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RESEARCH PAPERS

A Simple Theory for the Two-Dimensional Compressible Turbulent Boundary Layer

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

University of Rhode Island, Kingston, R. I.

G. H. Christoph

Mechanical Engineering and Applied Mechanics, University of Rhode Island, Kingston, R. I.

J. Basic Eng 94(3), 636-642 (Sep 01, 1972) (7 pages) doi:10.1115/1.3425519 History: Received December 07, 1971; Online October 27, 2010

Abstract

A new approach is proposed for analyzing the compressible turbulent boundary layer with arbitrary pressure gradient. Utilizing a compressible law-of-the-wall and a Crocco energy approximation, the new theory integrates the momentum equation across the boundary layer in terms of inner variables only. The result is a single first-order ordinary differential equation for skin friction, devoid of integral thicknesses and shape factors. When analyzed for flat plate flow, this new equation has an exact solution apparently superior in accuracy to any other flat plate theory (Table 1). The new equation also agrees well with supersonic skin friction data in both favorable and adverse pressure gradients. The new theory contains an explicit separation criterion and is the simplest and possibly most accurate existing analysis for compressible turbulent flow.

Copyright © 1972 by ASME
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