Theoretical and numerical analysis of key sub-grid quantities' effect on filtered Eulerian drag force

Abstract

An expression of the filtered Eulerian drag force is proposed based on the second order Taylor polynomial approximation of a microscopic drag coefficient. Theoretical computations of the expression at low particle Reynolds numbers show that four sub-grid quantities, the gas drift velocity, the solid drift velocity, the scalar variance of solid volume fraction and a third-order moment, are significant for an accurate estimation of the filtered drag force. Various drag models with different combinations of the four sub-grid quantities are proposed and their coefficients are optimized based on fine-grid two fluid model results. The gas drift velocity is demonstrated to be the most important marker in predicting the filtered drag force. The model with the solid drift velocity and the scalar variance of the solid volume fraction is found to be promising in computational fluid dynamic-discrete element model simulations due to the ready availability of the two sub-grid quantities.