Page 287 - Aerodynamics for Engineering Students

Finite wing theory 269

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Fig. 5.45 A schematic view of the vortex breakdown over a slender delta wing, showing both the
axisymmetric and spiral forms

5.8 Computational (panel) methods for wings

The application of the panel method described in Sections 3.5 and 4.10 above, to
whole aircraft leads to additional problems and complexities. For example, it can be
difficult to define the trailing edge precisely at the wing-tips and roots. In some more
unconventional lifting-body configurations there may well be more widespread
difficulties in identifying a trailing edge for the purposes of applying the Kutta
condition. In most conventional aircraft configurations, however, it is a relatively
straightforward matter to divide the aircraft into lifting and non-lifting portions -
see Fig. 5.46. This allows most of the difficulties to be readily overcome and
the computation of whole-aircraft aerodynamics is now routine in the aircraft
industry.
In Section 4.10, the bound vorticity was modelled by means of either internal or
surface vortex panels, see Fig. 4.22. Analogous methods have been used for the three-
dimensional wings. There are, however, certain difficulties in using vortex panels.
For example, it can often be difficult to avoid violating Helmholtz's theorem (see
Section 5.2.1) when constructing vortex panelling. For this and other reasons most
modern methods are based on source and doublet distributions. Such methods have
a firm theoretical basis since Eqn (3.89b) can be generalized to lifting flows to read

where n denotes the local normal to the surface and ~7 and p are the source and
doublet strengths respectively.