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A CRITERION FOR THE OCCURRENCE OF BUBBLE FISSION AND ITS
MODELING
Can F. Delale1, Şenay Pasinlioğlu2, Patrik Zima3
1Işık University, Istanbul, Turkey
2Istanbul Technical University, Istanbul, Turkey 3Institute of Thermomechanics, CAS, Prague, Czech Republic
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore
CONTENTS
1. Bubble Dynamics and Energy Dissipation Mechanisms
2. A Bubble Fission Model (Delale & Tunc, 2004)
3. New Criterion for Bubble Fission
4. Results
4. Conclusions and Future Perspectives
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore
1. Bubble Dynamics and Energy Dissipation Mechanisms
Viscous DampingThermal DampingAcoustic DampingBubble Fission
Free surface energy
Mixing
Turbulence
Brennen CE (2002) J. Fluid Mech. 472, 153.
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore
2. A bubble fission model
R
t
Rmax1
Rmin
rf
t1 t0
Rmax2
Product Bubble
Main Bubble
Assumptions:
• Bubble fission occurs at to , R=Rmin
• The original volume is conserved
• Pg remains the same during fission
mN
itbubbleproductitbubblemain VV
1,_,_ 00
min1/3
,fm
Rr
N 50E
Delale, Tunç (2004) Phys. Fluids 16, 4200-4203.
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore
RAYLEIGH-PLESSET EQUATION
2 3 1 33 4 2 11 0
2 2 Re 2k k
p
RRR R R R R C
R We
03
0 ttR
PP
k
gg
03
1 ttR
PP
k
gg
0
3
min1 g
k
fg P
R
rP
3 3
2 3 1 3
min min
3 4 2 11 0
2 2 Re 2
k k
f fk kp
r rRRR R R R R C
R R We R
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore
3. New Criterion for Bubble Fission
Transformation
Seminar Presented at the Institute of Thermomechanics,
Czech Academy of Sciences, Prague, 31 August 2011
Rayleigh-Taylor instability
The most unstable mode
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore
Solve the initial value problem for the most
unstable mode
where
Break-up time
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore
Volume Conservation
Energy Dissipation due to Bubble Fission
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore
Initial Value Problem for Bubble Fragments
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore
4. Results
Pressure Signal
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore
Delale & Tunc (2004) Model (Nm=20,2)
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore
Present Model (Nm=20,2)
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore
Delale & Tunc (2004) Model (Nm=20,2)
5. Conclusions and Future Perspectives
• The bubble fission model of Delale and Tunc (2004) is modified to shift the time break-time prior to the time at which the volume of the parent collapsing bubble attains its minimum value.
• A bubble break-up criterion, based on Rayleigh-Taylor instability analysis, is established for the occurrence of bubble fission and the bubble break-up time is estimated.
• The present model predicts more energy dissipation than that of Delale and Tunc (2004) as the number of fragments decrease.
• Thermal damping effects and nonlinear Rayleigh-Taylor instability is reserved for future work .
CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore