A variational approach for the dynamics of unsteady point vortices

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

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

Abstract

A Lagrangian formulation for the dynamics of unsteady point vortices is proposed. This Lagrangian is shown to be equivalent to the previously constructed Lagrangian in terms of yielding exact same dynamics for vortices of constant strength. However, different dynamics is obtained in the case of unsteady point vortices. The resulting Euler-Lagrange equation derived from the principle of least action based on the proposed Lagrangian exactly matches the Brown-Michael evolution equation for unsteady point vortices, which was derived from a completely different point of view that was based on conservation of linear momentum. The resulting dynamic model of time-varying vortices is applied to two cases of unsteady point vortices, namely the starting vortex and the vortex generated by a pitching flat plate. Validation of the results of the proposed Lagrangian are determined by comparing resulting aerodynamic coefficients with those of other models and experiments.

Original languageEnglish
Title of host publication17th International Forum on Aeroelasticity and Structural Dynamics, IFASD 2017
ISBN (Electronic)9788897576280
DOIs
StatePublished - 2017
Event17th International Forum on Aeroelasticity and Structural Dynamics, IFASD 2017 - Como, Italy
Duration: 25 Jun 201728 Jun 2017

Publication series

Name17th International Forum on Aeroelasticity and Structural Dynamics, IFASD 2017
Volume2017-June

Conference

Conference17th International Forum on Aeroelasticity and Structural Dynamics, IFASD 2017
Country/TerritoryItaly
CityComo
Period25/06/1728/06/17

Keywords

  • Lagrangian Approach
  • Pitching Airfoil
  • Starting Vortex
  • Unsteady Aerodynamics
  • Vortex Dynamics

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