On the Outer Layer Controversy for a Turbulent Boundary Layer over a Rough Wall

Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 22)

Abstract

An impressive number of experimental and numerical studies of turbulent flows over rough walls has appeared over the last 20 years. Much useful information has been obtained in terms of the turbulence structure both near the roughness canopy and in the outer flow region. However, the issue of whether or not the outer region of the boundary layer is affected by the nature of the wall has yet to be resolved satisfactorily. While the available data, mostly at sufficiently large values of the Reynolds numbers and δ∕k (δ and k are the boundary layer thickness and characteristic roughness height, respectively), seem to suggest that 3D and transverse 2D rough surfaces may affect the outer layer differently, this suggestion can only be tested rigorously once the measurement of the wall-normal velocity fluctuation over the transverse 2D roughness is improved. With the benefit of the channel flow DNS data, it is argued that, for this latter surface type, the wall shear stress, as inferred from the form drag or drag balance, has actually been measured reasonably accurately in the past.

Keywords

Wall Shear Stress Reynolds Stress Outer Region Roughness Element Reynolds Shear Stress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

RAA is most grateful to P-A. Krogstad, S. Leonardi and P. Burattini for useful discussions on several issues addressed on in this paper. The past support from the ARC and the collaboration with P. Orlandi, R. Smalley and H. Shafi are warmly acknowledged.

