Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T18:25:29.645Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Amoudry, L., Hsu, T.-J. & Liu, P. L.-F. 2008 Two-phase model for sand transport in sheet flow regime. J. Geophys. Res. Oceans 113, C03011.Google Scholar
Amoudry, L. O.2008 Two-phase modeling of granular sediment for sheet flows and scour. PhD thesis, Cornell University.Google Scholar
Barnocky, G. & Davis, R. H. 1988 Elastohydrodynamic collision and rebound of spheres: experimental verification. Phys. Fluids 31 (6), 1324–1329.CrossRefGoogle Scholar
Berzi, D. & Fraccarollo, L. 2013 Inclined, collisional sediment transport. Phys. Fluids 25 (10), 106601.Google Scholar
Berzi, D. & Fraccarollo, L. 2015 Turbulence locality and granularlike fluid shear viscosity in collisional suspensions. Phys. Rev. Lett. 115, 194501.Google Scholar
Berzi, D. & Fraccarollo, L. 2016 Intense sediment transport: collisional to turbulent suspension. Phys. Fluids 28 (2), 023302.Google Scholar
Capart, H. & Fraccarollo, L. 2011 Transport layer structure in intense bed-load. Geophys. Res. Lett. 38, L20402.Google Scholar
Chauchat, L. 2017 A comprehensive two-phase flow model for unidirectional sheet-flows. J. Hydraul. Res.. doi:10.1080/00221686.2017.1289260.Google Scholar
Chen, X., Li, Y., Niu, X., Li, M., Chen, D. & Yu, X. 2011 A general two-phase turbulent flow model applied to the study of sediment transport in open channels. Intl J. Multiphase Flow 37 (9), 1099–1108.Google Scholar
Chorin, A. J. 1968 Numerical solution of the Navier–Stokes equations. Math. Comput. 22 (104), 745–762.Google Scholar
Crowe, C. T. 2000 On models for turbulence modulation in fluid–particle flows. Intl J. Multiphase Flow 26 (5), 719–727.Google Scholar
Ding, J. & Gidaspow, D. 1990 A bubbling fluidization model using kinetic theory of granular flow. AIChE J. 36 (4), 523–538.Google Scholar
Dohmen-Janssen, C. M. & Hanes, D. M. 2002 Sheet flow dynamics under monochromatic nonbreaking waves. J. Geophys. Res. Oceans 107, 13.1–13.21.CrossRefGoogle Scholar
Dong, P. & Zhang, K. 1999 Two-phase flow modelling of sediment motions in oscillatory sheet flow. Coast. Engng 36 (2), 87–109.Google Scholar
Drew, D. A. 1983 Mathematical modeling of two-phase flow. Annu. Rev. Fluid Mech. 15 (1), 261–291.Google Scholar
Durán, O., Andreotti, B. & Claudin, P. 2012 Numerical simulation of turbulent sediment transport, from bed load to saltation. Phys. Fluids 24, 103306.Google Scholar
Durbin, P. A. 1991 Near-wall turbulence closure modeling without damping functions. Theor. Comput. Fluid Dyn. 3 (1), 1–13.Google Scholar
Elghobashi, S. E. & Abou-Arab, T. W. 1983 A two-equation turbulence model for two-phase flows. Phys. Fluids 26 (4), 931–938.Google Scholar
Favre, A. J.1965 The equations of compressible turbulent gases. Tech. Rep. DTIC Document.Google Scholar
Gore, R. A. & Crowe, C. T. 1989 Effect of particle size on modulating turbulent intensity. Intl J. Multiphase Flow 15 (2), 279–285.CrossRefGoogle Scholar
Houssais, M. & Lajeunesse, E. 2012 Bedload transport of a bimodal sediment bed. J. Geophys. Res. Earth Surface 117, F04015.Google Scholar
Hsu, T.-J.2002 A two-phase flow approach for sediment transport. PhD thesis.Google Scholar
Hsu, T.-J., Jenkins, J. T. & Liu, P. L.-F. 2004 On two-phase sediment transport: sheet flow of massive particles. Proc. R. Soc. Lond. A 460 (2048), 2223–2250.Google Scholar
Hwanc, G. J. & Shen, H. H. 1993 Fluctuation energy equations for turbulent fluid-solid flows. Intl J. Multiphase Flow 19 (5), 887–895.Google Scholar
