American Institute of Aeronautics and Astronautics

1

Enhanced Numerical Modeling in Simulation of a Generic

Propellant Tank Slosh Baffle

Sunil Chintalapati1, Joel M. Faure

2, Ran Zhou

3, Michael Vergalla

4, Daniel R. Kirk

5, and Héctor Gutiérrez

6

Florida Institute of Technology, Melbourne, Florida, 32901

The slosh dynamics in cryogenic fuel tanks under microgravity is a pressing problem that

severely affects the reliability of spacecraft launching. An accurate prediction of the slosh is

critical for successful mission planning and may influence vehicle control and positioning

during rendezvous, docking, and reorientation maneuvers. This paper defines a novel

method to assess this problem by coupling capabilities of ANSYS FLUENT and

MathWorks-MATLAB. While FLUENT solves the fluid dynamics aspect of problem,

MATLAB solves for dynamics part of motion profile and update CFD with new inputs every

new time step. Experiments performed on the Florida Tech 2-DOF motion table provided a

basis for validating the new method implemented in CFD simulation. Present work focuses

on enhancing the capabilities of CFD tool by reducing coding complexities due to inclusion

of 6-DOF dynamic mesh. The idea is to incorporate resulting forces and other multiple

inputs into FLUENT through MATLAB rather than a user defined function. MATLAB can

independently compute the force feedback due to fluid forces and tank motion and

incorporate it into simulation in the next incremental time-step.

Nomenclature

acv = Average cell volume, m3

Bo = Bond number, ratio of body to surface tension forces, gR2/

bh = Height of baffle relative to bottom of Tank, m

bt = Baffle thickness, m

bw = Baffle width, m

CFD = Computational Fluid Dynamics

Δt = time step

DOF = Degrees of Freedom

FLEVO = Facility for Liquid Experimentation and Verification in Orbit

g/g0 = Gravitational acceleration ratio relative to surface of Earth gravity 9.81 m/s²

NIST = National Institute of Standards and Technology

Re = Reynolds number, ratio of inertial to viscous forces, VD/

t = time, sec

Td = Tank diameter, m

Th = Tank height, m

tr = Computational run time

UDF = User designed function

VOF = Volume of Fluid

= Angular Velocity, rad/s

θ = Angular Orientation, rad

1 Undergraduate Research Assistant, Mechanical and Aerospace Engineering, 150 West University Blvd, Student Member AIAA. 2 Graduate Research Assistant, Mechanical and Aerospace Engineering, 150 West University Blvd, Senior Member AIAA. 3 Graduate Research Assistant, Mechanical and Aerospace Engineering, 150 West University Blvd, Student Member AIAA. 4 Graduate Research Assistant, Mechanical and Aerospace Engineering, 150 West University Blvd, Student Member AIAA. 5 Associate Professor, Mechanical and Aerospace Engineering, 150 West University Blvd, Senior Member AIAA. 6 Associate Professor, Mechanical and Aerospace Engineering, 150 West University Blvd.

46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit25 - 28 July 2010, Nashville, TN

AIAA 2010-6976

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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I. Introduction and Background

losh is a pressing problem for spacecraft stability and control. The motion of the vehicle may excite propellant

remaining inside a tank, and reaction forces and moments caused by slosh can degrade the pointing accuracy of

the system 18, 19

. 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 2.

Figure 1. Space Shuttle External Tank Slosh Baffle 9

Figure 2. Slosh baffle used by

Armadillo Aerospace 2

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

.

Numerical solution to slosh problem 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 used8, although very little work has been done in cases of very-low accelerations when the vehicle

is in space 16, 19

. 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 14, 16

,

and the development of an experimental framework to measure and characterize slosh under microgravity 19

.

Earlier published paper identifies the physics and criteria for evaluation of slosh baffle performance in regular

and microgravity 4. The paper used simple dam break profile to induce slosh and evaluate the baffle performance.

Advances in CFD have resulted in the ability of FLUENT to compute sloshing modes by a 6-DOF motion profile

with inclusion of a UDF. This was performed by slosh dynamics team at Florida Tech in development of a 6-DOF

dynamic mesh numerical model that is able to replicate slosh dynamics in regular gravity 17

. Advances have also

resulted in emergence of numerical solver like Flow-3D, oriented specifically for solving sloshing problems5.

