Hostname: page-component-7bb8b95d7b-2h6rp Total loading time: 0 Render date: 2024-09-12T14:39:03.109Z Has data issue: false hasContentIssue false

Pohlhausen's Method for Three-Dimensional Laminar Boundary Layers

Published online by Cambridge University Press:  07 June 2016

J. C. Cooke*
Affiliation:
University of Malaya
Get access

Summary

Wild has extended to three dimensions the von Kármán-Pohlhausen method for the laminar boundary layer flow over a fixed obstacle and used the method for an infinite yawed elliptic cylinder in a stream. In this paper the method is tested in two ways (which may be called full-Pohlhausen and semi-Pohlhausen) for the case of an infinite yawed cylinder when the velocity outside the boundary layer over the surface normal to the generators is of the form U=cxm. The exact solution is known in this case.

A table of the skin friction, displacement thickness and momentum thickness is given for various values of β [=2m/(m + 1)], and the agreement is found to be fairly good for β>0 (accelerated flow) but not so good for β<0 (retarded flow).)

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1951

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Wild, J. M. (1949). The Boundary Layer of Yawed Infinite Wings. Journal of the Aeronautical Sciences, Vol. 16, January 1949, p. 41.Google Scholar
2. Cooke, I. C. (1950). The Boundary Layer of a Class of Infinite Yawed Cylinders. Proc. Camb. Phil. Soc, Vol. 46, p. 645, 1950.Google Scholar
3. Tetervin, N. (1947). Boundary-Layer Momentum Equations for Three-Dimensional Flow. N.A.C.A. T.N. No. 1479, October 1947.Google Scholar
4. Howarth, L. (1934). On the Calculation of Steady Flow in the Boundary Layer in the Surface of a Cylinder in a Stream. R. & M. 1632, July 1934.Google Scholar
5. Edited by Goldstein, S. (1938). Modern Developments in Fluid Dynamics, Vol. I, Oxford, 1938.Google Scholar
6. Falkner, V. M. and Skan, S. W. (1930). Some Approximate Solutions of the Boundary Layer Equations. R. & M. 1314, April 1930.Google Scholar
7. Falkner, V. M. and Skan, S. W. (1931). Solution of the Boundary Layer Equations. Phil. Mag. 12 (Seventh Series), 1931, p. 865.Google Scholar
8. Hartree, D. R. (1937). On an Equation Occurring in Falkner and Skan's Approximate Treatment of the Equations of the Boundary Layer. Proc. Camb. Phil. Soc, Vol. 33, No. 2, 1937, p. 223.CrossRefGoogle Scholar
9. Edited by Von Mises, R. and Von Karman, T.H. (1948). Advances in Applied Mechanics. Academic Press, New York, 1948, p. 18.Google Scholar
10. Prandtl, L. (1946). On Boundary Layers in Three-Dimensional Flow. R. & T. No. 64, M.A.P. Volkenröde Report, May 1946.Google Scholar
11. Carrier, G. F. (1947). The Boundary Layer in a Corner. Quarterly of Applied Mathematics, Vol. IV., No. 4, January 1947, p. 367.CrossRefGoogle Scholar
12. Taylor, G. I. (1950). The Boundary Layer in the Converging Nozzle of a Swirl Atomiser. Quarterly Journal of Mechanics and Applied Mathematics, Vol. III., Part 2, June 1950, p. 129.CrossRefGoogle Scholar
13. Binnie, A. M. and Harris, D. P. (1950). The Application of Boundary Layer Theory to Swirling Liquid Flow through a Nozzle. Quarterly Journal of Mechanics and Applied Mathematics, Vol. III., Part I, March 1950, p. 89.CrossRefGoogle Scholar