texas tech - texas space grant consortium
Post on 09-Feb-2022
1 Views
Preview:
TRANSCRIPT
CRYOGENIC FLUID STORAGE FOR THE MISSION TO MARS
TEXAS TECH UNIVERSITY
DEPARTMENT OF MECHANICAL ENGINEERING
Kyle Chambliss
Sarah Kelly
Justin Kimble
Advisor: Dr. Darryl James
April 27, 1999
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
ABSTRACT
In the next thirty years, the National Aeronautics and Space Administration
(NASA) will conduct both manned and unmanned missions to Mars. For these missions,
cryogenic oxygen, hydrogen, and methane storage will be required. The purpose of this
project is to design tanks to store these cryogenic fluids for both the unmanned and
manned missions. The primary objectives of the tank design included minimizing heat
transfer and the weight of the tank system and finding an optimal balance between the
amount of insulation used and the capability of the cryocooler. The tank design included
inner and outer vessel design, insulation and cryocooler selection, inner and outer vessel
stiffening ring design, inner tank suspension design, external support design, and piping
and relief valve selection. The inner vessel of the tank will be constructed from Inconel,
a nickel alloy, and the outer vessel of the tank will be constructed from aluminum. A
combination of multi-layered insulation and vacuum insulation will be used to insulate
the storage vessels. Finally, spherical geometry was selected for the oxygen, hydrogen,
and methane tank designs to minimize the heat transfer and mass of the tanks.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
I. INTRODUCTION
The National Aeronautics and Space Administration (NASA) is currently
coordinating several missions to Mars. Initially, the missions will be unmanned robotic
missions and will serve to send equipment to Mars that will be necessary once the
manned missions begin. The trips to Mars are scheduled to leave every two years
beginning in 2001. The manned missions are scheduled to begin in 2011 and will
continue until 2031. Three of the supplies that will be used during both the unmanned
and manned missions to Mars are liquefied hydrogen, oxygen, and methane. This project
consisted of designing storage tanks and the necessary support systems for these
cryogenic fluids. The objective of this project was to design tanks that could be used to
transfer cryogenic fluids to Mars and store them once on the surface with minimal losses
due to heat transfer.
The two reasons for designing a storage tank system for cryogenic fluids were to
have the capability to produce a combustible fuel once on the surface of Mars and to have
oxygen to use for breathing air once people inhabit the planet. The space vehicles will
most likely be powered by nuclear energy, but as an alternate fuel source for the return
trip to Earth, a combustible fuel such as methane will be available. Methane can be
produced from carbon and hydrogen. Carbon can be obtained from the atmosphere of
Mars, but hydrogen cannot. Therefore, liquid hydrogen will need to be transported from
Earth to Mars. Oxygen can also be obtained from the atmosphere of Mars. Oxygen will
be used both as the oxidizing agent for the propellant fuel for the unmanned and manned
mission return trips to Earth and for breathing air. For the unmanned missions, enough
oxygen will be produced on the surface of Mars to satisfy the oxygen requirements, and
oxygen will not have to be taken to Mars. However, for the manned missions, oxygen
will need to be transported to Mars.
The design of tanks to store cryogenic hydrogen, methane, and oxygen is crucial
for the mission. Without fuel and oxygen, the crew of the missions will not be able to
return to Earth, and the inhabitants on Mars will not be able to breathe. Also, the storage
tanks must be designed to minimize fluid loss through vaporization, minimize heat
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
transfer in order to minimize the weight and volume of the tanks. Loss of fluid could be
disastrous for the mission, and any unnecessary weight drastically increases the cost of
the missions.
II. OBJECTIVES
The primary objective of this project was to design a tank system that could be
used to transport cryogenic fluids to Mars and to store the fluids upon arrival on Mars
while minimizing fluid loss, heat transfer, the volume of the tanks, and the weight of the
tanks. Another objective was to determine a balance between the amount of insulation to
be used and the power requirements of the cryocooler that will further minimize the
weight of the tank system and the amount of heat transfer to the cryogenic fluids.
III. METHODOLOGY
1.0 APPROACH)
This project consisted of both research and detailed design. First, research was
conducted on the climate, atmosphere, and geology of Mars; the behavior of cryogenic
fluids; and existing technology already in use by NASA for similar projects. The project
was then divided into two major portions: the unmanned mission and the manned
mission. As part of the design, insulation for the tanks, the sizing of the tanks, support
systems for the tanks, piping and valves for the tanks, and cryocooler selection were
considered. First, materials were chosen for insulation and the tank structure. Second,
both cylindrical and spherical vessels were examined, and the tank dimensions for each
geometry were determined. Third, the support systems for the tanks and the piping and
valves for the tanks were designed and sized. Finally, the cryocooler selection and the
corresponding insulation thickness were selected. Throughout the project, heat transfer
analyses and thermodynamic analyses were conducted. A cost analysis was also
conducted to determine the most cost-effective design.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Several requirements were outlined by NASA for the design of the cryogenic
fluid storage tanks. First, the amounts of hydrogen, methane, and oxygen to be stored
were mandated for both the unmanned and the manned missions. For the unmanned
mission, 48.2 kg of hydrogen will be taken to Mars and used in the formation of methane.
Once on Mars, 108 kg of methane and 379 kg of oxygen will be produced. For the
manned mission, 4107 kg of hydrogen will be taken to Mars to be used for the production
of methane. Oxygen will also be taken to Mars to be used for breathing air during the
journey to Mars and as for backup oxygen in case the methane and oxygen production
process fails. Once on Mars, methane and more oxygen will be produced. The total
amounts of methane and oxygen required are 8360 kg of methane, 29294 kg of oxygen to
be used for propellant, and 3000 kg of oxygen to be used for breathing. The storage
tanks for both the manned and unmanned missions were designed to accommodate the
corresponding volumes for these masses of fluid. NASA also specified a design safety
factor of two to be used in all designs.
2.0 TIMELINE
This project was completed over two semesters. Initially, the plan was to
complete the design for the unmanned robotic phase of the mission during the first
semester and the design for the manned phase of the mission during the second semester.
This assumption was re-evaluated in November because it became apparent the design
for the unmanned phase would take longer than one semester and the design for the
manned mission less than a semester. The design for the manned mission took less than
one semester since the design process was established during the unmanned mission
portion of the project in the first semester.
Preliminary research of the project was conducted during September. The design
of the tanks, insulation and reliquefaction process began in October and was completed in
early February. Sarah Kelly was responsible for the insulation, support system, and
accessory design, in addition to computer simulation. Kyle Chambliss was responsible
for the actual vessel design for the oxygen, hydrogen, and methane tanks. Finally, Justin
Kimble was responsible for the design of the reliquefaction process and the arrangement
of the tanks, as well as a physical model of one of the tank systems. Heat transfer,
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
thermodynamic, and cost analyses were completed for both the unmanned and manned
missions. Computer simulation was begun, and a physical model of one of the tank
systems was constructed. A detailed schedule of events is shown in Appendix B.
3.0 LOCATION OF WORK
Work was performed at Texas Tech University in the library and the Mechanical
Engineering department under the advisement of Dr. Darryl James.
4.0 BACKGROUND
4.1 Mars :
Research was conducted concerning the atmosphere, geography, geology, and
climate of Mars to design a storage tank system best suited to the environment on Mars.
The atmospheric conditions on Mars are important to the design of the storage vessels in
that the vessels need to be able to withstand the weight of the fluids due to the gravity of
Mars and also the atmospheric pressure of Mars. The average surface gravity on Mars is
3.7 m/s2. Although the atmospheric pressure varies about fifteen percent throughout the
year, the average atmospheric pressure on Mars is 0.61 kPa. Additionally, the
composition of the atmosphere is important in choosing a material for the storage tanks
and also for the carbon and oxygen extraction process from the atmosphere. The
atmospheric composition is demonstrated in the following figure (Kieffer 130).
0
20
40
60
80
100
120
CO2 N2 Ar Trace
Component
Pe
rce
nt
of
Atm
os
ph
eri
c
Co
mp
os
titi
on
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Figure 4.1.1 -- Atmospheric Composition of Mars
The geography of Mars also has an impact on the design of the storage vessels. The
tanks might need to be designed differently if they were to be located in a canyon as
opposed to if they were located on a plain. Also, if the plate tectonics on Mars were
active, the tank systems would need to be designed with possible earthquake activity
taken into consideration. The geography of Mars is extremely diverse. Mars contains
canyons, volcanoes, highlands, and plains. Further, Mars’ plate tectonics are not active.
Geography was assumed to not have an impact on the design of the storage tanks. The
geology of Mars should also be considered when selecting a tank design. For instance,
the material for the tanks should be compatible with the minerals on Mars. The soil of
Mars is predominantly composed of silicon dioxide (SiO2) and iron oxide (Fe2O3)
(Kieffer 31). Additionally, the climate of Mars is of extreme importance when designing
the storage tanks for the cryogenic fluids. The temperature of Mars varies from about
140K to 300K with an average temperature of about 210K. The following figure shows
the maximum and minimum temperatures for a 30 sol (Martian day) period, where Series
1 is the maximum temperature and Series 2 is the minimum temperature (Mars Pathfinder
Weather Data).
050
100150
200250300
0 5 10 15 20 25 30 35 40
Sol
Te
mp
era
ture
(K
)
Series1
Series2
Figure 4.1.2 -- Temperature Distribution for Sols 6 - 35
Mars also has strong winds. The wind speeds vary from 2 m/s to 30 m/s, which is
approximately 70 miles per hour. These winds carry a large amount of dust. The dust
particles consist of sixty percent SiO2, a mineral found in abundance in the soil. The dust
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
particle size ranges from 0.5 microns to 5 microns (um). On Mars, dust is moved by
suspension, saltation, and creep, where suspension occurs when fine dust particles “float”
in the air, saltation occurs when medium sized dust particles are picked up by the wind
and then dropped in a new location, and creep occurs when particles are moved when
other particles collide with them (Mutch 236). Because of the prevalence of dust in the
Martian atmosphere, physical and chemical weathering is a concern. Physical weathering
can occur by either riving, the process by which dust particles seep into abrasions in a
surface and the abrasions propagate into cracks, or by wind abrasion, which is basically
sand blasting of a surface. Chemical weathering can occur by oxidation, which occurs
when a material takes in oxygen to form oxides or higher oxidized silicates, by hydration,
which occurs when water reacts with a material to form hydroxide (OH-) or water ions,
by carbonation, which occurs when carbon dioxide reacts with a material to form
carbonates, and by solution dissolving, which occurs when a material is dissolved in
water (Kieffer 629). However, solution dissolving should not be a problem on Mars
since only trace amounts of water exist on Mars. The atmosphere, geography, geology,
and climate of Mars were considered when designing the cryogenic fluid storage tanks.
