Half-space Problem of Unsteady Evaporation and Condensation of Polyatomic Gas

On the basis of polyatomic version of the ellipsoidal-statistical Bhatnager-Gross-Krook (ESBGK) model, we consider time-periodic gas flows in a semi-infinite expanse of an initially equilibrium polyatomic gas (methanol) bounded by its planar condensed phase. The kinetic boundary condition at the vapor-liquid interface is assumed to be the complete condensation condition with periodically time-varying macroscopic variables (temperature, saturated vapor density and velocity of the interface), and the boundary condition at infinity is the local equilibrium distribution function. The time scale of variation of macroscopic variables is assumed to be much larger than the mean free time of gas molecules, and the variations of those from a reference state are assumed to be sufficiently small. We numerically investigate thus formulated time-dependent half-space problem for the polyatomic version of linearized ESBGK model equation with the finite difference method for the case of the Strouhal number Sh=0.01 and 0.1. It is shown that the amplitude of the mass flux at the interface is the maximum, and the phase difference in time between the mass flux and v(infinity) - v(l) (v(infinity): vapor velocity at infinity, v(l): velocity of the vapor-liquid interface) is the minimum absolute value, when the phase difference in time between the liquid surface temperature (the saturated vapor density) and the velocity of interface is close to zero.