256 819 9.65
0.634 0.935 0.321 1030 24.3
0.619 0.595 0.483 1550 45.9
0.518 0.411 0.578 1850 56.0
0.828 0.941 9.52×105
0.842 0.947 8.87x105
0.768 0.909 1.27x106
0.584 0.777 2.62×106
0.478 0.6_o 3.66× 106
38
, . ............. 1.0
1.5
-I--'
C
O
1.000
0k--
ou_._ 0.5(].)0
rr0.0
75
60
..-... 45
30
v
./ c,:(a)
I l I I , l . I . I . I
I I I I I
/
/(c)
I i I i I i I . I I t I
0 15 30 45 60 75 90
0i (degrees)
/•"•J
0.8
0.6
0.4 -._ I
0.2
(b)
, . , . , ....... ' 00.I " ! " I I ' 1 " I " I
1.0
_= 0.8
0.4
0.2
(d)
, , , , , , I • ' . ' , ' 0.00 15 30 45 60 75 90
Oi(degrees)
Fig;ure 27: The data for 3200 m/s CO incident upon Kapton.
"=:
Table 27:3200 m/s CO incident upon Kapton
0 (} 1.23 0.226 725 0
25 0.382 1.13 0.229 73,1 10.2
50 0.661 0.925 0.301 965 20.4
75 0.665 0.563 0.,128 1;370 44.7
85 0.562 (}.350 0.507 1620 58.8
0.875 0.962 7.40x 105
0.872 0.960 7.53x105
0.790 (}.921 1.15× 106
0.647 0.828 2.10× it) t;
0.557 0.753 2.87× 106
39
1.5
(D
E(1)
0
1.000
2O
1.1_
"o 0.5I11O
IDrr
0.0
75
6O
_. 45(D
II1
¢:_ 3O(D
"Ov
/
• (a)i , i , I , I • i • I . !
! " ! " ! ' I " I " I " I
(c)
m_ m
J
0 15 30 45 60 75 90
(degrees)
I I " I • I I I I
_ii _'i• "-'---------i / \1
(b)I • I | I i I _ I . I . I
I • I " ! ' I • I " I " I
• _m __m _-i _m
(d)
I . I i I • I I I , I . I
0 15 30 45 60 75 90
0i (degrees)
Fig-ure 28: The data for 3200 m/s CO incident upon Z-93-coated ahmfinunl.
1.0
0.8
0.6
0.4 -._ m
0.2
0.0
1.0
0.8
0.4
0.2
0.0
Table 28:3200 m/s CO incident upon Z-93-coated aluminmn
Oi (degrees) ft fn "gs/r.'i T8 (m/s) 08 (degrees) i t (:' v-7,_ (m/s) 2
0 0 1.17 0,172 550 0
25 0.42.(I 1.07 0.160 511 -2.46
50 0.807 0.844 0.205 658 -11.4
75 1.00 0.440 0.185 592 -11.1
85 1.01 0.244 0.157 503 -5.19
0.937 0.984 5.16×105
0.951 0.988 4.74×10 r)
0.899 0.971 6.,17× 105
0.922 0.979 5.65x105
0.953 0.989 4.66×105
4O
1.509
c-OD
,m
0,m
1.0o
0
0
0LL•_ 0.5
rO
"0
rr0.0
75
6O
.-. 45
Q)
o'_ 3OQ_
v
q_ 15
• _ (a)_O
1 • I • I * l , I , i . I
F " ! " I ' I ! I I
/
JI a I I I h I i I n a . I
0 15 30 45 60 75 90
O_(degrees)
(b)
/
U j
t I I I
0.8
0.6
0.4 -._ o
0.2
I , I , I , I , I , I , I 00.
I I I
1.0
0.8
0.6
0.4
0.2
• -------m _m
(d) \
n , I , i , i ' " ' ' J 00.0 15 30 45 60 75 90
0 i (degrees)
Figure 29: The data for 2840 m/s (102 incident upon the solar panel.
