American Institute of Aeronautics and Astronautics
1
Cryogenic Pressure Control Modeling for Ellipsoidal Space
Tanks in Reduced Gravity
Alfredo Lopez
1
, Gary D. Grayson
2
, and Frank O. Chandler
3
The Boeing Company, Huntington Beach, CA, 92647
Leon J. Hastings
4
Alpha Technology, Inc., Huntsville, Alabama, 35812
and
Ali Hedayat
5
NASA Marshall Space Flight Center, Huntsville, Alabama, 35812
A computational fluid dynamics (CFD) model is developed to simulate pressure control
of an ellipsoidal-shaped liquid hydrogen tank under external heating in low gravity.
Pressure control is provided by an axial jet thermodynamic vent system (TVS) centered
within the vessel that injects cooler liquid into the tank, mixing the contents and reducing
tank pressure. The two-phase cryogenic tank model considers liquid hydrogen in its own
vapor with liquid density varying with temperature only and a fully compressible ullage.
The axisymmetric model is developed using a custom version of the commercially available
FLOW-3D software and simulates low gravity extrapolations of engineering checkout tests
performed at Marshall Space Flight Center in 1999 in support of the Solar Thermal Upper
Stage Technology Demonstrator (STUSTD) program. Model results illustrate that stable low
gravity liquid-gas interfaces are maintained during all phases of the pressure control cycle.
Steady and relatively smooth ullage pressurization rates are predicted. This work advances
current low gravity CFD modeling capabilities for cryogenic pressure control and aids the
development a low cost CFD-based design process for space hardware.
Nomenclature
dp/dt = ullage pressure rise rate
V
max
= maximum velocity within the domain
I. Introduction
ASA’s space exploration program is considering high energy cryogenic propellants for the Earth departure,
Lunar descent, and Lunar ascent stages. The advancement of cryogenic fluid management (CFM) technology is
essential to the development of these upper stages. NASA is teaming with its industrial partners to progress
development/technology that will broaden the experience base for the CFM community as a whole. Microgravity
experiments and relevant data are highly expensive and limited. This issue has motivated the Marshall Space Flight
Center (MSFC)/Boeing team to aggressively explore combinations of ground testing and analytical modeling to the
greatest extent possible.
Cryogenic propellant computational fluid dynamics (CFD) tools offer low cost design solutions for the aerospace
industry to model low-g fluid dynamic effects. During earlier space programs, such as the Apollo and Space
1
Associate Engineer/Scientist, Propulsion & Cryogenic Technologies, 5301 Bolsa, Ave/H017-D725, Member.
2
Associate Technical Fellow, Propulsion & Cryogenic Technologies, 5301 Bolsa Ave/ H017-D725, Senior Member.
3
Director, Propulsion & Cryogenic Technologies, 5301 Bolsa Ave/ H017-D725, Associate Fellow.
4
CFM Technology Consultant, Propulsion Systems Dept. ER24/ATI, Associate Member.
5
Aerospace Engineer, Cryogenic Fluid Management Technology Team, Propulsion Systems Dept. ER24, Senior
Member.
N
American Institute of Aeronautics and Astronautics
2
Shuttle, design activity related to how a specific tank would perform in zero g was based on estimates for the
performance using simple models for the internal fluid components such as galleries and collectors. Qualification of
these components could involve drop tower testing, parabolic aircraft flight testing or extensive ground testing in
more severe g-level tank orientations than would be needed in actual flight. With the advent of these sophisticated
CFD codes and the ability to model these complex internal propellant management geometries, high fidelity
solutions and propellant tank operational verification can now be obtained by analysis at a fraction of the original
cost needed for an elaborate test.
Propellant tank pressure control in reduced gravity is an enabling technology for implementing in-space
cryogenic propulsion. Upper stage tank pressure control currently relies on propellant settling and venting as
required, however, auxiliary systems for propellant settling incur weight penalties in the form of setting propellant
and hardware. Complexity is also incorporated into the mission operations because venting/resettling of the
propellant can become necessary at inopportune times such as when liquid propellant is situated at the vent port. The
thermodynamic vent system (TVS) concept enables tank pressure control and venting without resettling.
A series of ground tests were conducted at MSFC for Boeing and SRS Technologies using the 2 m
3
(71 ft
3
) Solar
Upper Stage Technology Demonstrator (STUSTD) tank (Fig. 1) to demonstrate reduced gravity pressure control.
Details of the STUSTD program and engineering tests are available in Ref. 4. This paper expands on previously
published model results (Ref. 1) and presents the pressure control and active TVS performance data for the
STUSTD tank in a reduced gravity environment.
