UNIFIED GAS-KINETIC SCHEME FOR TWO PHASE INTERFACE CAPTURING

The study of interfacial motion of gas-liquid phase is very important in science and engineering. Considering the non-equilibrium flow calculation, a unified gas-kinetic scheme for gas-liquid two phase interface capturing is presented in this paper. Since the free transport and particle collision are coupled to update the macroscopic variables and microscopic distribution functions, the unified gas-kinetic scheme can solve the non-equilibrium flow. The van der Waals (vdW) equation of state (EOS) is included to describe the coexistence of gas and liquid and the phase transition between them. Because of the characteristics of vdW EOS, the interface between gas and liquid can be captured naturally through condensation and evaporation processes. As a result, the new scheme can solve the gas-liquid two phase problems. Finally, the proposed method is used to obtain the numerical solution of Maxwell construction, which agrees well with the corresponding theoretical solution. Then, the Laplace’s theorem is verified by numerical calculation of the surface tension of the droplet corresponding to the van der Waals state equation. In addition, the collision of the two droplets is simulated, which proves the validity of the scheme further. However, due to the characteristics of the van der Waals equation of state, the constructed scheme is only applicable to the case where the liquid/gas two-phase density ratio is less than 5.