Thermal Analysis of Nuclear
Dual Mode Spacecraft
By
Michael C. Cross
B.S., California Polytechnic State University
San Luis Obispo, 1981
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Mechanical Engineering
1993
U

I
This thesis for the Master of Science
degree by
Michael C. Cross
has been approved for the
Department of
Mechanical Engineering
by
Richard S. Passamaneck
William H. Claussey
John A. Trapp
Date
Cross, Michael Christopher (M.S., Mechanical Engineering)
Thermal Analysis of Nuclear Dual Mode Spacecraft
Thesis directed by Professor Richard Passamanic
ABSTRACT
This is a study of some of the major thermal design issues
relevant to a spacecraft in low earth orbit which has a Nuclear
Reactor for the generation of electrical and/or propulsive power
and a large liquid hydrogen propellant tank. The focus of the
study was the heat transfer analysis of the Nuclear Reactor,
aviojnics module, and liquid hydrogen tank. Consideration of the
spacje environment is also included. Some consideration of
materials and thermal insulation has been included when
necessary to complete the analysis. The thermal design practices
are as standard as possible to provide a solid base for more
refined thermal design work.
This) abstract accurately represents the content of the candidate's
thesis. I recommend its publication.
Signed
III
CONTENTS
Chapter
1.0
1.1
2.0
2.1
2.2
2.3
2.4
2.5
2.6
3.0
3.1
3.2
Introduction.....................................
Nuclear Induced Heating..........................
Reactor Thermal Influence........................
Radiation Shields..................................
Reactor Influence ANSYS Model Description...,
Reactor Influence ANSYS Model Results............
Hand Check of ANSYS Model Results................
Conduction Between Reactor and Tank..............
Total Heat Flux to Tank from Reactor.............
Avionics Thermal Influence.......................
Avionics Influence ANSYS Model Description.
Avionics Influence ANSYS Model Results...........
3.3 Hand Check of ANSYS Results.
4.0
4.1
5.0
Space Background Thermal Influence.
Heat Flux From Space Background...
Hydrogen Tank Heat Flux...........
5.1 Total Heat Flux and Resultant Boil Off.
6.0
Recommendation for Increased Performance.
Appendix
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A.
Plots and Program Listings for Reactor Influence
Model.....................................
B. Plots and Program Listings for Avionics
Influence Model...............................
References....................................
49
64
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1.0
Introduction
Spacecraft are normally very limited in available electrical power
for use by the onboard systems. This is because the power
systems are normally either Solar Cells, Fuel Cells, Radio Isotope
Thermal Generators (RTG), or for very short missions, Batteries.
The weight to power ratio of these systems ranges from 454
Kg/KW for Solar Cells to 188 Kg/KW for RTGs. A Nuclear Reactor
cor ld provide power for a spacecraft with a weight to power ratio
of 65 Kg/KW. The reason nuclear reactors have not been used in
the past by the United States is mostly because of cost,
complexity, and perceived risk. The former Soviet Union had a
Nuclear Reactor called the TOPAZ which was launched several
timps and is now being considered for purchase by this country.
The attraction of a proven "offtheshelf" design is great, but the
regulations and design practices of the Soviet Reactor generally do
not comply with the standards in this country. The U.S. is
developing its own reactor called the SP100. Political opposition
makes it difficult for this kind of system to be utilized in the U.S.
Large development costs and the perceived risk are also
burdening this system.
Spacecraft having an abundance of electrical power makes it
possible to employ electric propulsion systems. Ion thrusters and
Arc
An
the
Jet thrusters are two examples of electric propulsion.
Ion thruster uses a potential grid to accelerate molecules of
propellant gas to very high velocities.
Specific Impulse is a common way of expressing the efficiency of a
propulsion system. Specific Impulse is defined as the thrust in
pounds divided by the propellant flow rate in pounds per second.
The
resulting parameter has the units of seconds. Specific
Impulse of an Ion thruster can reach 2000 seconds while that of a
1
conventional chemical propulsion system is normally around 300
seconds.
Arcj Jet thrusters use an electric arc to heat the propellant gas to
very high temperatures, which then expands through a nozzle to
provide thrust. Arc Jet systems can reach specific impulse levels
of around 1000 seconds. The primary drawback of these systems
is that they provide low thrust levels. The time required to get
from place to place with these systems is usually much longer
than for chemical propulsion systems.
In i;he 1950's and early 1960's the U.S. was working on the
development of a nuclear powered rocket engine for use on
spacecraft. This system provided very high specific impulse and
thrust and was considered to be a superior propulsion system.
The obvious hazards of this system compared to chemical systems
and the public opinion opposing anything nuclear, caused the
program to be canceled.
In recent years there has been renewed interest in nuclear
powered spacecraft because of the extreme performance demands
of a manned mission to Mars. Nuclear propulsion, due to its high
specific impulse (about 1000 seconds) and high thrust compared
to chemical propulsion, is emerging as a viable option for
significantly reducing the size and cost of the program.
The concept of combining a Nuclear Reactor for generating large
quantities of electrical energy and a nuclear propulsion system for
providing superior propulsion was proposed at Martin Marietta in
1988. This system is described in (4), and the configuration is
shown in Figure 1.
The focus of the Martin Marietta design was an orbiting spacecraft
which required a large quantity of electrical power and the ability
to liiake significant changes in the orbital trajectory. The high
efficiency of the nuclear propulsion system made these orbit
changes achievable with a manageable quantity of propellant.
2
Some of the basic problems of integrating a Nuclear Reactor into a
spacecraft design were addressed in the Martin Marietta report.
One of the most striking problems was the thermal management
of the system. Reactor operation will result in temperatures of
around 1000K on most of its exterior surfaces, while the liquid
hydrogen propellant is at 20K. The relatively close proximity of
these two elements requires careful design to prevent excessive
boil off of the liquid hydrogen.
Thp hydrogen tank is located between the reactor and the avionics
in
its
the Martin Marietta design to facilitate placing the reactor with
nuclear radiation emissions as far as possible from the avionics
systems which have a limited ability to withstand radiation.
The addition of an active refrigeration system to the spacecraft to
limit liquid hydrogen boil off would add a significant amount of
weight and cost to the system. The option of designing the
spacecraft to passively minimize boil off of the hydrogen, and
including enough extra hydrogen propellant to last the length of
the mission was also considered.
To j perform an accurate comparison between refrigerators and
passive measures of boil off limitation requires an accurate
estimate of the effectiveness of passive thermal systems.
Determining the effectiveness of passive thermal measures is the
subiect of this thesis.
objective of this thesis is to determine the boil off rate of
The
hydrogen for a spacecraft system using thermal radiation shields
and
con
thermal conduction barriers described in section 2.0. This
iguration of the thermal control systems is the simplest and
most obvious for a first analysis. Additional systems may be
employed such as ridged radiation barriers between the structure
connecting the reactor and hydrogen tank. The benefit of these
additional systems versus the cost and weight, as well as the
3
question of whether any of the passive systems are preferable to
ac
ive refrigeration, is not summarized in this thesis.
Figure 1 shows the spacecraft configuration per the Martin
Marietta report (4).
Figure 2 shows the thermal approximation of the configuration
used in this analysis. It includes the major thermal sources and
sinjks and shows some simplifications and approximations used in
this analysis.
Nuclear Rocket
Nozzle
High Tenperature
Radiators
Outer Satellite Thrust
Structure 4.6 m Dia.
LH2 Tank 4.27 m Dia. 7.0 m
Cylinder Length
Avionics
Platform
Reactor to Satellite
Interface Structure
RC,S Mounting Ring & LH2
Tank Support Ring (2x)
Electronics &
Avionics
8x Electric
RCS Thrusters
Center Section Left
Out For Visibility
Total Satellite Length = 15.1 m
Figure 1 Spacecraft Configuration Per Martin Marietta Report (2)
1
4
T\yo separate computer analyses will be performed. The first will
address the reactor environment which primarily deals with the
radiation from the radiators to the hydrogen tank dome. The
second section of computer analysis will address the avionics bay
thermal environment.
The thermal radiation heat input to the hydrogen tank from the
Nuclear Reactor and its associated components will be the primary
result of the first section. The conduction heat transfer through
the structure which attaches the reactor to the hydrogen tank will
also be included. The temperature of the reactor support
structure will be determined which may be used to design this
structure for compatibility. Information gained in this section of
the analysis may allow the radiation shield to be improved as
needed.
Nuclear Radiation
Net Radiation
Sun Side
nun
Nuclear
Shield
Radiators
4444444
Net Radiation
Earth Side
Conductances
(Both ends)
Avionics
Thermal
Radiation
Figure 2 Spacecraft System Thermal Approximation
5
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The radiation and conduction heat transfer from the avionics
module to the hydrogen tank will be analyzed in the second part
of the computer analysis. Both sections will employ the ANSYS
finite element analysis program to arrive at the total amount of
heat flowing into the hydrogen tank (see Figure 3).
Avionics Influence Model
Reactor End
Skin Structure
Avionics Bay
Insulating Structure
Figure 3 Spacecraft Breakdown for ANSYS Solution
The next section of this report will focus on the space
environment and will address solar flux, planetary flux, earth
albido, and deep space background as sources and sinks of
thermal radiation for the spacecraft. The effects of orbital
geometry on the thermal radiation environment will be included.
