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Influence of permeable beds on hydraulically macro-rough flow

Published online by Cambridge University Press:  25 May 2018

Hongwei Fang ,
Xu Han ,
Guojian He Open the ORCID record for Guojian He [Opens in a new window]  and
Subhasish Dey Open the ORCID record for Subhasish Dey [Opens in a new window]
Hongwei Fang
Affiliation:
State Key Laboratory of Hydro-science and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China
Xu Han
Affiliation:
State Key Laboratory of Hydro-science and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China
Guojian He*
Affiliation:
State Key Laboratory of Hydro-science and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China
Subhasish Dey
Affiliation:
Department of Civil Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India
*
†Email address for correspondence: [email protected]
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Abstract

In this study, macro-rough flows over beds with different permeability values are simulated using the large-eddy simulation, and the results are analysed by applying the double-averaging (DA) methodology. Spheres of different sizes and arrangements were used to form the beds, which are deemed to be permeable granular beds. The influence of bed permeability on the turbulence dynamics and structure is investigated. It was observed that the scales of the spanwise vortical structures over more permeable beds are larger than those over less permeable beds. This is attributed to large-scale spanwise-alternate strips of varying Reynolds shear stress (RSS), emerging from the surface of macro-rough elements for the permeable beds. The DA stress balance suggests that the time-averaged spanwise vortical structure leads to a damping in DA RSS and an unusual peak of the form-induced stress in the main flow. In the streamwise direction, both large turbulent structures that originate from the Kelvin–Helmholtz-type instability and small turbulent structures that are associated with the turbulent transport across the gaps of the roughness elements are more prevalent over highly permeable beds. Near the bed, the relative magnitude of turbulent events shows a transition from a ejections-dominating to sweeps-dominating zone with vertical distance. Further, several hydrodynamic characteristics normalized by inner scales (kinematic viscosity to shear velocity ratio) show a greater dependency on permeability Reynolds number than those normalized by sediment size. The study provides an insight into the mechanism of mass transfer near the fluid–particle interface, which is vital to benthic and aquatic ecology.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 847 , 25 July 2018 , pp. 552 - 590
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Copyright
© 2018 Cambridge University Press 

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References

Amir, M., Nikora, V. I. & Stewart, M. T. 2014 Pressure forces on sediment particles in turbulent open-channel flow: a laboratory study. J. Fluid Mech. 757, 458–497.Google Scholar
Anderson, W., Barros, J. M., Christensen, K. T. & Awasthi, A. 2015 Numerical and experimental study of mechanisms responsible for turbulent secondary flows in boundary layer flows over spanwise heterogeneous roughness. J. Fluid Mech. 768, 316–347.Google Scholar
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207.Google Scholar
Bomminayuni, S. & Stoesser, T. 2011 Turbulence statistics in an open-channel flow over a rough bed. J. Hydraul. Engng 137 (11), 1347–1358.Google Scholar
