Theory and numerical analysis of cavitation inception for a vapor bubble accompanied with nonequilibrium evaporation

A cavitation inception theory of a vapor bubble in flowing liquid is presented by taking account of a set of fluid dynamics boundary conditions for nonequilibrium evaporation at the bubble wall. The boundary conditions for the vapor temperature, pressure and density at the wall are a set of solutions of the polyatomic type of ES-BGK Boltzmann equation. The evaporation rate and the vapor-liquid temperature discontinuity at the bubble wall are treated in a physically correct way at a molecular level. The theory also considers the translational motion of the bubble in a flowing liquid with arbitrary relative velocity between the bubble and the surrounding liquid. The translational motion largely reduces the liquid pressure at the bubble wall, and the inception process of cavitation is thereby influenced greatly. Furthermore, the numerical calculation of expansion process of the vapor bubble is performed for the case where the bubble is instantaneously exposed to the low liquid pressure, and its results are compared with those of the equilibrium evaporation. A critical liquid pressure considered as a criterion of expansion and contraction of the bubble is numerically estimated for the various relative velocities between the bubble and the liquid and the various initial bubble radii, and it is compared with the pressure of the classical theory. Numerical calculation reveals that the critical pressure for the relative velocity of zero in the case of nonequilibrium evaporation or condensation is lower than the classical one in any initial bubble radius.