Abstract:
The possibility of increasing the calculation efficiency by the joint use of two models of the dynamics of a single weakly-nonspherical vapor bubble under its strong collapse in liquid is studied. In both models the motion of liquid and vapor is split into a spherical component and its small nonspherical perturbation. The models differ in the description of the spherical component. In the first (simplified) model, it is described by a system of ODE together with partial differential equations in temperature, derived under the assumption of weak compressibility of liquid and bubble homobaricity. In the second model, one-dimensional gas dynamics equations are applied. The advantage of the simplified model consists in determining a numerical solution with much-less computer time costs in comparison with what is required for the numerical integration of gas dynamics equations. The assumptions used in the simplified model in the final stage of collapse become incorrect, and, as a result, the numerical solution errors increase. Therefore, the simplified model is applied at the beginning of bubble collapse, whereas the gas dynamics equations are used at its end. Within this approach, the numerical solution in the final stage of collapse is dependent on the moment of transition to the gas dynamics equations. It is shown that satisfactory description of evolution of bubble sphericity distortion is achieved when the transition is made under the condition that the Mach number $M$ of vapor in the vicinity of the bubble surface is less than 0.4. Satisfactory resolution of the shock wave in the bubble is attained when the transition is performed at $M<0.2$.
Keywords:vapor bubble collapse, shock waves, small nonsphericity of bubble.
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