Boudreau, B. P. 2001 Solute transport above the sediment–water interface. In The Benthic Boundary Layer: Transport Processes and Biogeochemistry (ed. Boudreau, B. P. & Jorgensen, B. B.), pp. 104–126. Oxford University Press.Google Scholar
Breuer, M. A. & Rodi, W. 1994 Large-eddy simulation of turbulent flow through a straight square duct and a 180° bend. In Direct and Large-Eddy Simulation I (ed. Voke, P. R., Kleiser, L. & Chollet, J. P.), pp. 273–285. Kluwer.CrossRefGoogle Scholar
Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562, 35–72.Google Scholar
Calmet, I. & Magnaudet, J. 1997 Large-eddy simulation of high-Schmidt number mass transfer in a turbulent channel flow. Phys. Fluids 9 (2), 438–455.Google Scholar
Castro, I. P., Cheng, H. & Reynolds, R. 2006 Turbulence over urban-type roughness: decutions from with tunnel measurements. Boundary-Layer Meteorol. 118 (1), 109–131.Google Scholar
Chaitanya, D. G. & Sourabh, V. A. 2016 DNS study of particle-bed-turbulence interactions in an oscillatory wall-bounded flow. J. Fluid Mech. 792, 232–251.Google Scholar
Clifton, A., Manes, C., Rüedi, J. D., Guala, M. & Lehning, M. 2008 On shear-driven ventilation of snow. Boundary-Layer Meteorol. 126 (2), 249–261.Google Scholar
Coceal, O., Dobre, A., Thomas, T. G. & Belcher, S. E. 2007 Structure of turbulent flow over regular arrays of cubical roughness. J. Fluid Mech. 589, 375–409.Google Scholar
Coleman, S. E., Nikora, V. I., McLean, S. R. & Schlicke, E. 2007 Spatially averaged turbulent flow over square ribs. J. Engng Mech. 133 (2), 194–204.Google Scholar
Defina, A. 1996 Transverse spacing of low-speed streaks in a channel flow over a rough bed. In Coherent Flow Structures in Open Channels (ed. Ashworth, P. J., Bennett, S. J., Best, J. L. & McLelland, S. J.), pp. 87–99. Wiley.Google Scholar
Dey, S. & Das, R. 2012 Gravel-bed hydrodynamics: double-averaging approach. J. Hydraul. Engng 138 (8), 707–725.Google Scholar
Dey, S. & Raikar, R. V. 2007 Characteristics of loose rough boundary streams at near-threshold. J. Hydraul. Engng 133 (3), 288–304.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Dybbs, A. & Edwards, R. 1984 A new look at porous media fluid mechanics – Darcy to turbulent. In Fundamentals of Transport Phenomena in Porous Media (ed. Bear, J. & Corapcioglu, M. Y.), pp. 199–256. Martinus Nijhoff Publishers.Google Scholar
Fang, H., Bai, J., He, G. & Zhao, H. 2014 Calculations of nonsubmerged groin flow in a shallow open channel by large-eddy simulation. J. Engng Mech. 140 (5), 04014016.Google Scholar
Ferraro, D., Servidio, S., Carbone, V., Dey, S. & Gaudio, R. 2016 Turbulence laws in natural bed flows. J. Fluid Mech. 798, 540–591.Google Scholar
Fröhlich, J. & Rodi, W. 2002 Introduction to large eddy simulation of turbulent flows. In Closure Strategies for Turbulent and Transitional Flows (ed. Launder, B. E. & Sandham, N. D.), pp. 197–224. Cambridge University Press.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids 3 (7), 1760–1765.CrossRefGoogle Scholar
Ghisalberti, M. & Nepf, H. M. 2002 Mixing layers and coherent structures in vegetated aquatic flows. J. Geophys. Res. 107 (C2), doi:10.1029/2001JC000871.Google Scholar
Giménez-Curto, L. A. & Corniero, M. A. 2002 Flow characteristics in the interfacial shear layer between a fluid and a granular bed. J. Geophys. Res. 107 (C5), 3044, doi:10.1029/2000JC000729.Google Scholar
Goharzadeh, A., Khalili, A. & Jørgensen, B. B. 2005 Transition layer thickness at a fluidporous interface. Phys. Fluids 17 (5), 057102.Google Scholar
Goyeau, B., Lhuillier, D., Gobin, D. & Velarde, M. G. 2003 Momentum transport at a fluid-porous interface. Intl J. Heat Mass Transfer 46 (21), 4071–4081.Google Scholar
