(Spacecraft Liquid Attenuation Simulation Hypothesis SAT)

Presented by

Nathan Clayburn

Casey Kuhns

Sage Andorka

•Introduction

I.Statement of Problem

II.Proposed SolutionIII.Proposed Experiment

•Background

I.Traditional Modeling Methods

II.Traditional Passive Method•Mathematical Model

•Experimental Design (Quantitative)

I.Data Collection

II.Data Analysis

•Experimental Design (Qualitative)

•Conclusion

Outline

Problem

Due to acceleration of their containers, onboard

liquids manifest reactive forces on their containers

that can have adverse effects on the performance

of the vehicle.

Solution

A simpler analytical model is presented to describe liquid slosh. This simplified

model, although not comprehensive, may yield practical results.

− ω [m1 A1m2

A2]= [− kA1�k

'�A

2− A

1�

− k'A2�k

'�A1− A2�]− i[

αω A1

βω A2]� k

'g

k�m 2− m1�[1− 1]

2

ω2m

1− k− k

'− iαω ��ω

2m

2− 2k

'− i βω �− k

¿0

m1

ẍ1= − k�x

1�

m1 g

k��k

'�x

2− x

1�− α ẋ

1

m2 ẍ2= − k'�x 2�

m2

g

k��k

'�x1− x2�− β ẋ2

�U

V�=�A

1

A2�e

iω tm

1Ü= − kU�k

'�V − U��

k'g

k�m

2− m

1�− α U̇

m2V̈ = − k

'V�k

'�U − V��

k'g

k�m

1− m

2�− β V̇

Experiment

• An experiment to verify the validity of such an analytical model will be conducted.

• By comparing the predictions made by the analytical model and actual slosh data, the accuracy of such a model can be assessed.

Background

Although models exist that predict the behavior of liquids onboard a spacecraft, the physical phenomena is poorly understood

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.

• These formulas, however, are not practical for

control implementations as they are highly

dependent on boundary conditions and are

computationally expensive.

Traditional Modeling Methods

• Additional models have been suggested including

• (Single and multi) mass-spring-damper

• Pendulum liquid slug,

• CFD/FEA models.

Traditional Modeling Methods

• These models work very well when dealing with small linear or angular motions and are considered acceptable for some aerospace craft.

• However, these methods have their limitations and a model needs to be developed in which the fuel can display a large range of movement.

For example, they work well for

rockets whose fuel pools at the

bottom after the main engine is

fired.

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 can not 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.

Traditional Passive Methods

• As a result, many passive ways have been developed to dissipate the energy of the fuel sloshing:

• Baffles,

• Slosh absorbers,

• Breaking a large tank into a smaller one

• However, these methods add weight and therefore increase launch costs.

Objectives

• GOAL: The primary mission of the SplashSAT experiment is to determine the validity of our analytical method.

• MODEL: This method assumes the liquid acts as an elastic mass distribution that influences the motion of its container.

• EXPERIMENT: In order to validate our hypothesis we will measure the motion of a fluid filled container on board a sounding rocket/microgravity simulation.

• RESULTS: Comparison of experimental data and mathematical modeling will allow us to check the accuracy of such a model.

Mathematical Model

Our mathematical model, which follows, can predict the modes of oscillation which the

undamped system can display.

Mathematical Model

Liquid filled Tank

Springs

Springs

Figure 1.1

m1

m2

k’

k’

k

Figure 1.2

We represent this situation as a pair

of coupled damped harmonic

oscillators where:

1. m1 represents the liquid's mass

2. m2 represents the mass of the

tank.

The motion of the liquid is

communicated to the tank by k’, the

constant describing the strength of

the coupling spring.

Mathematical Model

m1ẍ

1= − kx

1�k

'�x

2− x1�− m1 g− α ẋ1

m2

ẍ2= − k

'x

2�k

'�x

1− x2�− m2 g− β ẋ2

From the diagram the force equations are as follows:

After some manipulation and assumption of a trial solution we find

the following solution in matrix notation:

− ω [m1 A1m2 A2]= [− kA

1�k

'�A

2− A

1�

− k'A2�k

'�A1− A2�]− i[

αω A1

βω A2]�k

'g

k�m 2− m1�[1− 1]

Mathematical Model

Next we find the homogeneous equation:

[00]= [ω2m

1− k− k

'− i αω k

'

k'

ω2m

2− k

'− k

'− i βω ][A1A2]� k

'g

k�m

2− m

1�[1− 1]

We can then find the determinant of the matrix in order to

form a constraint for the solutions:

2

ω2m

1− k− k

'− iαω ��ω

2m

2− 2k

'− i βω �− k

¿0

Mathematical Model

For the undamped case, this

equation can be analytically solved for omega revealing

the frequencies for normal

mode oscillations.

However, the damped situation cannot be solved

analytically for omega.

Still, a computer can solve the

damped case by approximating roots of the

characteristic equation.

Experimental Description

(Long Term)

• A tank partially filled with liquid (water) will be constrained by rails so that it may only move along one axis throughout the duration of the flight.

• The displacement along the rails as the liquid filled tank moves will be recorded.

Data Collection

(Long Term)

• Velocity: During the experiment a series of photogates will record the displacement and velocity of the canister along the rail.

• Accelerometer: To record the acceleration of the craft we will use our own accelerometers.

Data Analysis

(Long Term)

• The data recorded will be quantitative in nature.

• The data collected by the photogates will allow us to determine the position, velocity, and acceleration of the container along the rail.

• The frequency of the system's oscillation will be obtained from these results. These results will then be used in conjunction with the mathematical model to determine the model’s accuracy.

Microgravity RocketSAT

Experimental Description

(Short Term)

• Before we are concerned with quantitatively

verifying our method we must first qualitatively

verify the motion of the liquid.

• This is a problem however. There exists a no

volt’s requirement that we must comply with at

Wallops. This requirement does not allow their

to be power running towards any device until

after launch.

Experimental Description

(Short Term)

• Current digital camera will not work due to boot and write times.

• So we return to old technology, 8 mm Film. The 2009 launch will test a film camera assembly that will later be

used to qualitatively verify the model.

References

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.

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.

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.

Sidi, M., Spacecraft Dynamics and Controls, Cambridge University Press, New York, 1997.

Hughes. P., Spacecraft Attitude Dynamics, John Wiley & Sons, New York 1986.