4.2 Cryogenics:
When a gas condenses at low temperatures, the gas becomes a liquid called a
cryogenic fluid. A given mass of a cryogenic fluid has a much smaller volume than the
same mass of a gas. The thermodynamic properties of a gas are needed in order to design
cryogenic tanks. Properties such as saturation temperature, saturation pressure, and
density are critical in the design of cryogenic tanks. Tables 4.2.1, 4.2.2, and 4.2.3 list the
cryogenic properties of hydrogen (H2), oxygen (O2), and methane (CH4), respectively.
The data in these tables came from Cryogenic Systems by Randall F. Barron.
Table 4.2.1 -- Thermodynamic Properties of Hydrogen
SaturationTemperature
SaturationPressure
Density
(K) (kPa) (kg/m3)14 7.88 76.8616 21.58 75.1118 48.23 73.2
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
20.27 101.2 70.7922 163.4 68.7224 264.6 66.0126 403.5 62.8328 587.1 58.9730 822.6 53.93
Table 4.2.2 -- Thermodynamic Properties of Oxygen
SaturationTemperature
SaturationPressure
Density
(K) (kPa) (kg/m3)60 0.73 1281.770 6.22 1236.780 30.09 1190.3
90.18 101.3 1141100 254.2 1090.7110 543.2 1035.4120 1021.6 974130 1747.8 902.8140 2786.5 813.1150 4219 675.4
Table 4.2.3 -- Thermodynamic Properties of Methane
SaturationTemperature
SaturationPressure
Density
(K) (kPa) (kg/m3)95 17.67 448.3100 34.5 440.4105 56.6 432.5
111.7 101.3 424.1115 132.5 419.4120 191.9 412.1125 269.3 404.7130 368 396.7135 491.3 388.4140 642.2 379.6150 1041.4 361.1160 1594 339.7170 2331 314.1180 3288.2 280
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
4.3 Hydrogen Tank Requirements:
Hydrogen will be needed to produce methane, CH4, on the surface of Mars. The
Martian atmosphere contains only trace amounts of hydrogen, so any hydrogen needed
must be transported from Earth. For the unmanned mission, 48.2 kg of hydrogen is
needed, and for the manned missions, 4107 kg is needed. The hydrogen tank will be full
from the beginning of the mission until the lander lands on Mars.
When the space shuttle launches, the cargo in the shuttle undergoes three G's of
force. The G forces during the landing must also be taken into consideration in the
design of the hydrogen tank. Also, since the in-flight temperature and Mars surface
temperature will be different, two heat transfer analyses were performed. The density of
cryogenic hydrogen changes by more than thirty percent from 14 to 30K. Cryogenic
fluids at lower temperatures have a greater density and a lower volume than at higher
temperatures. Because the density changes so much over a small temperature range, the
lower the temperature of the fluid, the smaller the volume of the fluid and the smaller the
size of the storage tank. The heat transfer for the cooler fluid is less because the surface
area of the tank is less, even though the temperature difference between ambient
temperature and cryogenic fluid is larger. Figure 4.3.1 is a graph of heat transfer vs.
temperature for a spherical hydrogen tank with 15.25 cm of MLI with 20 layers per inch.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Figure 4.3.1 -- Heat Transfer vs. Temperature for Spherical Hydrogen Tank
During transport, the tank experiences zero gravity. As a result, the gas and fluid will not
be separated but the cryocooler will still cool the liquid.
4.4 Methane Tank Requirements:
0.700
0.750
0.800
0.850
0.900
0.950
1.000
1.050
1.100
14 16 18 20 22 24 26 28 30
Temperature (K)
Heat
Tra
nsfe
r (W
)
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
The methane tank will need to store 108 kg of methane for the unmanned mission and
8366 kg for the manned mission. The methane tank will only store fluid on Mars. The
tank will be empty during the launch from Earth, and the added weight of the fluid during
the launch will not have to be taken into consideration, as in the hydrogen tank. Also,
when the tank contains fluid, the gas and liquid will be well separated due to the gravity
on Mars. The density of methane does not change much with temperature. When the
temperature and pressure of the fluid is in the higher range of cryogenic methane, the
temperature differential between ambient conditions and the fluid temperature is reduced,
and the heat transfer is minimized. Figure 4.4.1 is a graph of heat transfer vs.
temperature for a cryogenic methane tank.
Figure 4.4.1 -- Heat Transfer vs. Temperature for Spherical Methane Tank
4.5 Oxygen Tank Requirements:
0.500
0.550
0.600
0.650
0.700
0.750
0.800
0.850
0.900
80 90 100 110 120 130 140 150 160 170 180
Temperature (K)
Heat
Tra
nsfe
r (W
)
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
The oxygen tank design has the same requirements as the methane tank design
except for the mass of the fluid. For the unmanned mission, 379 kg of oxygen will be
needed. For the manned mission two tanks are required, one for breathing and one for
propellant. 3000 kg of breathing oxygen are required, and 29294 kg of propellant oxygen
are required.
4.6 Existing Technology:
Hydrogen is the only fluid that will be transported to Mars. The carbon dioxide
prevalent in the Martian atmosphere will be used to produce the required oxygen and
methane. The process to be employed is called the Sabatier process, named after the
Nobel prize winning chemist Paul Sabatier. The process combines carbon dioxide with
hydrogen to produce methane and water. The methane is stored, and the water is
electrolyzed to separate into hydrogen and oxygen. The hydrogen is reused in the
process and the oxygen is stored. The stored methane and oxygen are then used as a
propellant for the ascent vehicle. The chemical equation for the process is:
OHCHHCO 2422 24 +♦+ Eq. 4.6.1
Many companies produce cryocoolers, but not very many of them produce cryocoolers
for space applications. Currently, no cryocoolers are on the market that have the capacity
to cool, in a space environment, the amounts of fluids necessary for this project. One
possibility, however, is a cryocooler that has been developed at the National Institute of
Science and Technology. This cooler might be applicable, but in the event that it is not, a
cooler which meets the requirements of the tank design would need to be designed as
well.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
5.0 DESIGN THEORY OF STORAGE TANKS
5.1 Insulation:
Because the hydrogen, oxygen, and methane must be kept at cryogenic
temperatures to minimize the volume and weight of their storage tanks and because the
amount of heat transfer to the cryogenic fluids should be minimized, the storage tanks
will be well insulated with a weight efficient insulation minimizing heat transfer. The
storage vessels will consist of an inner vessel containing the cryogenic fluid, a layer of
insulation, and an outer vessel.
5.1.1 Material:
The insulation for the storage tanks will consist of two parts: multi-layer
insulation and vacuum insulation. Multi-layer insulations (MLI) consist of alternating
layers of a highly reflective material, such as aluminum or mylar, and a low conductivity
spacer material, such as paper or fibrous netting. The MLI prevents radiative heat
transfer, due to the highly reflective material, and conductive heat transfer, due to the
spacer material. MLI was selected as the insulation for the storage tanks because it has
the best performance (lowest thermal conductivity) of all other insulations, including
expanded foams, gas filled powders, evacuated powders, and opacified powders. The
following table shows the thermal conductivity (k) for each of the aforementioned
insulations (Barron).
Table 5.1.1.1 -- Thermal Conductivity of Several Insulation Types
Insulation k (W/mK)
Expanded Foam 0.026
Gas Filled Powders 0.019
Evacuated Powder 0.00059
Opacified Powders 0.00033
Multilayer Insulation 0.000014
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Multi-layer insulation is also low in weight but is high in cost. However, since
minimizing the weight of the storage tanks is a primary objective of this project, MLI was
chosen because of its relatively low weight in comparison to other insulations. Multi-
layer insulation having a 0.0087 mm aluminum foil layer and a 0.2 mm glass fiber paper
layer will be used to insulate the storage tanks.
Vacuum insulation will also be used. The entire region between the inner and
outer vessels of the tank will be evacuated. The MLI will not completely fill the
evacuated region; a small distance of evacuated space alone will be located between the
MLI and the outer vessel of the storage tank. This distance of evacuated space alone will
prevent conduction from the MLI to the outer shell of the vessel. A distance of 0.5 cm
will be used for each storage vessel. Vacuum insulation prevents heat transfer through
solid conduction and through gaseous convection. Further, the use of vacuum insulation
is needed to make the use of MLI effective because MLI must be evacuated to pressures
below 10mPa for MLI to be effective (Barron 396).
5.1.2 Multi-Layer Insulation:
As stated previously, multi-layer insulation prevents radiative heat transfer and
conductive heat transfer. The following equation is the Lockheed correlation for heat
loss due to radiation through MLI for any tank geometry.
q
A
SF C N T T T C T T
Nr mli c m h c r h c
s
,. . .[ * ( ) * ( )]
=− + −256 4 67 4 67ε
Eq. 5.1.2.1
where
qr,mli = radiative heat loss
A = tank surface area
SF = scale factor, accounts for non-ideal behavior
Cc = conduction coefficient
Cr = radiation coefficient
N = layers of MLI per cm
Ns = total number of layers of MLI
Th = external temperature
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Tc = temperature of cryogenic fluid
Tm = mean temperature between external and cryogenic fluid temperatures
ε = layer to layer emissivity
The numbers of layers of MLI per cm (N) and the total number of layers of MLI (Ns) can
be varied to obtain the optimum amount of MLI to be used. The following figure
demonstrates the variance in heat loss as the layers of MLI per centimeter increases.
0
10
20
30
40
50
60
7.87 9.84 11.81 13.78 15.75 17.72 19.69
Layers of MLI per cm
Heat
Lo
ss
(kJ/h
r-m
^2)
Figure 5.1.2.1 : Heat Loss vs. Layers of MLI per cm
As the number of layers of MLI per cm of MLI increases, the corresponding heat loss
increases also. The following figure shows the variance of heat loss as the total number
of layers of MLI increases.
