The mechanics of submerged granular flows

The thesis tackles the mechanics of submerged granular flows driven by gravity, focusing on the rheological formulations and on the numerical solutions of the equations that govern this type of flow. In particular, a two-phase approach is assumed. The liquid phase, usually water, is described with a Newtonian rheology. The rheology of the granular phase depends on the type of contacts among the particles. Two opposite conditions are identified: if the contacts among particles are instantaneous the regime is named collisional, while, when the contacts become long lasting and involved more particles at the same time the regime is called frictional. In the thesis a proper model for the rheology of the granular phase, able to account for both the regimes, is presented. This model is based on the fundamental evidence that the granular phase is characterized by the coexistence of the collisional regime, which dominates near the free surface, and of the frictional regime, which becomes relevant approaching the loose static bed Armanini et al. [5]. The kinetic theories of dense gases Jenkins and Savage [48] are adopted to describe the collisional regime, while for the frictional regime a new rheological formulation, dependent on the Savage number, which comes from the analysis of the force involved, is given. In addition, the model, named heuristic model [11], introduces a specific equation of state also for the frictional regime. The model is based only on a single parameter, which presumably depends on the properties of the contact forces of the material. A numerical code able to integrate the equations of the mass, momentum and energy of the two-phase, in uniform flow conditions, was developed by Armanini et al. [6] and the results are compared with the experimental data. In the applications to hyperconcentrated channel flows the effect of the side walls and of the internal stresses of the liquid phase are neglected in the momentum balance equations, therefore the drag force is balanced by the weight of the liquid phase. The heuristic model is able to predict in a satisfactory way the distributions across the flow depth of the velocity, concentration, granular temperature and stresses and in particular, it allows to discriminate between the collisional and the frictional components of the shear and of the normal stresses. Another important issue addressed in the thesis concerns the balances of the energy of the granular phase. The model is able to describe the mechanisms of production, diffusion and dissipation of energy, relevant to both the mean component of the flow and the fluctuating component (i.e., the collisional component). In uniform flow conditions, 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 as already observed by Armanini et al. [10]. Furthermore, the description of the mechanisms of exchange among the terms of the total energy balance and of the kinetic energy balance, and between the two energy balances is given. In the thesis, the role of the interaction between the liquid and the solid phase in the kinetic energy balance is analysed [59]. A specific experimental investigation to understand the difference between the drag averaged over time and the drag calculated with respect the average velocities and concentration is carried out. This difference between the two drags represents the contribution to the drag due to the correlations between the fluctuating components of the concentration and of the velocities. By integrating the heuristic model across the flow depth, it is possible, in principle, to derive a set of shallow water equations that are able to describe the behaviour of debris flows and wet avalanches.