Nonsinusoidal path optimization of a flapping airfoil

Kaya, Mustafa
Tuncer, İsmail Hakkı
The path of a flapping airfoil undergoing a combined, nonsinusoidal pitching and plunging motion is optimized for maximum thrust and/or propulsive efficiency. The nonsinusoidal, periodic flapping motion is described using nonuniform rational B splines. A gradient based algorithm is then employed for the optimization of the nonuniform rational B-spline parameters. Unsteady, low speed laminar flows are computed using a Navier-Stokes solver in a parallel computing environment. The numerical evaluation of the gradient vector components, which requires unsteady flow solutions, is also performed in parallel. It is shown that the thrust generation may significantly be increased in comparison to the sinusoidal flapping motion. For a maximum thrust generation, the airfoil stays at about a constant angle of attack during the upstroke and the downstroke, and may reach very high effective angle of attack values. The pitching motion mostly occurs at the minimum and maximum plunge positions.


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Flapping motion parameters of airfoils in a biplane configuration are optimized for maximum thrust and/or propulsive efficiency. Unsteady, viscous flowfields over airfoils flapping in a combined plunge and pitch are computed with a parallel flow solver on moving and deforming overset grids. The amplitudes of the sinusoidal pitch and plunge motions and the phase shift between them are optimized for a range of flapping frequencies. A gradient-based optimization algorithm is implemented in a parallel computing...
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Citation Formats
M. Kaya and İ. H. Tuncer, “Nonsinusoidal path optimization of a flapping airfoil,” AIAA JOURNAL, pp. 2075–2082, 2007, Accessed: 00, 2020. [Online]. Available: