Two-level, two-phase model for intense, turbulent sediment transport

Abstract

The study of sediment transport requires in-depth investigation of the complex effects of sediment particles in fluid turbulence. In this paper we focus on intense sediment transport flows. None of the existing two-phase models in the literature properly replicates the liquid and solid stresses in the near bed region of high concentration of sediment. The reason for this shortcoming is that the physical processes occurring at the length scale of the particle collisions are different from those occurring at larger length scales and therefore, they must be modelled independently. We present here a two-level theoretical derivation of two-phase, Favre averaged Navier–Stokes equations (FANS). This approach treats two levels of energy fluctuations independently, those associated with a granular spatial scale (granular temperature and small-scale fluid turbulence) and those associated with the ensemble average (turbulent kinetic energy for the two phases). Although similar attempts have been made by other researchers, the two level approach ensures that the two relevant length scales are included independently in a more consistent manner. The model is endowed with a semi-empirical formulation for the granular scale fluid turbulence, which is important even in the dense collisional shear layer, as has been recently recognized. As a result of the large and small scale modelling of the liquid and solid fluctuations, predictions are promising to be reliable in a wide range of flow conditions, from collisional to turbulent suspensions. This model has been validated for steady state flows with intense, collisional or mixed collisional–turbulent sediment transport, using various sources of detailed experimental data. It compares well with the experimental results in the whole experimental range of Shields parameters, better than previous models, although at the cost of increased complexity in the equations. Further experiments on turbulent suspensions would be necessary to definitely assess the model capabilities.