rlhble 29:2840 m/s C()2 incident upon tile solar panel
0
25
5o
75
85
0 1.1,1 O.136 387 0
0.369 1.06 0.159 451 19.9
0.619 0.8,11 0.247 700 36.5
0.618 0.525 0.438 1240 52.6
0.44,1 0.322 0.600 1700 67.0
0.964 0.992 2.86× 1() r)
0.939 0.985 3..lOx 10 r)
O. 841 0.9,19 6.30 × l ()r,
0.627 0.817 1.70×1() (;
0.446 0.647 3.07× 1() (_
41
, • , • .... , ..... • , • , 1.0
1.5o0
r-
O._
1.0o0
Ou..-o 0.50JO
ll0rr
0.0
75
60
.-. 45
0J
¢_ 300J
q:
(a)
I , I • I ° I o I a I i I
I U I " I " I " U " I
(c)
J a I , I a I , I , I , 1
0 15 30 45 60 75 90
(degrees)
(b)
J , I , I • I • I i | I |
U ; " I ' I " I " I " U
\
(d)
I . I • n . I o I n I a I
0 15 30 45 60 75 90
0i (degrees)
0.8
0.6
0.4 --_ o
0.2
0.0
1.0
0.8
0.4
0.2
0.0
Figure 30: The data for 2840 m/s (102 incident upon SiO2-coated Kapton.
Table 30:2840 m/s CO2 incident upon SiO2-coated Kapton
Oi (degrees) ft J;, g,,,_,/7 T,, (m/s) 0,. (degrees) it e' u-_'__ (m/s) 2
0
25
50
75
85
0 1.21 0.207 587 0
0.383 1.10 0.199 564 11.6)-,0.635 0.883 0..14 777 28.6
0.625 0.5,18 0.447 9"1, _0 49.6
0.518 0.368 0.555 1580 59.6
0.885 0.968 ,1.83×105
0.895 0.971 4.56×105
0.811 0.935 7.45× 105
0.617 0.80.(I 1.76×10 G
0.497 0.700 2.64×10 (;
42
, . , . , . , . , . ......... 1.0
1.5c/)¢-_D
.m
O,m
1.000
0ii
0.5
0D
0.0
75
60
..-. 45
30
15
0
0_
m _m \m"\
/ -• (a)l , I , I , l , I I l • l
l • l ' m • ! ' l • I I
/
/(c)
l _m"
0.8
0.6
0.4 -_ I
0.2
(b)
m , m , I , l , I , ' • _ 00.
! ! • i ' i • I • n i
1.0
0.8
0.6
0.4
0.2
I l i , I . I , I . I , I
0 15 30 45 60 75 90
Oi (degrees)
Figure 31: The data for 2840 m/s (!O2 incident upon Kal)ton.
(d)
, , , i , , • , • , • , 00.0 15 30 45 60 75 90
ei (degrees)
"l::
Tal)le 31:2840 m/s (-!O2 incident ut)on KaI>ton
Oi (degrees) ft f, "_8/"_i L"'Vs (Ill/S) 0 5 ((|e_l'f,es) [' (1 "'_ (Ill/S) 2
025
50
75
85
0 1.20 0.198 561 0
0.393 1.10 0.197 559 8.55
0.670 0.883 0.259 735 21.7
0.685 0.530 0.391 1110 16.1
0.574 0.321 0.483 1370 61.1
0.8!)6 0.972 4.52X 1()'_'
0.897 0.972 ,1.50X10 r'
0.827 0.94:{ 6.80× 10r'
0.680 0.857 1.38 × 106
0.578 0.776 2.03× 106
-13
1.5if)
t-
O.m
1.00
0
OLL.
0.5
O
2:3
rr0.0
75
6O
.... 45{D
c_ 3O
v
_' 15
--=raft
--'--O m fl I
(a)
m _m/./ \"I , I . I • | I I I | , I
I I I I I I I
(c)
• _-m •
I , , m ........,
0 15 3o 45 6o 75 90
O,(degrees)
(b)
• _m/_m _m _m
i • ¢ • i . m , I , I , I
I i i I • I • I • I
• _m _u _m _m
(d)
I i I . I . I • I • I • I
0 15 30 45 60 75 90
0i (degrees)
0.8
0.6
0.4 .c::m
0.2
0.0
1.0
0.8
0.4
0.2
0.0
Figm'e 32: The data for 2840 m/s CO2 incident upon Z-93-coated aluminunl.
Table 32:2840 in/s CO2 incident upon Z-93-coated alunfimun
oi (dea-_) f, y;, "e_/v_ v_ (m/_) 0._(d_,'ee_) # _' _'-7(m/_)20
25
50
75
85
0 1.15 0.148 421 0
0.429 1.04 0.134 380 -2.52
0.794 0.809 0.169 479 -9.54
0.998 0.414 0.158 449 -11.6
0.996 0.219 0.132 373 0.076
0.951 0.989 3.13×10 r_
0.967 0.993 2.80× 105
0.928 0.982 3.66×105
0.940 0.986 3.38× 105
0.969 0.993 2.75×105
44
O
e = 50 °
30 °
i .: • ,:e. = 75 ° t'. ..." /.,. / ._l ./
"'"_ // 2590 rn/sec H2.85 ° .......Solar Panel
...................!!iii_.... .......