References

  1. 1.
    J.C. Rotta, Turbulent boundary layers in incompressible flow. Prog. Aero. Sci. 2, 1–220 (1962)CrossRefGoogle Scholar
  2. 2.
    I. Tani, Some equilibrium turbulent boundary layers. Fluid Dyn. Res., 1, 49–58 (1968)CrossRefGoogle Scholar
  3. 3.
    R.J. Smalley, R.A. Antonia, L. Djenidi, Self-preservation of rough-wall turbulent boundary layers. Eur. J. Mech. B-Fluids 20, 591–602 (2001)MATHCrossRefGoogle Scholar
  4. 4.
    M.R. Raupach, R.A. Antonia, S. Rajagopalan, Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 1–25 (1991)CrossRefGoogle Scholar
  5. 5.
    P.-A. Krogstad, R.A. Antonia, L.W.B. Browne, Comparison between rough- and smooth-wall turbulent boundary layers. J. Fluid Mech. 245, 599–617 (1992)CrossRefGoogle Scholar
  6. 6.
    P.-A. Krogstad, R.A. Antonia, Structure of turbulent boundary layers on smooth and rough walls. J. Fluid Mech. 277, 1–21 (1994)CrossRefGoogle Scholar
  7. 7.
    P.-A. Krogstad, R.A. Antonia, Surface roughness effects in turbulent boundary layers. Exp. Fluids 27, 450–460 (1999)CrossRefGoogle Scholar
  8. 8.
    J. Jimenez, Turbulent flows over rough walls. Ann. Rev. Fluid Mech. 36, 173–196 (2004)MathSciNetCrossRefGoogle Scholar
  9. 9.
    S. Leonardi, P. Orlandi, R.J. Smalley, L. Djenidi, R.A. Antonia, Direct numerical simulations of turbulent channel flow with transverse square bars on the wall. J. Fluid Mech. 491, 229–238 (2003)MATHCrossRefGoogle Scholar
  10. 10.
    J. Cui, V.C. Patel, C.-L. Lin, Large eddy simulation of turbulent flow in a channel with rib roughness. Int. J. Heat, Fluid Flow 24, 372–388 (2003)CrossRefGoogle Scholar
  11. 11.
    A. Ashrafian, H.I. Andersson, M. Manhart, DNS of turbulent flow in a rod-roughened channel. Int. J. Heat, Fluid Flow 25, 373–383 (2004)CrossRefGoogle Scholar
  12. 12.
    T. Ikeda, P.A. Durbin, Direct simulations of a rough wall channel flow. J. Fluid Mech. 571, 235–263 (2007)MATHCrossRefGoogle Scholar
  13. 13.
    M.F. Tachie, D.J. Bergstrom, R. Balachandar, Rough wall turbulent boundary layers in shallow open channel flow. J. Fluids Eng. 122, 533–541 (2000)CrossRefGoogle Scholar
  14. 14.
    M.F. Tachie, D.J. Bergstrom, R. Balachandar, Roughness effects in low-Re number open-channel turbulent boundary layers. Exp. Fluids 35, 338–346 (2002)CrossRefGoogle Scholar
  15. 15.
    L. Keirsbulck, L. Labraga, A. Mazouz, C. Tournier, Surface roughness effects on turbulent boundary layer structures. J. Fluids Eng. 124, 127–135 (2002)CrossRefGoogle Scholar
  16. 16.
    K.A. Flack, M.P. Schultz, J.S. Connelly, Examination of a critical roughness height for outer layer similarity. Phys. Fluids 19, 095104 (2007)CrossRefGoogle Scholar
  17. 17.
    K.A. Flack, M.P. Schultz, T.A. Shapiro, Experimental support for Townsend’s Reynolds number similarity hypothesis on rough walls. Phys. Fluids 17, 035102 (2005)CrossRefGoogle Scholar
  18. 18.
    M.P. Schultz, K.A. Flack, Outer layer similarity in fully rough turbulent boundary layers. Exp. Fluids 38, 328–340 (2005)CrossRefGoogle Scholar
  19. 19.
    Y. Wu, K.T. Christensen, Outer-layer similarity in the presence of a practical rough-wall topography. Phys. Fluids 19, 085108 (2007)CrossRefGoogle Scholar
  20. 20.
    P. Orlandi, S. Leonardi, R.A. Antonia, Turbulent channel flow with either transverse or longitudinal roughness elements on one wall. J. Fluid Mech. 561, 279–305 (2006)MATHCrossRefGoogle Scholar
  21. 21.
    P. Orlandi, S. Leonardi, DNS of turbulent channel flows with two and three-dimensional roughness. J. Turb 7, no 53 (2006)Google Scholar
  22. 22.
    P. Orlandi, S. Leonardi, Direct numerical simulation of three-dimensional turbulent rough channels: parameterization and flow physics. J. Fluid Mech. 606, 399–415 (2008)MATHCrossRefGoogle Scholar
  23. 23.
    K. Bhaganagar, J. Kim, G. Coleman, Effect of roughness on wall-bounded turbulence. Flow Turb. Comb. 72, 463–492 (2004)MATHCrossRefGoogle Scholar
  24. 24.
    R.J. Volino, M.P. Schultz, K.A. Flack, Turbulence structure in rough- and smooth-wall boundary layers. J. Fluid Mech. 592, 263–293 (2007)MATHCrossRefGoogle Scholar
  25. 25.
    P.-A. Krogstad, H.I. Andersson, O.M. Bakken, A. Ashrafian, An experimental and numerical study of channel flow with rough walls. J. Fluid Mech. 530, 327–352 (2005)MATHCrossRefGoogle Scholar
  26. 26.
    P. Burattini, S. Leonardi, P. Orlandi, R.A. Antonia, Comparison between experiments and direct numerical simulations in a channel flow with roughness on one wall. J. Fluid Mech. 600, 403–426 (2008)MATHCrossRefGoogle Scholar
