Modelo de fechamento para o tensor de interface no modelo de dois fluidos: modelagem matemática e simulação numérica

Abstract

Abstract : The focus of this work is to propose a model for the closure problem of the interfacial force density required for solution of the two-fluid model widely used in the description of multiphase flows. The closure models employed so far do use of the decomposition of the various phenomena that occur in the interaction among the phases as drag, drift, the development of hydrodynamic boundary layers, adverse pressure gradients and vorticity forces as Lift and Magnus force, just to name a few. Each one has its own mathematics description and correlations to calculate its coefficients for their respective settings. The latter are dependent on a series of dimensionless numbers as Reynolds number, and Morton, Eötvös, these being the principal. Generally, the correlations are dependent upon the system and degree of interaction of the phases as well as their dispersion within the fluid flow. This particular description and the wide range of correlations create new ways of solving problems so far unsolved and/or even unsolved, however, they are not generic and its applicability beyond the limits that were calibrated is an approach that must be evaluated and not always the results, after a long time of trial and error, are satisfactory. The work aims to deal with the closure problem of interfacial force density in a distinct way, modeling how the stress tensor acts on the interface without separating the effects categorizing them on the types mentioned above, and, let the flow itself "takes a decision" that forces act on the interface of fluids. The proposed methodology is detailed described in their physical and mathematical aspects and some benchmarks are chosen to do that. The coding has been made in the commercial code ANSYS CFX. The results demonstrate the effectiveness of the approach to problems where the interface is well defined, such as free surface flows, even with local change of morphology, without, however, to present the same performance in dispersed flow with low void fractions. Nevertheless, the joint action of both approaches (the classical and the proposal) in the latter case has proved to be very efficient in capturing the physical behavior of a complex flow as a bubble column.