52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference<BR> 19th
4 - 7 April 2011, Denver, Colorado
AIAA 2011-2000
Investigation to Determine Resonant Behavior from
Propellant Slosh in Spinning On-Orbit Propellant Storage
and Transfer Systems
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Nathan L. Silvernail1, Dillon J. Sances2, Robert B. Morehead3 and Sathya Gangadharan4
Embry-Riddle Aeronautical University, Daytona Beach, Florida, 32114
Future space missions emphasize on long duration capabilities and the utilization of
on-orbit propellant storage and transfer systems as essential pieces of the space
transportation infrastructure. The development of orbital propellant storage and
transfer systems has been established as one of NASA’s Flagship Technology
Demonstration Programs in an effort to advance space exploration and mission duration
capabilities. Many conceptual designs utilize spinning upper-stages from existing launch
vehicle configurations. Liquid propellants onboard spinning space systems have a
significant effect on spacecraft attitude and stability. Resonant modes, propellant
excitations, and viscous effects can induce fluid motions within partially filled propellant
tanks, known as fuel slosh which causes energy dissipation. A thorough understanding
of fuel slosh dynamics and its effects on rotational stability are essential for developing
on-orbit propellant storage and transfer technologies. This investigation has a
significant impact on related NASA programs, slosh research, vehicle dynamics,
rendezvous operations, and advancements in fluid management technologies for long
duration space missions.
I. Introduction
S
PIN stabilization is a technique used to maintain a spacecraft’s trajectory during orbital and sub-orbital
maneuvers. This technique involves spinning the spacecraft about its major principal axis to prevent small
external torques from impeding the stability of its set trajectory. This spinning motion causes the liquid propellant
inside of the spacecraft’s onboard fuel tanks to slosh. As the liquid propellant sloshes, the kinetic energy of the fuel
dissipates on a molecular level, causing small forces and moments to act on the inner wall linings of the fuel tank.
The existence of these forces causes the spin angle of the spacecraft, relative to the axis of rotation, to fluctuate; this
is known as nutation. If the liquid propellant is excited at resonant modes, nutation can begin to grow exponentially,
causing attitude instability of the spacecraft which cannot be recovered.1
Future missions emphasize on long duration capabilities and the utilization of on-orbit propellant storage and
transfer systems as essential pieces of the space transportation infrastructure. These systems will enable robust
exploration and commercial transportation throughout the inner Solar System without the need to advance and
develop new heavy-lift vehicle technology; thus eliminating the time, capital, resources, and man power required to
develop such technology. In addition to the logistical advantages, economic benefits of orbital propellant storage and
transfer systems include: providing demand for launch services to help drive down launch costs, providing launch
demand to encourage commercial RLV development, enabling the reuse of in-space assets, and greatly increasing
the utility of future ISRU efforts. The development of orbital propellant storage and transfer systems has been
established as one of NASA’s Flagship Technology Demonstration Programs in an effort to advance space
exploration and mission duration capabilities.
Currently, the United Launch Alliance (ULA) is designing an on-orbit propellant storage and transfer system
that will utilize an existing upper stage of the Atlas Launch vehicle, the Centaur. The Centaur is composed of two
tanks, a lower liquid oxygen tank (spherical in geometry) and an upper liquid hydrogen tank (cylindrical).
To complete the storage and transfer system, the Centaur is fitted with a large upper tank. This tank is known as
the LH2 Storage Module and maintains similar geometry to the Centaur, with minor derivations. The LH2 Storage
Module and the Centaur are attached at the inner poles by the mission module; this system is shown below in Fig. 1.
1
Graduate Student, Department of Mechanical Engineering, AIAA Student Member.
Graduate Student, Department of Mechanical Engineering, AIAA Student Member.
3
Graduate Student, Department of Aerospace Engineering
4
Professor, Department of Mechanical Engineering, AIAA Associate Fellow.
1
American Institute of Aeronautics and Astronautics
2
Copyright © 2011 by Nathan L. Silvernail. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
Downloaded by EMBRY-RIDDLE AERO UNIV. on March 2, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2011-2000
During launch, the complete system is spun stabilized about its major axis or axis of greatest inertia. Upon reaching
apogee the system will enter a transfer mode or the mode in which it will conduct all transfers necessary to refuel a
docked spacecraft. In this mode, the system will be put into a transfer spin which is an end-over-end spin, or a spin
about its minor axis, which will force all the liquid within its tanks to settle at the outer poles where transfer valves
are located. The act of spinning the system in this way is unique, yet desirable due to the fact that a spin about the
minor axis is naturally stable and should allow the system to maintain its proper orientation with little to no
propellant being exhausted for attitude corrections.
