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Direct numerical simulation of open-channel flow over a fully rough wall at moderate relative submergence

Published online by Cambridge University Press:  11 July 2017

Marco Mazzuoli*
Affiliation:
Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy Institute for Hydromechanics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
Markus Uhlmann
Affiliation:
Institute for Hydromechanics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
*
Email address for correspondence: marco.mazzuoli@unige.it

Abstract

Direct numerical simulation of open-channel flow over a bed of spheres arranged in a regular pattern has been carried out at bulk Reynolds number and roughness Reynolds number (based on sphere diameter) of approximately 6900 and 120, respectively, for which the flow regime is fully rough. The open-channel height was approximately 5.5 times the diameter of the spheres. Extending the results obtained by Chan-Braun et al. (J. Fluid Mech., vol. 684, 2011, pp. 441–474) for an open-channel flow in the transitionally rough regime, the present purpose is to show how the flow structure changes as the fully rough regime is attained and, for the first time, to enable a direct comparison with experimental observations. Different statistical tools were used to investigate the flow field in the roughness sublayer and in the logarithmic region. The results indicate that, in the vicinity of the roughness elements, the average flow field is affected both by Reynolds number effects and by the geometrical features of the roughness, while at larger wall distances this is not the case, and roughness concepts can be applied. Thus, the roughness function is computed which in the present set-up can be expected to depend on the relative submergence. The flow–roughness interaction occurs mostly in the region above the virtual origin of the velocity profile, and the effect of form-induced velocity fluctuations is maximum at the level of sphere crests. In particular, the root mean square of fluctuations about the streamwise component of the average velocity field reflects the geometry of the spheres in the roughness sublayer and attains a maximum value just above the roughness elements. The latter is significantly weakened and shifted towards larger wall distances as compared to the transitionally rough regime or the case of a smooth wall. The spanwise length scale of turbulent velocity fluctuations in the vicinity of the sphere crests shows the same dependence on the distance from the wall as that observed over a smooth wall, and both vary with Reynolds number in a similar fashion. Moreover, the hydrodynamic force and torque experienced by the roughness elements are investigated and the footprint left by vortex structures on the stress acting on the sphere surface is observed. Finally, the possibility either to adopt an analogy between the hydrodynamic forces associated with the interaction of turbulent structures with a flat smooth wall or with the surface of the spheres is also discussed, distinguishing the skin-friction from the form-drag contributions both in the transitionally rough and in the fully rough regimes.

