Comparison of Shape Optimization Techniques Coupled with Genetic Algorithm for a Wind Turbine Airfoil

Abstract

Airfoil optimization is an important subject for wind turbines in order to increase the flow efficiency along the blade sections. The first important subject for airfoil shape optimization is the mathematical description of airfoil or its parametrical form. This subject directly effects computational cost of the optimization process and general efficiency of the airfoil. In this study, NACA 2411 airfoil has been optimized by a genetic algorithm coupled with an airfoil analysis software. Geometry of the airfoil is represented by two different airfoil shape parameterization techniques namely; PARSEC method (parametric section) and CST method (class/shape function transformation). The objective of this study is to find the best airfoil representation scheme which consumes less computational effort and gives the best lift to drag ratio in a large design space for the ideal aerodynamic design optimization. In order to generate different airfoil shapes and control the genetic algorithm, Matlab subroutines were developed in accordance with different airfoil parameterization schemes mentioned above. These airfoil shapes are used as individuals for the genetic algorithm. A Matlab script was embedded into the code that calls the potential flow solver software (XFOIL) to analyze the flow around the airfoils. Fitness function of each individual is specified as "lift to drag ratio" obtained by the flow analysis. The aim of the optimization process is to find the unique airfoil shape which gives the maximum of the lift to drag ratios in a certain solution space. The flow is assumed to be inviscid and uniform for the sake of simplicity. Mach number, Reynolds number and design lift coefficient are chosen as 0.03, 350,000 and 1, respectively. Tournament selection method is used to select the individuals which have high fitness values for the next generation. The genetic operators; cross-over and mutation rates are chosen as 0.45 and 0.1 respectively. The code can be executed until a pre-defined number of iterations or a certain convergence criteria is obtained. In the study, population and generation numbers are chosen as 8 and 200 respectively. Fitness increment with respect to generation is plotted in order to evaluate the results. The results for each shape function are compared in terms of sensitivity to the optimized geometry and computational cost. Design spaces for each parameterization method were balanced by changing the design parameters so that the control areas on the specified curves were similar. Hence, parameterization schemes are compared with respect to the CPU time, the number of scheme parameters and the best fitness values achieved by the analysis code. The results have showed that the final geometry obtained by CST method is superior to the geometry obtained by PARSEC parameterization method for the specified flow conditions.