Inhomogeneous drag models for gas-solid suspensions based on sub-grid quantities

Abstract

Inhomogeneous structures have significant impact on the drag. In this work, direct numerical simulations of flows past fluidized spheres are performed to investigate the effect of inhomogeneities on the drag at low Reynolds numbers. The inhomogeneities are quantified using various sub-grid quantities including a newly defined quantity named the solid drift flux, which is a measure of the correlation between the gas volume fraction and the particle phase velocity. Following the methodology of Rubinstein et al. (2017), a new drag model that depends simultaneously on the solid drift flux and the scalar variance of solid volume fraction is then developed. Given that these two sub-grid quantities are readily available in Eulerian-Lagrangian (EL) simulations, the developed model can be directly used in EL simulations without any additional closures for sub-grid quantities. An a priori analysis demonstrates that this model achieves satisfactory performance in predicting the drag in inhomogeneous structures.