0.50 0.25 0.00 0.25 0.50
I(e,180 °) I(o,O °)
60 °
90 °
Fig_u'e 33: The angular distribution flmcdons for 2590 m/s tt2 incident 11t)oi1 the solar panel.
Table 33: The Nocilla model parameters for 2590 m/s II2 incident, upon the solar panel.
o,:(d_.gre,,,) ,s' u (,,,/_) o. (de_,.,_,.,)r. (K)0 0.309 -154 0 263
25 0.334 ,191 33.7 263
50 0.718 968 2,1.3 221
7"5 O. 594 831 42.1 237
85 0.706 1070 114 , _8
45
o
e.= 75 °[
= 85 °
0.50
I(e,180 °) I(o,o°)
90 °
Figure 34: The angaflar distribution fmmtions for 2590 m/s H2 incident upon SiO2-coated Kapton.
'Fable 34: The Nocilla model parameters for 2590 m/s I-I2 incident upon SiO2-coated Kapton.
Oi (degrees) S U (m/s) 0.. (degrees) T. (K)
0 0.0860 136 180 304
25 0.326 482 38.5 265
50 0.657 901 31.5 228
75 0.831 1090 33.4 210
85 0.757 1030 58.6 225
46
o
e = 25 °!
\
e= 75 °!
e= 85 °z ....................iiii:._....
2590 m/sec Hd
Kapton
0.50 0.25 0.00 0.25 0.50
60 °
s(e,18o°) s(o,o °)
90 °
Figm'e 35: The angular distribution functions for 2590 m/s H2 incident upon Kapton.
Table 35: The Nocilla model paranieters for 2590 m/s H2 incident upon Kapton.
o, (d_a-,-c<_s) S r; (m/_) 0,, (d,,_,'_.) T. (i<)0 0.0360 55.8 0 2.91
25 0.447 641 19.5 2.1.9
50 0.697 945 22.7 223
7;5 0.758 1010 21.0 216
85 0.308 463 65.9 275
17
0
0.50 0.25 0.00 0.25 0.50
I(e,180 °) I(e,O °)
60 °
90 °
Figure 36: Tile angular distribution functions for 2590 m/s H2 incident upon Z-93-coated almninunl.
Table 36: The Nocilla model parameters for 2590 m/s H2 incident upon Z-93-coated aluinimlm
0 0.00438 6.83 0 291
25 0.115 177 30.4 249
50 0.466 663 4.69 223
75 0.289 428 -17.9 216
85 O.188 300 -146 '275
48
0
0 = 50 °!
e= 25 °' \
0._ 0 0I
30 °
1870 m/sec N2Solar Panel
0
60 °
3.0 2.0 1.0 0.0 1.0 2.0 3.0
I(e,180 °) I(e,O °)
90 °
Figm'e 37: The angular distribution functions for 1870 m/s N2 incident upon tile solar panel.
Table 37: The Nocilla model parameters for 1870 m/s N2 incident upon the solar panel.
o,(dc_,'ee_) S tv (,,,/_) O,(d_._.,-,_e,)r, (K)0 0.66.0 266 0 267
25 0.77-1 306 21.7 264
50 1.26 484 32.3 2-17
75 1.91 711 49.0 226
85 2.66 938 71.4 210
49
o
O= 25 °' \
e= 75 °
e = 85 °
0._- 0 0l
30 °
0
60 °
3.0 2.0 1.0 0.0 1.0 2.0 3.0
I(e,180 °) I(e,O °)
90 °
Figalre 38: The angular distribution functions for 1870 m/s N2 incident upon SiO2-eoated Kapton.
Table 38: Tile Nocilla model parameters for 187(/m/s N2 incident upon SiO2-coated Kapton.
0i (degrees) S U (m/s) 0_ (degrees) 7; (K)
0 0.531 214 0 273
25 0.718 286 28.4 268
50 1.32 505 37.5 246
75 2.18 781 47.7 216
85 2.68 925 58.0 202
5O
0
e. = 50 °l
0.= 25 °l
\
O= 75 °l .
= 85 °................. :i!_....
30 °
0
1870 m/sec N2
Kapton
1.5 1.0 0.5 0.0 0.5 1.0 1.5
60 °
I(e,180 °) I(0,0 °)
90 °
Figm'e 39: The angular disU'ibution functions for 1870 m/s N2 incident upon Kapton.
