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Liquid Sloshing Behavior in Microgravity with Application to Spacecraft Propulsion Systems Florida Institute of Technology Department of Mechanical and Aerospace Engineering Gabriel Lapilli Richard Schulman Charles Holicker Brian Wise Sunil Chintalapati Hector Gutierrez Daniel Kirk NASA Kennedy Space Center Launch Services Program Paul Schallhorn Brandon Marsell Jacob Roth Massachusetts Institute of Technology Space Systems Laboratory Dustin Hayhurst David Miller Alvar Saenz-Otero
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Page 1: Liquid Sloshing Behavior in Microgravity with Application ... · PDF fileLiquid Sloshing Behavior in Microgravity with Application to Spacecraft Propulsion Systems ... – Spin tank

Liquid Sloshing Behavior in Microgravity with Application to

Spacecraft Propulsion Systems

Florida Institute of Technology

Department of Mechanical and

Aerospace Engineering

Gabriel Lapilli

Richard Schulman

Charles Holicker

Brian Wise

Sunil Chintalapati

Hector Gutierrez

Daniel Kirk

NASA Kennedy Space Center

Launch Services Program

Paul Schallhorn

Brandon Marsell

Jacob Roth

Massachusetts Institute of

Technology

Space Systems Laboratory

Dustin Hayhurst

David Miller

Alvar Saenz-Otero

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Overview: Introduction

• Introduction

– Why Study Liquid Propellant Slosh?

– Sample Results

– Goal and Objectives

– ISS Slosh Experiment

• Slosh Experiment on the International Space Station

• Conclusions

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 2

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Upper-Stage Propellant Modeling

http://www.boeing.com/defense-space/space/delta/delta4/d4h_demo/book04.html

Lockheed Martin

Atlas V 401

Boeing Delta IV Heavy

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 3

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7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 4

http://www.osd.noaa.gov/GOES/ULA_GOES-P_Mission_Book.pdf

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Why Study Liquid Propellant Slosh?

• Delta IV launch postponed because of CFD

– Left: Original prediction of LH2 slosh

– Middle: Independent prediction of LH2 slosh

– Right: Redo of original prediction of LH2 slosh

• Two users get same result using same code, but is it true?

• How to validate models? What experimental data is there?

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 5

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Value

• NASA KSC LSP must ensure safety and performance of launch vehicles

• Current CFD slosh models lack benchmarking data and limited in predictive abilities

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 6

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Sample Results

• Data to improve CFD fluid slosh model predictions, benefiting spacecraft and launch vehicle design and operations

CFD Model Experiment

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 7

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Rationale for ISS Slosh Research

• ISS offers opportunity to acquire low-gravity slosh data

• Leverage proven SPHERES hardware on ISS

• World’s first long duration liquid slosh database 7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 8

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Goal and Objectives

• Goal

– Acquire long-duration, low-gravity slosh data for calibration of

detailed Computational Fluid Dynamics (CFD) models of

coupled fluid-vehicle behavior

• Objectives

– Utilize existing SPHERES satellites to propel transparent liquid-

filled tank

– Acquire system and liquid position data for known applied forces

using IMU and imaging systems

– Benchmark CFD model predictions

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 9

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SPHERES Slosh Experiment (SSE)

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• Picture above shows assembled SPHERES Slosh Experiment (SSE)

• SPHERES (x2) and VERTIGO (x2) already on ISS – items sent to ISS

referred to as ‘Slosh Payload’

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Slosh Payload

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 11

• Designed by Florida

Tech in collaboration

with NASA KSC LSP

• Slosh Payload

manufactured by Florida

Tech with exception of

– 3D printed plastic

– Liquid Slosh tank

– Electronics

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3D Printed Parts

• First SPHERES experiment to use 3D

printed Ultem parts

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 12

3D printed tanks, optical polish, pressure

tested to 1.5 atmospheres

3D printed backdrop, hood, saddles and

avionics boxes

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SPHERES Slosh Experiment (SSE)

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Overview: Slosh Experiment

• Introduction

• Slosh Experiment on the International Space Station

– Hydrodynamic Regimes

– Simulating Maneuvers on ISS

– Space to Ground interaction

– Test Sessions

– Initial Conditions

– Execution

• Conclusion

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 14

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Application of Non-dimensional Parameters

