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A numerical investigation of fine particle laden flow in an oscillatory channel: the role of particle-induced density stratification

Published online by Cambridge University Press:  06 December 2010

CELALETTIN E. OZDEMIR ,
TIAN-JIAN HSU  and
S. BALACHANDAR
CELALETTIN E. OZDEMIR*
Affiliation:
Civil and Coastal Engineering, University of Florida, Gainesville, FL 32611, USA
TIAN-JIAN HSU
Affiliation:
Civil and Environmental Engineering, Center for Applied Coastal Research, University of Delaware, Newark, DE 19716, USA
S. BALACHANDAR
Affiliation:
Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
*
†Email address for correspondence: [email protected]
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Abstract

Studying particle-laden oscillatory channel flow constitutes an important step towards understanding practical application. This study aims to take a step forward in our understanding of the role of turbulence on fine-particle transport in an oscillatory channel and the back effect of fine particles on turbulence modulation using an Eulerian–Eulerian framework. In particular, simulations presented in this study are selected to investigate wave-induced fine sediment transport processes in a typical coastal setting. Our modelling framework is based on a simplified two-way coupled formulation that is accurate for particles of small Stokes number (St). As a first step, the instantaneous particle velocity is calculated as the superposition of the local fluid velocity and the particle settling velocity while the higher-order particle inertia effect neglected. Correspondingly, only the modulation of carrier flow is due to particle-induced density stratification quantified by the bulk Richardson number, Ri. In this paper, we fixed the Reynolds number to be ReΔ = 1000 and varied the bulk Richardson number over a range (Ri = 0, 1 × 10−4, 3 × 10−4 and 6 × 10−4). The simulation results reveal critical processes due to different degrees of the particle–turbulence interaction. Essentially, four different regimes of particle transport for the given ReΔ are observed: (i) the regime where virtually no turbulence modulation in the case of very dilute condition, i.e. Ri ~ 0; (ii) slightly modified regime where slight turbulence attenuation is observed near the top of the oscillatory boundary layer. However, in this regime a significant change can be observed in the concentration profile with the formation of a lutocline; (iii) regime where flow laminarization occurs during the peak flow, followed by shear instability during the flow reversal. A significant reduction in the oscillatory boundary layer thickness is also observed; (iv) complete laminarization due to strong particle-induced stable density stratification.

JFM classification

Geophysical and Geological Flows: Sediment transport Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 665 , 25 December 2010 , pp. 1 - 45
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Akhavan, R., Kamm, R. D. & Shapiro, A. H. 1991 An investigation of transition to turbulence in bounded oscillatory Stokes flows. Part 2: Numerical simulations. J. Fluid Mech. 225, 423–444.CrossRefGoogle Scholar
Armenio, V. & Sarkar, S. 2002 An investigation of stably stratified turbulent channel flow using large-eddy simulation J. Fluid Mech. 459, 1–42.CrossRefGoogle Scholar
Bagchi, P. & Balachandar, S. 2003 Effect of turbulence on the drag and lift of a particle. Phys. Fluids 15 (3), 496–513.CrossRefGoogle Scholar
Bagchi, P. & Balachandar, S. 2004 Response of the wake of an isolated particle to an isotropic turbulent flow. J. Fluid Mech. 518, 95–123.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Barenblatt, G. F. 1953 On the motion of suspended particles in a turbulent stream. Prikladnaja Mat. Mekh. Engl. Trans. 17, 261–274.Google Scholar
Birman, V., Martin, J. E. & Meiburg, E. 2005 The non-Boussinesq lock–exchange problem. Part 2: High-resolution simulations. J. Fluid Mech. 537, 125–144.CrossRefGoogle Scholar