An estimate of the thermal flux into the hydrogen propellant from
this environment will be determined.
The final analysis section will sum the thermal radiation flux from
the  reactor, the induced heating from the nuclear particles, the
radiation and conduction heat fluxes from the avionics, and the
 7
thermal flux from the space environment. The sum of the heat
6
fluxes will allow the total boil off rate of the hydrogen propellant
to be calculated, which is the ultimate goal of this report
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Nuclear Induced Heating
The induced nuclear heating of the hydrogen fuel from the
radioactivity emitted by the reactor is summarized in Figure 4.
This chart shows the energy input to the hydrogen propellant as a
function of the distance into the tank measured from the nearest
parjt of the tank to the reactor. Two curves are included, one
illustrates the induced nuclear heating with the nuclear shield,
and the other illustrates the heating without the nuclear shield.
This study will only address the situation of induced nuclear
heating with a shield. There are two types of particles produced
by the reactor which interact with the hydrogen to cause heating
of the fluid, and they are Neutron and Gamma 'particles'. These
two sources of heating are combined into the 'total' heating as
shown in the figure.
Total Heating W/0 Shield
Figure 4 Nuclear Induced Heating
7
The induced nuclear heating of the hydrogen propellant is in
addition to the thermal flux to the tank as analyzed in the rest of
this thesis. This heating will result in a direct boil off of the
hyjdrogen and is unavoidable, assuming that the nuclear shield
design and the spacecraft configuration including the reactor to
tark spacing are fixed.
Ths hydrogen tank is 4.5m in diameter. The tank dome at the end
uses a truncated hemisphere which is shorter than a true
hemisphere by one over the square root of two. The volume of
the dome is about 18m3, and extends for 1.6m back from the end
of
the
wa
obti
by
the tank. If we assume this whole quantity of fluid receives
nuclear dose present at the closest end of the dome (2E06
:ts/gram), the total heating of this section is 2.55W. This is
ained by multiplying the hydrogen density of 70.789 Kg/m^
the volume of 18 m3 and then multiplying this result by the
specific heating of 2.0E6 W/gm.
Vol = 18 m3
Liquid Hydrogen Density = 70.789
Kg
Mass = Vol x Density = 1274 Kg
Heating = 2.0E06
Gram
Total Heating = Heating x Mass = 2.55 W
This assumption, that the heating throughout each lm section of
tank is the same as that at the front end of that section, may be
applied to the entire tank to arrive at a conservative
approximation of the total heating. With this method, the total
heating is approximately 3.0 W. The hydrogen boil off resulting
8
from this heating is obtained by multiplying the total heating by
the heat of vaporization of hydrogen.
Total Heating = 3.0 W
Heat of Vaporization of Hydrogen = 125.6 ^^
Vaporization Rate =
Heating
Heat of Vaporization
= .024 ^
hr
9
) Reactor Thermal Influence
2.
The inside of the Nuclear Reactor operates at a temperature of
abput 2300K. The outside of the reactor is expected to stay about
lOpOK. The low temperature sink for the reactor is provided by
the large array of heat pipe radiators which reject heat to space.
Th
ese radiators operate at 1000K
Figure 5 shows the heat pipe configuration. This was supplied by
the reactor designers at Idaho National Engineering Lab (INEL)
along with the following data (3):
Heat Pipe Radiator Temperature 1000 K
Total Heat Rejection Rate 360 kW
Radiator Heat Rejection Rate 360 kW
Radiator Area 7.6 m^
Radiator Length 1.5 m
Max. Diameter 1.65 m
To
the
tem
perform a check of this data, the energy emitted to space by
radiators may be calculated from knowledge of the area and
perature.
The heat transfer to space may be calculated using Stephan
Boltzmann's Law :
q = OEA(T{Tt)
Where:
e= .85
a = 5.669 E08
m2 K4
Th = 1000K
TC = 5K
A = 7.6m2
This gives a result of :
q=366 kW
Which is consistent with the supplied data.
The nuclear shield is located between the reactor and spacecraft
to block most of the emitted particles which can damage the
spacecraft electronics and induce heating of the hydrogen liquid.
The shield is a combination of Boron Carbide (B4C) and Lithium
Hydride (LiH). For this analysis the shield will be treated as a solid
piece of B4C. The fuel surface temperature inside the reactor is
225j02350K (3). The temperature is expected to drop to about
1000K at the bottom of the reactor body. The structure which
attajches the reactor to the shield should be of a low conductance
material such as titanium (7.35 W/m K), with radiation shields in
place as appropriate. The heat transfer into the shield should be
minimized through this juncture. The heat pipes come out of the
bottom of the reactor and obstruct most of the view between the
top
that
of the shield and the bottom of the reactor. Thus the
temperature of the radiation source to the top of the shield will be
of the heat pipes in this area, or 1000K.
Figure 5 shows the INEL reactor concept while Figure 6 shows an
approximation of this concept used in this analysis.
11
Reactor Body
j

j
(
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\
Nuclear Shield
1*41113^
Heat Pipes
.Poison Rod Actuator
Figure 5 INEL Reactor Concept
12
Multi Layer Insulation
30 K Hydrogen
Tank Dome With
Foam Insulation
Shield
Figure 6 Thermal Approximation of Reactor Configuration
2.1
The
Radiation Shields
heat transfer between the radiators and the nuclear shield
must be minimized through the use of radiation shields, making
the temperature of the shield as low as possible and the resulting
radiation to the hydrogen tank as low as possible. It is assumed
that] the radiators can be made structurally sound without the
need for a support structure to the shield. The support will come
from the heat pipes extending into the reactor. The radiation
shield used between the radiators and the shield will be thirty
13
I
layers of high emissivity material capable of withstanding
temperatures of 1000 K. Some candidate materials are listed (2):
tungsten e = .25
titanium e = .14
SSTL e = .18
nickel e = .04
Molybdenum E = .10
Tmelt = 3600 K
Tmelt = 1922 K
Tmelt = 16721783 K
Tmelt = 1700 K
Tmelt = 2894 K
The value of thermal conductivity through MultiLayer Insulation
may be calculated using a model developed by the Lockheed
Corporation. Lockheed did an extensive testing program to
develop this model. The results provide two equations as follows:
i
t
t
I
q =
2.07E10 x Ld284 x (Th2 Tc2)
2x(Nl+ 1)
q =
1.2E11 XEx(Th467 Tc467) xDf
N1
Wh
ere:
Ld = Layer Density
Th = Hot Side Temperature
Tc = Cold Side Temperature
N1 = Number of Layers
e = Emissivity
Df = Radiation Degradation Factor
The first equation gives the conduction contribution, and the
second equation gives the radiation contribution. These two
equations are then added together to get the total heat transfer.
This data was collected for several types of MultiLayer
14
Insulation, all of which used aluminized mylar or kapton as the
reflective material. This material will work well for the hydrogen
tank where the temperature will be low, but the insulation on the
backside of the radiator must withstand temperatures of 1000K
and must therefore be a metallic foil. The Lockheed equations
may be used with the emissivity of titanium, but the conduction
term will be wrong. To compensate for this, the conduction term
may be multiplied by the ratio of the metallic foil conductivity to
the conductivity of Mylar. This ratio is equal to 49.
These equations are semiempirical, the general similarity to the
basic conduction and radiation equations can be seen. Several
terms have been modified to more closely correlate to the
experimental data collected by the Lockheed researchers.
The thermal flux through the MLI between the radiators and the
nuclear shield could be calculated from these equations if the two
surface temperatures were known. The temperature of the
nuclear shield, however, is one of the unknowns in the problem.
This problem may be solved using the ANSYS thermal analysis
program.
The Lockheed equations for heat transfer through the MLI cannot
easily be input into ANSYS. In order for ANSYS to accurately
model this heat transfer, an equivalent emissivity of one surface
mayj be calculated which yields the same heat transfer as that
through 30 layers of MLI.
The
0.1.
the
emissivity of the nuclear shield is that of B4C, which is about
We will use this value and calculate a value of emissivity for
inner surface of the radiators. The Lockheed equation will tell
us the heat transfer between the inside surface of the radiators
and the outside of the shield if we assume a temperature
difference. Then we can solve for the emissivity of the radiator
surface to produce the same heat transfer.
The
equation to be solved is:
15
1 ofaT?)  t 1
eh q Â£c
where eh is the effective emissivity of the radiator surface, ec is
the emissivity of B4C, q is the heat transfer calculated from the
Lockheed equations, Th is 1000K, and Tc is some temperature less
than 1000K. Examination of the effective emissivity with
different values of the cold side temperature indicates a relatively
small effect. For values of the cold side temperature between the
expjected shield temperature range of 300 to 500K, the effective
emissivity ranges from 0.0016 to 0.0017. An effective emissivity
of 101 will be used. This is significantly greater than the values
calculated, but still results in very low heat transfer and will
make the analysis conservative.
The effective emissivity of the hydrogen tank dome to simulate
the presence of MLI would be .0018. The tank dome emissivity
will also be taken as .01.
The theoretical values of radiation heat transfer between two
parallel disks with multilayer radiation shields may be calculated
and! compared to the Lockheed semiempirical values. This will
shed some light on the performance of "real world" MLI versus
ideal radiation shields. The equation for radiation between
infinite parallel disks with radiation barriers is:
1
q_=
A (Nl + 1)~ 2.1
e
Where all surfaces have the same emissivity.
