Submerged granular channel flows driven by gravity
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The paper presents a rheological model for gravity driven granular flows saturated with water. The model adopts the kinetic theory for the collisional regime, which is dominant near the free surface, while for the frictional regime a specific model is proposed, which matches the Coulombian condition at the boundary with the loose static bed. The solution for the frictional regime is based on the observation that the frictional and the collisional regimes are not stratified but coexist across the flow depth. The model is able to predict the distribution along the depth of velocity, concentration, granular temperature, shear and normal stresses. In particular, it is possible to discriminate between the collisional and the frictional components of the normal and shear stresses. The results of the model are compared with the data of a laboratory investigation on a steady, uniform, highly concentrated saturated granular flow, composed of spheres with a uniform diameter of 6 mm. Another important issue addressed in the paper concerns the balances of the kinetic energy of the granular phase. The model is able to describe the mechanisms of production, diffusion and dissipation of kinetic energy, relevant to both the mean component of the flow and the fluctuating component (i.e., the collisional component). Also in this case the comparison with the experimental data is reasonably good. Near the static loose bed, the model predicts that the flux of the diffused fluctuating energy exceeds an order of magnitude the locally dissipated flux of fluctuating energy. This suggests that the motion of the grains, even at concentrations close to that of packing, is always accompanied by a certain degree of granular temperature.