Balabel, A: Numerical Simulation of Gas-Liquid Interface Dyn

The modern theory of nonlinear phenomena of two-phase flows requires a solution of the full Navier-Stokes equations along with a suitable and aeeurate surfaee traeking method. The purpose of this work is to develop a new numerical technique for the calculation of two-phase flows and consequently to achieve better predictions of the physical processes involved.The present work is concerned with the time aceurate numerical solution of Navier­ Stokes equations where the level set method is used to deal with the topological changes of the interface between incompressible, isothermalliquid-gas flows. The Navier-Stokes equations are solved in the primitive variable formulation by means of the control volurne approach on a non-staggered reetangular grid with specification of flow variables at the cell center. In order to capture the pressure and velocity field with proper coupling through the continuity equation, a Poisson equation for pressure is solved using the Successive Over-Relaxation method. Special efforts are made to modify the Poisson equation in order to deal with irregular boundaries which arise from the interface motion. Transition from the gas phase to the liquid phase is performed through consistent balancing of kinematie and dynamic conditions at the liquid-gas interface. The surfaee tension is defined explicitly as a boundary condition for the pressure on the interface, which through the Young-Laplace equation determines the pressure driving the fluid. The level set equation is solved with a new high resolution scheme, which through coupling with the flow solver results in an aeeurate two-phase flow solution algorithm. This enables the modelling of interfaces which are exposed to large scale motions. The merging and breaking of the interface is automatically handled by the level set method.