Numerical Simulation of Convergence of Nonspherical Shock Waves in a Cavitation Bubble

Abstract

An efficient numerical technique is developed for calculation of radially convergent shock waves arising inside an axially symmetric cavitation bubble during its collapse in a quiescent liquid. It allows one to consider the case in which the bubble remains nearly spherical at the end of its collapse and the shock wave significantly deviate from the spherical one only in a small central region. Motion of liquid and vapor is governed by the equations of gas dynamics. Heat conductivity of liquid and vapor as well as evaporation and codensation on the bubble surface are taken into account, wide-range equations of state are applied. The technique is based on a TVD-modification of the Godunov method, developed by the authors. Numerical convergence of the technique with refining the computational grid along the radial and angular coordinates is illustrated using a problem of collapse of a cavitation bubble in tetradecane. Resolution of non-sphericity of the convergent shock waves in the bubble is taken as a criterion of the numerical convergence. A case of collapse of a bubble is considered in which the radius of the bubble is initially 0.5 mm and the bubble is slightly prolate along the axis of symmetry. The liquid pressure and temperature are 60 bar and 663.15 K. The vapor in the bubble at the beginning of collapse is at the state of saturation at a temperature of the surrounding liquid with a pressure of 10.4 bar.