investigations(ref. l) of a soot-contalnlngflame, that is similar to the gas ... (window _ tube)may be significantlyless than the tube-onlythicknessand still provide ... fore, the absorption coefficient in this case is the following. 3 ___ rd/_> 1. (2) a ... g - Tra d,. Trad is the particletemperatureat a gas pressure,pg = 0.I atm, and a par-.
/t/,q_,4--v-m- 5>;>-7 _? NASA Technical Memorandum 88786 NASA-TM-88786 19860022180
Analysis of the Gas Particle Radiator
Donald L. Chubb Lewis Research Center Cleveland, Ohio
ANALYSIS OF THE GAS PARTICLE RADIATOR Donald L. Chubb National Aeronauticsand Space Administration Lewis Research Center Cleveland,Ohio 44135 SUMMARY '
Theoreticalperformanceof a new space radiator concept, the gas particle radiator (GPR), is calculated. The GPR uses a gas containingemitting, submicron particlesas the radiatingmedia. A transparentwindow contains the gas particle mixture around the solid radiator emitting surface. A major advantage of the GPR is that large emissivity(€T _ 0.8) is achieved without the use of emlsslve coatings. A radiationheat transferanalysis shows that for a modest volume fraction (~lO-4) of submlcronparticlesand gas thickness
(~l cm) the emissivity,_T' is limited by the window transmittance. Besides determiningthe emissivity,the window is the critical element for making it possible for the GPR to have lower mass than a tube type radiator. The window acts as a "bumper" to providemeteoroid protectionfor the radiatorwall. The GPR was compared to a proposed titanium wall, potassiumheat pipe radiator. For both radiatorsoperatingat a power level of l.O1MW at 775 K it was calculated that the GPR mass was 31 percent lower than the heat pipe radiator. I. INTRODUCTION High specific power (power radlated/radlatormass), small area and long lifetimeare the desirable characteristicsof a space radiator. These characteristicswill be attained if a low mass and high emlss_vity,_l' that is stable for long periods (7 to lO yr) can be achieved. For a tube type radiator (either a heat pipe or a pumped loop) high emlsslvlty (€ > 0.8) is achieved by the use of emlsslve coatings. Adhesion and emlsslve stabilityof these coatings must be obtained for long periods of time if a tube type radiator is to be a successfulspace radiator. Generally,the largestmass portion of a tube radiator is the armor that must be used to protect against meteoroid penetration. The gas particle radiator (GPR) is a new concept that has the potential forlong lifetime,high emissivitywith lower mass than tube radiators. Figure l is a conceptualdrawing of the GPR. A gas which contains a suspension of fine particles is containedin a sealed volume between the tube radiator
and an outer window that are separatedby a distance,D. On start-upof the radiator a temperaturegradientwill exist across the gas. This temperature gradient will induce a gas flow that will distributethe particles throughout the gas. However, this will have to be demonstratedfor a successfulGPR. In the mlcro-gravltyof space the particlesshould remain in suspension. Uniform particle distributionis critical to obtaininghigh emissivity. Therefore,it will be necessaryto prove uniform distributioncan be establishedbefore a GPR is a viable space radiator. If the window is transparentto the emitted radiation the gas particle mixture will yield a high, stable emissivity. Past investigations(ref. l) of a soot-contalnlngflame, that is similar to the gas particle mixture of the GPR, have yielded large emlttances. Obtaining high emissivitywithout the use of emlsslve coatings is a major advantageof the GPR. It would appear that the addition of the gas-partlclemixture plus a surrounding window will result in a larger mass for the GPR than a tube radiator. However, the addition of the window "bumper"will provide meteoroid protection for the emitting tube. This window "bumper"means the combined thickness (window _ tube) may be significantlyless than the tube-onlythickness and still provide the same meteoroid protection(refs. 2 and 3). lherefore,the GPR may have a lower mass than a tube radiator. The major problem for the GPR is finding a suitablewindow material. As will be shown, it is the window transmittancethat limits the emissivity. There are suitable choices for the gas and particle materials. However, there is a need to experimentallyverify the emissivitiespredicted in this study. Suitable window