Bed-load transport by laminar shearing flows
Seminar Room 1, Newton Institute
AbstractWhen beds constituted of sediment particles are submitted to shearing flows, the particles at the surface of the stream-bed are able to move as soon as hydrodynamic forces acting on them exceed a fraction of their apparent weight. Bed-load refers to the sediment in transport that is carried by intermittent contact with the stream-bed by rolling, sliding, and bouncing. This situation occurs in a wide variety of natural phenomena, such as sediment transport in rivers, and in industrial processes, such as problems due to hydrate formation in pipeline that are encountered in oil production and granular transport in food or pharmaceutical industries (Ouriemi, 2007). We propose to use a two-phase model having a Newtonian rheology for the fluid phase and Coulomb friction for the particulate phase. The model equations have been solved numerically in one-dimension and analytically in asymptotic cases. The model results have been compared with experimental data for a bed composed of spherical particles in laminar pipe flows (Ouriemi et al., 2008a). This continuum approach is able to provide an onset of motion for the particle phase and a description of the flow of the mobile granular layer. At some distance from threshold, we obtain the simpler analytical result of the particle flux varying cubically with the Shields number. This algebraic formulation seems quite satisfactory for describing experimental observations of bed-load transport in pipe flows. Based on this particle flux a simple linear stability analysis has been performed to predict the threshold for dune formation. This basic analysis accounts reasonable well for the experimental observations for the small dune formation (Ouriemi et al., 2008b). We are working on the implementation of the two-phase equations in a three dimensional numerical model to study the bed instability. This model will be used for better understanding of the coupling between the granular media and the fluid in terms of the bed instability.
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