  27. 27.
    K. Bhaganagar, G. Coleman, J. Kim, Effect of roughness on turbulent fluctuations in a turbulent channel flow. Phys Fluids 19, 028103 (2007)CrossRefGoogle Scholar
  28. 28.
    P.R. Spalart, Direct simulation of a turbulent boundary layer up to Re?=1410. J. Fluid Mech. 187, 61–98 (1988)MATHCrossRefGoogle Scholar
  29. 29.
    S.G. Saddoughi, S.V. Veeravalli, Local isotropy of turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333–372 (1994)CrossRefGoogle Scholar
  30. 30.
    M.P. Schultz, K.A. Flack, The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime. J. Fluid Mech. 580, 381–405 (2007)MATHCrossRefGoogle Scholar
  31. 31.
    P.M. Ligrani, R.J. Moffat, Structure of transitionally rough and fully rough turbulent boundary layers. J Fluid Mech. 162, 69–98 (1986)MathSciNetCrossRefGoogle Scholar
  32. 32.
    S.-H. Lee, H.J. Sung, Direct numerical simulation of the turbulent boundary layer over a rod-roughened wall. J. Fluid Mech. 584, 125–146 (2007)MATHCrossRefGoogle Scholar
  33. 33.
    M. Acharya, M.P. Escudier, Turbulent flow over mesh roughness, in Turbulent Shear Flows, vol 5 (Springer, 1987), pp. 177–185Google Scholar
  34. 34.
    A.E. Perry, K.L. Lim, S.M. Henbest, An experimental study of turbulence structure in smooth- and rough-wall turbulent boundary layers. J. Fluid Mech. 177, 437–466 (1987)CrossRefGoogle Scholar
  35. 35.
    T. Kameda, S. Mochizuki, H. Osaka, LDA measurement in roughness sub-layer beneath turbulent layer developed over two-dimensional square rough surface, in Proceedings of 12th International Symposium on Application of Laser Techniques to Fluid Mechanics (CDROM-paper 28.3), Lisbon, July 12–14 (2004)Google Scholar
  36. 36.
    L. Djenidi, R.A. Antonia, M. Amielh, F. Anselmet, A turbulent boundary-layer over a two-dimensional rough wall. Exp. Fluids 44, 37–47 (2008)CrossRefGoogle Scholar
  37. 37.
    R. Antonia, R.E. Luxton, 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 (1971)CrossRefGoogle Scholar
  38. 38.
    P. Mulhearn, Turbulent flow over a periodic rough surface. Phys Fluids 21, 1113–1115 (1978)CrossRefGoogle Scholar
  39. 39.
    T. Kameda, H. Osaka, S. Mochizuki, Mean flow quantities for the turbulent boundary layer over a k-type rough wall, in Proceedings of 13th AFMC, Monash Univerity, December 13–18, 1998, pp. 357–360Google Scholar
  40. 40.
    S. Leonardi, P. Orlandi, L. Djenidi, R.A. Antonia, Structure of turbulent channel flow with square bars on one wall. Int. J. Heat Fluid Flow 25, 384–392 (2004)CrossRefGoogle Scholar
  41. 41.
    J.D. Li, A.E. Perry, Shear stress profiles in zero pressure-gradient turbulent boundary layers, in Proceedings of 10th AFMC, University of Melbourne, December, 11–15, 7.9–7.12 (1989)Google Scholar
  42. 42.
    P.J. Mulhearn, J.J. Finnigan, Turbulent flow over a very rough random surface. Boundary-Layer Met. 15, 109–132 (1978)CrossRefGoogle Scholar
  43. 43.
    M.R. Raupach, A.S. Thom, I. Edwards, A wind-tunnel study of turbulent flow close to regularly arrayed rough surfaces. Boundary-Layer Met. 18, 373–397 (1980)CrossRefGoogle Scholar
  44. 44.
    A.E. Perry, W.H. Schofield, P. N. Joubert, Rough wall turbulent boundary layers. J. Fluid Mech. 37, 383–413 (1969)CrossRefGoogle Scholar
  45. 45.
    T. Kameda, H. Osaka, S. Mochizuki, Turbulent structure in the vicinity of a roughness element for boundary layer over a k-type rough wall. Trans. JSME Series B 50-458, 2299–2306 (2000)Google Scholar
  46. 46.
    S. Leonardi, P. Orlandi, R.A. Antonia, Properties of d- and k-type roughness in a turbulent channel flow. Phys. Fluids 19, 125101 (2007)CrossRefGoogle Scholar
  47. 47.
    F. Pineau, V.D. Nguyen, J. Dickinson, J. Belanger, Study of flow over a rough surface with passive boundary layer manipulators and direct wall drag measurements. AIAA-87-0357 (1987)Google Scholar
  48. 48.
    Y. Furuya, M. Miyata, H. Fujita, Turbulent boundary layer and flow resistance on plates roughened by wires. J. Fluids Eng. 98, 635–644 (1976)CrossRefGoogle Scholar
  49. 49.
    B.G. Brzek, R.B. Cal, G. Johansson, L. Castillo, Transitionally rough zero pressure gradient turbulent boundary layers. Exp. Fluids 44, 115–124 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.University of NewcastleCallaghanAustralia

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