Download The Liquid - Colorado Space Grant Consortium

University of Northern Colorado
Greeley, Colorado
Liquid Fuel Slosh during the Flight of a Sounding Rocket:
SLOSHSAT
Authors Names
Sage Andorka
Dan Welsh
Zach Sears
Maurice Woods III
Motoaki Honda
Faculty Advisers
Dr. Robert Walch
Dr. Mathew Semak
College of Natural and Health Sciences
School of Earth Sciences and Physics
Adopted from an earlier experiment by Nathan Clayburn
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March, 2010
Table of Contents
Cover Page
Signature Page
Table of Contents ................................................................................................................ 2
Acronym List ....................................................................................................................... 3
STATEMENT OF THE PROBLEM ........................................................................................... 4
Abstract ........................................................................................................................... 4
REVIEW OF RELATED RESOUCES ......................................................................................... 5
Introduction .................................................................................................................... 5
Traditional Modeling Methods ....................................................................................... 5
Traditional Passive Methods ........................................................................................... 6
MATHEMATICAL MODEL .................................................................................................... 7
Test Objectives .................................................................................................................... 9
Goal ................................................................................................................................. 9
Hypothesis and Expected Results ................................................................................... 9
Uniqueness.....................................................................Error! Bookmark not defined.
Data Collection .............................................................................................................. 10
Data Analysis ................................................................................................................. 10
References ........................................................................................................................ 11
EXPERIMENT ..................................................................................................................... 12
Mass .............................................................................................................................. 12
Physical Envelope.......................................................................................................... 13
Center of Gravity ........................................................................................................... 13
The Liquid ...................................................................................................................... 13
Liquid Containment Subsystem .................................................................................... 14
Electrical and Data Subsystem ...................................................................................... 15
Concept of Operations .................................................................................................. 17
BUDGET ESTIMATES .......................................................................................................... 18
Cost ............................................................................................................................... 18
APPENDIX .......................................................................................................................... 19
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Acronym List
UNCo
CSGC
NASA
WFF
University of Northern Colorado
Colorado Space Grant Consortium
National Aeronautics and Space Administration
Wallops Flight Facility
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STATEMENT OF THE PROBLEM
Abstract
During the launch of any liquid fueled rocket, the motion of the fuel and the
forces exerted on the rocket must be considered to ensure the safety of the flight. These
forces may cause dramatic wobble during flight leading to issues with control. The loss
of which could lead to the failure of the mission. Motion of this fluid is central to the
safety of the launch. Understanding what is going on inside of the fuel tanks is an
extremely relevant problem. It is also very difficult to solve. Years of research into fuel
slosh has yielded expansive solutions and computationally intensive analytical models.
The research begins with a mathematical model which should predict this
simplified fluid motion along the central axis of a two-stage Improved Orion Sounding
Rocket. The strongest forces will be exerted along this central axis during the flight and
thus will be where we focus our attention. The experiment allows us to isolate the
motion of the fluid by looking at the vertical motion of an inner cylinder housed by an
outer cylindrical container. We expect to see the data from the launch coincide with the
theoretical predictions given by the analytical model, thus validating the accuracy of our
simplified analytical model. If our experiment is successful, it will be possible in the
future to generalize the math to include all three dimensions.
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REVIEW OF RELATED RESOUCES
Introduction
When considering spacecraft attitude controls one must take into consideration
the motion of liquids aboard the spacecraft. The motion of these liquids exerts a torque
on their tank’s wall and, as a result, the spacecraft must adjust accordingly. Although
models exist that predict the behavior of liquids onboard a spacecraft, the physical
phenomena is poorly understood. (Diagnosis of Water Motion in the Sloshsat FLEVO
tank).
Traditional Modeling Methods
Numerous analytical models have been used to describe the motion of fluids.
The most accurate description of liquid motions requires use of the Navier-Stokes
equations. (Robust Nonlinear Attitude Control with Disturbance Compensation). These
formulas, however, are not practical for control implementations as they are highly
dependent on boundary conditions and are computationally expensive.
