About singularities at angular points of a trailing edge under the Joukowskii–Kutta Condition
✍ Scribed by Sergueï A. Nazarov
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 225 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0170-4214
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✦ Synopsis
The linear problem for the velocity potential around a slightly curved thin finite wing is considered under the Joukowskii-Kutta hypothesis. The exponents of possible singularities of solutions at angular points on wing's trailing edge are expressed in terms of eigenvalues of mixed boundary value problems for the Beltrami-Laplace operator on the hemisphere and the semicircle. These singularities have a structure such that the circulation function turns out to be continuous in interior angular points of the trailing edge. In the case of trapezoidal shape of the wing ends there occur square-root singularities of the velocity field at the trailing edge endpoints and the same singularities, of course, are extended along the lateral sides of the wake behind the wing. It is proved that for any angular point on the trailing edge the exponents of all above-mentioned singularities form a countable set in the upper complex half-plane with the only accumulation point at infinity.