Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-27T16:32:38.447Z Has data issue: false hasContentIssue false
  • English
  • Français

Parametric forcing approach to rough-wall turbulent channel flow

Published online by Cambridge University Press:  27 September 2012

A. Busse  and
N. D. Sandham
A. Busse*
Affiliation:
Aerodynamics and Flight Mechanics Research Group, Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK
N. D. Sandham
Affiliation:
Aerodynamics and Flight Mechanics Research Group, Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The effects of rough surfaces on turbulent channel flow are modelled by an extra force term in the Navier–Stokes equations. This force term contains two parameters, related to the density and the height of the roughness elements, and a shape function, which regulates the influence of the force term with respect to the distance from the channel wall. This permits a more flexible specification of a rough surface than a single parameter such as the equivalent sand grain roughness. The effects of the roughness force term on turbulent channel flow have been investigated for a large number of parameter combinations and several shape functions by direct numerical simulations. It is possible to cover the full spectrum of rough flows ranging from hydraulically smooth through transitionally rough to fully rough cases. By using different parameter combinations and shape functions, it is possible to match the effects of different types of rough surfaces. Mean flow and standard turbulence statistics have been used to compare the results to recent experimental and numerical studies and a good qualitative agreement has been found. Outer scaling is preserved for the streamwise velocity for both the mean profile as well as its mean square fluctuations in all but extremely rough cases. The structure of the turbulent flow shows a trend towards more isotropic turbulent states within the roughness layer. In extremely rough cases, spanwise structures emerge near the wall and the turbulent state resembles a mixing layer. A direct comparison with the study of Ashrafian, Andersson & Manhart (Intl J. Heat Fluid Flow, vol. 25, 2004, pp. 373–383) shows a good quantitative agreement of the mean flow and Reynolds stresses everywhere except in the immediate vicinity of the rough wall. The proposed roughness force term may be of benefit as a wall model for direct and large-eddy numerical simulations in cases where the exact details of the flow over a rough wall can be neglected.

JFM classification

Geophysical and Geological Flows: Topographic effects Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 712 , 10 December 2012 , pp. 169 - 202
Copyright
©2012 Cambridge University Press

