Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-17T18:21:58.411Z Has data issue: false hasContentIssue false
  • English
  • Français

Lagrangian model of bed-load transport in turbulent junction flows

Published online by Cambridge University Press:  06 January 2011

CRISTIAN ESCAURIAZA  and
FOTIS SOTIROPOULOS
CRISTIAN ESCAURIAZA
Affiliation:
St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55414, USA Departamento de Ing. Hidráulica y Ambiental, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, 7820436 Santiago, Chile
FOTIS SOTIROPOULOS*
Affiliation:
St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55414, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Motivated by the need to gain fundamental insights into the mechanisms of bed-load sediment transport in turbulent junction flows, we carry out a computational study of Lagrangian dynamics of inertial particles initially placed on the bed upstream of a surface-mounted circular cylinder in a rectangular open channel (Dargahi, J. Hydraul. Engng, vol. 116, 1990, pp. 1197–1214). The flow field at Re = 39000 is simulated using the detached eddy simulation (DES) approach (Spalart et al., In Advances in DNS/LES, ed. C. Liu & Z. Liu, 1997, Greyden), which has already been shown to accurately resolve most of the turbulent stresses produced by the low-frequency, bimodal fluctuations of the turbulent horseshoe vortex (Paik et al., J. Hydraul. Engng, vol. 131, 1990, pp. 441–456; Escauriaza & Sotiropoulos, Flow Turbul. Combust., 2010, in press). The trajectory and momentum equations for the sediment particles are integrated numerically simultaneously with the flow governing equations assuming one-way coupling and neglecting particle-to-particle interactions (dilute flow) but taking into account bed–particle interactions and the effects of the instantaneous hydrodynamic forces induced by the resolved fluctuations of the coherent vortical structures. The computed results show that, in accordance with the simulated clear-water scour condition (i.e. the magnitude of the particle stresses is near the threshold of motion), the transport of sediment grains is highly intermittent and exhibits essentially all the characteristics of bed-load sediment transport observed in laboratory and field experiments. Groups of sediment grains are dislodged from the bed simultaneously in seemingly random bursting events and begin to move, saltating or sliding along the bed. Furthermore, particles that are not entrained into the bed-load layer are found to form streaks aligned with near-wall vortices around the cylinder. The global transport of particles is studied by performing a statistical analysis of the bed-load flux to reveal scale-invariance of the process and multifractality of particle transport as the overall effect of the coherent structures of the flow. A major finding of this work is that a relatively simple Lagrangian model coupled with a coherent-structure resolving simulation of the turbulent flow is able to reproduce the sediment dynamics observed in multiple experiments performed under similar conditions, and provide fundamental information on the initiation of motion and the multifractal nature of bed-load transport processes. The results also motivate the development of new Eulerian bed-load transport models that consider unsteady conditions and incorporate the intermittency of the unresolved scales of sediment motion.

JFM classification

Geophysical and Geological Flows: Sediment transport Turbulent Flows: Turbulence simulation Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 666 , 10 January 2011 , pp. 36 - 76
Copyright
Copyright © Cambridge University Press 2011

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

REFERENCES