Additional models have been suggested including (single and multi) mass-springdamper, pendulum liquid slug, and CFD/FEA models. (Robust Nonlinear Attitude Control
with Disturbance Compensation). These models work very well when dealing with small
linear or angular motions and are considered acceptable for some aerospace craft. For
example, they work well for rockets whose fuel pools at the bottom after the main
engine is fired. However, these methods have their limitations, and a model needs to be
developed in which the fuel can display a large range of movement.
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Traditional Passive Methods
A modeling system that accounts for both the motion of the spacecraft and the
liquid fuel simultaneously would be most ideal. This is very difficult as one cannot
control or measure the position or orientation of the fuel aboard the spacecraft
accurately. It is only possible to measure the effects of the fuel slosh on the total
system.
As a result, many passive ways have been developed to dissipate the energy of
the fuel sloshing: baffles, slosh absorbers, and breaking a large tank into a smaller one
(A Standing-wave type Sloshing Absorber to Control Transient Oscillations). However,
these methods add weight and therefore increase launch cost.
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MATHEMATICAL MODEL
The goal of our project is to describe the motion of the liquid container instead
of focusing on the liquid itself. To begin analyzing the motion of the container, we first
derived the acceleration equation through Newton’s Second Law for a small cylindrical
volume of liquid. Instead of finding the entire gradient of the velocity for the
acceleration equation, the z-direction was isolated. For this initial attempt we assumed
that there would be a small change in pressure and density while the fluid is sloshing. By
using tensors, we were able to incorporate the changes in pressure and density into the
acceleration equation. After simplifying we arrived at an equation of motion for an
inviscid fluid. λ is the density of the fluid and p in the pressure.
This equation describes the motion using the pressures and densities, and is
simply a variation of Euler’s equation. These are features that we are not measuring in
our experiment. To describe the motion of the fluid at particular points through
acceleration, the motion equation had to be incorporated into the continuity equation
for inviscid fluid. The pressure and density ar related through the Bulk Modulus (BM), or
a sheer tensor. Applying this relation to the combined continuity and motion equation
and simplifying we get our final equation of generalized motion to be the following
equation.
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Where
Finding the homogenous solution using separation of variables, we get the first
form of the velocity equation to be:
After further simplification the final velocity equation becomes:
ehere Ψ-, Ψ+, and α are constant to be determined with initial conditions. These
initial conditions will be determined from the velocities of the rocket during launch.
The particular solution will be found by looking at the accelerations of the rocket
and how this acceleration will affect the liquid tank. The data from the launch in 2009
implies that the acceleration can be modeled with a Heaviside Step Function, the forcing
terms F(t) will become a piecewise function with different forcing at different times of
the launch.
By solving the equation above, we can find the Vk of the particular solution. The
Vk can be combined with the general velocity, Vh, to find our full equation of motion.
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Test Objectives
Goal
The primary mission of the SLOSHSAT experiment is to determine the validity of
our analytical model. This model begins by assuming that our fluid is idea, in other
words there is no energy lost due to heat transfer or viscosity. With these assumptions,
along with the use of Euler’s equation and our continuity equation, we arrive at our final
model which acts as a harmonic oscillator. These oscillations are what influence the
motion of the liquid container. In order to validate our hypothesis we will measure the
accelerations of a fluid filled container onboard a sounding rocket. Comparison of
experimental data and mathematical modeling will allow us to check the accuracy of the
analytical model.
Hypothesis and Expected Results
We hypothesize that our mathematical model will accurately describe the
motion of the liquid filled container. The SLOSHSAT experiment is designed to collect
vertical axis accelerometer data continuously during a two-stage parabolic flight path. It
is expected that the model will accurately represent the behavior of the canister-fluid
system. Comparison of the data from the canisters movement to the control data will
reveal if the system behaves in the manner that the model predicts. The success of the
project will depend on whether the model reasonably represents the behavior seen in
our data.
