Channel flow simulation of a mixture with a full-dimensional generalized quasi two-phase model

We consider a newly constructed, mechanics-based, non-linear generalized quasi two-phase model [55] for a rapid flow of mixture of viscous fluid and solid particles down a channel. Based on the underlying physics and simulation results, we present new non-linear phenomena and mechanical insights of the model. We also present a full discretization of the model for the generalized mixture viscosity, velocity, pressure and effective bulk friction with higher order central differences and donor-cell method. This suitably tackles the complexities. Fundamentally new results are presented for the generalized mixture viscosity, velocity, pressure and effective bulk friction. Detailed analyses are performed for the full dimensional evolution of mixture velocities, dynamic pressure and effective viscosity. Our analysis reveals several mechanically very important novel non-linear features associated with the model under consideration, but often ignored in mass flow simulations, including: (i) The non-linear dynamics; as characterized by the flow mobility, kinetic energy, and the flow evolution are strongly controlled by the initial material composition. (ii) The flow becomes thicker as solid fraction increases, the front head develops into bulking, and the main body shows depletion. (iii) A strong velocity shearing develops through the flow depth. (iv) The full dynamic pressure exhibits strongly non-linear structures. (v) It appears that the hydrostatic pressure may significantly underestimate the full dynamic pressure. (vi) Mixture viscosity increases in different rates (slowly and rapidly) in different regimes of solid volume fractions which is justified by mechanical perspective of the mixture flow. (vii) The proper understanding of the incipient flow behavior is important, and shows that the process of flow release must be described by the full dimensional models. These features highlight the application potential of our new mixture mass flow model and simulation strategy for the hazard mitigation and planning.