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Keywords Numerical methods, Fluids, Flow, Patterns
Abstract The volume of fluid (VOF) method is a numerical technique to track the developing free surfaces of liquids in motion. This method can, for example, be applied to compute the liquid flow patterns in a rotating cone reactor. For this application a spherical coordinate system is most suited. The novel derivation of the extended VOF algorithms for this class of applications is presented here. Some practical limitations of this method, that are inherent in the geometry of the described system, are discussed.
1. Introduction
Conventional finite difference representations of fluid flow equations (i.e. Navier-Stokes equations) often introduce averaging of the hydrodynamic key variables. This averaging results in a smoothing of spatial variations in flow variables and in particular in a smearing of discontinuities as encountered in the vicinity of a free surface. In order to apply the free surface boundary conditions to the discretized conservation equations and to advect the fluid through the computational mesh without any smearing of the free surface, the location of the free surface has to be determined. Conventional discrete Eulerian convective flow computations require an averaging of the flow variables of all fluid elements flowing through a grid cell during some time interval. This averaging process results in a smoothing of all variations in flow variables and in particular in a smearing of the free surface discontinuities....