Approximate calculations of the laminar boundary layer with suction, with particular reference to the suction requirements for boundary-layer stability on aerofoils of different thickness/chord ratios

Abstract

1. General Introduction.--In an earlier report an account was given of an approximate method for calculating the incompressible laminar boundary layer in two dimensions. Application of the method to the various cases for which exact (or nearly exact) solutions were available gave results which were in all cases in very satisfactory agreement with the accepted solutions. The accuracy of the method (essentially a development of one given earlier by Wieghardt), evidently resulted from satisfying both the momentum and energy integral equations of the boundary layer, together with the first compatibility condition at the surface. The doubly-infinite family of velocity profiles used in the method was obtained by a numerical procedure which gave a very much wider range of physically acceptable profiles than could be achieved by the use of simple analytic expressions (e.g., polynomials). In the present paper the approximate method just referred to has been applied to the class of problems for which it was specifically devised, namely problems where suction (or blowing) is applied through the surface. In Part I solutions are given for the following cases: (a) Flat plate with uniform suction and sinusoidal variation of external velocity (b) Flat plate with intermittent suction (c) Suction applied following the normal separation point to maintain a zero skin-friction layer for the flow U = 1 - x (d) Flat plate with uniform blowing. In Part II results are given of comprehensive calculations for a series of aerofoils with related pressure distributions. The distributions of suction required to maintain neutral stability of the boundary layer are given as functions of thickness/chord ratio and Reynolds number. The effect of Mach number is also inferred on certain simplifying assumptions.