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

Amir, M. & Castro, I. P. 2011 Turbulence in rough-wall boundary layers: universality issues. Exp. Fluids 51 (2), 313–326.CrossRefGoogle Scholar
Anderson, W. & Meneveau, C. 2010 A large-eddy simulation model for boundary-layer flow over surfaces with horizontally resolved but vertically unresolved roughness elements. Boundary-Layer Meteorol. 137, 397–415.CrossRefGoogle Scholar
Antonia, R. A. & Krogstad, P.-A. 2001 Turbulence structure in boundary layers over different types of surface roughness. Fluid Dyn. Res. 28, 139–157.CrossRefGoogle Scholar
Arnfield, A. J. 2003 Two decades of urban climate research: a review of turbulence, exchanges of energy and water, and the urban heat island. Intl J. Climatol. 23 (1), 1–26.CrossRefGoogle Scholar
Ashrafian, A. & Andersson, H. I. 2006 The structure of turbulence in a rod-roughened channel. Intl J. Heat Fluid Flow 27, 65–79.CrossRefGoogle Scholar
Ashrafian, A., Andersson, H. I. & Manhart, M. 2004 DNS of turbulent flow in a rod-roughened channel. Intl J. Heat Fluid Flow 25, 373–383.CrossRefGoogle Scholar
Bakken, O. M., Krogstad, P. A., Ashrafian, A. & Andersson, H. I. 2005 Reynolds number effects in the outer layer of the turbulent flow in a channel flow with rough walls. Phys. Fluids 17, 065101.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bechert, D. W., Bruse, M., Hage, W., VanderHoeven, J. G. T. & Hoppe, G. 1997 Experiments on drag-reducing surfaces and their optimization with an adjustable geometry. J. Fluid Mech. 338, 59–87.CrossRefGoogle Scholar
Bhaganagar, K., Kim, J. & Coleman, G. 2004 Effect of roughness on wall-bounded turbulence. Flow Turbul. Combust. 72, 463–492.CrossRefGoogle Scholar
Birch, D. M. & Morrison, J. F. 2011 Similarity of the streamwise velocity component in very-rough-wall channel flow. J. Fluid Mech. 668, 174–201.CrossRefGoogle Scholar
Bradshaw, P. 2000 A note on ‘critical roughness height’ and ‘transitional roughness’. Phys. Fluids 12 (6), 1611–1614.CrossRefGoogle Scholar
Breugem, W. P. & Boersma, B. J. 2005 Direct numerical simulations of turbulent flow over a permeable wall using a direct and a continuum approach. Phys. Fluids 17, 025103.CrossRefGoogle Scholar
Castro, I. P. 2007 Rough-wall boundary layers: mean flow universality. J. Fluid Mech. 585, 469–485.CrossRefGoogle Scholar
Castro, I. P. 2009 Turbulent flow over rough walls. In Advances in Turbulence XII – Proceedings of the 12th EUROMECH European Turbulence Conference (ed. Eckhardt, B). Springer Proceedings in Physics , vol. 132, pp. 381–388.Google Scholar
Chan-Braun, C., Garcia-Villalba, M. & Uhlmann, M. 2011 Force and torque acting on particles in a transitionally rough open-channel flow. J. Fluid Mech. 684, 441–474.CrossRefGoogle Scholar
Cheng, H. & Castro, I. P. 2002 Near wall flow over urban-like roughness. Boundary-Layer Meteorol. 104 (2), 229–259.CrossRefGoogle Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulations of turbulent flow over riblets. J. Fluid Mech. 255, 503–539.CrossRefGoogle Scholar
Coceal, O. & Belcher, S. E. 2005 Mean winds through an inhomogeneous urban canopy. Boundary-Layer Meteorol. 115, 47–68.CrossRefGoogle Scholar
Cui, J., Patel, V. C. & Lin, C.-L. 2003 Prediction of turbulent flow over rough surfaces using a force field in large eddy simulations. J. Fluids Engng 125, 2–9.CrossRefGoogle Scholar
Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans. ASME I: J. Fluids Engng. 100, 215.Google Scholar
DeAngelis, V., Lombardi, P. & Banerjee, S. 1997 Direct numerical simulation of turbulent flow over a wavy wall. Phys. Fluids 9 (8), 2429–2442.CrossRefGoogle Scholar
DeMarchis, M., Napoli, E. & Armenio, V. 2010 Turbulence structure over irregular rough surfaces. J. Turbul. 11 (3), 1–32.Google Scholar
Finnigan, J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519–571.CrossRefGoogle Scholar
Flores, O. & Jiménez, J. 2006 Effects of wall-boundary disturbances on turbulent channel flow. J. Fluid Mech. 566, 357–376.CrossRefGoogle Scholar
