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Numerical Modeling of the Mathematical Model of Single Spherical Bubble  

Kang, Dong-Keun (한양대학교 기계설계.메카트로닉스공학과)
Yang, Hyun-Ik (한양대학교 기계공학과)
Publication Information
Journal of the Korean Society of Manufacturing Technology Engineers / v.19, no.6, 2010 , pp. 731-738 More about this Journal
Abstract
Cavitation is described by formation and collapse of the bubbles in a liquid when the ambient pressure decreases. Formed bubbles grow and collapse by change of pressure, and when they collapse, shockwave by high pressure is generated. In general, bubble behavior can be described by Rayleigh-Plesset equation under adiabatic or isothermal condition and hence, phase shift by the pressure change in a bubble cannot be considered in the equation. In our study, a numerical model is developed from the mathematical model considering the phase shift from the previous study. In the developed numerical model, size of single spherical bubble is calculated by the change of mass calculated from the change of the ambient pressure in a liquid. The developed numerical model is verified by a case of liquid flow in a narrow channel.
Keywords
Cavitation; Bubble; Phase change; Mass transfer; Narrow channel; Rayleigh-Plesset equation;
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  • Reference
1 Cengel, Y. A., 2003, Heat Transfer, McGRAW-HILL, New York, pp. 868, 874.
2 Chapra, S. C. and Chnale, R. P., 1990, Numerical Methods for Engineers, McGRAW-HILL, pp. 596-617.
3 Cho, J. S., 2009, Analysis of Cavitation Effect in a Narrow Channel, A Thesis for a Master, Hanyang University, Republic of Korea.
4 Qin, Z., Bremhorst, K., Alehossein, H., and Meyer, T., 2007, "Simulation of cavitation bubbles in convergent-divergent nozzle water jet," J. Fluid Mechanics, Vol. 573, pp. 1-25.   DOI   ScienceOn
5 Brennen, C. E., 1995, Cavitation and Bubble Dynamics, Oxford University Press, New York, pp. 47-50.
6 Harris, P. J., 1996, "A Numerical Method for Modeling the Motion of a Spherical Bubble," Int.. J. Numerical Methods in Fluids, Vol. 22, pp. 1125- 1134.   DOI   ScienceOn
7 Sedov, L. I., 1996, Mechanics of Continuous Media, World Scientific Pub. Co Inc., USA, pp. 862-892
8 Yang, H., Desyatov, A. V., Cherkasov, S. G., and McConnell, D. B., 2008, "On the fulfillment of the energy conservation law in mathematical model of evolution of single spherical bubble," Int. J. Heat and Mass Transfer, Vol. 51, pp. 3623-3629.   DOI   ScienceOn
9 Mathew, S., Keith Jr., T. G., and Nikolaids, E., 2006, "Numerical simulation of traveling bubble cavitation," Int. J. Numerical Methods for Heat& Fluid Flow, Vol. 16 No. 4, pp. 393-416.   DOI   ScienceOn
10 Alehossein, H. and Qin, Z., 2007, "Numerical analysis of Ralyeigh-Plesset equation for cavitating water jet," Int. J. Numer. Meth. Engng., Vol. 72, pp. 780-807.   DOI   ScienceOn
11 Young, F. R., 1989, Cavitation, McGRAW-HILL, UK, pp. 4-37.
12 Plesset, M.. S. and Prosperetti, A., 1977, "Bubble Dynamics and Cavitation," Ann. Rev. Fluid Mech., Vol. 9, pp. 145-185.   DOI   ScienceOn