1. A CRITERION FOR THE OCCURRENCE OF BUBBLE FISSION AND ITS MODELING Can F. Delale 1, Şenay Pasinlioğlu 2, Patrik Zima 3 1 Işık University, Istanbul, Turkey 2 Istanbul Technical University, Istanbul, Turkey 3 Institute of Thermomechanics, CAS, Prague, Czech Republic CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore

2. 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

3. 1. Bubble Dynamics and Energy Dissipation Mechanisms Viscous Damping Thermal Damping Acoustic Damping Bubble 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

4. 2. A bubble fission model R t R max1 R min rfrf t1t1 t0t0 R max2 Product Bubble Main Bubble Assumptions: Bubble fission occurs at t o, R=R min The original volume is conserved P g remains the same during fission Delale, Tunç (2004) Phys. Fluids 16, 4200-4203. CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore

5. RAYLEIGH-PLESSET EQUATION CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore

6. 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

7. The most unstable mode CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore

8. 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

9. Volume Conservation Energy Dissipation due to Bubble Fission CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore

10. Initial Value Problem for Bubble Fragments CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore

11. 4. Results Pressure Signal

12. CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore Delale & Tunc (2004) Model (N m =20,2)

13. CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore Present Model (N m =20,2)

14. CAV2012 8th International Symposium on Cavitation, 14-16 August 2012, Singapore Delale & Tunc (2004) Model (N m =20,2)

15. 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