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Channel flow over large cube roughness: a direct numerical simulation study

Published online by Cambridge University Press:  07 April 2010

STEFANO LEONARDI  and
IAN P. CASTRO
STEFANO LEONARDI
Affiliation:
Department of Mechanical Engineering, University of Puerto Rico, Mayaguez 00680, Puerto Rico
IAN P. CASTRO*
Affiliation:
School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK
*
†Email address for correspondence: i.castro@soton.ac.uk
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Abstract

Computations of channel flow with rough walls comprising staggered arrays of cubes having various plan area densities are presented and discussed. The cube height h is 12.5% of the channel half-depth and Reynolds numbers (uτh/ν) are typically around 700 – well into the fully rough regime. A direct numerical simulation technique, using an immersed boundary method for the obstacles, was employed with typically 35 million cells. It is shown that the surface drag is predominantly form drag, which is greatest at an area coverage around 15%. The height variation of the axial pressure force across the obstacles weakens significantly as the area coverage decreases, but is always largest near the top of the obstacles. Mean flow velocity and pressure data allow precise determination of the zero-plane displacement (defined as the height at which the axial surface drag force acts) and this leads to noticeably better fits to the log-law region than can be obtained by using the zero-plane displacement merely as a fitting parameter. There are consequent implications for the value of von Kármán's constant. As the effective roughness of the surface increases, it is also shown that there are significant changes to the structure of the turbulence field around the bottom boundary of the inertial sublayer. In distinct contrast to two-dimensional roughness (longitudinal or transverse bars), increasing the area density of this three-dimensional roughness leads to a monotonic decrease in normalized vertical stress around the top of the roughness elements. Normalized turbulence stresses in the outer part of the flows are nonetheless very similar to those in smooth-wall flows.

