High-speed confined granular flows down smooth inclines: scaling and wall friction laws

Abstract

Recent numerical work has shown that high-speed confined granular flows down smooth inclines exhibit a rich variety of flow patterns, including dense unidirectional flows, flows with longitudinal vortices and supported flows characterized by a dense core surrounded by a dilute hot granular gas [1]. Here, we further analyzed the results obtained in [1]. More precisely, we characterize carefully the transition between the different flow regimes, including unidirectional, roll and supported flow regimes and propose for each transition an appropriate order parameter. Importantly, we also uncover that the effective friction at the basal and side walls can be described as a unique function of a dimensionless number which is the analog of a Froude number: $$Fr=V/\sqrt{gH\cos \theta }$$ where V is the particle velocity at the walls, $$\theta$$ is the inclination angle and H the particle holdup (defined as the depth-integrated particle volume fraction). This universal function provides a boundary condition for granular flows running on smooth boundaries. Additionally, we show that there exists a similar universal law relating the local friction to a local Froude number $$Fr^{loc}=V^{loc}/\sqrt{P^{loc}/\rho }$$ (where $$V^{loc}$$ and $$P^{loc}$$ are the local velocity and pressure at the boundary, respectively, and $$\rho$$ the particle density) and that the latter holds for unsteady flows.