Table 39: The Nocilla model parameters for 1870 m/s N2 incident upon Kat)ton.
o,(dea'e,_) ,S' l: (,,,/_) o,,(de_ree_)'r. (t<:)t) (I.540 217 0 273
25 0.896 351 17.5 259
50 1.31 ,199 28.8 214
75 1.86 682 38.1 225
85 1.85 682 ,18.9 229
51
O
/I'0.= 250 _1_-=_..._. .. ,,,./" ",="° .! .,_ <,-_ %. o
°,=5°° ....... ",! o
I o,=7_.5° _._, _...:_t " "__^'_I_ \_ ' /,/] 1870 m/sec N2
I O,=.85° +_::. % _;._ Z93-Coated AII I '''"-i I , "_"_. ,,,_' , I I I
0.50 0.25 0.00 0.25 0.50
I(o,180 °) I(o,O °)
90 °
Figure 40: The angular distribution functions for 1870 m/s N2 incident upon Z-93-coated ahmfinum.
Table 40: The Nocilla model parameters for 1870 m/s N2 incident upon Z-93-coated aluminum.
Oi (degrees) S U (m/s) 0u (degrees) T. (K)
0 0.153 63.4 0 289
25 0.237 97.7 16.2 286
50 0.529 213 9.71 274
75 0.532 214 1.86 273
85 0.265 109 8.92 284
52
o
e = 50 °l
O= 25 °' \
O = 75 °l
0. = 85 °
0 _ 00!
30 °
1870 m/sec CO0
Solar Panel
I
3.0 2.0 1.0 0.0 1.0 2.0 3.0
I(e,180 °) 1(o,o°)
90 °
Figure 41: The angular distribution functions for 1870 m/s (IO incident upon the solar panel.
Tat)le 41: The Nocilla model parameters for 1870 m/s CO incident ut)on tile solar panel.
0_ (degrees) 5; U (m/s) 0,, (degrees) 7_ (K)
0 0.655 261 0 268
25 0.822 324 19.0 262
50 1.24 477 31.2 2-18
75 1.88 693 48..q 229
85 2.5!) .()21 71.7 213
53
O
e. = 50 °l
0.= 25 °' \
O _ 0 0l
30 °
1870 m/sec CO
Si02-Coated Ka
0
60 °
3.0 2.0 1.0 0.0 1.0 2.0 3.0
1(0,180 ° ) I(e,O ° )
90 °
Figure 42: The angular distribution flmctions for 1870 m/s CO incident upon SiO2-coated Kapton.
Table 42: Tlle Nocilla model parameters for 1870 m/s CO incident upon SiO2-coated Kapton.
0_ (degrees) S U (m/s) 0. (degq'ees) T_ (K)
0 0.548 220 0 273
25 0.700 ")"- _9 28.2 269
50 1.28 492 36.2 247
75 2.09 756 48.0 220
85 2.57 898 58.2 206
54
_i _= 501
ei -75°
1.0
I(e,180 °)
O
/'"" /se -
_:, II::J/2j '/ y KaptonI ., _: " " I I I
0.0 1.0
I(O,O °)
90 °
Figqu'e 4:}: The angxllar distribution functions for 187(/m/s CO incident upon Kapton.
Table -13: The Nocilla model parameters for 187(I m/s (IO incident upon Kat)ton.
0 0.645 257 0 269
25 0.913 :t58 15.7 258
50 1.28 490 28.5 245
75 1.80 663 38.6 228
85 1.80 666 .18.9 232
55
o
z" ",--_° .< ,_- _ e
I '.._ _;._ Y,,4i_ V °l .......',f,, -- I;i: \/ e,=:s° !_:, J!i 1
' ""o "i \t;, "l" /,'_ 1870 m/sec CO _l
[ et ="85°.,,!_,,., _. I ,f..<'_" Z93-Coated AI I
0.50 0.25 0.00 0.25 0.50I(e,180 °) I(e,O °)
90 °
Figm'e 44: Tile ang_llar distribution functions for 1870 m/s CO incident llpon Z-93-coated alu-llli II12 ill.
Table 44: The Nocilla model parameters for 1870 m/s CO incident upon Z-93-coated aluminum.
0i (degrees) S U (m/s) o. (degrees) Ts (K)
0 0.204 84.1 0 287
25 0.268 110 13.3 284
50 0.542 218 9.9/ -c3
75 0.536 216 1.48 27385 " ')""u.-i _ 113 5.3.1 284
56
O
0 = 0° 30o!
o.= 25 ° 0' \ 1670 m/sec CO
Solar Panel
3.0 2.0 1.0 0.0
I (0,180 ° ) I(O,O ° )
60 °
1.0 2.0 3.0
90 °
Fig_u'c 45: The angaflar distribution functions for 1670 m/s CO2 incident upon the solar panel.
