Numerical Investigation of Adjoint Method in Aerodynamic Optimization

In this research, the continuous adjoint method is applied to optimize an airfoil in subsonic and transonic flows. An Euler flow solver is used to analyze the inviscid compressible flow over airfoils in each design cycle. Two design problems appearing in aerodynamic shape optimization, namely inverse pressure design and drag minimization were investigated. In the first part, a test case was carried out to evaluate the performance of the adjoint method in inverse design problem. The results show that we can use the adjoint method as an efficient tool in inverse aerodynamic design problems. In the second part, the constrained optimization was investigated in a drag minimization problem. The investigated samples show that a small variation of airfoil geometry has caused considerable decrease in the drag coefficient. To evaluate the performance of the adjoint method in design problems with numerous design variables and also to evaluate the effects of the adoption of the design vector on the optimization results, the constrained drag minimization was performed using two different design vectors. The results shows that the mechanism and the value of drag reduction are affected by the type of design vector. Also, computational cost of the adjoint method are independent of the number of design variables.