Boiling heat transfer by phase-field method

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 conservative 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 a second-order finite difference approach. Thanks to the numerical discretization employed, a constant coefficient Poisson equation for pressure is obtained, which can be efficiently solved using FFT-based direct solvers. The proposed method is validated against several benchmarks: an interface undergoing vaporization 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 density ratios, from \(\rho _v/\rho _l = 1\) ${\rho }_v/{\rho }_l=1$ down to \(\rho _v/\rho _l \simeq 5 \times 10^{-4}\) ${\rho }_v/{\rho }_l\simeq 5\times {10}^{-4}$ (where \(\rho _v\) ${\rho }_v$ identifies the vapor density and \(\rho _l\) ${\rho }_l$ the liquid density).