parametric study of a propellant tank slosh baffle -...
TRANSCRIPT
1
American Institute of Aeronautics and Astronautics
Parametric Study of a Propellant Tank Slosh Baffle Sunil Chintalapati
1 and Daniel R. Kirk
2
Florida Institute of Technology, Melbourne, FL, 32901, USA
A current problem that severely affects the performance of spacecraft is related to slosh dynamics in
liquid propellant tanks under microgravity conditions. Accurate prediction of the slosh dynamics is critical
for successful mission planning and may impact vehicle control and positioning during rendezvous, docking,
and reorientation maneuvers. The purpose of this work is to assess the performance of various slosh-
mitigating baffle designs and configurations using computational fluid dynamics. This work develops metrics,
including wall wetting, peak slosh amplitude, and bulk fluid motion, to assess the relevance of a particular
baffle geometry and placement within the tank for a prescribed bulk fluid motion over a range of
acceleration levels. The two- and three-dimensional studies are used to assess the slosh model’s sensitivity to
grid resolution, laminar versus turbulent flow models, and Bond number scaling. The results are used to
develop a foundation on which to build a full six-degree-of-freedom dynamic mesh model, allowing for fluid-
force interaction with a propellant tank, which will be benchmarked against low-gravity slosh flight data.
Nomenclature
Bo = Bond number, ratio of body to surface tension forces, ρgR2/σ
g/g0 = Gravitational acceleration ratio relative to surface of Earth gravity 9.81 m/s²
L = Maximum vertical length of tank (m)
µ = Viscosity (kg/m s)
R = Tank radius (m)
ρ = Liquid density (kg/m³)
σ = Surface tension (N/m)
t = Time (s)
Vmax = Maximum velocity (m/s)
Wemax = Weber number based on Vmax, ratio of inertial to surface tension forces, ρV2R/σ
I. Introduction and Background losh is a pressing problem for spacecraft stability and control. Propellant remaining inside a tank may be excited
by the motion of the vehicle, and reaction forces and moments caused by slosh can degrade the pointing
accuracy of the system, [21, 22]. For example, in preparation for orbital insertion of the payload, the upper-stage of
a rocket undergoes a series of maneuvers which may lead to large amplitude sloshing motion of the propellants.
Liquid propellant reaching the relief and orbital control vents may result in a significant increase in expelled mass
which may cause mission failure due to loss of the proper orbital attitude. As another example delicate docking
maneuvers between spacecraft and space stations may also be impacted by liquid slosh motion. Although baffles add
to the weight of the tank, they play a vital role in mitigating undesired slosh induced motion. Slosh baffles located
within the Space Shuttle external tank are shown in Figure 1, and Figure 2 shows an example of a baffle used by
Armadillo Aerospace to damp oscillations observed during test flights on a vehicle under development, [10].
Figure 1: Space Shuttle External Tank Slosh Baffle, [9] Figure 2: Slosh baffle used by
Armadillo Aerospace, [10]
1 Undergraduate Research Assistant, Department of Mechanical and Aerospace Engineering, [email protected] 2 Assistant Professor, Department of Mechanical and Aerospace Engineering, [email protected]
S
44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit21 - 23 July 2008, Hartford, CT
AIAA 2008-4750
Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
Dow
nloa
ded
by F
LO
RID
A I
NST
ITU
TE
OF
TE
CH
NO
LO
GY
on
July
27,
201
4 | h
ttp://
arc.
aiaa
.org
| D
OI:
10.
2514
/6.2
008-
4750
2
American Institute of Aeronautics and Astronautics
This paper utilizes computational fluid dynamics (CFD) to assess the performance of various slosh-mitigating
baffle configurations for spacecraft design. Depending on the type of disturbance and tank shape, the liquid
propellant can experience different types of motion including simple planer, non-planer, rotational, symmetric,
asymmetric, quasi-periodic and chaotic. In low-gravity, surface tension and capillary action may dominate even in
large booster size tanks and the liquid may be oriented randomly within the tank depending upon the wetting
characteristics of the tank wall, [11]. Theoretical research dates back decades, but only now have CFD models been
capable of handing complex sloshing motion. This work forms a foundation for the development of a six-degree-of-
freedom (6-DOF) dynamic mesh model that will be benchmarked against low-gravity experimental data. Before
such a model can be developed it is important to have an understanding of grid sensitivity, turbulence modeling, and
Bond number scaling during low-gravity conditions so that computation resources can be optimized. Metrics are
also developed for characterizing slosh baffle effectiveness and guidelines for comparing various slosh scenarios.
