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The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime

Published online by Cambridge University Press:  21 May 2007

M. P. SCHULTZ  and
K. A. FLACK
M. P. SCHULTZ
Affiliation:
Naval Architecture and Ocean Engineering Department, United States Naval Academy, Annapolis, MD 21402, USA
K. A. FLACK
Affiliation:
Mechanical Engineering Department, United States Naval Academy, Annapolis, MD 21402, USA
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Abstract

Turbulence measurements for rough-wall boundary layers are presented and compared to those for a smooth wall. The rough-wall experiments were made on a three-dimensional rough surface geometrically similar to the honed pipe roughness used by Shockling, Allen & Smits (J. Fluid Mech. vol. 564, 2006, p. 267). The present work covers a wide Reynolds-number range (Reθ = 2180–27 100), spanning the hydraulically smooth to the fully rough flow regimes for a single surface, while maintaining a roughness height that is a small fraction of the boundary-layer thickness. In this investigation, the root-mean-square roughness height was at least three orders of magnitude smaller than the boundary-layer thickness, and the Kármán number (δ+), typifying the ratio of the largest to the smallest turbulent scales in the flow, was as high as 10100. The mean velocity profiles for the rough and smooth walls show remarkable similarity in the outer layer using velocity-defect scaling. The Reynolds stresses and higher-order turbulence statistics also show excellent agreement in the outer layer. The results lend strong support to the concept of outer layer similarity for rough walls in which there is a large separation between the roughness length scale and the largest turbulence scales in the flow.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 580 , 10 June 2007 , pp. 381 - 405
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Adrian, R. J. 1983 Laser velocimetry. In Fluid Mechanics Measurements (ed. Goldstein, R. J.). Hemisphere.Google Scholar
Akinlade, O. G., Bergstrom, D. J., Tachie, M. F. & Castillo, L. 2004 Outer flow scaling of smooth and rough wall turbulent boundary layers. Exps. Fluids 37, 604–612.CrossRefGoogle Scholar
Andreopoulos, J. & Bradshaw, P. 1981 Measurements of turbulence structure in the boundary layer on a rough surface. Boundary-Layer Met. 20, 201–213.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
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
Bandyopadhyay, P. R. 1987 Rough-wall turbulent boundary layers in the transition regime. J. Fluid Mech. 180, 231–266.CrossRefGoogle Scholar
Bandyopadhyay, P. R. & Watson, R. D. 1988 Structure of rough-wall boundary layers. Phys. Fluids 31, 1877–1883.CrossRefGoogle Scholar
Bhaganagar, K., Kim, J. & Coleman, G. 2004 Effect of roughness on wall-bounded turbulence. Flow Turbulence Combust. 72, 463–492.CrossRefGoogle Scholar
Buchhave, P., George, W. K. & Lumley, J. L. 1979 The measurement of turbulence with the laser-Doppler anemometer. Annu. Rev. Fluid Mech. 11, 443–503.CrossRefGoogle Scholar
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aeronaut. Sci. 21, 91–108.CrossRefGoogle Scholar
Colebrook, C. F. 1939 Turbulent flow in pipes, with particular reference to the transitional region between smooth and rough wall laws. J. Inst. Civil Engrs 11, 133–156.CrossRefGoogle Scholar
Colebrook, C. F. & White, C. M. 1937 Experiments with fluid friction in roughened pipes. Proc. R. Soc. 161, 367–378.Google Scholar
Coleman, H. W. & Steele, W. G. 1995 Engineering application of experimental uncertainty analysis. AIAA J. 33, 1888–1896.CrossRefGoogle Scholar
Coles, D. E. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.CrossRefGoogle Scholar
Coles, D. E. 1962 The turbulent boundary layer in a compressible fluid. RAND Tech. Rep. R-403-PR.Google Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Durst, F., Fischer, M., Jovanovic, J. & Kikura, H. 1998 Methods to set up and investigate low Reynolds number, fully developed turbulent plane channel flows. Trans. ASME I: J. Fluids Engng 120, 496–503.Google Scholar
Edwards, R. V. 1987 Report of the special panel on statistical particle bias problems in laser anemometry. Trans. ASME I: J. Fluids Engng 109, 89–93.Google Scholar
Efron, B. 1982 The Jackknife, the Bootstrap, and Other Resampling Plans. 1st edn. Society of Industrial and Applied Mathematics.CrossRefGoogle Scholar
Fernholz, H. H. & Finley, P. J. 1996 Incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerospace Sci. 32, 245–311.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