Table 45: Tile Nocilla model parameters for 1670 m/s (?()2 incident upon the solar panel.
0,:(d_.gr,_e.) ._";' t; (m/.) 0,,(d_aTe_..)'r_(t_:)0 0.432 140 0 279
25 0.587 189 21.6 274
50 0.975 307 34.7 262
75 1.59 485 52.9 2.18
85 2.47 739 78.8 236
;) t
0
30 °
2.0 1.0 0.0 1.0
1(o,180 °) I(0,0 °)
0
2.0
90 °
Figure 46: The angxllar distribution flmctions for 1670 m/s CO2 incident upon SiO_-coated Kapton.
Table 46: The Nocilla model parameters for 1670 m/s CO2 incident upon SiO2-coated Kapton.
0i (degrees) S U (m/s) 8,, (degrees) T_ (K)
0 0.212 69.7 0 287
25 0.395 129 47.1 284
50 1.07 335 42.5 261
75 1.87 560 52.8 238
85 2.36 692 63.0 227
58
o
e= 25 °f. o
\
30 °
O,= 75 ° I •
= 85 ° /,/e
0
.:/"
1670 m/sec CO:
60 °
1.5 1.0 0.5 0.0 0.5 1.0
I(&180 °) I(e,O °)
90 °
1.5
Figure 47: The an#llar distribution functions for 167(/m/s CO2 incident upon Kapton.
Table 47: The Nocilla model t_arameters for 1670 m/s COu incident tlpOll Kapton.
0 0.41)5 132 0 2811
25 0.637 204 19.8 272
51) 1.02 318 32.4 2611
75 1.57 478 43.6 244
85 1.67 509 55.4 246
59
0
O_=_75 ° '_.
= 85 °
, I
0.50 0.25 0.00
I(0,180 °)
30 °
0
1670 m/sec C02] '/
Z93-Coated AI /I , 90 °
0.25 0.50
I(o,o°)
Figure 48: The angular distribution functions for 1670 ln/S (2102 incident upon Z-93-coated alu-
minunl.
Table 48: The Noeilla model parameters for 1670 m/s CO2 incident upon Z-93-coated ahlnlinmn.
Oi (degrees) S U (m/s) O_ (degrees) T8 (K)
0 0.00572 1.92 181) 295
25 0.0613 20.4 85.7 295
50 0.363 118 14.9 282
75 0.382 124 6.55 281
85 0.101 33.4 38.1 292
6O
0
"7.&
O__ 25 °
\
0.= 75 °
= 85 °
30 °
60 °
4620 m/sec H2Solar Panel
2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5
/(o,180 °) t(o,o °)
90 °
2.0
Figau'e 49: Tile angular distribution functions for 4620 m/s H2 incident upon the solar panel.
Table 49: Tile No(:illa model l)arameters for 4620 m/s It2 incident upon the solar panel.
o,(de_,',,e,_),s' r: (,,,/_) o,,(d,,_,',-e._)"1;(K)0 1.80 2290 0 197
25 1.81 2310 6.05 197
50 1.93 2420 12.1 191
75 2.06 2540 26.5 185
85 2.06 257(I 50.9 18.9
61
O
0. = 50 °
0.= 25 °
\
O.= 75 °!
= 85 °
2.0 1.5
30 °
,,/,,4620 m/sec H2
" SiO2-Coated Kapto
60 °
1.0 0.5 0.0 0.5 1.0 1.5 2.0
/(o,18o°) I(o,o °)
90 °
Figure 50: The angular distribution functions for 4620 m/s H2 incident upon SiO2-coated Kapton.
Table 50: Tile Nocilla model parameters for 4620 m/s H2 incident upon SiO2-coated Kapton.
Oi (degrees) S II (m/s) 0,_ (degrees) Ts (K)
,) -,0 1.68 _1 _(} 0 20,1
25 1.59 2080 10.2 208
50 1.93 2420 15.7 191
75 2.16 2630 28.6 180
85 2.19 2670 40.2 180
62
0
1.5
0i_25 °
\
O= 75 °
= 85 °
/0
4620 m/sec H 2 ._
Kapton, I ,/
1.0 0.5 0.0 0.5 1.0
I(e,180 °) I(e,O °)
90 °
1.5
Figure 51: The ang-ular disti'ibution functions for 4620 m/s H2 incident upon Kapton.
Table 51: The Nocilla model parameters for ,1620 m/s [I2 incident upon Kapton.