Blennerhassett, P. J. & Bossom, A. P. 2002 The linear stability of flat Stokes layers. J. Fluid Mech. 464, 393–410.CrossRefGoogle Scholar
Blennerhassett, P. J. & Bossom, A. P. 2006 The linear stability of high-frequency oscillatory flow in a channel. J. Fluid Mech. 556, 1–25.CrossRefGoogle Scholar
Bonometti, T. & Balachandar, S. 2008 Effect of Schmidt number on the structure and propagation of density currents. Theor. Comput. Fluid Dyn. 22, 341–361.CrossRefGoogle Scholar
Burton, T. M. & Eaton, J. K. 2005 Fully resolved simulations of particle–turbulence interaction. J. Fluid Mech. 545, 67–111.CrossRefGoogle Scholar
Cantero, M. I., Balachandar, S., Cantelli, A., Pirmez, C. & Parker, G. 2009 a Turbidity current with a roof: direct numerical simulation of self-stratified turbulent channel flow driven by suspended sediment. J. Geophys. Res. 114, C03008.Google Scholar
Cantero, M. I., Balachandar, S. & Garcia, M. 2008 An Eulerian–Eulerian model for gravity currents driven by inertial particles. Intl J. Multiph. Flow 34, 484–501.CrossRefGoogle Scholar
Cantero, M. I., Balachandar, S. & Parker, G. 2009 b Direct numerical simulation of stratification effects in a sediment-laden turbulent channel flow. J. Turbulence 10, 1–28.CrossRefGoogle Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1987 Spectral Methods in Fluid Dynamics. Springer.Google Scholar
Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189–214.CrossRefGoogle Scholar
Chang, Y. S. & Scotti, A. 2006 Turbulent convection of suspended sediments due to flow reversal. J. Geophys. Res. 111 (C07001), doi:10.1029/2005JC003240.Google Scholar
Conley, D. C., Falchetti, S., Lohmann, I. P. & Brocchini, M. 2008 The effects of flow stratification by non-cohesive sediment on transport in high-energy wave-driven flows. J. Fluid Mech. 610, 43–67.CrossRefGoogle Scholar
Conley, D. S. & Inman, D. L. 1992 Field observations of the fluid-granular boundary layer under near breaking waves. J. Geophys. Res. 97, C6, 9631–9643.CrossRefGoogle Scholar
Cortese, T. & Balachandar, S. 1995 High performance spectral simulation of turbulent flows in massively parallel machines with distributed memory. Intl J. Supercomput. Appl. 9 (3), 187–204.Google Scholar
Costamagna, P., Vittori, G. & Blondeaux, P. 2003 Coherent structures in oscillatory boundary layers. J. Fluid Mech. 474, 1–33.CrossRefGoogle Scholar
Dalrymple, R. A. & Liu, P. L. 1978 Waves over soft mud beds: a two-layer fluid mud model. J. Phys. Oceanogr. 8, 1121–1131.2.0.CO;2>CrossRefGoogle Scholar
Einstein, H. A. & Chien, N. 1955 Effects of heavy sediment concentration near the bed on velocity and sediment distribution. MRD Sediment Ser. 8, University of California, Berkeley.Google Scholar
Elgar, S. & Raubenheimer, B. 2008 Wave dissipation by muddy seafloors. Geophys. Res. Lett. 35 (L07611), doi:10.1029/2008GL033245.CrossRefGoogle Scholar
Elgobashi, S. 1991 Particle-laden turbulent flows: direct simulation and closure models. Appl. Sci. Res. 52, 301–314.CrossRefGoogle Scholar
Elgobashi, S. & Truesdell, G. C. 1992 Direct simulation of particle dispersion in a decaying isotropic turbulence. J. Fluid Mech. 242, 655–700.CrossRefGoogle Scholar
Elgobashi, S. & Truesdell, G. C. 1993 On the 2-way interaction between homogeneous turbulence and dispersed solid particles. Part 1: Turbulence modification. Phys. Fluids A 5, 1790–1801.CrossRefGoogle Scholar
Felix, M. 2002 Flow structure of turbidity currents. Sedimentology 49, 397–419.CrossRefGoogle Scholar
Forristall, G. Z. & Reece, A. M. 1985 Measurements of wave attenuation due to a soft bottom: the SWAMP experiment. J. Geophys. Res. 90, 3367–3380.CrossRefGoogle Scholar
Foster, D. L., Beach, R. A. & Holman, R. A. 2006 Turbulence observations of the nearshore wave bottom boundary layer. J. Geophy. Res. 111 (C04011).CrossRefGoogle Scholar
Gelfenbaum, G. & Smith, J. D. 1986 Experimental evaluation of a generalized suspended-sediment transport theory. In Shelf Sands and Sand Stones (ed. Knight, R. J. & McLean, J. R.), pp. 133–144, Canadian Society of Petroleum Engineers.Google Scholar
Glenn, S. M. & Grant, W. D. 1987 A suspended sediment stratification correction for combined wave and current flows. J. Geophys. Res. 92 (C8), 8244–8264.Google Scholar
