Interface capturing in multiphase flows using finite volume based level set method

Abstract

An important class of problems involves a substance transforming from one phase to another with absorption or emission of energy. Such cases arise in many settings, of which melting, solidification, condensation, and vaporization are the most important and abundant ones. The phase transition is isothermal if there is only one substance; in such a case, whatever heat energy crosses the interface is latent heat. Thermodynamics, fluid flow, heat transfer, and species transfer play vital roles in modelling the physics of phase?change phenomena. All of these physical processes are modelled using conservation laws. In this class of problems, there exists an interface separating the different phases. As the different phases move due to density differences, or as the substance changes phase, this interface moves and energy transfer takes place across it. The thermodynamic properties across this boundary may be different. The physics governing the movement of this boundary is very important, and determining it is a nonlinear problem. Problems with such characteristics are of great practical importance and include ocean waves, combustion flames, material boundaries, shapes against backgrounds, handwritten characters, and iso?intensity contours in images. The Level Set Method is one such approach. It is a Hamilton–Jacobi?based front?capturing algorithm for tracking fronts moving with speeds that are functions of their curvature. The Level Set Method has several advantages over other methods: the curvature of the interface can be easily evaluated at every instant, and it handles merging and breaking of interfaces very accurately. These algorithms are relatively new and approximate the equations of motion of propagating fronts, resembling Hamilton–Jacobi equations with viscosity terms. The Level Set Method forms the basis of the research work presented here. The algorithm has been used to capture interfaces for various multiphase or multicomponent flows. The Finite Volume Method has been used to discretize all governing equations in this work. High?resolution schemes such as SMART and CLAM are employed to solve the Level Set Equation. Several problems have been simulated in this research work using the Level Set Method. Most of them involve a rising bubble or a falling droplet without phase change. The breaking?dam problem has also been solved. The results compare well with those available in the literature. For example, in the rising bubble problem, the bubble rises due to its density being lower than that of the surrounding continuous medium. The density ratio is the critical parameter, not the absolute value of density. Parameters studied include density ratios, viscosity effects, gravity effects, and the influence of time step and mesh size.