The Steady Circulatory Flow about a Circular Cylinder with Uniformly Distributed Suction at the Surface

Abstract

Summary and ConclusionsExact solutions for the steady circulatory flow about a circular cylinder with suction applied at its surface have been obtained for the following cases: — (a)the cylinder at rest and a circulation at infinity,(b)the cylinder rotating and zero circulation at infinity,(c)the cylinder rotating in either direction with a circulation at infinity,provided that, in general, the suction velocity is greater than a certain limiting value.There is a particular case of (c) when the circulation at the cylinder equals that at infinity in magnitude and direction, for which the circulation is constant at all radii, for all values of R—presumably for blowing as well as suction.The addition of a uniform stream parallel to the cylinder axis does not affect the circulatory motion, and the solution for the combined flow, which is exact, has some practical interest in that it demonstrates that the boundary layer on a long, circular, rotating boss can be kept thin and that the circulatory motion outside the boundary layer can be prevented by the suitable application of suction before starting the rotation.The flow (a) is important in connection with the withdrawal of the Thwaites flap. The existence of steady state solutions, coupled with the arguments of Section 5.2, make it appear highly probable that a wing employing this device will retain its lift indefinitely, when the flap is withdrawn.For high rates of suction flow, the flows exhibit the characteristics of boundary layer flows, in that the vorticity is confined to a narrow annulus enveloping the cylinder and the velocity distribution near the wall tends to the well-known asymptotic distribution of Griffith and Meredith.It would be interesting to investigate these flows experimentally and to examine the stability of the laminar flow under suction conditions.The analysis throughout is simple and expressions are obtained for the velocity distribution, the stresses, the vorticity and the torque, and so on.