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, chintals@fit.edu 2 Assistant Professor, Department of Mechanical and Aerospace Engineering, dkirk@fit.edu

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.

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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

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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

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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

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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

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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

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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

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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.

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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,

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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.

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