• Impossible to match all numbers

simultaneously

• Flow regimes and individual non-

dimensional numbers can be matched

• Settling Thrust maneuver: By Froude

number matching

• Pitch to Reorient maneuver: By matching

rotation rates for each individual upper-

stage non-dimensional number

• Passive Thermal Control maneuver: By

matching scaled rotation rate

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Hydrodynamic Regimes

• Ratio of Weber to Bond

provides insight to

either inertial

dominated regime or a

gravitational dominated

regime

• Ratio of Reynolds to

Froude provides insight

to either gravitational

dominated regime or a

viscous dominated

regime

Froude=1

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 16

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Example Maneuver: BBQ Roll

• BBQ roll performed for an upper-stage propellant tank to ensure even solar heating

• What are impacts of BBQ roll on liquid distribution inside a tank?

17 7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL

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Example Maneuver: Turn to Attitude

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Maneuvers on ISS • Maneuver 1: Simulate an Engine shut down

– Accelerate system along major axis of tank for a fixed duration

– Apply reverse thrust to accelerate system in opposite direction for a fixed duration

• Maneuver 2: Simulate a turn to attitude

– Spin tank about a minor axis to settle all propellants

– Make sharp 45 degree turn out of spin plane to 2nd burn attitude

• Maneuver 3: Simulate a thermal roll

– Slowly spin tank about minor axis to attain constant spin rate and settle fluid

– Thermal roll about major axis while maintaining constant major axis spin rate

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 19

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Control Room

• Purposely-setup control room at Florida Tech to support live ISS operations

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Test Sessions • Checkout Session: Jan 22nd, 2014

– Test Systems

– Execute first set of tests:

• Translation (engine shut down)

• Rotation (thermal roll)

• Turn to Attitude

• Results showed:

– Sensitivity to initial conditions

– Bubble count reduction required

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 21

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Initial Conditions

• Initial distribution of liquid in slosh tank unknown before experimentation

• Modeling feasibility is critical

Option 1: Abrupt acceleration and braking

Not effective at reducing bubble count

Option 3: Spinning about major axis

Effective at reducing bubbles, easy to execute. Attempted Initial Conditions

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 22

Option 2: Spinning about offset axis

Effective at reducing bubbles, hard to achieve

(large experiment, small space to move)

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Test Sessions • Science 1 Session: Feb 28th, 2014

• Executed with 40% fill level tank

– Crewmembers found best way to create

bubble-free initial condition with cover

off

– Executed tests

• Translation (engine shut down)

• Rotation (thermal roll)

• Turn to Attitude

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 23 (Playback speed 2x)

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Overview: Conclusion

• Introduction

• Slosh Experiment on the International Space Station

• Conclusion

– Conclusions

– Summary

– Future Research

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 24

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Conclusions

• Slosh Experiment launched in January 2014

• Two Tanks (20% fill level, 40% fill level)

• Three test sessions

• Slosh Experiment testbed ultimately handed over to SPHERES

Program office at NASA AMES for continuing research

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 25

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Summary

Slosh experiment on ISS fills a gap in available data to benchmark models

Agreement

Being determined

Agreement

± 8%

Agreement

± 3%

Comparison Simulation Experiment Testing Platform

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 26

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Future Research Possibilities

• Create and improve control algorithms that

include sloshing liquid behavior control and

prediction for trajectory optimization

• Study Propellant Management Devices

• Study cryogenic propellants

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 27

Courtesy of ATK – Alliant Techsystems

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Acknowledgements

NASA KSC – Launch Services Program

NASA Game Changing Development Program

NASA AMES

NASA Johnson Space Center

NASA Marshall Space Flight Center

MIT – Space Systems Laboratory

Florida Tech team – Aerospace Systems And Propulsion (ASAP) laboratory

Crewmembers in the ISS

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Supplemental Slides

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Flammability/Off-gassing

• Flammability and Off-gassing analysis/assessment performed on all components of Slosh

payload

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 31

OpNom Material Flammability Assessment Status

Aluminum 2024 T351 On MAPTIS list of approved material

ULTEM 9085Passed flammability and offgassing test, reference:

Slosh_ULTEM_Flammability Assessment

Center Hub Aluminum 2024 T351 On MAPTIS list of approved material Passed

IDS UI-5580CP-C GigE camera

Acceptable by analysis (reference: discussion at

flammability and offgassing meeting via

teleconference on March 29, 2013)

Stainless-steel On MAPTIS list of approved material

Aluminum 2024 T351 On MAPTIS list of approved material

ULTEM 9085Passed flammability and offgassing test, reference:

Slosh_ULTEM_Flammability Assessment

LED light panel

Acceptable by analysis (reference: discussion at

flammability and offgassing meeting via

teleconference on March 29, 2013)

Lexan sheet On MAPTIS list of approved material

BellowAcceptable by analysis (reference: email from Dr.

