SloshSATConceptual Design Review

Dr. Robert WalchSage Andorka 

Dan Welsh Zach Sears 

 Maurice Woods IIIMotoaki HondaRyan Estrick  

14 Oct. 2009

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Liquid SloshDue to acceleration of their containers, onboard liquids manifest reactive forces on their containers that can have adverse effects on the performance of the vehicle.However, understanding these reactive forces is limited and modeling is computationally intense. Our goal is to create a simpler analytical model to describe liquid slosh. This simplified model, although not comprehensive, may yield practical results.

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Current SolutionsPassive Attenuation • 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.

• 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.

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.

• Additional models have been suggested including

• (Single and multi) mass-spring-damper

• Pendulum liquid slug, • CFD/FEA models.

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Our Idea- Mathematical ModelWe begin by analyzing one particle in the fluid. To find its motion by the following equations:

(eq.1)The acceleration of the particle in the liquid

(eq. 2)

The motion equation where λ is the density of our fluid and p is the pressure gradient.

(eq. 3) The continuity equation derived form the conservation of mass

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Mathematical ModelNow we substitute and simplify to get:

(eq. 4)

(eq. 5)

Our new motion equation

Simplified continuity

Assuming that:

we get a simplified acceleration equation and can find our new motion equation to be:

Where BM is the Bulk Modulus

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Mathematical ModelFrom solving the motion equation, we find that:

And our final equation is just a product.

By applying boundary conditions and approximating times and displacements, we can graph v(z,t).

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The success of the project will depend on the times and displacements during stage separation. These values should give reasonable solutions to the velocity equation that when graphed match the theoretical graph shown.

Graphed in Mathematica with singular coefficients

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Benefits• The model predicts the slosh with fewer

assumptions than the Navier-Stokes equations. • Use is applied to anyone who travels with a

liquid: gas or milk trucks, airplanes, NASA, etc.• Although this initial model is only in one

dimension, the math can be revised to include three dimensions.

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The “liquid”From last year’s project, we learned that NASA will not allow a liquid on the rocket.Our solution is a fine granular Silica powder. Research into Granular Physics has found that granular substances act as a liquid.

The movie shows a comparison between the silica powder and water at 18.928 Hz. The silica takes a while to develop the “sloshing” motion, but after a few seconds, the silica will form “droplets”.Frame Rate: 320 frames/sec.

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Mission Requirements

Mass/Volume

•Does not exceed 3.17 Kg•Height no more than 12 cm•Met

Center of Gravity

•Within 1” radius of center of payload•Pending

Self contained

•G-switch•RBF wires•On board AVR & power source•Met

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Required HardwareAnalog Devices:Z-Axis Low-Range AccelerometerZ-Axis High-Range Accelerometer

RockON! AVR Board without the pressure sensor and Geiger counter and G-switch.

Experiment Design

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Functional Block Diagram

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The “liquid” Canister

The outer canister will stand at 9 cm tall and the diameter is about 5.08 cm.The z-axis accelerometer will be housed in a compartment on top of the “liquid” container.

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Expected Results• It is expected that the canister and fluid will

model the oscillation of a dampened harmonic oscillator.  

• As outlined in our mathematical model, the displacements of the canister can be experimentally determined as well as times. If the canister and fluid behave as expected, the data we collect will yield a graphical solution like the graph shown in slide 7.

• Comparison of the data from the canisters movement with the control output will reveal if the system behaves in the manner that the model predicts.

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RockSat Payload Canister User Guide Compliance

• Mass:Total Mass0.5542 Kg1/6 of our weight for half the canister

The tallest part of the canister will stand at 9 cm- 3 cm shorter than the maximum allotted height.

• The RockON! AVR Board is prepared for a Remove-Before-Flight Pin. The voltage demands of the payload are small and can be powered with one 9 Volt battery.

Part Mass (kg)device disc 0.361

2 battery 0.092

outer cylinder 0.0652

inner cylinder 0.0157

Silica 0.0203

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Shared Can Logistics Plan• The University of Northern Colorado (UNC) and Colorado State

University (CSU) will be sharing a canister on board this rocket flight.