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Relevance
The experiment is unique in its relevance. Current unmanned and future manned
missions will require a careful understanding of liquid slosh and its dynamics. Both the
experiment and the mathematical model were constructed and developed by students
anticipating the importance of liquid dynamics to the aerospace field now and in the
coming years.
Data Collection
There will be two accelerometers in the payload. One will be attached to the
experiment plate to characterize the accelerations of the rocket. This will give us
control data. The other accelerometer will be attached to the inner container that holds
the liquid. This accelerometer will characterize the motions of the liquid canister. The
data from the accelerometers will be read by AVR, sampling every 20 milliseconds, and
stored on an eight mega byte flash drive for future retrieval.
Data Analysis
The data collected by the accelerometers will allow us to determine the motions
of the container and rocket in various parts of the flight. The accelerations from the
rocket will be subtracted from the acceleration from the liquid canister to get an idea of
the motion of the liquid canister itself. These results will then be used to test the
accuracy of the analytical model.
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References
Anderson J., Turan, O., and Semercigil, S., “A Standing-wave Type Sloshing
Absorber to Control Transient Oscillations,” Journal of Sound Vibration,
Vol 232, No 5, 2000, pp 839-856.
Clayburn N., Andoka S., Kuhns C., “Analytical Model of Liquid Slosh-Verification
Experiment”
El-Sayad, M., Hanna, S., and Ibrahim, R “Parametric Excitation of Nonlinear
Elastic Systems involving Hydrodynamic Sloshing Impact,” Nonlinear
Dynamics, Vol 18, 1999, pp 25-50.
Hughes. P., Spacecraft Attitude Dynamics, John Wiley & Sons, New York 1986.
Sidi, M., Spacecraft Dynamics and Controls, Cambridge University Press, New
York, 1997.
Vreeburg, J.P.B., “Diagnosis of Water Motion in the Sloshsat FLEVO Tank”,
National Aerospace Laboratory NLR, 2000.
Walchko, K., “Robust Nonlinear Attitude Control with Disturbance
Compensation”, Graduate Thesis, University of Florida, 2003.
Experiment
Mass
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EXPERIMENT
Launch
The SLOSHSAT experiment is expected to launch on June 25, 2010 from
Wallops Island. This project opportunity is available through the combined efforts of the
Colorado Space Grant Consortium and Virginia Space Grant Consortium. Results will be
available following the completion of the flight and data analysis.
Mass
Another restriction of this project concerned mass. The entire canister, complete
with payloads, cannot mass more than 9.07 kg. Our particular canister is being shared
by UNCo and CSU. We decided to split the mass in half so each university gets 4.5 kg.
The following chart is the mass of each hardware item used in the payload.
The total mass of our payload is 0.7099 Kg, 1/5 of the total mass for half the canister.
Part
Mass (kg)
device disc
0.361
2 battery
0.092
outer cylinder
0.0652
inner cylinder
0.0157
Galden 110
0.176kg
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Physical Envelope
The canister that houses the payloads in the payload section of the rocket is 24.0
cm tall. This allowed us 12.0 cm of vertical space. The tallest part of the payload is the
canister which will stand at 9.0 cm. This is 3 cm shorter than the maximum allotted
height for our half. The diameter of the payload canister is 23.6 cm.
Center of Gravity
Due to time constraints while at WFF, some very crucial design requirements
have to be completed prior to delivery to WFF. One requirement involves the center of
gravity. The center of the payload had to be contained in a one inch cube directly in the
center of the payload. When Sounding Rockets are launched, they spin with a very high
frequency. If the rocket is not perfectly balanced, the rocket will wobble and the
mission will be a failure. To reduce the amount of time spent on balancing the rocket by
WFF engineers, all payloads have to have the center of gravity within the 1 inch cube of
the payload section.
