A critical comparison of surface tension models for the volume of fluid method

Abstract

In many different fields of research, the interactions between two immiscible fluids are of importance. To study these flows in industrial equipment, a multi-scale modeling approach is often used. In this approach, the smallest scale models apply detailed information in the form of closure equations for the larger scale models, which can model complete industrial equipment. This paper will focus on the improvement of the smallest scale model; direct numerical simulations employing the Volume of Fluid model. In this model, mass is inherently conserved because of the surface treatment, but this treatment also poses a challenge in calculating the surface properties like the surface tension. In this paper, three different surface tension models for the Volume of Fluid were tested: the generally used Continuum Surface Force (CSF) model, the height function model and the novel tensile force method. From the verification tests, it was concluded that both the height function model and the tensile force method are an improvement of the CSF model. The single bubble simulations showed that the height function method works best for small bubble (Eo<1). This is due to problems with connectivity for the tensile force method. While for the larger bubbles (Eo>10), the tensile force method is the best functioning surface tension model, because the calculation of the curvature in the height function method uses a stencil in which the distance between two interfaces in the direction of the normal should at least be four grid cells. In all the other tested cases, the height function model and the tensile force method perform equally well. The Morton number changes the ranges for the region of use of the surface tension models slightly when logMo≤−7 (the height function model can only be used when Eo≤2, while the tensile force method can only be used at Eo≥2) and logMo≥1 (the height function model can in this region also be used when Eo>10).