Supercritical shallow granular flow through a contraction: experiment, theory and simulation

Supercritical granular flow through a linear contraction on a smooth inclined plane is investigated by means of experiments, theoretical analysis and numerical simulations. The experiments have been performed with three size classes of spherical glass beads, and poppy seeds (non-spherical). Flow states and flow regimes are categorized in the phase space spanned by the supercritical Froude number and the minimum width of the contraction. A theoretical explanation is given for the formation of steady reservoirs in the contraction observed in experiments using glass beads and water. For this purpose, the classical, one-dimensional shallow-water theory is extended to include frictional and porosity effects. The occurrence of the experimentally observed flow states and regimes can be understood by introducing integrals of acceleration. The flow state with a steady reservoir arises because friction forces in the reservoir are much smaller than in other parts of the flow. Three-dimensional discrete-particle simulations quantitatively agree with the measured granular flow data, and the crucial part of the theoretical frictional analysis is clearly confirmed. The simulations of the flow further reveal that porosity and frictional effects interact in a complicated way. Finally, the numerical database is employed to investigate the rheology in a priori tests for several constitutive models of frictional effects.