Early work in slosh dynamics has been mostly theoretical, and treats the liquid as a variable inertia only, i.e. the
viscosity, surface tension and other important effects are not considered, [5, 6, 7, 18]. Early research includes
comparison of experimental data to theory by Abramson, et al., [2], Babskii, et al. developed a mathematical theory
for behavior of liquid under total or partial weightlessness, [3], and Narimanov, et al. developed the equations of
motion for the nonlinear dynamics of liquid-containing flight vehicles, [15]. Analytical solutions of fluid motion
based on first principles have been developed for simple tank geometries, excitations, and boundary conditions using
potential theory, [1, 5, 8, 12, 13, 14, 20], and experimental verification of simple, low-amplitude slosh has been
performed, [1]. When liquid excursions remain small, a linear second-order oscillator provides a useful
representation of the slosh dynamics, which can be integrated with the state equations of the complete vehicle
system. More complicated plants result from nonlinear slosh models, which have been shown to yield reliable
predictions over larger ranges, or by including additional oscillators and an increased state dimension [7].
Numerical solution to slosh has been emerging in recent times, owing to the major advances in computational
capabilities. CFD models to make slosh predictions during the high acceleration ascent phases of a rocket have been
used, although very little work has been done in cases of very-low accelerations when the vehicle is in space, [20,
22]. When available, predictions can be used to validate the performance of simpler models, and a direct comparison
with CFD-predicted damping is of significant interest, however, these models dynamic mesh simulations, which
allow the container to move in 6-DOF with feedback from the liquid acting on the tank walls.
Another approach for predicting slosh motion is to use scaled model testing, such as that done at Southwest
Research Institute, but thus far the results are largely qualitative and there has not yet been direct data comparison
with detailed CFD models. Other studies have focused on analyzing available flight data to identify conditions
leading to mission failure. The FLEVO project, under the direction of the National Aerospace Laboratory (The
Netherlands) has been the most substantial effort devoted to fill the gap between numerical simulations, [13, 20],
and the development of an experimental framework to measure and characterize slosh under microgravity, [22].
II. Computational Setup and Numerical Modeling Overview CFD studies were performed utilizing the transient Volume of the Fluid (VOF) method, which is well suited to
multiphase flows involving two immiscible fluids. The method relies on the basis that the fluid state is described in
each cell by one value; the method introduces a function F whose value F=1 correspond to a cell full of fluid, and
F=0 to an empty cell, and a geo-reconstruct scheme is used to track the fluid-air interface, [4]. A generic tank was
modeled and meshed with several grids to check the dependency of solution on the grid density. The tank has a
cylindrical section and is caped by two elliptical domes. The diameter of the cylindrical section is 4 m and tank
height is 3.5 m. Figure 3 shows the geometry and various meshes with increasing grid density used. Since
computational run time increases as grid density is increased, there is motivation to find a grid density which gives
an accurate approximation of the bulk fluid behavior in low-gravity conditions with slosh motions of interest.
Tank used in all studies Grid 1 ~ 2,000 Cells Grid 2 ~ 10,000 Cells Grid 3 ~ 27,000 Cells
Figure 3: Tank geometry and mesh details
Dow
nloa
ded
by F
LO
RID
A I
NST
ITU
TE
OF
TE
CH
NO
LO
GY
on
July
27,
201
4 | h
ttp://
arc.
aiaa
.org
| D
OI:
10.
