Kinetic-theory-based model of dense granular flows down inclined planes

This work extends a continuum model of sheared granular material comprising two-dimensional disks [C. H. Lee and C. J. Huang, Phys. Fluids 22, 043307 (2010)] to elucidate the dynamics of three-dimensional spheres. The proposed model is applied to investigate dense granular flows down an inclined plane. In the model, stress has a static component and a kinetic component. The constitutive model for shear stress reduces to the Bagnold model when the diffusion of granular temperature is small. The predicted rheological characteristics are identical to those observed in the preceding experiments and numerical simulations, validating the present model. The predicted rheological characteristics reveal that dense granular flows down an inclined plane are characterized by three special angles that determine the phase diagram. The predicted thick granular flow on an inclined plane exhibits the Bagnold velocity profile and a uniform volume fraction throughout its depth. The governing equation of granular temperature is simplified and solved analytically. The proposed shear granular flow model is also solved completely using the finite volume method. The predicted velocity and volume fraction agree very well with previous discretely simulated results. This work also proposes an equation for determining the characteristic length of dense granular flows and shows that its static component is close to the stopping height.