Mike Pedley on May 8, 2013)

Aluminum 2024 T351 On MAPTIS list of approved material

ULTEM 9085Passed flammability and offgassing test, reference:

Slosh_ULTEM_Flammability Assessment

LED light panel

Acceptable by analysis (reference: discussion at

flammability and offgassing meeting via

teleconference on March 29, 2013)

Lexan sheet On MAPTIS list of approved material

L20 Tank 3D printed LexanAcceptable by analysis (reference: email from Dr.

Mike Pedley on February 12, 2013)Passed

L40 Tank 3D printed LexanAcceptable by analysis (reference: email from Dr.

Mike Pedley on February 12, 2013)Passed

S40 Mass ULTEM 9085Passed flammability and offgassing test, reference:

Slosh_ULTEM_Flammability AssessmentPassed

Internal electronic components

Acceptable by analysis(reference: discussion at

flammability and offgassing meeting via

teleconference on March 29, 2013)

ULTEM 9085Passed flammability and offgassing test, reference:

Slosh_ULTEM_Flammability Assessment

Slosh Flash Drive

Small printed circuit board carrying

the circuit elements and a USB

connector, insulated electrically and

protected inside a plastic, metal, or

rubberized case

Acceptable by analysis (reference:

SSE_Flammability_Offgassing_Summary.pdf)Passed

Slosh Hard Drive

Flash Hard Disk is manufactured by

InnoDisk, contains no magnets, (this

is similar to a USB thumb drive,

except uses the SATA port)

Hard Drives manufactured identically as VERTIGO

Hard Drives, Acceptable by analysis (reference:

SSE_Flammability_Offgassing_Summary.pdf)

Passed

Frame Arm

Camera

Hood

Backdrop

Slosh Avionics Box

Passed

Passed

Passed

Passed

Passed

NASA WSTF

flammability

and

offgassing

test results of

3D printed

plastic

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Tank Pressure

• Requirement from Safety Data Package, standard hazard form are:

– Have a maximum delta pressure of 1.5 atmospheres (22 psia, 1.5 bars)

• Four different pressure tests performed

– Gradual increase of pressure within Wet Slosh tank (full of water)

– Rapid increase of pressure within the Wet Slosh tank (full of water)

– Gradual increase of pressure within Dry Slosh tank (no water)

– Rapid increase of pressure within the Dry Slosh tank (no water)

• Leak check performed with dry towel (for Wet tank test) and soap solution (for Dry tank

test)

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Touch Temperature Test

• Requirements for touch temperature are based of SSP 50005, section 6.5.3

• Minimum temperature of 4 ºC (39 ºF) and a maximum temperature of 45 ºC (113 ºF)

• Touch Temperature testing was performed at NASA MSFC, EMC/EMI facility for Slosh

hardware articles in the ISS configuration

– Temperature readings were taken at pre-defined locations on surface of the SSE

– Temperature readings were taken every five minutes after SSE startup for a total

duration of 60 minutes.

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 33

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Vibration Test

• Slosh hardware vibration tested in its

stowage configuration (bubble

wrapped and packed in class III triple

CTB)

• Maximum flight random vibration

envelope as specified in SSP 50835

• Post-vibration analysis, inspection,

and verification performed

– Functioning of Slosh Avionics

Box

– Structural integrity of the Slosh

tank

– Camera lens (shatter)

– Slosh hardware (fit check)

– LED panels (shatter) in Hood and

Backdrop

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 34

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EMI/EMC Test

• EMI testing is required to verify that the SSE

meets EMI requirements set forth in SSP

30237

• SSE did not pass the RE02 test, but waiver

has been issued for flight certification

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 35

• Two tests

performed for

entire SSE

– Radiated

Emissions

– Radiated

Susceptibility

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Clamp Functionality

• A frame arm consisting of a directional

positioning system (saddle) and a sliding screw

clamping mechanism is utilized for attachment

of SPHERES to the Slosh Experiment frame.

