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The flat plate trailing edge problem

Published online by Cambridge University Press:  29 March 2006

Frank E. Talke and
Stanley A. Berger
Frank E. Talke
Affiliation:
University of California at BerkeleyPresent address: IBM Research Laboratory, San Jose, California.
Stanley A. Berger
Affiliation:
University of California at Berkeley
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Abstract

The trailing edge region of a finite flat plate in laminar, incompressible flow is examined for the limit of high Reynolds numbers.

It is shown that the trailing edge region is an elliptic region of O(R−¾) and therefore a correct mathematical description must be based upon the full Navier–Stokes equations.

The ‘method of series truncation’ is used to reduce the full Navier–Stokes equations, written in parabolic co-ordinates, to an infinite set of non-linear, coupled, ordinary differential equations. Two sets of asymptotic boundary conditions, called simplified and exact boundary conditions, are determined by matching the Navier–Stokes region downstream with Goldstein's near wake solution.

By numerical integration the solutions for the first and second truncations are obtained for both sets of asymptotic boundary conditions. The results confirm that the size of the trailing edge region is of O(R−¾).

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 40 , Issue 1 , 14 January 1970, pp. 161 - 189
Copyright
© 1970 Cambridge University Press

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