0
10
20
30
40
12.5 25 37.5 50 62.5 75
Total Layers of MLI
He
at
Lo
ss
(k
J/h
r/m
^2
)
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Figure 5.1.2.2: Heat Loss vs. Total Number of Layers of MLI
As the total number of layers of MLI increases, heat loss decreases. As can be
determined from the previous two figures, a small number of layers of MLI per cm
should be used, and a large number of total number of layers of MLI, or thickness of
MLI, should be used to minimize the heat loss.
The conductive heat transfer for the insulation for a cylindrical vessel can be
determined by modeling the tank as a series of thermal resistances. The conductive heat
loss can then be given by the following equation.
LrhLk
rr
Lrh
TTq io
mlic
πππ 22
12
11
,
2
1
2
)/ln(
2
1 ++
−= Eq. 5.1.2.2
where
qc,mli = conductive heat loss in MLI
To = external temperature
Ti = cryogenic fluid temperature
h1 = internal convection coefficient
r1 = inner vessel radius
L = length of cylinder
r2 = outer vessel radius
k = thermal conductivity of MLI
h2 = external convection coefficient
The conductive heat transfer for the insulation for a spherical vessel can be
determined by modeling the tank as a series of thermal resistances. The spherical vessel
was approximated as a flat plate since the radius of curvature of the sphere was so large.
The conductive heat transfer for the spherical vessel was determined using the following
equation.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
AhAk
L
Ah
TTq io
mlic
22
2
1
, 11 ++
−= Eq. 5.1.2.3
where
A = area of heat transfer
L2 = insulation thickness
k2 = thermal conductivity of insulation
The convection through the MLI is minimal and can be neglected in the analysis. The
resultant heat transfer through the MLI is the sum of the conductive and radiant heat
transfer.
5.1.3 Vacuum Insulation:
Again, as stated previously, the vacuum insulation works as a barrier against solid
conduction and gaseous convection. However, some radiant and gaseous conduction heat
transfer does occur through the insulation. The radiant heat transfer for vacuum
insulation is given in the following equation (Barron 386).
)( 44112, ioevr TTAFFq −= σ Eq. 5.1.3.1
where
qr,v = radiant heat transfer in vacuum
Fe = emissivity factor
F12 = configuration factor = 1
σ = Stefan Boltzmann constant = 5.67x10-8 W/m2K4
A1 = surface area of inner vessel
F12 equals one because the inner vessel is completely enclosed by the outer vessel. The
emissivity factor, Fe, is determined by the number of radiation shields within the vacuum.
As the number of radiation shields increase, emissivity decreases. Smaller emissivity
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
values result in smaller amounts of radiant heat transfer. The formulation for the
emissivity factor can be found in Appendix A.
Because an air space cannot be completely evacuated, heat can be transferred
through the residual gas in the vacuum region by gaseous conduction, or free molecular
conduction. Free molecular conduction is defined by the mean free path of the gas
molecules within the vacuum where the mean free path of a molecule is the distance that
a molecule must have in order to avoid collision with another molecule. For free
molecular conduction to occur, the mean free path of the gas molecules must be larger
than the thickness of the evacuated region. Gaseous conduction can be given by the
following equation (Barron 389).
q GpA T Tg v o i,( )= −1 Eq. 5.1.3.2
where
qg,v = gaseous conduction in vacuum
G = function of temperature, accommodation coefficient factor, gas constant,
specific heat ratio
p = pressure in evacuated region
The derivation of this expression can be found in Appendix A. The total heat transfer for
the vacuum insulation is the sum of the gaseous conduction and radiant heat transfer.
5.1.4 Insulation System:
The total amount of heat transfer occurring in the MLI and vacuum insulation
system is the sum of the heat transfer accrued in each insulation section.
q q q q qtot r mli c mli r v g v= + + +, , , , Eq. 5.1.4.1
5.2 Inner and Outer Vessel Design:
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
5.2.1 Materials:
The inner and outer vessels of the storage tanks will be constructed from Inconel,
a ductile nickel alloy. The piping used to drain the vessel will also constructed of
Inconel. Inconel has many properties that make it suitable for use on the Martian surface.
First, Inconel forms a thin, protective layer when subjected to oxidizing conditions, thus
making it suitable for chemical weathering conditions on Mars (Mantell). Heavily cold
worked Inconel is very corrosion resistant. Further, Inconel has a high modulus of
elasticity, improving its resistance to stress, and a low coefficient of expansion. Inconel
also has a large ultimate strength value at low temperatures. Some of the mechanical
properties of Inconel are included in the table below (Mantell).
Table 5.2.1.1 -- Properties of Inconel
Property Value unit
Density 8415 kg/m 3
Modulus of Elasticity (E) 213.7 GPaModulus of Rigidity (G) 75.85 GPa
Yield Strength (S y ) 292 MPa
Ultimate Strength (S ut) 1250 MPa
Inconel will also be used to construct the inner and outer vessel support rings and the
inner support rod brackets discussed in detail later in this report. The piping used to drain
the vessel will also constructed of Inconel.
The outer shells of the storage vessels will be constructed from Aluminum.
Although aluminum is not as strong as Inconel, aluminum weighs much less. Because
the outer shells of the storage vessels are so large and because the minimization of the
weight of the storage vessels was the primary goal for this project, aluminum was
selected for the design of the outer shells. Aluminum has a very high specific strength, or
strength to weight ratio. Aluminum also has excellent resistance to oxidation and
corrosion. When subjected to oxidation conditions, a thin aluminum oxide layer will
form on the aluminum, thus protecting it from corrosion. Additionally, aluminum can be
treated with a variety of coatings to further prevent corrosion and wear. Aluminum has a
high reflectivity, making it an ideal material for the outer shell of the storage vessels.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
The high reflectivity of aluminum will help prevent radiation heat transfer to the
cryogenic fluids stored. Some of the mechanical properties of aluminum are provided in
the table below.
Table 5.2.1.2 -- Properties of Aluminum
Property Value unitDensity 2800 kg/m3
Modulus of Elasticity (E) 71.7 GPa Modulus of Rigidity (G) 26.8 GPa
Yield Strength (S y) 169 MPa
Ultimate Strength (S ut) 324 MPa
Furthermore, because two different materials will be used in the storage vessel
designs, galvanic corrosion was considered. Galvanic corrosion occurs when two metals
with vastly different oxidation potentials are in contact with one another. If two metals
with different oxidation potentials are placed in an electrolytic medium, a galvanic cell is
produced. Current is driven from one metal to the other through the electrolytic medium.
As a result, if the difference between oxidation potentials is large, corrosion will occur.
The material with the higher oxidation potential is called the anode, and this material will
be the one to corrode. The material with the lower oxidation potential is called the
cathode, and this material will not corrode. Protective coatings such as oxides or various
platings can be placed on the metals to prevent galvanic corrosion. However, aluminum
and Inconel are not significantly far apart in the Galvanic series, so galvanic corrosion
should not be a problem. A thermal expansion analysis was also performed. With a
special piping design discussed later, thermal expansion will not be a problem.
Fiberglass will be used to construct the inner support rods and the external
support system described later in this report. Fiberglass using kevlar fibers was selected
because of its low weight, high strength, and low thermal conductivity. Kevlar fiberglass
has an ultimate strength of 4.58 GPa and a thermal conductivity of 0.26 W/m2K
(Incropera).
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
The aluminum outer tank will be coated with an anodic coating. Anodizing the
aluminum will protect the tank from corrosion. Both the outer tank and the external
supports will be coated with a highly reflective material to further decrease radiant heat
transfer. In this design, highly polished gold film with an emissivity of 0.01 to 0.03 will
be used (Incropera 851). Weathering could damage the gold film. If this happens the
anodic coating will protect the aluminum tank from further weathering.
5.2.2 Volume:
The tank volume was determined using the density of the cryogenic fluid and the
mass of the fluid needed. The volume was calculated using Equation 5.2.2.1 where ρ is
density and m is mass.
ρm
V = Eq. 5.2.2.1
Since density changes as a function of temperature, volume is also a function of
temperature. For this reason, volume must be calculated for every temperature. A ten
percent ullage, or extra volume, factor was used in the tank designs.
5.2.3 Inner Vessel:
The inner vessel of the storage system stores the cryogenic fluid. For a spherical
vessel, the internal radius (rip) can be found using Equation 5.2.3.1.
3
4
3
πV
rip = Eq. 5.2.3.1
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
The inner vessel must be thick enough to withstand the pressure of the fluid within the
vessel. From the ASME Boiler Code, Section VIII, the shell thickness for a spherical
pressure vessel is given in Equation 5.2.3.2.
peS
pDt
wtup 4.0−
= Eq. 5.2.3.2
where
p = internal pressure
D = internal vessel diameter
Sut = ultimate strength of material
we = weld efficiency = 1
Once the thickness of the inner shell was determined, the mass of the shell was
calculated. The outer radius is the sum of the inner radius and the inner vessel thickness
calculated previously. The mass of the inner tank was determined using Equation 5.2.3.3.
( )33
3
4iomm rrm −= πρ Eq. 5.2.3.3
5.2.4 Outer Vessel:
The outer vessel of a cryogenic tank contains the inner vessel and the MLI
vacuum insulation. The inner radius of the outer tank, ris, was calculated using Equation
5.2.4.1, where ψ is the thickness of the MLI and ipr is the inner radius of the inner tank
and pt is the thickness of the inner pressure vessel.
ψ++= pipis trr Eq. 5.2.4.1
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
When designing the outer vessel of the storage tank, the external pressure is of great
importance. The external pressure could cause the vessel to collapse. The external
pressure acting on the storage tank is atmospheric pressure. From the ASME Code,
Section VIII, the thickness of the exterior spherical tank is given by Equation 5.2.4.2,
where υ is Poisson's Ratio and E is Young's Modulus.
( )[ ]
1
2
12
113
5.0−
���
�
�
���
�
�−
−=
υp
Ert iss Eq. 5.2.4.2
For a cylinder, the external shell thickness is given by Equation 5.2.4.3.
