Airfoil shape optimization using improved simple genetic algorithm (ISGA)

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.cs201

Aerodynamic shape optimization of natural laminar flow (NLF) airfoils via discrete adjoint approach

In this research the γ-Rẽ_θt transition model is combined with the k-ω SST turbulence model to predict the transition region for a laminar-turbulent boundary layer and redesign the geometry to achieve lower skin friction drag coefficients. The present work addresses several modifications necessary for a robust transition model and investigates the accuracy of the model for a wide range of angles of attack and Reynolds numbers. The transition model is employed to predict the transition locations and an assessment of the various transition mechanisms, Reynolds number effects, sectional characteristics, and aerodynamic performance for two subsonic airfoils are presented with comparisons to experimental data and numerical solutions. Discrete adjoint equations for the transition and turbulence models are derived and implemented into the design framework. The adjoint-based optimization procedure is employed to optimize the S809 wind turbine profile and NLF(1)-0416 airfoil to postpone the onset of transition and extend the natural laminar region of the transitional flow for minimizing the total drag, while maintaining the lift, or maximizing the lift-to-drag ratio. The obtained results demonstrate the ability of the developed optimization framework to design new natural laminar flow airfoils.Dans cette recherche, le modele de transition γ-Rẽ_θt est combine avec le modele de turbulence k-ω SST afin de predire la transition vers le regime turbulent et d'obtenir des formes aerodynamiques au frottement visqueux minimal. Nous presentons les modifications necessaires a l'amelioration de la robustesse du modele de transition et etudions la precision du modele pour une large gamme d'angles d'attaque et de nombres de Reynolds. Le modele de transition est utilise pour predire le point de transition, pour evaluer les mecanismes de transition ainsi que les differents effets relies au nombre de Reynolds, et pour etudier les caracteristiques et les performances aerodynamique de deux profils aerodynamiques. Des comparaisons avec des donnees experimentales et des solutions numeriques sont presentees. Les equations adjointes discretes des modeles de transition et de turbulence sont derivees et employees dans un processus d'optimization. Cette procedure d'optimisation est utilisee pour modifier le profil d'eolienne S809 et le profil NLF(1)-0416 afin de retarder la transition et d'etendre la zone laminaire de l'ecoulement, de minimiser le coefficient de trainee totale tout en maintenant la portance, ou de maximiser la finesse aerodynamique. Les resultats obtenus demontrent la capacite du processus d'optimisation developpe} a concevoir de nouveaux profils ecoulement laminaire naturel