Type
Papers
Copyright
© 2017 Cambridge University Press 

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References

Amir, M. & Castro, I. P. 2011 Turbulence in rough-wall boundary layers: universality issues. Exp. Fluids 51 (2), 313326.CrossRefGoogle Scholar
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, 458497.CrossRefGoogle Scholar
Balachandar, R. & Ramachandran, S. S. 1999 Turbulent boundary layers in low Reynolds number shallow open channel flows. J. Fluids Engng 121 (3), 684689.CrossRefGoogle Scholar
Bandyopadhyay, P. R. 1987 Rough-wall turbulent boundary layers in the transition regime. J. Fluid Mech. 180, 231266.CrossRefGoogle Scholar
Bayazit, M. 1976 Free surface flow in a channel of large relative roughness. J. Hydraul. Res. 14 (2), 115126.CrossRefGoogle Scholar
Bossuyt, J., Howland, M. F., Meneveau, C. & Meyers, J. 2017 Measurement of unsteady loading and power output variability in a micro wind farm model in a wind tunnel. Exp. Fluids 58 (1), 1.CrossRefGoogle Scholar
Chan-Braun, C.2012 Turbulent open channel flow, sediment erosion and sediment transport. PhD thesis, Karlsruhe Institute of Technology.Google Scholar
Chan-Braun, C., García-Villalba, M. & Uhlmann, M. 2011 Force and torque acting on particles in a transitionally rough open-channel flow. J. Fluid Mech. 684, 441474.CrossRefGoogle Scholar
Chan-Braun, C., Garcia-Villalba, M. & Uhlmann, M. 2013 Spatial and temporal scales of force and torque acting on wall-mounted spherical particles in open channel flow. Phys. Fluids 25 (7), 075103.CrossRefGoogle Scholar
Cheng, H. & Castro, I. P. 2002 Near wall flow over urban-like roughness. Boundary-Layer Meteorol. 104 (2), 229259.CrossRefGoogle Scholar
Chouippe, A. & Uhlmann, M. 2015 Forcing homogeneous turbulence in DNS of particulate flow with interface resolution and gravity. Phys. Fluids 27 (12), 123301.CrossRefGoogle Scholar
Coles, D.1968 The young person’s guide to the data. Tech. Rep. DTIC Document.Google Scholar
Cooper, J. R., Aberle, J., Koll, K. & Tait, S. J. 2013 Influence of relative submergence on spatial variance and form-induced stress of gravel-bed flows. Water Resour. Res. 49 (9), 57655777.CrossRefGoogle Scholar
Del Alamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135144.CrossRefGoogle Scholar
Dwivedi, A.2010 Mechanics of sediment entrainment. PhD thesis, ResearchSpace@ Auckland.Google Scholar
Flack, K. A. & Schultz, M. P. 2010 Review of hydraulic roughness scales in the fully rough regime. J. Fluids Engng 132 (4), 041203.Google Scholar
Florens, E., Eiff, O. & Moulin, F. 2013 Defining the roughness sublayer and its turbulence statistics. Exp. Fluids 54 (4), 1500.CrossRefGoogle Scholar
Flores, O. & Jimenez, J. 2006 Effect of wall-boundary disturbances on turbulent channel flows. J. Fluid Mech. 566, 357376.CrossRefGoogle Scholar
Garcia-Villalba, M., Kidanemariam, A. G. & Uhlmann, M. 2012 DNS of vertical plane channel flow with finite-size particles: Voronoi analysis, acceleration statistics and particle-conditioned averaging. Intl J. Multiphase Flow 46, 5474.CrossRefGoogle Scholar
George, W. K. 2007 Is there a universal log law for turbulent wall-bounded flows? Phil. Trans. R. Soc. Lond. A 365 (1852), 789806.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), 3565.Google Scholar
Hofland, B.2005 Rock and roll: turbulence-induced damage to granular bed protections. TU Delft, Delft University of Technology.Google Scholar
Hong, J., Katz, J., Meneveau, C. & Schultz, M. P. 2012 Coherent structures and associated subgrid-scale energy transfer in a rough-wall turbulent channel flow. J. Fluid Mech. 712, 92128.CrossRefGoogle Scholar
Hong, J., Katz, J. & Schultz, M. P. 2011 Near-wall turbulence statistics and flow structures over three-dimensional roughness in a turbulent channel flow. J. Fluid Mech. 667, 137.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.Google Scholar
Jackson, P. S. 1981 On the displacement height in the logarithmic velocity profile. J. Fluid Mech. 111, 1525.CrossRefGoogle Scholar
