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

Published online by Cambridge University Press:  26 January 2018

Jose M. Gonzalez-Ondina Open the ORCID record for Jose M. Gonzalez-Ondina [Opens in a new window] ,
Luigi Fraccarollo  and
Philip L.-F. Liu
Jose M. Gonzalez-Ondina*
Affiliation:
Department of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14850, USA Plymouth Ocean Forecasting Centre, Plymouth University, PL4 8AA, UK
Luigi Fraccarollo
Affiliation:
Department of Civil, Environmental and Mechanical Engineering, Universita degli Studi di Trento, Trento, 38123, Italy
Philip L.-F. Liu
Affiliation:
Department of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14850, USA Department of Civil and Environmental Engineering, National University of Singapore, Singapore 117576, Singapore Institute of Hydrological and Oceanic Sciences, National Central University, Jhongli, Taoyuan, 320, Taiwan
*
†Email address for correspondence: jg656@cornell.edu
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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.

JFM classification

Geophysical and Geological Flows: Sediment transport Geophysical and Geological Flows: Stratified flows Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 839 , 25 March 2018 , pp. 198 - 238
Copyright
© 2018 Cambridge University Press 

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