Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-23T02:28:03.697Z Has data issue: false hasContentIssue false

Numerical studies of the laminar boundary layer for Mach numbers up to 15

Published online by Cambridge University Press:  29 March 2006

Henry A. Fitzhugh
Affiliation:
Department of Aeronautics, Imperial College, London University Present address: Research Division, McDonnell Douglas Corporation, St Louis, Missouri, U.S.A.

Abstract

A comprehensive set of exact solutions to the first-order boundary-layer equations has been computed using the finite difference computer programme of Sells, with and without wall cooling. The effects of Prandtl number, wall cooling and Mach number on separation point location were studied. Values of displacement thickness, skin friction coefficient and Stanton number are displayed graphically for the supersonic flow over a circular concave arc, for a subsonic cooled cylinder and for the case of a linearly retarded velocity distribution. The influence of pressure gradient on recovery factor was studied. Velocity and temperature profiles are shown for four cold wall cases. The exact computer results show the errors in many of the more approximate methods available for the case where Ue = U(1 - X/L). The importance of second-order effects and the applicability of a first-order solution are discussed briefly.

Type
Research Article
Copyright
© 1969 Cambridge University Press

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

Adams, J. C. 1967 Higher order boundary layer effects on analytic bodies of revolution. ARO, Inc. Arnold Air Force Station, Tennessee.Google Scholar
Clutter, D. W. & Smith, A. M. O. 1963 Solutions of the general boundary layer equations for compressible laminar flow, including transverse curvature. Douglas Aircraft Co. Dept. LB 31088.Google Scholar
Cohen, C. B. & Reshotko, E. 1956 The compressible laminar boundary layer with heat transfer and arbitrary pressure gradient. NACA Rep. 1294.Google Scholar
Cooke, J. C. & Mangler, K. W. 1967 The numerical solution of the laminar boundary layer equations for an ideal gas in two and three dimensions. RAE Tech. Memo AERO 999.Google Scholar
Gadd, G. E. 1957 A review of theoretical work relevant to the problem of heat transfer effects on laminar separation ARC CP 331.Google Scholar
Head, M. R. & Hayasi, N. 1967 Approximate calculation of the incompressible laminar boundary layer Aero. Quarterly, 18, 259.Google Scholar
Lewis, C. H. 1967 First- and second-order boundary layer effects at hypersonic conditions. ARO, Inc. Arnold Air Force Station, Tennessee.Google Scholar
Luxton, R. E. & Young, A. D. 1962 Generalised methods for calculation of the laminar compressible boundary layer characteristics with heat transfer and non-uniform pressure distribution. Aero Res. Counc. R. & M. no. 3233.Google Scholar
Monaghan, R. J. 1961 Effects of heat transfer on laminar boundary layer development under pressure gradients in compressible flow. Aero. Res. Counc. R. & M. no. 3218.Google Scholar
Morduchow, M. 1965 Review of theoretical investigations on effect of heat transfer on laminar separation AIAA J. 3, 1377.Google Scholar
Sells, C. C. L. 1966 Two-dimensional laminar compressible boundary layer programme for a perfect gas. RAE TR 66243.Google Scholar
Stewartson, K. 1964 The Theory of Laminar Boundary Layers in Compressible Fluids. Oxford: Clarendon.
Terrill, R. M. 1960 Laminar boundary layer flow near separation with and without suction. Phil. Trans. A 253, 55.Google Scholar