0 1.23 1680 0 228
25 1.26 1720 11.5 226
511 1.72 2220 13.,1 202
75 1.76 22611 26.-1 200
85 1.46 1970 45.1 220
63
0
0.= 75 °
= 85 °
30 °
0
4620 m/sec H2Z93-Coated AI
60 °
1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75
I(0,180 °) I(O,O °)
90 °
1.00
Figure 52: The angular distribution functions for 4620 m/s H2 incident upon Z-93-coated aluminum.
Table 52: The Nocilla model parameters for 4620 m/s H2 incident upon Z-93-coated alunfinum.
Oi (degrees) S U (m/s) 0u (degrees) 7"8 (K)
0 0.760 1100 0 254
25 0.598 881 7.95 263
50 1.12 1560 -3.17 234
75 1.02 1440 -13.6 240
85 0.618 910 -17.4 263
64
0
0.= 25 °1
\
30 °
3180 m/sec N
Solar Panel
0
6.0 4.0 2.0 0.0 2.0 4.0 6.0
1(o,o°)I(e,180 °)
60 °
90 °
Fig_u'e 53: The angular distribution flmctions for 3180 m/s N2 incident upon the solar panel.
Table 53: The Nocilla model parameters for 3180 m/s N2 incident upon the solar panel.
Oi (degrees) ,S' U (m/s) 0_ (degrees) 7[. (K)
0 2.06 802 0 318
25 2.11 8211 5.12 255
50 2.38 926 20.8 255
75 3.54 1400 45.3 264
85 4.55 1860 64.6 28:t
65
O
e.= 25 °!
\
30 °
3180 m/sec N2
SiO2-Coated Ka
s
• " /
0(= 75 ° ,/ .........../..- ..
= 85 ° Z: ......./"s
0
6.0 4.0 2.0 0.0 2.0 4.0 6.0
I(0,180 °) I(o,o °)
60 °
90 °
Figure 54: The anglflar distribution flmctions for 3180 m/s N2 incident upon SiO2-coated Kapton.
Table 54: The Nocilla model parameters for 3180 m/s N2 incident 1.1pon SiO2-coated Kapton.
0i (degrees) S U (m/s) 0,, (degrees) T8 (K)
0 1.98 771 0 255
25 1.83 714 10.9 256
50 2.43 947 26.5 256
to 3.77 1500 48.4 -61
85 4.48 1820 58.5 277
66
o
e_= 25 o\
4.0
3180 m/sec N 2
Kapton
0
2.0 0.0 2.0 4.0
i(o,18o o) ir(o,o°)
60 °
90 °
Figure 55: The angular distribution functions for 3180 m/s N2 incident upon Kapton.
Table 55: Tile Nocilla model parameters for 3180 m/s N2 incident upon Kapton.
0 1.44 565 0 260
25 1.46 572 14.1 260
50 2.1 .q 854 2,1.8 256
75 3.31 1310 48.8 26.1
85 3.89 157'0 63.1 276
67
0
0. = 50 °
0.= 75 °l
0.= 85 °
30 °
0
3180 m/sec N2Z93-Coated AI
60 °
1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00
I(0,180 °) I(0,0 °)
90 °
Figure 56: The anDllar distribution functions for 3180 m/s N2 incident upon Z-93-coated aluminum.
Table 56: The Nocilla model parameters for 3180 m/s N2 incident upon Z-93-coated ahmfinum.
Oi (degrees) S U (m/s) 0. (dega'ees) Ts (K)
0 0.846 339 0 260
25 0.669 270 -4.05 260
50 1.15 456 -12.7 256
75 1.02 405 -16.8 264
85 0.64 259 -8.51 276
68
O
j o,
6.0 2.04.0
I(o,180 °)
o
3200 m/sec CO'X'_ _'
Solar Panel "_,%
- .. .... '_ 60°
_:'-i'_ ......I .... , I , I , 190 o
0.0 2.0 4.0 6.0
I(O,O °)
Figure 57: The angular distribution functions for 3200 m/s (_O incident upon the solar panel.
Table 57: The Nocilla model parameters for 3200 m/s CO incident upon the solar panel.
Oi (degrees) H U (m/s) O, (degrees) 7_ (K)
0 2.12 821 0 254
25 2.16 836 4.32 25-1
511 2.12 .9:/!) 20.1 25-1
75 3.51 1380 4-1.9 261
85 4.56 1850 64.9 278
6!)
o
0= 25 °l
\
0= 75 °
= 85 °
30 °
3200 m/sec CO
Si02-Coated Ka
0
6.0 4.0 2.0 0.0 2.0 4.0 6.0
I(e,180 °) I(O,O °)
60 °
90 °
Figure 58: The ang_tlar distribution functions for 3200 m/s CO incident upon SiO2-coated Kapton.
