Numerical simulation of radially converging shock waves in a bubble cavity

Abstract

This paper presents a numerical technique investigating the final stage of focusing a radially converging nonspherical shock wave in the neighborhood of center of the axially symmetric cavitation bubble subjected to strong compression. Hydrodynamic model used includes liquid compressibility, heat conductivity of vapor and liquid, as well as evaporation and condensation on the interphase surface; the realistic wide-range equations of state are used. The calculation is performed on moving grids with explicit accentuation of the bubble surface. This technique is based on the TVD modification of the Godunov second order accuracy scheme in space and time. Its efficiency is due to an allowance for the special features of the problem in the final stage of focusing of nonspherical shock wave in the central part of the bubble. After the value of deformation of the shock exceeds the threshold (i.e., when the shock wave becomes largely nonspherical) in the central field of the bubble the curvilinear radially diverging grid is changed by the rectilinear oblique-angled grid close to Cartesian. At the same moment, the spherical immovable system of the reference frame is changed to a cylindrical system. The recalculation of the cell parameters from grid to grid is made by the method of conservative interpolation. The efficiency of the proposed approach is shown by the test problem’s calculation results and an illustrative example.