( )irE
pt 222
11
3
12
−−
���
�
�
���
�
�+√√↵
����
−= υEq. 5.2.4.3
To calculate the mass of the external tanks, equations from Section 5.2.3 were used.
Stiffening rings were added to provide additional support to the external vessel, and as a
result, the thickness of the shell was reduced. The formula for the maximum critical
pressure on the outside of the exterior tank with stiffening rings is given by Equation
5.2.4.4, where L is the distance between stiffening rings, and cp , the critical pressure, is
four times the allowable pressure.
( )
( ) ( )���
�
�
���
�
�
√√↵
����
+
−+
−
√√↵
����
+
=2
1
4
32
2
5
245.0
(21
242.2
tr
t
tr
L
tr
tE
p
ii
ic
υ
Eq. 5.2.4.4
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
The critical pressure must be greater than the atmospheric pressure to prevent the tanks
from collapsing. The size of the intermediate stiffening rings can be calculated from the
moment of inertia, 1I , given in Equation 5.2.4.5.
E
LDpI oc
24
3
1 = Eq. 5.2.4.5
When calculating the mass of the exterior tank and stiffening rings, the mass of the
stiffening rings needs to be added to the mass of the tank.
5.2.5 Support Systems:
The design of the storage vessels also includes various support systems. The
support systems consist of stiffening rings for the inner vessel, stiffening rings for the
outer vessel, a suspension system for the internal vessel, and an external support
mechanism. The inner vessel stiffening rings support the weight of the fluid within the
inner vessel. The stiffening rings will be formed from beams of Inconel, and the size of
the stiffening ring was determined by calculating the section modulus of the beam. The
minimum allowable section modulus was determined from the following equation
(Barron 361).
as
MZ max
min = Eq. 5.2.5.1
where
Z = section modulus
Mmax = maximum bending moment
sa = allowable stress
The maximum bending moment was derived from Roark’s elastic energy method and is
shown in Appendix A. Once the minimum allowable section modulus of the stiffening
rings was determined, the beams from which the rings will be constructed were sized to
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
have a greater section modulus than the minimum allowable value in order to be able to
support the maximum loading conditions.
The outer vessel stiffening rings support the weight of the inner vessel, the weight
of the insulation, and any external pressure and help maintain the shape of the outer
vessel. For short vessels, only two stiffening rings are used. For long vessels, two main
stiffening rings are used to support the weight of the vessel, and additional intermediate
rings are used to maintain the shape of the vessel. The outer vessel stiffening rings will
be formed from beams of Inconel also. The size of the stiffening rings was determined
from the area moment of inertia of the beams. The area moment of inertia used to
determine the size of the intermediate stiffening rings was determined from the following
equation (Barron 367).
Ip D L
Ec o
1
3
24= Eq. 5.2.5.2
where
I1 = area moment of inertia
pc = critical pressure (four times allowable pressure)
Do = outside diameter of outer shell
L = distance between stiffening rings
E = modulus of elasticity of ring material
The minimum allowable area moment of inertia (Imin) used to size the main support rings
is shown in the following expression (Barron 368).
as
cMII max
1min += Eq. 5.2.5.3
where
c = distance to the centroid of the tank geometry
The derivation for the calculation for the bending moment of inertia, Mmax, is shown in
Appendix A. Once the minimum allowable area moments of inertia were calculated, the
beams from which the stiffening rings will be constructed were sized to have a larger
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
moment of inertia than the minimum allowable value in order withstand maximum
loading equations.
The suspension system for the internal vessel suspends the internal vessel within
the outer vessel and must support the weight of the inner vessel and any loads that are
caused during transportation. The suspension system consists of support rods that
suspend the inner vessel within the outer vessel and brackets that will attach the rods to
the inner and outer vessel walls. A cross-section of a storage tank showing the
suspension system is pictured in the figure below.
Figure 5.2.5.1 -- Storage Vessel Suspension System
During transportation to Mars, the storage tank will be subjected to dynamic loads
including vertical, transverse, and longitudinal loads. The diameter and the number of
rods were selected on the basis of the maximum load in each direction, vertical,
transverse, and longitudinal. The number of rods (N) for each direction was determined
from the equation below (Barron 377).
NF
Fd
= Eq. 5.2.5.4
where
F = maximum force in each given direction (vertical, transverse, or longitudinal)
Fd = design force in each rod
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
The equations used to determine the dynamic loads in each direction and the design force
in each rod are shown in Appendix A. Additionally, brackets to attach the rods to the
inner and outer vessel walls were designed. The bracket is shown in the following figure.
Figure 5.2.5.2 -- Bracket Design
The brackets will be welded to the vessel walls with fillet welds. As a result, the bracket
design depended on the size of the area where the weld would be formed. The weld will
be subjected to mostly shear stresses, and accordingly, will fail in shear. The bracket was
sized using the American Welding Society expression for maximum shear. The
maximum shear (τmax) occurring in a weld is given in the following equation (Shigley
387).
bt
F
2
414.1max =τ Eq. 5.2.5.5
where
F = maximum vertical force
b = weld width
t = weld thickness
The maximum vertical force used was the maximum vertical force calculated in the
dynamic loadings used to size the support rods. The weld width and thickness are also
the width and thickness of the bracket. The length of the bracket was chosen to be
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
slightly larger than the diameter of the hole through which the support rod will be
positioned.
The external support serves as a base on which the tanks can be placed. The
external support will also help minimize heat transfer from the storage tank to the ground,
both in transit and on Mars. The external support will be constructed from fiberglass as
mentioned previously and will consist of two cradles on which the storage tank will rest.
A sketch of the external support is shown in the following figure.
Figure 5.2.5.3 -- External Support Structure
The external support was modeled as a simply supported beam with a distributed loading
and two end supports. The simply supported beam approximation can be seen in the
figure below.
Figure 5.2.5.4 -- Simply Supported Beam Approximation
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
As in a simply supported beam, the external support will deflect due to the weight of the
storage tanks. The deflection of the support structure can be determined from the
following expression (Norton 1003).
ywx Lx x L
EI=
− −( )224
2 3 3
Eq. 5.2.5.6
where
y = deflection
w = distributed load
x = any given location on beam
L = length of beam
The legs of the support structure were also designed so they would not buckle. The legs
were approximated as short Euler columns. The determining factor in the design of the
support legs was the critical pressure acting on the legs. The expression used to
determine the critical pressure (Pcr) in the legs is provided below (Norton 239).
PEI
Lcr =π 2
2 Eq. 5.2.5.7
where
L = length of leg
The critical pressure was then used to determine the allowable force (Fall) acting on each
leg, shown in the following equation.
FP
NAallcr= Eq. 5.2.5.8
where
N = safety factor
A = cross-sectional area of the leg
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
The dimensions of the leg were chosen so that the actual force acting in each leg was
less than the allowable force in each leg. The actual force acting in each leg is the
distributed loading, w, multiplied by the distance to the centroid of the leg. Furthermore,
the external supports must be able to support the weight of the storage tanks while being
of minimal weight themselves. For this reason, sections of material from the support will
be removed to reduce the weight of the support. When removing sections from the
support, the support must still be able to withstand the weight of the storage tank. When
a section is removed from the support structure, a stress concentration in the area of
removal results. Stress concentrations increase the stress occurring in a particular region
by a factor Kt. This relationship is shown in the following equation (Norton 231).
σ σmax = Kt nom Eq. 5.2.5.9
where
σmax = maximum stress
Kt = stress concentration factor
σnom = nominal stress (stress occurring in region without stress concentration)
The removed sections were designed so the external support would still withstand the
weight of the storage tank and so the stress concentration resulting from the removed
sections was still below the allowable stress in the support. However, since fiberglass is
a ductile material, any stress concentrations could be ignored. Stress concentrations can
be neglected in ductile materials because ductile materials yield at a point and the
material will not fail until the entire cross section of the material yields (Norton 232).
The external support system does not need to account for any wind drag effects on Mars.
Although high wind speeds occur frequently on the surface of Mars, since the atmosphere
has such a low density, the maximum wind speeds on Mars will not significantly affect
the tank structures.
5.2.6 Piping and Valves:
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
The design of the storage tanks for the cryogenic hydrogen, methane, and oxygen
must also include piping from which the vessels can be drained and a safety relief valve.
The length of piping inside the vessel will be as long as is reasonably possible to
minimize heat transfer. Thin-walled piping should also be used to minimize heat transfer
because it has a smaller cross-sectional area. The piping will be enclosed by a vacuum
region into the fluid in the inner vessel as shown in number 1 in Figure 5.2.6.1. The
vertical part of the piping should be as long as possible to act as a spring to keep the
stresses developed from thermal expansion from damaging the piping.
Figure 5.2.6.1 -- Various Piping Designs
The minimum wall thickness was determined from the ASA Code for Pressure Piping in
the following expression (Barron 379).
tpD
s po
a
=+2 8.
Eq. 5.2.6.1
where
t = thickness of the pipe
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
p = internal pressure
Do = outside diameter of pipe
sa = allowable stress of pipe material
Once the minimum pipe wall thickness was found, standard steel pipe data tables such as
the table included in Crane’s Flow of Fluids Through Valves, Fittings, and Pipe were
used to determine the pipe size and schedule.
The thickness of the vacuum jacket around the piping is found from the following
equation.
( )irE
pt 222
11
3
12
−−
���
�
�
���
�
�+√√↵
����
−= υ Eq. 5.2.6.2
where
t = thickness of the pipe
p = external pressure
ri = internal radius
The safety relief valve is a device that prevents the pressure within the storage
vessel from exceeding its design pressure. If the pressure within the vessel were to
surpass the design pressure, the safety relief valve would release the extra pressure before
the vessel was damaged. Safety relief valves are sized based on the discharge area of the
valve. The area of the discharge valve for the safety relief valve was found using the
ASME code in the following equation (Barron 383).
