WELL-BALANCED ALGORITHM AND HEIGHT FUNCTION METHOD FOR DYNAMIC CONTACT ANGLE IN TWO-PHASE SYSTEMS

Abstract

The well-balanced algorithm combined with dynamic contact angle was well studied in the literature but was never implemented with the pressure-implicit with splitting of operators (PISO) algorithm in a collocated grid commonly used in an incompressible, transient simulation. This article presents a well-balanced algorithm for PISO schemes coupling with the height function method for curvature estimation. The dynamic contact angle model from Kistler and Cox is also integrated to improve the modelling of the curvature at the wall boundary. In collocated finite volume schemes, the well-balanced PISO algorithm is developed by modifying both the calculation of the gradients in the momentum equation and the Rhie and Chow algorithm. This new gradient calculation method ensures that surface tension force and pressure gradient are identically discretized at the same location. The Rhie and Chow algorithm is also modified by adding the surface tension force to balance the pressure forces. The stationary droplet case in two-dimensions is presented first to validate the proposed methodology. The well-balanced algorithm coupling with the height function method shows its benefits by damping spurious currents by two to three orders of magnitude. The 3D surface-driven flow and water-spreading droplets are then simulated; the results show that the new scheme coupled with dynamic contact angle model outperforms the unbalanced scheme of the smooth void fraction method for theoretical and experimental comparisons.