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The aerodynamic efficiency in airfoil theory is defined as the ratio between the lift and drag force, which is the main objective function to be maximized in a wide kind of vehicle design due to its strong relationship between fuel consumption and range. This work employs the 4-digits NACA parameterization, a recently developed 6-parameters method, and the PARSEC technique with a correction of the matrices available in the literature, to compare the computational cost and the ability to achieved higher efficiency of these parameterizations. A genetic algorithm and particle swarm optimization routines are developed and implemented in Matlab, also a sine-cosine algorithm is tested, where Xfoil and the open-source computational fluid dynamic software OpenFOAM are coupled with the optimization algorithms. Finally, a Reynolds number impact study is performed related to the airfoil shape and the angle of attack which maximizes the aerodynamic efficiency. The results showed a faster convergence for the particle swarm optimization and the highest aerodynamic efficiency achieved by the 6-parameter method. Furthermore, with a higher Reynolds number, a higher angle of attack for the optimum lift-to-drag ratio as well a less camber is obtained.

Airfoil Shape Optimization: Comparative Study of Meta-heuristic Algorithms, Airfoil Parameterization Methods and Reynolds Number Impact