A variational approach for the dynamics of unsteady point vortices with application to impulsively started aerofoil

Ahmed Hussein, Haithem E. Taha, Saad Ragab, Muhammad R. Hajj

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

A Lagrangian formulation for the dynamics of unsteady point vortices is introduced and implemented. The proposed Lagrangian is related to previously constructed Lagrangian of point vortices via a gauge-symmetry in the case of vortices of constant strengths; i.e., they yield the exact same dynamics. However, a different dynamics is obtained in the case of unsteady point vortices. The resulting Euler-Lagrange equation derived from the principle of least action exactly matches the Brown-Michael evolution equation for unsteady point vortices, which was derived from a completely different point of view; based on conservation of linear momentum. The resulting dynamic model of time-varying vortices is applied to the problem of an impulsively started flat plate. The resulting lift coefficient using the dynamics of the proposed Lagrangian is compared to that using previously constructed Lagrangian and other models in literature.

Original languageEnglish
Title of host publication2018 Applied Aerodynamics Conference
DOIs
StatePublished - 2018
Event36th AIAA Applied Aerodynamics Conference, 2018 - [state] GA, United States
Duration: 25 Jun 201829 Jun 2018

Publication series

Name2018 Applied Aerodynamics Conference

Conference

Conference36th AIAA Applied Aerodynamics Conference, 2018
Country/TerritoryUnited States
City[state] GA
Period25/06/1829/06/18

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