Hall, P. 1978 The linear stability of flat Stokes layers. Proc. R. Soc. Lond. A 359, 151–166.Google Scholar
Hall, B., Meiburg, E. & Kneller, B. 2008 Channel formation by turbidity currents: Navier–Stokes based linear stability analysis. J. Fluid Mech. 615, 185–210.CrossRefGoogle Scholar
Harris, T. C., Hogg, A. J. & Huppert, H. E. 2001 A mathematical framework for the analysis of particle-driven gravity currents. Proc. R. Soc. Lond. A 457, 1241–1272.CrossRefGoogle Scholar
Harris, C. K., Traykovski, P. A. & Geyer, W. R. 2005 Flood dispersal and deposition by near-bed gravitational sediment flows and oceanographic transport: a numerical modeling study of the Eel River shelf, northern California. J. Geophys. Res. 110, C09025, doi:10.10292004JC002727.Google Scholar
Hino, M. 1963 Turbulent flow with suspended particles. J. Hydraul. Div. Am. Soc. Civ. Engng 89 (HY4), 161–185.Google Scholar
Hino, M., Kashiwayanagi, M., Nakayama, A. & Hara, T. 1983 Experiments on the turbulence statistics and the structure of a reciprocating oscillatory flow. J. Fluid Mech. 131, 363–400.CrossRefGoogle Scholar
Hino, M., Sawamoto, M. & Takasu, S. 1976 Experiments on transition to turbulence in an oscillatory pipe flow. J. Fluid Mech. 75, 193–207.CrossRefGoogle Scholar
Howard, L. N. 1961 Note on a paper by John W. Miles. J. Fluid Mech. 10, 509–512.CrossRefGoogle 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.CrossRefGoogle Scholar
Hsu, T.-J., Ozdemir, C. E. & Traykovski, P. A. 2009 High resolution numerical modeling of wave-supported sediment gravity-driven mudflows. J. Geophys. Res. 114, C05014, doi:10.1029/2008JC005006.Google Scholar
Hsu, T.-J., Traykovski, P. A. & Kineke, G. C. 2007 On modeling boundary layer and gravity driven fluid mud transport. J. Geophys. Res. 112, C04011, doi:10.1029/2006JC003719.Google Scholar
Huppert, H. E., Turner, J. S. & Hallworth, M. A. 1995 Sedimentation and entrainment in dense layers of suspended particles stirred by an oscillating-grid. J. Fluid Mech. 289, 263–293.CrossRefGoogle Scholar
Ivey, G. N. & Imberger, J. 1991 On the nature of turbulence in a stratified fluid. Part 1: The energetics of mixing. J. Phys. Oceanogr. 21, 650–658.2.0.CO;2>CrossRefGoogle Scholar
Jensen, B. L., Sumer, M. & Fredsóe, J. 1989 Turbulent oscillatory boundary layers at high Reynolds numbers. J. Fluid Mech. 206, 265–297.CrossRefGoogle Scholar
Lamb, M. P., D'Asaro, E. & Parsons, J. D. 2004 Turbulent structure of high-density suspensions formed under waves. J. Geophys. Res. 109, C12026.Google Scholar
Maxey, M. R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.CrossRefGoogle Scholar
McLaughlin, J. B. 1989 Aerosol particle deposition in numerically simulated channel flow. Phys. Fluids A 1, 1211–1224.CrossRefGoogle Scholar
Mei, C. C. & Liu, K. F. 1987 A Bingham plastic model for a muddy seabed under long waves. J. Geophys. Res. 94 (C13) 14 581–14 594.CrossRefGoogle Scholar
Miles, J. W. 1961 On the stability of heterogeneous shear flows. J. Fluid Mech. 10, 496–508.CrossRefGoogle Scholar
Necker, F., Hartel, C., Kleiser, L. & Meiburg, E. 2002 High-resolution simulations of particle-driven gravity currents. Intl J. Multiph. Flow 29, 279–300.CrossRefGoogle Scholar
Noh, Y. & Fernando, J. S. 1991 Dispersion of suspended particles in turbulent flow. Phys. Fluids A 3 (7), 1730–1740.CrossRefGoogle Scholar
Nowak, N., Kakade, P. P. & Annapragada, A. V. 2003. Computational fluid dynamics simulation of airflow and aerosol deposition in human lungs. Ann. Biomed. Engng 31, 374–390.CrossRefGoogle ScholarPubMed
Ozdemir, C. E., Hsu, T.-J. & Balachandar, S. 2010 Simulation of fine sediment transport in oscillatory boundary layer. J. HydroEnviron. Res. 3, 247–259.Google Scholar
Rogers, C. B. & Eaton, J. K. 1991 The effect of small particles on fluid turbulence in a flat-plate, turbulent boundary layer in air. Phys. Fluids A 3, 928–937.CrossRefGoogle Scholar
Ross, M. A. & Mehta, A. J. 1989 On the mechanics of lutoclines and fluid muds. J. Coastal. Res. 5, 51–61.Google Scholar