2514
/6.2
008-
4750
3
American Institute of Aeronautics and Astronautics
Figure 4 shows a 2D transient simulation from 0 to 5 seconds at 2 different gravity levels. The three different
series are for three different grid densities shown in Figure 3. The domain is patched with water and free flow is
induced by gravity, with surface tension (σ = 0.073 N/m) and the contact angle for water and the tank wall is set to
55 degrees. Initially water occupies the lower left quadrant of the domain while air occupies the remainder.
Computational run time depends on cell density and run times increase from grid 1 to grid 3. The figures also shows
the qualitative difference between gravity levels on Earth and gravity levels of 1/1,000 of Earth levels, as might be
experienced by a spacecraft coasting with a low settling thrust.
0 sec
g/g0 = 1, Bo = 536,000, Wemax = 493,366 g/g0 = 0.001, Bo = 536, Wemax = 615
Grid 1 Grid 2 Grid 3 Grid 1 Grid 2 Grid 3
1 sec
2 sec
3 sec
4 sec
5 sec
Grid 2 – Grid 1 Grid 3 – Grid 1 Grid 3 – Grid 2 Grid 2 – Grid 1 Grid 3 – Grid 1 Grid 3 – Grid 2
1 sec
5 sec
Figure 4: Free flow of fluid at g/g0=1 and g/g0= 0.001, three different grids, and solution grid dependence
Dow
nloa
ded
by F
LO
RID
A I
NST
ITU
TE
OF
TE
CH
NO
LO
GY
on
July
27,
201
4 | h
ttp://
arc.
aiaa
.org
| D
OI:
10.
2514
/6.2
008-
4750
4
American Institute of Aeronautics and Astronautics
An assessment of the dependence of the solution on grid density is important in order to minimize
computational time, which can be significant especially under low-gravity conditions. The bottom of Figure 4 shows
the difference between solutions at 1 and 5 seconds. The dark region is an area of no difference, which means both
grids model fluid behavior identically, and light region shows a difference near the liquid-gas interface. Grid 1 is in
relatively good agreement with the finer grids even for the low gravity case. The results of this study show that for a
tank on the order of 4 m diameter, relatively coarse grid densities can be used to capture the bulk features of slosh
motion, such as wall wetting and peak slosh amplitude, and can be effectively used when details such as wave and
droplet breakup are not the critical elements under investigation.
III. Two-Dimensional Preliminary Slosh Baffle Effectiveness Studies Studies were performed to determine the effectiveness of various baffles placed in the container discussed above.
Figure 5 shows an example result with 3 different baffle sizes (large, medium, and small) at two different gravity
levels (g/g0=1, Bo=536,000 and g/g0=0.001, Bo=536). Water is patched in 25% of the domain and free flow is
induced by gravity at t=0. The fluid is then allowed to flow until the fluid motion completely settles.
g/g0=1, Bo = 536,00 g/g0=0.001, Bo = 536
Large baffle Medium baffle Small baffle Large baffle Medium baffle Small baffle
0.1 sec
0.5 sec
1 sec
2 sec
3 sec
4 sec
5 sec
Dow
nloa
ded
by F
LO
RID
A I
NST
ITU
TE
OF
TE
CH
NO
LO
GY
on
July
27,
201
4 | h
ttp://
arc.
aiaa
.org
| D
OI:
10.
2514
/6.2
008-
4750
5
American Institute of Aeronautics and Astronautics
10 sec
20 sec
30 sec
40 sec
50 sec
60 sec
Figure 5: Example of slosh using three different baffles sizes at two different gravity levels
Three metrics are used to qualitatively assess the performance of the slosh baffle in suppressing slosh motion: (1)
the peak height of wall wetting, (2) the peak height of bulk flow, which is defined as that on the inner side of the
slosh baffle, or the height of any flow that does not pass between the small gap between the slosh baffle and the tank
wall, and (3) the maximum fluid velocity in the domain, which also sets the maximum Weber number. For three-
dimensional studies a fourth metric is introduced, (4) percentage of wall coverage. A methodology was developed
which allowed the CFD results to be imported into analysis program to determine the peak location of any cell that
contains the fluid phase at any time step. Figure 6 shows an example of how the CFD result is interrogated.