For this problem we will choose arbitrary values to compare
theoretical versus empirical results. Thirty layers of insulation
withj an emissivity of .043 will be used. The hot temperature will
be I000K and the cold temperature will be 500K. The resultant
16
Lockheed heat flow is 84 W/m^, and the theoretical heat flow is
38 W/m^. The difference is 46 W/m^, which results from
increased radiation heat transfer through the less than ideal
insulation, and heat transfer through conduction.
2.2 Reactor Influence Ansys Model Description
The ANSYS model consists of four bodies. These include the tank
dome, nuclear shield, reactor radiator, and a disk simulating the
bottom of the reactor and the top of the heat pipes. The tank
dome was modeled as a disk to simplify the geometry input to the
computer. The configuration is shown in Figure 7.
/
\
\ / \ / V
w\XV \ ymf
o o hi
\ / \ / \
/
Figure 7 ANSYS Model of Reactor End Configuration
The tank dome was 76cm (30 inches) thick and 483cm (190
inches) in diameter. The actual thickness of the tank dome is
13cm (5 inches), but had to be increased in order for the elements
in the finite element model, which make up the dome, to have an
aspect ratio closer to one. The aspect ratio for the elements
comprising the dome would have been about 6.5. When the
model was run with this aspect ratio, an error was generated
indicating unacceptable aspect ratios. The thermal conductivity of
the foam insulation which comprises most of the thickness of the
dome was reduced by an amount scaled by the ratio of the proper
tank insulation thickness to the modeled tank insulation thickness.
Thils is 13/76 or 1/6. The actual insulation conductivity is 0.205
W/m K (.01 Btu/inhrF), so the value used in the analysis for
the z direction property was six times that or 1.23 W/m K (.06
Btu/inhrF). The conductivity in the perpendicular directions
was reduced to account for the increased cross sectional area.
The temperature of the backside of the dome was 20K (5R) which
is the saturation temperature of liquid hydrogen at a vapor
pressure of 0.103 MPa (15psi). The conductivity of the aluminum
tank is so high relative to the conductivity of the foam insulation
that essentially no additional resistance to heat flow is introduced
to the system. The model did not include the aluminum tank wall.
The emissivity of the tank dome exterior (as discussed in section
2.1) is .01. This is the result of MultiLayer Insulation applied to
the tank surface over the foam insulation. The model of the dome
included a single thickness of material with the conductivity of
foam insulation and the surface emissivity of MLI.
The heat pipe radiator was modeled as a hollow cylindrical cone of
uniform thickness. The inside and outside surfaces of the radiator
are at a uniform temperature of 1000K at all times per the INEL
data (3). The conductivity of the radiator was set very high at
205 W/m K (10 Btu/inhrF) so that the inside surface would
attain the same temperature as the outside. The outside surface
18
I
of jthe radiator was made to be at 1000K with boundary
conditions.
The nuclear shield was modeled as a truncated cone of
homogenous material with the conductivity of Boron Carbide at
17.8 W/m K (.8676 Btu/inhrF). As discussed earlier, the
shield was assumed to be solid Boron Carbide. The shield is
insulated from the radiator by MultiLayer Insulation which is
accounted for in the ANSYS model by assuming the radiator has
an effective emissivity of .01 on the sides facing the shield. After
the system has achieved steady state operation, the heat that
flows to the shield has only one path out, which is by radiation
from the front surface toward the hydrogen tank and space. The
emissivity of the shield face should therefore be high to reduce
the steady state temperature of the shield. An emissivity of .8
was used in the model to reflect the idea that the boron Carbide
surface would be treated or coated as necessary to achieve the
highest emissivity possible. This includes the effects of the
degradation of the surface with time, UV exposure, and sustained
high temperature. As a reference, the emissivity of rough
stainless steel is about 0.60.
The nuclear shield is essentially enclosed by the radiator on all
but one side as seen in the Figures 1,5,6 and 7. The small end of
the shield, or the end toward the reactor, is exposed to the upper
ends of the heat pipes which are at 1000K. The heat pipes are
fairly closely spaced allowing the assumption that the shield is
facing a solid surface at 1000K.
The nuclear shield has a direct heat input by conduction due to
the reactor support structure which attaches to the shield at the
back side. This heat input was calculated and input to the model
as a} boundary condition. Assuming a shield temperature, the
conductivity from the 1000K reactor structure through the attach
structure was calculated by hand, and input to the model. The
structure was assumed to be made of titanium. The results of the
model were checked to insure that the temperature assumption
19
was good. The actual shield temperature came out to be about
395K (712R) at the perimeter of the back side. The assumed
temperature for the final run after several iterations was 405K.
The calculation of the heat flux through this structure is as
foil
ows:
T = 1000K
i 
L = .30m
I____________
T = 395K
Cross Sectional
Area = 11cmA2
Conductivity =
7.35 W/mK
_KA(TiT2) 7.35*01l*(1000395)
q L .30
q = 16.0 W
It was necessary to specify a boundary condition temperature of
one point on the shield in order to get the model to run
successfully. This may have been because the ANSYS program
needed a constraint on the body. Without this, a zero diagonal is
generated in the temperature matrix. The structural analogy of
temperature is displacement. It may be easier to visualize the
20
effects of a specified displacement on a structural body than a
temperature specification on a thermal body. It is possible that
all bodies in the ANSYS analysis must have a specified
displacement or else they may in effect "float" in space. In reality
the temperature of the shield is free to float to any temperature
in Response to the incoming radiation from the radiator and the
outgoing radiation to the tank and space.
Specifying a temperature which did not impact the model was an
iterative process. Initially a temperature of 472K (850R) was
assumed. This was found to be too high. The model was run and
it was found to be the hottest point on the shield. The
temperature was lowered to 399K (718R). Subsequent runs found
little effect from this artificially specified temperature.
The dominate method of heat transfer between the
reactor/radiator, and the hydrogen tank and shield in this
problem is radiation. In the vacuum of space there is obviously
no Jconvection, so radiation, conduction, and nuclear induced
heating are the only forms of heat transfer. The ANSYS model
hanales radiation between two surfaces by generating radiation
shape factors that indicate the portion of radiant energy leaving
one surface that impinges upon the other surface. These shape
factors are time consuming to calculate since the calculation must
be performed between each radiating element and every other
radiating element. This results in the calculation of shape
factors where N is the number of radiation elements in the model.
In this analysis there are 224^ or 50,176 calculations. The
ANSYS module which performs these calculations is called the
AUX12 module. Approximately 40 minutes of CPU time on the
VAX Computer was required to execute this module each time the
shape factors were recalculated.
The
university edition of ANSYS is limited to a maximum of 500
unknowns in the matrix solution. This limit is exceeded easily in
this
problem. The final solution of the radiation model between
21
the reactor and the tank contained 447 nodes. It was necessary to
increase the mesh size to a larger value than was optimum to
allpw the problem to be executed with this software. It would
haye been interesting to investigate the effects of increased mesh
density upon the model results, but this was not possible. As
shown in Sections 2.4 and 3.3, the results agree with the hand
calculations, so the mesh density is assumed to be adequate.
2.3
Reactor Influence ANSYS Model Results
Appendix A contains the results of the ANSYS solution of the
radiation between the reactor, shield structure and the tank dome.
The first part of this data shows the temperature profiles for the
bodies comprising the ANSYS model. The disk representing the
bottom of the reactor is not shown since it was constrained by
boundary conditions to be a uniform 1000K. The temperatures in
the shield range from 387K (697R) in the center of the face
toward the tank dome to 397K (714R) on the back of the shield
closest to the reactor.
The temperatures of the tank dome range from 20K (36R) across
the inside of the tank which was input as a boundary condition, to
a high of 20.9K (37.55R) in the center of the face of the tank
facing the radiators and shield.
The reaction heat flow rates at the nodes on the inside of the
dome may be obtained from the ANSYS solution. These nodes
were constrained to be 20K. The reaction heat flow rates
represent the quantity of heat which was absorbed from each
nod^ by the liquid hydrogen in order to maintain the specified
temperate of 20K at each node. This data is presented in
Appendix A. The total heat transfer to the hydrogen may be
obtained by summing the reaction heat flow from each node on
the back of the dome. This quantity is 15.58W (53.19 Btu/hr) and
represents the total thermal radiation heating of the hydrogen by
the reactor.
22
2.4 Hand Check of ANSYS Model Results
It is possible to perform a simplified analysis and compare those
results with the results obtained from the computer analysis.
The simplified system is composed of two opposing disks of
different size. One disk is the size of the tank dome, and the
other disk is the size of the nuclear shield face in one instance and
the radiator inside surface in another instance. The two results
will be added together to obtain an approximate total heat
transfer rate. The inside radiator surface is an annular ring. The
shalpe factor was calculated by subtracting the shape factor for the
hole in the middle from the shape factor of a disk with the same
outside diameter as the radiator. The size, temperature, and
emissivity of the small disk in the sample problem will first be
taken as that of the radiator to get the heat transfer to the dome
disk, then the small disk will be taken at the size, temperature,
and emissivity of the shield face to get the other part of the heat
transfer. The temperature of the tank dome is taken to be one
degree higher than the liquid hydrogen inside the tank. This is
based on the results from the ANSYS analysis.