Salon, S., Armenio, V. & Crise, A. 2007 A numerical investigation of the Stokes boundary layer in the turbulent regime. J. Fluid Mech. 570, 253–296.CrossRefGoogle Scholar
Sarpkaya, T. 1993 Coherent structures in oscillatory boundary layers. J. Fluid Mech. 253, 105–140.CrossRefGoogle Scholar
Schumann, U. & Gerz, T. 1995 Turbulent mixing in stably stratified shear flows. J. Appl. Meteor. 34, 33–48.CrossRefGoogle Scholar
Scotti., A. & Piomelli, U. 2001 Numerical simulation of pulsating turbulent channel flow. Phys. Fluids 13 (5), 1367–1384.CrossRefGoogle Scholar
Sequeiros, O. E., Cantelli, A., Viparelli, E., White, J. D. L., Garcia, M. H. & Parker, G. 2009 Modeling turbidity currents with non-uniform sediment and reverse buoyancy. Water Resour. Res. 45, W06408.CrossRefGoogle Scholar
Sheremet, A. & Stone, G. W. 2003 Observations of nearshore wave dissipation over muddy sea beds. J. Geophys. Res. 108 (C11), 3357.Google Scholar
Spalart, P. R. & Baldwin, B. S. 1989 Direct simulation of a turbulent oscillating boundary layer. In Turbulent Shear Flows 6 (ed. Andre, J. C.), pp. 417–440, Springer.CrossRefGoogle Scholar
Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3, 1169.CrossRefGoogle Scholar
Strang, E. J. & Fernando, H. J. S. 2001 Entrainment and mixing in stratified shear flows. J. Fluid Mech. 428, 349–386.CrossRefGoogle Scholar
Styles, R. & Glenn, S. M. 2000 Modeling stratified wave and current bottom boundary layers in the continental shelf. J. Geophys. Res. 105, 24119–24139.CrossRefGoogle Scholar
Tanaka, T. & Eaton, J. K. 2008 Classification of turbulence modification by dispersed spheres using a novel dimensionless number. Phys. Rev. Lett. 101, 114502.CrossRefGoogle ScholarPubMed
Taylor, G. I. 1931 Effect of variation in density on the stability of superposed streams of fluid. Proc. R. Soc. Lond. A 132, 499–523.Google Scholar
Taylor, M. G. 1959 The influence of the anomalous viscosity of blood upon its oscillatory flow. Phys. Med. Biol. 3, 273–290.CrossRefGoogle ScholarPubMed
Traykovski, P., Geyer, W. R., Irish, J. D. & Lynch, J. F. 2000 The role of wave-induced fluid mud flows for cross-shelf transport on the Eel River continental shelf. Cont. Shelf Res. 20, 2113–2140.CrossRefGoogle Scholar
Trowbridge, J. H. & Kineke, G. C. 1994 Structure and dynamics of fluid mud on the Amazon continental shelf. J. Geophys. Res. 99 (C1), 865–874.CrossRefGoogle Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.CrossRefGoogle Scholar
Vanoni, V. A. 1946 Transportation of suspended sediment by water. ASCE Trans. 111, 67–133.Google Scholar
Vittori, G. & Verzicco, R. 1998 Direct simulation of transition in an oscillatory boundary layer. J. Fluid Mech. 371, 207–232.CrossRefGoogle Scholar
Winterwerp, J. C. 2001 Stratification effects by cohesive and non-cohesive sediment. J. Geophys. Res. 106 (C10), 22559–22574.CrossRefGoogle Scholar
Winterwerp, J. C. 2002 On the flocculation and settling velocity of estuarine mud. Cont. Shelf Res. 22, 1339–1360.CrossRefGoogle Scholar
Winterwerp, J. C. & Van Kesteren, W. G. M. 2004 Introduction to the Physics of Cohesive Sediment in the Marine Environment. Elsevier.Google Scholar
Yang, J. N., Chung, T. R., Troutt, , & Crowe, C. T. 1990 The influence of particles on the spatial stability of two-phase mixing layers. Phys. Fluids A 2, 1839.CrossRefGoogle Scholar
Yu, X, Hsu, T.-J. & Hanes, D. M. 2010 Sediment transport under wave groups: the relative importance between wave shape and boundary layer streaming. J. Geophys. Res. 15, C02013, doi:10.1029/2009JC005348.Google Scholar
Zeng, L., Balachandar, S., Fischer, P. & Najjar, F. M. 2008 Interactions of a stationary finite-sized particle with wall turbulence. J. Fluid Mech. 594, 271–305.CrossRefGoogle Scholar
Zeng, L., Balachandar, S. & Najjar, F. M. 2010 Wake response of a stationary finite-sized particle in a turbulent channel flow. Intl J. Multiph. Flow 36, 406–422.CrossRefGoogle Scholar
Zhou, D. & Ni, J. R. 1995 Effects of dynamic interaction on sediment laden turbulent flows. J. Geophys. Res. 100 (C1), 981–996.CrossRefGoogle Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar