Data-driven inverse airfoil design using class shape transformation parameterization

Abstract

Inverse airfoil design aims to identify a geometry that satisfies specified aerodynamic performance targets. This study presents a data driven inverse modeling framework that predicts airfoil geometry using key input parameters such as lift coefficient (C _L ), drag coefficient (C _D ), pitching moment coefficient (C _m ), angle of attack (AOA), and Reynolds number (R _e ). Airfoil shapes are represented using Class Shape Transformation (CST) coefficients, which provide a compact description by requiring only a small number of parameters to accurately define both the upper and lower surfaces. A fully connected feedforward artificial neural network(ANN) is trained on a combined dataset comprising multiple NACA airfoils with diverse geometric and aerodynamic characteristics. Aerodynamic data is generated using JavaFoil/XFOIL simulations, and corresponding CST coefficients are derived via curve fitting. The model is validated on both interpolated training cases and extrapolated predictions for unseen airfoils NACA 0021 and NACA 23012. Additionally, experimental validation is conducted using wind tunnel data for NACA 0012, demonstrating the model’s ability to reconstruct geometry from real world performance inputs. Evaluation includes MAE, RMSE and geometric fidelity through explicit camber line analysis together with CST based shape reconstruction. Results confirm that the ANN model can reliably infer CST defined geometries aligned with target aerodynamic conditions. The demonstrated accuracy supports deploying the ANN model for rapid airfoil synthesis and early-phase inverse design.