Jayatilleke, C. L. V.1966 The influence of Prandtl number and surface roughness on the resistance of the laminar sub-layer to momentum and heat transfer. PhD thesis, University of London.Google Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173196.CrossRefGoogle Scholar
Kidanemariam, A. G. & Uhlmann, M. 2014a Direct numerical simulation of pattern formation in subaqueous sediment. J. Fluid Mech. 750, R2.CrossRefGoogle Scholar
Kidanemariam, A. G. & Uhlmann, M. 2014b Interface-resolved direct numerical simulation of the erosion of a sediment bed sheared by laminar channel flow. Intl J. Multiphase Flow 67, 174188.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.CrossRefGoogle Scholar
Ligrani, P. M. & Moffat, R. J. 1986 Structure of transitionally rough and fully rough turbulent boundary layers. J. Fluid Mech. 162, 6998.CrossRefGoogle Scholar
Marusic, I., Mckeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22 (6), 065103.CrossRefGoogle Scholar
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.CrossRefGoogle Scholar
Mazzuoli, M., Kidanemariam, A. G., Blondeaux, P., Vittori, G. & Uhlmann, M. 2016 On the formation of sediment chains in an oscillatory boundary layer. J. Fluid Mech. 789, 461480.CrossRefGoogle Scholar
Mckeon, B. J., Li, J.-d., Jiang, W., Morrison, J. F. & Smits, A. J. 2004 Further observations on the mean velocity distribution in fully developed pipe flow. J. Fluid Mech. 501, 135147.CrossRefGoogle Scholar
Nikora, V., Goring, D., McEwan, I. & Griffiths, G. 2001 Spatially averaged open-channel flow over rough bed. J. Hydraul. Engng 127 (2), 123133.CrossRefGoogle Scholar
Nikuradse, J. 1933 Strömungsgestze in rauhen rohren. Forschungsheft, Verein Deutscher Ingenieure 361.Google Scholar
Orlandi, P., Leonardi, S., Tuzi, R. & Antonia, R. A. 2003 Direct numerical simulation of turbulent channel flow with wall velocity disturbances. Phys. Fluids 15 (12), 35873601.CrossRefGoogle Scholar
Österlund, J. M., Johansson, A. V., Nagib, H. M. & Hites, M. H. 2000 A note on the overlap region in turbulent boundary layers. Phys. Fluids 12 (1), 14.CrossRefGoogle Scholar
Pimenta, M. M., Moffat, R. J. & Kays, W. M.1975 The turbulent boundary layer: an experimental study of the transport of momentum and heat with the effect of roughness. Tech. Rep. DTIC Document.Google Scholar
Placidi, M. & Ganapathisubramani, B. 2015 Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers. J. Fluid Mech. 782, 541566.CrossRefGoogle Scholar
Reynolds, A. J. 1974 Turbulent Flows in Engineering. Wiley.Google Scholar
Schlichting, H. 1936 Experimentelle untersuchungen zum rauhigkeitsproblem. Arch. Appl. Mech. 7 (1), 134.Google Scholar
Schlichting, H. 1968 Boundary-Layer Theory, 6th edn. McGraw-Hill.Google Scholar
Schultz, M. P. & Flack, K. A. 2007 The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime. J. Fluid Mech. 580, 381405.CrossRefGoogle Scholar
Tachie, M. F., Bergstrom, D. J. & Balachandar, R. 2000 Rough wall turbulent boundary layers in shallow open channel flow. J. Fluids Engng 122 (3), 533541.CrossRefGoogle Scholar
Tani, I. 1987 Turbulent boundary layer development over rough surfaces. In Perspectives in Turbulence Studies, pp. 223249. Springer.CrossRefGoogle Scholar
Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209 (2), 448476.CrossRefGoogle Scholar
Uhlmann, M.2006 Direct numerical simulation of sediment transport in a horizontal channel. Tech. Rep. 1088, CIEMAT, Madrid, Spain, ISSN 1135-9420.Google Scholar
Uhlmann, M. 2008 Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys. Fluids 20 (5), 053305.CrossRefGoogle Scholar
Uhlmann, M. & Chouippe, A. 2017 Clustering and preferential concentration of finite-size particles in forced homogeneous-isotropic turbulence. J. Fluid Mech. 812, 9911023.CrossRefGoogle Scholar
Uhlmann, M. & Doychev, T. 2014 Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion. J. Fluid Mech. 752, 310348.CrossRefGoogle Scholar
Willingham, D., Anderson, W., Christensen, K. T. & Barros, J. M. 2014 Turbulent boundary layer flow over transverse aerodynamic roughness transitions: induced mixing and flow characterization. Phys. Fluids 26 (2), 025111.CrossRefGoogle Scholar