Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-28T03:09:21.223Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulation of open-channel flow over smooth-to-rough and rough-to-smooth step changes

Published online by Cambridge University Press:  13 March 2019

Amirreza Rouhi Open the ORCID record for Amirreza Rouhi [Opens in a new window] ,
Daniel Chung Open the ORCID record for Daniel Chung [Opens in a new window]  and
Nicholas Hutchins
Amirreza Rouhi*
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
Daniel Chung
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
Nicholas Hutchins
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
*
†Email address for correspondence: amirreza.rouhi@unimelb.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations (DNS) are reported for open-channel flow over streamwise-alternating patches of smooth and fully rough walls. The rough patch is a three-dimensional sinusoidal surface. Owing to the streamwise periodicity, the flow configuration consists of a step change from smooth to rough, and a step change from rough to smooth. The friction Reynolds number varies from 437 over the smooth patch to 704 over the rough patch. Through the fully resolved DNS dataset it is possible to explore many detailed aspects of this flow. Two aspects motivate this work. The first one is the equilibrium assumption that has been widely used in both experiments and computations. However, it is not clear where this assumption is valid. The detailed DNS data reveal a significant departure from equilibrium, in particular over the smooth patch. Over this patch, the mean velocity is recovered up to the beginning of the log layer after a fetch of five times the channel height. However, over the rough patch, the same recovery level is reached after a fetch of two times the channel height. This conclusion is arrived at by assuming that an error of up to 5 % is acceptable and the log layer, classically, starts from 30 wall units above the wall. The second aspect is the reported internal boundary-layer (IBL) growth rates in the literature, which are inconsistent with each other. This is conjectured to be partly caused by the diverse IBL definitions. Five common definitions are applied for the same DNS dataset. The resulting IBL thicknesses are different by 100 %, and their apparent power-law exponents are different by 50 %. The IBL concept, as a layer within which the flow feels the surface underneath, is taken as the basis to search for the proper definition. The definition based on the logarithmic slope of the velocity profile, as proposed by Elliot (Trans. Am. Geophys. Union, vol. 39, 1958, pp. 1048–1054), yields better consistency with this concept based on turbulence characteristics.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 866 , 10 May 2019 , pp. 450 - 486
Copyright
© 2019 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

Albertson, J. D. & Parlange, M. B. 1999a Natural integration of scalar fluxes from complex terrain. Adv. Water Resour. 23, 239–252.Google Scholar
Albertson, J. D. & Parlange, M. B. 1999b Surface length scales and shear stress: implications for land–atmosphere interaction over complex terrain. Water Resour. Res. 35, 2121–2132.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
Andreopoulos, J. & Wood, D. H. 1982 The response of a turbulent boundary layer to a short length of surface roughness. J. Fluid Mech. 118, 143–164.Google Scholar
Antonia, R. A. & Luxton, R. E. 1971 The response of a turbulent boundary layer to a step change in surface roughness. Part 1. Smooth to rough. J. Fluid Mech. 48, 721–761.Google Scholar
Antonia, R. A. & Luxton, R. E. 1972 The response of a turbulent boundary layer to a step change in surface roughness. Part 2. Rough-to-smooth. J. Fluid Mech. 53, 737–757.Google Scholar
Bou-Zeid, E., Meneveau, C. & Parlange, M. B. 2004 Large-eddy simulation of neutral atmospheric boundary layer flow over heterogeneous surfaces: blending height and effective surface roughness. Water Resour. Res. 40, W02505.Google Scholar
