Abstract
Classical scaling relationships for rheological quantities such as the $\mu (J)$ -rheology have become increasingly popular for closures of two-phase flow modelling. However, these frameworks have been derived for monodisperse particles. We aim to extend these considerations to sediment transport modelling by using a more realistic sediment composition. We investigate the rheological behaviour of sheared sediment beds composed of polydisperse spherical particles in a laminar Couette-type shear flow. The sediment beds consist of particles with a diameter size ratio of up to 10, which corresponds to grains ranging from fine to coarse sand. The data was generated using fully coupled, grain resolved direct numerical simulations using a combined lattice Boltzmann–discrete element method. These highly resolved data yield detailed depth-resolved profiles of the relevant physical quantities that determine the rheology, i.e. the local shear rate of the fluid, particle volume fraction, total shear and granular pressure. A comparison against experimental data shows excellent agreement for the monodisperse case. We improve upon the parameterization of the $\mu (J)$ -rheology by expressing its empirically derived parameters as a function of the maximum particle volume fraction. Furthermore, we extend these considerations by exploring the creeping regime for viscous numbers much lower than used by previous studies to calibrate these correlations. Considering the low viscous numbers of our data, we found that the friction coefficient governing the quasi-static state in the creeping regime tends to a finite value for vanishing shear, which decreases the critical friction coefficient by a factor of three for all cases investigated.
Highlights
The fluid mediated transport of granular sediment is a key process for the mass movement in a geophysical and an engineering context (e.g. Frey & Church 2011)
Since the goal of the present study is to investigate the rheological behaviour of sediment beds in the framework of the μ(J)-rheology, we have to obtain the values for pp, μ = τ/pp and J = ηf γ /pp
Previous studies on dry granular flows have suggested accounting for polydispersity by using the weighted arithmetic mean of the particle diameter in the definition of the inertial number (Tripathi & Khakhar 2011). Since this geometric quantity does not appear in the definitions of the μ(J)-rheology framework, we identified φm as the more suitable measure to account for polydispersity of dense suspensions in a quantitative manner
Summary
The fluid mediated transport of granular sediment is a key process for the mass movement in a geophysical and an engineering context (e.g. Frey & Church 2011). The transport typically occurs along a slope or by a fluid flow shearing the sediment (Jerolmack & Daniels 2019) and can lead to bedform evolution, such as ripples and dunes, even for laminar flow conditions (Lajeunesse et al 2010) This consideration allows us to characterize sediment transport in laminar flows in terms of the rheology to investigate the fluid–particle mixture’s deformation behaviour in shearing flows (Aussillous et al 2013; Houssais et al 2016; Kidanemariam 2016; Vowinckel et al 2021). All these studies justified their approach by comparing the results with data previously obtained in rheometer studies with dense suspensions of neutrally buoyant particles The total shear comprises hydrodynamic and frictional interparticle stresses, with the latter becoming more important with increasing particle volume fraction φ (Gallier et al 2014; Guazzelli & Pouliquen 2018; Vowinckel et al 2021)
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