II. Approach
A. FLOW-3D Software
FLOW-3D is a general Navier-Stokes equation solver with an extensive history of cryogenic tank modeling in
both reduced and normal gravity environments. FLOW-3D allows several options to be enabled based on what is
important to the problem. The current two-phase cryogenic tank model is developed using a custom version of the
commercially available FLOW-3D software. The customization enables the model to treat phase change effects at
the liquid-gas interface. First order approximations for momentum and energy equations including the two equation
k-ε and Renormalization-Group (RNG) turbulence models are enabled. The ullage region is treated as fully
compressible and liquid density varies with temperature only. Modeling the heat transfer between liquid, gas and
tank walls is included to capture thermal stratification within the fluids. For details of the formulations and
assumptions within the FLOW-3D code see Ref. 6.
Figure 1. STUSTD Tank Configuration.
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3
B. Model Description
The model uses a 3,250 cell axisymmetric mesh to simulate the 71 ft
3
ellipsoidal STUSTD tank (Fig. 2). The
mesh is derived from a similar tank pressurization model (Ref. 2) The S-IVB mesh has previously been shown to be
independent of grid size therefore the current STUSTD mesh is expected to provide a grid insensitive solution. The
tank has a width of 5.78-ft. and a height of 4.08-ft. Liquid acquisition devices (LADs) are omitted from the model
because the engineering checkout tests do not include LAD operation. The Active TVS (ATVS) is located in the
center of the tank and is 1-ft. in diameter and 0.63-ft. tall. The outlet of the axial jet is 0.14-ft. (1.7-in.) in diameter.
A series of dual capacity (20 W and 40 W) tank wall heaters are imbedded in the tank insulation. Due to the
axisymmetric mesh, the STUSTD model incorporates these variable power tank heaters as solid obstacles adjacent
to the bulk liquid. The actual tank heaters are approximately 6 inches wide by 26 inches long. Four of these tank
heater strips are evenly distributed on the tank wall. The tank heat leak is distributed between the tank wall and the
imbedded heater obstacles. When heaters are not used the incoming tank heat leak is evenly distributed along the
tank walls including the surface of the inactive heaters.
The ATVS body is considered adiabatic thus contributing a negligible amount of heat to the liquid. The self-
pressurization models are initially quiescent. The liquid is assumed saturated at a given tank pressure and allowed to
heat up. Ullage stratification profiles are derived from available test data and applied on a case by case basis.
Table 1 lists the test cases considered in the present analysis. The focus is on tank self-pressurization and ATVS
performance in reduced gravity environments.
By correlating the two-phase cryogenic model to normal gravity test data and using verified low-gravity slosh
modeling techniques for spacecraft and
launch vehicles, cryogenic tank pressure
control in reduced gravity environments
can be simulated. Here, each of the
normal gravity cases previously
discussed (Ref. 1) is run in a 1E-5-g
acceleration environment with identical
fills and heat conditions as the normal
gravity cases. The low gravity model
uses an identical computational mesh as
the normal gravity models. Predicted
ullage pressure, ullage temperature and
liquid temperature histories are
presented. Temperature contour and
velocity plots are included to track
liquid/gas interaction and illustrate how
the surface tension dominated fluid
regions react to external heating in
reduced acceleration environments.
20W/40W
Tank Heaters
ATVS
Outlet
ATVS
Inlet
ATVS
Heat Exchanger
Tank Wall
20W/40W
Tank Heaters
ATVS
Outlet
ATVS
Inlet
ATVS
Heat Exchanger
Tank Wall
Figure 2. STUSTD Model Mesh and Tank Geometry.
Test Case Test Fluid Heat Leak Rate Fill Level
Mixer Type & Flow
Rate
1
LH2
25.7 W
87%
none
2
LH2
25.7 W
44%
none
3
LH2
6.7 W
90%
axial jet / 27 gpm
Table 1. STUSTD Reduced Gravity Test Cases.
American Institute of Aeronautics and Astronautics
4
III. Results and Discussion
When in reduced gravity, the surface tension forces in the STUSTD tank are significant compared to all other
forces. As expected in a low-gravity environment with a tank of this size, the meniscus at the tank wall begins to
grow as surface tension forces pull the liquid towards a curved shape. The ullage will eventually form a nearly
spherical ullage bubble within the tank to minimize surface energy. Accordingly in Cases 1 and 3, the initial bubble
shape is specified as precisely spherical and then the model simulates the equilibrium shape from that initial bubble.
For the lower fill fraction simulations (Cases 2) a flat initial free surface is specified and the code is allowed to
develop that initial shape into the equilibrium shape for the fluid, geometry, and tank considered.
