Improved modelling of interfacial terms in the second-moment closure for particle-laden flows based on interface-resolved simulation data

Correlations for the interfacial terms in the fluid dissipation rate equation and Reynolds stress equations are established for particle-laden flows, based on data from the interfaced-resolved direct numerical simulations of particle sedimentation in a periodic domain at a density ratio ranging from 0.01 to 1000, a particle concentration ranging from 2.3 % to 30.2 % and a particle Reynolds number below 250. The correlations for the mean drag and the pseudo-turbulent kinetic energy are also reported, which are used for the modelling of the interfacial term in the fluid dissipation rate equation. The interfacial term correlations obtained are then incorporated in the Reynolds stress model (RSM) (i.e. second-moment closure) for the simulation of vertical turbulent channel flows laden with the finite-size particles at relatively low particle volume fractions. The results show that the RSM with new interfacial term correlations can quantitatively predict particle-induced turbulence enhancement or suppression in vertical channel flows.