Agui, J. H. & Andreopoulos, J. 1992 Experimental investigation of a three dimensional boundary layer flow in the vicinity of an upright wall mounted cylinder. Trans. ASME: J. Fluids Engng 114, 566–576.Google Scholar
Albayrak, I., Hopfinger, E. J. & Lemmin, U. 2008 Near-field flow structure of a confined wall jet on flat and concave rough walls. J. Fluid Mech. 606, 27–49.CrossRefGoogle Scholar
Allen, J. R. L. 1994 Fundamental properties of fluids and their relation to sediment transport processes. In Sediment Transport and Depositional Processes (ed. Pye, K.), pp. 25–60. Blackwell.Google Scholar
Ancey, C., Böhm, T., Jodeau, M. & Frey, P. 2006 Statistical description of sediment transport experiments. Phys. Rev. E 74, 011302.CrossRefGoogle ScholarPubMed
Ancey, C., Davison, A. C., Böhm, T., Jodeau, M. & Frey, P. 2008 Entrainment and motion of coarse particles in a shallow water stream down a steep slope. J. Fluid Mech. 595, 83–114.CrossRefGoogle Scholar
Armenio, V., Piomelli, U. & Fiorotto, V. 1999 Effect of the subgrid scales on particle motion. Phys. Fluids 11, 3030–3042.CrossRefGoogle Scholar
Auton, T. R., Hunt, J. C. R. & Prud'homme, M 1988 The force exerted on a body in inviscid unsteady non-uniform rotational flow. J. Fluid Mech. 197, 241–257.CrossRefGoogle Scholar
Bagnold, R. A. 1956 The flow of cohesionless grains in fluids. Phil. Trans. R. Soc. Lond. A 225, 49–63.Google Scholar
Bagnold, R. A. 1973 The nature of saltation and of ‘bed-load’ transport in water. Proc. R. Soc. Lond. A 332, 473–504.Google Scholar
Bak, P. 1986 The devil's staircase. Phys. Today 39, 38–45.CrossRefGoogle Scholar
Bec, J. 2005 Multifractal concentrations of inertial particles in smooth random flows. J. Fluid Mech. 528, 255–277.CrossRefGoogle Scholar
Boivin, M., Simonin, O. & Squires, K. D. 2000 On the prediction of gas-solid flows with two-way coupling using large eddy simulation. Phys. Fluids 12, 2080–2090.CrossRefGoogle Scholar
Bunte, K. & Abt, S. R. 2005 Effect of sampling time on measured gravel bed load transport rates in a coarse-bedded stream. Water Resour. Res. 41, W11405.CrossRefGoogle Scholar
Burton, G. C. & Dahm, W. J. A. 2005 Multifractal subgrid-scale modeling for large-eddy simulation. I. Model development and a priori testing. Phys. Fluids 17, 075111.CrossRefGoogle Scholar
Burton, T. M. & Eaton, J. K. 2005 Fully resolved simulations of particle-turbulence interaction. J. Fluid Mech. 545, 67–111.CrossRefGoogle Scholar
Chang, Y. S. & Scotti, A. 2003 Entrainment and suspension of sediments into a turbulent flow over ripples. J. Turbul. 4, 019.CrossRefGoogle Scholar
Chang, Y. S. & Scotti, A. 2006 Turbulent convection of suspended sediments due to flow reversal. J. Geophys. Res 111, C07001.Google Scholar
Crowe, C. T., Sommerfeld, M. & Tsuji, Y. 1998 Multiphase Flows with Droplets and Particles. CRC Press LLC.Google Scholar
Crowe, C. T., Troutt, T. R. & Chung, J. N. 1996 Numerical models for two-phase turbulent flows. Annu. Rev. Fluid Mech. 28, 11–43.CrossRefGoogle Scholar
Dargahi, B. 1989 The turbulent flow field around a circular cylinder. Exp. Fluids 8, 1–12.CrossRefGoogle Scholar
Dargahi, B. 1990 Controlling mechanism of local scour. J. Hydraul. Engng 116, 1197–1214.CrossRefGoogle Scholar
Dellenback, P., Metzger, D. & Neitzel, G. 1988 Measurements in turbulent swirling flow through an abrupt axisymmetric expansion. AIAA J. 26, 669–681.CrossRefGoogle Scholar
Devenport, W. J. & Simpson, R. L. 1990 Time-dependent and time-averaged turbulence structure near the nose of a wing-body junction. J. Fluid Mech. 210, 23–55.CrossRefGoogle Scholar
Doligalski, T. L., Smith, C. R. & Walker, J. D. A. 1994 Vortex interactions with walls. Annu. Rev. Fluid Mech. 26, 573–616.CrossRefGoogle Scholar
