Harnessing Sloshing as a Passive Dampener

Harnessing Sloshing as a Passive Dampener

Taylor Killian Robert Klaus*,with: Prof. Tadd Truscott*

Department of Mathematics, Department of Mechanical Engineering*Brigham Young UniversitySupported by NSF Grant No. 0639328

Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 1 / 17

Objectives

Focus Areas

Determine the dynamics of rebound mitigation.

I Quantify the motion of the sphere.I Discover the influence of varying physical parameters

Determine the details of the internal energy exchange.

I Investigate the interplay of cavity collapse and rebound mitigation.F Video analysis shows the formation of an internal jet at the same time

as rebound mitigation.

I Extract the dimensionless parameters that define the energy loss


Objectives

Focus Areas

Determine the dynamics of rebound mitigation.I Quantify the motion of the sphere.I Discover the influence of varying physical parameters

Determine the details of the internal energy exchange.

I Investigate the interplay of cavity collapse and rebound mitigation.F Video analysis shows the formation of an internal jet at the same time

as rebound mitigation.



Objectives

Focus Areas

Determine the dynamics of rebound mitigation.I Quantify the motion of the sphere.I Discover the influence of varying physical parameters

Determine the details of the internal energy exchange.I Investigate the interplay of cavity collapse and rebound mitigation.

F Video analysis shows the formation of an internal jet at the same timeas rebound mitigation.



Fill Volume Influence on Rebound Mitigation

Different fluid responses arose when varying the interior volume.

Trials of (l-r) 10%, 30% and 70% of internal volume and are dropped from 20 cm


Effect of Drop Height

The measured rebound heights of a 10cm drop: water filled.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Water: Ball Height = 10

Time (s)

Non−

Dim

ensio

nal B

all

Heig

ht

0% filled

10% filled

40% filled

100% filled




0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Time (s)

Non−

Dim

ensio

na

l B

all

Heig

ht

0% filled

10% filled

40% filled

100% filled




0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Time (s)

Non−

Dim

ensio

na

l B

all

Heig

ht

0% filled

10% filled

40% filled

100% filled


Viscosity’s Influence on Rebound Mitigation

Different viscosities were tested, varied fluid behavior was observed.

All trials are filled to 30% of internal volume and are dropped from 20 cm

Trials of (l-r): Water µ = 8.9 × 10−4 N sm2 , Alcohol µ = 1.92 × 10−3 N s

m2 , Glycerin µ = 9.5 × 10−1 N sm2


Viscosity’s Influence on Rebound Mitigation

Analysis of our data showed that the global effect of the sphere’smotion is unchanged.

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Water: % Rebound of Second Bounce (based on first bounce)

Percentage of volume filled, by weight

Perc

ent R

ebound (

h2/h

1)

10 cm

20 cm

30 cm

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Alcohol: % Rebound of Second Bounce (based on first bounce)


Perc

ent R

ebound (

h2/h

1)

10 cm

20 cm

30 cm


Previous Work

Antkowiak et. al. 2006, Short-term dynamics of a density interface

following an impact

I “The interface curvature reverses violently, forming a concentrated jetthanks to a purely inertial mechanism...”

Gekle et. al. 2009, High-Speed Jet Formation after Solid Object ImpactI “Jet formation...depends crucially on the kinetic energy contained in

the entire collapsing wall of the cavity...”


Previous Work


following an impact





Previous Work


following an impact





Channeling Antkowiak and Gekle

This conceptual approach validates our direction and focus.

Sequence above: fill volume of 20%, dropped from 20cm.


Energy Exchange: System Overview

We investigate the mechanism of cavity collapse in kinematic terms.

ho

h1

h2

Pos 0

Pos 1A Pos 1B Pos 2A Pos 2B

Pos 1C

Pos 2C


Energy Exchange: Formulation

Investigating the energy exchange

PE0 = Mgh0

KE1A = PE0

KE1B = KE1A − flloss − dynloss

PE1C = KE1B

· · ·

Determining the losses to fluid fillflloss,1=Mg(h0−h1)+mbg(h1,empty−h0)

flloss,2=Mg(h0−h2)+mbgh2,empty−flloss,1

ho

h1

h2

Pos 0


Pos 1C

Pos 2C


Energy Exchange: Formulation

Investigating the energy exchange

PE0 = Mgh0

KE1A = PE0

KE1B = KE1A − flloss − dynloss

PE1C = KE1B

· · ·

Determining the losses to fluid fillflloss,1=Mg(h0−h1)+mbg(h1,empty−h0)

flloss,2=Mg(h0−h2)+mbgh2,empty−flloss,1

ho

h1

h2

Pos 0


Pos 1C

Pos 2C


Energy losses to the fluid

flloss,1 = Mg(h0 − h1) + mbg(h1,empty − h0)

flloss,2 = Mg(h0 − h2) + mbgh2,empty − flloss,1

From these relations we establish the non-dimensional parameter E.I E = flloss

Mgh0

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


En

erg

y L

oss t

o F

luid

[E

]

Energy Losses of Water Trials

Loss1 10 cm

Loss1 20 cm

Loss1 30 cm

Loss2 10 cm

Loss2 20 cm

Loss2 30 cm

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


En

erg

y L

oss t

o F

luid

[E

]

Energy Losses of Alcohol Trials

Loss1 10 cm

Loss1 20 cm

Loss1 30 cm

Loss2 10 cm

Loss2 20 cm

Loss2 30 cm


Normalizing the second rebound

Second rebound data is normalized to extract global information.

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Water: 2nd rebound


No

rma

lize

d R

eb

ou

nd (

h/h

0)

10 cm

20 cm

30 cm

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Alcohol: 2nd rebound

Percentage of volume filled, by weightN

orm

aliz

ed

Re

bo

un

d (

h/h

0)

10 cm

20 cm

30 cm

Serves as an analog/description for Roller Hockey Ball dynamics.


Conclusions

Sloshing within a partially fluid filled sphere acts as a passivedampener.

Rebound suppression depends on drop height and fill volume.

There is an exchange of energy from the sphere to the fluid.

This exchange of energy occurs at cavity collapse and jet formation.


Future/Continued Work

Build and verify numerical model using ADINA.

Analyze experiments performed with different sphere elasticity andgreater drop height.

I Determine convergence of data.

Refine energy method to replicate observed data.


Acknowledements

Department of Mathematics, *Department of Mechanical EngineeringBrigham Young UniversitySupported by NSF Grant No. 0639328


Documents

Harnessing Sloshing as a Passive Dampener