Am R T g M
CK pv
g u c
D
=& ( / )
max
Eq. 5.2.6.3
where
Av = discharge area of valve
mg = maximum mass flow rate through valve
Ru = universal gas constant
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
T = temperature of cryogenic fluid at inlet to valve
M = molecular weight of cryogenic fluid
gc = gravitational constant
KD = discharge coefficient
pmax = 1.1 x fluid pressure + atmospheric pressure
C = constant dependent on the specific heat ratio of the cryogenic fluid
5.2.7 Temperature Sensors:
In order to reduce the amount of time the cryocoolers will run, temperature
sensors will be used. The temperature sensors will be used with each individual tank to
measure the temperature of the fluid within the storage vessel. When the temperature
sensor indicates a temperature equal to the design temperature for the given cryogenic
storage vessel, the cryocooler will turn on and cool the fluid until the fluid is several
degrees below the design temperature for that particular tank. Although the loads that the
cryocoolers will have to withstand will most likely cause the cryocoolers to run
continuously, the temperature sensors will still be in place in the event the cryogenic
fluids become cool enough to enable the cryocoolers to cease running. Thus, the
temperature sensors will be utilized to help conserve power.
Temperature can be measured in a variety of ways. The temperature of a
substance can be determined by measuring the height of mercury in a capillary tube, the
electrical resistance of a platinum wire, the pressure of an ideal or near-ideal gas, the
equilibrium pressure of a gas above a boiling liquid, the difference in thermal expansion
of two metals in a composite beam, the speed of sound in a gas, and the magnetic
susceptibility of a paramagnetic material (Barron 310). When measuring temperature,
properties of the measuring instrument must be taken into consideration. The properties
of a temperature measuring device include accuracy, the deviation of the indicated
temperature from the temperature scale; sensitivity, the rate of change of the temperature
indicating property with temperature; reproducibility, the range of temperature when
several measurements were made at the same temperature; and stability, the change in the
indication of the device over a period of time.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Some commonly used temperature measuring devices employing these methods
are metallic resistance thermometers, semiconductor resistance thermometers, and
thermocouples. Metallic resistance thermometers indicate temperature by measuring the
variance of electrical resistivity of a metal with temperature. Platinum, copper, lead, and
other metals whose resistivities vary linearly with temperature are commonly used in
metallic resistance thermometers. Metallic resistance thermometers are calibrate using
( )R
RAt Bt Ct te
o
= + + + −1 1002 3 Eq. 5.2.7.1
where
Re = measured resistance
Ro = resistance at 0 °C
A, B, C = constants found by calibration at three standard temperatures
t = temperature (°C)
The sensitivity of a metallic resistance thermometer is the rate of change of resistivity
with temperature. The sensitivity, So, of a metallic resistance thermometer is
( )[ ]SdR
dTR A Bt Ct to
eo= = + + −2 4 3002 Eq. 5.2.7.2
Another commonly used type of temperature measuring device is a semiconductor
resistance thermometer. Semiconductor resistance thermometers use the same principle
as metallic resistance thermometers, except the resistivity of a semiconductor is measured
instead of the resistivity of a metal. Semiconductor resistance thermometers can be
calibrated by
( )TB R
R A R K
e
e e
=+ +
log
log log10
10
2
10
Eq. 5.2.7.3
where
T = temperature
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
A, B, K = calibration constants
A third type of commonly used measuring device is the thermocouple. A thermocouple
consists of a pair of dissimilar metals connected at two junctions. One junction of the
thermocouple is placed where the temperature is to be measured, and the other junction is
placed at a reference temperature location, such as an ice bath. The temperature
indication of a thermocouple is determined by measuring the electromotive force induced
in the thermocouple. Thermocouples are calibrated using
t b e b e b e b e= + + +1 22 3
44
3 Eq. 5.2.7.4
where
e = electromotive force
Metallic and semiconductor resistance thermometers are extremely effective for
measuring cryogenic temperatures while thermocouples are only moderately effective.
Many resistance thermometers appropriate for use with cryogenic temperatures are
available from many different companies.
5.2.8 Tank Connections:
A variety of connections can be used in conjunction with cryogenic tanks and
piping. Several available connectors include bayonet connections, threaded connections,
and field joint couplings. Bayonet connections are connections between two sections of
pipe that do not require welding. Bayonet connections consist of telescoping male and
female parts. The male part is inserted into the female part, and the two sections are then
clamped together. Bayonet connections have a low heat inleak and are ideal for
cryogenic applications. A bayonet connection is shown in Figure 5.2.8.1.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Figure 5.2.8.1 -- Bayonet Connection
Threaded connections are simply connections made by screwing two threaded parts
together. Threaded connections do not have as low of a heat inleak as bayonet
connections, and are not as well suited for cryogenic applications as bayonet connections.
A final type of connection is the field joint coupling. Field joint couplings are vacuum
insulated connections between two sections of pipe. However, field joint couplings
require field welding. Once the weld is made, the joint is then insulated, and the coupling
is put into place and evacuated to vacuum pressures. This type of coupling usually
requires an experienced field crew. Field joint couplings also have a low heat inleak and
are ideal for use with cryogenic fluids.
5.3 Heat Transfer Analysis:
Cryogenic fluids must be stored below the saturation temperature for the
corresponding vessel pressure. If the fluid were to reach a temperature greater than the
saturation temperature at a certain pressure, the fluid would vaporize and the tank
pressure would increase, possibly causing the tank to explode. Because of this, heat
transfer analysis is crucial in the design of cryogenic tanks. Heat transfer must be held to
a minimum. If the heat transfer through the tank were greater than the amount of energy
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
removed by the cryocooler, the fluid would eventually turn to a gas. Also, as heat
transfer through the tank decreases, the energy required to cool the liquid decreases.
Figure 5.3.1 is a sketch of the cryogenic tank wall.
Figure 5.3.1 -- Cryogenic Tank Wall
Figure 5.3.2 is a schematic of the heat transfer resistances of a cryogenic tank wall.
Figure 5.3.2 -- Heat Transfer Schematic of Cryogenic Tanks
The heat transfer through the MLI is given in section 5.1.2. Heat transfer through the
tank walls is also shown in section 5.1.2, as well as heat transfer through the vacuum
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
insulation. The heat transfer from the atmosphere to the outer surface is given in
Equation 5.3.1, where h is the convection coefficient.
( ) ( )44sss TTFTTh
A
q −+−= ××−× σ Eq. 5.3.1
5.4 Design Results:
5.4.1 Tank Designs:
The results of the calculations for the volume, inner tank, and outer tank designs
are given in table 5.4.1. The values were calculated using formulas from sections 5.2.2,
5.2.3, and 5.2.4.
Table 5.4.1 -- Design results of inner and outer tanks
O2
Unmanned
Propellant
CH3
Unmanned
H2
Unmanned
O2
Manned
Propellant
O2
Manned
Breathing
CH3
Manned
H2
Manned
Fluid Mass
(kg)
379 108 48.2 29294 3000 8366 4107
Design Temp.
(K)
90.18 111.7 14 90.18 90.18 111.7 14
Volume
(m3)
0.332 0.263 0.681 25.67 2.63 19.73 58.02
Inner Tank rI
(m)
0.90 0.94 1.10 3.66 1.71 3.35 4.67
Inner Tank t
(m)
0.0008 0.0032 0.0021 0.0007 0.0003 0.0006 0.0002
Inner Tank Mass
(kg)
9 24 22 122 12 86 41
Outer Tank rI
(m)
0.96 0.99 1.27 3.76 1.75 3.44 4.84
Outer Tank t 0.0015 0.0015 0.0020 0.0058 0.0027 0.0054 0.0075
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
(m)
Outer Tank Mass
(kg)
11.8 12.7 27.2 703 71 538 1500
5.4.2 Insulation:
As stated previously, for both the manned and unmanned mission cryogenic
storage vessels, both multi-layered insulation (MLI) and vacuum insulation will be used
to prevent heat transfer to the cryogenic fluid from occurring. Table 5.4.2.1 shows the
MLI design results for each of the tanks for the unmanned mission.
Table 5.4.2.1 -- Insulation Selection for the Unmanned Mission
Number of InsulationLayers Thickness (cm) Qmli (W) Qtot (W) mass (kg)
O2 12 1.5 14.9 15.1 0.71H2 60 7.6 4.4 5 5.97CH4 11 1.3 14.23 14.5 0.67
The hydrogen tank has a significantly larger number of layers of MLI and larger resulting
insulation thickness than the oxygen and methane tanks. Because the hydrogen will be
stored at a much lower temperature (14K) than the oxygen (100K) and the methane
(180K), a larger amount of insulation is needed to prevent heat transfer to the cryogenic
fluids. The heat transfer occurring due to radiation through the MLI and the total
insulation heat transfer are also shown in Table 5.4.2.1. All three storage vessels have
total heat transfers under 15 W. A cryocooler will be used with each tank to maintain the
fluid design temperature.
Similarly, the design results for each of the manned mission storage vessels are
given in Table 5.4.2.2.
Table 5.4.2.2 -- Insulation Selection for the Manned Mission
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Number of InsulationLayers Thickness (cm) Qmli (W) Qtot (W) mass (kg)
O2-propellant 34 4.32 86.9 90.5 33.5O2-breathing 10 1.27 64.5 65.3 2.1H2 60 7.62 80.2 89.4 97.1CH4 28 3.56 88.4 91.4 23.1
The vessels for the manned mission have larger insulation thicknesses than do the vessels
for the manned mission. The manned mission vessels store much more cryogenic fluid
than the vessels for the manned mission. As a result, more insulation is needed to prevent
heat transfer to the cryogenic fluid. Because the weight of the vessels was a primary
concern in the design of the cryogenic storage vessels, the vessels for the manned mission
have a much greater total heat transfer due to the insulation than the tanks for the
unmanned mission. As a result, the cryocoolers will require a great deal more input
power than for the unmanned mission. If the insulation for the manned mission tanks
were selected to result in only 15 W of heat transfer, the insulation thicknesses would be
very large. As the insulation thickness increases, the size of the outer vessel also
increases. For 15 W of heat transfer due to insulation, the outer shells of the storage
tanks would be tremendously heavy. As part of the design, weight minimization was
decided to be more important than the minimization of power consumption because
power is probably more easily compensated for than is weight. If the vessels are too
heavy, the vessels may not be able to be launched into space without great difficulty or
cost. Therefore, for the manned mission, extra power will need to be produced for
cryocooler consumption in order to help minimize the weight of the storage vessels.
5.4.3 Internal Support Rings:
The internal support rings will be used to support the weight of the cryogenic
fluid within the inner vessels of the storage tanks. The dimensions for the internal
support rings for the storage vessels for the unmanned mission are shown in Table
5.4.3.1.