Drake, T. G. & Calantoni, J. 2001 Discrete particle model for sheet flow sediment transport in the nearshore. J. Geophys. Res. 106, 19859–19868.CrossRefGoogle Scholar
Drake, T. G., Shreve, R. L., Dietrich, W. E., Whiting, P. J. & Leopold, L. B. 1988 Bedload transport of fine gravel observed by motion-picture photography. J. Fluid Mech. 192, 193–217.CrossRefGoogle Scholar
Einstein, H. A. 1950 The bed-load function for sediment transportation in open channels. Tech. Bull. 1026. USDA Soil Conservation Service.Google Scholar
Engelund, F. & Hansen, E. 1967 A Monograph on Sediment Transport to Alluvial Streams. TeknikGoogle Scholar
Escauriaza, C. 2008 Three-dimensional unsteady modeling of clear-water scour in the vicinity of hydraulic structures: Lagrangian and Eulerian perspectives. PhD thesis, University of Minnesota, Minneapolis, MN.Google Scholar
Escauriaza, C. & Sotiropoulos, F. 2009 Trapping and sedimentation of inertial particles in three-dimensional flows in a cylindrical container with exactly counter-rotating lids. J. Fluid Mech. 641, 169–193.CrossRefGoogle Scholar
Escauriaza, C. & Sotiropoulos, F. 2010 Reynolds number effects on the coherent dynamics of the turbulent horseshoe vortex system. Flow Turbul. Combust (in press).CrossRefGoogle Scholar
Fede, P. & Simonin, O. 2006 Numerical study of the subgrid fluid turbulence effects on the statistics of heavy colliding particles. Phys. Fluids 18, 045103.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence, the Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Frisch, U. & Parisi, G. 1985 On the singularity structure of fully developed turbulence. In Turbulence and Predictability in Geophysical Fluid Dynamics (ed. Gil, M., Benzi, R. & Parisi, G.), pp. 84–88. North-Holland.Google Scholar
Grass, A. J. 1970 Initial instability of fine bed sand. J. Hydraul. Engng 96, 619–632.Google Scholar
Grass, A. J. 1971 Structural features of turbulent flows over smooth and rough boundaries. J. Fluid Mech. 50, 233–255.CrossRefGoogle Scholar
Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Proccacia, I. & Shraiman, B. I. 1986 Fractal measures and their singularities: the characterization of strange sets. Phys. Rev A 33, 1141–1151.CrossRefGoogle ScholarPubMed
Harte, D. 2001 Multifractals: Theory and Applications. Chapman and Hall/CRC Press.CrossRefGoogle Scholar
Heald, J., McEwan, I. & Tait, S. 2004 Sediment transport over a flat bed in a unidirectional flow: simulations and validation. Phil. Trans. R. Soc. Lond. A 362, 1973–1986.CrossRefGoogle Scholar
Hopfinger, E. J., Kurniawan, A., Graf, W. H. & Lemmin, U. 2004 Sediment erosion by Görtler vortices: the scour-hole problem. J. Fluid Mech. 520, 327–342.CrossRefGoogle Scholar
Hu, G. & Celik, I. 2008 Eulerian-Lagrangian based large-eddy simulation of a partially aerated flat bubble column. Chem. Engng Sci. 63, 253–271.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. In Proceedings of the Summer Program. Center for Turbulence Research, NASA Ames/Stanford University, pp. 193–208.Google Scholar
Kaftori, D., Hetsroni, G. & Banerjee, S. 1995 Particle behavior in the turbulent boundary layer: I. Motion, deposition, and entrainment. Phys. Fluids 7, 1095–1106.CrossRefGoogle Scholar
Kirkil, G. & Constantinescu, G. 2009 Nature of flow and turbulence structure around an in-stream vertical plate in a shallow channel and the implications for sediment erosion. Water Resour. Res. 45, W06412.CrossRefGoogle Scholar
Kirkil, G., Constantinescu, G. & Ettema, R. 2008 Coherent structures in the flow field around a circular cylinder with scour hole. J. Hydraul. Engng 134, 572–587.CrossRefGoogle Scholar
Kirkil, G., Constantinescu, G. & Ettema, R. 2009 Detached eddy simulation investigation of turbulence at a circular pier with scour hole. J. Hydraul. Engng 135, 888–901.CrossRefGoogle Scholar