Hwang, W. & Eaton, J. K. 2006 Homogeneous and isotropic turbulence modulation by small heavy (st ∼ 50) particles. J. Fluid Mech. 564, 361–393.Google Scholar
Jenkins, J. T. & Berzi, D. 2010 Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory. Granul. Matt. 12 (2), 151–158.Google Scholar
Jenkins, J. T. & Hanes, D. M. 1998 Collisional sheet flows of sediment driven by a turbulent fluid. J. Fluid Mech. 370, 29–52.Google Scholar
Jenkins, J. T. & Savage, S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187–202.Google Scholar
Kurose, R., Misumi, R. & Komori, S. 2001 Drag and lift forces acting on a spherical bubble in a linear shear flow. Intl J. Multiphase Flow 27 (7), 1247–1258.Google Scholar
Liu, H. & Sato, S. 2005 Modeling sediment movement under sheetflow conditions using a two-phase flow approach. Coast. Engng J. 47 (04), 255–284.Google Scholar
Liu, H. & Sato, S. 2006 A two-phase flow model for asymmetric sheetflow conditions. Coast. Engng 53 (10), 825–843.Google Scholar
Longo, S. 2005 Two-phase flow modeling of sediment motion in sheet-flows above plane beds. J. Hydraul. Engng ASCE 131 (5), 366–379.CrossRefGoogle Scholar
Ma, D. & Ahmadi, G. 1988 A kinetic model for rapid granular flows of nearly elastic particles including interstitial fluid effects. Powder Technol. 56 (3), 191–207.Google Scholar
Matoušek, V. 2009 Concentration profiles and solids transport above stationary deposit in enclosed conduit. J. Hydraul. Engng ASCE 135 (12), 1101–1106.Google Scholar
Maurin, R., Chauchat, J. & Frey, P. 2016 Dense granular flow rheology in turbulent bedload transport. J. Fluid Mech. 804, 490–512.Google Scholar
Midi, GDR 2004 On dense granular flows. Eur. Phys. J. E 14 (4), 341–365.Google Scholar
Pähtz, T. & Durán, O. 2017 Fluid forces or impacts: What governs the entrainment of soil particles in sediment transport mediated by a newtonian fluid? Phys. Rev. Fluids 2, 074303.Google Scholar
Pope, S. B. 2001 Turbulent Flows. IOP Publishing.Google Scholar
Revil-Baudard, T. & Chauchat, J. 2013 A two-phase model for sheet flow regime based on dense granular flow rheology. J. Geophys. Res. Oceans 118, 619–634.Google Scholar
Revil-Baudard, T., Chauchat, J., Hurther, D. & Barraud, P.-A. 2015 Investigation of sheet-flow processes based on novel acoustic high-resolution velocity and concentration measurements. J. Fluid Mech. 767, 1–30.Google Scholar
Revil-Baudard, T., Chauchat, J., Hurther, D. & Eiff, O. 2016 Turbulence modifications induced by the bed mobility in intense sediment-laden flows. J. Fluid Mech. 808, 469–484.Google Scholar
Richardson, J. & Zaki, W. 1954 Fluidization and sedimentation–part i. Trans. Inst. Chem. Engrs 32, 38–58.Google Scholar
Schlichting, H. 1979 Boundary Layer Theory. McGraw-Hill.Google Scholar
Schmeeckle, M. W. 2014 Numerical simulation of turbulence and sediment transport of medium sand. J. Geophys. Res. Earth Surface 119 (6), 1240–1262.Google Scholar
Sumer, B. M., Kozakiewicz, A., Fredsøe, J. & Deigaard, R. 1996 Velocity and concentration profiles in sheet-flow layer of movable bed. J. Hydraul. Engng ASCE 122 (10), 549–558.Google Scholar
Telluride Team2003 Truchas: physics and algorithms. Tech. Rep. LA-UR-03-0166.Google Scholar
Torquato, S. 1995 Nearest-neighbor statistics for packings of hard spheres and disks. Phys. Rev. E 51 (4), 3170–3182.Google Scholar
Van Wijngaarden, L. 1998 On pseudo turbulence. J. Theor. Comput. Fluid Dyn. 10 (1), 449–458.Google Scholar
Vanoni, V. A. & Brooks, N. H.1957 Laboratory studies of the roughness and suspended load of alluvial streams.Google Scholar