Diffusion-based coarse graining in hybrid continuum–discrete solvers: Applications in CFD–DEM

Abstract

In this work, a coarse-graining method previously proposed by the authors in a companion paper based on solving diffusion equations is applied to CFD-DEM simulations, where coarse graining is used to obtain solid volume fraction, particle phase velocity, and fluid-particle interaction forces. By examining the conservation requirements, the variables to solve diffusion equations for in CFD-DEM simulations are identified. The algorithm is then implemented into a CFD-DEM solver based on OpenFOAM and LAMMPS, the former being a general-purpose, three-dimensional CFD solver based on unstructured meshes. Numerical simulations are performed for a fluidized bed by using the CFD-DEM solver with the diffusion-based coarse-graining algorithm. Converged results are obtained on successively refined meshes, even for meshes with cell sizes comparable to or smaller than the particle diameter. This is a critical advantage of the proposed method over many existing coarse-graining methods, and would be particularly valuable when small cells are required in part of the CFD mesh to resolve certain flow features such as boundary layers in wall bounded flows and shear layers in jets and wakes. Moreover, we demonstrate that the overhead computational costs incurred by the proposed coarse-graining procedure are a small portion of the total computational costs in typical CFD-DEM simulations as long as the number of particles per cell is reasonably large, although admittedly the computational overhead of the coarse-graining procedure often exceeds that of the CFD solver. Other advantages of the diffusion-based algorithm include more robust and physically realistic results, flexibility and easy implementation in almost any CFD solvers, and clear physical interpretation of the computational parameter needed in the algorithm. In summary, the diffusion-based method is a theoretically elegant and practically viable option for practical CFD-DEM simulations.

Diffusion-based coarse graining in hybrid continuum–discrete solvers: Theoretical formulation and a priori tests

“…In particular, the diffusion should be applied on the momentum and not on the velocities. Detailed derivations and CFD-DEM simulation results obtained with the coarse graining method proposed here are presented in (Sun and Xiao, 2015).…”

SediFoam: A general-purpose, open-source CFD–DEM solver for particle-laden flow with emphasis on sediment transport

“…The validation case of fluidized bed (Sun and Xiao, 2015a) is applied to test the parallel efficiency of SediFoam. PCM-based averaging, which requires little computational cost, is applied to reduce the influence of averaging algorithm.…”

Investigation of Void Fraction Schemes for Use with CFD-DEM Simulations of Fluidized Beds

“…The simplest void fraction scheme is the particle-centered method (PCM), which assumes that the entire particle volume is located at the centroid of the particle 8 . Void fraction fields in simulations using the PCM display large fluctuations with time due to particle centers crossing cell boundaries 9 . If the cell size to particle diameter ratio is greater than 3.8, then unrealistic spikes in the local gas pressure do not occur 5 .…”