HE EFFECTS OF OBJECTIVE FUNCTION COMPUTATION METHOD ON DESIGN OPTIMIZATION OF TRANSONIC AIRFOILS USING ENHANCED GENETIC ALGORITHM

One of the fundamental problems in aerodynamic shape optimization with Genetic Algorithm (GA) and numerical flow solution is the computational time required to obtain the optimum airfoil. This is mainly due to the large number of flow solution calls that contributes the majority of the total computational time in an optimization process. In transonic flows the computational cost will further increase due to the existence of shock wave and flow instabilities especially when the fitness function is calculated by solving full Navier Stokes equations. Thus, one simple idea could be using the inviscid flow solution instead of viscous flow one. Thus, the purpose of the present paper is to study the effects of the flow viscosity on the optimum airfoil and investigate the possibility of using inviscid flow solution for objective function calculation instead of expensive viscous solver. The modified PARSEC parameterization method is used for airfoil shape modeling that is able to generate airfoils with divergent trailing edge suitable for viscous flow calculations. The linear and torsional spring analogy are used simultaneously for moving computational grids. The optimization process used an adaptive range Genetic Algorithm for obtaining the optimum geometry in the less number of generations. The fitness function is calculated by solving the compressible flow equations using a cell centered finite volume scheme on unstructured grids. The time integration is also carried out using a dual time implicit approach. A two equations k-e turbulence model is also used for high Reynolds number flow computations. The results show that the optimum geometry at real transonic flow conditions can only be achieved when viscous effects are fully considered in the fitness function computations. They also show that using the viscous flow solution for fitness calculation can increase the objective function by about 70% in comparison with the inviscid optimum airfoil.