The CFD modeling of two-dimensional multiphase flows is a useful tool in industry, although accurate modeling itself remains a difficult task. One of the difficulties is to track the complicated topological deformations of the interfaces between different phases. This paper describes a marker-particle method designed to track fluid interfaces for fluid flows of at least three phases. The interface-tracking scheme presented in this paper is the first part of a series of papers presenting our complete model based on a one-field Godunov markerparticle projection scheme (GMPPS). In this part, we shall focus on the presentation of the interface-tracking scheme and the kinematic tests we conducted to examine the scheme's ability to accurately track interfacial movements typified by vorticity-induced stretching and tearing of the interface. Our test results show that for a set of carefully designed and commonly used error measures, relative percentage errors never exceed 2% for all of the tests and grid sizes considered, provided a sufficient number of marker particles are used. We shall also demonstrate that the method is of second-order accuracy and the interface transition width remains constant never exceeding three cell widths. Crown
SUMMARYThe problem of droplet deformation and break-up is considered. A hybrid Eulerian-Lagrangian method is used in which the velocity and pressure are discretized on a fixed mesh and Lagrangian particles are used to implicitly track the interface between the two phases. The Navier-Stokes equations are solved using an approximate Godunov projection method, collectively called the Godunov marker-particle projection scheme. The results show good qualitative agreement with previous research as well as demonstrating the efficacy of the method.
A numerical method for simulating variable density multiphase fluid flows is presented in this paper. It is a hybrid Eulerian-Lagrangian method solving the incompressible Navier-Stokes equations on a fixed Eulerian grid for velocity and pressure. Fluid phase is tracked in a Lagrangian manner by using marker-particles (Bierbrauer and Zhu, 2007a) to update the grid density and viscosity. A high order Godunov advection scheme, together with an approximate projection scheme to ensure incompressibility, is used to deal with rapid changes in fluid properties. We call this scheme the Godunov-Marker-Particle Projection Scheme (GMPPS), which implements pressure corrections to avoid spurious numerical boundary layers for multiphase flows. We have validated the GMPPS by comparing our numerical results with those calculated from an exact solution, with constant density, as well as some available physical experimental results for a variable density case. It is demonstrated that the scheme has secondorder accuracy in time and space for a range of Reynolds numbers. The fact that test results of a two-phase droplet impacting on solid and liquid surfaces compare well with experimental results suggests that the GMPPS has great potential to be used to solve multiphase flow problems.
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