Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-13T01:42:40.473Z Has data issue: false hasContentIssue false
  • English
  • Français

Near-wall turbulence statistics and flow structures over three-dimensional roughness in a turbulent channel flow

Published online by Cambridge University Press:  14 January 2011

JIARONG HONG ,
JOSEPH KATZ  and
MICHAEL P. SCHULTZ
JIARONG HONG
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
JOSEPH KATZ*
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
MICHAEL P. SCHULTZ
Affiliation:
Department of Naval Architecture and Ocean Engineering, United States Naval Academy, Annapolis, MD 21402, USA
*
†Email address for correspondence: katz@jhu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Utilizing an optically index-matched facility and high-resolution particle image velocimetry measurements, this paper examines flow structure and turbulence in a rough-wall channel flow for Reτ in the 3520–5360 range. The scales of pyramidal roughness elements satisfy the ‘well-characterized’ flow conditions, with h/k ≈ 50 and k+ = 60 ~ 100, where h is half height of the channel and k is the roughness height. The near-wall turbulence measurements are sensitive to spatial resolution, and vary with Reynolds number. Spatial variations in the mean flow, Reynolds stresses, as well as the turbulent kinetic energy (TKE) production and dissipation rates are confined to y < 2k. All the Reynolds stress components have local maxima at slightly higher elevations, but the streamwise-normal component increases rapidly at y < k, peaking at the top of the pyramids. The TKE production and dissipation rates along with turbulence transport also peak near the wall. The spatial energy and shear spectra show an increasing contribution of large-scale motions and a diminishing role of small motions with increasing distance from the wall. As the spectra steepen at low wavenumbers, they flatten and develop bumps in wavenumbers corresponding to k − 3k, which fall in the dissipation range. Instantaneous realizations show that roughness-scale eddies are generated near the wall, and lifted up rapidly by large-scale structures that populate the outer layer. A linear stochastic estimation-based analysis shows that the latter share common features with hairpin packets. This process floods the outer layer with roughness-scale eddies, in addition to those generated by the energy-cascading process. Consequently, although the imprints of roughness diminish in the outer-layer Reynolds stresses, consistent with the wall similarity hypothesis, the small-scale turbulence contains a clear roughness signature across the entire channel.

JFM classification

Boundary Layers: Boundary Layers Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 667 , 25 January 2011 , pp. 1 - 37
Copyright
Copyright © Cambridge University Press 2011

