Numerical simulation of compression of the single spherical vapor bubble on a basis of the uniform model

Abstract

The problem of the response of a single spherical vapor bubble is considered for the case of an abrupt increase of pressure in the surrounding infinite liquid. The mathematical model adopted is based on the assumption of the uniformity of pressure, temperature and density throughout the bubble volume. The temperature field around the bubble is calculated using the energy equation for the liquid. Thermal–physical characteristics, exclusive of specific heats of the liquid and vapor, are considered to be temperature-dependent. A notable feature of the model is the exact fulfillment of the integral law of conservation of system energy, disregarding the relatively small vapor kinetic energy. The initial bubble radius and the pressure rise in the liquid were varied in the calculations. It was found that the temperature increment in the bubble due to vapor condensation and heat exchange with the liquid is approximately two orders of magnitude less than that due to adiabatic compression. To study the effect of condensation, calculations were performed in which phase transitions were artificially blocked at the bubble boundary. It was found that the character of the process in the latter case changes both quantitatively and qualitatively; in particular, the temperature increment increases by about an order of magnitude.