Figure 1. Complete propellant storage and transfer system being developed by ULA.2
Although the system is being spun about a naturally more stable axis, the physical act of transferring liquid
propellants introduces new complications. The flowing liquid propellant will cause rapid changes to the vehicles
mass distribution, thus creating a potential threat to the rotational stability of the system. Also, the flow of liquid
propellant through transfer lines may cause capillary effects or chocking within the transfer lines due to fluid viscous
characteristics and high mass flow rates. Lastly, the act of transferring liquid propellant via the means of a stored
pressurant will inevitably lead to pressure gradients, should these pressure gradients become higher than expected,
the simple act of opening a transfer valve may induce an internal force to the system that could cause further
rotational instability. To further develop this type of technology and raise its corresponding Technology Readiness
Level (TRL) all of these potential concerns need to be fully understood.
To begin, testing will be conducted to determine the effects of fuel slosh on the Centaur upper stage while it is
spun about its major axis. This testing will provide insight as to how this section of the propellant storage and
transfer system will perform under dynamic launch conditions and open the door to future testing that will allow the
systems other operational characteristics to be investigated.
II. Experimental Testing
To determine the rotational stability of the Centaur
upper stage, an experiment has been designed and
performed that enabled a scale mock-up of the Centaur
to be spun about its major axis inside of NASA’s
Reduced Gravity Simulation Aircraft. As this aircraft
performed steep parabolic arcs 25,000 feet above the
Gulf of Mexico, a reduced gravity environment was
simulated. During this time the scale mock-up was
mechanically lifted and spun via the use of the Tri-Axis
Spin Rig (TASR) developed at Embry-Riddle
Aeronautical University (ERAU), shown in Fig. 2.
Once the microgravity environment was induced, the
mock-up was lifted to the center of the test enclosure,
spun, and released to spin unharnessed at a rate which
allowed the maximum amount of nutation growth to
occur. While spinning, a tri-axis accelerometer,
mounted at the vehicle’s outer pole and tangential to
the spin axis, wirelessly transmitted angular
acceleration changes to the experiments data
acquisition system. Once gravity was restored inside of
Figure 2. Tri-Axis Spin Rig used in microgravity flight
the aircraft, the mock-up would come to rest at the
testing.
bottom of the test enclosure and the next parabolic test
would be prepared. The Centaur mock-up was created
from aluminum 6061 and polycarbonate. The liquid oxygen and hydrogen tanks were scaled to closely resemble the
geometry of the actual Centaur upper stage. A graphical representation of the mock-up used in the microgravity
flight testing is shown below in Fig. 3.
2
American Institute of Aeronautics and Astronautics
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Figure 3. Graphical representation of the Centaur mock-up used in microgravity flight testing.
During the microgravity testing, the mock-up was filled to various levels with water; water was chosen to
substitute the actual liquid propellants for safety reasons. The fill levels for each tank are shown below; the tests
were conducted in the mentioned order for operational testing specificities.
Flight Day One Test 1: Liquid Oxygen Tank (Empty); Liquid Hydrogen Tank (~90% Full)
Test 2: Liquid Oxygen Tank (Empty); Liquid Hydrogen Tank (~30% Full)
Test 3: Liquid Oxygen Tank (Empty); Liquid Hydrogen Tank (Empty)
It is important to note that test 3, on flight day one, was performed to provide a control and to determine the
initial rotational characteristics of the mock-up based solely on its inertial parameters. The control ensures all
angular acceleration changes observed during previous tests were solely caused by the dynamic behavior of the
liquid propellant.
Flight Day Two Test 1: Liquid Oxygen Tank (Full); Liquid Hydrogen Tank (~90% Full)
Test 2: Liquid Oxygen Tank (Full); Liquid Hydrogen Tank (~30% Full)
Test 3: Liquid Oxygen Tank (Full); Liquid Hydrogen Tank (Empty)
Once all flight tests were conducted, the data was analyzed and the rotational stability of the Centaur upper stage
was concluded upon. The flight data was then compared to the data gathered from the computational model created
using Matlab SimMechanics. The comparison of these two different sets of data was then used to determine the
accuracy of the modeling approach taken and validate it for used with this and similar space systems.