Table 58: The Nocilla model parameters for 3200 m/s CO incident upon SiO2-coated Kapton.
o_(deg,'ees) S U (n,/s) 0,,(deg,'ee_)T, (t,:)0 1.95 758 0 254
25 1.83 713 11.1 256
50 2.44 947 26.6 255
75 3.79 1490 :18.1 263
85 4.48 1800 58.2 273
7O
o
O.= 50 °l
0.= 25 °I
\
0.= 75 °l
= 85 °
I(0,180 °)
90 °
Figalre 59: The angular distribution functions for 3200 m/s ('O incident upon Kapton.
Table 59: The Nocilla model parameters for 3200 m/s (IO incident upon Kapton.
0 1.53 5.99 0 258
25 1.56 610 12.3 258
50 2.26 879 22.5 255
7;5 3.33 1310 47 A 261
85 3.91 1570 62.2 271
71
o
0 = 50 °l
e.= 75 °[
e.= 85 °!
e. = 25 sl
l
\
30 °
0
60 °
3200 m/sec CO
Z93-Coated AI
1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00
I (e,180 ° ) I(&0 ° )
90 °
Figure 60: The angular distritmtion functions for 3200 m/s CO incident upon Z-93-coated alu-
minnln.
"Fable 60: The Nocilla model parameters for 3200 m/s CO incident upon Z-93-coated aluminunl.
Oi (degrees) S U (m/s) 0u (degrees) T. (K)
0 0.889 356 0 270
25 0. _24 999 -4.31 . _4
50 1.30 511 -14.7 262
) -,75 1.06 420 -15.7 26_
85 0.688 278 -9.42 275
72
o
0.= 50 °
0.= 25 °
\
30 °
2840 m/sec CO 2Solar Panel
B
0i = 75 ° / ,/,
= 85 ° ..../- ........
0
60 °
8.0 6.0 4.0 2.0 0.0 2.0 4.0 6.0 8.0
I(0,180 °) I(e,0 °)
90 °
Fig-tire 61: The angular distribution flmctions for 2840 m/s (102 incident upon the solar panel.
Table 61: The Nocilla model parameters for 2840 m/s (102 incident Ul)On the solar panel.
Oi (deg;rees) ,b' (; (m/s) 0u, (degrees) T_ (K)
0 0.605 196 0 278
25 0.942 302 30.5 273
50 1..05 618 42.4 261
75 3.71 12(10 55.5 277
85 4.87 1670 7(I.3 310
73
0
0 = 50 °[
O_= 25 °\
0._. 0 0
1
2840 m/sec CO 2
SiOKCoated Ka
0
60 °
8.0 6.0 4.0 2.0 0.0 2.0 4.0 6.0 8.0
I(0,0 °)I(0,180 °)
90 °
Figlu'e 62: Tile angular distribution functions for 2840 m/s CO2 incident upon SiO2-coated Kapton.
rlhble 62: The Nocilla model parameters for 2840 m/s (?02 incident upon SiO2-coated Kapton.
0 1.56 489 0 260
25 1.46 459 14.3 262
50 2.26 707 31.8 260
,)_'75 3.80 1230 52.1 __6
85 4.61 1540 62.1 295
74
o
0. = 50 °!
0.= 25 °' \
30 °
2840 m/sec CO 2
Kapton
6.0 4.0 2.0 0.0 2.0 4.0
I(0,180 °) I(0,0 °)
90 °
6.0
Figm'e 63: The ang_llar distribution functions for 2840 m/s CO2 incident upon Kapton.
Table 63: The Nocilla model parameters for 2840 m/s CO2 incident upon Kapton.
o_ (4,_r,,,_) ,s' t: (,,,/_) o,, (d,._roe.) T. (t,:)
0 1.45 455 0 261
25 1.4J 452 10.6 261
50 2.11 660 24.3 25!I
7;5 3.32 1060 ,18.9 270
85 4.03 1380 64.7 288
75
o
0. = 50 °!
0.= 75 °1
Oi= 85 °..................iiii_....
30 °
0
2840 m/sec CO 2Z93-Coated AI
1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00
I(8,180 °) I(0,0 °)
60 °
90 °
Fig-ure 64: The anDllar distribution flmctions for 2840 m/s (702 incident Z-93-coated aluminum.
Table 64: The Nocilla model parameters for 2840 m/s CO2 incident upon Z-93-coated ahuninunl.
