Numerical Simulation Of The Viscous Two-Phase Flow Based On VOF And IBM

The numerical simulation of free surface flow is not only an attractive research topic butalso a difficult task for engineers. With the development of computer technology and CFD(computational fluid dynamics) methods in the past few years, it is desirable to directly solvethe Navier–Stokes equations for the simulation of many problems of free-surface flow tounderstand natural hydrodynamic processes.It should be pointed out that nowadays many studies for the simulation of the freesurface problem are based on one-phase flow models, in which the effects of air movementabove the free surface are ignored and the density difference between gas and liquid is alsoneglected. This may result in missing information about the quantities, and become a sourceof errors of the numerical simulation.Thus, in order to avoid the difficulties mentioned above;it is preferable to construct a two-phase flow model coupling with the VOF method forsolving the problems of a free surface flow. The purpose of this study is to develop a viscoustwo-phase flow model, whose incompressible Navier-Stokes equations are solved by thefinite-difference method, based on the VOF (Volume of Fluid) method and IBM (ImmersedBoundary Method) for the problems of a free surface flow considering both gas and liquideffects. Then the viscous two-phase flow of2-D fluid sloshing in a horizontally excitedrectangular tank and its interaction with baffles in the tank are simulated and studiedpreliminarily.The incompressible Navier-Stokes equations of the two-phase flow model are solved inall cells, so it is no need to impose boundary conditions for the free surface, which is verydifferent from the one-phase flow models. In this study, utilizing VOF method to treat freesurface, a fluid fraction function F, with values between zero and one, is used to indicate thefraction of each computational cell that is filled with a liquid phase. And the density andviscosity can be obtained by the fluid fraction function F. PLIC (Piecewise Line InterfaceCalculation) method is an interface reconstruction algorithm for reconstructing the interfaceby a sloping segment. Once the interface has been reconstructed, F is updated by themotion of underlying fluid with Lagrangian propagation method.When2-D fluid sloshing in a horizontally excited rectangular tank is simulated, to satisfythe no-slip boundary conditions on baffles in tanks, IBM is utilized and virtual force terms arecalculated and imposed inside the baffles. The complication caused by discrepancy betweenLagrangian grid of immersed boundary and Eulerian grid of fluid are treated with bilinear interpolation to impose the velocity field at the grid points near the interface.The gas-liquid two-phase flow model based on VOF is first validated by simulating thedam break over a dry bed, showing its reliability and superiority. Then the viscous two-phaseflow of2-D fluid sloshing in a horizontally excited rectangular tank and its interaction withbaffles in the tank are simulated and analyzed preliminarily using this gas-liquid two-phasemodel coupling IBM. The results of this study show that the gas-liquid two-phase flow modelbased on VOF method and IBM is a potential tool for the simulation of nonlinear fluidsloshing. These studies demonstrate the capability of this gas-liquid two-phase model tosimulate complex flow with a free surface.