Experimental Investigation and CFD Simulation of Active Damping Mechanisms

for Propellant Slosh in Spacecraft and Launch Vehicles

Dhawal Leuva

Graduate Student, Aerospace Engineering, Embry Riddle Aeronautical University

Daytona Beach, Florida 32114

Priya Sathyanarayan

Student Research Assistant, Mechanical Engineering, Embry Riddle Aeronautical University

International Baccalaureate Program, Spruce Creek High School, Daytona Beach, Florida 32114

Deepak Sathyanarayan

Student Research Assistant, Bio-Medical Engineering, Duke University

Durham, North Carolina 27708

and

Sathya Gangadharan

Professor, Mechanical Engineering, Embry Riddle Aeronautical University

Daytona Beach, Florida 32114

ABSTRACT

Violent motion of propellant in the tank due to inertial forces

transferred from actions like stage separation and trajectory

correction is termed as propellant slosh. If unchecked,

propellant slosh can reach resonance and lead to complete loss

of the stability of spacecraft, change the trajectory or increase

consumption of propellant from the calculated requirements,

thereby causing starvation of the latter stages. A spherical tank

modeled for CFD simulation in ANSYS CFX software package

considers free surface of the propellant exposed to atmospheric

pressure. The propellant is hydrazine. Hydrazine being toxic

and its properties being close to that of water, water is used as

propellant for experimental study. For close comparison of the

data, water is chosen as propellant in CFD simulation. The

research is done in three phases. First phase is modeling of CFD

simulation and validation of model by comparison to previous

experimental results. Second phase is developing a damping

mechanism and simulating the behavior by FSI model. Third

phase is experimental development of damping mechanism and

comparing the FSI simulation and experimental results. Various

passive damping devices (diaphragm and baffles) and active

damping device (frequency control) are compared in terms of

their effectiveness in damping of fuel slosh.

I. INTRODUCTION

For spin stabilized spacecraft, unwanted vibrations lead to

propellant slosh [1]. Energy dissipation of this propellant slosh

is difficult. This energy causes nutation of spacecraft about its

spin axis [2, 3]. For non-spinning spacecraft, actions like

trajectory control and stage separation induced propellant slosh.

Sloshing is of two types. First type is small amplitude sloshing

caused by transient excitation so the amplitude is small with

well-defined oscillation frequency. It is the function of gravity,

tank shape and propellant fill level in the tank [4]. Second type

of sloshing is large amplitude sloshing caused during main

engine ignition and burnout, the waves begin to break and

oscillations become erratic in large amplitude sloshing.

When slosh waves are allowed to freely oscillate, they have a

tendency to reach resonance. At resonance, slosh waves have

maximum amplitude. The forces of sloshing propellant cause

the spacecraft to nutate about its spin axis. Traditional vector

correction methods are used to correct the nutation, but high

frequency of direction change and high magnitude of sloshing

propellant forces quickly overpower the corrections being made

and sometimes results in more nutation and complete loss of

spacecraft.

To prevent sloshing, presently many passive damping devices

are being used. These passive damping devices (diaphragms and

baffles) provide excellent propellant slosh damping for a small

range of frequency and small amplitude of sloshing, but they are

not effective when propellant fill level changes and sloshing

frequency is outside their design range. These devices are

bulky, consume space, add significant weight, have small

operation range and requires extensive testing [5]. Active

damping devices are developed to overcome the disadvantages

of passive damping devices. Active damping devices work for a

wide range of amplitude and frequencies and for all the

propellant fill level in the tanks.

An active damping device consist a device that can generate

high frequency small amplitude waves with opposite phase to

that of sloshing waves. The ultimate goal for active damping

device development research is to make an automated device

with a feedback loop that can measure tank fill level, amplitude

and frequency of propellant slosh in real time and apply

required input of amplitude and frequency of damping waves to

quickly stop propellant sloshing [6].

II. APPROACH

CFD Theory

Computational Fluid Dynamics (CFD) is used to model the

propellant slosh behavior. The CFD method solves Navier

Stokes equations at required points in the fluid domain to get

the properties of the fluid flow at those points. Simple CFD

problems were solved analytically, but with increase in fluid

flow complexity, mathematical complexity increases

exponentially. With the advancement of computers since 1950s,

with powerful graphics and 3D interactive capability, use of

CFD has gone beyond research and into industry as a design

tool. Experiments can give macro data at certain points in the

flow field, but with CFD, flow field can be resolved to details

like turbulence, viscous forces and velocity. All this makes

CFD an essential and useful tool for complex flows like

propellant slosh.