Recent enhancements are multi-physics solver, capable of solving slosh coupled with force feedback from both bulk

fluid movements transferred to the vehicle and from the vehicle motion due to the engines. One such example would

be FLUENT solving for fluid dynamics aspect of the problem and ANSYS Mechanical solving for dynamics of

motion profile updated at every time-step based on both motion of the vehicle and sloshing forces from cryogens

inside the tank.

This paper utilizes computational fluid dynamics (CFD) to assess the performance of a generic propellant tank

baffle in low gravity condition. This is done by simulating a possible motion profile with arbitrary acceleration and

angular velocities, which would induce violent slosh inside the tank. This paper defines a new proof of concept, a

link between MATLAB and FLUENT1. This link is pertinent to enhance the modeling capabilities of CFD by

including complex motion profile and additional inputs including heat transfer, phase change, force feedback, etc.

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II. Experimental Setup

Florida Tech’s slosh platform has been in development for past couple of years. Since its inception, the design

has been constantly upgraded to keep discrepancies from creeping into experimentation. The goal of the slosh team

at Florida Tech is to reduce the redundancies that cannot be modeled in a CFD simulation, to have one to one

comparison between experiment and CFD. Figure 3 and Figure 4 shows the overview of the capabilities of slosh

platform. The platform is currently capable of 2-DOF, one being linear translation in x-axis (Figure 3) and other

being free rotation in y-axis (Figure 4). This paper focuses on validation of the linear translation motion along x-

axis, depicted on the left hand side of the picture.

Figure 3. Free Linear Translation Figure 4. Free Rotation Coupling

Data acquisition plays a pivotal role in slosh

experimentation because the assumptions that form

the input for CFD are derived from the experimental

results. The acceleration experienced by the tank and

captured by the accelerometers is used as the input

conditions for the CFD model. The other important

aspect of this work is image-capturing technique,

which plays an important part in comparing results

between experiment and CFD. The whole process of

initializing the experiment, data acquisition and

synchronized image capturing is controlled via

LabView and the data gathered is post processed in

MATLAB. Efforts are still in progress concerning

explicitly compare image data from experiments and

CFD. Preliminary results of which will be discussed

in the next section. Figure 5 shows the overall setup

for the motion table, data acquisition and the

experiment17

.

III. Computational Setup

Analysis for current paper used ANSYS FLUENT, version 12.11 for solving fluid dynamics aspect of the

problem. The 3D geometry was created and meshed using Gambit (version 2.4), preprocessor for FLUENT.

MathWorks-MATLAB15

implemented motion profile, some boundary conditions and post processing the results.

Sloshing in CFD is modeled using the VOF model. Transient Volume of the Fluid (VOF) method utilized 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 3. This section is

Figure 5. Motion Table Setup: Tank in Lighting

Control box, Work Station, Overview, LabView

instrumentation, and New Encoder Position Sensor

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divided into three major components between grid sensitivity studies, computational setup for ANSYS FLUENT,

and computational setup for MATLAB

A. Grid Sensitivity Studies

Grid sensitivity check is one of the most important verifications for any computational study. The importance of

computational results is not only dependent on assumptions made in the model but also depend on variation of

results with different mesh densities. The ideal grid balance is to capture accurate physics while keeping the number

of cells to a minimum; thereby, reducing computational run-time. A series of simulations performed on a generic

domain with exact initial conditions but varying node spacing yielded the criteria for grid spacing for this current

paper. 1 below displays the parameters involved in conducting the grid sensitivity studies.