If the radiation heat transfer between the radiator and tank dome
and the heat transfer by conduction through the foam insulation
on the tank are equal, then the results are consistent and there is
further assurance that the ANSYS results are correct.
Figure 8 shows the problem setup. The small disk is at
temperature T2 and the large disk is at temperature Tl. The
separation of the disks is LI. The ambient temperature is taken
as 2K to represent deep space background. The emissivity of the
'dome' disk is 0.01 as used in the ANSYS solution. The emissivity
of the small disk is taken as 0.01 with a temperature of 1000K to
reflect the characteristics of the radiator inside surfaces. The
emissivity of 0.8 with a temperature of 387K is taken for the
shield face.
23
T1
e1
D1
L1
Figure 8 Reactor Influence ANSYS Model Check Problem Setup
This is a three body problem, two disks and the space background.
The radiation network showing the thermal resistance in an
electrical analogy is shown in Figure 9.
1 ~Â£1 1 1 Â£2
Ai Â£i J1 F12A1 J2 A2 Â£2 Eb2
(lFujAi
(1F2i)A2
Eb3 = J3
Figure 9 Electrical Analogy of Check Problem
24
For the shield face portion of the solution, the following values are
appropriate:
I
Ti = 21K
T2 = 698K
T3 =2K
Ai = 18.3m2
A 2 = 1.16m2
L = 4.10m
El = .01
Â£2 = 0.80
The shape factor from the large disk to the small disk may be
determined from tables in (2). The value for this geometry is:
F12 = .026
Thejn the other shape factors may be calculated as follows:
F21=^n = ,392
A2
F13 = 1 Fi2 = .975
F23 = 1 F21 = .608
The
resistances may be calculated as:
Ri =
R2 =
r3
1 ei _
Aiei
1
F12A1
. 1
F13A1
5.412
= 2.178
= 5.57E2
25
R4 =
1
F23A2
1.408
R5=Vl^= 2140
A5E2
J3 is deep space, which is a black body, so that the surface
resistance is zero and the network is as shown in Figure 9.
Kiichkoffs current law may be used to solve this problem. It
stares that the sum of currents into any node is zero. Writing two
equations for nodes Ji and J2 gives two equations and two
unknowns.
Ebi Ji h~ Ji, Eb3 Ji Q
Ri R2 R3
Ji J2 1 Eb3 J2 Eb2 J2 q
R2 R4 r5
Solving for Ebl, Eb2, and Eb3, allows the determination of Jl and
J2 by solving the system of simultaneous equations.
Ebi = oTj = 1.102E02
Eb2 = oT42 = 1.272E 03
Eb3 = cT43 = 9.070E07
Ji = 25.227
J2= 1.019 E 03
The
total heat lost by disk 1 is:
q1= EbiJi .
41 (lei)/Aiei
4.66W
The negative value indicates that there is a heat gain by the tank
dome.
26
The analysis for the inside radiator surface is identical except the
values of A2, T2, e2, and F12 are changed to 2.41m, 1000K, .01,
and .11 respectively. This analysis results in a heat gain by disk 1
of
9.93W.
Therefor the total heat flow is :
l
q = 14.59W
This value agrees reasonably well with the ANSYS results of
15.b3W. The difference is 6.4%.
1
This heat flow may be used to determine the temperature
difference across the foam insulation on the tank necessary to
sustain this heat transfer through the foam insulation. The
conduction equation is (1) :
KAff! T2)
4 L
Where:
i
q = 14.59W
L = .127M
K = .205 W/m K
A = 18.3 M2
Which gives:
= Ti T2= 0.49K
ivA
This is approximately the temperature difference between the
outside surface of the foam insulation and the inside surface of
the foam insulation per the ANSYS solution. The ANSYS model
results show a temperature range across the outside of the dome l
l
27
of between 20.33K (36.60R) to 20.8K (37.55R). The temperature
difference of .49K would equate to 20.49K which falls between the
ANSYS values.
2.5 Conduction Between Reactor and Tank
The thermal conduction between the reactor and the tank may be
estimated by knowing the shield temperature from the ANSYS
analysis and the tank structure temperature.
The connecting structure which ties the reactor shield to the rest
of Ithe spacecraft structure is shown in the Figure 1. The thermal
approximation used in this analysis is shown in Figure 10.
Tank
Figure 10 Thermal Approximation of Conductive Path Between
shield and tank
28
An approximation of the cross sectional area of the structural
attachments indicates that each member might be nineteen
square centimeters. There are six such members totaling 116
square centimeters of cross sectional area for thermal conduction.
If the material is titanium to minimize conduction, the
conductivity will be 7.35 W/m K. The calculation of the heat flux
thrpugh this structure follows:
Area =116 cm^
Length = 448 cm
Conductivity = 7.5 W/m K
Delta Temperature = 389 20 = 369K
_ KAfTi T2)
4 L
q = 7.02 W
2.6
Total Heat Flux to Tank from Reactor
The total heat flux to the tank from the reactor, not including
induced nuclear heating, is the sum of radiation calculated from
the
ANSYS model, and conduction calculated by hand,
qtot = 15.58 + 7.02 = 22.60W
The heat conducted down the connecting members would affect
the results of the radiation problem which did not take that heat
flow into account. The heat flow would reduce the temperature of
the  shield and the corresponding radiation from the shield.
!
i
29
3.0
Avionics Thermal Influence
The avionics systems are located on the opposite end of the
spacecraft from the reactor. This provides as much separation as
possible between the nuclear radiation source and the electronics
components which cannot tolerate a large nuclear particle flux.
The specific avionics in this spacecraft configuration are
undefined.
The unique feature of this satellite is that it provides a large
amount of electrical power from the Nuclear Reactor. The reactor
for the Martin Marietta concept provides 40KW. All of this
electrical power is assumed to be converted to heat in the
avionics. This is a conservative approximation since the
electronics are typically on the order of 10% efficient, and an
antenna may be 50% efficient. A spacecraft with this much power
would likely use this power for some kind of power transmission
and would take advantage of the 50% efficiency of an antenna.
The assumption that all of this power is dissipated in the
electronics results in the largest possible heat input to the avionics
bay.
Thd configuration of the avionics bay is shown in Figure 1 which
shojvs the Martin Marietta configuration. The thermal
approximation used in this analysis is shown in Figure 11.
30
External Surfaces Radiate
To
Deep Space At 2 K
Avionics Bay
40KW Internal
Vehicle Skin
Heat
Conductances Through
Aluminum Skin and
Titanium Structure
Figure 11 Thermal Approximation of Avionics Bay Area
3.1
Avionics Influence ANSYS Model Description
The model consists of four bodies including the aft tank dome, the
avionics module, the outside spacecraft skin, and a titanium
interface ring which is located between the tank dome and the
spacecraft skin to limit conduction from the skin to the tank. The
tank dome is modeled as a flat disk as was done in the analysis of
the reactor radiation heat flux. The complexity of the ANSYS
model is much greater with a concave tank dome and the thermal
effect is small.
The; ANSYS model is shown in Figure 12. The tank dome and the
avidnics module are divided into 45 elements each. The number
of elements must be kept to a minimum due to the limitations on
31
the; size of the models which may be solved using the University
version of the ANSYS program. The skin is divided into 20
elements around the perimeter, which matches with the elements
and nodes of the dome and avionics modules at each end. The
total number of elements in the skin is 80. The interface ring also
has the matching 20 elements around the perimeter to interface
with the dome and skin. It is only one element deep so it only has
20 elements. The total element count is 190.
Figure 12 ANSYS Model of Avionics Bay Area
The] aspect ratio of an element is important to the accuracy of the
solution. If an element of the type used here deviates too far
from being a square, the ANSYS program will not perform the
solution. For this reason the thickness of the dome and skin had
to fcje artificially increased to make the elements thicker and more
I
32
square. The thickness of the dome was increased from 12.7cm (5
inches) to 76.2cm (30 inches) and the conductivity of the dome
material was increased six times in that direction (Z axis) to
compensate while the conduction in the perpendicular direction
was decreased to 1/6 of the original value. Likewise the thickness
of the skin was increased from about .25cm (.1 inches) to 76.2cm
(30 inches) and the conductivity of the skin material was
increased in the X and Y directions by a factor of 300 to
compensate and was reduced in the Z direction to 1/300 of the
original value.
The conductivity of the dome was taken as that of Polyurethane
foam insulation which is nominally 0.205 W/m K (.01 Btu/inhr
F). The foam surface facing the avionics module is insulated with
Mill and thus has the emissivity of 0.01 as was determined
earlier.
The avionics module was treated as a solid piece of aluminum
with internal heat generation of 40 kW. The emissivity of the
surfaces facing out to space should be high to reject as much heat
as possible. These surfaces were given an emissivity of 0.8. The
surfaces facing inward toward the dome are insulated with MLI
and have an emissivity of 0.01.
The skin structure will conduct heat along its length into the
hydrogen tank. To limit this, the insulating ring is included in the
model. The insulating ring is of small surface area and was not
considered to radiate. The conductivity of the ring was taken as
that of titanium knowing that it is a structural member with low
conductivity.
The skin structure is aluminum with a high outside emissivity of
0.8 and a low inside emissivity of 0.01 corresponding to MLI
insulation. As discussed earlier the thickness of the skin is very
exaggerated and the material conductivity is adjusted to
compensate.