III. Mathematical/Modeling Approach
To determine how the dynamics of a particular vehicle or other space system is affected by the sloshing
movement of the liquid propellant being stored within its fuel tanks, physical testing is required. However, the
utilization of modern computational modeling methods can be used to develop pre-defined performance predictions
of the particular space system being tested and allow engineers to have a better understanding and hypothesis of the
conclusions that will made from that testing. In order to advance these methods and further develop computational
modeling techniques, the results obtained from such methods must first be validated. Once validated, the results that
particular modeling method provides can be trusted to withhold an agreeable amount of accuracy. In the case being
addressed, Matlab SimMechanics was used to model the Centaur upper stage and simulate the testing that was
performed onboard NASA’s Reduced Gravity Simulation Aircraft.
Matlab SimMechanics utilizes a block system with predefined functions and variables to simulate the dynamical
behavior of systems in a physical environment. To begin modeling the Centaur upper stage, a few initial parameters
needed to be adjusted. The physical environment, geometrical and inertial parameters of the body, and initial masses
of the liquid propellant were defined. From there, script code could be written to initialize other needed parameters
such as oscillatory frequencies and various damping coefficients. A mathematical approach to modeling the
interaction of the liquid propellant with the physical body of the Centaur upper stage was used to develop a
background for the computational model and to determine what parameters were needed.
3
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This approach utilizes a spring and pendulum analogy. This analogous representation can be adapted to testing
liquid propellant slosh by visualizing the pendulum as having a defined and constant length as well as being
conceptually attached to a mass. This mass is known as the slosh mass and is characterized as being 20 percent of
the overall mass of the liquid propellant. The other 80 percent of the liquid mass is known as the fixed mass. This
mass is fixed in space and a constant parameter. As the fill level changes, as it does in physical testing, the slosh
mass and fixed mass are reduced accordingly. The pendulum is then attached, at some defined location, to a spring.
This spring is allocated a certain stiffness to incorporate various viscous and damping parameters of the fluid. It can
also be increased to include the representation of any other internal damping mechanisms such as a diaphragm.3
The block system created for the computational simulation is shown in Fig. 4. The main body of the spacecraft is
shown as the large block in the center. The blocks to the right of it represent both the liquid hydrogen and liquid
oxygen tanks. These tanks are then implemented with a pendulum and spring damper. These are shown in the blocks
to the far right of the system. Other various blocks are used to observe the rotational characteristics of the spacecraft
in real time, these are shown as scopes. These blocks simulate the basic functions of the accelerometers used in the
microgravity flight testing. Once the model is completed, it can be ran for a time duration that resembles that of the
experimental testing performed. The data gathered can then be analyzed and compared to the results from the
experimental testing and validity of this modeling approach can be determined.
Figure 4. Block system created using Matlab SimMechanics.4
IV. Results
A. Experimental Results
The figures below represent the change in the Centaur mock-up’s angular acceleration with time, an important
parameter to consider when determining the oscillatory stability of any space system. As can be seen in Fig. 5, the
solid trend line denotes that the mock-up experiences an increase in angular acceleration as the test time increases.
Therefore, when this type of space system is being spun about its major axis with approximately 90 percent of its
onboard propellant still intact, it appears that it will depict a physical behavior that would tend to an unstable state
over a longer period of time. Though this type of behavior is not preferable, the on-orbit propellant storage and
transfer system, derived from the Centaur upper stage, only requires a spin about the major axis during ascent, a
relatively short amount of time. While the results of this flight test provided evidence of nutation growth, the results
of the two other tests appear to show the opposite.
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Figure 5. Angular acceleration changes measured while mock-up was filled to 90% capacity.
As seen below in Fig. 6, the Centaur mock-up did not seem to experience nutation growth, in fact the results
show that the angular acceleration actually decreased with time. This means that the amount of liquid slosh was not
large enough to overcome the angular momentum of the mock-up space system. By comparing these results to the
results found from the first test conducted, it is evident that as the amount of fuel stored in the liquid hydrogen tank
decreases, the space system tends to a more rotationally stable state; an expected outcome. Also, it is important to
note that the results of the control test, Fig. 7, show that once the mock-up was released from the experimental
apparatus the angular acceleration decreased rapidly as the test time increased. This verifies that the mock-up is
inertially stable due to its tendency to revert to a stable rotation about its spin axis when no internal force is present.