Grass, A. J., Stuart, R. J. & Mansour-Tehrani, M. 1991 Vortical structures and coherent motion in turbulent flow over smooth and rough boundaries. Phil. Trans. R. Soc. Lond. A 336 (1640), 33–65.Google Scholar
Hahn, S., Je, J. & Choi, H. 2002 Direct numerical simulation of turbulent channel flow with permeable walls. J. Fluid Mech. 450, 259–285.Google Scholar
Han, X., He, G. & Fang, H. 2017 Double-averaging analysis of turbulent kinetic energy fluxes and budget based on large-eddy simulation. J. Hydrodyn. 29 (4), 567–574.Google Scholar
Horton, N. A. & Pokrajac, D. 2009 Onset of turbulence in a regular porous medium: an experimental study. Phys. Fluids 21 (4), 045104.Google Scholar
Jackson, P. S. 1981 On the displacement height in the logarithmic velocity profile. J. Fluid Mech. 111, 15–25.Google Scholar
Jimenez, J., Uhlmann, M., Pinelli, A. & Kawahara, G. 2001 Turbulent shear flow over active and passive porous surfaces. J. Fluid Mech. 442, 89–117.Google Scholar
Khosronejad, A. & Sotiropoulos, F. 2014 Numerical simulation of sand waves in a turbulent open channel flow. J. Fluid Mech. 753, 150–216.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Kironoto, B. A. & Graf, W. H. 1994 Turbulence characteristics in rough uniform open-channel flow. Proc. Inst. Civ. Engrs Wat., Marit. Energy 106 (4), 333–334.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluids at very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299–303.Google Scholar
Kong, F. Y. & Schetz, J. A.1982 Turbulent boundary layer over porous surfaces with different surface geometries. In AIAA Paper 82-0030, 1–10.Google Scholar
Krogstad, P. Å. & Antonia, R. A. 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27 (5), 450–460.Google Scholar
Kuwata, Y. & Suga, K. 2016 Lattice Boltzmann direct numerical simulation of interface turbulence over porous and rough walls. Intl J. Heat Fluid Flow 61 (October), 145–157.Google Scholar
Liu, Q. & Prosperetti, A. 2011 Pressure-driven flow in a channel with porous walls. J. Fluid Mech. 679, 77–100.Google Scholar
Lopez, F. & Garcia, M. H. 1999 Wall similarity in turbulent open channel flow. J. Engng Mech. 125 (7), 789–796.Google Scholar
Lu, S. S. & Willmarth, W. W. 1973 Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60, 481–511.Google Scholar
Manes, C., Poggi, D. & Ridolfi, L. 2011 Turbulent boundary layers over permeable walls: scaling and near-wall structure. J. Fluid Mech. 687, 141–170.CrossRefGoogle Scholar
Manes, C., Pokrajac, D. & McEwan, I. 2007 Double-averaged open-channel flows with small relative submergence. J. Hydraul. Engng 133 (8), 896–904.Google Scholar
Manes, C., Pokrajac, D., McEwan, I. & Nikora, V. 2009 Turbulence structure of open channel flows over permeable and impermeable beds: a comparative study. Phys. Fluids 21 (12), 125109.Google Scholar
Mignot, E., Barthelemy, E. & Hurther, D. 2009a Double-averaging analysis and local flow characterization of near-bed turbulence in gravel-bed channel flows. J. Fluid Mech. 618 (January), 279–303.CrossRefGoogle Scholar
Mignot, E., Hurther, D. & Barthelemy, E. 2009b On the structure of shear stress and turbulent kinetic energy flux across the roughness layer of a gravel-bed channel flow. J. Fluid Mech. 638 (November), 423–452.Google Scholar
Nezu, I. 2005 Open-channel flow turbulence and its research prospect in the 21st century. J. Hydraul. Engng 131 (4), 229–246.Google Scholar
Nezu, I. & Nakagawa, H. 1993 Turbulence in Open-Channel Flows. A. A. Balkema.Google Scholar
Nikora, V. & Goring, D. 2000 Flow turbulence over fixed and weakly mobile gravel beds. J. Hydraul. Engng 126 (9), 679–690.Google Scholar