Table 5.4.3.1 -- Internal Support Ring Dimensions for the Unmanned Mission
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
b (m) h (m) l (m) Z (m3) mass (kg)O2 0.002 0.017 2.83 1.45E-07 0.81H2 0.002 0.0075 3.46 2.81E-08 0.44CH4 0.002 0.0088 2.95 3.87E-08 0.44
Since for the unmanned mission the oxygen vessel contains the greatest mass of
cryogenic fluid, the support ring for the oxygen tank has the largest cross sectional area
and largest mass. The hydrogen and methane tanks do not contain as much fluid mass as
does the oxygen tank and thus have smaller cross sectional areas than the oxygen tank.
However, the hydrogen and methane tanks are larger and as a result, have inner support
rings larger in diameter than the oxygen tank.
The dimensions for the internal support rings for the manned mission are shown
in Table 5.4.3.2.
Table 5.4.3.2 -- Internal Support Ring Dimensions for the Manned Mission
b (m) h (m) l (m) Z (m3) mass (kg)O2-propellant 0.015 0.1 11.51 3.75E-05 145.2O2-breathing 0.008 0.045 5.38 4.05E-06 16.3H2 0.008 0.058 14.68 6.73E-06 57.3CH4 0.008 0.069 10.53 9.52E-06 48.9
Because the vessels for the manned mission are much larger than the vessels for the
unmanned mission, the dimensions for the internal support rings for the storage vessels
for the manned mission are greater than those for the unmanned mission. Again, because
the propellant oxygen tank contains the largest mass of fluid, the support rings for this
tank were much larger than those for the tanks containing less fluid mass.
5.4.4 Outer Rings :
The external support rings support the weight of the inner vessel, the insulation,
and the fluid. The external support rings also help maintain the spherical shape of the
storage vessels. Two external support rings will be used for each of the tanks for both the
manned and unmanned missions. The dimensions for the external support rings for the
unmanned mission are shown in Table 5.4.4.1.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Table 5.4.4.1 -- External Support Ring Dimensions for the Unmanned Mission
N b (m) h (m) I (m4) L (m) mass (kg)O2 2 0.004 0.271 6.73E-06 2.97 30.58H2 2 0.004 0.271 6.73E-06 3.98 41CH4 2 0.004 0.271 6.73E-06 3.08 31.68
For the unmanned missions, the external support rings for the storage tanks only vary in
length. As a result, the masses are similar for all three tanks.
The dimensions for the external support rings for the manned mission are shown
in Table 5.4.4.2.
Table 5.4.4.2 -- External Support Ring Dimensions for the Manned Mission
N b (m) h (m) I (m4) L (m) mass (kg)O2-propellant 2 0.048 0.41 5.51E-04 11.85 3924.6O2-breathing 2 0.023 0.23 4.66E-05 5.52 491H2 2 0.05 0.485 9.51E-04 15.25 6224.98CH4 2 0.02 0.215 3.31E-05 10.84 784.53
Because the four tanks to be used in the manned missions will contain dissimilar masses
of fluid and are dissimilar in dimension, the dimensions and masses for the external
support rings for these tanks differ also. The propellant oxygen and hydrogen tanks have
external supports with the greatest mass and dimensions. These two tanks larger external
supports because these two tanks have the greatest total mass.
5.4.5 Internal Support Structure:
The internal support structure consists of a system of rods and brackets that
support the inner vessel within the outer vessel of each storage tank. These rods and
brackets allow the multi-layered vessels to be subjected to dynamic loadings without
damage. The support rods are connected to the inner and outer vessel walls by brackets
that are welded to the inner and outer vessel walls. The rods will fit through circular
holes in the brackets. The dimensions for the internal support rods for the unmanned
mission storage tanks are shown in Table 5.4.5.1, while the dimensions for the internal
support rod brackets for the unmanned mission are shown in Table 5.4.5.2.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Table 5.4.5.1 -- Internal Support Rod Dimensions for the Unmanned Mission
d (m) l (m) Fmax (N) Mass,each (kg) # RodsO2 0.005 0.04 4.85E+03 0.002 12H2 0.006 0.16 2.43E+03 0.008 12CH4 0.005 0.04 2.62E+03 0.002 12
Table 5.4.5.2 -- Internal Support Rod Bracket Dimensions for the Unmanned Mission
t (m) b (m) l (m) Mass,each (kg) #bracketsO2 0.002 0.01 0.02 0.004 24H2 0.002 0.01 0.02 0.004 24CH4 0.002 0.01 0.02 0.004 24
Each of the tanks for the unmanned mission will require twelve support rods. The
dimensions of the rods vary only slightly. The rods for the hydrogen tank are a little
larger in diameter than those for the oxygen and methane tanks because the hydrogen
tank has a larger mass. The length of the rods for the hydrogen tank are longer than those
for the methane and oxygen tanks since the hydrogen tank has a larger thickness of
insulation. Since each rod requires one bracket for each end where the ends are attached
to the vessel walls, 24 brackets will be needed for each tank. For the unmanned missions,
the brackets are identical in dimension.
The dimensions for the internal support rods and internal support rod brackets for
the manned missions are shown in Tables 5.4.5.3 and 5.4.5.4, respectively.
Table 5.4.5.3 -- Internal Support Rod Dimensions for the Manned Mission
d (m) l (m) Fmax (N) Mass,each (kg) # RodsO2-propellant 0.018 0.097 3.60E+05 0.244 20O2-breathing 0.006 0.035 3.69E+04 0.01 20H2 0.011 0.163 5.08E+04 0.154 12CH4 0.014 0.081 1.03E+05 0.125 12
Table 5.4.5.4 -- Internal Support Rod Bracket Dimensions for the Manned Mission
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
t (m) b (m) l (m) Mass,each (kg) #bracketsO2-propellant 0.009 0.07 0.04 0.17 40O2-breathing 0.003 0.022 0.02 0.017 40H2 0.0035 0.025 0.04 0.053 24CH4 0.006 0.03 0.04 0.106 24
The tanks for the manned missions have varying numbers of internal support rods and
varying dimensions for the support rods. The numbers of support rods were selected to
minimize the combined weight of the rods and brackets. The breathing oxygen tank has
the smallest internal support rods and brackets. This is because the breathing oxygen
tank has the least mass. The propellant oxygen tank has the largest internal support rods
and brackets since the propellant oxygen tank has the largest mass. Again, as stated
previously, twice as many brackets are needed as internal support rods since each rod
must have one bracket to attach each end to the internal and external vessel walls.
5.4.6 External Support Structure:
Each cryogenic storage vessel will rest on two external supports. The external
supports will be strapped to the vessels using kevlar straps to prevent the tanks from
moving off of the supports. The supports serve as a means to hold the storage tanks
stationary and also as a means to reduce heat transfer from the surface on which the tanks
rest to the tanks themselves. The dimensions for the external supports to be used for the
unmanned mission are shown in Table 5.4.6.1.
Table 5.4.6.1 -- External Support Dimensions for the Unmanned Mission
O2 H2 CH4length, L (m) 0.384 0.454 0.400thickness, t (m) 0.003 0.0032 0.003leg height, h (m) 0.036 0.042 0.039width, w (m) 0.051 0.056 0.051base , b (m) 0.044 0.048 0.044cutout radius (m) 0.012 0.015 0.013mass (kg) 0.360 0.490 0.360
The dimensions for the external supports for the unmanned mission storage vessels are
fairly similar. Again, the external supports for the hydrogen tank are larger than those for
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
the oxygen and methane tanks since the hydrogen tank is more massive. The supports are
all fairly lightweight, each support having a mass of less than 0.5 kg.
The dimensions for the external supports for the unmanned mission are provided
in Table 5.4.6.2.
Table 5.4.6.2 -- External Support Dimensions for the Manned Mission
O2 - Propellant O2 - Breathing H2 CH4length, L (m) 1.320 0.620 1.700 1.210thickness, t (m) 0.030 0.007 0.020 0.020leg height, h (m) 0.144 0.060 0.167 0.126width, w (m) 0.174 0.117 0.135 0.137base , b (m) 0.300 0.050 0.300 0.200cutout radius (m) 0.090 0.011 0.100 0.080mass (kg) 18.000 2.460 14.600 6.400
The dimensions for the external supports for the storage vessels for the manned mission
are much greater than the dimensions for the unmanned mission. The difference in
dimensions results because the storage tanks for the manned missions are much larger
than those for the unmanned mission. As a result, the external supports for the manned
mission are larger in mass than those for the unmanned mission. The external supports
for the propellant oxygen and hydrogen tanks are much larger and massive than those for
the breathing oxygen and methane tanks for the manned mission since the propellant
oxygen and hydrogen tanks have more mass than the breathing oxygen and methane
tanks.
5.4.7 Temperature Sensors:
Temperature sensors will be used with each of the storage vessels for both the
manned and unmanned mission to determine when the cryocoolers should run. For each
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
of the oxygen and methane tanks, a LakeShore PT-100 Platinum RTD (platinum
resistance thermometer) will be used. For each of the hydrogen tanks, a Scientific
Instruments Germanium Resistance Thermometer will be used. Some of the properties of
these two temperature sensors are listed in Table 5.4.7.1.
Table 5.4.7.1 -- Properties of Selected Temperature Sensors
Germanium Resistance Platinum ResistanceThermometer Thermometer
Termperature Range 1.5K - 100K 30K - 873KRepeatability +/- 0.0005 K +/- 0.01 KSensitivity, dR/dT 35000 Ohms/K nearly constantAccuracy indefinite +/- 0.35 KStability indefinite +/- 0.01 KManufacturer Scientific Instruments LakeShore
A different temperature sensor had to be selected for the hydrogen since the temperature
range of the platinum resistance thermometer does not include the design temperature for
the hydrogen. Each of the sensors has a high repeatability. The germanium resistance
thermometer repeats measurements within +/- 0.0005 K for each measurement. The
platinum resistance thermometer repeats measurements within +/- 0.01 K for each
measurement. Each of the two thermometers has a nearly constant sensitivity. A nearly
constant sensitivity means that as the electrical resistance of the material in the
thermometer changes, the temperature changes at the same rate. The platinum resistance
thermometer is accurate within +/- 0.35 K and stable within +/- 0.01 K. The germanium
resistance thermometer remains accurate and stable for an indefinitely long period of
time.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
5.4.8 Piping and Valves:
The following tables provide the pipe dimensions and valve sizes for both the
unmanned and the manned missions.
