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Laminar airfoil shape optimization using an improved genetic algorithm

Mazaheri, K ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.2514/6.2008-913
  3. Publisher: 2008
  4. Abstract:
  5. To study efficiency of the genetic algorithms (GAs) in optimization of aerodynamic shapes, shape of an airfoil is optimized by a genetic algorithm to obtain maximum lift to drag ratio and maximum lift. The flow field is assumed to be two dimensional, viscous, and transonic and is analyzed numerically. The camber line and thickness distribution of the airfoil are modeled by a fourth order polynomial. The airfoil chord length is assumed constant. Also, proper boundary conditions are applied. A finite volume method using the first order Roe's flux approximation and time marching (explicit) method is used for flow analysis. The simple genetic algorithm (SGA) is used for optimization. This algorithm can 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 are 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 are 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 are shown. Also, by finding the optimum values of its parameters, maximum speed and minimum run time is obtained. It is shown that for engineering purposes, the speed of GAs is fairly high, and acceptable results are sought by a fairly low number of generations of computations. Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc
  6. Keywords:
  7. Aerodynamic shape ; Airfoil chord ; Airfoil shape optimization ; Cross-over probability ; First order ; Flow analysis ; Fourth order polynomial ; Improved genetic algorithms ; Lift to drag ratio ; Maximum speed ; Mutation probability ; Optimization procedures ; Optimum value ; Population sizes ; Runtimes ; Simple genetic algorithm ; Speed of convergence ; Thickness distributions ; Time frame ; Time marching ; Aerodynamic drag ; Aerospace engineering ; Airfoils ; Flight dynamics ; Genetic algorithms ; Lift ; Lift drag ratio ; Parameter estimation ; Population statistics ; Shape optimization ; Speed ; Convergence of numerical methods
  8. Source: 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 7 January 2008 through 10 January 2008 ; Jun , 2008 ; 9781563479373 (ISBN)
  9. URL: https://arc.aiaa.org/doi/10.2514/6.2008-913