Consistency and accuracy in the simulation of two-phase flows with phase change using sharp interface capturing methods

In this paper, the modelling of phase change in an incompressible two-phase flow solver is detailed without restricting the numerical methods to a specific interface capturing method. The main challenge when including phase-change is the handling of flux discontinuities at the interface when advancing temperature and species mass fraction. An accurate and second order discretization is proposed for any Eulerian representation of the interface either by adding a sharp source term or by imposing a boundary condition at the interface. As the accuracy and convergence rate of such solver are driven by the reconstruction of the evaporation rate ṁ, particular attention is devoted to the reconstruction of gradient normal to the interface. Several methodologies are proposed to compute second-order gradients at the interface location adapted to any interface representation. Applying such techniques to a second-order accurate field leads to an expected first order accuracy of ṁ but with remarkable accuracy improvements using ghost cell methods with quadratic extrapolation. Then, several phasechange procedures are built by combining a selection of numerical methods to handle flux discontinuities and evaluate gradients. The procedures are investigated on planar phase-change simulations to bring out inconsistent combination choices. Finally, a multidimensional evaporation test case is presented to show the final accuracy and limitations of phase-change modelling in today two-phase flow solvers