A CRITERION FOR THE OCCURRENCE OF BUBBLE FISSION AND ITS MODELING Can F. Delale 1, Şenay Pasinlioğlu 2, Patrik Zima 3 1 Işık 2 Istanbul 3 Institute University, Istanbul, Turkey Technical University, Istanbul, Turkey of Thermomechanics, CAS, Prague, Czech Republic CAV 2012 8 th 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 CAV 2012 8 th International Symposium on Cavitation, 14 -16 August 2012, Singapore
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. CAV 2012 8 th International Symposium on Cavitation, 14 -16 August 2012, Singapore
2. A bubble fission model Delale, Tunç (2004) Phys. Fluids 16, 4200 -4203. Assumptions: R • Bubble fission occurs at to , R=Rmin Rmax 1 • The original volume is conserved Main Bubble • Pg remains the same during fission Rmax 2 Rmin Product Bubble rf t t 1 t 0 CAV 2012 8 th International Symposium on Cavitation, 14 -16 August 2012, Singapore
RAYLEIGH-PLESSET EQUATION CAV 2012 8 th International Symposium on Cavitation, 14 -16 August 2012, Singapore
3. New Criterion for Bubble Fission Rayleigh-Taylor instability Transformation Seminar Presented at the Institute of Thermomechanics, Czech Academy of Sciences, Prague, 31 August 2011
The most unstable mode CAV 2012 8 th International Symposium on Cavitation, 14 -16 August 2012, Singapore
Solve the initial value problem for the most unstable mode Break-up time where CAV 2012 8 th International Symposium on Cavitation, 14 -16 August 2012, Singapore
Volume Conservation Energy Dissipation due to Bubble Fission CAV 2012 8 th International Symposium on Cavitation, 14 -16 August 2012, Singapore
Initial Value Problem for Bubble Fragments CAV 2012 8 th International Symposium on Cavitation, 14 -16 August 2012, Singapore
4. Results Pressure Signal CAV 2012 8 th International Symposium on Cavitation, 14 -16 August 2012, Singapore
Delale & Tunc (2004) Model (Nm=20, 2) CAV 2012 8 th International Symposium on Cavitation, 14 -16 August 2012, Singapore
Present Model (Nm=20, 2) CAV 2012 8 th International Symposium on Cavitation, 14 -16 August 2012, Singapore
Delale & Tunc (2004) Model (Nm=20, 2) CAV 2012 8 th International Symposium on Cavitation, 14 -16 August 2012, Singapore
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 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. CAV 2012 8 th International Symposium on Cavitation, 14 -16 August 2012, Singapore
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