| Résumé | Analyses of Wake Vortex formation and downstream development have been conducted, using mutual field induction calculations of the shed vorticity sheet. In order to illustrate and compare the formation and downstream development of wingtip vortices, the analyses were conducted for two widely-different cases of spanwise distribution of bound-vorticity. Termed inboard and outboard distributions, the loadings were nearly triangular and rectangular, respectively. For development analysis, Biot-Savart field calculations were conducted for the induced velocity field, and hence displacement of the elements of the shed vorticity sheet. Although an induced field calculation does not represent all fluid-element forces (in particular, the expansion pressure field) and thus, might over-estimate core radius for example), the comparative calculations provided results of interest, regarding the properties of developed wingtip vortices, such as core radius, span location, core asymmetry and peak velocity location. Following this and with reference to the NRC flight measurements of small, intense vortex elements with peaks greater than potential vortex peaks, centrifugal stability analysis is conducted, using a number of models: (1) the developed vortices for the outboard loading case were stimulated with, and released from, radial forcing; (2) a physical model of the centrifugal balance between inertia and pressure forces was examined by time-wise solution of the equations of elemental equations of motion, and (3) the Euler equations in axisymmetric, cylindrical coordinate form were numerically, spatiotemporally solved for excess-velocity vortex profiles. An example of resultant radial flow behaviour is compared to flight data. © 2012 by The Crown in Right of Canada. Published by the American Institute of Aeronautics and Astronautics, Inc. |
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