Table 5.4.8 -- Pipe and Valve Sizing Results
O2
BreathingO2
PropellantH2 CH4
Nom. Pipe Size (in) 1.5 1.5 1.5 1.5Pipe Thickness (in) 0.065 0.065 0.065 0.065
Pipe OD (in) 1.9 1.9 1.9 1.9Vacuum Jacket ID (in) 2.2 2.2 2.2 2.2
Safety Valve Area (cm2) 2.2 2.2 1.7 2.5
5.4.9 Connections:
Bayonet connectors will be used for any piping connections that need to be made.
1.5” Quality Cryogenics bayonet connections will be used. All of the associated piping
for the cryogenic storage vessels and the Sabatier process will not be assembled until on
the surface of Mars. The piping will be attached to the storage tanks using these bayonet
connections. Bayonet connectors were selected because of the relative ease with which
they can be assembled. Astronauts will have to connect the piping to the tanks while
wearing cumbersome spacesuits. Bayonet connections should be fairly simple for the
astronauts to handle, even while wearing their gear.
5.4.10 Heat Transfer Analysis:
The results for the calculations of total heat transfer analysis are shown in Table
5.4.10.1. The values were calculated using equations from section 5.3.
Table 5.4.10.1 -- Heat Transfer Analysis
O2
Unmanned
CH3
Unmanned
H2
Unmanned
O2
Manned
O2
Manned
CH3
Manned
H2
Manned
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Propellant Propellant Breathing
Insulation
(W)
15.0 14.0 4.5 90.5 65.3 91.4 89.4
Piping
(W)
9.1 5.7 3.3 10.3 12.5 9.6 11.5
Supports
(W)
0.6 0.3 0.4 11.0 3.4 4.3 1.3
Totals
(W)
24.6 20.0 8.2 111.8 81.2 105.3 102.3
5.4.11 Total Tank Mass:
The results for the calculations of total mass are shown in Table 5.4.11.1. The
mass values have been presented previously and are now itemized and totaled.
Table 5.4.11.1 -- Itemized Tank Masses
O2
Unmanned
Propellant
CH3
Unmanned
H2
Unmanned
O2
Manned
Propellant
O2
Manned
Breathing
CH3
Manned
H2
Manned
Inner Tank Mass
(kg)
8.67 24.07 21.66 122 12 86 41
Outer Tank Mass
(kg)
11.75 12.67 27.19 703 71 538 1500
Rods
(kg)
0.012 0.011 0.048 4.9 0.2 1.5 1.2
Brackets
(kg)
0.046 0.025 0.023 6.8 0.7 2.5 0.9
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Inner Rings
(kg)
0.81 0.80 0.99 145.2 16.3 48.9 57.3
Outer Rings
(kg)
30.6 31.7 41.0 4276 739 838 6612
Insulation
(kg)
0.71 0.67 5.95 33.5 2.1 23.1 97.1
External Supports
(kg)
0.359 0.360 0.487 18.0 2.5 6.4 14.6
Piping
(kg)
2.0 2.0 2.0 2.1 2.0 2.1 2.2
Totals
(kg)
55.0 72.3 99.4 5312 846 1547 8326
5.5 Cryocooler:
5.5.1 Significance:
The cryocooler is important to the overall scope of the project in that it addresses
one of the main objectives, to determine a balance between the amount of insulation to be
added to the tanks and the cooling to be restored. Much of the other design occurring in
the project depends on the capacity of the cryocooler. The actual design of a cryocooler
is not within the scope of the project at this time. However, in the cryocooler analysis,
the cryocooler requirements for each tank design were determined.
5.5.2 Initial Questions:
This segment of the analysis in the project has been somewhat vague from the
outset. Initially, some form of condensing the vaporized fluid in the tanks was known to
be necessary. Whether design of a condensation system was required or the purchase an
existing process or mechanism accomplishing the task was not known. However,
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
designing a condensation system or cryocooler would extend the scope of the project too
far and, therefore, work was begun to research cryocooler technology.
Much time was spent finding what is currently available on the market in the form
of cryogenic cooling systems. During this investigation, it became apparent that there
might not be anything on the market made for cooling hydrogen, oxygen, and methane in
a space environment. However, with the advisement, the scope of the project was
changed to only include finding the input power a cryocooler would need to have to
produce a given amount of cooling.
A plot of input power as a function of cooling capacity is the tool through which
the cryocooler was evaluated. The analysis to achieve this plot was acquired from Eric
Marquardt at the National Institute of Standards and Technology in Boulder, Colorado.
5.5.3 Information from NIST:
Eric Marquardt’s name was obtained from Todd Peters at Johnson Space Center.
Marquardt had already designed a cryocooler for space applications as is shown in the
schematic in Figure 5.5.3.1.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Figure 5.5.3.1 -- Schematic of Pulse Tube Cryocooler Designed at NIST
This cryocooler is a pulse tube cryocooler in which the condensation occurs at the end of
the condenser, sometimes called a “cold finger.” Initially, this cryocooler was selected
for use in this project. However, since the scope of the project changed, the actual
selection of a cryocooler does not need to be completed. All that is necessary is a method
to evaluate how much power will have to be delivered to the cryocooler selected. The
previous schematic is a good example of what the cooler will look like when installed to
a tank, and the following equations show how to calculate the input power requirements
for a cryocooler. This cryocooler is the model upon which that method is based. That is
to say, the cryocooler evaluation was done for a cryocooler with similar efficiency.
There is not a good way to approximate the power required by the cryocooler for the
hydrogen tank because such technology has not been developed. Therefore, the
following process was conducted for the oxygen and methane tanks only.
5.5.4 Equation Derivation:
The performance of a cryocooler can be modeled as a Carnot cycle. Specifically,
the coefficient of performance of a Carnot refrigeration cycle is
Wcycle
Qc=maxβ Eq. 5.5.4.1
where Qc (Watts) is the heat transfer from the cold reservoir and Wcycle (Watts) is the net
work input to the cycle. Equation 5.5.4.1 becomes
TcTh
Tc
−=maxβ Eq. 5.5.4.2
where Tc (K) is the cold liquid temperature and Th (K) is the hot ambient temperature.
Rearranging Equations 5.5.4.1 and 5.5.4.2 give
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
)(max Tc
TcThQc
QcWcycle
−==β
Eq. 5.5.4.3
which can be used to calculate the input power required by the cryocooler. Qc is a
function of the amount of insulation added to the tank. Qc,max would occur in the case of
no insulation. One of the objectives of this project is to find a balance between either no
insulation or no cryocooler. These are the two extreme limits guiding the design.
The actual process for calculating Wcycle was obtained from Eric Marquardt. The
first step is to calculate what is called the Carnot power, Pc.
Tc
TcThPc
−= Eq. 5.5.4.4
The next step was to read the efficiency off of a performance curve such as the Strobridge
plot in Figure 5.5.4.2.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Figure 5.5.4.2 -- Strobridge Plot
This plot was put together from experimental data during the 1970’s. For use in
these calculations, a curve was drawn through the top data points in order to approximate
the higher efficiency of coolers in the present time. This plot is shown in Figure 5.5.4.3.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Figure 5.5.4.3. Strobridge Data for Cryocoolers Operating at 90K
The cooling capacity is a function of the amount of insulation on the tank. The efficiency
and the Carnot power are used to calculate the electrical power, Pe.
eff
PcPe = Eq. 5.5.4.5
The total power, Pt, required is calculated by dividing the electrical power by a power
conversion factor for the electronics of about 85%.
85.0
PePt = Eq. 5.5.4.6
Finally, the input power required by the cryocooler to achieve a given cooling capacity is
obtained by multiplying the total power by the amount of cooling desired.
1
10
100
2 5 15 60 100 800
Cooling Capacity (Watts)
Car
no
t E
ffic
ien
cy
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
5.5.5 Results:
The result of the previous equations was a curve that shows the input power
(Watts) required by a cryocooler to produce a given amount of cooling (Watts). This
relationship was investigated for four different ambient temperatures of 200, 220, 240,
and 300 K. The final product of this process is a curve which shows input power as a
function of cooling capacity. Curves of this nature are shown in Figures 5.5.5.1 and
5.5.5.2. Figure 5.5.5.1 shows the input power a cryocooler would require in order to
replace the cooling lost in the oxygen tank. Figure 5.5.5.2 shows the same relationship
for the methane tank.
Figure 5.5.5.1 -- Input Power as a Function of Cooling Capacity for the Oxygen Tank
0
500
1000
1500
2000
2500
0 50 100 150 200 250
Cooling Capacity (W)
Inp
ut
Po
wer
(W)
300K
240K
220K
200K
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
Figure 5.5.5.2 -- Input Power as a Function of Cooling Capacity for the Methane Tank
The requirements for the cryocoolers for both the unmanned and manned missions are
shown in Table 5.5.5.1.
Table 5.5.5.1 -- Cryocooler Requirements for Unmanned and Manned Missions.
Input Power (W)
Cooling Capacity (W)
O2 519 25CH4 130 20Total Unmanned 649
O2 (prop) 1535 111.8O2 (breath) 1350 81.2CH4 1129 105.3Total Manned 4014
0
200
400
600
800
1000
1200
1400
1600
1800
0 50 100 150 200 250
Cooling Capacity (W)
Inp
ut
Po
we
r (W
)
300K
240K
220K
200K
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
5.6 Cost Analysis:
The cost analysis for this project consisted of a comparison between the cost to
manufacture the design and the cost to transport the design to Mars. The purpose of the
cost analysis was to minimize the total cost for the storage vessel designs. In any
government project, reducing the cost of the project should be an issue, since the
taxpayers are basically responsible for the cost of the project. The costs for the cryogenic
storage vessel design include material costs for the vessels, the cost to construct the
vessels, and the cost to launch the vessels into space. The predominant cost for the
design is the launch cost. The cost for transporting objects into space is very high,
approximately $20,000 per kg of mass. As a result, an objective of this project was to
minimize the weight of the storage tank designs. However, at some point, minimizing
the weight of the design could have caused the cost to construct the vessels to
dramatically increase. For example, a lighter tank might cost an exorbitant amount to
construct. If the lighter tank’s construction costs cause it to cost more overall than a
heavier tank, then the launch cost benefit of the lighter tank is overruled by its high
construction costs. For this reason, the cost of the materials for the tank designs and the
cost to construct the tank designs were examined to determine whether the lightest tank
design was in fact the most cost effective design.
