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Path optimization of flapping airfoils based on unsteady viscous flow solutions

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2008
Kaya, Mustafa
The flapping path of a single airfoil and dual airfoils in a biplane configuration is optimized for maximum thrust and/or propulsive efficiency. Unsteady, low speed viscous flows are computed using a Navier-Stokes solver in a parallel computing environment. A gradient based algorithm and Response Surface Methodology (RSM) are employed for optimization. The evaluation of gradient vector components and the design of experiments for RSM, which require unsteady solutions, are also carried out in parallel. Parallel computations are performed using Parallel Virtual Machine (PVM) library. First, a single airfoil undergoing a combined sinusoidal or non-sinusoidal pitching and plunging motion is studied. The non-sinusoidal flapping motion is described using an elliptic curve or Non-Uniform Rational B-Splines (NURBS). It is shown that the thrust generation may significantly be increased in comparison to the sinusoidal flapping motion. For a high thrust, the airfoil stays at high effective angle of attack values during the upstroke and the downstroke, and the effective pitching occurs at minimum and maximum plunge positions. Secondly, the optimization of sinusoidal and non-sinusoidal flapping paths of dual airfoils is considered. Moving and deforming overset grids are used for computations. The deforming overset grids remove the restrictions on the flapping motion, and improve the optimization results obtained earlier. At low flapping frequencies, an airfoil in a biplane configuration produces more thrust than a single airfoil. Yet, at high frequencies the airfoil in biplane configuration produces less thrust at a significantly lower efficiency than the single airfoil.