We present accurate and mathematically consistent formulations of a diffuse-interface model for two-phase flow problems involving rapid evaporation. The model addresses challenges including discontinuities in the density field by several orders of magnitude, leading to high velocity and pressure jumps across the liquid-vapor interface, along with dynamically changing interface topologies. To this end, we integrate an incompressible Navier-Stokes solver combined with a conservative level-set formulation and a regularized, i.e., diffuse, representation of discontinuities into a matrix-free adaptive finite element framework. The achievements are three-fold: First, we propose mathematically consistent definitions for the level-set transport velocity in the diffuse interface region by extrapolating the velocity from the liquid or gas phase. They exhibit superior prediction accuracy for the evaporated mass and the resulting interface dynamics compared to a local velocity evaluation, especially for strongly curved interfaces. Second, we show that accurate prediction of the evaporation-induced pressure jump requires a consistent, namely a reciprocal, density interpolation across the interface, which satisfies local mass conservation. Third, the combination of diffuse interface models for evaporation with standard Stokes-type constitutive relations for viscous flows leads to significant pressure artifacts in the diffuse interface region. To mitigate these, we propose to introduce a correction term for such constitutive model types. Through selected analytical and numerical examples, the aforementioned properties are validated. The presented model promises new insights in simulation-based prediction of melt-vapor interactions in thermal multiphase flows such as in laser-based powder bed fusion of metals.

翻译：本文提出了一种针对涉及快速蒸发的两相流问题的扩散界面模型的精确且数学上一致的公式。该模型解决了若干挑战，包括密度场跨越数个数量级的不连续性（这导致气液界面处存在高速和高压跳跃）以及动态变化的界面拓扑结构。为此，我们将一个不可压缩Navier-Stokes求解器与保守水平集公式以及对不连续性的正则化（即扩散）表示相结合，集成到一个无矩阵自适应有限元框架中。取得的成果体现在三个方面：首先，我们通过从液相或气相外推速度，为扩散界面区域中的水平集输运速度提出了数学上一致的定义。与局部速度评估相比，这些定义在蒸发质量及由此产生的界面动力学预测方面表现出更高的准确性，尤其对于强弯曲界面。其次，我们证明，要准确预测蒸发引起的压力跳跃，需要在界面处采用一致的（即倒数形式的）密度插值，以满足局部质量守恒。第三，将用于蒸发的扩散界面模型与用于粘性流动的标准Stokes型本构关系相结合，会在扩散界面区域产生显著的压力伪影。为了缓解这些问题，我们建议为此类本构模型类型引入一个修正项。通过选定的解析和数值算例，验证了上述特性。所提出的模型有望为热多相流（例如金属激光粉末床熔融）中熔体-蒸气相互作用的基于模拟的预测提供新的见解。