• Two types of buffer materials are used on either

side of clamp mechanism.

– An Ultem buffer that is part of saddle

extends into clamping region from top.

– A thick rubber buffer is used on sliding

portion of clamp to ensure a spread contact

force.

• SPHERES is positioned into saddle with tank

protruding through clamp mechanism.

• Thumbscrew is tightened to a high finger tight

torque securing SPHERES unit to Slosh

Experiment.

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 36

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Clamp Over Tightening

• Multiple methods to prevent over-torquing

are implemented:

– Small knob size reduces amount of

torque an astronaut can apply

– Mechanical stop ramps ensure that tank

cannot be deflected by more than 0.072”

– Rubber buffer can compress by more

than 0.072”

– Carrier mount screws sized shear/deform

prior to thumbscrew pull out

• DOT-SP 10776 Rev. 10 §178.42 (f) (2) states

tank certification hydrostatic test:

– Conducted at 3000 psi and flattened with

60° wedges containing a 1/2” radii nose.

Must not rupture under six times the

seam thickness of deformation.

– Tank seam of 1/8” allows for 3/4” of

deflection. Far less than 0.072”

maximum mechanically allowed by

system

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 37

NASA-STD-3000 207 lists maximum

torque applied by an astronauts hands.

Design numbers used worst case hand

torque over lesser finger torque.

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Structural Failure of CO2 Tank due to Clamp Mechanism Cause 1

• Over torqueing of tank clamp thumbscrew has potential to damage SPHERES CO2 tank

Control 2.A: Tank must not Must not rupture under six times the seam thickness of deformation per DOT-

SP 10776 Rev. 10 §178.42 (f) (2). SPHERES CO2 tank has 0.125” seam therefore allowing 0.750”

deflection.

Test/Verification 1:

• Verification 1.1 Micrometer 4 CO2 tanks diameter, two empty and two full, in three different

orientations each to take average. Secure CO2 tank in clamp, tighten thumbscrew to maximum

supination torque as define by NASA-STD-3000 207 and micrometer diameter in three different areas.

Verify no value exceeding maximum deflection criteria.

• Verification 1.2 Leave CO2 tank clamped for 3 hours and recheck tank diameter

dimensions. Verify no value above the maximum deflection.

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 38

Retaining Pin

Free Spinning

End

Cross-Sectional View Bottom View

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Experimental Validation Overview

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 39

• Two tanks and two SPHERES units used

in MSVP experimental validation.

• CO2 tanks are flight size, but do not

include thermal coating used on ISS flight

tanks.

• Tank diameters measured at three different

stations from the non-threaded end of the

tank: 1.75 inches, 3.50 inches and 5.00

inches on each tank.

• Tank 1 diameter: 2.01 – 2.013 inches

• Tank 2 diameter: 2.008 – 2.0195 inches

• BLUE sleeve diameter: 2.055 inches

• ORANGE sleeve diameter: 2.065 inches

• Nominal gap on radius: 0.021 inches (0.53

mm) between tank wall and sleeve

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CO2 Tank – Sleeve Contact

• CO2 tank (tank 2) threaded into

blue SPHERE

• Zoom-in picture shows nominal

gap between CO2 tank and metal

sleeve

• Nominal gap on radius: 0.021

inches (0.53 mm)

• Pushing in any orientation (left,

right, up, down) it is ‘easy’ to push

the CO2 tank into the wall of the

SPHERES metal sleeve using just

finger pressure.

• It is easy to push either CO2 tank

into the sleeve of either SPHERES.

• No change to operation (no

damage) occurs when the CO2 tank

is pushed into the sleeve.

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 40

Metal sleeve

CO2 tank

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Example of Clamp Mechanism Holding CO2 Tank

• Upper Left: photo of underside of

clamp assembly. No CO2 tank inserted.

Clamp is fully retracted.

• Upper Right: photo of underside of

clamp assembly with CO2 tank fully

clamped into place. Thumb screw is

finger tightened. Notice compression of

orange rubber pad, no compression of

ULTEM sleeve occurs.

