An improved model for interface pressure calculations in free-surface flows

A new three-dimensional method for the calculation of interface pressure in the computational modeling of free surfaces and interfaces which use volume tracking methods is developed. This method is based on the calculation of the pressure force at the interfacial cell faces. The pressure forces at the interfacial cell faces are calculated according to the pressure imposed by each fluid on the portion of the cell face that is occupied by that fluid. Special formulations for the pressure in the interfacial cells are derived for different orientations of an interface. The present method, referred to as Pressure Calculation based on the Interface Location (PCIL), is applied to a three-dimensional motionless drop of liquid in an initially stagnant fluid with no gravity force. A two-fluid, PLIC-VOF method is used for numerical simulation of the flow. Both the Continuum Surface Force (CSF) and the Continuum Surface Stress (CSS) methods are used for surface tension calculations. A wide range of Ohnesorge numbers and density and viscosity ratios of the two fluids are tested. It is shown that the presence of spurious currents (artificial velocities present in case of considerable capillary forces) is mainly due to the inaccurate calculation of pressure forces on the interfacial cells. The new model reduces the spurious currents up to more than two orders of magnitude for the cases tested. (author)