A Benchmark and Comparison of Airfoil Parameterization and Optimization Techniques
Aaron Godfrey, Christopher C. Nelson · 2025
Aerodynamic optimization is a field of active commercial and research interest. Successful optimization requires navigating a complex set of decisions regarding the creation of a parameter space, selection of an optimization problem statement, and the choice of an appropriate optimization framework and algorithm. Though they are often studied independently, each of these decisions has implications for each of the others. The current work investigates the interaction between a selected parameterization technique and the later success or failure of an optimization framework and algorithm. Two widely studied parameterization techniques are used to define a suitable geometric parameter space: modified class function shape function transformation (CST) and singular value decomposition (SVD). The robustness and flexibility of these parameter spaces is then investigated, and each is used to create a parametric model for the NASA Common Research Model (CRM) transonic airfoil. A computational fluid dynamics (CFD) optimization benchmark is then completed using both a hybrid-adaptive global search algorithm and a state of the art gradient-based optimization technique. The latter method leverages the adjoint of the CFD solution in order to compute the search direction without the need for finite differences. The relative strengths and weaknesses of each parameterization method and optimization technique are presented. It is shown there is a strong interplay between the selection of parameterization technique and the subsequent success of an optimization algorithm.