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

REFERENCES

Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.CrossRefGoogle Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Adrian, R. J. & Moin, P. 1988 Stochastic estimation of organized turbulent structure: homogeneous shear flow. J. Fluid Mech. 190, 531–559.CrossRefGoogle Scholar
Antonia, R. A., Kim, J. & Browne, L. W. B. 1991 Some characteristics of small-scale turbulence in a turbulent duct flow. J. Fluid Mech. 233, 369–388.CrossRefGoogle 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.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.-Å., 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 Turbulence Combust. 72, 463–492.CrossRefGoogle Scholar
Bigillon, F., Niño, Y. & Garcia, M. H. 2006 Measurements of turbulence characteristics in an open-channel flow over a transitionally-rough bed using particle-image velocimetry. Exp. Fluids 41, 857–867.CrossRefGoogle Scholar
Burattini, P., Leonardi, S., Orlandi, P. & Antonia, R. A. 2008 Comparison between experiments and direct numerical simulations in a channel flow with roughness on one wall. J. Fluid Mech. 600, 403–426.CrossRefGoogle Scholar
Champagne, F. H., Friehe, C. A., Larue, J. C. & Wyngaard, J. C. 1977 Flux measurements, flux estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land. J. Atmos. Sci. 34, 515–530.2.0.CO;2>CrossRefGoogle Scholar
Christensen, K. T. 2004 The influence of peak-locking errors on turbulence statistics computed from PIV ensembles. Exp. Fluids 36, 484–497.CrossRefGoogle Scholar
Christensen, K. T. & Adrian, R. J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433–443.CrossRefGoogle Scholar
Dancey, C. L., Balakrishnan, M., Diplas, P. & Papanicolaou, A. N. 2000 The spatial inhomogeneity of turbulence above a fully rough, packed bed in open channel flow. Exp. Fluids 29, 402–410.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: J. Fluids Engng 100, 215–223.Google Scholar
Djenidi, L., Antonia, R. A., Amielh, M. & Anselmet, F. 2008 A turbulent boundary layer over a two-dimensional rough wall. Exp. Fluids 44, 37–47.CrossRefGoogle Scholar
Falkovich, G. 1994 Bottleneck phenomenon in developed turbulence. Phys. Fluids 6, 1411–1414.CrossRefGoogle Scholar
Finnigan, J. J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519–571.CrossRefGoogle Scholar
Flack, K. A., Schultz, M. P. & Shapiro, T. A. 2005 Experimental support for Townsend's Reynolds number similarity hypothesis on rough walls. Phys. Fluids 17, 035102.CrossRefGoogle Scholar
Fujita, H., Yokosawa, H. & Hirota, M. 1989 Secondary flow to the second kind in rectangular ducts with one rough wall. Exp. Therm. Fluid Sci. 2, 72–80.CrossRefGoogle Scholar
Grass, A. J. 1971 Structural features of turbulent flow over smooth and rough boundaries. J. Fluid Mech. 50, 233–255.CrossRefGoogle Scholar
Hackett, E. E., Luznik, L., Katz, J. & Osborn, T. R. 2009 Effect of finite spatial resolution on the turbulent energy spectrum measured in the coastal ocean bottom boundary layer. J. Atmos. Ocean. Technol. 26, 10–25.CrossRefGoogle Scholar
Hackett, E. E., Luznik, L., Nayak, R. A., Katz, J. & Osborn, T. R. 2010 Field measurements of turbulence at an unstable interface between current and wave bottom boundary layer. J. Geophys. Res. (in press).CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20, 101511.CrossRefGoogle Scholar
Ikeda, T. & Durbin, P. A. 2007 Direct simulations of a rough-wall channel flow. J. Fluid Mech. 571, 235–263.CrossRefGoogle Scholar
Inoué, S. & Spring, K. 1997 Video Microscopy: The Fundamentals. Plenum.CrossRefGoogle Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Keirsbulck, L., Labraga, L., Mazouz, A. & Tournier, C. 2002 Surface roughness effects on turbulent boundary layer structures. Trans. ASME: J. Fluids Engng 124, 127.Google Scholar
Kim, J., Moin, P. & Moser, R. D. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Krogstad, P.-Å., Andersson, H. I., Bakken, O. M. & Ashrafian, A. 2005 An experimental and numerical study of channel flows with rough walls. J. Fluid Mech. 530, 327–352.CrossRefGoogle Scholar
Krogstad, P.-Å. & Antonia, R. A. 1994 Structures of turbulent boundary layers on smooth and rough walls. J. Fluid Mech. 277, 1–21.CrossRefGoogle Scholar
Krogstad, P.-Å. & Antonia, R. A. 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27, 450–460.CrossRefGoogle Scholar
Krogstad, P.-Å., Antonia, R. A. & Browne, L. W. 1992 Comparison between rough and smooth-wall turbulent boundary layers. J. Fluid Mech. 245, 599–617.CrossRefGoogle Scholar
Lavoie, P., Avallone, G., De Gregorio, F., Romano, G. P. & Antonia, R. A. 2007 Spatial resolution of PIV for the measurement of turbulence. Exp. Fluids 43, 39–51.CrossRefGoogle Scholar
Lee, S. H. & Sung, H. J. 2007 Direct numerical simulation of turbulent boundary layer over a rod-roughened wall. J. Fluid Mech. 584, 125–146.CrossRefGoogle Scholar
Leutheusser, H. J. 1963 Turbulent flow in rectangular ducts. J. Hydraulic Div. ASCE 89, HY3, 1–19.CrossRefGoogle Scholar
