Steady flow of smooth, inelastic particles on a bumpy inclined plane: hard and soft particle simulations

Abstract

We study smooth, slightly inelastic particles flowing under gravity on a bumpy inclined plane using event-driven and discrete-element simulations. Shallow layers (ten particle diameters) are used to enable simulation using the event-driven method within reasonable computational times. Steady flows are obtained in a narrow range of angles (13°-14.5°); lower angles result in stopping of the flow and higher angles in continuous acceleration. The flow is relatively dense with the solid volume fraction, v≈0.5, and significant layering of particles is observed. We derive expressions for the stress, heat flux, and dissipation for the hard and soft particle models from first principles. The computed mean velocity, temperature, stress, dissipation, and heat flux profiles of hard particles are compared to soft particle results for different values of stiffness constant (k). The value of stiffness constant for which results for hard and soft particles are identical is found to be k≥2×10⁶mg/d, where m is the mass of a particle, g is the acceleration due to gravity, and d is the particle diameter. We compare the simulation results to constitutive relations obtained from the kinetic theory of Jenkins and Richman [J. T. Jenkins and M. W. Richman, Arch. Ration. Mech. Anal. 87, 355 (1985)] for pressure, dissipation, viscosity, and thermal conductivity. We find that all the quantities are very well predicted by kinetic theory for volume fractions v<0.5. At higher densities, obtained for thicker layers (H=15d and H=20d), the kinetic theory does not give accurate prediction. Deviations of the kinetic theory predictions from simulation results are relatively small for dissipation and heat flux and most significant deviations are observed for shear viscosity and pressure. The results indicate the range of applicability of soft particle simulations and kinetic theory for dense flows.