On Persen theory of two dimensional turbulent boundary layer

• Autorzy: Mazumdar H. P. , Mandal B. C.
• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to the examination of Persen's theory of two dimensional turbulent boundary layers over a smooth flat plate in the light of recent measurements by Österlund. In Persen's approach, the zero-pressure gradient turbulent boundary layer may be divided into two regions only, e.g., I) the inner region, wherein an universally valid structure prevails and modified Spalding's formula is applicable and II) the outer region, which can be described within a similarity framework by a wake law due to Persen. It is shown that the establishment of the theory depends on an experimentally supported relation between the non-dimensional velocity at the end point of the boundary layer and the corresponding non-dimensional distance from the wall. The solution to the problem is achieved by another relation between this velocity and the momentum thickness Reynolds number. The coefficients of skin-friction and velocity profiles, as obtained here for a range of high Reynolds numbers, are found to be in good agreement with Österlund's data. Finally, the results are discussed in the light of the applicability of Österlund's experimental data to the verification of Persen's turbulent boundary layer theory.

Słowa kluczowe

EN

turbulent boundary layer; law of the wall; law of the wake; oil-film interferometry; momentum thickness Reynolds number and skin friction coefficient

PL

prawo wyniku; liczba Reynoldsa

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2009
• Tom: Vol. 14, no 4
• Strony: 1009--1028
• Opis fizyczny: Bibliogr. 15 poz., wykr.

Twórcy

autor

Mazumdar H. P.

autor

Mandal B. C.

• Indian Statistical Institute 203 B. T. Road, Kolkata-700108, INDIA,

Bibliografia

• Barenblatt G.I., Chorin A.J., Hald O. and Prostokishin V.M. (1997): Structure of the zero pressure gradient turbulent boundary layer. - Proc. Natl. Acad. Sci. USA, vol.94, pp.7817-7819.
• Buschman M.H. and Gad-El-Hak M. (2003): Debate concerning the mean velocity profile of a turbulent boundary layer. - AAIJ, vol.41, No.4, pp.565-572.
• Coles D.E. (1956): The law of the wake in the turbulent boundary layer. - J. Fluid Mech., vol.1, pp.191-226.
• Coles D.E. (1968): Young Person's guide to the data. - Proc. AFSOR-IFP- Stanford conf. on computation of Turbulent Boundary Layers, edited by D.E. Coles and E.A. Hirst, vol.2, Thermo Sc. Div., Dept. of Mech. Eng., Stanford Univ., Palo Alto, CA, pp.1-45.
• George K.W. (2006): Recent advancements toward the understanding of turbulent boundary layers. - AIAA Journal, vol.44, No.11, pp.2435-2449.
• Laufer J. (1954): The structure of turbulence in fully developed pipe flow. - Report 1174, National Advisory Committee of Aeronautics, Washington, DC.
• Nezu I. and Rodi W.A. (1986): Open-channel flow measurements with a laser doppler anemometer. - J. Hyd. Eng., ASCE, vol.112, No.5, pp.335-355.
• Österlund J.M. (1999): Experimental studies of zero pressure - gradient turbulent boundary layer flow. - Ph. D. Thesis, Royal Institute of Technology, Stockholm, Sweden.
• Persen L.N. (1974): The turbulent boundary layer and the closure problem. - Proc. AGARD Conf. on Turbulent Boundary Layer - Experiments, Theory and Modelling. pp.17-1 to 17-14.
• Persen L.N. (1976): An examination of the law of the wake in a turbulent boundary layer. - Proceedings from the Theodorsen Colloquium, Universitetsforlaget.
• Persen L.N. (1999): An Examination of Compressible Boundary Layer Data Based on Data from AGARDOGRAPHS 223 & 253". Calcutta Math. Soc.
• Schlichting H (1955): Boundary-layer theory. - New York: lst. Edn. Mc.Graw - Hill.
• Spalding D.B. (1961): A single formula for the law of the wall. - J. Appl. Mech., vol.28, Ser.E., pp.455-458.
• Zagarola M.V. (1996): Mean flow scaling of turbulent pipe flow. - Ph.D Dissertation, Department of Mechanical and Aerospace Engineering, Princeton Univ., Princeton, N.J.
• Zanoun E.S., Durst F. and Nagib H. (2003): Evaluating the law of the wall in two dimensional fully developed turbulent channel flows. - Physics of Fluids, vol.15, No.10, pp.3079-3089.