CFD is solution of Navier Stokes equations. Navier Stokes

equations are set of partial differential equations describing

processes of momentum and heat and mass transfer. These

equations have no known general analytical solution, but can be

solved numerically by discretization. The four Navier Stokes

equations are: x-momentum, y-momentum, z-momentum and

continuity equation respectively shown below in their

conservation cartesian coordinate form.

�(��)

��+ ∇. (��) = −

��

��+����

��+����

��+����

��+ ��� ……………(1)

�(��)

��+ ∇. (��) = −

��

��+����

��+����

��+����

��+ ���……………(2)

�(��)

��+ ∇. (��) = −

��

��+����

��+����

��+����

��+ ��� ……………(3)

��

��+∇. (�) = 0……………(4)

CFD applies these equations across a discretized domain. This

process is called discretization. These equations are solved

numerically using finite volume technique (explained in

ANSYS CFX Theory) and further discretization makes CFD

method at best an approximation to the exact solution. Though

being an approximation, CFD gives an accurate understanding

of the flow process and is known to give exceptional results.

Apart from using Navier Stokes equations, free surface

problems like propellant slosh pose an additional difficulty of

tracking free surface, clearly defining the boundary of the

different phase fluids. All the CFD software use Volume of

Fluid (VOF) model to track velocity, location and shape of the

free surface between different phases of fluids.

Finite volume technique used to solve Navier Stokes equation

stores the values of all the properties like velocity, pressure,

density, temperature and volume fraction of the fluid at center

of each control volume. VOF model extracts the volume

fraction data at each control volume to determine the shape and

location of the free surface.

Volume fraction, as the name suggests is the ratio between the

volumes of the two fluids at each control volume. For the case

of water and air, if the volume fraction of water is 1 at the

control volume, means control volume is completely filled with

water. If the volume fraction of water at a control volume is 0.5,

means 50 percent of the control volume is filled with water and

the other 50 percent is filled with air (Figure 1). If the volume

fraction of water at a control volume is 0, means that control

volume does not contain water but at the same time the volume

fraction of air at that control volume will be one. In short, for

any fluid system such as air-water fluid system, the summation

of individual volume fractions of air and water at each control

volume should equal to 1.

Figure 1. Volume fraction distribution, volume fraction of air is 0.5

and volume fraction of water is 0.5.

Solution of volume fraction conservation equation defined by

Hirt and Nichols [6] is used in tracking of the free surface

throughout the volume

��

��+ �

��

��+

��

��+ �

��

��= 0……………(5)

The function F in the above equation represents volume fraction

at each control volume. The range of function F is 0 ≤ F ≤ 1 as

discussed above. Finding the location of free surface does not

solve the problem completely since still the orientation of the

free surface is unknown (Figure 2). The three diagrams (Figure

2) show the simplest possibility of the orientation of the free

surface. VOF technique uses the gradient of volume fraction at

each control volume across the free surface to determine the

slope of the free surface and there by the orientation of the free

surface over the entire control volume can be known and

plotted.

Figure 2. Free surface orientation for 0.5 volume fraction

Propellant slosh is a transient process. The slosh waves changes

with time, with the change in slosh waves, the forces acting on

the wall of the tank changes. Simulation of such problems is

done by breaking the duration of entire simulation run into

small time segments known as time steps in CFD software. The

size of the time step is chosen depending on the velocity of the

propellant slosh. For this research, usually the entire time for

the simulation including time for tank excitation and time for

natural damping of slosh waves took 10 seconds. If the time

step of 0.1 second is selected, the simulation fails since for this

time step the velocity of the slosh wave is very high and the

solution diverges. After careful analysis, time step of 0.01

second is chosen which gives sufficient convergence of the

solution and accuracy. Size of the time step depends on the

mesh size and the change in the velocity between the time step.

Finer the mesh, bigger the time step. Meaning, 0.1 second time

step can work for propellant slosh if the mesh used is fine. But

on the other hand finer mesh means more calculation time

without improving quality of the result. Also for the educational

versions of CFD software, there is a limitation of number of

nodes that can be used for simulation, hence for this research

time step size is reduced instead of having finer mesh.

Forces acting on the tank wall are plotted against time. These

results require further analysis to extract natural frequency.

ANSYS CFX Theory

Navier Stokes equations can be solved numerically using

various techniques. Finite volume technique is one of the most

commonly used methods for the solution of these equations and

ANSYS CFX also uses this technique. In finite volume

technique, the flow field is divided into sub-regions called

control volume. The above mentioned discretized Navier Stokes

equations are solved numerically over the control volume. Thus

approximate values of the variables are calculated throughout

the domain at specific points to form full flow characteristic.

ANSYS CFX converts Navier Stokes equations into integral

form over each control volume. Gauss’s Divergence Theorem is

used to convert these integrals with divergent and gradient

operators into surface and volume integrals which are further

discretized and converted to linearized equations and assembled

into a solution matrix and solved using First or Second order

Backward Euler Schemes [6].

