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- Title
Self-Induced Velocity of a Vortex Ring Using Straight-Line Segmentation.
- Authors
Bhagwat, Mahendra J.; Leishman, J. Gordon
- Abstract
The accuracy of discretized induced velocity calculations that can be obtained using straight-line vortex elements has been reexamined, primarily using the velocity field induced by a vortex ring as a reference. The induced velocity of a potential (inviscid) vortex ring is singular at the vortex ring itself. Analytical results were found by using a small azimuthal cutoff in the Biot-Savart integral over the vortex ring and showed that the singularity is logarithmic in the cutoff. Discrete numerical calculations showed the same behavior, with the self-induced velocity exhibiting a logarithmic singularity with respect to the discretization, which introduces an inherent cutoff in the Biot-Savart integral. Core regularization or desingularization can also eliminate the singularity by using an assumed "viscous" core model. Analytical approximations to the self-induced velocity of a thin-cored vortex ring have shown that the self-induced velocity has a logarithmic singularity in the core radius. It is further shown that the numerical calculations require special treatment of the self-induced velocity caused by curvature, which is lost by the inherent cutoff in the straight-line discretization, to correctly recover this logarithmic singularity in the core radius. Numerical solution using straight-line vortex segmentation, augmented with curved vortex elements only for the self-induced velocity calculation, is shown to be second-order accurate in the discretization.
- Subjects
VORTEX motion; INVISCID flow; BIOT-Savart law; VELOCITY; LOGARITHMIC functions
- Publication
Journal of the American Helicopter Society, 2014, Vol 59, p1
- ISSN
0002-8711
- Publication type
Article
- DOI
10.4050/JAHS.59.012004