• The case shown is for medium slosh baffle size, laminar
flow model, and g/g0=0.001 (Bo=536)
• Maximum height the fluid reaches which flows between
through the slosh baffle gap is 3.35 m and occurs 35 s.
• Bulk flow column of fluid reaches a height of 2.01 m.
• Bo = 536, Wemax = 699 (based on Vmax)
Figure 6: Methodology used to assess slosh baffle performance
Dow
nloa
ded
by F
LO
RID
A I
NST
ITU
TE
OF
TE
CH
NO
LO
GY
on
July
27,
201
4 | h
ttp://
arc.
aiaa
.org
| D
OI:
10.
2514
/6.2
008-
4750
6
American Institute of Aeronautics and Astronautics
Figure 7 shows the velocity vectors colored by velocity magnitude in a non-baffled tank at 1 second into the
simulation. The picture also shows the direction of slosh and the velocity with which it is travelling. Such data is
useful for optimizing the placement of the slosh baffle and for estimating its required structural integrity based on
the momentum of the incident fluid. Figure 8 shows the velocity vectors colored by velocity magnitude in a baffled
tank at 1 second. The difference in slosh behavior can be seen clearly; the baffles help in mitigating the amplitude of
the slosh wave and the peak location of the wall wetting. The fluid motion which tends to move towards the upper
region of tank is mitigated by the baffle and directed towards the lower middle region of tank. The high velocity
regions are in the middle region of the tank, which is major difference from a non-baffle case.
Figure 7: Velocity vectors colored by velocity
magnitude for a smooth tank, g/g0=1
Figure 8: Velocity vectors colored by the
velocity magnitude for Baffled tank, g/g0=1
An important aspect of this investigation is to compare the differences laminar and turbulent flow models.
Although the dynamics of low-gravity slosh take longer to develop, the resulting slosh can be just as violent as in
high gravity cases, see Figure 5. Figure 9 shows a sequence of 5 images, from 1 to 5 seconds, comparing the laminar
and turbulent flow models, applied at Earth gravity conditions (g/g0=1) using grid 2. A subtraction of the two images
to highlight the differences in the solution is shown in the bottom row.
1 sec 2 sec 3 sec 4 sec 5 sec
Laminar flow model, Bo = 536,000, Wemax = 1,748,121
Turbulent flow model, Bo = 536,000, Wemax = 1,338,405
Absolute difference between the laminar and turbulent flow models
Figure 9: Comparison of use of laminar versus turbulent flow solvers using grid 2, g/g0=1
Comparisons between the two models were performed and in all cases good qualitative agreement was
observed. These observations are consistent with slosh results employing laminar and turbulent models discussed in
[17], which are also conducted at Earth gravity. The results of this study demonstrate that similar agreement occurs
between laminar and turbulent models at low-gravity (g/g0=0.001) conditions, suggesting that if bulk motion is
Dow
nloa
ded
by F
LO
RID
A I
NST
ITU
TE
OF
TE
CH
NO
LO
GY
on
July
27,
201
4 | h
ttp://
arc.
aiaa
.org
| D
OI:
10.
2514
/6.2
008-
4750
7
American Institute of Aeronautics and Astronautics
being sought, the laminar model, which requires less computational time, is adequate. The details of droplet breakup
and free surface structure do show some differences between the two models, and for the conditions shown in Figure
9, the maximum velocity of fluid, and thus Weber number, is higher for the laminar flow model.
IV. Summary of Two-Dimensional Slosh Baffle Performance
Three different baffle sizes (large, medium, and small) at two different tank locations, both with and without a
gap between the baffle and the tank side wall were examined in this study. The large baffle has a width of 0.5 m, the
medium baffle 0.25 m, and the small baffle 0.125 m. The vertical location of the baffle is either at the middle of the
cylindrical section or at the bottom at the intersection with the elliptical end cap. The gap is 0.1 m, and the baffle
size does not change if a gap is introduced. Figure 10 shows several configurations considered in this study.
