We derive new boundary conditions (BCs) for collisional granular flows of spheres at flat frictional walls. A new theory is proposed for the solids stress tensor, translational and rotational energy dissipation rate per unit area and fluxes of translational and rotational fluctuation energy. In the theory we distinguish between sliding and sticking collisions and include particle rotation. The predictions are compared with literature results obtained from a discrete particle model evaluated at a given ratio of rotational to translational granular temperature. We find that the new theory is in better agreement with the observed stress ratios and heat fluxes than previous kinetic theory predictions. Finally, we carry out two fluid model simulations of a bubbling fluidized bed with the new BCs, and compare the simulation results with those obtained from discrete particle simulations. The comparison reveals that the new BCs are better capable of predicting solids axial velocity profiles, solids distribution near the walls and granular temperatures.
- frictional collision
- kinetic theory of granular flow
- partial slip boundary
- rough particles
- two-fluid model