experimental investigation and cfd simulation of active ... · experimental investigation and cfd...
TRANSCRIPT
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.