materialsand a verified emissivityare the critical issues for the GPR. However, even if these issues can be resolved satlsfactorlly there are other design problems that will also have to be solved. It will be necessaryto provide a seal between the window and the radiating surface. Also, provisionwill have to be made for the differencein thermal expansion of the window material and the metallic radiatingsurface material. The analysis and results for the emissivityof the GPR are presented in the following section. A discussionof possiblewindow materialsis presented in section III, and a mass comparisonis made between the GPR and tube type radlators in section IV. Finally, conclusionsare presentedin section V. II. EMISSIVITYOF GAS PARTICLE RADIATOR A number of studies (summarizedin ref. l) of the emlttanceof sootcontaininggases have been carried out. These investigationsyield large 2
emlttancesfor modest amounts of soot concentration. Seedingwith small particles has also been proposed to increase gas absorptionof incident radiation (ref. 4) or as a means of shieldinga surface from incident radiation(refs. 5 and 6). The success of the GPR depends on large emlttance(or absorption)of the gas-partlclemixture, similar to these concepts. In reference4 large absorptionwas measured as a function of wavelength,x, in the range 0.2 _ l _m for carbon, aluminum oxide, hafnium carbide, and tungsten particles suspendedin water. Particle diametersranged from 0.02 to 2 _m. The total emissivity,_T' for the GPR is derived in Appendix A. The most importantapproximationsused in this derivationare that the gas, particles, and radiator surface are at the same temperatureand the absorption g of the gas-partlclemedium is uniform and is determinedby coefficient,k_, the particle optical properties. It is assumed that the gas is transparentto the emitted radiation. Also, the emissivityof the radiator surface, Cp, is neglected. Two ranges of particle size are consideredin Appendix A. For particles of small radius, rd, (rd/k < l) the followingabsorptioncoefficient is assumed,
K is a constant,
rd -- < 1
in the gas-partlcle fits
and m is the volume fraction
is an absorption
coeffi1 and 6).
ax, for 2the partlcles is assumed to be equal to the particle cross-sectlonal area, _r d. Therefore, the absorption coefficient in this case is the following. k Where nd
a = n_O_u= 4 3 ___' rd
rd/_ > 1
is the particle number density.
m_ : _ nd=
4 _rd 3
For the emission temperaturerange of interest for the GPR (300 to 1200 K), more than 90 percent of the radiationwill be in the range 1 _ x _ 75 _m. Therefore,the small particlesmust satisfy rd < 1 _m and the large particles are defined by rd > 75 _m.
As mentioned above, It was assumed that same temperature.
the gas and particles
of this approximation
are at the
Is examined In Appendix B.
For small particles (r d < _g where _g is the mean free path) the heat transfer between the gas and particles wtll be determined by free-molecular flow, whereas for large particles (r d _ _g) the heat transfer Is determined by contlnuum flow. Results for the temperature difference, AT = T where g - Tra d, Trad
is the particle temperatureat a gas pressure,pg = 0.I atm, and a par-
ticle temperature,Trad = lO00 K are calculatedin Appendix B. For both small particles (free molecularflow) and large particles (continuumflow) AT < O.Ol Trad. Under these conditionsof pressure and temperatureIt appears reasonable to neglect the differencein temperaturebetween the gas and the particles. An importantpart of the cT W
calculationis the window specular transW
mission, T_. For most window materials TX can be approximatedby a square w wave (ref. 7). Therefore,equation (A31)was used to approximate TX. Using thls window approximationand the assumptionsdescribedabove the following results for cT were derived in Appendix A for large particles,
CT = _w
- e-B) Fo-_uTp ,
rd _ 75 _m
and for small particles,
3.6KkT P Y " hc mD ,
rd > 75 _m
rd _ l _m
The quantities FO-Xu - T p and Q[x21u] are integral functionsgiven by equations (A36) and (A40). Other quantitiesappearingIn equations (4) to (7) are the speed of light, c, Plank's constant,h, and Boltzmann'sconstant, k, w (hc/k = 14,388 _m-K). The window transmission,_w, Is the magnitude of _ between the lower, X_, and upper, _u' cutoff wavelengthson the window transmission, (eq. (A31)),and T is the temperatureof the emitting radiation P surface.
