A Lagrangian-Lagrangian coupled method for three-dimensional solid-liquid flows involving free surfaces in a rotating cylindrical tank

Numerical modeling of solid-liquid flows involving free surface and fluid-particles interactions is of great importance for chemical engineering. In this article, the DEM-MPS method for the simulation of complex two-dimensional solid-liquid flows proposed by Sakai et al. (2012) has been evolved to perform fully-resolved three-dimensional Lagrangian-Lagrangian simulations. As in the previous work, the discrete element method (DEM) and the moving particle semi-implicit (MPS) method were coupled via the local averaging technique. In this study, new discretization schemes are proposed to improve the accuracy and stability of the DEM-MPS method. Furthermore, the explicit pressure calculation is introduced to close the model instead of the previous semi-implicit algorithm, which largely reduces the computational cost in three-dimensional cases. The resulting numerical method is simple and efficient, and able to treat free surfaces and moving boundaries with ease. As for fundamental principles of multiphase hydrodynamics, the present formulation can naturally deal with water displacement of solid particles. Focusing on the macroscopic behavior of granular flows, a comparison of simulation results obtained for the solid-liquid mixture in a revolving cylindrical tank with experimental reference data is carried out, from which good agreements have been confirmed concerning the width and height of the solid bed. By further referring to the solution yielded by the previous two-dimensional model, the present DEM-MPS method seems to better reproduce the bed shape in a quasi-steady state. Hence, the validation tests show the adequacy and suitability of the present DEM-MPS method for three-dimensional simulation of solid-liquid flows involving free surfaces. (C) 2014 Elsevier B.V. All rights reserved.