Grass, A. J. 1971 Structural features of turbulent flow over smooth and rough boundaries. J. Fluid Mech. 50, 233–255.CrossRefGoogle Scholar
Hama, F. R. 1954 Boundary-layer characteristics for rough and smooth surfaces. Trans. SNAME 62, 333–351.Google Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Johansson, A. V. & Alfredsson, P. H. 1983 Effects of imperfect spatial resolution on measurements of wall bounded turbulent shear flows. J. Fluid Mech. 137, 409–421.CrossRefGoogle Scholar
von, Kármán, T. 1930 Mechanishe aehnlichkeit and turbulenz. Nachr. Ges. Wiss. Göttingen 58–76.Google Scholar
Keirsbulck, L., Labraga, L., Mazouz, A. & Tournier, C. 2002 Surface roughness effects on turbulent boundary layer structures. Trans. ASME I: J. Fluids Engng 124, 127–135.Google Scholar
Krogstad, P.-A. & Antonia, R. A. 1999 Surface roughness effects in turbulent boundary layers. Exps Fluids 27, 450–460.CrossRefGoogle Scholar
Krogstad, P.-A., Antonia, R. A. & Browne, L. W. B. 1992 Comparison between rough- and smooth-wall turbulent boundary layers. J. Fluid Mech. 245, 599–617.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
Kunkel, G. J. & Marusic, I. 2006 Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow. J. Fluid Mech. 548, 375–402.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
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
Lu, S. S. & Willmarth, W. W. 1973 Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60, 481–571.CrossRefGoogle Scholar
Luchik, T. S. & Tiederman, W. G. 1985 Effect of spanwise probe volume length on laser velocimeter measurements in wall bounded turbulent flows. Exps. Fluids 3, 339–341.CrossRefGoogle Scholar
McKeon, B. J., Li, J., Jiang, W., Morrison, J. F. & Smits, A. J. 2004 Further observations on the mean velocity distribution in fully developed pipe flow. J. Fluid Mech. 501, 135–147.CrossRefGoogle Scholar
Millikan, C. M. 1938 A critical discussion of turbulent flows in channels and circular tubes. Proc. 5th Intl Congress on Appl. Mech. Cambridge, MA, pp. 386–392.Google Scholar
Moffat, R. J. 1988 Describing the uncertainties in experimental results. Expl Thermal Fluid Sci. 1, 3–17.CrossRefGoogle Scholar
Moody, L. F. 1944 Friction factors for pipe flow. Trans. ASME 66, 671–684.Google Scholar
Murlis, J., Tsai, H. M. & Bradshaw, P. 1982 The structure of turbulent boundary layers at low Reynolds numbers. J. Fluid Mech. 122, 13–56.CrossRefGoogle Scholar
Nikuradse, J. 1933 Laws of flow in rough pipes. NACA TM 1292.Google Scholar
Österlund, J. M., Johansson, A. V., Nagib, H. M. & Hites, M. H. 2000 A note on the overlap region in turbulent boundary layers. Phys. Fluids 12, 1–4.CrossRefGoogle Scholar
Patel, V. C. 1998 Perspective: flow at high Reynolds number and over rough surfaces – Achilles heel of CFD. Trans. ASME I: J. Fluids Engng 120, 434–444.Google Scholar
Perry, A. E. & Joubert, P. N. 1963 Rough wall boundary layers in adverse pressure gradients. J. Fluid Mech. 17, 193–211.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., Schofield, W. H. & Joubert, P. N. 1969 Rough-wall turbulent boundary layers. J. Fluid Mech. 37, 383–413.CrossRefGoogle Scholar
Raupach, M. R. 1981 Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers. J. Fluid Mech. 108, 363–382.CrossRefGoogle Scholar
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall boundary layers. Appl. Mech. Rev. 44, 1–25.CrossRefGoogle Scholar
Schubauer, G. B. & Tchen, C. M. 1961 Turbulent Flow. Princeton University Press.Google Scholar
Schultz, M. P. & Flack, K. A. 2003 Turbulent boundary layers over surfaces smoothed by sanding. Trans. ASME I: J. Fluids Engng 125, 863–870.Google Scholar
Schultz, M. P. & Myers, A. 2003 Comparison of three roughness function determination methods. Exps. Fluids 35, 372–379.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
Snyder, W. H. & Castro, I. P. 2002 The critical Reynolds number for rough-wall boundary layers. J. Wind Engng Indust. Aerodyn. 90, 41–54.CrossRefGoogle Scholar
Tachie, M. F., Bergstrom, D. J. & Balachandar, R. 2000 Rough wall turbulent boundary layers in shallow open channel flow. J. Fluids Engng 122, 533–541.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Wallace, J. M., Eckelmann, H. & Brodkey, R. S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 54, 39–48.CrossRefGoogle Scholar
Willmarth, W. W. & Sharma, L. K. 1984 Study of turbulent structure with hot wires smaller than the viscous length. J. Fluid Mech. 142, 121–149.CrossRefGoogle Scholar