In figure 2, CT/_w
for large particles (eq. (4)) is shown as a function
of XuTp for several values of B. For large values of B (>4) the exponential term in equation (4) is negligibleand CT _ TwFo-_ T . In this case cT is up determinedentirely by the window transmission. For small particles (eq. (5)) the quantity CT/_W is shown as a function of _uTp for several values of y. Similar to the case for large particles,when y is large (y > l) £T
_wFo_xuTp. Therefore,for both small and large particlesthe total emissivitywill be determinedby the window transmissionif the parameters B and T
Consider the volume fraction,m, necessaryto attain large B (>4) and large y (>l). In the case of large particles (eq. (6)) the smallest rd yields the largest value of B. Therefore,assume rd _ 75 _m and for a practical GPR, D _ l cm. As a result m > O.Ol is requiredto attain B > 4. Now consider small articles (eq. (7)). The parameter,K, is in the range 4 to 6 um/_m for soot (ref. 1). Therefore,assume K _ 5 _m/_m. Also, considering the lowest temperatureof interest T _ 300 K and again using D _ l cm the P volume fraction necessaryto attain y > 1 is m > 2.7x10-4. A much smaller volume fraction (m > lO-4) is required to attain y > 1 than to attain B > 4
for small partlc'les
for large particles (m > O.Ol). The smallest m
most desirable for the GPR since the total particlemass will be a minimum. Therefore,the use of small particles(rd < l _m) will yield the same cT with less mass than with large particles(rd > 75 _m). Based on the above discussion,m > lO-4, should insure that the maximum feasible emissivity\ (cT _ _wFo_XuTp_ ! will be attained for small particles. However, as figures 2 and 3 show, only for _uTp _>7xlO3 _m K will _T/_w be > 0.8). At T _ 300 K this means k > 20 _m. There are few large (CT/Tw P u materialswith good transmissionat wavelengthsthis long. Therefore,the GPR will be more appropriatefor higher temperatures. Window materials that can possibly be used for the GPR will be discussed in the next section. Ill. WINDOW MATERIALS As.shown in the previous section it is the window transmissionthat determinesthe GPR emissivity. Therefore,it is critical to have a window With large transmittancein the wavelengthrange of interest. Since the radiator temperaturesof interestare 300 to 1200 K the majority of emitted radiation will be in the infrared (_ > 1 pm). Therefore,window materials such as ordinary glass will not be suitable. 5
Several materials in the infrared. metal fluoride
The optical glasses,
in Table I that
(HMFG), were obtained
except the heavy
properties except the yield stress were obtained from reference 8. The yield stresses were obtained from the noted references. All properties of the HMFG systems were obtained are alkali
would be a serious operation large
which are soluble problem for
Although water solubility
in a water-contalnlng this
of the required
shown in Table I
may be a
of cesium bromide and have been manufactured
I0). The window material
of the material (refs.
windows ( 1
y _ 1
€o/€T > 1 + €_/€ T
P thickness, t
of the heat pipe wall
In 0.072 < t
possible to use such a thin wall
AT/A° (eq. (12)), Is found that
t o : 0.6 mm.
