A New Integral Method for Analyzing the Turbulent Boundary Layer With Arbitrary Pressure Gradient

[+] Author and Article Information
F. M. White

University of Rhode Island, Kingston, R. I.

J. Basic Eng 91(3), 371-376 (Sep 01, 1969) (6 pages) doi:10.1115/1.3571122 History: Received August 19, 1968; Online November 03, 2011


For routine calculations of the properties of the incompressible turbulent boundary layer with arbitrary pressure gradient, the presently accepted method is the Karman integral technique, which consists of three simultaneous equations, the three unknowns being the momentum thickness, the skin friction, and the shape factor. Considerable empiricism is contained in the Karman method, so that the reliability is only fair. The present paper derives an entirely new method, based upon a suggestion of R. Brand and L. Persen. The new approach results in a single equation for the skin friction coefficient, with the only parameter being the nominal Reynolds number and the only empiricism being a single assumption about the effect of pressure gradient. No other variables, such as shape factor or momentum thickness, are needed, although they can of course be calculated as byproducts of the analysis. The new method also contains a built-in separation criterion, which was the most glaring omission of the Karman technique. Agreement with experiment is as good or better than the most reliable Karman methods in use today.

Copyright © 1969 by ASME
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