Magnetic Sloshing Damping in Microgravity

Álvaro Romero-Calvo

Gabriel Cano Gómez

Elena Castro-Hernández

Miguel Ángel Herrada Gutiérrez

Filippo Maggi

An alternative for small satellites

Index

1. Liquid sloshing

2. Magnetic liquid sloshing in microgravity

3. Qualitative and quantitative effects

4. Case of application

5. Conclusions & next steps

6. UNOOSA DropTES - StELIUM

8th iCubeSat Workshop 2019 2Image Credit: Isabel Romero Calvo

1. Liquid sloshing - g

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Physical Properties

Tank Geometry

Inviscid ModelMechnical Analogy

Implementation

Adapted from “Nonlinear dynamics and control of space vehicleswith multiple fuel slosh modes”, M. Reyhanoglu, J. Rubio Hervas

1. Liquid sloshing - g

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Physical Properties

Tank Geometry

Inviscid ModelMechnical Analogy

Implementation

1st modedominates

Excellent agreement

z

r

Experiment(𝒓𝒂𝒅/𝒔)

Model(𝒓𝒂𝒅/𝒔)

𝒘𝟏 18.65 18.46

𝒘2 35.37 33.14

𝒘𝟑 44.37 42.15

Analytical high-g sloshing models are reliable and widely used

Handpicking

1. Liquid sloshing - 𝝁𝒈

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Physical Properties

Tank Geometry

Inviscid ModelMechnical Analogy

Implementation

Surface Tension (𝜎)

Surface Tension (𝜎)

𝜎𝜎

“Experimental and Theoreticla Studies of Liquid Sloshing atSimulated Low Gravity”, F.T. Dodge, L.R. Garza

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So then, problem solved!

Telemetereing and Data Relay Satellite(TDRS) tanks with bladders. Extractedfrom “The New Dynamic Behavior ofLiquids in Moving Containers”, F.T. Dodge.

CFD simulation of liquid motion after a settlingacceleration of 3.27 X 10-6𝑔0. Extracted from “TheNew Dynamic Behavior of Liquids in MovingContainers”, F.T. Dodge.

Large amplitude sloshing analogy.Extracted from “The New DynamicBehavior of Liquids in MovingContainers”, F.T. Dodge.

Highly sensitive dynamics in 𝜇𝑔. CFD models are required

2. Magnetic liquid sloshing in microgravity

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Physical Properties

Tank Geometry

Inviscid ModelMechnical Analogy

Implementation

Surface Tension

Surface Tension

Magnetic Force

Coupled magnetofluidodynamic problem

Can be decoupled for small oscillations

Volume force density

being• 𝑴: Magnetization• 𝑀𝑛 : Normal surface component of M• 𝑯: Magnetic field

𝒇𝑲 = 𝜇0𝑴∇𝑯

Surface force density

+ 𝒇𝒔 =1

2𝜇0𝑀𝑛

2

3. Qualitative and quantitative effects

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Qualitative• Restoring force “equivalent” to gravity• Inhomogeneous magnetic acceleration• Short range of action, suitable for CubeSats• Modified free-surface shape

Quantitative• Shift of oscillation frequencies• Increase of damping ratios

Magnetic liquid sloshing can be predicted and quantified

“Experimental and Theoreticla Studies of Liquid Sloshing atSimulated Low Gravity”, F.T. Dodge, L.R. Garza

4. Case of Application

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Detumbling of a 3U CubeSat

1U cylindrical propellant tank (50% filling ratio)

Passive magnetic damping system(neodymium magnet magnetized at 1800 kA/m)

Control Law𝑴 = −𝑀0 · 𝑠𝑖𝑔𝑛 𝒘 −𝒘𝒅

Parameters

𝐼 = 1.09, 5, 5.5 · 10−2 𝑘𝑔𝑚2

𝒘𝟎 = 0 , 0,0.6 𝑟𝑎𝑑/𝑠𝒘𝒅 = 0 , 0,0.01 𝑟𝑎𝑑/𝑠𝑀0 = 5mNm

CubeSat STF-1. Adapted from NASA, West Virginia Space Grant Consortium (WVSGC), West Virginia’s University (WVU)

X

Z

Y

4. Case of Application

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h

Width

Ferrofluid1:10 vol EMG-700

Magnet

Curved Interface

𝑩𝒐𝒎𝒂𝒈

Magnet of 60 g -> 100% increase in fundamental frequency

4. Case of Application

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Equivalent spring-mass system

𝑇𝑅 =𝑋

𝑌

The magnet increases the natural frequencies and reduces the transmissiblity in the 0-2 rad/s band

1 2 3 4 5Mode

4. Case of Application

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Magnetic analogyFree sloshing analogy

Pendulum𝐶𝑦𝑧 = 0.5 𝑠−1, 𝐶𝑥 = 0.1 𝑠−1

(damping in terms of ang. mom.)

𝑚 = 0.4 𝑘𝑔, 𝑙 = 0.025 𝑚

𝒎𝒏 (Kg) 𝒌𝒏 (N/m) 𝒍𝒏 (m)

0 0.0735 - 0.0375

1 0.1572 1.1995 0.0373

2 0.0032 0.3296 0.0411

3 0.0009 0.3230 0.0444

Spring-MassDamping Coeff: 𝛾 = 0.15

VS

4. Case of Application

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No

n-m

agn

etic

Mag

net

icAngular Velocity (rad/s)

First 20 s First 1.5 h

4. Case of Application

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No

n-m

agn

etic

Mag

net

icSloshing disturbance (Nm)

First 20 s First 1.5 h

4. Case of Application

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No

n-m

agn

etic

Mag

net

icMechanical Displacement (m)

First 20 s First 1.5 h

5. Conclusions & next steps

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1. Magnetic fields can be used to position a magnetic liquid in microgravity

2. A significant increase in the sloshing frequencies of ferrofluid-based propellants can be achieved with low-mass magnets

3. Magnetic liquid sloshing can be predicted and quantified

4. The benefits for pointing angle accuracy have to be explored

5. The interaction with the spacecraft and the space environmenthas to be analysed

6. UNOOSA DropTES - StELIUM

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INGENIERÍA AEROESPACIAL Y MECÁNICA DE FLUIDOS

(TEP-956)

Validation of the magnetic sloshing model

Magnetic Sloshing Damping in Microgravity

Álvaro Romero-Calvo

Gabriel Cano Gómez

Elena Castro-Hernández

Miguel Ángel Herrada Gutiérrez

Filippo Maggi

Thank you for your attention!