Abstract
This work is concerned with the reliable determination of the value of the von Kármán constant for the logarithmic law of the wall. For this purpose, direct measurements of the mean velocity distribution in two-dimensional fully developed turbulent plane-channel flows were carried out. The results obtained were also employed to explain the wide scatter and the discrepancies in the von Kármán constant found in the literature. In addition, the entire set of the current data provides a good basis for assessing questions regarding the scaling of the mean velocity profiles in turbulent channel flows and also to make contributions to answer the question of whether a logarithmic or a power law exists in the overlap region. Data obtained in channel flow, over a wide range of Reynolds numbers, unequivocally support a Reynolds number-independent logarithmic law to describe the overlap region with κ = 0.37 which is very close to κ = 1/e = 0.368 and B = 3.7 for Reτ>2 × 103.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barenblatt, G. I. (1993a). “Scaling laws for fully developed shear flows. Part 1. Basic hypotheses and analysis,” J. Fluid Mech. 248, 513–520.
Barenblatt, G. I. and Chori, A. J. (1993b). “Scaling laws for fully developed shear flows. Part 2. Processing of experimental data,” J. Fluid Mech. 248, 521–529.
Clark, J. A. (1968). “A study of incompressible turbulent boundary layers in channel flow,” ASME Journal of Basic Engineering 90, pp. 455–467.
Clauser, F. H. (1956). “The turbulent boundary layer,” Adv. Appl. Mech. 4, 1–51.
Comte-Bellot, G. (1963). “Turbulent flow between two parallel walls,” PhD thesis (in French) University of Grenoble, (In English as ARC 31609), FM 4102.
Dean, R. B. (1978). “Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow,” ASME J. Fluid Eng. 100, 215–223.
Deissler, R. G. (1955). “Analysis of turbulent heat transfer, mass transfer and friction in smooth tubes at high Prandtl and Schmidt numbers,” NACA Tech. Rep. 1210 (supersedes NACA Tech. Note 3145, 1954).
Durst, F., Zanoun, E. S., Pashtrapanska, M. (2001). “In situ calibration of hot wires close to highly heat-conducting walls,” Exp. Fluids 31, 103–110.
Eggels, J. G. M., Unger, F., Weiss, M. H., Westerweel, J., Adrian, R. J., Friedrich, R., Nieuwstadt, F. T. M. (1994). “Fully developed turbulent pipe flow: A comparison between direct numerical simulation and experiment,” J. Fluid Mech. 268, 175–209.
Fischer, M. (1999). “Turbulente wandgebundene Strömungen bei kleinen Reynoldszahlen” Dissertation, Universität Erlangen Nürnberg.
Gad-el-Hak, M. and Bandyopadhyay, P. R. (1993). “Reynolds number effect on wall-bounded flows,” Appl. Mech. Rev. 47, 307–365.
Goldstik, M. A. and Stern, V. N (1977). “Hydrodynamic laws and turbulence,” Academy of Science of the Soviet Union, Siberian Dep., Institute for Thermal Physics, Novosibirsk, 326–329 (in Russian).
Huffman, G. D. and Bradshaw, P. (1972). “A note on von Karman constant in low Reynolds number turbulent flows,” J. Fluid Mech. 53, 45–60.
Johansson, A. V. and Alfredsson, P. H. (1982) “On the structure of turbulent channel flow,” J. Fluid Mech. 122, 295–314.
Kim, J., Moin, P., Moser, R. (1987). “Turbulence statistics in fully developed channel flow at low Reynolds number,” J. Fluid Mech. 177, 133–166.
Laufer, J. (1954). “Investigation of turbulent flow in a two-dimensional channel,” Report 1053-National Advisory Committee for Aeronautics, 1247–1266.
Loehrke, K. I. and Nagib, H. M. (1972). “Experiments on Management of free-stream turbulence,” AGARD Report No. 598, IIT, Chicago, IL.
Longwell, P. A. (1966). “Mechanics of Fluid Flow,” McGraw-Hill, New York.
Millikan, C. M. (1938). “A critical discussion of turbulent flows in channels and circular tubes,” In Proc. 5th Intl Congress of Appl. Mech., 386–392.
Moser, R. T., Kim, J., Mansour, N. N. (1999). “Direct numerical simulation of turbulent channel flow up to Re τ=590,” Phys. Fluids 11, 943–945.
Nikuradse, J. (1932). “Gesetzmässigkeit der turbulenten Strömung in glatten Rohren,” Forschg. Arb. Ing.-Wes. No. 356.
Österlund, J. M., Johansson, A. V., Nagib, H. M., Hites, M. H. (1999). “Wall shear stress measurements in high Reynolds number boundary layers from two facilities,” 30th AIAA Paper 99-3814, Fluid Dynamics Conference, Norflok, Virginia.
Österlund, J. M., Johansson, A. V., Nagib, H. M., and Hites, M. H. (2000). “A note on the overlap region in turbulent boundary layers,” Phys. Fluids 12, 1–4.
Patel, V. C. and Head, M. R. (1969). “Some observations on skin friction and velocity profiles in fully developed pipe and channel flows,” J. Fluid Mech. 38, 181–201.
Perry, A. E., Hafez, S., Chong, M.S. (2001). “A possible reinterpretation of the Princeton superpipe data,” J. Fluid Mech. 49, 395–401.
Prandtl, L (1925). “Uber die ausgebildete Turbulenz,” Z. angew. Math. Mech., 5, 136.
Prandtl, L. (1932). “Zur turbulenten Str”omung in Rohren und laengs Platten,” Ergeb. Aerodyn. Versuch. Göttingen IV. Lieferung, p. 18.
Reichardt, H. (1951). “Vollständige Darstellung der turbulenten Geschwindigkeitsverteilungen in glatten Leitungen,” Z. Angew. Math. Mech. 31, 208–219.
Spalding, D. B. (1961). “A single formula for the law of the wall,” ASME Journal of Applied Mechanics, 455–458.
Taylor, G. I. (1932). “The transport of vorticity and heat through fluid in turbulent motion,” Proc. Roy. Soc. London, 135, 685–706.
von Kármán, Th. (1930). “Mechanische Aehnlichkeit und Turbulenz,” Nachr. Ges. wiss. Goettingen, p. 68.
Wei, T. and Willmarth, W. W., (1989). “Reynolds number effects on the structures of a turbulent channel flow,” J. Fluid Mech. 204, 57–95.
Wosnik, M., Castillo, L., George, W. (2000). “A theory for turbulent pipe and channel flows,” J. Fluid Mech. 421, 115–145.
Zagarola, M. V., Smits, A. J. (1998). “Mean-flow scaling of turbulent flow,” J. Fluid Mech. 373, 33–79.
Zanoun, E. S., Nagib, H., Durst F., Monkewitz, P. (2002). “Higher Reynolds number channel data and their comparison to recent asymptotic theory,” 40th AIAA-1102, Aerospace Sciences Meeting, Reno.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Durst, F., Zanoun, E.S., Nagib, H. (2004). The Mean Velocity Profile of Two-Dimensional Fully Developed Turbulent Plane-Channel Flows. In: Smits, A.J. (eds) IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow. Fluid Mechanics and its Applications, vol 74. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0997-3_22
Download citation
DOI: https://doi.org/10.1007/978-94-007-0997-3_22
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3763-1
Online ISBN: 978-94-007-0997-3
eBook Packages: Springer Book Archive