(458d) Turbulence Modeling of Collisional Gas-Particle Flows
Starting from the kinetic theory (KT) model for granular flow, the exact Reynolds-average (RA) equations have been derived for the particle phase in a collisional gas-particle flow. The corresponding equations for a constant-density gas phase have been derived from a model that includes drag and buoyancy coupling with the particle phase. The fully coupled hydrodynamic model is written in terms of the particle-phase volume fraction, the particle-phase velocity and the granular temperature (or total granular energy). In contrast, the RA model solves for the RA particle-phase volume fraction, the phase-average (PA) particle-phase velocity, the PA granular temperature, and the PA turbulent kinetic energy of the particle phase. Thus, unlike in most previous derivations of turbulence models for moderately dense gas-particle flows, a clear distinction is made between the PA granular temperature, which appears in the KT constitutive relations, and the particle-phase turbulent kinetic energy, which appears in the turbulent transport coefficients. The exact RA equations contain unclosed terms due to nonlinearities in the hydrodynamic model. We introduce closures for some of these terms and validate them using mesoscale direct-numerical simulation results for moderately dense turbulent riser flow. Of particular interest are the unclosed source terms due to phase iteractions such as drag coupling for mean momentum and turbulent kinetic energy, and turbulence production due to the mean velocity difference.