A conservative sharp interface method for two-dimensional incompressible two-phase flows with phase change

Abstract

A conservative sharp interface method is proposed in this work to simulate two-dimensional/axisymmetric incompressible two-phase flows with phase change. In this method, we use the cut cell method to generate unstructured meshes near the interface, of which the cell edges overlap with the interface at each time step. On such mesh, the mass and heat transfer during phase change and all the jump conditions can be incorporated into the calculation of fluxes at the cell edges, to ensure that they are strictly satisfied at the interface in a sharp manner. The governing equations, including the incompressible Navier–Stokes equations, heat equation, and vapor mass fraction equation, are discretized by a second-order finite volume method in the arbitrary Lagrangian–Eulerian framework. To well couple the mass, heat, momentum, and interface evolution, the solution procedure is carefully designed and performed with several techniques. In such a way, the sharp discontinuity of the velocity, stress, temperature gradient, and vapor fraction, caused by the mass/heat transfer during phase change, can be simulated accurately and robustly. The performance of this method is systematically examined by cases of phase change at or below the saturated temperature, including vapor bubble in superheated liquid, film boiling, droplet evaporation at different relative humidity conditions, droplet evaporation under gravity, and droplet evaporation under forced convection. The applicability of the present method for incompressible two-phase flows with phase change is well demonstrated by comparing the numerical results with the benchmark, theoretical or experimental ones.