Vortex and source rings

Emmanuel Simon Pierre Branlard

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review

Abstract

The velocity field, vector potential and velocity gradient of a vortex ring is derived in this chapter. The Biot-Savart law for the vector potential and velocity is expressed in a first section. Then, the flow is derived at specific locations: on the axis, near the axis and in the far field where the analogy to a doublet field is made. The following section derive the value of the vector potential and velocity field in the full domain. The expression for the velocity gradient is also provided since it may be relevant in a simulation with vortex particles and vortex rings. Most of this chapter is dedicated to vortex rings. Source rings are only briefly mentioned.
Original languageEnglish
Title of host publicationWind Turbine Aerodynamics and Vorticity-Based Methods
Number of pages10
Volume7
PublisherSpringer
Publication date2017
Pages419-428
Chapter35
ISBN (Print)978-3-319-55163-0
ISBN (Electronic)978-3-319-55164-7
DOIs
Publication statusPublished - 2017
SeriesResearch Topics in Wind Energy
ISSN2196-7806

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