• Lower Left: Example of measurement

of tank diameter with thumb screw

tightened.

• Lower Right: Example of CO2 tank

clamped in one of three positions used

to measure possible deflection of CO2

tank diameter

• Conclusion: with tank clamped under

thumb screw torque no tank

deformation measured.

• Conclusion: using maximum finger

tightening, clamp can not be over-

torqued – stop works as intended.

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 41

Completed: Verification 1.1 and Verification 1.2

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Structural Failure of Frame arm due to Collision Cause 2

• Collision of SPHERES Slosh Experiment has potential to damage frame arm and tank clamp

mechanism.

Control 2: Frame arm and tank clamp must not yield and maintain functionality under loading conditions

defined in section 7.18 of SLOSH FSDP Phase-I-II .

Test/Verification 2.A:

• Verification 2.A.1 Clamp SPHERES in with nominal finger torque. Mount frame arm

vertically so that the CO2 tank axis is parallel with the floor. Apply a total static load of 36.6 N to the

end of spheres. Verify no yielding by dimensional and visual inspection.

• Verification 2.A.2 Clamp the SPHERES in with nominal finger torque. Mount frame arm

horizontally with CO2 tank axis parallel with the floor. Apply an incremental static load of 50 N up to a

maximum load of 227 N to the upward facing side of SPHERES. Verify no yielding by dimensional

and visual inspection after each load increment.

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 42

V 2.1

V 2.2

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Examples of Clamp Holding SPHERES in Various Orientations

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Maximum Loading Summary

• Upper: Blue SPHERES with CO2 tank (tank 2) loaded

into cantilevered test fixture.

• Note that blue SPHERE with CO2 tank is about 4.2 kg

(9.2 lb).

• Force transmitted to CO2 tank and saddle is about 40 N

• Visual inspection indicates that CO2 tank contacts wall

sleeve

• Lower: Blue SPHERES with CO2 tank (tank 2) loaded

into cantilevered test fixture.

• Additional weight: 25.4 kg (56 lb).

• Force transmitted to CO2 tank and saddle is about 250 N

• Visual inspection indicates that CO2 tank contacts wall

sleeve

• Test repeated on three sides of SPHERES unit (not

repeated on side that holds VERTIGO).

• Test repeated by placing weight on top of SPHERES

with saddle on bottom

• Conclusion: no loss of functionality or damage to

SPHERES, CO2 tank, saddle, clamp, etc.

7/21/2014 AAS 3rd ISS Research and Development Conference - Chicago, IL 44

Completed: Verification 2.A.1

and Verification 2.A.2

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Testing of Both Clamps

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Notes/Observations/Comments

• Orientation saddle performs as intended

– Alignments of SPHERES with frame axis arm is better than 2 degrees (note cosine 2

degrees = 0.99939)

– Clamp mechanism/grip itself prevents rotation of the CO2 tank once clamped down

• With thumb screw tightened down using nominal finger torque, I was not able to pull CO2

tank out of clamping mechanism

• With thumb screw tightened down using nominal finger torque, placing 250 N (56 lb) on

top of SPHERES did not cause tank to slide or move within clamping mechanism or create

any measureable deflection of saddles (indicated good base contact).

• Shaking frame arm with SPHERES unit attached did not result in any movement of clamp

relative to CO2 tank. Works exactly as anticipated.

• Tests repeated multiple times – no instances of clamp not working as intended.

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Liquid Slosh Tank Design • Bo can be maximized for given fill level (balance between r2 and

m)

– Approaching peak from small radius, acceleration ↓, and Bo ↑

– Past peak, radius ↑, acceleration ↓, and Bo ↓

• Purpose: Bond analysis not sufficient – how much impact does fill

level have on creating a slosh event that alters system trajectory

• Liquid impacts tank and entire system is ‘pushed’ to a new

velocity, given by conservation of momentum

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Surrogate Fluid Options

• Surrogate fluid options Novec Fluid and Silicone Fluid (vs. water)

• Both fluid have low viscosity, surface tension and contact angle

• Non-dimensional numbers reflect Novec fluid has high Bond number and Weber number

ranges

• High Bond and Weber numbers would favor slosh as fluid tends to be in gravity or inertia

dominated regime

Water Novec Silicone

Bond Number 1.62 12.95 5.61

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PTC Maneuver: Non-dimensional Mapping Results

• For a specified rotation rate (deg/s) for an rocket upper-stage, can the non-dimensional number suggest

rotation rates for ISS slosh experiment?

