A zero-order turbulence closure model of a dry granular dense flow is proposed, with the boundary considered an energy source and sink of the turbulent kinetic energy of the grains. Muller-Liu entropy principle is carried out to derive the equilibrium closure relations, with their dynamic responses postulated from the experimental calibrations. A gravity-driven flow with incompressible grains down an inclined moving plane is studied to investigate the influence of velocity slip near solid boundary on the turbulent features of the flow. While the calculated mean porosity and velocity correspond to the experimental outcomes, increasing velocity slip on the boundary tends to enhance the turbulent dissipation nearby. The distribution of the turbulent dissipation shows a similarity with that of conventional Newtonian fluids in turbulent boundary layer flows. Boundary as an energy sink is more apparent in the zero-order model.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanical Engineering
- Applied Mathematics