Boiling heat transfer by phase-field method

Abstract In this work, we propose and test the validity of a phase-field method tailored specifically for modeling boiling phenomena. The method relies on numerical solutions of the Navier-Stokes equations coupled with a phase-field method and the energy equation. The continuity and Navier-Stokes equations have been modified introducing a source term that accounts for phase change. Likewise, in the con- servative Allen-Cahn equation (phase-field method) a source term that accounts for the volume is introduced. The system of governing equations is solved using a projection-correction method and equations are discretized using second-order finite difference approach. Thanks to the type of discretization employed, a con- stant coefficient Poisson equation for the pressure is obtained, which can be efficiently solved using FFT-based direct solvers. The proposed method is vali- dated against different benchmarks: an interface undergoing phase change at a constant rate, the Stefan problem, the adsorption problem and the growth of a 2D vapor bubble. For all the benchmarks, the present method well matches with analytical and archival literature results for a wide range of vapor-to-liquid den- sity ratios, from ρv /ρl = 1 down to ρv /ρl ≃ 5 × 10−4 (where ρv identifies the vapor density and ρl the liquid density).