< 0.078 mm. Although It may be
= O.l mmwas arbitrarily chosen P as a practical limit on t P. This same limit was also chosen for t w, so that t = t = 1/6 t = O.l mm. With t + t = 0.2 mmmeteoroid protection will w p o w p be more than required, (tw + tp _ to /6.9). Titanium of thickness,ts = tp = 0.I mm, wlll also be assumed for the connectlngmember between the plate and window. As well as providingmeteoroid protection,the wlndow and emitting piate must be of sufflclentthickness to contain the pressure loads of the helium gas and heat plpe fluid. The window must contain the helium pressure of 15 torr. If the distance, L = 20 cm (eq. (el)), then the maximum shear stress (pg L/tw) will be 4 n/mm2 (600 psi). This is well within the yield stress for NaCl with impuritiesadded to increase the yield strength (Table I). The potasslum heat plpe of reference14 operates at a pressure of 4124 n/m2 (31 torr). Therefore, the pressure load on the titanium Is PH = 31 - 15 = 16 tort, which for heat plpe length (ref. 14), L' = 5.15 m, produces a maximum shear stress (PHL'/tp) 5 of l.lxlO2 n/mm2 (l.6xlO4 psi) well wlthln the yleld stress (1.55xi0 psi). Using the materials,wall thicknesses,and dimensionsalready described, the specificmass ratio, _T/_o, can be calculatedusing equation (C14). _T --
tp tw = _0 to _W
+ 2(20"----_ + 1
Thus the reductionin wall thicknessmade possible by the window meteoroid bumper results in a 75 percent reductionin the specific mass. It should be rememberedthat the specificmass includes only the radiatingarea. It does not include the heat pipe working fluid nor other supportingstructure. These parts will be includedwhen MT/M° (eq. (lO)) is calculated. In order to calculate MT/M° the ratios _/a T and a_/a° in equation (lO) must be known. From the data of reference14, a'/a = 1.26. Assuming o o ' = ao), then that the auxiliarymaterial specificmasses are the same (aT a_/a T = a_/ao(ao/aT).
aT/a ° = 0.25,
AT/Ao = 1.03,
a'/aO 0 = 1.26 in equation (lO) yields MT/Mo = 0.69. Thus the GPR results in a 31 percent mass reductionfrom the comparableheat pipe radiator. The masses and areas obtalned from these calculationsare shown in Table II. For the hypotheticalGPR the wall thicknesses,tw
and tp were not
reduced to the minimum required for meteoroid protection(tW + tp = to/6.9). If tw, tp, ts * 0 then aT * o and the minimum possible mass ratio MT/M° will be obtained. From equation (lO) the following is derived, MT M
o aT*° assuming a'o = ST"
o l +_"
ao/ao = 1.26 and AT/A° = 1.03,
= 0.57 aT* o
Thus MT/Ho = 0.69 obtained for tw = tp = ts = O.l mm is close to the minimum possible mass ratio MT/Mo a * o = 0.57. Therefore,littlewill be gained by reducing the wall thicknesses T further. V. CONCLUSION This study was directed at predictingthe performanceof a new space radiator concept, the gas partlcle radiator (GPR). The GPR uses a gas contalnlng emitting,submlcronparticlesas the radiatingmedia. The gas particle mixture is containedbetween the radiator emitting surfaceand a transparentwindow. There are two major advantagesthe GPR has over conventionalheat pipe
or pumpedloop radiators.
the use of emlsslve coatings. A radlatlon
of a11, high emissivity
Is achieved wtthout
Secondly, the GPRpotentially
has a lower mass.
of the gas particle
expresslon for the GPR emlsslvlty, €T. For a modest volume fractlon (_ > 10-4 ) of submlcron particles and gas thickness (D = 1 cm) It was found that the emissivity
was determlned by the window transmittance.
element In the GPRconcept.
In the Infrared are alkali
Another crltlcal gas so that
and oxides of silicon,
for maklng possible
aluminum and magneslum.
a uniform particle
the window Is the critical
the lower mass for the GPR. The window acts as a "bumper"
(wlndow + radiator
for the radiator
thickness alone and still
to provide meteoroid protection wall
are presented In Table I.
Issue Is maintaining
The wlndow must have high transmittance
and be strong enough to contain the gas partlcle
Several candidate wtndow materials rials
Thus the window becomes
Thus the combined
can be significantly
less than the radlator
provide the samemeteoroid protection.
the GPRcan have a lower mass than a tube type radiator. The GPRwas compared to a proposed titanium
For both radiators
was found that
potassium heat pipe
at a power level
of 1.01 Mw at 775 K It the GPRmass was 31 percent lower than the heat pipe radiator.
There are many design tssues that will make the GPRa vlable
have to be addressed and solved to
Two of the most Important
(1) Providing a seal between the window and the emitting
(2) A uniform and compatible thermal expansion of the window material the emlttlng
Results of this tube type radlators crltlcal sufflclent
study Indicate without
the GPRcan have a lower mass than
the use of emtss_ve coatings.
element for the GPRand must provide high Infrared structural
a uniform particle
Also, to obtaln
The window Is the transmittance
In the gas must be maintained.
