TY - GEN
T1 - A variational approach for the dynamics of unsteady point vortices with application to impulsively started aerofoil
AU - Hussein, Ahmed
AU - Taha, Haithem E.
AU - Ragab, Saad
AU - Hajj, Muhammad R.
N1 - Publisher Copyright:
© 2018, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
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U2 - 10.2514/6.2018-3172
DO - 10.2514/6.2018-3172
M3 - Conference contribution
AN - SCOPUS:85051719641
SN - 9781624105593
T3 - 2018 Applied Aerodynamics Conference
BT - 2018 Applied Aerodynamics Conference
T2 - 36th AIAA Applied Aerodynamics Conference, 2018
Y2 - 25 June 2018 through 29 June 2018
ER -