×

Direct numerical simulation of open-channel flow over a fully rough wall at moderate relative submergence. (English) Zbl 1374.76094

Summary: 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 C. Chan-Braun et al. [J. Fluid Mech. 684, 441–474 (2011; Zbl 1241.76393)] 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.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence

Citations:

Zbl 1241.76393
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Amir, M.; Castro, I. P., Turbulence in rough-wall boundary layers: universality issues, Exp. Fluids, 51, 2, 313-326, (2011) · doi:10.1007/s00348-011-1049-7
[2] Amir, M.; Nikora, V. I.; Stewart, M. T., Pressure forces on sediment particles in turbulent open-channel flow: a laboratory study, J. Fluid Mech., 757, 458-497, (2014) · doi:10.1017/jfm.2014.498
[3] Balachandar, R.; Ramachandran, S. S., Turbulent boundary layers in low Reynolds number shallow open channel flows, J. Fluids Engng, 121, 3, 684-689, (1999) · doi:10.1115/1.2823524
[4] Bandyopadhyay, P. R., Rough-wall turbulent boundary layers in the transition regime, J. Fluid Mech., 180, 231-266, (1987) · doi:10.1017/S0022112087001794
[5] Bayazit, M., Free surface flow in a channel of large relative roughness, J. Hydraul. Res., 14, 2, 115-126, (1976) · doi:10.1080/00221687609499676
[6] Bossuyt, J.; Howland, M. F.; Meneveau, C.; Meyers, J., Measurement of unsteady loading and power output variability in a micro wind farm model in a wind tunnel, Exp. Fluids, 58, 1, 1, (2017) · doi:10.1007/s00348-016-2278-6
[7] Chan-Braun, C.2012 Turbulent open channel flow, sediment erosion and sediment transport. PhD thesis, Karlsruhe Institute of Technology.
[8] Chan-Braun, C.; García-Villalba, M.; Uhlmann, M., Force and torque acting on particles in a transitionally rough open-channel flow, J. Fluid Mech., 684, 441-474, (2011) · Zbl 1241.76393 · doi:10.1017/jfm.2011.311
[9] Chan-Braun, C.; Garcia-Villalba, M.; Uhlmann, M., Spatial and temporal scales of force and torque acting on wall-mounted spherical particles in open channel flow, Phys. Fluids, 25, 7, (2013) · doi:10.1063/1.4813806
[10] Cheng, H.; Castro, I. P., Near wall flow over urban-like roughness, Boundary-Layer Meteorol., 104, 2, 229-259, (2002) · doi:10.1023/A:1016060103448
[11] Chouippe, A.; Uhlmann, M., Forcing homogeneous turbulence in DNS of particulate flow with interface resolution and gravity, Phys. Fluids, 27, 12, (2015) · doi:10.1063/1.4936274
[12] Coles, D.1968 The young person’s guide to the data. Tech. Rep. DTIC Document.
[13] Cooper, J. R.; Aberle, J.; Koll, K.; Tait, S. J., Influence of relative submergence on spatial variance and form-induced stress of gravel-bed flows, Water Resour. Res., 49, 9, 5765-5777, (2013) · doi:10.1002/wrcr.20464
[14] Del Alamo, J. C.; Jiménez, J.; Zandonade, P.; Moser, R. D., Scaling of the energy spectra of turbulent channels, J. Fluid Mech., 500, 135-144, (2004) · Zbl 1059.76031 · doi:10.1017/S002211200300733X
[15] Dwivedi, A.2010 Mechanics of sediment entrainment. PhD thesis, ResearchSpace@ Auckland.
