FLOW AROUND A CYLINDER

In this chapter we will analyse in more detail the irrotational flow field around a cylinder due to a uniform flow.

The cylinder is a bluff body while a wing that is well oriented with respect to flow is a slender body. In reality (in the sense of a real viscous fluid) separation of the boundary layer with the formation of a wake will be unavoidable for the cylinder. The irrotational solution cannot handle such phenomena and the resulting flow field does not resemble the real flow around a cylinder.

So why do we study the irrotational flow around a cylinder? First because it is a good example of an irrotational flow in a relatively complex geometry. Second, and most important, because using conformal mapping we can transform the flow around a cylinder into the flow around a Joukowski wing.

If a wing profile is well oriented (small angle of attack) with respect to the uniform flow, boundary layer separation is negligible and the pressure field obtained by means of the irrotational flow solution can be considered as a good approximation of the actual pressure field. Therefore the resulting lift is in good agreement with experimental measurements.

In the following sections several animations show how the velocity and pressure fields vary as the circulation around the cylinder is changed. A sequential browsing of these pages is suggested, at least for first time visitors.

Stream function	Smoke lines	Velocity field	Pressure field	Forces on the body