- Bliss, Donald B. and Miller, Wayne O., Efficient free wake calculations using analytical/numerical matching,
Journal of the American Helicopter Society, vol. 38 no. 2
pp. 43 - 52 .
(last updated on 2007/04/09)
A hybrid analytical and numerical method called analytical/numerical matching is used to calculate the velocity field of rotor wake vortex filaments. A simple discretization of the Biot-Savart law is used to obtain an efficient but low order numerical calculation of the velocity field. An artificially large vortex core is introduced and the discretized velocity field is calculated accurately for a smooth large core filament. At points close to the filament, a local analytical correction is applied to correct for the near-field velocity associated with the physical vortex core size. Because this correction is infrequently applied, the overall approach is both efficient and accurate. Closed analytical expressions for the analytical/numerical matching velocity derivatives were obtained, resulting in a linearized form of the method. The accuracy of the analytical/numerical matching method is studied in detail for vortex rings. Several tip vortex rotor free wake solutions are obtained using the linear and fully nonlinear analytical/numerical matching methods, and are compared to another method having comparably high accuracy.
Numerical methods;Vortex flow;Aerodynamics;Wakes;Mathematical models;Nonlinear equations;