Robust Algorithm Software for NACA 4-Digit Airfoil Shape Optimization Using the Adjoint Method

Abstract

Optimizing the aerodynamic shape of an airfoil is a critical concern in the aviation industry. The introduction of flexible airfoils has allowed the shape of the airfoil to vary, depending on the flight conditions. Therefore, in this study, we propose an algorithm that is capable of robustly optimizing the shape of the airfoil based on variable parameters of the airfoil and flight conditions. The proposed algorithm can be understood as an optimization method, which employs the adjoint method, a powerful tool for estimating the sensitivity of the model output to the input in numerous studies. From an aerodynamic perspective, the development of shape geometry is a crucial step in airfoil development. The study used NACA-4 digit airfoils as input for the initial assumption and the range of shape change. The optimal shape was found using the proposed algorithm by defining one NACA profile as the initial value and another NACA profile as the limit for the optimized shape, considering the aerodynamic coefficients and flight conditions. However, morphing airfoils have certain deformation limitations. As an innovation in the algorithm, bounds were defined for the shape change during optimization so that the result can be constructed within the capabilities of the morphing wing. These bounds can be adjusted (depending on the capabilities of the airfoils). To validate the proposed algorithm, the study compared it with a previous flow solver for the same airfoil.