Page 164 - Aerodynamics for Engineering Students

Potential flow 147

Fig. 3.34 Flow at angle of yaw around a body of revolution as the superposition of two flows

Doublei

t
usin a

Fig. 3.35 Cross-flow over slender body of revolution modelled as distribution of doublets

of the cross-flow, as depicted in Fig. 3.35. Slender-body theory will not be
taken further here. The reader is referred to Thwaites and Karamcheti for
further details.*

3.5 Computational (panel) methods

In Section 3.3.7, it was shown how the two-dimensional potential flow around an
oval-shaped contour, the Rankine oval, could be generated by the superposition of
a source and sink on the x axis and a uniform flow. An analogous three-dimensional
flow can also be generated around a Rankine body ~ see Section 3.4.4 above - by
using a point source and sink. Thus it can be demonstrated that the potential flow
around certain bodies can be modelled by placing sources and sinks in the interior of
the body. However, it is only possible to deal with particular cases in this way. It is
possible to model the potential flow around slender bodies or thin aerofoils of any
shape by a distribution of sources lying along the x axis in the interior of the body.
This slender-body theory is discussed in Section 3.4 and the analogous thin-wing
theory is described in Section 4.3. However, calculations based on this theory are
only approximate unless the body is infinitely thin and the slope of the body contour
is very small. Even in this case the theory breaks down if the nose or leading edge is
rounded because there the slope of the contour is infinite. The panel methods
described here model the potential flow around a body by distributing sources over
the body surface. In this way the potential flow around a body of any shape can be

*see Bibliography.