Bou-Zeid, E., Meneveau, C. & Parlange, M. B. 2005 A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17, 025105.Google Scholar
Bou-Zeid, E., Parlange, M. B. & Meneveau, C. 2007 On the parameterization of surface roughness at regional scales. J. Atmos. Sci. 64, 216–227.Google Scholar
Bradley, E. F. 1968 A micrometeorological study of velocity profiles and surface drag in the region modified by a change in surface roughness. Q. J. R. Meteorol. Soc. 94, 361–379.Google Scholar
Brutsaert, W. 1998 Land-surface water vapor and sensible heat flux: spatial variability, homogeneity, and measurement scales. Water Resour. Res. 34, 2433–2442.Google Scholar
Calaf, M., Meneveau, C. & Meyers, J. 2010 Large eddy simulation study of fully developed wind-turbine array boundary layers. Phys. Fluids 22, 015110.Google Scholar
Carper, M. A. & Porté-Agel, F. 2008 Subfilter-scale fluxes over a surface roughness transition. Part I: measured fluxes and energy transfer rates. Boundary-Layer Meteorol. 126, 157–179.Google Scholar
Chamorro, L. P. & Porté-Agel, F. 2009 Velocity and surface shear stress distributions behind a rough-to-smooth surface transition: a simple new model. Boundary-Layer Meteorol. 130, 29–41.Google Scholar
Chan, L., MacDonald, M., Chung, D., Hutchins, N. & Ooi, A. 2015 A systematic investigation of roughness height and wavelength in turbulent pipe flow in the transitionally rough regime. J. Fluid Mech. 771, 743–777.Google Scholar
Chan, L., MacDonald, M., Chung, D., Hutchins, N. & Ooi, A. 2018 Secondary motion in turbulent pipe flow with three-dimensional roughness. J. Fluid Mech. 854, 5–33.Google Scholar
Cheng, H. & Castro, I. P. 2002 Near-wall flow development after a step change in surface roughness. Boundary-Layer Meteorol. 105, 411–432.Google Scholar
Chung, D., Chan, L., MacDonald, M., Hutchins, N. & Ooi, A. 2015 A fast direct numerical simulation method for characterising hydraulic roughness. J. Fluid Mech. 773, 418–431.Google Scholar
Chung, D., Monty, J. P. & Ooi, A. 2014 An idealised assessment of Townsend’s outer-layer similarity hypothesis for wall turbulence. J. Fluid Mech. 742, R3.Google Scholar
Dupont, S. & Brunet, Y. 2009 Coherent structures in canopy edge flow: a large-eddy simulation study. J. Fluid Mech. 630, 93–128.Google Scholar
Efros, V. & Krogstad, P. 2011 Development of a turbulent boundary layer after a step from smooth to rough surface. Exp. Fluids 51, 1563–1575.Google Scholar
Elliott, W. P. 1958 The growth of the atmospheric internal boundary layer. Trans. Am. Geophys. Union 39, 1048–1054.Google Scholar
Fadlun, E. A., Verzicco, R., Orlandi, P. & Mohd-Yusof, J. 2000 Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161, 35–60.Google Scholar
Ham, F., Mattsson, K. & Iaccarino, G. 2006 Accurate and stable finite volume operators for unstructured flow solvers. In Center of Turbulence Research Annual Research Briefs, pp. 243–261. Stanford University.Google Scholar
Hanson, R. E. & Ganapathisubramani, B. 2016 Development of turbulent boundary layers past a step change in wall roughness. J. Fluid Mech. 795, 494–523.Google Scholar
Ismail, U., Zaki, T. A. & Durbin, P. A. 2018 Simulations of rib-roughened rough-to-smooth turbulent channel flows. J. Fluid Mech. 843, 419–449.Google Scholar
Jacobi, I. & McKeon, B. J. 2011 New perspectives on the impulsive roughness-perturbation of a turbulent boundary layer. J. Fluid Mech. 677, 179–203.Google Scholar
Jegede, O. O. & Foken, T. H. 1999 A study of the internal boundary layer due to a roughness change in neutral conditions observed during the linex field campaigns. Theor. Appl. Climatol. 62, 31–41.Google Scholar
Jiménez, J., Hoyas, S., Simens, M. P. & Mizuno, Y. 2010 Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335–360.Google Scholar
Kaimal, J. C. & Finnigan, J. J. 1994 Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press.Google Scholar
Lee, J. H. 2015 Turbulent boundary layer flow with a step change from smooth to rough surface. Intl J. Heat Fluid Flow 54, 39–54.Google Scholar
Lin, C. L. & Glendening, J. W. 2002 Large eddy simulation of an inhomogeneous atmospheric boundary layer under neutral conditions. J. Atmos. Sci. 59, 2479–2497.Google Scholar
