Lifting Flow over a Circular Cylinder

When a doublet flow is superimposed on a uniform flow, the combined flow fields can be visualized as possible flow pattern over a circular cylinder. In addition, both lift and drag force are zero for such flows. However, there are other possible flow patterns around a circular cylinder resulting non-zero lift. Such lifting flows are discussed here.

Consider the flow synthesized by addition of the non-lifting flow over a cylinder and a vortex of strength as shown in Fig. 3.8.1. The stream function of for a circular cylinder of radius R is given by the following equation.

(3.8.1)

Fig. 3.8.1: Superposition of non-lifting flow over a cylinder and a vortex.

As discussed in the previous lecture, different values of R can be obtained by assigning the various values of doublet strength and uniform free stream velocity to synthesize the flow over a circular cylinder. Now, the stream function for a vortex of strength may be written as,

(3.8.2)

Since is any arbitrary constant, it can be replaced with in the Eq. (3.8.2). The resulting stream function for the flow pattern is given by the sum of the stream functions, i.e.

(3.8.3)

The streamlines expressed by Eq. (3.8.3), represents the equation of a circle of radius R. A special case will arise that will represent the flow over a circular cylinder when . If then for all values of θ. The velocity fields can be obtained by differentiating Eq. (3.8.3) i.e.

(3.8.4)