Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T01:44:11.167Z Has data issue: false hasContentIssue false
  • English
  • Français

Measurement of wall shear stress in turbulent boundary layers subject to strong pressure gradients

Published online by Cambridge University Press:  21 April 2006

F. Hirt  and
H. Thomann
F. Hirt
Affiliation:
Institut für Aerodynamik, Swiss Federal Institute of Technology, Zurich, Switzerland Present address: Eidgenössisches Flugzeugwerk Emmen, CH-6032 Emmen, Switzerland.
H. Thomann
Affiliation:
Institut für Aerodynamik, Swiss Federal Institute of Technology, Zurich, Switzerland
Get access Rights & Permissions [Opens in a new window]

Abstract

Measurements of the wall shear stress with a floating element and with Preston tubes were conducted in turbulent boundary layers. Sudden application and removal of adverse pressure gradients resulted in boundary layers far from equilibrium. Positive and negative errors of the Preston-tube results were observed for adverse pressure gradients. The negative errors occurred mainly in regions with dτw/dx > 0. The relation between the error, the pressure gradient and the tube size (1.1) suggested by Frei & Thomann (1980) predicts only positive errors for dp/dx > 0. Therefore, it cannot be used for the present pressure distributions and is not as general as was expected. The present results show that indirect methods to determine the wall shear stress should not extend beyond y+ - 3 if accuracies of ± 1% are required for pressure distributions similar to the ones used in the present investigation. Predictions from Ludwieg & Tillmann's relation (4.21) agree to within ± 10% with the present measurements. The Preston-tube readings indicate velocities below the law of the wall in regions with a decreasing adverse pressure gradient. No local parameters could be found that correlated the errors of the Preston-tube results for the large pressure gradients used in the present investigation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 171 , October 1986 , pp. 547 - 562
Copyright
© 1986 Cambridge University Press

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

Brown, K. C. & Joubert P. N.1969 The measurement of skin friction in turbulent boundary layers with adverse pressure gradients. J. Fluid Mech. 35, 737–757.Google Scholar
Clauser F. H.1954 Turbulent boundary layers in adverse pressure gradients. J. Aero. Sci. 21, 91–108.Google Scholar
Coles D.1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.Google Scholar
Coles, D. & Hirst E. A.1968 AFOSR-IFP Stanford Conf. on Turbulent Boundary Layer Prediction, vol. 2.
Fernholz H.1964 Halbempirische Gesetze zur Berechnung turbulenter Grenzschichten nach der Methode der Integralbedingungen. Ing. Archiv 33, 384–395.Google Scholar
Frei, D. & Thomann H.1980 Direct measurements of skin friction in a turbulent boundary layer with a strong adverse pressure gradient. J. Fluid Mech. 101, 79–95.Google Scholar
Hinze J. O.1959 Turbulence. McGraw-Hill.
Hirt F.1984 Anzeige des Prestonrohres im Druck-gradient. Diss. ETH Nr. 7531.Google Scholar
Hirt F., Zurfluh, U. & Thomann H.1986 Skin friction balances for strong pressure gradients. Experiments in Fluids 4, 296–300.Google Scholar
Kader, B. A. & Yaglom A. M.1978 Similarity treatment of moving-equilibrium turbulent boundary layers in adverse pressure gradients. J. Fluid Mech. 89, 305–342.Google Scholar
Ludwieg, H. & Tillmann W.1949 Untersuchungen überdie Wandschubspannung in turbulenten Reibungsschichten. Ing. Archiv 17, 228–299.Google Scholar
Mcdonald H.1969 The effect of pressure gradient on the law of the wall in turbulent flow. J. Fluid Mech. 35, 311–336.Google Scholar
Mcmillan A. F.1956 Experiments on pitot tubes in shear flow. ARC R & M, no. 3028.
Mellor, G. L. & Gibson D. M.1966 Equilibrium turbulent boundary layers. J. Fluid Mech. 24, 225–253.Google Scholar
Patel V. C.1965 Calibration of the Preston tube and limitations on its use in pressure gradients. J. Fluid Mech. 23, 185–208.Google Scholar
Perry A. E., Bell, J. B. & Joubert P. N.1966 Velocity and temperature profiles in adverse pressure gradient turbulent boundary layers. J. Fluid Mech. 25, 299–320.Google Scholar
Pozzorini R.1976 Das turbulente Strömungsfeld in einem langen Kreiskegel Diffusor. Diss. ETH, nr. 5646.
Preston J. H.1954 The determination of turbulent skin friction by means of Pitot tubes. J. R. Aeron. Soc. 58, 109–121.Google Scholar
Schofield W. H.1981 Equilibrium boundary layers in moderate to strong adverse pressure gradients. J. Fluid Mech. 113, 91–122.Google Scholar
Simpson R. L., Strickland, J. H. & Barr P. W.1977 Features of a separating turbulent boundary layer in the vicinity of separation. J. Fluid Mech. 79, 553–594.Google Scholar
Smits, A. J. & Wood D. H.1985 The response of turbulent boundary layers to sudden perturbations. Ann. Rev. Fluid Mech. 17, 321–358.Google Scholar
Stratford B. S.1959 An experimental flow with zero skin friction throughout its region of pressure rise. J. Fluid Mech. 5, 17–35.Google Scholar
Townsend A. A.1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97–120.Google Scholar
Yaglom A. M.1979 Similarity laws for constant-pressure and pressure-gradient turbulent wall flows. Ann. Rev. Fluid Mech. 11, 505–540.Google Scholar
Zurfluh U. E.1984 Experimentelle Bestimmung der Wandschubspannung in turbulenten Grenzschichten. Diss. ETH Nr. 7528.