Abstract
A novel method is proposed that allows accurate estimates of the local wall shear stress from near-wall mean velocity data in fully developed pipe and channel flows. DNS databases are used to demonstrate the accuracy of the method and to provide the reliability requirements on the experimental data.
To demonstrate the applicability of the method, near-wall LDA measurements in turbulent pipe and channel flows were performed. The estimated wall shear stress is shown to be accurate to within 1%. Streamwise mean velocity and turbulence intensity profiles normalized with the wall friction velocity at several Reynolds numbers are presented.
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References
Antonia RA; Teitel M; Kim J; Browne LWB (1992) Low-Reynolds-number effects in a fully developed turbulent channel flow. J Fluid Mech 236: 579–605
Barenblatt GI (1993) Scaling laws for fully developed turbulent shear flows. Part 1. Basic hypotheses and analysis. J Fluid Mech 248: 513–520
Barenblatt GI; Prostokishin VM (1993) Scaling laws for fully developed turbulent shear flows. Part 2. Processing of experimental data. J Fluid Mech 248: 521–529
Bradshaw P; Huang GP (1994) The law of the wall in turbulent flow. Proc. of Osborne Reynolds Centenary Symp., UMIST, Manchester, pp 1–22
Clauser FH (1954) Turbulent boundary layers in adverse pressure gradients. J Aeronaut Sci 21: 91–108
Comte-Bellot G (1963) Contribution à l'étude de la turbulence de conduite. PhD thesis, University Grenoble
Dean RB (1978) Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans ASME, J Fluids Eng 100: 215–223
Djenidi L; Antonia RA (1993) LDA measurements in low Reynolds number turbulent boundary layer. Exp Fluids 14: 280–288
Durst F; Jovanović J; Sender J (1993) Detailed measurements of the near wall region of turbulent pipe flows. Turbulent Shear Flows 9, Springer, Berlin, pp 225–240
Durst F; Martinuzzi R; Sender J; Thevenin D (1992) LDA measurements of mean velocity, rms value, and high-order moments of turbulence intensity fluctuations in flow fields with strong velocity gradients. 6th International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, pp 5.1.1–5.1.6
Eggels JGM; Unger F; Weiss MH; Westerweel J; Adrian RJ; Friedrich R; Nieuwstadt FTM (1994) Fully developed turbulent pipe flow: A comparison between direct numerical simulation and experiment. J Fluid Mech 268: 175–209
Gilbert N; Kleiser L (1991) Turbulence model testing with the aid of direct numerical simulation results. 8th Symp. on Turbulent Shear Flows. Sept. 9–11, TU of Munich, pp 26.1.1–26.1.6
Karlsson RI; Johansson TG (1987) LDV measurements of higher order moments of velocity fluctuations in a turbulent boundary layer. Laser Anemometry in fluid mechanics III (ed. R.J. Adrian), LADOAN Pub Co., Lisabon, Portugal, pp 273–289
Kasagi N; Shikazono N (1994) Contribution of direct numerical simulation to understanding and modelling turbulent transport. Proc. of Osborn Reynolds Centenary Symp., UMIST, Manchester, pp 1–27
Kim J; Moin P; Moser R (1987) Turbulence statistics in fully developed channel flow at low Reynolds number. J Fluid Mech 177: 133–166
Kreid DK (1974) Laser Doppler velocimeter measurements in nonuniform flow: Error estimates. Appl Optics 13: 1872–1881
Kuroda A; Kasagi N; Hirata M (1989) A direct numerical simulation of the fully developed turbulent channel flow. Int. Symp. on Comput. Fluid Dynamics, Nagoya, pp 1174–1179
Kuroda A; Kasagi N; Hirata M (1993) Direct numerical simulation of the turbulent plane Couette-Poiseulle flows: Effect of mean shear on the near wall turbulence structures. 9th Symp. on Turbulent Shear Flows, Kyoto, Japan, Aug. 16–18, pp 8.4.1–8.4.6
Lekavich J (1986) Basics of acousto-optic devices: Acousto-optic beam modulators and deflectors control laser beams in many applications. Lasers Appl, April, pp 59–64
Lekakis I; Durst F; Sender J (1994) LDA measurements in the near-wall region of an axisymmetric sudden expansion. 7th Inter. Symp. on Appl. of Laser Techniques to Fluid Mech, Lisbon, Portugal, S pp 13.6.1–13.6.8
Lumley JL (1970) Stochastic Tools in Turbulence. Academic Press, New York
McLaughlin DK; Tiederman WG (1973) Biasing correction for individual realisation of laser anemometer measurements in turbulent flow. Phys Fluids 16: 2082–2088
Niederschulte MA; Adrian RJ; Hanratty TJ (1990) Measurements of turbulent flow in a channel at low Reynolds numbers. Exp Fluids 9: 222–230
Patel VC; Head MR (1969) Some observations on skin friction and velocity profiles in fully developed pipe and channel flows. J Fluid Mech 38: 181–201
Perry AE; Abell CJ (1975) Scaling laws for pipe flow turbulence. J Fluid Mech 67: 257–271
Polyakov AF; Shindin SA (1983) Some aspects of measuring the structure of non-isothermic turbulence by simultaneous application of DISA's LDA and hot-wire anemometer. DISA Inform 28: 10–14
Spalart PR (1988) Direct simulation of a turbulent boundary layer up to R θ=1410. J Fluid Mech 187: 61–98
Tennekes H; Lumley JL (1972) A first course in turbulence. MIT Press, Cambridge, MA
Wei T; Willmarth WW (1989) Reynolds-number effects on the structure of a turbulent channel flow. J Fluid Mech 204: 57–95
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The current research was funded in part by the European Community under the BRITE-EURAM program, Deutsche Forschungsgemeinschaft (Du 101/16-1,2) and Deutscher Akademischer Austauschdienst. The authors are also grateful to Professors F. Nieuwstadt, N. Kasagi, P. Moin and Drs. J. Kim and N. Gilbert for providing their direct simulation data.
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Durst, F., Kikura, H., Lekakis, I. et al. Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows. Experiments in Fluids 20, 417–428 (1996). https://doi.org/10.1007/BF00189380
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DOI: https://doi.org/10.1007/BF00189380