The objective of this paper is to investigate the effectiveness of two shape parameterization techniques for robust aerodynamic shape optimization of airfoils in transonic, viscous flow under the variation of Mach number defined as an uncertain variable. The effectiveness of the shape parameterization techniques is evaluated in terms of the computational cost of optimization and the performance increase achieved with the final design. In this study, Hicks-Henne and B-spline shape parameterization techniques are studied. The same shape parameterization techniques are also utilized for deterministic shape optimization and the results are compared to the observations made for the robust design case. For each method, the effect of the number of design variables and their distribution (cosine or uniform) over the geometry on the effectiveness of deterministic and robust optimization are studied. The results of the current study show that the number of design variables and their distributions can significantly impact the computational cost and the aerodynamic performance metrics in both robust and deterministic designs. The improvement of the robustness of the final design obtained with stochastic optimization approach is demonstrated over the Mach number range considered as the uncertain operating condition for the aerodynamic optimization problem studied in this paper.
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