• It is the mission of UNC's team to monitor fluid slosh during the flight of the sounding rocket, use this data for comparison to control data produced by a mathematical model, and determine the effects on the vehicle produced by this slosh.

• It is the mission of CSU's team to use an optical mass gauging system to monitor fluid in a container as it is exposed to any gravitational environment, as well as to monitor the exchange of fluid between two tanks simulating loss (usage) of the fluid on board the rocket.

• Communication between UNC and CSU has been established.  Although exact location within the canister has not been determined, no conflicts of space limitation, undesired interaction, or port usage is expected.

• Communication will continue between the teams to determine structural interfacing between payloads, as well as to the craft.

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Management

Project AdvisorDr. Robert Walch

Project ManagerSage Andorka

MathZach Sears

Granular ResearchMaurice Woods III

Motoaki Honda

MaterialsDan Welsh

ProgrammingRyan Estrick

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ScheduleThe official Schedule10/14/2009 Conceptual Design Review (CoDR) Due 10/16/2009 (CoDR) Teleconference 10/30/2009 Online Progress Report 1 Due 11/4/2009 Preliminary Design Review (PDR) Due 11/6/2009 (PDR) Teleconference 11/25/2009 Critical Design Review (CDR) Due 11/27/2009 Online Progress Report 2 Due 11/27/2009 (CDR) Teleconference 1/8/2010 Final Down Select—Flights Awarded 1/29/2010 Online Progress Report 3 Due 1/30/2010 RockSat Payload Canisters Sent to Dedicated Customers2/17/2010 Individual Subsystem Testing Reports Due 2/19/2010 Teleconference 2/26/2010 Online Progress Report 4 Due 3/24/2010 Payload Subsystem Integration and Testing Report Due 3/26/2010 Teleconference 4/9/2010 Final Installment Due 4/9/2010 Weekly Teleconference 1 4/14/2010 First Full Mission Simulation Test Report Due 4/16/2010 Weekly Teleconference 2 (FMSTR) 4/23/2010 Weekly Teleconference 3 4/30/2010 Weekly Teleconference 4 5/7/2010 Weekly Teleconference 5 5/14/2010 Weekly Teleconference 6 5/19/2010 Second Full Mission Simulation Test Report Due 5/21/2010 Weekly Teleconference 7 (FMSTR 2) 5/28/2010 Weekly Teleconference 7 6/2/2010 (LRR) Teleconference 6/4/2010 Weekly Teleconference 8 (LRR) 6/11/2010 Weekly Teleconference 9 6/17/2010 Visual Inspections at Refuge Inn 06-(18-21)-2010 Integration/Vibration at Wallops 6/23/2010 Presentations to Next Years RockSat 6/24/2010 Launch Day

Our additions11/1/09 Order Accelerometers & Have

“liquid” container and outer container built -- testing

12/04/09 Have Electrical systems wired together- begin coding for new Accelerometers

1/12/10 Back to school! Begin subsystems testing

2/ 18/10 Integration of “liquid” canister and casing with Accelerometers.

4/1/10 Fully assembled competent payload– Full Missions Sim. #1

4/ sometime/10 BalloonSAT launch6/01/10 Full payload- tested and prepared-

to hand over to Wallops

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BudgetItem Cost

RockSAT Payload Slot $7000.00

1-Axis Low-Range Accelerometer $16.00

2-Axis Low-Range Accelerometer $23.00

1-Axis High-Range Accelerometer $12.00

2-Axis High-Range Accelerometer $16.00

50 µ mesh Fine Grain Silica Donation from Chemistry Department

Polycarbonate Tubing inside $05.00 outside $20.00

Other Misc. Materials(glues, wire, etc.)

$50.00

Travel for two to Wallops $2,000.00

Total $9,142.00

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Conclusions

• Concerns: – Vibration frequency and duration during flight– production of significant data (confidence that

fluid will produce distinctive characteristics), e.g. quality of data

– Static build up of granular substance