SloshSATPreliminary Design Review

Dr. Robert WalchDan Welsh

Maurice Woods IIIMotoaki Honda

Zach Sears

6/11/2010

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.

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.

Our Idea- Mathematical Model

We 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

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

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).

Expected Results

The success of the project will depend on the times and accelerations 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

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 accelerations 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 8.

• 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.

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.

Subsystems

• Liquido Requires z axis movemento 25 mL maximum

• Powero Will be supplied by two 9 volt batterieso Power can only be supplied to the payload when RBF is

short and G-switch is activated

• Accelerometero Requires 5V supplied by power systemo Must remain perpendicular to the plane of the payload disk

• Datao Information stored on 8 MB

SubsystemLiquid

• Special Requirement- Design Driver• Galden

o a non-corrosive, non-conductive, non-combustible fluid. o The team has put forth efforts to confirm with the manufacturer of this fluid, Solvay

Solexis, that it's properties will suit our needs as well as our budget.  Background research indicates that this fluid is intended for aerospace applications due to its thermal stability, non flammability, chemical inertness, low toxicity, and low volatility, and therefore will meet our needs.  Direct communication with Solvay Solexis and acquisition of the liquid has not yet been accomplished.

• use of multiple iterations of containment is intended to ensure safety and non-interference with other experiments.

Container System

The outer container will not only restrict the movement of the system to the z- axis, but will also act as a redundant container for the system.Container will be located near the center of the payload since we may not be using the center bolt with CSU.

Possible end cap for containers

Container System

Outer Diameter of outer container: 5.08cm

Height of outer Container:9cm

Height of Inner container:3cm

Outer diameter of inner container: 4.13cm

The area between the containers : 1/100 of an inch with the end caps.

The liquid will occupy 2/3 of the inner container.Volume of Galden: 26 mL

SubsystemPower

• Two 9 Volt batteries

• Supplies 5 Volts to the Accelerometers and the data system

• Current can only flow by shorting the RBF and activating the G-switch

Subsystem Accelerometer

• Must remain perpendicular to the base plate.

• Requires 5 Volts to operate.

• Functions in the range of +/- 37g’s

• Can operate in -40 C to 105 C.o This will work for our experiment. Our goal is to

find a generalized movement of the liquid system.

Subsystem Accelerometer

We will have one accelerometer on our container to characterize the movement of the container. We will use data characterizing the movements of the craft from a second accelerometer on our payload tied directly to the craft. The purpose for this is because we have hardware and code that has been tested and proves to work. For us to alter an already functioning payload would not be recommended. We understand that there will be slight error differences between the two accelerometers and we will account for this as best we can. Our experiment focuses on finding a general characteristic of movement because that is the focus of our model. The slight error difference between the two accelerometers is expected to be negligible.

Electronic Schematic(Eric Pahlke and COSGC)

SubsystemData

• Requires 5 volts• AVR has 8 MB of storage room• Samples will be taken at a rate of 20ms.

o This rate has been used in past missions o This sampling rate proved to acquire an adequate

amount of data for our analysis• Data will flow from the accelerometer to the Flash.

The data will then be stored in the AVR• Payload can be in Active or Safe mode.

SubsystemData

• Code concept map (COSGC)

Functional Block DiagramConnection of Subsystems

Will be open to WFF.When closed, payload will be armed

Open prior to launch.Closes at launch to activate payload

Testing

• October 29- we began testing. o Power on test and operations test of AVRo The payload still works after two years!

• November 5- o Test accelerometers for accuracy.o Force and Impact testing of container

prototypes o Liquid Slosh testing of Galdeno Center of Masso Balance/Spin Test

Testing

• Software Requirementso Data Retrieval Utility and Parser Utility from

RockON! kito Computer with XP

• Hardware Requirementso Vibe tableo Vacuum chamber

Testing

The main concern for failure comes mainly from the liquid container.

We will run the container under a series of impact tests to ensure the stability and strength of the polycarbonate and end cap structure.

Total Parts List

• 1-Axis Low Range Accelerometer (COSGC)• 1-Axis High Range Accelerometer (COSGC)• 2-axis Low Range Accelerometer (COSGC)• 2-axis High Range Accelerometer (COSGC)• .0203kg 5024μ mesh Fine Grain Silica (donated from

Chemistry)• 25 mL Galden (Solvey Solexis)• 9cm Outer Polycarbonate Tubing (Small Parts) $20.00• 5cm Inner Polycarbonate Tubing (Grainger) • RockOn! Board and Acrylic Plate (COSGC)• Spare Acrylic Plate to Allow for Bolting to the Top Bulkhead

of Canister (CSU)

Parts List

Parts on Hand Parts and Pieces to Order /Build

All Accelerometers.1L Galden Fluid at $150/pint from

Solvey Solexis

Fine Grain Solid Spare Acrylic Plate from CSU

RockOn! Board and Acrylic PlateAssemble Tubing into Final Designed

Liquid Container

Inner and Outer Polycarbonate Tubing Fully Assemble Board and Container

All parts have already been obtained and are ready to fabricate into the final design of the payload. The next step is to assemble all parts onto the payload and conduct center of mass testing before vibe table and vacuum chamber testing.

Monetary BudgetItem Cost

DemoSAT Payload Slot $??.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

Polycarbonate Tubing inside $05.00 outside $20.00

25 mL Galden 135 $30.00

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

$50.00

Travel to Launch $100.00

Total $272.00

Mission Requirements

RockSat Payload Canister User Guide Compliance

• Using the Galden fluid we will be approximately 1/5 of our allotted mass.

• Activation of the payload will occur once our G-Switch is flippedo We have a Remove Before Flight Pin

• Center of Gravity verification is complete. The liquid canister system is centered on the payload, thus the x-and y- directions will be acceptable because there will be little movement of mass in those directions. To compensate for the z- axis movement, more weight may be added to the base of the container.

Mass Budget

Part Mass (kg)

device disc 0.361

2 battery 0.092

outer cylinder 0.0652

inner cylinder 0.0157

Galden .176kg

• Mass: Total mass of .7099 Kg

1/5 of our total 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.

Management

ScheduleThe Official Schedule

6/29/2010-Reassemble to peruse modification of payload for balloon flight, after rocket flight

7/15/2010 Commence full system testing (if not already began)E.g.: pressure, temperature, duration, impact

7/22/2010 Full mission simulation testing complete

Our Additions

DemoSat-B 2010 Summer Schedule

Kick-Off Telecon 6/8/2010

PDR Slides Due 6/11/2010

Design Document Rev. A/B Due 6/11/2010

PDR Teleconference6/14/2010, 1:00pm MDT

CDR Slides Due 6/24/2010

CDR Teleconference 6/25/2010

Design Document Rev. C Due 6/30/2010

Test Readiness Review7/8/2010

First Full Mission Test Results Due7/16/2010

LRR Slides Due 7/26/2010

LRR (Boulder ??) 7/30/2010

Launch 7/31/2010

Design Document Rev. D (Final Reports) Due 8/5/2010

On-Site Visits TBA

Conclusions

Issues and concerns

• Vacuum tests and temperature control tests must be performed before any consensus on payload can be fully implemented.