Filtered Two-Fluid Models of Fluidized Gas-Particle Flows: New Constitutive Relations
New const itutive relations for ﬁltered two-ﬂuid models (TFM) of gas-particle ﬂows are obtained by systematic ally ﬁltering results generated thro ugh highly resolved simulations of a kinetic theory-based TFM. It was found in our earlier studies that the residual correlations appearing in the ﬁltered TFM equations depended principally on the ﬁlter size and ﬁltered particle volume fraction. Closer inspection of a large amount of computational data gathered in this study reveals an additional, systematic dependence of the correction to the drag coefﬁcient on the ﬁltered slip velocity, which serves as a marker for the extent of subﬁlter-scale inhomogeneity. Furthermore, the residual correla tions for the momentum ﬂuxes in the gas and particle phases arising from the subﬁlter-scale ﬂuctuations are found to be modeled nicely using constitutive relations of the form used in large-eddy simulations of single-phase turbulent ﬂows.