Abstract
The current chapter presents the expressions of different analytical two-dimensional flows: uniform flow, point source, point vortex, continuous distribution of points, periodic point vortices, doublet, multipole, cylinder flow (cyclic/acyclic, i.e. with or without circulation), ellipse and quadric, rigid rotation and corner flow. For most of the flows, the following quantities are provided: the complex velocity and potential, the scalar potential and stream function and the velocity in polar and Cartesian coordinates. These elementary flows are essential for the implementation and validation of two-dimensional vortex methods. The solutions can be used to validate two-dimensional panel codes. General results from 2D potential flow theory are presented in Sect. 2.10. Conformal maps are introduced in Sect. 2.11.
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Notes
- 1.
The factor \(\pi \) appears here only as a convention for the definition of a doublet intensity \(\mu \).
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Branlard, E. (2017). Elementary Two-Dimensional Potential Flows. In: Wind Turbine Aerodynamics and Vorticity-Based Methods. Research Topics in Wind Energy, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-55164-7_32
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DOI: https://doi.org/10.1007/978-3-319-55164-7_32
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