No Baffle
and Tank
Coordinate
System
L Baffle
H = -0.5
OD = 4
ID = 3
Gap = 0
L Baffle
H = 0
OD = 4
ID = 3
Gap = 0
L Baffle
H = -0.5
OD = 3.8
ID = 2.8
Gap = 0.1
L Baffle
H = 0
OD = 3.8
ID = 2.8
Gap = 0.1
M Baffle
H = -0.5
OD = 3.8
ID = 3.3
Gap = 0.1
S Baffle
H = -0.5
OD = 4
ID = 3.75
Gap = 0
S Baffle
H = 0
OD = 3.8
ID = 3.55
Gap = 0.1
Figure 10: Example of various baffle geometries
Table 1 summarizes the performance of various baffle configurations using the metrics discussed above and
shown in Figure 6. In the table OD and ID are the outer and inner diameter of the slosh baffle, gap is the space
between the baffle and tank wall, and H is the vertical location of the baffle along the cylindrical section of the tank.
Table 1: Summary of Two-Dimensional Slosh Baffle Performance
Baffle Geometry Parameters Fluid Dynamics Settings Metric CFD Results
Lam Size OD ID Gap H g/g0 Bo
Turb
Peak
Amp
Bulk
Peak Vmax Wemax
No Baffle 1 536,000 Lam NA 1.66 4.25 493,366
No Baffle 0.001 536 Lam NA 1.66 0.15 615
L 3.8 2.8 0.1 -0.5 1 536,000 Lam 1.43 -0.32 8 1,748,121
L 3.8 2.8 0.1 -0.5 0.001 536 Lam 1.64 -0.19 0.17 789
L 4 3 0 -0.5 1 536,000 Lam NA -0.01 8 1,748,121
L 4 3 0 -0.5 1 536,000 Turb NA -0.19 7.1 1,376,918
L 3.8 2.8 0.1 0 1 536,000 Lam 1.66 -0.06 5.75 903,082
L 3.8 2.8 0.1 0 1 536,000 Turb 1.46 -0.06 4.5 553,116
L 4 3 0 0 1 536,000 Lam NA -0.06 10 2,731,438
L 4 3 0 0 1 536,000 Turb NA -0.06 8.25 1,859,085
M 3.8 3.3 0.1 -0.5 1 536,000 Lam 1.48 0.35 6.75 1,244,512
M 3.8 3.3 0.1 -0.5 0.001 536 Lam 1.61 0.27 0.16 699
S 3.8 3.55 0.1 -0.5 1 536,000 Lam 1.35 1.1 4.25 493,366
S 3.8 3.55 0.1 -0.5 0.001 536 Lam 1.54 0.89 0.11 331
S 4 3.75 0 -0.5 1 536,000 Lam NA 1.48 5.5 826,260
S 4 3.75 0 -0.5 1 536,000 Turb NA 1.02 5.5 826,260
S 4 3.75 0 0 1 536,000 Lam NA 0.97 8 1,748,121
S 4 3.75 0 0 1 536,000 Turb NA 0.45 8.25 1,859,085
S 3.8 3.55 0.1 0 1 536,000 Lam 1.66 0.19 6.5 1,154,033
S 3.8 3.55 0.1 0 1 536,000 Turb 1.43 0.06 5.2 738,581
Dow
nloa
ded
by F
LO
RID
A I
NST
ITU
TE
OF
TE
CH
NO
LO
GY
on
July
27,
201
4 | h
ttp://
arc.
aiaa
.org
| D
OI:
10.
