Experiments in Fluids

, 47:1045 | Cite as

Determination of skin friction in strong pressure-gradient equilibrium and near-equilibrium turbulent boundary layers

Research Article


The conventional Clauser-chart method for determination of local skin friction in zero or weak pressure-gradient turbulent boundary layer flows fails entirely in strong pressure-gradient situations. This failure occurs due to the large departure of the mean velocity profile from the universal logarithmic law upon which the conventional Clauser-chart method is based. It is possible to extend this method, even for strong pressure-gradient situations involving equilibrium or near-equilibrium turbulent boundary layers by making use of the so-called non-universal logarithmic laws. These non-universal log laws depend on the local strength of the pressure gradient and may be regarded as perturbations of the universal log law. The present paper shows that the modified Clauser-chart method, so developed, yields quite satisfactory results in terms of estimation of local skin friction in strongly accelerated or retarded equilibrium and near-equilibrium turbulent boundary layers that are not very close to relaminarization or separation.


  1. Aubertine CD, Eaton JK (2005) Turbulence development in a non-equilibrium turbulent boundary layer with mild adverse pressure gradient. J Fluid Mech 532:345–365MATHCrossRefGoogle Scholar
  2. Bradshaw P, Ferriss DH (1965) The response of a retarded equilibrium turbulent boundary layer to the sudden removal of pressure gradient. NPL Aero Report 1145Google Scholar
  3. Brereton GJ (1989) Deduction of skin friction by Clauser technique in unsteady turbulent boundary layers. Exp Fluids 7:422–424CrossRefGoogle Scholar
  4. Buschmann MH, Gad-el-hak M (2003) Generalized logarithmic law and its consequences. AIAA J 41(1):40–48CrossRefGoogle Scholar
  5. Chauhan KA, Nagib HM, Monkewitz PA (2007) Evidence on non-universality of Kármán constant. In: Proceedings of iTi conference in Turbulence 2005, Springer, Proceedings in Physics, Progress in turbulence II, Part IV:159–163Google Scholar
  6. Clauser FH (1954) Turbulent boundary layers in adverse pressure gradients. J Aeronaut Sci 21:91–108Google Scholar
  7. Clauser FH (1956) The turbulent boundary layer. Adv Appl Mech 4:1–51CrossRefGoogle Scholar
  8. Coles DE (1968) The young person’s guide to the data. In: Coles DE, Hirst EA (eds) Proceedings of AFOSR-IFP-STANFORD conference on computation of turbulent boundary layers, vol IIGoogle Scholar
  9. Dixit SA, Ramesh ON (2008) Pressure-gradient-dependent logarithmic laws in sink flow turbulent boundary layers. J Fluid Mech 615:445–475MATHCrossRefMathSciNetGoogle Scholar
  10. Erm LP, Joubert PN (1991) Low-Reynolds-number turbulent boundary layers. J Fluid Mech 230:1–44CrossRefGoogle Scholar
  11. Fernholz HH (2006) The role of skin-friction measurements in boundary layers with variable pressure gradients. In: Meier GEA, Sreenivasan KR (eds) IUTAM symposium on One Hundred Years of Boundary Layer Research, SpringerGoogle Scholar
  12. Fernholz HH, Warnack D (1998) The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer Part 1. The turbulent boundary layer. J Fluid Mech 359:329–356MATHCrossRefGoogle Scholar
  13. Fernholz HH, Janke G, Schober M, Wagner PM, Warnack D (1996) New developments and applications of skin-friction measuring techniques. Meas Sci Technol 7:1396–1409CrossRefGoogle Scholar
  14. Herring HJ, Norbury JF (1967) Some experiments on equilibrium turbulent boundary layers in favourable pressure gradients. J Fluid Mech 27:541–549CrossRefGoogle Scholar
  15. Jones MB, Marusic I, Perry AE (2001) Evolution and structure of sink flow turbulent boundary layers. J Fluid Mech 428:1–27MATHCrossRefGoogle Scholar
  16. Kendall A, Koochesfahani M (2008) A method for estimating wall friction in turbulent wall-bounded flows. Exp Fluids 44:773–780CrossRefGoogle Scholar
  17. MacMillan FA (1956) Experiments on Pitot-tubes in shear flow. ARC London R&M 3028Google Scholar
  18. McKeon BJ, Li J, Jiang W, Morrison JF, Smits AJ (2004) Further observations on the mean velocity distribution in fully developed pipe flow. J Fluid Mech 501:135–147MATHCrossRefGoogle Scholar
  19. Millikan CB (1938) A critical discussion of turbulent flows in channels and circular tubes. In: den Hartog JP, Peters H (eds) Proceedings of 5th international congress on applied mechanics, Wiley/Chapman & Hall, pp 386–392Google Scholar
  20. Musker AJ (1979) Explicit expression for the smooth wall velocity distribution in a turbulent boundary layer. AIAA J 17(6):655–657MATHCrossRefGoogle Scholar
  21. Nagib HM, Chauhan KA (2008) Variations of von Kármán coefficient in canonical flows. Phy Fluids 20: Article no. 101518Google Scholar
  22. Nickels TB (2004) Inner scaling for wall-bounded flows subject to large pressure gradients. J Fluid Mech 521:217–239MATHCrossRefMathSciNetGoogle Scholar
  23. Österlund JM (1999) Experimental studies of zero pressure-gradient turbulent boundary layer flow. PhD thesis, Department of Mechanics, Royal Institute of Technology, KTH, StockholmGoogle Scholar
  24. Österlund JM, Johansson AV, Nagib HM, Hites MH (2000) A note on the overlap region in turbulent boundary layers. Phy Fluids 12: No.1 (Letters section)Google Scholar
  25. Patel VC (1965) Calibration of the Preston tube and limitations on its use in pressure gradients. J Fluid Mech 23:185–208CrossRefGoogle Scholar
  26. Patel VC, Head MR (1968) Reversion of turbulent to laminar flow. J Fluid Mech 34:371–392CrossRefGoogle Scholar
  27. Rotta JC (1962) Turbulent boundary layers in incompressible flow. Prog Aeronaut Sci 2:1–220CrossRefGoogle Scholar
  28. Skåre PE, Krogstad PÅ (1994) A turbulent equilibrium boundary layer near separation. J Fluid Mech 272:319–348CrossRefGoogle Scholar
  29. Skote M, Henningson DS, Henkes RAWM (1998) Direct numerical simulation of self-similar turbulent boundary layers in adverse pressure gradients. Flow Turbul Combust 60:47–85MATHCrossRefGoogle Scholar
  30. Spalart PR, Leonard A (1986) Direct numerical simulation of equilibrium turbulent boundary layers. In: Durst J et al (eds) Turbulent shear flows, vol 5. Springer, BerlinGoogle Scholar
  31. Spalart PR, Watmuff JH (1993) Experimental and numerical study of a turbulent boundary layer with pressure gradients. J Fluid Mech 249:337–371CrossRefGoogle Scholar
  32. Townsend AA (1976) The structure of turbulent shear flow, 2nd edn. Cambridge University Press, UKMATHGoogle Scholar
  33. Wei T, Schmidt R, McMurtry P (2005) Comment on the Clauser chart method for determining the friction velocity. Exp Fluids 38:695–699CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia

Personalised recommendations