Kuerten, J. G. M. 2006 Subgrid modeling in particle-laden channel flow. Phys. Fluids 18, 025108.CrossRefGoogle Scholar
Kuerten, J. G. M. & Vreman, A. W. 2005 Can turbophoresis be predicted by large-eddy simulation? Phys. Fluids 17, 011701.CrossRefGoogle Scholar
Lakehal, D. 2002 On the modelling of multiphase turbulent flows for environmental and hydrodynamic applications. Intl J. Multiphase Flow 28, 823–863.CrossRefGoogle Scholar
Loth, E. 2000 Numerical approaches for motion of dispersed particles, droplets, and bubbles. Prog. Energy Combust. Sci. 26, 161–223.CrossRefGoogle Scholar
Martinuzzi, R. & Havel, B. 2000 Turbulent flow around two interfering surface-mounted cubic obstacles in tandem arrangement. Trans. ASME: J. Fluids Engng 122, 24–31.Google Scholar
Maxey, M. R., Patel, B. K., Chang, E. J. & Wang, L. P. 1997 Simulations of dispersed turbulent multiphase flow. Fluid Dyn. Res. 20, 143–156.CrossRefGoogle Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a non-uniform flow. Phys. Fluids 26, 883–889.CrossRefGoogle Scholar
McCoy, A., Weber, L. J. & Constantinescu, G. 2008 Numerical investigation of flow hydrodynamics in a channel with a series of groynes. J. Hydraul. Engng 134, 157–172.CrossRefGoogle Scholar
Mei, R. 1992 An approximate expression for the shear lift force on a spherical particle at finite Reynolds number. Intl J. Multiphase Flow 18, 145–147.CrossRefGoogle Scholar
Melville, B. W. & Coleman, S. E. 2000 Bridge Scour. Water Resources.Google Scholar
Meneveau, C. & Sreenivasan, K. R. 1991 The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429–484.CrossRefGoogle Scholar
Michaelides, E. E. 2003 Hydrodynamic force and heat/mass transfer from particles, bubbles, and drops. Trans. ASME: J. Fluids Engng 125, 209–238.Google Scholar
Nadaoka, K., Nihei, Y. & Yagi, H. 1999 Grid-averaged Lagrangian LES model for multiphase turbulent flow. Intl J. Multiphase Flow 25, 1619–1643.CrossRefGoogle Scholar
Nelson, J. M., Shreve, R. L., McLean, S. R. & Drake, T. G. 1995 Role of near-bed turbulence structure in bed load transport and bed form mechanics. Water Resour. Res. 31, 2071–2086.CrossRefGoogle Scholar
Nikora, V. I. & Goring, D. G. 2002 Fluctuations of suspended sediment concentration and turbulent sediment fluxes in an open-channel flow. J. Hydraul. Engng 128, 214–224.CrossRefGoogle Scholar
Olsen, N. R. B. & Kjellesvig, H. M. 1998 Three-dimensional numerical flow modelling for estimation of maximum local scour depth. J. Hydraul. Res. 36, 579–590.CrossRefGoogle Scholar
Olsen, N. R. B. & Melaaen, M. C. 1993 Three-dimensional calculation of scour around cylinders. J. Hydraul. Engng 119, 1048–1054.CrossRefGoogle Scholar
Paik, J., Escauriaza, C. & Sotiropoulos, F. 2007 On the bimodal dynamics of the turbulent horseshoe vortex system in a wing-body junction. Phys. Fluids 19, 045107.CrossRefGoogle Scholar
Paik, J., Ge, L. & Sotiropoulos, F. 2004 Toward the simulation of complex 3D shear flows using unsteady statistical turbulence models. Intl J. Heat Fluid Flow 25, 513–527.CrossRefGoogle Scholar
Paik, J. & Sotiropoulos, F. 2005 Coherent structure dynamics upstream of a long rectangular block at the side of a large aspect ratio channel. Phys. Fluids 17, 115104.CrossRefGoogle Scholar
Paik, J. & Sotiropoulos, F. 2010 Numerical simulation of strongly swirling turbulent flows through an abrupt expansion. Intl J. Heat Fluid Flow 31, 390–400.CrossRefGoogle Scholar
Paik, J., Sotiropoulos, F. & Porté-Agel, F. 2009 Detached eddy simulation of the flow around two wall-mounted cubes in tandem. Intl J. Heat Fluid Flow 30, 286–305.CrossRefGoogle Scholar
Paik, J., Sotiropoulos, F. & Sale, M. J. 2005 Numerical simulation of swirling flow in complex hydroturbine draft tube using unsteady statistical turbulence models. J. Hydraul. Engng 131, 441–456.CrossRefGoogle Scholar
