A Two-Scale Solution of the Forced Rayleigh-Plesset Equation Governing the Dynamics of Cavitation Bubble Vaporous Growth
PENNSYLVANIA STATE UNIV UNIVERSITY PARK APPLIED RESEARCH LAB
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A two-scale analysis of the forced Rayleigh Plesset equation of cavitation bubble dynamics is performed. The problem of cavitation inception as it relates to bubble dynamics involves vaporous cavitation nucleus growth as it is influenced by the pressure distribution on a submerged body. This brings into prominence two widely varying time scales. The laboratory time is characterized by the bubbles travel over the body, while the bubble time is characterized by the very high natural frequency oscillations of the individual bubble. The laboratory time is expected to much longer than the bubble time thus they can be related by a very small parameter, epsilon. Using these two time scales, a perturbation expansion is performed on the forced Rayleigh-Plesset equation and its initial conditions up to the third order in epsilon. The resulting zero and first order equations are solved, subject to these solutions being independent of the laboratory time. In this case the integrability condition for each step is thereby identically satisfied.
- Numerical Mathematics
- Fluid Mechanics