Table 1. Grid Sensitivity Study Matrix

GRID SENSITIVITY STUDY MATRIX

Grid # Interval Size (m) Total Cells tr (mins) acv (m3) Mesh Type

1 0.05 9000 75 1.31E-04 structured

2 0.025 52800 160 2.23E-05 structured

3 0.1 1575 45 7.48E-04 structured

4 0.01 825000 1800 1.43E-06 structured

5 0.0325 24150 90 4.88E-05 structured

6 0.0125 422400 900 2.79E-06 structured

The Td is 1.0 m and the Th is 1.5 m, and the

overall tank volume is 1.1775 m3. Coarse and fine

versions of initial node spacing provided results of

grid dependency of solution. Dam break model in

earth’s gravity was preferred because it would induce

vigorous slosh in the simulation. A simulation where

the column of fluid is patched and at time equals zero

is allowed to slosh freely in domain (see Figure 6).

Realizable k-epsilon (two equation turbulence) model

is used due to the violent slosh induced in this

simulation (Re is determined by Td and velocity of

the fluid interface). Properties of water at 297.15K

are taken from NIST13

and earth’s gravity is

9.81m/s2. The wall contact angle is 55 degrees

4.

Capillary effects are small due the gravity being a

dominant factor and thus Bo would be large in

magnitude.

Two methods were determined to assess the impact of grid on the solution. One is setting up pressure and phase

monitors at predefined locations in tank and other being comparing fluid interface at certain time with the help of

MATLAB. Three monitors were set up in domain before the start of simulation. Location of three monitors were set

on the interface of the column of water on and shown in Figure 6. The monitors were to ascertain the static pressure

and interface of the fluid.

Figure 7 shows the results of pressure monitors at location 1 for the different mesh densities considered. The

overall trend follows a similar pattern based on the same initial conditions and location of the monitor. The

difference in results due to mesh density is visible by overlap of data lines (picture on right in Figure 7). The results

from this plots show that data lines from Grid4 and Grid6 overlap each other and hence the results are grid

independent.

Figure 6. Location of monitor in grid study domain

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Pressure vs. time at location 1 Close up of drop of pressure

Figure 7. Plot of pressure monitor at location 1

Figure 8 shows the plot of phase monitor with flow time. This monitor is a measure to track the fluid interface as

the flow passes through the monitor. Fluid interface has no units. At zero, the cell is completely air and at one, it is

completely water. At value 0.5 in phase panel in FLUENT determines the fluid interface. The plot on the left shows

the interface tracking by the monitor while the plot on the right shows the peak of the fluid interface. It is

determined from the plot that Grid4 and Grid 6 are still the best mesh densities to capture fluid interface.

Fluid interface vs. time at location 1 Close up of a spike in plot

Figure 8. Plot of fluid interface monitor at location 1

The third step followed in grid sensitivity check is looking at the overall fluid interface in the domain, since fluid

interface is a primary form of comparing experiments and CFD. A planar slice oriented towards the movement of

initial fluid interface is compared numerically with other mesh densities. Figure 9 shows the resulting difference due

to different mesh densities, performed in MATLAB. Series of picture on top are from grid 6 and series of picture in

the middle column are from grid 5. The last column is the difference between the two grids. The region of complete

black has no difference, but region of green color is the region where the actual difference between the two grid

exists. This technique was used for all the mesh densities considered; Figure 9 shows a typical comparison of fluid

interface between two different grids.

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Grid 6

Grid 5

Difference

0.00 sec 0.50 sec 1.00 sec 1.50 sec 2.00 sec 2.50 sec 3.00 sec t

Figure 9. Numerical difference between Grid6 and Grid5

B. CFD Setup

All tank geometries created and meshed in Gambit, version 2.4. A structured O-grid scheme used in all tank

constructed with node spacing determined from grid sensitivity studies. The mesh was then imported into ANSYS

FLUENT. Pressure based, double precision, transient VOF model used in CFD. Second order discretization was

preferred for momentum and geo-construct scheme for fluid interface. Fluid is patched accordingly in domain with

respect to the problem being analyzed. Table 2 gives the dimensions and statistics for all domains used in this paper.

The required cell volume and node spacing criteria deviates from the grid resolution study for experimental tank due

to the need to validate the CFD method used in this paper. In earth’s gravity, sloshing cause wide spread fluid

splatter, droplets and highly chaotic fluid interface; thus, needs a lot of grid resolution to capture fluid splatter and

random droplets. The grid resolution for microgravity case is less dense due to the fact that fluid tends to be more

viscous, fluid splatter is minimal and thus the droplets in model not taken into consideration. The concern is more

for the bulk fluid capture which all three-grid resolution are adequate to capture and save computational run time at

the same time. Note that generic propellant tank has two baffles and thus two dimensions are noted in the third

column of Table 2.

