Starting from the kinetic theory (KT) model for monodisperse granular flow, the exact Reynolds-average (RA) equations were recently derived for the particle phase in a collisional gas-particle flow by Fox [1]. The turbulence model solves for the RA particle volume fraction, the phase-average (PA) particle velocity, the PA granular temperature, and the PA particle turbulent kinetic energy (TKE). A clear distinction is made between the PA granular temperature, which appears in the kinetic theory constitutive relations, and the particle-phase turbulent kinetic energy, which appears in the turbulent transport coefficients. Mesoscale direct numerical simulation (DNS) can be used to assess the validity of the closures proposed for the unclosed terms that arise due to nonlinearities in the hydrodynamic model. In order to extract meaningful statistics from simulation results, a separation of length scales must be established to distinguish between the PA particle TKE and the PA granular temperature. In this work, we introduce an adaptive spatial filter with an averaging volume that varies with the local particle-phase volume fraction. This filtering approach ensures sufficient particle sample sizes in order to obtain meaningful statistics while remaining small enough to avoid capturing variations in the mesoscopic particle field. Two-point spatial correlations are computed to assess the validity of the filter in extracting meaningful statistics. The filtering approach is applied to fully-developed cluster-induced turbulence (CIT), where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. Simulation results show a strong correlation between the local volume fraction and granular temperature, with maximum values located just upstream of clusters (i.e., where maximum compressibility of the particle velocity field exists), and negligible particle agitation is observed within clusters.

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