Mathematical Simulation of the Compression Process of a Vapor Bubble at a Pressure Increase in the Surrounding Liquid

摘要

The thermophysical and hydrodynamic processes in a spherical vapor bubble and the surroundingliquid at increasing external pressure are investigated by using a numerical simulation method. The investiga-tion is performed on the basis of a new mathematical model belonging to the class of models of homobaric bub-bles (the pressure in the bubble is homogeneous at nonhomogeneous temperature and density). The model takesinto account the following main physical effects: the viscosity of the liquid, the heat conductivity of the liquidand vapor, the surface tension, and the phase transitions at the bubble surface. An energy equation taking intoaccount convective heat transfer and viscous dissipation in the liquid is used to calculate the temperature fieldsin the liquid and vapor. The model also takes into account the dependence of the thermophysical properties onthe temperature. A distinctive feature of the proposed model is that the integral conservation law of the system'stotal energy (including the kinetic energy of the liquid, the surface energy, and the internal energy of the liquidand vapor) is exactly satisfied (without allowance for the kinetic energy of the vapor). As a result of the numer-ical simulation of the compression of vapor bubbles in water, we obtained data for the major characteristics ofthe process at considerable degrees of compression. It is shown that the heat and mass transfer between thevapor in a bubble and the surrounding liquid considerably slow down the temperature increase in the bubble.