A dynamic Spatially Averaged Two-Fluid Model for heat transport in moderately dense gas–particle flows

Abstract

In this study, we derive a spatially averaged two-fluid model for heat transport in moderately dense gas–particle flows. In the context of multiphase turbulence modeling, closure models for the unresolved terms in the filtered transport equations in the presence of mesoscale heterogeneous particle clusters are postulated. In analogy to the drift velocity correction for the resolved gas–particle drag force, we propose to approximate the filtered interphase heat transfer by the resolved heat transfer corrected by a drift temperature. This drift temperature represents the gas-phase temperature fluctuations seen by the particles and can be expressed as a correlation between the solid volume fraction variations and the gas-phase temperature fluctuations, i.e., the turbulent internal energy. Therefore, transport equations for the turbulent internal energies of the phases are derived, where a cluster-induced turbulence production term arises in the gas-phase. Except for the interphase exchange terms, we find that closure models based on single phase turbulence modeling can be applied to the unresolved terms in the transport equations for both the filtered and turbulent internal energies. The interphase exchange terms can be expressed by the variances of the temperatures scaled by correlation coefficients. A dynamic adjustment of the correlation coefficients by using test-filters in coarse-grid simulations is proposed. In an a priori study, the developed closure models show good agreement with the predictions obtained by filtering fine-grid, two-fluid model simulation data of Geldart type A and B particles in three-dimensional wall-bounded fluidized beds.