Energy flow investigations of Rayleigh-Plesset equation for cavitation simulations

Abstract

Nonlinear Rayleigh-Plesset Equation (RPE) for cavitation simulations is investigated using energy-flow theory. Nondimensional RPE affected by Reynolds-number, surface-tension, bubble-pressure, and liquid static-dynamic pressure ratio is derived to examine its equilibrium points with stability, possible periodical/chaotic motions by the energy-flow criteria. An example is numerically analyzed to illustrate the developed method. Five cases of the example reveal: 1) It is a damped system, where initial disturbances are gradually reduced with its phase point tends to its stable equilibrium-point; 2) Reynolds-number affects the damping of system, large one corresponds small damping; 3) Bubble-pressure, surface-tension and liquid static-dynamic pressure ratio affect the position of equilibrium point; 4) Periodical orbit appears only in forced vibrations, in which free vibration is reduced with time forward and the system finally shows a stable periodical oscillation; 5) Energy flow criteria for chaotic motions is not reached, and there are no chaotic motions for the cases of example. Numerical simulations confirm the developed energy-flow means with available computer code is effective to investigate generalized RPEs to reveal their inherent characteristics affected by required parameters in engineering cavitation analysis and designs, such as considering mass transports across the boundary of bubble by evaporation or condensation of liquids.

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