Turbulent Boundary Layer Flows Above a Porous Surface Subject to Flow Injection
Publication: Journal of Engineering Mechanics
Volume 132, Issue 10
Abstract
A new analytical expression for velocity profile in a fully developed turbulent boundary layer above a porous surface subject to flow injection is derived by solving the coupled Reynolds equations and turbulent kinetic energy equation. The advection of turbulent kinetic energy is considered during the derivation, whereas the earlier studies have neglected it. The new solution reduces to the universal logarithmic law in the case of no flow injection. For the small injection, the solution can be expanded into a series form in terms of the normalized injection velocity. The leading order terms are found to be equivalent to those in the earlier works in which the advection of turbulent kinetic energy has been neglected in the derivation. The new solution can provide more accurate prediction of bed shear stress for a wide range of flow injection rate, fluid type (e.g., from air to water), and surface roughness. On the other hand, the earlier theories may significantly underestimate bed shear stress under high injection rates.
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Acknowledgments
The study was supported, in part, by research grants provided by the National University of Singapore (Grant Nos. UNSPECIFIEDR-264-000-136-112 and UNSPECIFIEDR-264-000-182-112) and ONR Grant No. ONRN00014-01-1-0457.
References
Bradshaw, P., Ferriss, D. H., and Atwell, N. P. (1967). “Calculation of boundary-layer development using the turbulent energy equation.” J. Fluid Mech., 28(3), 593–616.
Cebeci, T., and Smith, A. M. O. (1974). Analysis of turbulent boundary layers, Academic, New York.
Cheng, N.-S., and Chiew, Y.-M. (1998). “Modified logarithmic law for velocity distribution subjected to upward seepage.” J. Hydraul. Eng., 124(12), 1235–1241.
Karunarathna, S. A. S. A. (2005). “A numerical study of wave interaction with porous media.” Ph.D. thesis, National Univ. of Singapore, Singapore.
Schlichting, H. (1979). Boundary layer theory, 7th Ed., McGraw–Hill, New York.
Simpson, R. L. (1967). “The turbulent boundary layer on a porous plate: An experimental study of the fluid dynamics with injection and suction.” Ph.D. thesis, Stanford Univ., Stanford, Calif.
Spalding, D. B. (1977). GENMIX: A general computer program for two-dimensional parabolic phenomena, Pergamon, Oxford, U.K.
Stevenson, T. N. (1963). “A law of the wall for turbulent boundary layers with suction or injection.” Cranfield Rep. Aero. No. 166, The College of Aeronautics, Cranfield, England, U.K.
Townsend, A. A. (1956). The structure of turbulent shear flow, Cambridge University Press, Cambridge, U.K.
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© 2006 ASCE.
History
Received: Sep 28, 2004
Accepted: Feb 7, 2006
Published online: Oct 1, 2006
Published in print: Oct 2006
Notes
Note. Associate Editor: Michelle H. Teng
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