The Liquid
The liquid used in this experiment was chosen with careful considerations. WFF
is very concerned about launching water on the rocket. If the liquid container were to
break, then the mission would be a failure. We are launching with 20 other payloads. If
our liquid were to spill in the payload section, there could be damage done to other
payloads resulting in failure of their missions. As a result, the containment subsystem
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was designed to be fail-safe, and the liquid was carefully chosen to be as safe to all
payload systems as possible. Galden 110 was donated to our project by Solvey Solexis,
the makers of Galden. This product is used to cool large servers. The liquid is a
nonreactive fluid that is safe for electrical devices. To test this, we dunked an operating
cell phone in a sample. The cell phone continued to work and would ring when called
inside the sample. The only special handling requirement for the Galden 110 is that the
external environment cannot get above 110° Celsius. Because the payload section of
the rocket is pressurized, the internal environment is not expected to fluctuate more
than ± 25° from standard ambient (27° Celsius) temperature.
Liquid Containment Subsystem
The goal of the experiment is to determine the viability of our mathematical
model. A cylindrical container partially filled with Galden 110 will be constrained by an
outer container so that it may only move along the vertical axis throughout the duration
of the flight. The acceleration of the liquid container will be recorded as it moves within
the outer container. This data will be later used for analysis on the ground. We expect
that the actual flight data will match the predictions of our mathematical model. Figure
1 shows an exploded view of the experimental apparatus; Figure 2 is a close up
prototype image of the containment system.
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Figure 1: Exploded Experimental Apparatus
Figure 2: Full Canister Prototype
Electrical and Data Subsystem
The power will be supplied by two 9V NiCd batteries. This computer board
consists of an AVR micro controller, flash storage, a temperature sensor, an x- and y-axis
accelerometer, and the z-axis accelerometer. As a safety requirement by WFF, there
are two shorts in the electrical system. The other short is the G-switch. This switch is
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will be closed when the payload is subjected to an extreme G-force, like those
experienced at launch. This switch is the final step in allowing power to the payload.
The first short is for the Remove Before Flight Pin which is a short in power that will be
connected by WFF engineers before launch. This is to prevent any accidental activation
of payloads while the WFF engineers are performing the required tests on the payload
section of the rocket. It is also a very important safety mechanism to reduce accidental
sparks from payloads that could ignite the engines while finalizing construction of the
rocket. Figure 3 is a functional block diagram explaining the connection between the
electrical and data subsystems.
Figure 3: Block Diagram of Electronics
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Concept of Operations
What the payload will do during the flight is very simple. When the payload
is given to Wallops for final rocket integration, the Remove Before Flight Pin will be
connected to all the others in the payload section. Prior to launch, Wallops engineers
will short the Remove Before Flight Pin allowing power to the G-Switch. At launch, the
G-switch will be activated due to the sudden increase of G-forces. When the G-switch is
enabled data collection will begin. Upon activation the data logger will collect data until
the batteries die or are disconnected. The following flow chart shows the overviews of
the Concept of Operations.
Figure 4: Concept of Operation flow chart
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BUDGET ESTIMATES
Cost
The money for the SLOSHSAT experiment will be provided in part by a grant from
COSGC, NHS Research Grant, and the UNC travel funds. A big push in our experiment is
to be as conservative with our cost as much as possible. We did recycle the Electrical
and Data subsystem hardware and AVR code from the RockON! workshop that was
attended by students from UNCo the summer before.
Item
Cost
RockSAT Payload Slot
$7000.00
(donated by COSGC)
1-Axis Low-Range Accelerometer
$16.00
(included on RockON! board)
2-Axis Low-Range Accelerometer
$23.00
(included on RockON! board)
1-Axis High-Range Accelerometer
$12.00
(included on RockON! board)
2-Axis High-Range Accelerometer
$16.00
(included on RockON! board)
Polycarbonate Tubing
inside $05.00
outside $20.00
.1L Galden 110
$150
Donation from Solvey Solexis
Travel for two to Wallops
$2,000.00
Total
$9,242.00 ($7,217 donated)
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APPENDIX
Link to the RockSAT 2010 User’s Guide
http://spacegrant.colorado.edu/index.php?option=com_content&view=article&id=153&It
emid=120
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