Table 2. Domain dimensions and statistics

Grid Td (m) Th (m) bh (m) bt (m) bw (m) # cells acv (m3) Type

Grid-study-domain 1 1.5 na na na 422400 2.79E-06 structured

Experimental Tank 0.2413 0.2413 0.138 0.011176 0.01905 411110 2.68E-08 structured

Microgravity Tank 5 4 0.9 0.1 0.3

913176 6.18E-05 structured 1.9 0.1 0.3

Figure 10 shows the initial conditions for the three domains given in Table 2. The picture on left is the domain

for the grid sensitivity study; the picture in middle is the domain of the experimental tank with an initial water patch;

the picture on the right is a generic propellant tank based on a Delta IV Heavy upper stage LH2 tank with an initial

cryogen patch.

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Domain for grid sensitivity

study with initial water patch

Domain of experimental tank

with initial water patch

Generic propellant tank with

initial cryogen patch

Figure 10. Domain overview

C. MATLAB Setup

The MATLAB-FLUENT link allows users to call FLUENT as a function, change the necessary input conditions

in FLUENT, and output results that can be used for various solutions in MATLAB. The current uses for this link

are: high fidelity rocket simulations, slosh dynamics, and automation routines for determining the aerodynamic

characteristics of external flows with the use of neural networks to optimize convergence. The raw experimental

acceleration data is imported in MATLAB, then filtered and stored as an array. A loop iterates time from 1e-3

seconds (Δt) to 10 seconds of experiment time in increments of 1e-3 seconds. The stored acceleration array is

linearly interpolated as a function of time and inputted into the MATLAB-FLUENT link for every time-step. Once

convergence criteria has been met in FLUENT all relevant data is saved, MATLAB then moves onto the next time

step and repeats the process until the loop ends.

IV. Experimental and Computational Results

The time for experimental and CFD simulation was set to 10 seconds. A motion profile for experimental tank

was set and the experimental acceleration data output from all accelerometers used as tank motion profile input for

CFD simulation. Figure 12 shows the motion profile for the CFD simulation recorded by accelerometers from the

experimental tank.

Figure 13 shows liquid surface contours of simulation results compared with liquid surface motion pictures

captured by the cameras. A black surface enclosure is set around the experiment table to disregard any background

disturbance to fluid interface in experiment. A bright light used for illumination of fluid from the bottom of cylinder,

helps in identifying the thickness of gradient of slosh waves. 1e-03 was the Δt used in simulation resulting in 10,000

time-steps. The tr was approximately 136 hours on a six core i7 (3.6 GHz processors) and the two additional cores

were used for MATLAB and post processing data. Saved case and data files from CFD are post processed with

automated journal in FLUENT 12.1.

Automation procedure for getting pictures alone resulted in 6-7 hours of computational time on a single 3.6 GHz

core machine. The image results from FLUENT lacks the sharp crisp quality compared to other professional post

processing software’s (Tecplot, CFD-Post), which is regrettable; but they serve the purpose here. Special note to the

kink in the middle of the tank (in Figure 13) that was unavoidable during rendering process in FLUENT. The

pictures from CFD were extrapolated using an automated journal file and hence the all the CFD pictures are aligned

to positive x-axis or slightly towards x-axis. In comparison to experiment pictures which have a slight angle noted

by the cross-wires on the top surface of tank.

Figure 11 shows the sample of the quantitative analysis done on the sample of results from experiment and CFD.

Three metric are defined to assess the difference between experiment and CFD. They are peak height: which is the

height of the peak of the wave at certain time. Axis height: which is the height of the fluid on the center axis of tank

and Wetted wall: which is height of the fluid on the corner of the tank. Sample results on the top (1.9 second) are

from one of worst comparable sample. The experiment slice has two peaks while the CFD slice has only one bulk

peak. Thus, the difference for the missing second bulk peak comes to about 19%, but on comparison to the peak

below, the difference comes to 4%. Note this is one such sample where the difference between CFD and experiment

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was at its maximum. Comparison with a good case at 3.9 seconds, the difference between peak height is around 4%,

while axis height is around 3% and the wetted wall comes to around 3% too.