APPENDIX A - EMISSIVITYOF GAS-PARTICLERADIATOR Approximate the gas particle radiatoras an infinite flat plate with gas between the plate and a cover window. Figure (Al) is a schematicof this configuration. In deriving an expressionfor the spectral emissivity,c_, of the gas-partlcleradiator the followingapproximationsare used. (1) Window at uniform temperature,TW, and behaves in a diffuse manner (2) Plate at uniform temperature,T and behaves in a diffuse manner P (3) Gas at uniform temperature,T (no conductionor convection) g (4) Negligiblescatteringof radiationby particles (5) Absorptioncoefficient k, of gas-partlclemedium is uniform and is ' g determinedby particle optical properties(gas is transparentto radiation) (6) Steady state conditions,a/at = 0 For the one-dlmenslonalgeometry shown in equation (Al) and neglectingconduction and convectionthe energy equation is the following, dQR dx
is the total radiativeheat flux, (W/m2)
is the specular heat flux (W/m2m). As a result of equation (Al)
q_ d_ = constant
where q_ P is the heat supplied to the plate and q_ is the heat leavingthe window. The hemisphericalspectral emissivityis defined as, W
cx(TP'X) - _B_(Tp,E) where B
is the black body specific intensity, 2 B[(Tp,X) =
2hc _5 ehC/XkTp - I) 13
Note that c}, is defined in terms of the plate temperature,TP . Also, the total hemisphericalemissivityis the following. w dx q_
€_B_ d_ CT(Tp) =
o aT4 P
QR _ aT4 P
In order to determine c and €T the heat flux leaving the window, qx must wX be found. To obtain qx the radiativetransfer equationmust be solved with appropriateboundary conditions. First consider the boundary conditions. Taking a heat balance for a unit area of the window the following is obtained (eq. (Al)).
Where q_i_ is the heat from the gas incidenton the window, q_W_ris the heat reflected from the window back into the gas qW ' _t the heat transmittedthrough the window and 2c_B_ is the heat emitted from the window to the gas and to the outside. In obtainingequation (AT) it has been assumed that no heat is being lost by conductionand that no radiationis incident on the window from the outside. The total heat that leaves the window is the following. W
q_ = qxt + €}_Bx
Using equation (A7) to obtain q_t and then substitutingin equation (AB) yields the following, W
qE. = qxi(l - °x) - cx_B_
where p_ 3 qxr/q_l is the window reflectlvlty. Also, since it is assumed that the window behaves in a diffuse manner, the specific radiationintensity leaving
the window and entering w heat flux q_ as follows.
Iw , ' _o can be written in terms of the
w cos Q d, ix °
= w w
+ ck_Bk °xqxl ww
Now consider an energy balance for a unit area of the emitting
P = qP _ qP qx _o xt
P is the where qxo P Is the heat leaving the plate and entering the gas and qM heat leaving the gas and striking the plate. Since the plate is assumed to behave in a diffusemanner then a relation similarto equation (AlO) for the window is obtained.
The boundary conditions
(A9) to (A12)) will
be applied to the radiative
intensity,Iw xI(S), at the window resultingfrom radiationwithin the solid angle, d_, (fig. (Al)) Is the following.
IW e Xi(S) = I_o
E( "):] KX - KX dK
Where Kk Is the optical depth,
Is the gas-partlcleabsorptioncoefficient. Also, D S = cos O
Therefore, since Tg is assumed uniform (as a result Is uniform, equation (A13) becomesthe following.
IW = Ip e Xi Xo
g is uniform) BX
g and kX
The heat flux at the window resultingfrom radiationover all solid angles seen by a point on the window Is,
qxl = Xi cos e d_ w _ =2_ iw 15
equation (A16) in (AI?) ylelds
qklW= _ip-oTk+ _Bg_=k m
where _k Is the gas transmittanceand _k
TX = _
COS 0 d_ = 2 D2
_k = -_
l - e
is the gas absorptivity.
