Download - 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
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 2 / 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
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 2 / 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 timeas rebound mitigation.
I Extract the dimensionless parameters that define the energy loss
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 2 / 17
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
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 3 / 17
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
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 4 / 17
Effect of Drop Height
The measured rebound heights of a 20cm drop: water 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
Water: Ball Height = 20
Time (s)
Non−
Dim
ensio
na
l B
all
Heig
ht
0% filled
10% filled
40% filled
100% filled
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 5 / 17
Effect of Drop Height
The measured rebound heights of a 30cm drop: water 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
Water: Ball Height = 30
Time (s)
Non−
Dim
ensio
na
l B
all
Heig
ht
0% filled
10% filled
40% filled
100% filled
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 6 / 17
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
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 7 / 17
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)
Percentage of volume filled, by weight
Perc
ent R
ebound (
h2/h
1)
10 cm
20 cm
30 cm
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 8 / 17
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...”
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 9 / 17
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...”
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 9 / 17
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...”
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 9 / 17
Channeling Antkowiak and Gekle
This conceptual approach validates our direction and focus.
Sequence above: fill volume of 20%, dropped from 20cm.
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 10 / 17
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
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 11 / 17
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 1A Pos 1B Pos 2A Pos 2B
Pos 1C
Pos 2C
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 12 / 17
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 1A Pos 1B Pos 2A Pos 2B
Pos 1C
Pos 2C
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 12 / 17
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
Percentage of volume filled, by weight
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
Percentage of volume filled, by weight
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
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 13 / 17
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
Percentage of volume filled, by weight
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.
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 14 / 17
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.
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 15 / 17
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.
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 16 / 17
Acknowledements
Department of Mathematics, *Department of Mechanical EngineeringBrigham Young UniversitySupported by NSF Grant No. 0639328
Killian, Truscott (APS DFD–2011) Harnessing Sloshing as a Passive Dampener November 21, 2011 17 / 17