33
The back of the dome is in contact with liquid hydrogen. The
boundary condition of 20K is input at all nodes on the back of the
dome.
The internal heat generation of 40KW is input uniformly to the
avionics module by determining the heat generation per unit
volume. The space background temperature is assumed to be 2K.
3.2 Avionics Influence ANSYS Model Results
Appendix B contains the results of the ANSYS solution of the
radjiation and conduction between the avionics module and the aft
hydrogen tank dome. The first part of the data shows the
temperature solutions for each body comprising the model. The
second part of the data includes the tabular results of the reaction
heat flow rates at the constrained nodes on the back of the dome.
The temperatures at these nodes were constrained by the
boundary conditions to 20K, and the ANSYS solution gives the heat
floy at these nodes. As with the reactor end solution, the heat
flux out of these nodes flows into the liquid hydrogen and
represents the heat leak into the hydrogen.
The temperature of the tank dome ranges from 20K to 24K on the
surface facing the avionics module. The avionics module surface
temperature ranges from 434K to 444K on the side facing space,
and from 442K to 445K on the internal side facing the tank dome.
The reaction heat flow to the inside surface of the tank dome
which represents the heat flow into the hydrogen propellant is
404W (1378 Btu/hr).
The surface temperature of the skin ranges from 25K to 433K on
the inside and outside surfaces. The material is too thin to
support a significant thermal gradient through its thickness, so the
inside and outside temperatures are the same.
34
Hand Check of ANSYS Results
A simplified version of this system may be analyzed theoretically
without using the ANSYS program. This serves as a check on the
ANSYS results.
The approach will be to determine the amount of heat that leaves
thej exterior surfaces of the avionics bay area. This quantity of
heat should be the difference between the 40KW input to the
avibnics bay and the amount of heat which ANSYS predicts as
input to the hydrogen.
The exterior surfaces radiate to space at 2K. The outside surface
of
he avionics bay is a disk with the following properties:
Th = 440K
Area = 18.3m^
e = 80
Thej temperature is an average of the gradient across the surface
as determined by the ANSYS solution. The radiation equation may
be solved to determine the quantity of radiated energy. The
result is 31.1KW.
The outside skin geometry in the avionics bay area is a cylinder.
The temperature of the skin per the ANSYS results ranges from
47K at the end near the hydrogen tank to over 366K at the end
near the avionics bay. In order to determine the radiant energy
fluxj from this surface, it will be divided into four equal cylinders.
In this way, an average temperature for each area may be
estimated fairly accurately. The properties of the sections are:
Total Area = 38m^
Each Area = 9.5m2
35
! Ti= 366K
I A
T2 = 206K
T3= 115K
T4 = 47K
i
The radiation heat flux from each area is:
j
qi = i.iw
^2= 77W
Q3 = .075W
Q4 = .002W
Thq total thermal radiation from the exterior surfaces of the
vehicle in the avionics bay area is 39.65KW. Which leaves .35KW
for the hydrogen tank. The ANSYS solution for this quantity was
.404KW. The close correlation indicates that the ANSYS model
does not contain any serious errors.
36
4.0 Space Background Thermal Influence
A spacecraft in nearearth orbit experiences thermal radiation
flux from the sun by direct radiation, and from the earth as
reflected radiation or 'earth albido'. There is also planetary
radiation from the earth due to its surface and atmospheric
temperature which is effectively about 249K.
The radiation values applicable to
are (2):
a spacecraft in low earth orbit
Solar Direct
Earth albido
Earth emission
Earth Effective Temp.
Deep space temp.
=1393 W/m2
=.38
=214 W/m2
=249K
=1.7K
The orientation of the spacecraft and the orbit geometry can play
a large part in determining the actual radiation that is incident on
the1 spacecraft. For example, if the spacecraft is in a tail to sun
orientation, there will be less surface area presented to the sun.
The avionics, which are located in the aft section of the spacecraft,
and
the separation of this area from the liquid hydrogen, will
result in higher temperatures in this area. This surface of the
hydrogen tank would absorb less energy than the larger and
colder sides. Also, if the space craft is in a very high orbit, it will
be shielded from the sun for a smaller portion of the orbit than if
it is in a low earth orbit, where it is shadowed by the earth as
soon as it crosses the horizon. A polar orbit will be constantly in
the sun for a relatively long period of time where the orbit plane
is perpendicular to the earth to sun axis. Since the purpose of this
study is to determine the magnitude of the thermal environment
without a specific mission or orbit identified, the analysis has
been performed for a worst case in which the space craft is in a
37
low earth orbit, between the earth and sun and is assumed to stay
there indefinitely.
4.1 Heat Flux from Space Background
Almost all of the energy absorbed by the spacecraft skin is re
radiated. The energy absorbed may be calculated using the above
assumptions of the orbital position and radiation levels if the
absorptivity and emissivity of the surface are known. A common
surface coating used on space craft to maintain a low temperature
is
ITRI Z93 white paint. The properties of this paint are (2):
a = 0.15
e = 0.90
Exposure to ultraviolet solar radiation will degrade this surface
somewhat after a period of time. Tests indicate that after 1000
hours of exposure to ultraviolet radiation in a vacuum chamber,
the
value of absorptivity has risen to (2):
a = 0.171
Since data was not available on the degradation of the emissivity
factor it was assumed that an equivalent degradation occurred, in
order to insure a conservative analysis. This degradation
amounted to 14% which resulted in an emissivity increase to:
e = 0.79
The incident radiation energy from the sun and earth reflection is
kno^vn in terms of the projected perpendicular area. Since the
exterior of the spacecraft is a cylinder, the projected area divided
by the surface area can be used to scale down the radiation levels,
which can then be applied over the entire half surface as
appropriate.
38
For a spacecraft in a low earth orbit, the altitude is small
compared to the diameter of the earth. The side facing the earth
at any point in time will "see" almost 2tc steradians of earth
surface. The Martin Marietta Thermal Design Manual (2) lists the
shape factor between spacecraft and earth as .95 for the side
facjing the earth. Figure 13 shows the relative situation and gives
an' intuitive verification that this is indeed the case. This
illustration is valid for a satellite in an lOOKm orbit.
Figure 13 Relative Scale of Earth and Spacecraft in Low Earth Orbit
Figure 14 shows a cross section of the spacecraft indicating how
the
surface radiant heat exchange is portioned.
39
1393/1.57 = 887 W/m2
The energy absorbed by the spacecraft skin on the sunlit side is
the product of the absorptivity and the incident energy:
887 X .171 = 152 W/m2
The! reflected energy from the earth, or Albido, was listed as a
fraction of the incident solar energy on the earth. This is the
portion of solar energy incident upon the earth which is reflected
back into space, and which encounters the spacecraft from the
earth side. The energy absorbed on the earth side of the
40
spacecraft may be calculated in the same way as was done on the
sun side above with the exception of the scaled solar flux:
(1393/1.57) X .38 X .171 = 57.6 W/m2
The absorptivity and emissivity of a surface are the same at any
specific frequency. However, different values are used here
because the absorptivity in these calculations represents the
radiant properties of the surface at the high frequencies which are
characteristic of solar radiation. The emission of energy from the
surface uses the emissivity from the radiant properties for low
frequencies, which are the primary source of emitted energy from
low temperature surfaces like the surface of a spacecraft.
Since the spacecraft is rotating in its orbit, the absorbed energy on
the earth and sun sides were averaged to arrive at the nominal
value of the absorbed energy over the entire spacecraft.
q = 152+57.6/2 = 105 W/m2
A small portion of this energy is conducted into the spacecraft and
results in the vaporization of liquid hydrogen. The majority of
this energy is reradiated. The background to which it is re
radiated is deep space on one side and earth on the other. If an
assumption is made that all of the incident energy is reradiated,
the surface temperature of each side needed to radiate the
required energy may be calculated, then averaged to account for
the spacecraft rotation.
&+t4
T earth = 28 IK
Tspace 220K
The average of the fourth power of these temperature is:
I
41
TAve = 256K
This calculation is based on the approximation that the spacecraft
rejradiated all of the incident energy and absorbed none. This
approximation is valid since the great majority of energy is re
radiated, and the radiation is a function of temperature to the
fourth power. Thus, a small reduction in radiated energy results
in! an even smaller reduction in surface temperature. The fraction
of j energy conducted into the spacecraft may be calculated. The
surface temperature may be used to determine the heat transfer
into the hydrogen tank through the sides of the spacecraft.
The hydrogen tank is insulated on all sides with 12 cm foam
insulation and fifty layers of highly reflective foil or MLI which
actjs as a radiation barrier. The foam insulation used in this
analysis was polyurethane foam which has a thermal conductivity
of 1.73 E02 W/m K (2). This value was increased to .205 W/mk
for the ANSYS solutions to assure a conservative result and to
reflect the preliminary nature of the structural design. When the
composition of the vehicle skin is well known, a more realistic
value of thermal conductivity will be used. The MLI has an
effective emissivity of .01 as determined earlier in this report.