Oi (degrees) S U (m/s) 0,, (degTees) T. (K)
0 0.792 254 0 273
25 0.564 183 -5.25 279
50 1.08 344 -13.3 267
75 0.935 299 17.6 271
85 0.526 171 0.166 280
76
Table65: Conlparisonof the [ReducedForce(!oeflicientmeasurenlentsforuponthe solarpanelmadewith the carriergasesII2 and lie.
1870m/s N,eincident
0_ (,tegree_) ft H," f: ti2 f, ';/_Diff. .L, lie f,, I12 L, _ Diff.
1) 0 0 0 1.3,1 1.26 6.0
25 0.379 0.362 4.6 1.2.1 1.17 6.4
50 0.648 t).628 3.2 1.02 (I.9.19 7.7
75 0.696 0.679 2.6 0.643 0.581 111.7
85 0.578 0.522 1/).7 0A30 0.3,111 26.6
Table 66: (!omparison of the Reduee(t Fol"('e Coefficient
upon the solar panel made with the carrier gases tt2 and He.
nleasurements for 1870 Ill/S ("O incident
Oi (degrees) fl lie ./'ttI_ ft _7_Diff. f_, tie .f_, H2 f,, 7( Diff.
0 0 0 0 1.33 1.26 5.6
25 0.382 0.366 4.3 1.24 1.18 5.1
50 0.656 0.631 3.5 0.997 0.948 5.1
7,5 0.725 0.688 5.3 0.632 0.577 9.6
85 (1.595 0.530 12,2 0.414 0.338 22.5
Tabh, 67: ('Oral)arisen of the Reduced Force Coefficient measul"enlents for 1670 m/s (!O_ incident
upon lhe solar panel made with the carrier gases [12 and He.
0_ (degrees) .f, He .ft II.2 f, _7_Diff. J'_ He .f,, ti2 .f,, _/ I)ifl'.
9"0 0 0 0 1 .- t 1.21 5.3
25 (1.37,1 (1.381 1.7 1.19 1.13 5.:_
5/1 0.653 (1.661 1.2 0.961 0.891 7.8
75 [). 71.9 O.734 '2.1 0.588 [).51.9 13.4
85 0.608 0.562 8.3 0.368 11.288 27.6
77
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1. AGENCY USE ONLY (Leave Blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED
November 1997 NASA Technical Paper
5. FUNDING NUMBERS4. TITLE AND SUBTITLE
Measurement of Momentum Transfer Coefficients for H2, N2, CO, and CO2 Incident Upon
Spacecraft Surfaces
6. AUTHOR(S)Steven R. Cook* and Mark A. Hoffbauer*
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
Lyndon B. Johnson Space Center
Houston, Texas 77058
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
National Aeronautics and Space Administration
Washington, D.C. 20546-0001
8. PERFORMING ORGANIZATIONREPORT NUMBERS
S-834
10. SPONSORING/MONITORINGAGENCY REPORT NUMBER
TP 3701
11. SUPPLEMENTARY NOTES
* Los Alamos National Laboratory
12a. DISTRIBUTION/AVAILABILITY STATEMENT
Unclassified/unlimited
Available from the NASA Center for AeroSpace Information (CASI)
800 Elkridge Landing Rd
Linthicum Heights, MD 21090-2934 (301) 621-0390 Subject Category: 15
12b. DISTRIBUTION CODE
13. ABSTRACT (Maximum 200 words)
Measurements of momentum transfer coefficients were made for gas-surface interactions between the Space Shuttle reaction control
jet plume gases and the solar panel array materials to be used on the International Space Station. Actual conditions were simulated
using a supersonic nozzle source to produce beams of the gases with approximately the same average velocities as the gases have in
the Shuttle plumes. Samples of the actual solar panel materials were mounted on a torsion balance that was used to measure the force
exerted on the surfaces by the molecular beams. Measurements were made with H2, N2, CO, and CO2 incident upon the solar array
material, Kapton, SiO2-coated Kapton, and Z93-coated AI. The measurements showed that molecules scatter from the surfaces more
specularly as the angle of incidence increases and that the scattering behavior has a strong dependence upon both the incident gas and
velocity. These results show that for some technical surfaces the simple assumption of diffuse scattering with complete thermal
accommodation is entirely inadequate. It is clear that additional measurements are required to produce models that more accurately
describe the gas-surface interactions encountered in rarefied flow regimes.
14. SUBJECT TERMS
solar arrays, plumes, momentum transfer, rarefied gas dynamics
15. NUMBER OFPAGES
81
16. PRICE CODE
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None