2514
/6.2
008-
4750
8
American Institute of Aeronautics and Astronautics
The large baffle geometry ensures that none of the bulk fluid rises above the centerline of the tank – or none of
the bulk fluid rises above the initial condition of the fluid. This is not true for either the medium or small slosh
baffles, and in these cases the bulk fluid reaches above the initial fluid height at the centerline of the tank. This is an
important result because it provides criteria for the size of the slosh baffle that will ensure that the bulk of the fluid
does not hit the upper dome of the tank. For the cases of no baffle, the bulk fluid reaches a height of 1.66 m, so all
baffles provide some mitigation of peak slosh height, with the large size being most effective for this simple
scenario. For the baffles with a gap between the baffle and tank side wall, irrespective of baffle size, the fluid tends
to flow to the top of the dome and forms a thin layer along the in side of the tank. Results between the laminar and
turbulent models are consistent and show minimal differences. For example, for the large slosh baffle with and
without a gap, the laminar results show 10-25% higher peak velocities and high peak slosh amplitude (when gap is
present), but the bulk fluid height is identical. Similar results are observed for the other baffle sizes with the laminar
model always exhibiting larger heights and velocities of slosh. Placing the slosh baffle in the lower portion of the
cylindrical section leads to lower velocities within the tank (the fluid travels a shorter distance before encountering
the baffle), however lower placement of the baffle is not as effective in minimizing the height of the bulk fluid.
From this study, assuming that the slosh baffles are rigid enough to withstand the fluid momentum, the placing of
the baffle in the center of the cylindrical section more effectively suppresses the bulk slosh motion.
V. Three-Dimensional, Laminar vs. Turbulent Flow Models, and Dynamic Mesh Modeling Studies
Another important component of this study is to determine how to extend the two-dimensional studies shown
above to a true three-dimensional simulation. Figure 11 provides an example of the 3D analog to the 2D simulation
of Figure 4. The metrics discussed above were used to assess baffle effectiveness along with percentage wall wetting
for the 3D cases. Baffle configurations were identified to minimize overall percentage of wall wetting.
0.1 sec 0.3 sec 0.7 sec 1.0 sec 2 sec 5 sec
Figure 11: Example 3D tank flow inside with an annular slosh baffle, g/g0=1, Bo = 536,000, Wemax = 437,030
An additional three-dimensional example is shown in Figure 12. The tank is a cylinder, which contains 3 slosh
baffles. Multiple baffle configurations have been examined but are not discussed in this paper.
0.02 sec 0.21 sec 0.41 sec 0.61 sec 0.71 sec 0.91 sec 1.11 sec
Figure 12: Simulation of flow inside a tank with 3 annular slosh baffles, g/g0=1, Bo = 1,205,793
Another important aspect of this investigation was to determine grid sensitivity, baffle performance, and Bond
number scaling when different fluids are used. The most important fluid to examine from a rocket propulsion
standpoint is cryogenic hydrogen, LH2, which has a density of 75.2 kg/m3 at 16 K, surface tension of 0.0026 N/m,
and a wall contact angle of 2 degrees. Figure 13 compares slosh behavior between water and LH2, over a 5 second
interval. The first row shows slosh of liquid water and the second row shows slosh of LH2 in a tank without baffles
at g=9.81 m/s2, and the behavior can be seen to be qualitatively different, which is due to the different density and
surface tension of the two fluids. In the third row of Figure 13 the gravity level was set to match the Bond number of
water from the first row, and as can be seen the results still show differences. It is likely that the physics of slosh in
these scenarios also depends on other parameters like viscosity and wall contact angle, and simple Bond number
scaling is not accurate between different fluids.
Dow
nloa
ded
by F
LO
RID
A I
NST
ITU
TE
OF
TE
CH
NO
LO
GY
on
July
27,
201
4 | h
ttp://
arc.
aiaa
.org
| D
OI:
10.
2514
/6.2
008-
4750
9
American Institute of Aeronautics and Astronautics
1 sec 2 sec 3 sec 4 sec 5 sec
Water, g=9.81 m/s2, Bo=536,00, wall contact angle = 55°, ρρρρ = 1000 kg/m
3, σσσσ = 0.073 N/m, µµµµ = 1.003E-03
LH2, g=9.81 m/s
2, Bo=1,077,406, wall contact angle = 2°, ρρρρ = 75.2 kg/m
3, σσσσ = 0.0026 N/m, µµµµ = 1.989e-05
LH2 g =4.722 m/s
2, Bo=540,000, wall contact angle = 2°, ρρρρ = 75.2 kg/m
3, σσσσ = 0.0026 N/m, µµµµ = 1.989e-05
Figure 13: Comparison between water and liquid hydrogen at similar Bond numbers
In the models developed above, there is no feedback of liquid forces on the motion of the tank; the tank is kept
rigidly still. Liquid sloshing behaviors in a moving fuel tank can be simulated by applying Dynamic Mesh model.