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Papers
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Journal of Fluid Mechanics , Volume 651 , 25 May 2010 , pp. 519 - 539
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Andreas, E. L., Claffey, K. J., Jordan, R. E., Fairall, C. W., Guest, P. S., Persson, C. W. & Grachev, A. A. 2006 Evaluations of the von Kármán constant in the atmospheric surface layer. J. Fluid Mech. 559, 117–149.CrossRefGoogle Scholar
Andreas, E. L. & Trevino, G. 2000 Comments on ‘A physical interpretation of von Kármán's constant based on asymptotic considerations – a new value’. J. Atmos. Sci. 57, 1189–1192.2.0.CO;2>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 with rough walls. Phys. Fluids 17, 065101.CrossRefGoogle Scholar
Bhaganagar, K., Kim, J. & Coleman, G. 2004 Effect of roughness on wall-bounded turbulence. Flow Turbul. Combust. 72, 463–492.CrossRefGoogle Scholar
Breugrem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562, 35–72.CrossRefGoogle Scholar
Castro, I. P. 2007 Rough-wall boundary layers: mean flow universality. J. Fluid Mech. 585, 469–485.CrossRefGoogle Scholar
Cheng, H. & Castro, I. P. 2002 Near wall flow over urban-like roughness. Boundary-Layer Meteorol. 104, 229–259.CrossRefGoogle Scholar
Cheng, H., Hayden, P., Robins, A. G. & Castro, I. P. 2007 Flow over cube arrays of different packing densities. J. Wind Engng Ind. Aerodyn. 95, 715–740.CrossRefGoogle Scholar
Coceal, O. & Belcher, S. E. 2004 A canopy model of mean winds through urban areas. Q. J. R. Meteorol. Soc. 130, 1349–1372.CrossRefGoogle Scholar
Coceal, O., Dobre, A., Thomas, T. G. & Belcher, S. E. 2007 b Structure of turbulent flow over regular arrays of cubical roughness. J. Fluid Mech. 589, 375–409.CrossRefGoogle Scholar
Coceal, O., Thomas, T. G. & Belcher, S. E. 2007 a Spatial variablity of flow statistics within regular building arrays. Bound. Layer Meteorol. 125, 537–552.CrossRefGoogle Scholar
Coceal, O., Thomas, T. G., Castro, I. P. & Belcher, S. E. 2006 Mean flow and turbulence statistics over groups of urban-like cubical obstacles. Bound. Layer Meteorol. 121, 491–519.CrossRefGoogle Scholar
Erm, L. P. & Joubert, P. N. 1991 Low-Reynolds-number turbulent boundary layers. J. Fluid Mech. 230, 1–44.CrossRefGoogle Scholar
Finnigan, J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519–571.CrossRefGoogle Scholar
Frenzen, P. & Vogel, C. A. 1995 On the magnitude and apparent range of variation of the von Kármán constant in the atmospheric surface layer. Bound. Layer Meteorol. 72, 371–395.CrossRefGoogle Scholar
Grimmond, C. S. B. & Oke, T. R. 1999 Aerodynamic properties of urban areas derived from analysis of surface form. J. Appl. Meteorol. 38, 1262–1292.2.0.CO;2>CrossRefGoogle Scholar
Hagishima, A., Tanimoto, J., Nagayama, K. & Meno, S. 2009 Aerodynamics parameters of regular arrays of rectangular blocks with various geometries. Bound. Layer Meteorol. 132, 315–338.CrossRefGoogle Scholar
Ikeda, T. & Durbin, P. A. 2007 Direct simulations of a rough-wall channel flow. J. Fluid Mech. 571, 235–263.CrossRefGoogle Scholar
Jackson, P. S. 1981 On the displacement height in the logarithmic velocity profile. J. Fluid Mech. 111, 15–25.CrossRefGoogle Scholar
Kanda, M. 2006 Large-Eddy Simulations of the effects of surface geometry of building arrays on turbulent organized structures. Bound. Layer Meteorol. 118. 151–168.CrossRefGoogle Scholar
Kanda, M., Moriwaki, R. & Kasamatsu, F. 2004 Large-eddy simulation of turbulent organized structures within and above explicitly resolved cube arrays. Bound. Layer Meteorol. 112, 343–368.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1985 Application of a fractional step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–223.CrossRefGoogle Scholar
Krogstad, P.-A. & Antonia, R. A. 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27, 450–460.CrossRefGoogle Scholar
Leonardi, S., Orlandi, P., Smalley, R. J., Djenidi, L. & Antonia, R. A. 2003 Direct numerical simulations of turbulent channel flow with transverse square bars on one wall. J. Fluid Mech. 491, 229–238.CrossRefGoogle Scholar
Li, X., Zimmerman, N. & Princevac, M. 2008 Local imbalance of turbulent kinetic energy in the surface layer. Bound. Layer Meteorol. 129, 115–136.CrossRefGoogle Scholar
Macdonald, R. W. 2000 Modelling the mean velocity profile in an urban canopy layer. Bound. Layer Meteorol. 97, 25–45.CrossRefGoogle Scholar
Macdonald, R. W., Griffiths, R. F. & Hall, D. J. 1998 An improved method for the estimation of surface roughness of obstacle arrays. Atmos. Environ. 32, 1857–1864.CrossRefGoogle Scholar
Martilli, A. & Santiago, J. L. 2007 CFD simulations of airflow over a regular array of cubes. Part I. Three-dimensional simulation and validation with wind tunnel measurements. Bound. Layer Meteorol. 122, 609–634.Google Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to Re τ = 590. Phys. Fluids 11, 943–945.CrossRefGoogle Scholar
Nagib, H. M. & Chauhan, K. A. 2008 Variations of von Kármán coefficient in canonical flows. Phys. Fluids 20, 101518.CrossRefGoogle Scholar
Oncley, S. P., Friehe, C., Larue, J. C., Businger, J. A., Itswheire, E. C. & Chang, S. S. 1996 Surface-layer fluxes, profiles and turbulence measurements over uniform terrain under near-neutral conditions. J. Atmos. Sci. 53, 1029–1044.2.0.CO;2>CrossRefGoogle Scholar
Orlandi, P. 2000 Fluid Flow Phenomena: A Numerical Toolkit. Kluwer Academic.CrossRefGoogle Scholar
Orlandi, P. & Leonardi, S. 2006 DNS of turbulent channel flows with two- and three-dimensional roughness. J. Turbul. 7, 1–22.CrossRefGoogle Scholar
Orlandi, P., Leonardi, S. & Antonia, R. A. 2006 Turbulent channel flow with either transverse or longitudinal roughness elements on one wall. J. Fluid Mech. 561, 279–305.CrossRefGoogle Scholar
Perry, A. E., Schofield, W. H. & Joubert, P. N. 1969 Rough wall turbulent boundary layers. J. Fluid Mech. 37, 383–413.CrossRefGoogle Scholar
Poggi, D., Porporato, A., Ridolfi, L., Albertson, J. D. & Katual, G. G. 2004 The effect of vegetation density on canopy sublayer turbulence. Bound. Layer Meteorol. 111, 565–587.CrossRefGoogle Scholar
Raupach, M. R., Finnigan, H. J. & Brunet, Y. 1996 Coherent eddies and turbulence in vegetation canopies: the mixing layer analogy. Bound. Layer Meteorol. 78, 351–382.CrossRefGoogle Scholar
Santiago, J. J., Coceal, O., Martilli, A. & Belcher, S. E. 2008 Variation of the sectional drag coefficient of a group of buildings with packing density. Boundary-Layer Meteorol. 128, 445–457.CrossRefGoogle Scholar
Stoesser, T., Mathey, F., Frohlich, J. & Rodi, W. 2003 LES of flow over multiple cubes. Bulletin No. 56. ERCOFTAC.Google Scholar
Vogel, C. A. & Frenzen, P. 2002 On reasons for the observed variation of the von Kármán constant in the atmospheric surface layer. In Fifteenth Symposium on Boundary Layers and Turbulence, American Meteorological Society, Wageningen, Holland, 15–19 July, pp. 422–423.Google Scholar
Xie, Z.-T. & Castro, I. P. 2006 LES and RANS for turbulent flow over arrays of wall-mounted cubes. Flow Turbul. Combust. 76 (3), 291–312.CrossRefGoogle Scholar
Xie, Z.-T., Coceal, O. & Castro, I. P. 2008 Large-eddy simulation of flows over random urban-like obstacles. Bound. Layer Meteorol. 129, 1–23.CrossRefGoogle Scholar