Figure 6. Angular acceleration changes measured while mock-up was filled to 30% capacity.
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Figure 7. Control data taken while mock-up was completely drained of all fluid.
B. Computational Results
The results gathered from the computational model created using Matlab SimMechanics has shown that when the
Centaur is filled to 90 percent capacity, as in the experimental testing scenario, the space system is inherently
unstable, as shown in Fig. 8. However, the magnitude and nutation rate the simulation predicted did not match that
of the flight data. The difference in rotational frequency observed from the comparison of the two data sets is
believed to be caused by a large amount of noise the experimental accelerometers exhibit during testing. This noise
has been said to be caused by the vibrations in the mechanical equipment being used. Additionally, when the
simulation was run to determine the stability of the Centaur when it was in the same configuration as the second
flight test conducted, i.e. when the system was tested with 30 percent fuel remaining, the system was found to still
be unstable. As mentioned prior, this was not the case during physical testing. No simulation was performed to
replicate the control test, this test involved no liquid sloshing, thus could not be used to validate the technique.
Figure 8. Results of computational simulation performed for 90% full case.
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American Institute of Aeronautics and Astronautics
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V. Conclusion
The data gathered from the microgravity flight testing performed on the scale Centaur mock-up determined that
this space system experiences an unstable behavior while rotating about its major axis when approximately 90
percent of its propellant remains. This behavior was as expected; the large amount of propellant provides an increase
in the internal force that is present when the system becomes excited. When excited at resonant frequency, this large
internal force overcomes the angular momentum of the spacecraft and causes it to nutate about the spin axis.
Furthermore, this unstable behavior appears to subside when the amount of propellant within the propellant tanks of
the spacecraft is decreased to about 30 percent capacity. The smaller amount of fuel in the spacecraft’s tanks
decreased the internal force the sloshing propellant would induce when the space system was excited.
Therefore, the investigation to determine the rotational stability of the Centaur upper stage, while it was spun
stabilized about its major axis was, a success. A basic range of stability for this space system has been determined,
however, to further define this window and determine the exact point at which the system becomes stable, additional
testing may be required. This investigation has provided a good starting point for testing the rotational stability of
the complete propellant storage and transfer system being developed by the ULA.
The modeling approach taken to computationally simulate the behavior the Centaur upper stage would exhibit in
microgravity was not validated. The simulation provided data that was not correlated by the physical data gathered
from microgravity flight testing. When dealing with this type of propellant tank configuration, that is when a space
system has both a spherical and cylindrical propellant tank, as described in the background section, the dynamics of
fuel slosh become much more complicated. In this case, when various types of fuel slosh exist, i.e. when free surface
slosh and sub-surface inertial wave slosh exists within one system, various modeling techniques need apply. This
can cause the modeling software being used to provide inconsistent results.
Acknowledgments
On behalf of the authors of this paper, we would like to thank the following people for assisting in the
microgravity flight experiments and for their inspirational guidance: James Sudermann, Brandon Marsell, and Keith
Schlee. We would like to thank Embry-Riddle Aeronautical University for the use of their manufacturing facilities
and for the laboratory space they provided. We would like to thank the Florida Space Grant Consortium for all of
their monetary donations toward not only this research but all future research in support of it. We would also like to
thank the United Launch Alliance for all of their help and financial support, the information and aid they provided
made this research possible.
References
1
Hubert, C., “Behavior of Spinning Space Vehicles with Onboard Liquids,” NASA/Kennedy Space Center NAS10-02016,
2003.
2
McLean, Christopher, Brian Pitchford, and Shuvo Mustafi. "Simple, Robust Cryogenic Propellant Depot for Near Term
Applications." Institute of Electrical and Electronics Engineers. Web. 17 Feb. 2011.
3
Silvernail, N. Sances, D. Gangadharan, S.N., Modeling of Fuel Slosh in a Spin Stabilized Spacecraft with On-Axis Propellant
Tanks Implemented with Diaphragms, AIAA Journal 2009
4
Matlab Simulink, Software Package, Ver. 7.0, The Mathworks Corporation, Natick, Massachusetts, 2009.
7
American Institute of Aeronautics and Astronautics