• Table below shows expected rotation rate (in deg/s) for slosh experiment to match non-dimensional numbers for

typical rocket upper-stage

• Bond, Weber and Reynolds numbers from upper-stage are used to derive individual rotation rates for specified fluid

and slosh experiment dimensions (tank radius) and each non-dimensional number provides a unique rotation rate

Rotation Rate (Deg/s) 0.1 0.1 0.1 0.1 0.1 0.1

Velocity (m/s) 4.36E-03 3.49E-03 2.66E-03 4.36E-03 3.49E-03 2.66E-03

Acceleration (m/s2) 7.62E-06 6.09E-06 4.65E-06 7.62E-06 6.09E-06 4.65E-06

Bond Number 1.29E+00 6.61E-01 2.93E-01 4.12E+00 2.11E+00 9.35E-01

Weber Number 1.29E+00 6.61E-01 2.93E-01 4.12E+00 2.11E+00 9.35E-01

Reynolds Number 5.65E+04 3.62E+04 2.10E+04 6.34E+04 4.06E+04 2.36E+04

Froude Number 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00

Rotation Rate (Deg/s) 27.1 19.4 12.9 48.4 34.7 23.1

Rotation Rate (Deg/s) 27.1 19.4 12.9 48.4 34.7 23.1

Rotation Rate (Deg/s) 515.8 330.1 191.9 578.8 370.4 215.4

Bond Number 1.29E+00 6.61E-01 2.93E-01 4.12E+00 2.11E+00 9.35E-01

Weber Number 4.24E+03 2.17E+03 9.62E+02 1.35E+04 6.92E+03 3.07E+03

Froude Number 3.28E+03 3.28E+03 3.28E+03 3.28E+03 3.28E+03 3.28E+03

Reynolds Number 1.70E+05 1.22E+05 8.11E+04 3.04E+05 2.18E+05 1.45E+05

Bond Number 4.24E+03 2.17E+03 9.62E+02 1.35E+04 6.92E+03 3.07E+03

Weber Number 1.29E+00 6.61E-01 2.93E-01 4.12E+00 2.11E+00 9.35E-01

Froude Number 3.05E-04 3.05E-04 3.05E-04 3.05E-04 3.05E-04 3.05E-04

Reynolds Number 2.97E+03 2.13E+03 1.42E+03 5.31E+03 3.80E+03 2.53E+03

Bond Number 1.53E+06 6.28E+05 2.12E+05 1.93E+06 7.91E+05 2.67E+05

Weber Number 4.67E+02 1.91E+02 6.47E+01 5.88E+02 2.41E+02 8.14E+01

Froude Number 3.05E-04 3.05E-04 3.05E-04 3.05E-04 3.05E-04 3.05E-04

Reynolds Number 5.65E+04 3.62E+04 2.10E+04 6.34E+04 4.06E+04 2.36E+04

Water

LH2 LOX

Rocket Upper-Stage

Tank Slosh Experiment

Bond Matching

Weber Matching

Reynolds Matching

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Surrogate Fluid

• Deviation in displacement between frozen solid

and liquid is:

– CG Displacement: 100 mm

– Velocity: 2 mm/s

– No rotations induced in this case

• Deviation in displacement between frozen solid

and liquid is:

– CG Displacement: 38 mm

– Velocity: 2 mm/s

– No rotations induced in this case

LIQ SOL LIQ SOL LIQ SOL LIQ SOL LIQ SOL LIQ SOL LIQ SOL LIQ SOL LIQ SOL

Man Fill Vol X X Δ Y Y Δ Z Z Δ X X Δ Y Y Δ Z Z Δ X X Δ Y Y Δ Z Z Δ

1 20 -1 0 1 813 713 100 -14 -13 2 0 0 0 143 145 2 0 0 0 0 0 0 0 0 0 0 0 0

1 20 -1 0 1 725 686 38 -24 -12 12 -1 0 1 142 140 2 -1 0 1 0 0 0 0 0 0 0 0 0

POSITION (mm) VELOCITY (mm/s) ROTATION (Deg/s)

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