Ligrani, P. M. & Moffat, R. J. 1986 Structure of transitionally rough and fully rough turbulent boundary layers. J. Fluid Mech. 162, 69–98.CrossRefGoogle Scholar
Lumley, J. L. 1967 Similarity and the turbulent energy spectrum. Phys. Fluids 10, 855–858.CrossRefGoogle Scholar
Luznik, L., Gurka, R., Nimmo Smith, W. A. M., Zhu, W., Katz, J. & Osborn, T. R. 2007 Distribution of energy spectra, Reynolds stresses, turbulence production, and dissipation in a tidally driven boundary layer. J. Phys. Oceanogr. 37, 1527–1550.CrossRefGoogle Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.CrossRefGoogle Scholar
Meinhart, C. D., Wereley, S. T. & Gray, M. H. B. 2000 Volume illumination for two-dimensional particle image velocimetry. Meas. Sci. Technol. 11, 809–814.CrossRefGoogle Scholar
Monty, J. P. 2005 Developments in smooth wall turbulent duct flows. PhD thesis, the University of Melbourne.Google Scholar
Monty, J. P., Hutchins, N., NG, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.CrossRefGoogle 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
Nimmo Smith, W. A. M., Katz, J. & Osborn, T. R. 2005 On the structure of turbulence in the bottom boundary layer of the coastal ocean. J. Phys. Oceanogr. 35, 72–93.CrossRefGoogle Scholar
Perry, A. E. & Li, J. D. 1990 Experimental support for the attached-eddy hypothesis in zero pressure-gradient turbulent boundary layers. J. Fluid Mech. 218, 405–438.CrossRefGoogle Scholar
Perry, A. E., Lim, K. L. & Henbest, S. M. 1987 An experimental study of the turbulence structure in smooth- and rough-wall boundary layers. J. Fluid Mech. 177, 437–466.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Raffel, M., Willert, C., Wereley, S. & Kompenhans, J. 2007 Particle Image Velocimetry: A Practical Guide, 2nd edn. Springer.CrossRefGoogle Scholar
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 1–25.CrossRefGoogle Scholar
Roth, G. I., Mascenik, D. T. & Katz, J. 1999 Measurements of the flow structure and turbulence within a ship bow wave. Phys. Fluids 11, 3512–3523.CrossRefGoogle Scholar
Saddoughi, S. G. & Veerravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333–372.CrossRefGoogle Scholar
Schultz, M. P. & Flack, K. A. 2003 Turbulent boundary layers over surfaces smoothed by sanding. Trans. ASME: J. Fluids Engng 125, 863–870.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, 381–405.CrossRefGoogle Scholar
Schultz, M. P. & Flack, K. A. 2009 Turbulent boundary layers on a systematically varied rough wall. Phys. Fluids 21, 015104.CrossRefGoogle Scholar
Seginer, I., Mulhearn, P. J., Bradley, E. F. & Finnigan, J. J. 1976 Turbulent flow in a model plant canopy. Bound. Layer Meteorol. 10, 423–453.CrossRefGoogle Scholar
Shah, M. K., Agelinchaab, M. & Tachie, M. F. 2008 Influence of PIV interrogation area on turbulent statistics up to 4th order moments in smooth and rough wall turbulent flows. Exp. Therm. Fluid Sci. 32, 725–747.CrossRefGoogle Scholar
Shockling, M. A., Allen, J. J. & Smits, A. J. 2006 Roughness effects in turbulent pipe flow. J. Fluid Mech. 564, 267–285.CrossRefGoogle Scholar
Soranna, F., Chow, Y. C., Uzol, O. & Katz, J. 2006 On the effect of IGV wake impingement on the flow around the leading edge of a rotor blade. J. Turbomach. 128, 82–95.CrossRefGoogle Scholar
Tachie, M. F., Bergstrom, D. J. & Balachandar, R. 2000 Rough wall turbulent boundary layers in shallow open channel flow. Trans. ASME: J. Fluids Engng 122, 533–541.Google Scholar
Tachie, M. F., Bergstrom, D. J. & Balachandar, R. 2003 Roughness effects in low-Re θ open-channel turbulent boundary layers. Exp. Fluids 35, 338–346.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Volino, R. J., Schultz, M. P. & Flack, K. A. 2009 Turbulence structure in a boundary layer with two-dimensional roughness. J. Fluid Mech. 635, 75–101.CrossRefGoogle Scholar
Wei, T. & Willmarth, W. W. 1989 Reynolds-number effects on the structure of a turbulent channel flow. J. Fluid Mech. 204, 57–95.CrossRefGoogle Scholar
Westerweel, J. 1997 Fundamentals of digital particle image velocimetry. Meas. Sci. Technol. 8, 1379–1392.CrossRefGoogle Scholar
Wu, Y. & Christensen, K. T. 2007 Outer-layer similarity in the presence of a practical rough-wall topography. Phys. Fluids 19, 085108.CrossRefGoogle Scholar
Yokoshawa, H., Fujita, H., Hirota, M. & Iwata, S. 1989 Measurement of turbulent flow in a square duct with roughened walls on two opposite sides. Intl J. Heat Fluid Flow 10, 125–130.CrossRefGoogle Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar
Zhu, W., van Hout, R. & Katz, J. 2007 On the flow structure and turbulence during sweep and ejection events in a model canopy. Bound. Layer Meteorol. 124, 205–233.CrossRefGoogle Scholar
Zhu, Y. & Antonia, R. A. 1996 The spatial resolution of hot-wire arrays for the measurement of small-scale turbulence. Meas. Sci. Technol. 7, 1349–1359.CrossRefGoogle Scholar
Supplementary material: PDF

Hong et al. supplementary material

Hi-res figure 19a

Download Hong et al. supplementary material(PDF)
PDF 2.2 MB