However, the cost analysis confirmed the original assumption that a lighter tank
would be more cost effective. Logically, the materials for the cryogenic storage vessels
cost less for smaller (lighter tanks). For smaller vessels, less material is needed, and
therefore, the materials cost less for smaller vessels. Additionally, several manufacturers
of cryogenic storage vessels, including Minnesota Valley Engineering and Cryofab,
confirmed that smaller vessels are less expensive to construct. In conclusion, the smaller
and lighter the storage vessel, the more cost effective is the design since the material,
construction, and launch costs are reduced.
The Taguchi method as described in The Engineering Design Process, by Ertas
and Jones, was also examined as a possible tool for the cost analysis. However, the
Taguchi method was not appropriate for the type of cost analysis to be completed in this
project since the Taguchi method is based on experimental data and this project produced
no experimental data.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
5.7 Simulation:
The design for the cryogenic storage vessels was intended to conclude with
physical and computer simulation of the basic design created during this project. Both
physical and computer simulation of the basic cryogenic storage vessel design have been
attempted. A physical model of the storage vessel design showing how the vessel will
be constructed and how the vessel will appear internally was also attempted. Computer
simulation of the basic vessel design was begun to determine whether or not the
theoretical designs completed throughout this project could actually withstand loadings
expected to occur during the life of the storage vessels. However, due to lack of
experience with finite element analysis and simulation software and also to a shortness of
time, the computer simulations were not able to be completed. Some simulation was
completed, but the results of the simulation were inconclusive.
IV. Conclusions
At this time, the designs for the cryogenic storage vessels for both the manned
and unmanned missions have been completed. The primary objectives of this project
were to minimize the weight and volume of the storage vessels, to minimize heat transfer
to the cryogenic fluids, and to determine a balance between the amount of insulation to be
used and the power requirements of cryocooler. The objectives of this project have been
met. The designs for each of the cryogenic storage vessels minimize the weight and
volume of the tanks and minimize heat transfer. Inconel and aluminum were selected as
the materials for the inner and outer vessels of the storage vessel, respectively. Fiberglass
was selected as the material for the suspension rods and external support to help reduce
the total weight of the vessels. Multi-layered insulation and vacuum insulation were
selected to minimize heat transfer to the cryogenic fluids. A balance between the amount
of insulation and the cryocooler power was also determined and from this balance, the
insulation thickness and power requirements for the cryocooler were determined. The
only remaining work for this project is simulation and testing of the designs.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
BIBLIOGRAPHY
Barron, Randall F. Cryogenic Systems. 2nd ed. New York: Oxford University Press,1985.
Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. New York: Crane Co.,1982.
Ertas, Atila and Jesse C. Jones. The Engineering Design Process. 2nd ed. New York:John Wiley & Sons, Inc., 1996.
“Exobiology Strategy Report.” World Wide Web.
Hoffman, Stephen J. and David Kaplan, eds. Human Exploration of Mars: TheReference Mission of the NASA Mars Exploration Study Team. NASA, JohnsonSpace Center, 1997.
Incropera, Frank and David P. DeWitt. Fundamentals of Heat and Mass Transfer. NewYork: John Wiley & Sons, Inc., 1996.
Kieffer, H. H., et al., eds. Mars. Tuscon: The University of Arizona Press, 1992.
Mantell, Charles L. Engineering Materials Handbook. 1st ed. New York: McGraw HillBook Company, 1958.
Moran, Michael J. and Howard N. Shapiro. Fundamentals of EngineeringThermodynamics. 3rd ed. New York: John Wiley & Sons, Inc., 1996.
Mutch, Thomas A., et al., eds. The Geology of Mars. Princeton: Princeton UniversityPress, 1976.
National Aeronautics and Space Administration. “Mars Fact Sheet.” World Wide Web.
National Aeronautics and Space Administration. Mars Pathfinder - Weather Data.World Wide Web.
National Aeronautics and Space Administration. Scientific Results of the VikingMission.
Norton, Robert L. Machine Design: An Integrated Approach. Upper Saddle River:Prentice-Hall, 1996.
Peters, Todd. Propulsion and Fluid Systems Branch, Johnson Space Center.
Shigley, Joseph Edward and Charles R. Mischke. Mechanical Engineering Design. 5th
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
ed. New York: McGraw-Hill, Inc., 1989.
Strobridge, T. R. "Cryogenic Refrigerators-An Updated Survey." NBS Technical Note655 (June 1974): 12 pages.
Tillman, James E. “Mars.” World Wide Web.
Weaver, David B., Michael B. Duke, and Barney B. Roberts. Mars ExplorationStrategies: A Reference Design Mission. American Institute of Aeronautics andAstronautics, Inc., 1993.
White, Frank M. Fluid Mechanics. 3rd ed. New York: McGraw-Hill, Inc., 1994.
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
APPENDIX A: EQUATION DERIVATION
Vacuum Insulation Radiation Analysis
The radiant heat transfer for vacuum insulation is given in the following equation.
q F F A T Tr v e o i, ( )= −12 14 4σ Eq. 1
where
qr,v = radiant heat transfer in vacuum
Fe = emissivity factor
F12 = configuration factor = 1
σ = Stefan Boltzmann constant = 5.67x10-8 W/m2K4
A1 = surface area of inner vessel
The emissivity factor was determined using the expression shown below.
1 1 11 1
21
1 11
1 2F e eN
e e ee s s s
= + −��
�↵√+ − −
��
�↵√+ + −
��
�↵√( ) Eq. 2
where
e1 = emissivity of surface 1 (inner vessel)
e2 = emissivity of surface 2 (outer vessel)
es = shield emissivity
N = number of shields
The addition of heat shields reduced the radiant heat transfer drastically. The heat shields
used in this design were the reflective layers of the MLI.
Vacuum Insulation Gaseous Conduction Analysis
Gaseous conduction also occurs in the vacuum insulation region of the tank. The gaseous
conduction is given by the following expression.
q GpA T Tg v o i,( )= −1 Eq. 3
where
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
qg,v = gaseous conduction in vacuum
G = function of temperature, accommodation coefficient factor, gas constant,
specific heat ratio
p = pressure in evacuated region
G is provided in the following equation.
Gk
k
g R
TFc
a=+−
��
�↵√
11 8 π
Eq. 4
where
k = specific heat ration for gas in vacuum (air)
T = temperature of air in vacuum
Fa = accommodation coefficient factor = 1
For gaseous conduction to occur, the mean free path of the gas molecules within the
vacuum must be larger than the distance between the inner and outer vessels. The mean
free path of the gas molecules (again, air) was calculated using the following equation.
λµ π
=��
�↵√
��
�↵√
p
RT
gc2Eq. 5
where
λ = mean free path
µ = gas viscosity at T
p = absolute pressure of gas in vacuum (2 mPa was used)
Inner Vessel Stiffening Rings Analysis
As discussed in the body of this report, the inner stiffening ring was sized based upon a
required section modulus which was dependent on the bending moment occurring in the
rings. The bending moment for the inner stiffening rings is shown in the following
expressions.
For 0≤φ≤θ
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
θφθθθπφφφπ 2sincoscossin)(sincos5.2 ++−−+=WR
MEq. 6
For θ ≤ φ ≤ π:
θφθθφφπφπ 2sincoscossin)(cos5.2 +++−−=WR
MEq. 7
where
M = bending moment
W = weight of fluid and vessel
R = radius of vessel
φ = location
θ = location angle of supports
The maximum bending moment resulting from these expressions was used to determine
the section modulus of the rings, and the section modulus was used to determine the
dimensions of the beam from which the rings would be made.
Outer Vessel Stiffening Rings Analysis
As discussed in the body of this report, the outer stiffening ring was sized based upon a
required area moment of inertia which was dependent on the bending moment occurring
in the rings. The bending moment for the inner stiffening rings is shown in the following
expressions.
For 0 ≤φ ≤θ1:
2 22
21 2 1 2 2 1 1
M
WR
πφ θ θ θ θ π θ θ π θ θ= − + − − − + −cos (sin sin ) (cos cos ) ( )sin ( )sin Eq. 8
For θ1 ≤φ ≤θ2:
2 22
21 2 1 2 2 1 1
M
WR
πφ θ θ θ θ π θ θ π φ θ θ= − + − − − + −cos (sin sin ) (cos cos ) ( )sin sin sin Eq. 9
For θ2 ≤φ ≤π:
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
2 22
21 2 1 2 2 1 1
M
WR
πφ θ θ θ θ θ θ θ θ= − + − + −cos (sin sin ) (cos cos ) ( sin sin ) Eq. 10
Again, the maximum bending moments were used to calculate the area moment of inertia
of the ring which was then used to size the beam from which the rings would be made.
Suspension System Support Rod Analysis
The dynamic loadings acting on the support rods are as follows:
( )[ ]
( )[ ]
( )[ ]
( )[ ]
FN W
FN W
F N W
FN W
FN W
F N W
FN W
FN W
FN W
v
g
t
g
vt g
t
g
t
g
tt g
v
g
v
g
l
g
=+
=
=
=+ −
=− −
=
=+ +
=− −
=
( )
cos
1
2
2
2
2 1 1
2
2 1 1
2
2
1 2 1
2
1 2 1
2
1
2
1
2
θ
Eq. 11 - 19
where
Written by Undergraduate Students Distributed ByMay 1999 Texas Space Grant ConsortiumTexas Tech University http:// www.tsgc.utexas.edu/tsgc
F Vertical Down
F Vertical Up
F Transverse I
F Transverse I
F Transverse I
F t Transverse II
F Transverse II
F Transverse II
F Longitudinal
v
t
vt
t
t
t
v
v
l
= −= −= −= −= −= −
= −= −
=
1
2
1
2
2
top related