On the effects of the flow macro-scale over sub-grid modelling in dense gas-solid fluidized flows

Multiscale modelling of gas-particle fluidized flows is frequently approached by means of sub-grid modelling, which provides constitutive closures for filtered formulations applied to large scale simulations. A widely practiced procedure for the derivation of sub-grid models consists of filtering over predictions from highly resolved simulations under two-fluid modelling. The present work is intended as a contribution in this field by providing new supporting evidence for the enhancement of sub-grid closure models. Most of the efforts in the area have been directed to providing sub-grid models dependent on meso-scale filtered effects alone, and under low gas Reynolds number suspension conditions. In this work, macro-scale conditions are added to the analysis thereby accounting for flow topology, particularly for dense gas-solid fluidized flows. Two macro-scale variables are considered in the simulations, namely the domain average solid volume fraction and the domain average gas Reynolds number. So, in addition to the usual meso-scale filtered markers, relevant filtered parameters are also related to those macro-scale conditions. The filtered parameters of interest here are the effective interphase drag coefficient and filtered and residual stresses in both of the phases. Various domain average solid volume fractions and domain average gas Reynolds numbers were enforced, thereby providing for a variety of macro-scale dense conditions. It was found that both these macro-scale parameters considerably affect the meso-scale and the resulting filtered parameters of dense gas-solid flows, even though this occurs in a milder way when compared to results for dilute flow conditions available in the literature.