A. Self-Pressurization
In Case 1, self-pressurization of the STUSTD LH2 tank is simulated using an 87% fill level with 25.7 W heat
leaks. Heat is distributed between tank walls (5.7 W) and tank heaters operating at 20 W. Figure 3 shows that an
average tank pressurization rate of 0.72 psi/hr is predicted for Case 1 and remains relatively smooth throughout the
10,000-sec simulation. Ullage temperatures (Fig. 4) and liquid temperatures (Fig. 5) are measured at 44 inches and
25 inches from the bottom of the tank respectively. Model results for ullage and liquid temperature for Case 1
experience a small (1°R) increase in magnitude during self-pressurization. Figures 6a and 6b illustrate that a stable
liquid/gas interface is maintained throughout the self-pressurization phase. Small localized bubble interface
disturbances, with velocities on the order of 0.004 ft/s to 0.02 ft/s, are noted but they do not affect the ullage bubble
significantly. In a reduced gravity environment, the energy exchange between the bulk liquid and tank heater has a
significant effect on the total tank thermal distribution. In Figure 6a, the influence the tank heaters have on the
surrounding fluid can be observed. In the absence of strong natural convection currents, warm spots begin to form
throughout the tank. More noticeably the center of the ullage bubble is generally warmer (typically 1.5 °R warmer
than surround liquid) than other areas of the tank. The ullage bubble begins to warm the surrounding liquid as well.
This is illustrated throughout the temperature contour plots where slightly warmer liquid surrounds the ullage
bubble.
32
33
34
35
36
37
38
0 2000 4000 6000 8000 10000 12000
time (s)
ullage pressure (psi)
Model
0.72 psi/hr
32
33
34
35
36
37
38
0 2000 4000 6000 8000 10000 12000
time (s)
ullage pressure (psi)
Model
0.72 psi/hr
Figure 3. Case 1 Ullage Pressure History.
41
42
43
44
0 2000 4000 6000 8000 10000 12000
time (s)
ullage tempture (°R)
Model
41
42
43
44
0 2000 4000 6000 8000 10000 12000
time (s)
liquid tempture (°R)
Model
Figure 4. Case 1 Ullage Temperature History. Figure 5. Case 1 Liquid Temperature
History (25-in.).
American Institute of Aeronautics and Astronautics
5
In Case 2 (25.7 W, 44% fill) the tank heaters are activated. A steady self-pressurization rate of 1.44 psi/hr is
predicted. Figure 10b illustrates pockets of warm gas at the liquid-heater interface slowly traveling along the
sidewall. The transient motion within the tank cause small scale oscillations in ullage temperatures on the order of
less than 2 °R. Liquid temperature (Fig. 9) is recorded at 15 inches from the bottom of the tank and experiences little
change during self-pressurization. At a 44% fill, the liquid-gas interface becomes notably curved as velocity and
temperature fields with in the tank develop. Surface tension forces draw liquid hydrogen along the walls. The liquid
has a higher heat capacity than the ullage and therefore when the liquid intercepts incident tank wall heat leak the
overall heat leak into the ullage region is reduced. This leads to slightly lower ullage pressurization rates than in
normal gravity for the STUSTD/SRS configurations studied (Ref. 1).
43.49
43.25
43.01
42.77
42.52
42.28
42.04
T (°R)
43.49
43.25
43.01
42.77
42.52
42.28
42.04
T (°R)
43.65
43.39
43.12
42.86
42.60
42.33
42.07
T (°R)
43.65
43.39
43.12
42.86
42.60
42.33
42.07
T (°R)
a.) t = 4680 s, V
max
= 0.00159 ft/s b.) t = 10,320 s, V
max
= 0.00832 ft/s
Figure 6. Case 1 Temperature and Velocity Field Plots.
34
35
36
37
38
0 1000 2000 3000 4000 5000 6000 7000
time (s)
ullage pressure (psi)
Model
1.44 psi/hr
34
35
36
37
38
0 1000 2000 3000 4000 5000 6000 7000
time (s)
ullage pressure (psi)
Model
1.44 psi/hr
Figure 7. Case 2 Ullage Pressure History.
40
42
44
46
48
50
52
0 1000 2000 3000 4000 5000 6000 7000
time (s)
ullage tempture (°R)
Model
42
43
44
45
46
47
48
49
0 1000 2000 3000 4000 5000 6000 7000
time (s)
liquid tempture (°R)
Model
Figure 8. Case 2 Ullage Temperature History. Figure 9. Case 2 Liquid Temperature
History (15-in.).