The dynamic mesh model is used to model flows where the shape of the domain is changing with time due to motion
on the domain boundaries. In certain cases, the tank motion can be defined as a prescribed, e.g., the tank is driven by
strong external forces such that the liquid motion feedback can be ignored. In a dynamic mesh model, this case can
be simulated by defining the linear and angular velocities about the center of gravity of the tank with time, and
liquid forces do not impact the tank’s trajectory. When fluid force feedback is enabled the tank’s motion is non-
prescribed, and subsequent liquid motion pushed back on the tank walls. For example, in the space, the motion of
the propellant contained in a vehicle’s tank may have a significant effect on the vehicle’s orientation. In the dynamic
mesh model the linear and angular velocities are determined from a force balance on the tank which is calculated by
6-DOF solver. An example of a tank whose motion is impacted by internal fluid forces is shown in Figure 14.
Figure 14: 2D half-filled box with 6-DOF movement in free space
As the diagram shows, a 2D box filled with half of water is moving in the free space. Initially this box has a
horizontal acceleration and an external force applied to the bottom. Since there is no constrained force acting on the
other surfaces, the box is free to translate and rotate in space. The box’s motion is calculated by combing the
acceleration and external force of the box as well as the water motion feedback.
VI. Conclusions This paper utilizes CFD to assess the performance of various slosh baffle configurations for spacecraft design. In
low-gravity fields, surface tension and capillary action may dominate even in large booster size tanks, and simple
Bond number scaling is not adequate. Key results from this investigation assessed the importance of grid resolution,
Dow
nloa
ded
by F
LO
RID
A I
NST
ITU
TE
OF
TE
CH
NO
LO
GY
on
July
27,
201
4 | h
ttp://
arc.
aiaa
.org
| D
OI:
10.
2514
/6.2
008-
4750
10
American Institute of Aeronautics and Astronautics
laminar versus turbulent flow models, and Bond number scaling between water and liquid hydrogen during low-
gravity conditions so that computation resources can be optimized. Metrics associated with maximum wall wetting
and bulk flow motion were developed for characterizing slosh baffle effectiveness and guidelines for comparing
various slosh scenarios. This work indicated that relatively coarse grids and laminar flow models can be used with
relatively good accuracy if a qualitative assessment of bulk fluid motion during slosh events is sought at both Earth
and low-gravity conditions. This result is fortuitous as computational times are reduced. This study also showed that
the models can be used to help determine a baffle geometry and location within the tank that should be employed to
minimize bulk fluid motion, as well as the effect of having a gap between the tank wall and the baffle. Three-
dimensional studies were performed and percentage internal tank wall wetting was used as an additional metric to
assess the performance of various baffle configurations.
Future work will take into account the effect of the weight-saving isogrid structure located on the internal surface
of many modern propellant tanks. Isogrid is a ribbed structure lining the inside a propellant tank, which provide the
same strength and toughness as a regular uniform material, with the advantage of reduced weight. Other analyses
will also include the effects of wall heating from solar radiation, as well as the effect of tank rotation about its
longitudinal axis for thermal conditioning. Rotation at low gravity conditions caused the bulk fluid inside the tank to
assuming a parabolic free-surface shape. Wall heating is critical because when cold propellant comes in contact with
a hot surface, boil off occurs tank pressure is increased and venting of useful propellant occurs.
VII. References 1. Abramson, H. N., The Dynamic Behavior of Liquids in Moving Containers," NASA-SP-106, 1966.
2. Abramson, H. N., et. al., Some studies of nonlinear lateral sloshing in rigid containers. NASA-CR-375, 1966.
3. Babskii, V. G., et. al., Hydromechanics of weightlessness. Izdatel'stvo Nauka , 504, 1976.
4. Best practices for the VOF Model. Ansys., 2006.
5. Dodge, F. T. et al.: "The new dynamic behavior of liquids in moving containers", Technical Report, Southwest
Research Institute, San Antonio, TX, 2000.