= 2 E3 kgD)
cos e d_ = 1 - T k- = 1 - 2E3 k D
and E3(x) Is the exponentialintegral.
-_e du 1 -xu
Similar to Equation (AI8) for the window heat flux, qkl, the following result Is obtained for the plate heat flux, qp w _B_ k kl = _Iko_k +
w If the boundary conditions,equations(AlO) and (A12) are substitutedfor Ik o equation (A22) and
In equation (A18) then two equationsfor q_ I
q_i are obtained• These can be solved to obtain the following result for qW kl. W qkl = 1
_ p w-2 - pXpXTX
. Bkck_k + °kckPkTk
Equation (A23) can now be used In equation (Ag) to obtain the heat flux leaving W
the window, qk" Therefore,the spectral emissivity(eq. (A4)) Is the following. qk
l - ok
equatton (A24) Ktrchhoff's
=x = cx, and the relations
p P p P PX .. %, = PX . %, = ]
.. • :
Pk + _k . _X = P_ + ck + Tk = 1 were used, where p}, mittance.
_}, Is trans-
The spectral emissivity, €), was derived under the assumptions given at the beginning of th_s appendix. Nowmake the addltlona] assumptions that
T.=Tg=Tp_ndthatthe._ndow h_negligible e_v_ty €_=1- ._>. Therefore,
equatton (A24) ytelds
the following. N
To obtain the total emissivity, €T, equation (A27) ts substituted (A6) and the Integration ts performed. In order to slmpltfy the tlon the fo]lowlngaddltlona]approxlmatlonsare made; €p 0.9 (5)
Material thickness. mm
Water solubility, gm/lO0 gm
Sodium chloride (NaCl)
Silver chloride (AgCl)
Calcium fluoride (CaF2)
Lithium fluoride (LiF)
Sodium fluoride (NaF) Potassium bromide (KBr) Cesium bromide (CsBr)
Magnesium oxide (MgO, crystal) Cesium iodide (Csl, crystal)
(Compressive) II 0.69 to 41.3 (100 to 6000)
(Shear) 12 1.2 to 6.0 (174 to 870)
(Compressive) II 0.69 to 40 (10 to 5800)
(Compressive) I0 22.5 (3270)
Aluminum oxide (A1203. crystal)
(Type) Yiel d stressA N/mm_ (Ib/in L)
Heavy-metal fluoride glasses (HMFG) HF4.BaF 2" LaF3°AIF 3
(Shear) 12 36 (5225)
- COMPARISON BETWEENHEATPIPE RADIATORAND GAS PARTICLE RADIATOR [Radiator conditions; radiated power = 1.01 MW, radiator temperature = 775 K]. Radiator area, A, _2
Radiating surface mass, Mrad = sA, kg
Auxiliary mass, Total mass, Ma = s'A, kg Mrad + Ma, kg
Heat pipe radiator (ref. 14)
Gas particle radiator
Titanium wall potassium heat pipe data (ref. 14): Emissivity, co = 0.9; radiating wall thickness, to = 0.6 mm; area redundancy, r = 321/360 Gas particle radiator data: Emissivity, €T = 0.84, NaCI window (_u = 15 _m, Tw = 0.9); wall thicknesses, tp = tw = ts = 0.1 mm; area redundancy, r = 321/360; redundant area emissivity, €_ = 0.3; helium pressure, pg = 15 torr. Calculated results used to obtain GPR results:
--=So 0.25 ,
7_o: 1.03 ,
So - 1.26
UNCOATED METALLIC RADIATING
,- WINDOW /
SURFACE "-,,, "
D HEATPIPEOR PUMPEDLOOP
PARTICLE MIXTURE Figure1. - Gasparticleradiatorconcept.
1.0 I .8
3.6K kTp_oD> I
_uTu, pmK Figure2. - Totalemissivityfor small particles (rd < I pm, Tp< 1200K).
i• 0 --
(Y> i) _ = F°-_'uTp
3.6 K kTp Y:
;_uTp , PmOK Figure3. - Totalemissivityfor smallparticles(rd