Papanicolaou, A. N., Diplas, P., Dancey, C. L. & Balakrishnan, M. 2001 Surface roughness effects in near-bed turbulence: implications to sediment entrainment. J. Engng Mech. 127, 211–218.Google Scholar
Parker, G., Seminara, G. & Solari, G. 2003 Bedload at low shields stress on arbitrarily sloping beds: alternative entrainment formulation. Water Resour. Res. 39, 1183.CrossRefGoogle Scholar
Radice, A., Malavasi, S. & Ballio, F. 2008 Sediment kinematics in abutment scour. J. Hydraul. Engng 134, 146–156.CrossRefGoogle Scholar
Roulund, A., Sumer, B. M., Fredsøe, J. & Michelsen, J. 2005 Numerical and experimental investigation of flow and scour around a circular pile. J. Fluid Mech. 534, 351–401.CrossRefGoogle Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400.CrossRefGoogle Scholar
Schmeeckle, M. W., Nelson, J. M., Pitlick, J. & Bennett, J. P. 2001 Interparticle collision of natural sediment grains in water. Water Resour. Res. 37, 2377–2391.CrossRefGoogle Scholar
Seminara, G., Solari, L. & Parker, G. 2002 Bedload at low shields stress on arbitrarily sloping beds: Failure of the bagnold hypothesis. Water Resour. Res. 38, 1249.CrossRefGoogle Scholar
Shotorban, B. & Mashayek, F. 2005 Modeling subgrid-scale effects on particles by approximate deconvolution. Phys. Fluids 17, 081701.CrossRefGoogle Scholar
Shotorban, B. & Mashayek, F. 2006 A stochastic model for particle motion in large-eddy simulation. J. Turbul. 7, 18.CrossRefGoogle Scholar
Simpson, R. L. 2001 Junction flows. Annu. Rev. Fluid Mech. 33, 415–443.CrossRefGoogle Scholar
Singh, A., Fienberg, K., Jerolmack, D. J., Marr, J. & Foufoula-Georgiou, E. 2009 Experimental evidence for statistical scaling and intermittency in sediment transport rates. J. Geophys. Res 114, F01025.Google Scholar
Sotiropoulos, F. & Abdallah, S. 1992 A primitive variable method for the solution of 3D, incompressible, viscous flows. J. Comput. Phys. 103, 336–349.CrossRefGoogle Scholar
Sotiropoulos, F. & Constantinescu, G. 1997 Pressure-based residual smoothing operators for multistage pseudocompressibility algorithms. J. Comput. Phys. 133, 129–145.CrossRefGoogle Scholar
Sotiropoulos, F., Ventikos, Y. & Lackey, T. C. 2001 Chaotic advection in three-dimensional stationary vortex-breakdown bubbles: Šil'nikov's chaos and the devil's staircase. J. Fluid Mech. 444, 257–297.CrossRefGoogle Scholar
Spalart, P. R. 2009 Detached-eddy simulation. Annu. Rev. Fluid Mech. 41, 181–202.CrossRefGoogle Scholar
Spalart, P. R. & Allmaras, S. R. 1994 A one-equation turbulence model for aerodynamic flows. Rech. Aerosp. 1, 5–21.Google Scholar
Spalart, P. R., Jou, W. H., Strelets, M. & Allmaras, S. R. 1997 Comments on the feasibility of LES for wings and on a hybrid RANS/LES approach. In Advances in DNS/LES (ed. Liu, C. & Liu, Z.), pp. 137–147. Greyden.Google Scholar
Sreenivasan, K. R. 1991 Fractals and multifractals in fluid turbulence. Annu. Rev. Fluid Mech. 23, 539–600.CrossRefGoogle Scholar
Sturm, T. W. 2001 Open Channel Hydraulics. McGraw-Hill.Google Scholar
Sumer, B. M., Chua, L. H. C., Cheng, N. S. & Fredsøe, J. 2003 Influence of turbulence on bed load sediment transport. J. Hydraul. Engng 129, 585–596.CrossRefGoogle Scholar
Teruzzi, A., Ballio, F. & Armenio, V. 2009 Turbulent stresses at the bottom surface near an abutment: laboratory-scale numerical experiment. J. Hydraul. Engng 135, 106–117.CrossRefGoogle Scholar
Vreman, B., Geurts, B. J., Deen, N. G., Kuipers, J. A. M. & Kuerten, J. G. M. 2009 Two- and four-way coupled Euler Lagrangian large-eddy simulation of turbulent particle-laden channel flow. Flow Turbul. Combust. 82, 47–71.CrossRefGoogle Scholar
Wiberg, P. L. & Smith, J. D. 1985 A theoretical model for saltating grains in water. J. Geophys. Res. 90, 7341–7354.CrossRefGoogle Scholar