CFD Simulation

Figure 3. Flowchart showing CFD simulation process

In ANSYS CFX, the simulation process is split into four steps:

1. Creating geometry and mesh

2. Defining the physics of the problem

3. Solving the CFD problem

4. Analyzing the result in post processor

An axisymmetric model of a spherical tank with a cut opening

at the top of the tank is generated in CATIA. Pointwise software

is used to generate mesh. ANSYS CFX and ANSYS

Workbench software package are used for CFD simulations,

FSI simulations and for result interpretation respectively.

The spherical tank is 12.9 inches in diameter. The diameter is

chosen to confirm with the tank diameter used for experiment to

validate the preliminary free surface sloshing model simulated

in ANSYS CFX. These experiments were performed in a

spherical tank which had opening at the top, exposed to

atmospheric pressure and temperature. The preliminary CFD

model is generated to closely match those conditions. The tank

is excited laterally for amplitudes ranging from 3 millimeter to

3 centimeter. Lateral excitation amplitude is chosen to prevent

spillage of propellant form the tank top. Usually hydrazine is

used as propellant in rockets. Since hydrazine is toxic and has

physical properties similar to water, water was used as

propellant in experimental analysis. To confirm CFD

simulation results closely to experimental data, CFD model is

developed using water as propellant. Also, it has been proven

by experiments that at 60 percent tank fill level, amplitude of

the sloshing waves are maximum. So all CFD models and

subsequent experiments are performed with 60 percent tank fill

level. The simulation is done for 10 second with 0.01 time step

size.

The active damping device being simulated presently consist a

thin flexible membrane at the bottom of the tank. The

membrane is moved by plunger mechanism. The frequency of

the membrane can be controlled manually. This model is for

FSI simulation. For FSI simulation, ANSYS mechanical is

coupled with ANSYS CFX. The tank is first simulated to

oscillate laterally for 3 second and generate sloshing waves at

natural frequency, the oscillation of the tank stops at 3 second

and the vertical oscillation of the flexible membrane will being

at very high frequency of 13.5 hertz. This FSI simulation is

being done for 10 second with time step size of 0.01s.

Experimental Testing

The Embry-Riddle Aeronautical University Fuel Slosh Test

Facility has a pre-existing experimental set-up to test lateral fuel

slosh. The experimental rig, seen in Figure 4, is an adjustable

force-balance fixture which rests atop a single-axis linear

actuator. An adjustable rotary scroll allows for the experimental

set-up to accommodate a variety of different tank shapes and

sizes. However, in keeping with the purpose of the experiment,

the experimental set-up used in this research will be exactly the

same as in past tests.

The fuel tank will be made of standard polycarbonate and will

measure 12 inches in diameter. All test cases will use this fuel

tank. The research will also include four standard diaphragm

shapes used in current spacecraft fuel tanks, the crater-shape,

the mountain-shape, the yin-yang-shape and the high-ridge-

shape. Instead of a flexible, rubber-like diaphragm, the new

diaphragm will be a rigid, metallic diaphragm. In order to

eliminate the costly manufacturing of the metallic diaphragm,

an alternative diaphragm will be used to simulate a metallic

diaphragm. All four metallic diaphragm geometries will be

manufactured using machine-molded foam profiles cut from a

three axis CNC surface router. The molds will then be coated in

fiberglass to give the geometries rigid, metallic-like properties.

Continuing to follow past research methods, a liquid propellant

fill level of 60% will be used as this is the fill level of greatest

interest to researchers. It is at this fill level that the fluid slosh

imparts the highest forces on the sidewalls of the tank and the

diaphragm.[5] Liquid Hydrazine is a common spacecraft

propellant which is highly flammable and toxic and not suitable

to store in the lab or use in the experiment. Therefore, a non-

hazardous substitute, water, will be used. Water has similar

density and viscous properties to liquid Hydrazine which make

this an acceptable substitution.

Data from experimental tests will be acquired via six dynamic

load cells mounted in equal intervals around the center-line of

the fuel tank. These six load cells will resolve the forces and

moments in the radial, tangential and vertical directions. The

load cells will transmit the data through a six channel signal

amplifier and conditioner where they are filtered, amplified and

transmitted to the data acquisition system, LabVIEW.

LabVIEW outputs the data into six frequency vs. time graphs to

represent the 3 forces and moments from the load cells.

III. RESULTS AND DISCUSSION

Resonant Frequency

The resonant frequency of the slosh is found by performing a

frequency sweep from 3.75 Hz to 6.75 Hz. The Figure 5

illustrates the experimental frequency sweep performed to

determine the resonant frequency.

