Model and algorithmic augmentation in phase field method for simulating the pool boiling phenomenon with high-density ratio

Although the dynamic van der Waals model has great potential in numerically simulating pool boiling, it is still limited to low liquid–vapor density ratios (about 10:1) due to the inherent thermodynamic inconsistency. This study proposes a thermodynamic consistency simplified dynamic van der Waals model to simulate pool boiling with large liquid–vapor density ratios. This model is based on the thermodynamic relationship associating the gradients of temperature and generalized chemical potential with the divergence of the reversible viscous stress tensor. A novel semi-discrete numerical algorithm that satisfies the thermodynamic consistency for this mathematical model is also proposed. The numerical results exhibit excellent agreement with that of analytical, validating the effectiveness and applicability of the proposed model for vapor–liquid coexistence. Compared to the original dynamic van der Waals model, the proposed model and algorithm can effectively reduce the spurious velocity at the vapor–liquid interface, breaking the limitations of low-density ratio and leading to stable simulation at higher-density ratios under low saturation temperatures. The approach is used to model pool boiling at low saturation temperatures with different wettability and liquid–vapor density ratios, and the saturation temperature significantly lower than reported in comparable literature (as low as
and the liquid–vapor density ratio is about 225:1). Compared to low liquid–vapor density ratios, larger liquid–vapor density ratios inhibit bubble coalescence, thereby suppressing the formation of large bubbles. In addition, larger density ratios more effectively maintain the shape of bubbles.