Loureiro, J. B. R., Sousa, F. B. C. C., Zotin, J. L. Z. & Freire, A. P. S. 2010 The distribution of wall shear stress downstream of a change in roughness. Intl J. Heat Fluid Flow 31, 785–793.Google Scholar
Miller, N. E. & Stoll, R. 2013 Surface heterogeneity effects on regional-scale fluxes in the stable boundary layer: aerodynamic roughness length transitions. Boundary-Layer Meteorol. 149, 277–301.Google Scholar
Miyake, M.1965 Transformation of the atmospheric boundary layer over inhomogeneous surfaces. Tech. Rep., Washington University Department of Atmospheric Sciences.Google Scholar
Morinishi, Y., Lund, T. S., Vasilyev, O. V. & Moin, P. 1998 Fully conservative higher order finite difference schemes for incompressible flow. J. Comput. Phys. 143, 90–124.Google Scholar
Mulhearn, P. J. 1978 A wind-tunnel boundary-layer study of the effects of a surface roughness change: rough to smooth. Boundary-Layer Meteorol. 15, 3–30.Google Scholar
Munro, D. S. & Oke, T. R. 1975 Aerodynamic boundary-layer adjustment over a crop in neutral stability. Boundary-Layer Meteorol. 9, 53–61.Google Scholar
Munters, W., Meneveau, C. & Meyers, J. 2016 Turbulent inflow precursor method with time-varying direction for large-eddy simulations and applications to wind farms. Boundary-Layer Meteorol. 159 (2), 305–328.Google Scholar
Nickels, T. B. 2004 Inner scaling for wall-bounded flows subject to large pressure gradients. J. Fluid Mech. 521, 217–239.Google Scholar
Panofsky, H. A. & Townsend, A. A. 1964 Change of terrain roughness and the wind profile. Q. J. R. Meteorol. Soc. 90, 147–155.Google Scholar
Pendergrass, W. & Arya, S. P. S. 1984 Dispersion in neutral boundary layer over a step change in surface roughness: I. Mean flow and turbulence structure. Atmos. Environ. 18, 1267–1279.Google Scholar
Perot, J. B. 1993 An analysis of the fractional step method. J. Comput. Phys. 108, 51–58.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Rao, K. S., Wyngaard, J. C. & Coté, O. R. 1974 The structure of the two-dimensional internal boundary layer over a sudden change of surface roughness. J. Atmos. Sci. 31, 738–746.Google Scholar
Saito, N. & Pullin, D. I. 2014 Large eddy simulation of smooth–rough–smooth transitions in turbulent channel flows. Intl J. Heat Mass Transfer 78, 707–720.Google Scholar
Savelyev, S. A. & Taylor, P. A. 2005 Internal boundary layers: I. Height formulae for neutral and diabatic flows. Boundary-Layer Meteorol. 115, 1–25.Google Scholar
Scotti, A. 2006 Direct numerical simulation of turbulent channel flows with boundary roughened with virtual sandpaper. Phys. Fluids 18, 031701.Google Scholar
Silva-Lopes, A., Palma, J. M. L. M. & Piomelli, U. 2015 On the determination of effective aerodynamic roughness of surfaces with vegetation patches. Boundary-Layer Meteorol. 156, 113–130.Google Scholar
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297–324.Google Scholar
Stevens, R. J., Graham, J. & Meneveau, C. 2014 A concurrent precursor inflow method for large eddy simulations and applications to finite length wind farms. Renew. Energy 68, 46–50.Google Scholar
Stoll, R. & Porté-Agel, F. 2006 Dynamic subgrid-scale models for momentum and scalar fluxes in large-eddy simulations of neutrally stratified atmospheric boundary layers over heterogeneous terrain. Water Resour. Res. 42, W01409.Google Scholar
Verstappen, R. W. C. P. & Veldman, A. E. P. 2003 Symmetry-preserving discretization of turbulent flow. J. Comput. Phys. 187, 343–368.Google Scholar
Win, A. T., Mochizuki, S. & Kameda, T. 2010 Response of the fully developed pipe flow to rough wall disturbances (mean velocity field). J. Fluid Sci. Technol. 5, 340–350.Google Scholar
Yang, X. I. A. & Meneveau, C. 2017 Modelling turbulent boundary layer flow over fractal-like multiscale terrain using large-eddy simulations and analytical tools. Phil. Trans. R. Soc. A 375, 20160098.Google Scholar
Yuan, J. & Piomelli, U. 2014 Numerical simulations of sink-flow boundary layers over rough surfaces. Phys. Fluids 26, 015113.Google Scholar