Airfoil shape optimization using improved simple genetic algorithm (ISGA)

Abstract

Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.

To study the efficiency of genetic algorithms (GAs) in the optimization of aerodynamic shapes, the shape of an airfoil was optimized by a genetic algorithm to obtain maximum lift to drag ratio and maximum lift. The flow field is assumed to be two dimensional, Invicsid, transonic and is analyzed numerically. The camber line and thickness distribution of the airfoil were modeled by a fourth order polynomial. The airfoil chord length was assumed constant. Also, proper boundary conditions were applied. A finite volume method using the first order Roe’s flux approximation and time marching (explicit) method was used for the flow analysis. The simple genetic algorithm (SGA) was used for optimization. This algorithm could find the optimum point of this problem in an acceptable time frame. Results show that the GA could find the optimum point by examining only less than 0.1% of the total possible cases. Meanwhile, effects of parameters of GA such as population size in each generation, mutation probability and crossover probability on accuracy and speed of convergence of this SGA were studied. These parameters have very small effects on the accuracy of the genetic algorithm, but they have a sensible effect on speed of convergence. The parameters of this genetic algorithm were improved to obtain the minimum run time of optimization procedure and to maximize the speed of convergence of this genetic algorithm. Robustness and efficiency of this algorithm in optimizing the shape of the airfoils were shown. Also, by finding the optimum values of its parameters, maximum speed and minimum run time was obtained. It is shown that for engineering purposes, the speed of GAs is incredibly high, and acceptable results are sought by a fairly low number of generations of computations.