Abstract
This chapter derives the expressions of the analytical velocity field and gradient (with or without regularization/mollification) for the following elementary three-dimensional flows: point source, vortex point (vortex blobs/vortex particles), vortex segments of constant and linearly varying strengths and dipoles. Reference to multi-poles, constant source panels, and constant vorticity panels are given. The velocity fields are determined by application of the Biot–Savart law. Different regularization functions are used and gradients of the regularized fields are also provided. Such equations are relevant for the implementation of grid-free vortex methods as presented in Part VII and used in different applications of Part V.
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Branlard, E. (2017). Elementary Three-Dimensional 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_31
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DOI: https://doi.org/10.1007/978-3-319-55164-7_31
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