Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension

Abstract

The sharp-interface resolution of compressible liquid–vapor flows is cumbersome due to the necessary tracking of the interface. The global dynamics are governed by local interface phenomena like surface tension effects as well as mass and energy transfer across the interface. These effects impose subtle jump conditions that have to be resolved locally at the interface. The exact solution of the two-phase Riemann problem is done by a complicated time-consuming iteration process. In addition most of the detailed knowledge of the Riemann pattern is not used in the overall algorithm such that the development of a much simpler approximative Riemann solver is desirable. The concept in this paper is to use an approximate solution of a two-phase Riemann problem at the phase interface. Extending the classical HLL Riemann solver for compressive shock waves, an additional intermediate state is introduced to distinguish between the liquid and vapor phase and to resolve the phase interface accurately. To get a thermodynamically consistent approximation a kinetic model is applied that determines the phase transition rate. The suitability of this approximative Riemann solver is validated by comparing the numerical results to the exact solution in one- and three-dimensional frameworks. The evaporation rates are compared to experiments with rapid evaporation and boiling. The two-phase approximative Riemann solver is then used in a compressible two-phase code with a sharp-interface resolution based on a ghost fluid approximation with data from this novel approximative two-phase Riemann solver. For a shock-droplet interaction this method provides a fast and accurate resolution of phase transfer and surface tension effects at much lower costs than the exact solution.