[16] Flack, K. A.; Schultz, M. P., Review of hydraulic roughness scales in the fully rough regime, J. Fluids Engng, 132, 4, (2010)
[17] Florens, E.; Eiff, O.; Moulin, F., Defining the roughness sublayer and its turbulence statistics, Exp. Fluids, 54, 4, 1500, (2013) · doi:10.1007/s00348-013-1500-z
[18] Flores, O.; Jimenez, J., Effect of wall-boundary disturbances on turbulent channel flows, J. Fluid Mech., 566, 357-376, (2006) · Zbl 1275.76146 · doi:10.1017/S0022112006001534
[19] Garcia-Villalba, M.; Kidanemariam, A. G.; Uhlmann, M., DNS of vertical plane channel flow with finite-size particles: Voronoi analysis, acceleration statistics and particle-conditioned averaging, Intl J. Multiphase Flow, 46, 54-74, (2012) · doi:10.1016/j.ijmultiphaseflow.2012.05.007
[20] George, W. K., Is there a universal log law for turbulent wall-bounded flows?, Phil. Trans. R. Soc. Lond. A, 365, 1852, 789-806, (2007) · Zbl 1152.76405 · doi:10.1098/rsta.2006.1941
[21] Grass, A. J.; Stuart, R. J.; Mansour-Tehrani, M., Vortical structures and coherent motion in turbulent flow over smooth and rough boundaries, Phil. Trans. R. Soc. Lond. A, 336, 1640, 35-65, (1991) · doi:10.1098/rsta.1991.0065
[22] Hofland, B.2005 Rock and roll: turbulence-induced damage to granular bed protections. TU Delft, Delft University of Technology.
[23] Hong, J.; Katz, J.; Meneveau, C.; Schultz, M. P., Coherent structures and associated subgrid-scale energy transfer in a rough-wall turbulent channel flow, J. Fluid Mech., 712, 92-128, (2012) · Zbl 1275.76139 · doi:10.1017/jfm.2012.403
[24] Hong, J.; Katz, J.; Schultz, M. P., Near-wall turbulence statistics and flow structures over three-dimensional roughness in a turbulent channel flow, J. Fluid Mech., 667, 1-37, (2011) · Zbl 1225.76017 · doi:10.1017/S0022112010003988
[25] Hoyas, S.; Jiménez, J., Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003, Phys. Fluids, 18, 1, (2006) · doi:10.1063/1.2162185
[26] Jackson, P. S., On the displacement height in the logarithmic velocity profile, J. Fluid Mech., 111, 15-25, (1981) · Zbl 0482.76053 · doi:10.1017/S0022112081002279
[27] 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.
[28] Jiménez, J., Turbulent flows over rough walls, Annu. Rev. Fluid Mech., 36, 173-196, (2004) · Zbl 1125.76348 · doi:10.1146/annurev.fluid.36.050802.122103
[29] Kidanemariam, A. G.; Uhlmann, M., Direct numerical simulation of pattern formation in subaqueous sediment, J. Fluid Mech., 750, (2014) · doi:10.1017/jfm.2014.284
[30] Kidanemariam, A. G.; Uhlmann, M., Interface-resolved direct numerical simulation of the erosion of a sediment bed sheared by laminar channel flow, Intl J. Multiphase Flow, 67, 174-188, (2014) · doi:10.1016/j.ijmultiphaseflow.2014.08.008
[31] Kim, J.; Moin, P.; Moser, R., Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech., 177, 133-166, (1987) · Zbl 0616.76071 · doi:10.1017/S0022112087000892
[32] Ligrani, P. M.; Moffat, R. J., Structure of transitionally rough and fully rough turbulent boundary layers, J. Fluid Mech., 162, 69-98, (1986) · doi:10.1017/S0022112086001933
[33] Marusic, I.; Mckeon, B. J.; Monkewitz, P. A.; Nagib, H. M.; Smits, A. J.; Sreenivasan, K. R., Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues, Phys. Fluids, 22, 6, (2010) · Zbl 1190.76086 · doi:10.1063/1.3453711
[34] Marusic, I.; Monty, J. P.; Hultmark, M.; Smits, A. J., On the logarithmic region in wall turbulence, J. Fluid Mech., 716, (2013) · Zbl 1284.76206 · doi:10.1017/jfm.2012.511