6. Dodge, F. T.: "Engineering study of flexible baffles for slosh suppression", NASA TR, Sep. 1, 1971.
7. Dodge, F. T.; Garza, L. R.: "Simulated low-gravity sloshing in spherical tanks and cylindrical tanks with
inverted ellipsoidal bottoms", NASA Technical Report, Feb. 1, 1968
8. Grayson, G. et. al., "Cryogenic Tank Modeling for the Saturn AS-203 Experiment", 42nd
AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 9-12 July 2006.
9. http://en.wikipedia.org/wiki/Image:Sts_et_cutaway.jpg
10. http://www.armadilloaerospace.com/n.x/Armadillo/Home/News?news_id=344
11. Ibrahim, R., A., Liquid Sloshing Dynamics: Theory and Applications. Cambridge University Press, © 2005.
12. Lamb, H., Hydrodynamics, Cambridge University Press, Cambridge, 7th ed., 1945.
13. Luppes, R., Helder, J. A. and Veldman, A.E.P.: "The Numerical Simulation Of Liquid Sloshing In
Microgravity", European Conference on Computational Fluid Dynamics, Delft, The Netherlands, 2006.
14. Miles, J. W., On the Sloshing of Liquid in a Cylindrical Tank," Tech. Rep. GM-TR-18, The Ramo-Woolridge
Corp. Guided Missile Research Div., April 1956.
15. Narimanov, G. S., Koruchaev, L. V., & Lukovskii, I. A. (1977). Nonlinear dynamics of liquid-containing flight
vehicles. Moscow: Izdatel'stvo Mashinostroenie.
16. NASA Technical Report "Slosh Suppression", NASA-SP 8031, May 1969.
17. Rhee, S. H., “Unstructured Grid Based Reynolds-Averaged Navier-Stokes Method for Liquid Tank Sloshing,”
Journal of Fluids of Engineering, Vol. 127, May 2005, p. 572-582.
18. Schlee,K., Gangadharan, S., Ristow, J., Sudermann,J., Walker, C., Hubert, C.: "Modeling and Parameter
Estimation of Spacecraft Fuel Slosh Mode", Proc. 2005 Winter Simulation Conference.
19. Stephens, D. G., Leonard, H. W., and Perry, T. W., Investigations of the damping of liquids in right-circular
cylindrical tanks, including the effects of time-variant liquid depth," TR., NASA, LaRC, 1962.
20. Veldman, A.E.P.: "The Simulation of Violent Free-Surface Dynamics At Sea And In Space", European
Conference on Computational Fluid Dynamics, Delft, The Netherlands, 2006.
21. Vreeburg, J. P. B.: "Spacecraft Maneuvers and Slosh Control, IEEE Control Systems Magazine, June 2005.
22. Vreeburg, Jan P.B. and Chato, David, "Models for Liquid Impact Onboard Sloshsat FLEVO", NASA Technical
Report NASA/TM—2000-210475, November 2000.
Dow
nloa
ded
by F
LO
RID
A I
NST
ITU
TE
OF
TE
CH
NO
LO
GY
on
July
27,
201
4 | h
ttp://
arc.
aiaa
.org
| D
OI:
10.
2514
/6.2
008-
4750
This article has been cited by:
1. H. Q. Yang, John Peugeot. 2014. Propellant Sloshing Parameter Extraction from Computational-Fluid-Dynamics Analysis.Journal of Spacecraft and Rockets 51:3, 908-916. [Abstract] [Full Text] [PDF] [PDF Plus]
Dow
nloa
ded
by F
LO
RID
A I
NST
ITU
TE
OF
TE
CH
NO
LO
GY
on
July
27,
201
4 | h
ttp://
arc.
aiaa
.org
| D
OI:
10.
2514
/6.2
008-
4750