The calculation to determine the thermal flux through the
spacecraft skin into the hydrogen has two parts, conduction and
radiation. The temperature at the interface between the MLI and
the inner foam is not known. The conduction through each
medium is the same, so the equations may be set equal to each
other and the intermediate temperature may be determined.
q = OEA(TjTS1)
I
kA(TmTc)
q L
42
oea(tJ.t4) ^t^o
Where:
k = 1.73E02 W /M K
A = 101 M2
L = .05 M
Th = 256K
Tc = 20K
e = .01
cr = 5.669E08
K4M2
Solving for Tm gives:
I
Tm = 27K
The resulting heat flux by conduction and radiation through the
walls of the spacecraft into the liquid hydrogen is:
q = 247 W
The total incident energy on the outside of the spacecraft was 105
W/m2. Over the entire surface area of the spacecraft, this equates
to 10605W. The percentage of incident energy conducted into the
spacecraft is:
The
247/10605 = .023 = 2.3%
remainder of the energy is reradiated to space.
43
10605247 = 10358 W
The exterior surface temperature of the spacecraft required to
radiate this amount of energy to space would be:
T = 220K
This is the same temperature determined earlier. The amount of
energy conducted into the spacecraft may be ignored when
calculating the surface temperature of the spacecraft.
5.0 Hydrogen Tank Heat Flux
Four sources of heat input to the hydrogen tank have been
investigated. They are radiation and conduction from the reactor,
nuclear induced heating, radiation and conduction from the
avionics module, and radiation from the sun, earth and deep
space.
I
i
The heat flux to the hydrogen tank results in the boil off of the
liquid propellant. The sum of the four heat sources is:
Reactor Radiation and Conduction Flux (from Section 2.6) = 23W
Heating Due to Interaction with Nuclear Particles
(from Section 1.1) = 3W
Avionics Flux Including Both Radiation and Conduction (from
Section 3.2) = 404W
Space Environment Flux (from Section 4.1) = 247W
Total Heat Flux = 676W
5.1
Total Heat Flux and Resultant Boil Off
Using the value of total heat flux calculated in the previous
section, we may determine the resultant boil off rate of the liquid
hydrogen propellant.
Total Heating = 676 W

Heat of Vaporization of Hydrogen = 125.6 J
Kg
45
Vaporization Rate = Heating= 5.38
Heat of Vaporization hr
j
i
There is 7100 Kg of propellant at the beginning of the mission.
The vehicle will retain some propellant for a total of 1319 hours
before it has been evaporated. Obviously this is an unacceptable
ratb of boil off of the propellant. The mission length would be less
than this since the engines would consume some of the propellant.
46
6.0 Recommendations for Increased Performance
The results of this study presented in the previous two sections,
show that the largest heat flux to the hydrogen tank is from the
avionics bay heating. The second largest heat flux is from the
space environment. The assumption at the start of this study was
that the Nuclear Reactor at the front of the vehicle would be the
largest source of heating.
The relatively small size and large separation of the reactor from
the hydrogen tank caused the radiation exchange to be relatively
minor. Since the reactor was expected to be a problem, the design
was focused on limiting its radiation and conduction heat transfer.
Now that the avionics module is seen to be the largest remaining
problem, several design changes could be implemented to
drastically reduce the heat transfer from this source.
The problem with the current avionics module design is that the
hot  surface is large and close to the tank. The volume required by
the i electronics may require the large surface area. A large
portion of the heat from the electronics could be dissipated by a
radiator located off the back end of the spacecraft and not in the
view of the tank. This radiator might cool a circulating liquid
which carries the heat from the electronics.
A layer of foam insulation in addition to the MLI on the avionics
module between the avionics module and the hydrogen tank
would further reduce the heat transfer.
As was discussed in Section 3.0, an assumption was made that all
of the 40KW generated by the reactor was dissipated in the
electronics. In reality this was a very conservative approach
which resulted in the very high heat transfer rate. As discussed,
the electronics would likely drive an energy transmission
mechanism such as an antenna or laser which would be at least
47
50% efficient. The amount of heat generated in the electronics
might be more accurately estimated at around 20KW. If the
majority of this energy were dissipated through radiators, the
heat flux to the hydrogen would be drastically reduced from the
va
ue calculated in this report.
The spacecraft skin which surrounds the hydrogen tank is
insulated with 12.7cm of high quality foam insulation and MLI
radiation barrier as discussed previously. This system is
reasonably effective, and therefore increases in either foam or
MLI thickness would have marginal effect. A vacuum jacket
dewar is frequently employed for long term storage of cryogenic
propellants. This approach is used in the storage of liquid helium
in spacecraft. These spacecraft use liquid helium to cool infrared
defectors for astronomical and defense observations. Liquid
helium can be stored for up to five years in orbit. Incorporation
of a system such as this would greatly reduce the heating of the
hydrogen from the space environment.
48
1
Appendix A, Plots and Program Listings for Reactor
Influence Model
!
I
i
The ANSYS program listings for the Reactor Influence Analysis are
included in the following appendix. There are three programs for
this ANSYS model. They are the geometry definition, the
geometry meshing, and the boundary condition definition.
Also included in Appendix A are the results of the ANSYS model
solution. The first section includes graphic plots of the model
shpwing temperature profiles. Plots of each individual body are
included along with the system as a whole.
A listing of the reaction heat flow rates is also included. These are
the heat flow rates which ANSYS calculated at each node that had
a temperature constraint as defined in the boundary conditions.
These nodes are those on the inside of the tank domes. They
represent the presence of liquid hydrogen that maintains the
temperature at 20K by changing phase to absorb any incoming
energy. The heat flow rates at these nodes represent the energy
being absorbed by the hydrogen.
The! ANSYS model is in English units. All dimensions are in inches,
heat flow rates are Btu/hr, all temperatures are in degrees
Rankeen.
49
eoiit/tpu remodel. dat;2
/(3REP7
/com,remodel.dat data set for reactor end
/com,setup and geometry deffinition
/TITLE, 326 MODEL
KAN,1
E T, 1,7 0
ET,2,57
/com,Boron Caride
MP, KXX 1, .8676
/corn, Radiator artificially high conductvity
MPj, KXX, 2,10.
/com,Foam Insulation Conductivity /6 for thickness
MP
MP
,KXX,3,.0017
,KYY,3,.0017
/c om, Foarn In
MP , KZ 2,3,.06
CS /S, 1
K, ,18 . .5,90
K, ,18 .5
K, ,15
K, ,15 ,90
L, 1,2
CS fS
A, i.,2 ,3,4
CSYS, 1
K, l 24 ,90,13
l<, ; 24 , 1 ^ 5
K, ] 20 , 13.5
K, ] 20 ,90,13 .5
L, 5,6
CSYS
A, 5,8 , 7,6
A , 1,5 ,6,2
V,. 1,2 i 3 ,3,4,5 , 6
CSYjS,l
VGEN,4,1,,,
NUMMRG,KPOI
cs/s
,90
A,8,16,24,7
A, 4;, 3,20,12
V,^,16,24,7,4,12,20,3
CSYS,1
K ,25.5
K
,19.5
K, ,19.5,90
K,,25.5,90
50
,10,11,14,15
52,,56
, ,42,,56
KU 42,90,56
K[,52,90,56
A J, 18,19,22,23
CSYS
A11,19,22,14
V 1,10,11,14,15,18,19,22,23
CSYS,1
VGEN,4,6 , , 90
NUJMMRG,KP0I
CSYS,1
Kj,95,90,175
,95,,175
,85,,175
,85,90,175
25,26
CSYS
AJ25,26,29,30
AOFFSET,30,30
V 25,26,29,30,33,34,37,38
CSYS,1
L,
VGEN,4,10:
i 90
NUIMMRG KPOI IE2
A ,29,52,44,30
V j29,52,44,30,37,56,48,38
ARSEL,,1
ARASEL,,7
ARASEL,,13
ARASEL,,15;H4h}i208
ARASEL,,19
AcFFSET ALL 1
ARSEL,,63,69,2
ARASEL,,68
AOFFSET ALL 7
MUMMRG,KPOI,IE2
ARSEL,,63,69,2
ARASEL,,68
AD[ELE, ALL
A,
A,
A,
42,50,55,47
50,57,60,55
43,45,60,57
A,42,47,45,43
A,
V,
47,55,60,45
69,73,76,72,42,50,55,47
I
i
j
51
V ,73,77,80,76,50,57,60,55
V,77,70,71,80,57,43,45,60
V ,70,69,72,71,43,42,47,45
V,72,76,80,71,47,55,60,45
ARALL
EDIT/TPU REMESH.DAT;3
ls!all
,/doM, MESH ALL PARTS WITH 4 ELEMENTS PER QUARTER
LDVS,ALL,,4
/doM.MESH TANK DOME WITH 4 ELEMENTS PER QUARTER AND ONE THICK
VLiSEL, ,10,14
LDyS,128,,1
L..DVS 115 ,1
LDvS 116 , .1
ld/s,iis, ,1
LDjVS,81,,1
LDVS,4,,1
LDOV'S, 16 ,1
L.d/S 28 ,1
LDVS,2,,1
LDjVS ALL , 4
LSALL
LDjVS 32 , 1
LDjVS 54 , 1
LDjVS, 66, ,1
LDjVS 26 , 1
LDjVS 20 , 1
LDVS,47,,1
LDjVS 59 , 1
LDVS .14 , .1
LDVS,104,,1
LDjVS, ill,,1
LDjVS, 85, ,1
LDjVS 120 , 1
LDjVS
1 nwS,97,,1
f S,108,,1
LDjVS ,124,, .1
LDVS,107,,1
LDjVS, 112, ,1
LDyS,114,,1
52
I
LEWS', 8, ,1
LDVS,6,,1
LEWS, 24, ,1
LOWS 36 , .1
/COM,MESH SHIELD WITH 2 THICK
LEWS 9 ,2
LEWS', 12 ,2
LtWs,17, ,2
LEWS, 23, ,2
LDVS,35,,2
LDVS 29 ,2
LDVS,11,,2
LDVS ,10, 9
LDVS , 51, , 1
j LDVS  ,79, ,1
LDVS o'? > ,1
LDVS ,49, ,1
LDVS ,61, ,1
LEiVS , 6 o, ,1
ld',vs ,88, ,1
LCjVS ,100 9 9
LDVS ,71, ,1
LDVS ,74, ,1
LEWS , 83, , .1
LDVS ,87, , 1
LD/S ,99, , .1
LDVS ,95, ,1
LDVS ,73, , 1
LD*/S ,69, ,1
/COM,MESH RADIATOR SKIN
ARSEL,,25
ARASEL,,31
ARASEL, ,37
ARASEL,,43
ARASEL,,63,69,2
ARASEL,,68
AATT,2, 2
AMESH,ALL
/COM,SHIELD MESHING
ARSEL,,2
ARflEL,,9
ARASEL,,12
ARASEL,,18
ARASEL,,24
ARASEL,,3
ARASEL,,8
ARASEL,,14
I
53
ARASEL a,20
arIasel,,1
ARiASEL, ,7
ARASEL,,13
ARfASEL , 15
ARASEL,,19
AATT,1, MESH, ALL
/COM, MESHING OF TANK ********************
AR^EL,,30
ARASEL,,49
ARASEL,,51
ARASEL,,55
ARASEL., ,61
AAJT,3,,2
AMESH,ALL
/COM,MESH RADIATOR VOLUME
VLSEL,,6,9
VLflSEL, ,15,19
I'YfpE, 1
/COM,MESH SHIELD VOLUME
VLSEL,,1,5
TYffE.l
MAT, 1
VMESH,ALL
/COM, START OF WRAPUP *****************
**4*ESEL,STIF,57
****NELEM
****EWRITE
***.*N WRITE
MAT, 2
VMESH,ALL
/COM, MESH TANK. VOLUME
VLSEL,,10,14
TYPE,1
MAT, 3
VMESH,ALL
i 3
54
I
I
!
