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On the turbulent boundary layer of a dry granular avalanche down an incline. II – closure model and numerical simulations

Fang C.

Journal of Theoretical and Applied Mechanics

2016

Vol. 54 nr 4

1245--1256

Dynamic responses of the closure relations, specific turbulent Helmholtz free energy and turbulent viscosity are postulated followed by experimental calibrations. The established closure model is applied to analyses of a gravity-driven stationary avalanche with incompressible grains down an incline. While the mean velocity and volume fraction increase from their minimum values on the plane toward maximum values on the free surface exponentially, two-fold turbulent kinetic energies and dissipations evolve in a reverse manner. Most two-fold turbulent kinetic energies and dissipations are confined within the thin turbulent boundary layer immediately above the plane, with nearly vanishing two-fold turbulent kinetic energies and finite two-fold turbulent dissipations in the passive layer. The two layers are similar to those of Newtonian fluids in turbulent boundary layer flows, and are preferable recognized by the distributions of turbulent kinetic energies and dissipations.

On the turbulent boundary layer of a dry granular avalanche down an incline. I. Thermodynamic analysis

Fang C.

Journal of Theoretical and Applied Mechanics

2016

Vol. 54 nr 3

1051--1062

Characteristics of the turbulent boundary and passive layers of an isothermal dry granular avalanche with incompressible grains are studied by the proposed zero-order turbulence closure model. The first and second laws of thermodynamics are applied to derive the equilibrium closure relations satisfying turbulence realizability conditions, with the dynamic responses postulated within a quasi-static theory. The established closure model is applied to analyses of a gravity-driven stationary avalanche down an incline to illustrate the distributions of the mean solid content, mean velocity, turbulent kinetic energy and dissipation across the flow layer, and to show the influence of turbulent fluctuation on the mean flow features compared with laminar flow solutions. In this paper, detailed thermodynamic analysis and equilibrium closure relations are summarized, with the dynamic responses, the complete closure model and numerical simulations reported in the second part.