TYPE EXP(in) CFD(in) Difference (%)

Axis height 8.79 7.13 18.92

7.36 7.13 3.23

Peak height 8.71 7.69 11.69

7.39 7.69 -4.09

Wetted wall 1.48 1.43 3.64

Evaluation of results from CFD and Experiment at 1.9 sec

TYPE EXP(in) CFD(in) Difference(%)

Axis height 6.91 6.72 2.75

Peak height 8.11 7.79 3.95

Wetted wall 1.00 0.97 2.63

Evaluation of results from CFD and Experiment at 3.9 sec

Figure 11. Quantitative analysis of results from experiment and CFD

As seen in Figure 13, the series of pictures show the results obtained from the experiment and CFD. The bulk

fluid behavior and fluid interface in general agree very well with each other. There are some slight discontinuities in

some slices of simulation; for example, the height of slosh wave obtained in CFD at 1.6 sec is slightly lower than

experimental slice at the same time. The slice at 1.85 second shows the overall bulk fluid motion capture after the

wave hits the baffle. Experiment at this point of time shows a response wave of bulk fluid peak with a partial second

peak on top of the bulk fluid with relatively less fluid. In CFD, we see that the response wave is compromised of

bulk peak with relatively less splatter. Experimental slices 1.3, 2.1, 2.2, 2.9, 6.4 and 6.9 seconds shown in the above

figure agree well with CFD, especially 3.9 where CFD is able to capture the little distinctive hump on the slosh

wave in the experiment.

The assumptions that go into CFD are precise than assumption and discrepancies that might creep into

experiments. The goal of this paper is not to accurately match experiment with CFD but rather create a foundation

for simple modeling enhancements to provide overall accurate answers to the slosh problem.

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Figure 12. Input motion profile for CFD simulation

A: t=1.3 sec B: t=1.6 sec

C: t=1.9 sec D: t=2.1 sec

E: t=2.5 sec F: t=2.9 sec

G: t=3.6 sec H: t=3.9 sec

I: t=6.4 sec J: t=8.8 sec

Figure 13. Bulk fluid and interface comparison between experiment and CFD

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V. Slosh Baffle Performance in Microgravity

Results from the experiment and CFD are in good agreement with each other for bulk motion and fluid interface.

This prompted the need to expand on the capabilities of enhancing the capabilities of modeling slosh baffle

performance in microgravity conditions using the UCAT-FLUENT link. One such simulation was identified to

provide a sample for the capabilities of this new method.

A. Simulation #1

The first simulation is a motion profile in microgravity with tank spinning and moving from a location to

another. The domain tank used in this simulation is based on Delta IV heavy LH2 tank (5 m diameter). The picture

on extreme right in Figure 10 shows the domain used in microgravity simulation. A moving reference frame model

was used on FLUENT side to accomplish this task. The principle behind the model is given by excerpt below, The principal reason for employing a moving reference frame is to render a problem, which is unsteady in the stationary

(inertial) frame steady with respect to the moving frame. For a steadily rotating frame (i.e., the rotational speed is

constant), it is possible to transform the equations of fluid motion to the rotating frame such that steady-state solutions are

possible1.

Simulation time was combination of two

assumptions. The motion profile implemented by

MATLAB for the first 30 seconds of simulation,

followed by a period of no motion input where the

fluid is allowed to re-orient itself in microgravity

condition. The computational run-time was massive

owing to the nature of the problem.

