The asymptotic theory of boundary-layer flow with suction part 1 the theory of similar velocity distributions part 2 flow with uniform suction part 3 flow with variation of suction velocity

Abstract

General Summary.--The subject of this report is the steady two-dimensional flow of a boundary layer over a permeable surface through which the fluid is withdrawn at a known rate of suction. This rate of suction is assumed, in accordance with the hypotheses of the boundary layer, to be small compared with the stream velocity, and of order R (to the minus 0.5) where R is the Reynolds number. It is supposed here that the suction is relatively large, though still of the same order. Part I deals with the similar solutions of the boundary-layer equations, Part II with an arbitrary pressure distribution but constant suction velocity, and Part III with the general problem. Thus the results of Parts I and II can be obtained from Part III, but they are of interest in themselves. Attempts are made in both Parts I and II to find when separation occurs, but only rough estimates can be made as the series do not converge well. In Part II the theory is applied to the flow over a porous circular cylinder in a uniform stream, and also to the use of suction round the nose of an aerofoil to prevent stalling at high incidence. The only previous work on this approach appears to be a report by Pretsch, which according to Mangler contains a study of the similar profiles on the same lines as Part I. The report by Pretsch has not been examined, and it is therefore not known if his results agree with those given here. A special case of Part I is in course of publication.