Boundary Layer Flow Over Long Cylinders With Suction

Abstract

The full, axisymmetric boundary layer equations over a long circular cylinder have been repeatedly solved in the past by a variety of approximate Pohlhausen-type and series expansion methods. These methods are not suitable however, for axisymmetric solutions with wall suction boundary condition. In the present paper, the basic equations are solved by a simple approximate method, based on successive derivatives of the wall compatibility condition. A family of velocity profiles, which coincides with the asymptotic suction profile at infinity, is assumed, and the wall shear force is found by integrating an ordinary differential equation. The computed boundary layer properties for the impermeable (zero-suction) cylinder case are shown to be in good agreement with solutions of other, more sophisticated techniques. The case of an infinite cylinder with constant suction asymptotically approaches the well-known constant thickness boundary layer solution, in analogy with the case of constant suction on a flat plate. The present method is further explored to exhibit the drag reduction properties of wall suction. An optimal suction profile is found, as a function of free stream conditions and the cylinder fineness ratio. For example, in the case of a cylinder fineness ratio 5, and Re = 25 × 106, the flow can be laminarized with only 80 percent of the mass sucked off, relative to uniform suction.