Wall-bounded, gas-particle flows are common in many environmental and industrial applications, and are most often turbulent. In vertical risers with significant mass loading, strong coupling between the phases leads to the spontaneous generation of dense clusters that fall at the walls of the riser, while dilute suspensions of particles rise in the central region. Sustained volume fraction and velocity fluctuations caused by the clusters produce fluid- and particle-phase turbulent kinetic energy. In fully developed vertical risers, the multiphase turbulence statistics are stationary and depend only on the distance from the wall. However, these statistics depend strongly on the distribution of the mass loading, which itself depends on the wall-normal component of the particle-phase Reynolds stresses.
In our recent work, the exact Reynolds-average (RA) equations were derived for collisional gas-particle flow. These equations contain unclosed terms due to nonlinearities in the hydrodynamic model, including new constants that arise from correlations between the particle-phase volume fraction and fluid-phase velocity fluctuations. To assess the accuracy of the turbulence model, and determine modeling constants that appear in the unclosed terms, Eulerian-Lagrangian simulations of statistically stationary, three-dimensional, gas-solid flows in vertical channels are performed with different mass loadings. Recent work has demonstrated the capability of the numerical framework to capture particle clustering in wall-bounded risers with physical characteristics, including descent velocity and mean and fluctuating particle concentration.
To extract useful information consistent with the Eulerian turbulence model, a clear distinction is made between the phase-average granular temperature, which appears in the kinetic theory constitutive relations, and the particle-phase turbulent kinetic energy, which appears in the turbulent transport coefficients. To accomplish this, an adaptive spatial filter is employed on the particle data with an averaging volume that varies with the local particle-phase volume fraction, allowing direct comparisons with the multiphase turbulence model. Wall-normal profiles from the turbulence model are compared with the three-dimensional Eulerian-Lagrangian results, and details on the nature of the unclosed terms are presented.
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