Dense granular flow rheology in turbulent bedload transport

TL;DR

This study investigates the granular rheology in turbulent bedload transport through numerical simulations, revealing a collapse of stress ratios and volume fractions across inertial numbers, and proposing a rheology model validated by a 1D continuum approach.

Contribution

It introduces a granular rheology model for bedload transport based on numerical data, challenging existing concepts and extending the $rac{I}$ rheology to higher inertial numbers.

Findings

Negligible effect of interstitial fluid on granular rheology.

Collapse of shear to normal stress ratio and volume fraction over wide inertial number range.

Proposed rheology accurately predicts flow profiles and sediment transport rates.

Abstract

The local granular rheology is investigated numerically in turbulent bedload transport. Considering spherical particles, steady uniform configurations are simulated using a coupled fluid-discrete-element model. The stress tensor is computed as a function of the depth for a series of simulations varying the Shields number, the specific density and the particle diameter. The results are analyzed in the framework of the $\mu(I)$ rheology and exhibit a collapse of both the shear to normal stress ratio and the solid volume fraction over a wide range of inertial numbers. Contrary to expectations, the effect of the interstitial fluid on the granular rheology is shown to be negligible, supporting recent work suggesting the absence of a clear transition between the free-fall and turbulent regime. In addition, data collapse is observed up to unexpectedly high inertial numbers $I\sim2$, challenging the existing conceptions and parametrization of the $\mu(I)$ rheology. Focusing upon bedload transport modelling, the results are pragmatically analyzed in the $\mu(I)$ framework in order to propose a granular rheology for bedload transport. The proposed rheology is tested using a 1D volume-averaged two-phase continuous model, and is shown to accurately reproduce the dense granular flow profiles and the sediment transport rate over a wide range of Shields numbers. The present contribution represents a step in the upscaling process from particle-scale simulations toward large-scale applications involving complex flow geometry.