Two-way coupling of Eulerian–Lagrangian model for dispersed multiphase flows using filtering functions

Eulerian–Lagrangian approaches for dispersed multiphase flows can simulate detailed flow structures with a much higher spatial resolution than the Eulerian–Eulerian approaches. However, there are still unsolved problems regarding the calculation method for accurate two-way interaction, especially on the numerical instability due to the dispersion migration through discrete computational grids. Inadequate solvers sometimes produce false velocity fluctuation which makes the simulation unstable. In this paper, a new calculation method for dispersion-to-continuous phase interaction, which is accompanied by spherical dispersion migration, is proposed. The basic principle of the method is the introduction of Lagrangian filtering functions which convert discrete dispersion volume fractions to a spatially differentiable distribution. The performance of linear, Gaussian and sinewave filtering functions is examined by simple benchmark tests and applied to the simulation of dispersion-generated fluctuation. Using the present method, three-dimensional continuous phase flow structures induced by rising spherical bubbles and/or settling solid particles are demonstrated.