Experiments in Fluids

, Volume 51, Issue 2, pp 313–326 | Cite as

Turbulence in rough-wall boundary layers: universality issues

Research Article

Abstract

Wind tunnel measurements of turbulent boundary layers over three-dimensional rough surfaces have been carried out to determine the critical roughness height beyond which the roughness affects the turbulence characteristics of the entire boundary layer. Experiments were performed on three types of surfaces, consisting of an urban type surface with square random height elements, a diamond-pattern wire mesh and a sand-paper type grit. The measurements were carried out over a momentum thickness Reynolds number (Re θ) range of 1,300–28,000 using two-component Laser Doppler anemometry (LDA) and hot-wire anemometry (HWA). A wide range of the ratio of roughness element height h to boundary layer thickness δ was covered (\(0.04 \leq h/\delta \leq 0.40\)). The results confirm that the mean profiles for all the surfaces collapse well in velocity defect form up to surprisingly large values of h/δ, perhaps as large as 0.2, but with a somewhat larger outer layer wake strength than for smooth-wall flows, as previously found. At lower h/δ, at least up to 0.15, the Reynolds stresses for all surfaces show good agreement throughout the boundary layer, collapsing with smooth-wall results outside the near-wall region. With increasing h/δ, however, the turbulence above the near-wall region is gradually modified until the entire flow is affected. Quadrant analysis confirms that changes in the rough-wall boundary layers certainly exist but are confined to the near-wall region at low h/δ; for h/δ beyond about 0.2 the quadrant events show that the structural changes extend throughout much of the boundary layer. Taken together, the data suggest that above h/δ ≈ 0.15, the details of the roughness have a weak effect on how quickly (with rising h/δ) the turbulence structure in the outer flow ceases to conform to the classical boundary layer behaviour. The present results provide support for Townsend’s wall similarity hypothesis at low h/δ and also suggest that a single critical roughness height beyond which it fails does not exist. For fully rough flows, the data also confirm that mean flow and turbulence quantities are essentially independent of Re θ; all the Reynolds stresses match those of smooth-wall flows at very high Re θ. Nonetheless, there is a noticeable increase in stress contributions from strong sweep events in the near-wall region, even at quite low h/δ.

Notes

Acknowledgments

The authors are grateful to the UK’s Engineering & Physical Sciences Research Council, who provided funding for this work under grant number EP/D036771, and to staff in the School of Engineering Sciences’ workshop, who provided willing and excellent technical support throughout the experimental programme. We also thank Paul Hayden of the University of Surrey for his valuable support with the EnFlo software used for all our data collection and Karen Flack, Per-Åge Krogstad, Jonathan Morrison and David Birch for helpful discussions.