Figure 5. Frequency sweep performed to determine resonant

frequency of sloshing liquid.

Figure 6 shows the CFD results obtained by simulation of free

surface slosh. Tank is excited for 8 seconds to determine natural

frequency trend. The model for free surface slosh is shown in

Figure 7.

Figure 6. CFD results showing the force response characteristics.

To experimentally determine the physical effects the active

damping mechanism posed on the dynamic behavior of the

propellant tank, a model tank was mounted on a linear actuator

and excited at various frequencies’ to excite the liquid inside

and cause the fuel to slosh. To conclude on the damping

effectiveness of the active damping mechanism and understand

how this mechanism compares to passive types of Propellant

Management Devices (PMD’s) that are currently in use, four

different tests were run. The first test acted as a control, this test

consisted of the model propellant tank being excited with no

PMD implemented, this type of tank is known as a bare tank.

The test provided the settling time of the liquid within the tank

when no internal force or structure was present. For validation

purposes, the model propellant tank was filled to approximately

-1.00E-02

-8.00E-03

-6.00E-03

-4.00E-03

-2.00E-03

0.00E+00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

0 500 1000 1500 2000

Fo

rce

(P

ou

nd

s)

TimestepsTangential Force on Wall (X) Tangential Force on Wall (Y)

Tangential Force on Wall (Z)

Diaphragm

Load Cells

Adjustable

Rotary Scroll

Figure 4. Fuel slosh experimental test facility at Embry-Riddle

Aeronautical University.

Tank

Actuator

60% maximum capacity. This fill level was maintained

throughout all of the testing (Figure 8).

The second and third tests were performed exactly like the

control test except a certain type of passive PMD was installed

within the tank. The two types of PMD’s used were an

elastomeric diaphragm (Figure 9) and a rigid baffle (Figure 10).

These structures remain stationary within the tank and provide a

barrier to the liquid to minimize the sloshing distance the liquid

can travel; thus minimizing the total amount of force the liquid

can pose within the system.

The fourth and final test was performed the same as the first

three, however, in this instance the active damping mechanism

was placed within the tank. The active damping mechanism

proved to significantly dampen the liquid (Figure 11). The

results of all four tests illustrate the settling time for each test.

Figure 7. CFD simulation model and experimental setup

representing the free surface slosh in the tank.

Figure 8. Experimental results of control test performed on bare

propellant tank configuration.

Figure 9. Experimental results depicting settling time of diaphragm

implemented experimental setup.

Figure 10. Experimental results of tests performed on propellant

tank with baffle implemented.

Figure 11. Experimental results gathered from active damping

experimental procedures.

IV. CONCLUSION

Based on the experimental data, the active damping mechanism

provided a settling time that fell closely between that of the two

commonly used PMD’s. As expected the diaphragm was the

most effective, with a settling time of approximately 1.25

seconds, it dampened the liquid slosh quicker than any of the

other PMD’s. However, the active damping mechanism

provided a settling time of approximately 4.8 seconds that is 0.4

seconds quicker than the baffle. While the active damping

mechanism proved to provide less damping than the diaphragm,

it did prove to provide more damping than the baffle. These

results show that the theory of active damping is, indeed, valid.

It is important to note that the active damping mechanism was

not optimized. Future testing needs to be done that will provide

an optimized mechanism to determine the full potential of the

damping method. Furthermore, all experimental results will be

compared to a model made using Computational Fluid

Dynamics (CFD) to validate the test results as well as further

advance the ability to model active damping techniques.

V. REFERENCES

[1] Hubert, C., “Behavior of Spinning Space Vehicles with

Onboard Liquids,” NASA/Kennedy Space Center

NAS10-02016, 2003.

[2] Chapman, Y., “Modeling and Parameter Estimation of

Spacecraft Lateral Fuel Slosh,” Embry-Riddle

Aeronautical University, 2008.

[3] Abramson, H., “The Dynamic Behavior of Liquids in

Moving Containers,” NASA SP-106, 1966.

[4] Marsell, B., “A Computational Fluid Dynamics Model

for Spacecraft Liquid Propellant Slosh”, M.S. Thesis,

Embry-Riddle Aeronautical University, Daytona

Beach, Florida, 2009.

[5] Schlee, K., “Modeling and Parameter Estimation of

Spacecraft Fuel Slosh Using Pendulum Analogs”, M.S.

Thesis, Embry-Riddle Aeronautical University,

Daytona Beach, Florida, 2006.

[6] Leuva, D., “Experimental Investigation and CFD

Simulation of Active Damping Mechanism for

Propellant Slosh in Spacecraft Launch systems”,

M.S. Thesis, Embry-Riddle Aeronautical University,

Daytona Beach, Florida, 2012.