edit/tpu rebndcon.dat;5
/ (3 rep 7
resume
et,3,50,1
tijpe, 3
e j 1,8
E^LL
NALL
n'2000,200,200,200
wsort,z
fcijinif 500
/COM, START OF BOUNDRY CONDITIONS **********
/COM, SPACE NODE AT 5R
n tu, 2000, temp 5
/COM, CONSTRAIN ONE SHIELD NODE
KhjiT 1, TEMP 718
/COM, SELECT DOME INSIDE SURFACE
arjsel,,36
arase1,,54
l ' _
arrasei , 5 /
aijasel , 60
arrasei, 66
NAREA,1
Nlj ALL TEMP 36 .
/COM, SELECT RADIATOR OUT31FFACE
arsel, 28
arase1,,33
aijasel, 39
arjasel , 45
ARASEL,,70,74
NA}REA,1
NT,ALL,TEMP,1800
/GOM, SELECT AREAS ON BACK OF SHIELD
AFjSEL, 1
ARASEL,,7
ARASEL,,13
ARASEL,,15
ARASEL,,19
lsar
kpils
/COM, CONDUCTION HEAT INTO SHIELD
KHflow,all,heat,(56/8)
nail
eall 1
vial 1
arjal I
55
I sail
kpal 1
i ter,20,20,20
kbc, 1
krrf 2
eiisel ,stlf ,57
aij write
finish
56
I0ST1 IMP=
8NSYS 4.4R
OCT 21 1992
21:57:51
POST1 STRESS
STEP=i
ITER=20
TEMP
SMH =36
SMX =1880
XU =2
YU =1
ZV =3
DIST=151.932
ZF =98.5
PRECISE HIDDEN
R =134
B =338
C =526
D =722
E =918
F =1114
6 =1318
H =1586
I =1782
326 MODEL
cn
oo
IOST1 IHP=
326 MODEL
RNSVS__4 .AR
SEP 9 1992
21:50:09
POST1 STRESS
STEP=1
ITER=20
TEMP
SMN =36
SMX =37.548
XU =2
VU =1
ZU =3
DIST=119.86
ZF =190
PRECISE HIDDEH
R =36.086
B =36.258
C =36.43
D =36.602
E =36.774
F =36.946
G =37.118
H =37.29
I =37.462
Tank Dome Backside
CXI
CO
ItQSTl"IMP*
RttSYS 4.4(1
OCT 21 1992
21:54:14
P0ST1 STRESS
STEP=1
ITER=20
TEMP
SMH 36
SMX =37.548
XU =2
VU =1
ZU =3
DIST=119.86
ZF *198
PRECISE HIDDEN
R *36.086
B *36.258
C *36.43
D *36.602
E =36.774
F *36.946
G =37.118
H *37.29
I *37.462
326 MODEL
Tank Dome, Towards Reactor
O)
o
RNSVS 4.4 n
SEP 3 1992
8:34:26
P0ST1 STRESS
STEP = 1
ITER=28
TEMP
SMH =1799
SMX =1800
XU =2
VU =1
ZU =3
DIST = 70.448
ZF =28
PRECISE HIDDEN
R =1799
B =1799
C =1799
D =1799
E =1800
F =1800
G =1800
H =1800
I =1800
Thermal Radiators
0)
I0ST1 IHP=
326 MODEL
ON SYS4.40
SEP 9 1992
21x26:45
P0ST1 STRESS
STEP1
ITER=28
TEMP
SMN =697.862
SMX 718
XV =2
vu =1
zu =3
DIST31.885
ZF =6.75
PRECISE HIDDEN
R 698.981
B 781.218
C 783.456
D 785.693
E 787.931
F 718.169
G 712.486
H 714.644
I 716.881
Nuclear Shield, Towards Tank
O)
N>
fcOSTl
IMP*
326 MODEL
RMSVS 4.4ft
SEP 9 1992
21:18i44
POST1 STRESS
STEP=1
ITER28
TEMP
SMH =697.862
SMX =718
XU =2
vu =1
zu =3
DIST=31005
ZF =6.75
PRECISE HIDDEN
n =698.981
B =701.218
C =703.456
D =705.693
E =707.931
F =710.169
G =712.406
H =714.644
I =716.881
Nuclear Shield, Towards Reactor
prrfor
PRjINT REACTION FORCES PER NODE
***** POST1 REACTION FORCE LISTING *****
mSTE8.0000iE*SSERATIÂ£8AD CA& SfCTI0N= 1
THE FOLLOWING X,Y,Z FORCES ARE IN GLOBAL COORDINATES
?81$i IN?!'19 Units are Btu/Hr
I
63
Appendix B, Plots and Program Listings for Avionics
Influence Model
ANSYS program listings and results from the Avionics Influence
Analysis are included in Appendix B. The order and description of
each is the same as that for the Reactor Influence Analysis
included in Appendix A.
This ANSYS model is in English units. All dimensions are in inches,
heat flow rates are Btu/hr, all temperatures are in degrees
Ra
nkeen.
/PREP7
/cpom,setup and geometry deffinition
/TjITLE, Avionics bay model
KAN,1
Eli, 1,70
E/,2,57
/COM,AL PROPS x .0033 for area
MR,KZZ,1,.0279
/COM,AL SKIN x 300 PROP
MFj, KXX, 1,2511
MFj, KYY, 1,2511
/COM,TANK DOME FOAM PRO X .1667 FOR AREA
Mpj, KXX 2 .0017
MP,K.YY,2, .0017
/COM,FOAM X 6 FOR THICKNESS
MR, K.ZZ, 2, .06
/COM,AVIONICS MODULE ALUMINUM
MP,KXX,3,8.33
/COM,CONNECTION RING TITANIUM
MP
CS
,KXX,4,.3583
YS, 1
/COM,TANK DEFINITION
K,
K,
K,
,95,90
,95
,85
K ,85,90
L 1,2
PROPS
CSYS
A 1,2,3,4
CSYS, 1
K ,1,95,90, 30..
K. /,95,, 30.
K, I 85, 30
K, 185,90,30.
L, i>, 6
CSYS
A,5,8,7,6
A, i 5,6,2
V,1,2,3,4,5,6,7,8
CSYS,1
VGEN,4,1,,,,90
NUI'llMRG, KPOI
CSYS
A, 8,16,24,7
A 4,3,20,12
V 8,16,24,7,4,12,20,3
I
65
/COM,SKIN DEFFINITION
CSYS,1
Kl ,123
r
K[ ,95
K *95,90
K* ,125,90
A 110,11,14,15 '
K ,125,,75
K* ,95,,75
Ki,95,90,75
K],125,90,75
A}18,19,22,23
CSYS
A 111,19,22,14
V J10,11,14,15,18,19.22,23
CSYS, 1.
VGEN ,4,6, ,, , 90
Nll'MMRG, KPO I
/cjoM, avionics moduli:::
c: fO.,1
K ,95, 90, 45
K. , 95, ,45
K ,85 , ,45
K 9 ,85, 90, 45
L 5 14,1 1.