Hama, F. R. 1954 Boundary-layer characteristics for smooth and rough surfaces. Trans. Soc. Nav. Arch. Marit. Engrs 62, 333–351.Google 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, 1–37.CrossRefGoogle Scholar
Hu, Z. W., Morfey, C. L. & Sandham, N. D. 2006 Wall pressure and shear stress spectra from direct simulations of channel flow. AIAA J. 44 (7), 1541–1549.CrossRefGoogle Scholar
Iccarino, G. & Verzicco, R. 2003 Immersed boundary technique for turbulent flow simulations. Appl. Mech. Rev. 56, 331–347.CrossRefGoogle Scholar
Jiménez, J. 2004 Turbulent flow over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Karniadakis, G. E. & Choi, K.-S. 2003 Mechanisms on transverse motions in turbulent wall flows. Annu. Rev. Fluid Mech. 35, 45–62.CrossRefGoogle Scholar
Krogstad, P.-A., Andersson, H. I., Bakken, O. M. & Ashrafian, A. 2005 An experimental and numerical study of channel flow with rough walls. J. Fluid Mech. 530, 327–352.CrossRefGoogle Scholar
Langelandsvik, L. I., Kunkel, G. J. & Smits, A. J. 2008 Flow in a commercial steel pipe. J. Fluid Mech. 595, 323–339.CrossRefGoogle Scholar
Lee, J. H., Sung, H. J. & Krogstad, P.-A. 2011 Direct numerical simulation of the turbulent boundary layer over a cube-roughened wall. J. Fluid Mech. 669, 397–431.CrossRefGoogle Scholar
Leonardi, S. & Castro, I. P. 2010 Channel flow over large cube roughness: a direct numerical simulation study. J. Fluid Mech. 651, 519–539.CrossRefGoogle Scholar
Leonardi, S., Orlandi, P., Djenidi, L. & Antonia, R. A. 2004 Structure of turbulent channel flow with square bars on one wall. Intl J. Heat Fluid Flow 25, 384–392.CrossRefGoogle Scholar
Lumley, J. L. 1978 Computational modelling of turbulent flows. Adv. Appl. Mech. 18, 123–176.CrossRefGoogle Scholar
Marusic, I., McKeon, B. J., Monkewitz, P. A., Nagib, H. M. & Smits, A. J. 2010 Wall bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22, 065103.CrossRefGoogle Scholar
Mittal, R. & Iccarino, G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 35, 239–261.CrossRefGoogle Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to ${\mathit{Re}}_{\tau } = 590$ . Phys. Fluids 11 (4), 943–945.CrossRefGoogle Scholar
Nikuradse, J. 1950 Laws of flow in rough pipes. Tech. Rep. NACA Technical Memorandum 1292.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, 3587–3601.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 1–25.CrossRefGoogle Scholar
Reynolds, R. T. & Castro, I. P. 2008 Measurements in an urban-type boundary layer. Exp. Fluids 45, 141–156.CrossRefGoogle Scholar
Rothstein, J. P. 2010 Slip on superhydrophobic surfaces. Annu. Rev. Fluid Mech. 42, 89–109.CrossRefGoogle Scholar
Schlichting, H. 1968 Boundary-Layer Theory, 6th edn. McGraw-Hill.Google Scholar
Schultz, M. P. & Flack, K. A. 2009 Turbulent boundary layers on a systematically varied rough wall. Phys. Fluids 21, 015104.CrossRefGoogle Scholar
Scotti, A. 2006 Direct numerical simulation of turbulent channel flows with boundary roughened with virtual sandpaper. Phys. Fluids 18, 031701.CrossRefGoogle Scholar
Simonsen, A. J. & Krogstad, P. A. 2005 Turbulent stress invariant analysis: clarification of existing terminology. Phys. Fluids 17, 088103.CrossRefGoogle Scholar
Singh, K. M., Sandham, N. D. & Williams, J. J. R. 2007 Numerical simulation of flow over a rough bed. J. Hydraul. Engng ASCE 133, 386–398.CrossRefGoogle Scholar
Smalley, R. J., Leonardi, S., Antonia, R. A., Djenidi, L. & Orlandi, P. 2002 Reynolds stress anisotropy of turbulent rough wall layers. Exp. Fluids 33, 31–37.CrossRefGoogle Scholar
Taylor, R. P., Coleman, H. W. & Hodge, B. K. 1985 Predicition of turbulent rough-wall skin friction using a discrete element approach. J. Fluids Engng 107, 251–257.CrossRefGoogle Scholar
Tuck, E. O. & Kouzoubov, A. 1995 A laminar roughness boundary condition. J. Fluid Mech. 300, 59–70.CrossRefGoogle Scholar
Xie, Z.-T., Coceal, O. & Castro, I. P. 2008 Large-eddy simulation of flows over random urban-like obstacles. Boundary-Layer Meteorol. 129, 1–23.CrossRefGoogle Scholar