A stochastic formulation for the drag force based on multiscale numerical simulation of fluidized beds

In Esteghamatian, A., Bernard, M., Lance, M., Hammouti, A. and Wachs, A., 2017, Micro/meso simulation of a fluidized bed in a homogeneous bubbling regime, International Journal of Multiphase Flow, 92, 93-111, we performed a one-to-one comparison of micro-scale Particle-Resolved Simulation (PRS) results and meso-scale two-way coupled Euler-Lagrange (a. k. a. DEM-CFD for Discrete Element Method-Computational Fluid Dynamics) simulation results in a homogeneous bi-periodic liquid/solid fluidized bed. These data showed an acceptable agreement between micro- and meso-scale predictions for integral measures as, e.g., pressure drop and bed height. However, particles fluctuations are markedly underpredicted in DEM-CFD simulations, especially in the direction transverse to the main flow. The filtered DEM-CFD porosity appears to be a coarse descriptor of the local microstructure and hence is the primary reason for the inability of the meso-scale DEM-CFD model to fully recover the actual features of the flow. In this paper, we explore two different directions in improving the meso-scale model: (a) we adopt an improved inter-phase coupling scheme and (b) we introduce a stochastic formulation for the drag law derived from our PRS results. The new stochastic drag law, which incorporates information on the first and second-order moments of PRS results, shows promises to recover the appropriate level of particles fluctuations.