Searching for a mesh-independent sub-grid model for CFD simulation of gas–solid riser flows

This work aims to examine the effects of grid size in applying the two-fluid model (TFM), and thereby attempts to search for a mesh-independent sub-grid model for simulating gas–solid riser flows. To this end, we performed a series of TFM simulations over a periodic domain with various grid resolutions and drag closures. Of these drag models, EMMS/matrix model in its simplified version was chosen to be the focus of discussion. It was found that TFM simulation with a homogeneous drag model reaches its numerically asymptotic solution when the grid scale is as small as 10 times the particle diameter, but it still fails to capture the characteristic S-shaped axial voidage profile and highly over-predicts the solids flux. By comparison, EMMS/matrix model seems to reach a mesh-independent solution of the effect of sub-grid structures on the drag force, and predict successfully the axial voidage profile and the solids flux with even coarse grid. Therefore, the fine-grid TFM simulation is inadequate for gas–solid riser flows. We need sub-grid modeling of the heterogeneous structure.