Stagnation Points for a lifting circular cylinder

The stagnation points we saw in Fig. 4.33 are for the case when the circulation imposed on the cylinder was such that $\Gamma < 4 \pi U_\infty a$. But from Eqn. 4.131 it is evident that angle $\beta$, hence the position of the stagnation points is a strong function of circulation, $\Gamma$. This is illustrated in Fig.4.34. With zero circulation the stagnation points lie at $\theta$ = o, $2 \pi$. As circulation $\Gamma$ increases the stagnation points move (upwards or downwards depending upon the direction of rotation). When $\Gamma = 4 \pi U_\infty a$ they coincide at $\theta$ = $\frac{\pi}{2}$ or $\theta$ = - $\frac{\pi}{2}$. If circulation is further increased the stagnation point will no longer be found on the cylinder surface, but will appear in the flow as shown in D in Fig. 4.34.

Figure 4.34: Effect of circulation on flow about a cylinder

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney