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Abstract

Classical Euler-Euler two-fluid models based on the kinetic theory of granular flows assume the particle phase to be dominated by collisions, even when the particle volume fraction is low and hence collisions are negligible. This leads to erroneous predictions of the particle-phase flow patterns and to the inability of such models to capture phenomena like particle trajectory crossing for finite Stokes numbers. To correctly predict the behavior of dilute gas-particle flows a more fundamental approach based on solving the Boltzmann kinetic equation is necessary to treat non-zero Knudsen-number and finite Stokes-number conditions. In this chapter an Eulerian quadrature-based moment method for the direct solution of the Boltzmann equation is adopted to describe the particle phase, and it is fully coupled with an Eulerian fluid solver to account for the two-way coupling between the phases. The solution algorithm for the moment transport equations derived in the quadrature-based moment method and the coupling procedure with a fluid solver are illustrated. The predictive capabilities of the method are shown considering a lid-driven cavity flow with particles at finite Stokes and Knudsen numbers, and comparing the results with both Euler-Euler two-fluid model predictions and with Euler-Lagrange simulations.