[35] Mazzuoli, M.; Kidanemariam, A. G.; Blondeaux, P.; Vittori, G.; Uhlmann, M., On the formation of sediment chains in an oscillatory boundary layer, J. Fluid Mech., 789, 461-480, (2016) · doi:10.1017/jfm.2015.732
[36] Mckeon, B. J.; Li, J.-D.; Jiang, W.; Morrison, J. F.; Smits, A. J., Further observations on the mean velocity distribution in fully developed pipe flow, J. Fluid Mech., 501, 135-147, (2004) · Zbl 1067.76513 · doi:10.1017/S0022112003007304
[37] Nikora, V.; Goring, D.; Mcewan, I.; Griffiths, G., Spatially averaged open-channel flow over rough bed, J. Hydraul. Engng, 127, 2, 123-133, (2001) · doi:10.1061/(ASCE)0733-9429(2001)127:2(123)
[38] Nikuradse, J., Strömungsgestze in rauhen rohren, Forschungsheft, Verein Deutscher Ingenieure, 361, (1933) · JFM 59.1462.02
[39] Orlandi, P.; Leonardi, S.; Tuzi, R.; Antonia, R. A., Direct numerical simulation of turbulent channel flow with wall velocity disturbances, Phys. Fluids, 15, 12, 3587-3601, (2003) · Zbl 1186.76406 · doi:10.1063/1.1619137
[40] Österlund, J. M.; Johansson, A. V.; Nagib, H. M.; Hites, M. H., A note on the overlap region in turbulent boundary layers, Phys. Fluids, 12, 1, 1-4, (2000) · Zbl 1149.76503 · doi:10.1063/1.870250
[41] 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.
[42] Placidi, M.; Ganapathisubramani, B., Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers, J. Fluid Mech., 782, 541-566, (2015) · Zbl 1381.76110 · doi:10.1017/jfm.2015.552
[43] Reynolds, A. J., Turbulent Flows in Engineering, (1974), Wiley
[44] Schlichting, H., Experimentelle untersuchungen zum rauhigkeitsproblem, Arch. Appl. Mech., 7, 1, 1-34, (1936)
[45] Schlichting, H., Boundary-Layer Theory, (1968), McGraw-Hill
[46] Schultz, M. P.; Flack, K. A., The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime, J. Fluid Mech., 580, 381-405, (2007) · Zbl 1113.76009 · doi:10.1017/S0022112007005502
[47] Tachie, M. F.; Bergstrom, D. J.; Balachandar, R., Rough wall turbulent boundary layers in shallow open channel flow, J. Fluids Engng, 122, 3, 533-541, (2000) · doi:10.1115/1.1287267
[48] Tani, I.1987Turbulent boundary layer development over rough surfaces. In Perspectives in Turbulence Studies, pp. 223-249. Springer. doi:10.1007/978-3-642-82994-9_9
[49] Uhlmann, M., An immersed boundary method with direct forcing for the simulation of particulate flows, J. Comput. Phys., 209, 2, 448-476, (2005) · Zbl 1138.76398 · doi:10.1016/j.jcp.2005.03.017
[50] Uhlmann, M.2006 Direct numerical simulation of sediment transport in a horizontal channel. Tech. Rep. 1088, CIEMAT, Madrid, Spain, ISSN 1135-9420.
[51] Uhlmann, M., Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime, Phys. Fluids, 20, 5, (2008) · Zbl 1182.76785 · doi:10.1063/1.2912459
[52] Uhlmann, M.; Chouippe, A., Clustering and preferential concentration of finite-size particles in forced homogeneous-isotropic turbulence, J. Fluid Mech., 812, 991-1023, (2017) · Zbl 1383.76295 · doi:10.1017/jfm.2016.826
[53] Uhlmann, M.; Doychev, T., Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion, J. Fluid Mech., 752, 310-348, (2014) · doi:10.1017/jfm.2014.330
[54] Willingham, D.; Anderson, W.; Christensen, K. T.; Barros, J. M., Turbulent boundary layer flow over transverse aerodynamic roughness transitions: induced mixing and flow characterization, Phys. Fluids, 26, 2, (2014) · doi:10.1063/1.4864105
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.