Nikora, V., Goring, D., McEwan, I. & Griffiths, G. 2001 Spatially averaged open-channel flow over rough bed. J. Hydraul. Engng 127 (2), 123–133.Google Scholar
Nikora, V., McEwan, I., McLean, S., Coleman, S., Pokrajac, D. & Walters, R. 2007a Double-averaging concept for rough-bed open-channel and overland flows: theoretical background. J. Hydraul. Engng 133 (8), 873–883.Google Scholar
Nikora, V., McLean, S., Coleman, S., Pokrajac, D., McEwan, I., Campbell, L., Aberle, J., Clunie, D. & Koll, K. 2007b Double-averaging concept for rough-bed open-channel and overland flows: applications. J. Hydraul. Engng 133 (8), 884–895.Google Scholar
Nikora, V. I. & Smart, G. M. 1997 Turbulence characteristics of New Zealand gravel-bed rivers. J. Hydraul. Engng 123 (9), 764–773.Google Scholar
Peskin, C. S. 1972 Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10 (2), 252–271.Google Scholar
Pokrajac, D., Campbell, L. J., Nikora, V., Manes, C. & McEwan, I. 2007 Quadrant analysis of persistent spatial velocity perturbations over square-bar roughness. Exp. Fluids 42 (3), 413–423.Google Scholar
Raupach, M. R., Antonio, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 1–25.Google Scholar
Rosgen, D. L. 1994 A classification of natural rivers. Catena 22 (3), 169–199.Google Scholar
Sarkar, S. & Dey, S. 2010 Double-averaging turbulence characteristics in flows over a gravel-bed. J. Hydraul. Res. 48 (6), 801–809.Google Scholar
Sarkar, S., Papanicolaou, A. N. & Dey, S. 2016 Turbulence in gravel-bed stream with an array of large gravel obstacles. J. Hydraul. Engng 142 (11), 04016052.Google Scholar
Singh, K. M., Sandham, N. D. & Williams, J. J. R. 2007 Numerical simulation of flow over a rough bed. J. Hydraul. Engng 133 (4), 386–398.Google Scholar
Smart, G. M. & Habersack, H. M. 2007 Pressure fluctuations and gravel entrainment in rivers. J. Hydraul. Res. 45 (5), 661–673.Google Scholar
Song, T. & Graf, W. H. 1994 Nonuniform open-channel flow over a rough bed. J. Hydrosci. Hydraul. Engng 12 (1), 1–25.Google Scholar
Suga, K. 2016 Understanding and modelling turbulence over and inside porous media. Flow Turbul. Combust. 96 (3), 717–756.Google Scholar
Suga, K., Matsumura, Y., Ashitaka, Y., Tominaga, S. & Kaneda, M. 2010 Effects of wall permeability on turbulence. Intl J. Heat Fluid Flow 31 (6), 974–984.Google Scholar
Suga, K., Mori, M. & Kaneda, M. 2011 Vortex structure of turbulence over permeable walls. Intl J. Heat Fluid Flow 32 (3), 586–595.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Vanderwel, C. & Ganapathisubramani, B. 2015 Effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers. J. Fluid Mech. 774, R2.Google Scholar
Voermans, J. J., Ghisalberti, M. & Ivey, G. N. 2017 The variation of flow and turbulence across the sediment–water interface. J. Fluid Mech. 824, 413–437.Google Scholar
Whitaker, S. 1996 The Forchheimer equation: a theoretical development. Transp. Porous Med. 25 (1), 27–61.Google Scholar
Wilson, A. M., Huettel, M. & Klein, S. 2008 Grain size and depositional environment as predictors of permeability in coastal marine sands. Estuar. Coast. Shelf Sci. 80 (1), 193–199.Google Scholar
Wilson, N. R. & Shaw, R. H. 1977 A higher order closure model for canopy flow. J. Appl. Meteorol. 16 (11), 1197–1205.2.0.CO;2>CrossRefGoogle Scholar
Yuan, J. & Piomelli, U. 2014 Roughness effects on the Reynolds stress budgets in near-wall turbulence. J. Fluid Mech. 760, R1.Google Scholar
Zagni, A. F. E. & Smith, K. V. H. 1976 Channel flow over permeable beds of graded spheres. J. Hydraul. Div. 102 (2), 207–222.Google Scholar
Zippe, H. J. & Graf, W. H. 1983 Turbulent boundary-layer flow over permeable and non-permeable rough surfaces. J. Hydraul. Res. 21 (1), 51–65.Google Scholar