C s YS
A J, 11,1 4,2 5,2 6
AQFFSET,30,30
V , 111, 14,25,26,22,19,30,33
csys 1
VGEN,4,10,,,,90
MUMMRG,KPOI,1E~2
A,26,25,48,38
V , j26,25,48,38,33,30,52,44
/COM,SKIN EXTENSION DIFFINITION
AOFFSET,29,30
V , 1,15,28,9,5,27,37,13
CS/S,1
VGEN,4,15,,,,90
NUlfiMRG, KPOI, le~l
A,1,4,3,2
VDELE,2
A,1,9,12,4
V, 1,9,12,4,5,13,16,8
VDELE,3
A,9,17,20,12
I
66
Vi 9,17,20,12,13,21,24,16
A 12,3,20,17
A i 4,12,20,3
AL 22,33,30,19
Al22,31,44,33
A 131,39,52,44
A>52,39,19,30
A 133,44,52,30
ARALL
EDIT/TPU AVME3H.DAT;2
/ffREP?
RESUME
/COM,MESH AVMODEL DATA SET
LSALL
/COM,MESH DENSITY IS 5 PER QUARTER CIRCLE
LDVS,ALL,,5
LDVS,2,,1
LDVS,4,,1
LDVS,6,,1
Ld>VS 8, .1
LDVS,9,,1
LDVS,10,,1
LDVS,11,,1
LDVS,12,,1
LDVS,14,,1
LDVS,16,,1
LDVS,17,,1
Ld>VS 20 , 1
LDVS,23,,1
Lcjvs, 24, ,1
LDVS,26,,1
LDVS,28,,1
LDVS,29,,1
LDVS,32,,1
LcjvS 35, ,1
Lcjvs, 36 ,1
LDVS,44,,1
Lcjvs, 47, ,1
LDVS,49,,1
LDVS,50,,1
LDVS,51,,1
67
LDVS,54, ,1
l_dvs,58, ,1
LDVS,59,,1
LID VS, 61, ,1
LDVS,62,,1
LDVS,66,,1
LDVS,69,,1
LDVS,70,,1
LDVS,71, ,1
LDVS,77,,1
L(i)VS, 78 ,1
LDVS,81,,1
LDVS,82,,1
LDVS,85,,1
LDVS,86,,1
LDVS,90, ,1
LDVS,93,,1
LDVS,97,,1
LDVS,98,,1
LDVS,103,,1
LDVS,105,,1
LDVS,116,,1
LDVS,118,,1
/COM, SKIN LENGTH HAS 4 DIVISIONS
LDVS,41,,4
LDVS,43,,4
LDVS,55, ,4
LDVS,67,,4
L(I)VS 38 ,4
LDVS,40,,4
LDVS,53,,4
LDVS,65,,4
/COM,MESH FOAM SURFACE
ARSEL,,1,19,6
ARASEL,,15
AATT 2 ,:
AMESH,ALL
/COM,MESH SKIN
ARSEL,,25,43,6
AATT,2,,2
AMESH,ALL
/COM,MESH SKIN
ARSEL,,28,33,5
ARASEL,,39,45,6
AATT,1,,2
AMESH,ALL
INSIDE SURFACE
OUTSIDE SURFACE
68
i
I
/cjo'M, MESH AVMODULE INSIDE SURFACE
ARSEL,,30,50,20
ARASEL,,49,56,7
AR^SEL,,62
AA/T,2, ,2
AMESH,ALL
,/cbM MESH AVMODULE OUTSIDE SURFACE
ARSEL,,36,52,16
AR!ASEL ,,55,61,6
AR^SEL,,67
AAjTT,3,,2
AMESH,ALL .
/COM,MESH DOME VOLUME
VLSEL,,1,5
MAT,2
TYffE.l
V'MESH, ALL
/COM,MESH SKIN VOLUME
VLSEL, ,,6,9
MAT, 1
V'MESH, ALL
/COM,MESH AVMODEL VOLUME
VLSEL,,10,14
MAT, 3
V'MESH, ALL
/COM,MESH INSULATOR RING VOLUME
VLSEL,,15,18
MAT, 4
VMESH,ALL
***ESEL,STIF,57
***;NELEM
***EWRITE
***NWRITE
* ^FINISH
I
69
I
j
edit/tpu avbndcon.dat;2
/com,run after meshmodel and Radiation Shape Factor Solution
/p[rep7
resume
eti, 3,50,1
type, 3
e,jl,8
EA'LL
NALL.
n ,2000,200,200,200
wsjort, z
tubif,500
/COM, START OF BOUNDRY CONDITIONS *************************:
nt',2000 temp 5
/corn, select dome inside surface
arsel,,2
arase 1,,12
arase.1,,9
arase 1,,18
arkse.1,,24
na'rea, 1
nt!, al 1, temp, 36
/corn, select avionics module volume
vlsel,,10,14
evbl u
nelem
qej.al1,.1616
kternp, 1
v 1 a 11
l
aral 1
Isa 11
kpal 1
eall
nail
i ter ,, 20,20,20
kbc, 1
Krf ,2
euiel,stif,57
i
I
I
70
fcQSTl IHP=
flHSVS 4.4 H
RUG 12 1992
15:25 :15
POST1 STRESS
STEP=1
XTER=28
TEMP
SMH =36
SMX =800.834
XU = 2
vu = 1
zu = 3
DIST =165.725
ZF = 22.5
PRECISE HIDDEN
R =78.491
B =163.472
C =248.454
D =333.435
E =418.417
F =503.398
G =588.38
H =673.361
I =758.343
Hvionics bay Model
N)
*0ST1 IMP =
Avionics bay model
RNSVS 4.4R
RUG19 1992
18:24:08
P0ST1 STRESS
STEP=1
ITER=29
TEMP
SMH =780.914
SMX =800.834
XU = 2
vu = 1
zu = 3
DIST =119.86
ZF = 60
PRECISE HIDDEN
R =782.021
B =784.234
C =786.447
D =788.66
E =790.874
F =793.087
G =795.3
H =797.514
I =799.727
Avionics Bay, Towards Space
>1
CO
RNSYS 4,4fl
OCT 26 1992
8:00:57
POST1 STRESS
STEP=i
ITER=20
TEMP
SMH =788.914
SMX =800.834
XV =2
YV =1
ZV =3
DIST=119.86
ZF =60
PRECISE HIDDEN
R =782.021
B 784.234
C =786.447
D =788.66
E =790.874
F =793.087
6 =795.3
H =797.514
I =799.727
ftvionics bay node!____________
Avionics Bay, Towards Tank
Vj
*0ST1 INP =
asgg
/ ";i
" ^8.. ?>.
_ ______ V
\ \. \n H.
aa \,
\ /mm
NW\kV<>K
M*
x / / "\ w/zC/y
jp
ED8*
flvionics bay model
RNSYS 4.4fl
BUG 19 1992
18:38:44
P0ST1 STRESS
STEP=1
ITER=28
TEMP
SMH =44.194
SMX =780.948
XU = 2
VU = 1
ZU = 3
DIST =162.056
ZF = 37.5
PRECISE HIDDEN
n =85.125
B =166.987
C =248.848
D =330.71
E =412.571
F =494.432
G =576.294
H =658.155
I =740.017
Vehicle Skin / Structure
>>l
tn
*0ST1 IHP=
lx ^
RUG 19 1992 18:41:44 POST1 STRESS
STEP = 1
ITER TEMP = 20
"x; \ SMH = 36
/ J>\ SMX =44.196
 \ XU = 2
XX\ YU = 1
ZU = 3
\ \\ \ DIST =156.552
\ ZF = 15
 PRECISE HIDDI
t 1 R =36.455
l( i B =37.366
Li* ,lJ 1 C =38.277
1 / D =39.187
FI E =48.098
  I1 I F =41.008
/ G =41.919
H =42.83
\ JF ///' w I =43.74
Avionics bay model
RNSYS 4.4fl
Low Conductance Structure
">4
O)
HNSVS 4.4H
HUG 19 1992
18:38:45
POST1 STRESS
STEP=1
ITER=28
TEMP
SMN =36
SMX =44.196
XU =2
VU =1
ZU =3
DIST = 119.86
ZF =15
PRECISE HIDDEN
fi =36.455
B =37.366
C =38.277
D =39.187
E =40.098
F =41.088
G =41.919
H =42.83
I =43.74
Tank Dome, Towards Avionics Bay
PRRFQR
pr!int REACTION FORCES PER NODE
***** POST1 REACTION FORCE LISTING *****
!=steS.ooooJe+55erati28Id cAÂ§g= 8!CT10N' 1
THE FOLLOWING X,Y,Z FORCES ARE IN GLOBAL COORDINATES
Units are Btu/Hr
77
References
1 ! Holman, J.P., Heat Transfer. Fourth Edition, McGraw Hill
1 (1976)
2 j Martin Marietta Corp., "Thermal Control Design Manual"
I (8 July 1966)
3
Jacox, Michael G., Bennett, Ralph G. "Small ExCore Heat Pipe
Thermionic Reactor Concept" INEL (inhouse. report)
4 ! Martin Marietta Report, "SLC Final Report," Submitted to
j Idaho National Laboratory (July 1991) I
I
i
I
l
l
78