The angular velocity vector inside FLUENT is in

the inertial frame. In order to get slosh inside the tank

it is necessary to induce a jerking motion. The current

model accomplishes this by placing the tank on a

rotating frame and having variable angular

acceleration. The initial position of the tank is along

the -Y-axis in the inertial frame, the tank rotates along

the Z-axis in a counter-clockwise direction (for the

first angular velocity component). The tank’s

rotational motion along the inertial frame begins to

decelerate after it has reached the positive X-axis it

decelerates to zero angular velocity in one second. The

angular velocity is split up into two components time

varying angular velocity along the ―Z-axis‖ in the

inertial frame and a constant angular velocity along the

―y’-axis‖ in the body frame, both as seen in Figure 14

FLUENT requires the angular velocity inputs in the following form: magnitude, and unit vector in the inertial

frame. The second angular velocity component needs to transform to the inertial vector as seen in Eq. 110

.

1

12

12

1

1

2

1

211

11

1

21 cos

sin

0

cos

sin

0

0

0

0

100

0cossin

0sincos

0

0

(1)

Qualitative results of this simulation are shown below in Figure 15 with flow time in simulation. Orientations of the

pictures are different and are not on same axis. Fluid used is liquid hydrogen and gaseous hydrogen forms the other

phase. Laminar flow model is used, based on the Reynolds number with diameter of tank as length. Hydrogen

properties taken from NIST considered are at 18 K and 21 K12

. Gravity is 0.00981m/s2

in negative Y direction and

the wall contact angle is 2 degrees4. Surface tension is 0.0019N/m

7. The effect of Bond number on the outcome of

the slosh is more dominant in a microgravity environment. The tr for the current simulation at 27 seconds is 15 days

on a six-core machine. Present results shows the motion profile input re-orients the fluid towards the upper region of

Figure 14. Inertial and body coordinate frames

for Simulation #1

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tank, thus prompting the need to have a delicate maneuvering of tank. A slow and stable motion profile would not

impart significant momentum to the interior fluid. The latter half of simulation showing the liquid re-orientation is

unavailable at this moment owing to the immense amount computational time needed for current simulation;

therefore, the results from latter half will be presented at the conference. The implementation of complex motion

profile through MATLAB was successful, demonstrating the link between ANSYS FLUENT and MATLAB and

enhancement in numerical modeling.

10 sec 15 sec

20 sec 25 sec 30 sec ( end of motion profile)

Contours of Liquid Hydrogen

Figure 15. Motion profile (including angular and rotational components) in microgravity environment

VI. Conclusion

This paper utilizes the capabilities of ANSYS FLUENT and MATLAB to implement motion profiles into tanks

and to assess the performance of slosh baffle in microgravity. Importance of grid resolution study is emphasized;

methods to find the critical balance between grid independent results and lower cell count are charted out.

Validations of enhancement provided by the link are successful against ground slosh experiments. The bulk fluid

behavior and fluid interface results from the validation case agreed well with the experiment case. Although the

author regrets the rendering capabilities of ANSYS FLUENT, it still does not negate the fact the results provided by

the simulation are outstanding. Performance of a generic propellant tank with slosh baffles and the ability of the

UCAT-FLUENT link are put to test in a typical maneuver applicable for an orbital insertion. Input magnitude of

acceleration and velocities in simulation are exaggerated, to induce immense sloshing mode. Implementation of

motion profile through the link is successful.

The motivation for this work is not only to prove the link between MATLAB and ANSYS FLUENT, but also to

open number of enhancements this link could provide. A typical UDF has its own limitation; namely, only able to

triggering one specific enhancements in a simulation. UDF also needs an understanding of C++ code tailored to

ANSYS standards and lack parallelization in most instances.

Future work will take into account the possibility of adding a neural network component that could potentially

stabilize and control the simulation in real time. This could also lead to huge saving in computational run time by

modifying time-step size based on Courant–Friedrichs–Lewy condition (Courant number).

Acknowledgments

The authors wish to thank Dr. Paul Schallhorn and Laurie Walls of NASA John F. Kennedy Space Center

Launch Services Program for supporting this research effort.

The authors wish to thank Mr. Hao Jiang (Graduate research assistant) for checking the dynamics calculation for

microgravity case. The authors also wish to thank the exceptional undergraduate team (Amber Wright, Brittany

Essink, Namrata Dhingreja, Nicholas Pennington, and Richard Schul) for their assistance during the experiment on

2-DOF motion table.

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