Multiphase flows are commonly found in chemical engineering processes such as distillation columns, bubble columns, fluidized beds and heat exchangers. The physical boundaries of domains in numerical simulations of multiphase flows are generally defined by a conformal unstructured mesh which, depending on the complexity of the physical system, results in time-consuming mesh generation which frequently requires user-intervention. Furthermore, the resulting conformal unstructured mesh could potentially contain a large number of skewed elements, which is undesirable for numerical stability and accuracy. The diffuse-interface approach allows for the use of a simple structured meshes to be used while still capturing the desired physical (e.g., solid-fluid) boundaries. In this work, a novel diffuse-interface method for the imposition of physical boundaries is developed for the incompressible two-fluid multiphase flow model. This model is appropriate for dispersed multiphase flows which are pervasive in chemical engineering processes, in that this flow regime results in high levels of mass and energy transfer between phases. A diffuse interface is used to define the physical boundaries and boundary conditions are imposed by blending the conservation equations from the two-fluid model with that of the nondeformable solid. The results from the diffuse-interface method are compared with results from a conformal unstructured mesh for different interface functions and widths. For small interface widths, the accuracy of the flow profile is unaffected by the choice of interface function and the phase fraction distribution and flow behavior are within 3% compared to those from a conformal mesh. As the interface width increases, the diffuse-interface solution deviates from the conformal mesh solution in both the localized gas fraction and the overall gas hold-up, resulting in a difference up to 30%.

翻译：多相流常见于化工过程，如蒸馏塔、鼓泡塔、流化床和换热器。在多相流数值模拟中，物理边界通常由适配非结构化网格定义，该网格因物理系统的复杂性而需耗费大量时间生成，且常需用户干预。此外，生成的适配非结构化网格可能包含大量扭曲单元，这对数值稳定性和精度不利。扩散界面方法允许使用简单结构化网格，同时仍能捕获所需的物理边界（如固-液边界）。本文针对不可压缩两相多相流模型，开发了一种施加物理边界的新型扩散界面方法。该模型适用于化工过程中普遍存在的弥散型多相流，这种流态导致相间发生高水平的质量和能量传递。通过扩散界面定义物理边界，并将两相流模型中的守恒方程与不可变形固体的方程进行混合，从而施加边界条件。将扩散界面方法的结果与适配非结构化网格的结果进行比较，涉及不同的界面函数和宽度。对于小界面宽度，流动剖面的精度不受界面函数选择的影响，相分数分布和流动行为与适配网格结果的偏差在3%以内。随着界面宽度增加，扩散界面解在局部气相分数和整体气含率上均偏离适配网格解，差异最高达30%。