References

  1. Bergstrom DJ, Akinlade OG, Tachie MF (2005) Skin friction correlation for smooth and rough wall turbulent boundary layers. ASME J Fluids Eng 127:1146–1153CrossRefGoogle Scholar
  2. Bhaganagar K, Kim J, Coleman GN (2004) Effect of roughness on wall-bounded turbulence. Flow Turb Comb 72:463–492MATHCrossRefGoogle Scholar
  3. Birch DM, Morrison JF (2010) Similarity of the streamwise velocity component in very-rough-wall channel flow. J Fluid Mech 668:174–201Google Scholar
  4. Castro IP (2007) Rough-wall boundary layers: mean flow universality. J Fluid Mech 585:469–485MATHCrossRefGoogle Scholar
  5. Cheng H, Castro IP (2002) Near-wall flow over urban-type roughness. Boundary Layer Meteorol 104:229–259CrossRefGoogle Scholar
  6. Coles DE (1987) Coherent structures in turbulent boundary layers. In: Meier HU, Bradshaw P (eds) Perspectives in turbulence studies. Springer, Berlin, pp 93–114Google Scholar
  7. Connelly JS, Schultz MP, Flack KA (2006) Velocity defect scaling for turbulent boundary layers with a range of relative roughness. Exp Fluids 40:188–195CrossRefGoogle Scholar
  8. Erm LP, Joubert PN (1991) Low Reynolds number turbulent boundary layers. J Fluid Mech 230:1–44CrossRefGoogle Scholar
  9. Fernholz HH, Finley PJ (1996) The incompressible zero-pressure gradient turbulent boundary layer: an assessment of the data. Prog Aerosp Sci 32:245–311CrossRefGoogle Scholar
  10. Flack KA, Schultz MP, Connelly JS (2007) Examination of critical roughness height for outer layer similarity. Phys Fluids 19:095104Google Scholar
  11. Flack KA, Schultz MP, Shapiro TA (2005) Experimental support for Townsend’s Reynolds number similarity hypothesis on rough walls. Phys Fluids 17:035102CrossRefGoogle Scholar
  12. Grass AJ (1971) Statistical features of turbulent flow over smooth and rough boundaries. J Fluid Mech 50:233–255CrossRefGoogle Scholar
  13. Kline SJ, Reynolds WC, Schraub FA, Rundstadler PW (1967) The structure of turbulent boundary layers. J Fluid Mech 30:741–773CrossRefGoogle Scholar
  14. Krogstad P-A, Antonia RA, Browne LWB (1992) Comparison between rough- and smooth-wall turbulent boundary layers. J Fluid Mech 245:599–617CrossRefGoogle Scholar
  15. Krogstad P-A, Antonia R (1999) Surface roughness effects in turbulent boundary layers. Exp Fluids 27:450–460CrossRefGoogle Scholar
  16. Krogstad P-A, Andersson HI, Bakkem OM, Ashrafian A (2005) An experimental and numerical study of channel flow with rough walls. J Fluid Mech 530:327–352MATHCrossRefGoogle Scholar
  17. Kunkel GJ, Marusic I (2006) Study of the near-wall turbulent region of the high Reynolds number boundary layer using an atmospheric flow. J Fluid Mech 548:375–402CrossRefGoogle Scholar
  18. Jackson PS (1981) On the displacement height in the logarithmic velocity profile. J Fluid Mech 111:15–25MATHCrossRefGoogle Scholar
  19. Jiménez J (2004) Turbulent flows over rough walls. Ann Rev Fluid Mech 36:173–196CrossRefGoogle Scholar
  20. Leonardi S, Castro IP (2010) Channel flow over large cube roughness: a direct numerical simulation study. J Fluid Mech 651:519–539MATHCrossRefGoogle Scholar
  21. Leonardi S, Orlandi P, Smalley RJ, Djenidi L, Antonia RA (2003) Direct numerical simulations of turbulent channel flow with transverse square bars on one wall. J Fluid Mech 491:229–238MATHCrossRefGoogle Scholar
  22. Lu SS, Willmarth WW (1973) Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J Fluid Mech 60:481–511CrossRefGoogle Scholar
  23. Perry AE, Li JD (1990) Experimental support for the attached eddy hypothesis in zero-pressure gradient turbulent boundary layers. J Fluid Mech 218:405–438CrossRefGoogle Scholar
  24. Perry AE, Lim KL, Henbest SM (1987) An experimental study of the turbulence structure in smooth and wough wall turbulent boundary layers. J Fluid Mech 177:437–466CrossRefGoogle Scholar
  25. Raupach MR (1981) Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers. J Fluid Mech 108:362–382CrossRefGoogle Scholar
  26. Raupach MR, Antonia RA, Rajagopalan S (1991) Rough-wall turbulent boundary layers. Appl Mech Rev 44:1–25CrossRefGoogle Scholar
  27. Reynolds RT, Hayden P, Castro IP, Robins AG (2007) Spanwise variations in nominally two-dimensional rough-wall boundary layers. Exp Fluids 42:311–320CrossRefGoogle Scholar
  28. Reynolds RT, Castro IP (2008) Measurements in an urban-type boundary layer. Exp Fluids 45:141–156CrossRefGoogle Scholar
  29. Rotta JC (1962) The calculation of the turbulent boundary layer. Prog Aeronaut Sci 2:1–219CrossRefGoogle Scholar
  30. Schultz MS, Flack K (2007) The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime. J Fluid Mech 580:381–405MATHCrossRefGoogle Scholar
  31. Schultz MP, Volino RJ, Flack KA (2010) Boundary layer structure over a two-dimensional rough wall. In: Nickels T (ed) Proc. of IUTAM symposium on the physics of flow over rough walls. SpringerGoogle Scholar
  32. Tachie MF, Bergstrom DJ, Balachandar R (2000) Rough wall turbulent boundary layers in shallow open channel flow. J Fluids Eng 122:533–541CrossRefGoogle Scholar
  33. Tutu N, Chevray R (1975) Cross-wire anemometry in high-intensity turbulence. J Fluid Mech 71:785–800CrossRefGoogle Scholar
  34. Townsend AA (1976) The structure of turbulent shear flow, 2nd ed. CUP, p 429Google Scholar
  35. Volino RJ, Schultz MP, Flack KA (2009) Turbulence structure in a boundary layer with two-dimensional roughness. J Fluid Mech 635:75–101MATHCrossRefGoogle Scholar
  36. Wallace JM, Eckelmann H, Brodkey RS (1972) The wall region in turbulent shear flow. J Fluid Mech 54:39–48CrossRefGoogle Scholar
  37. Wallace JM, Brodkey RS (1977) Reynolds stress and joint probability density distributions in the u-v plane of a turbulent channel flow. Phys Fluids 20:251–355CrossRefGoogle Scholar
  38. Wei T, Schmidt R, McMurty P (2005) Comment on the Clauser chart method for determining the friction velocity. Exp Fluids 38:695–699CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.School of Engineering SciencesUniversity of SouthamptonHighfieldUK
  2. 2.Department of EngineeringUniversity of AberdeenAberdeenUK

Personalised recommendations