Page 231 - Aerodynamics for Engineering Students

21 4 Aerodynamics for Engineering Students

Fig. 5.4 The simplified horseshoe vortex

Study of the completely equivalent vortex system is largely confined to investigat-
ing wing effects in close proximity to the wing. For estimation of distant phenomena
the system is simplified to a single bound vortex and trailing pair, known as the
simplified horseshoe vortex (Fig. 5.4). This is dealt with in Section 5.3, before the more
involved and complete theoretical treatments of wing aerodynamics.

5.2 Laws of vortex motion

The theoretical modelling of the flow around wings was discussed in the previous
section. There the use of an equivalent vortex system to model the lifting effects of
a wing was described. In order to use this theoretical model to obtain quantitative
predictions of the aerodynamic characteristics of a wing it is necessary first to study
the laws of vortex motion. These laws also act as a guide for understanding how
modern computationally based wing theories may be developed.
In the analysis of the point vortex (Chapter 3) it was considered to be a string of
rotating particles surrounded by fluid at large moving irrotationally under the
influence of the rotating particles. Further, the flow investigation was confined to
a plane section normal to the length or axis of the vortex. A more general definition is
that a vortex is a flow system in which a finite area in a normal section plane contains
vorticity. Figure 5.5 shows the section area S of a vortex so called because S possesses
vorticity. The axis of the vortex (or of the vorticity, or spin) is clearly always normal

Fig. 5.5 The vorticity of a section of vortex tube