A CRITERION FOR THE OCCURRENCE OF BUBBLE FISSION AND ITS MODELING Can F. Delale 1, Şenay...

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