Aerodynamic design optimization is typically performed at fixed flight conditions, without considering the variation and uncertainty in operating conditions. The objective of robust aerodynamic optimization is to design an aerodynamic configuration, which will keep its optimum performance under varying conditions such as the speed of aircraft. The primary goal of this study was to investigate the impact of turbulence models used in RANS simulations on the 2-D airfoil and 3-D wing designs obtained with gradient-based deterministic and robust optimization in transonic, viscous, turbulent flows. The main contribution of this research to the aerodynamic design area was to quantify the impact of turbulence models (Spalart-Allmaras and Menter\u27s Shear Stress Transport) and shape parameterization techniques (Hicks-Henne bump functions, B-Spline curves and Free-Form Deformation) on the computational cost, optimal shape, and its performance obtained with robust optimization under uncertainty. The effect of changing the relative weight of mean drag reduction and robustness measures used in the objective function was also investigated for the 3-D robust design. The robustness of the final design obtained with stochastic optimization approach was demonstrated over the Mach number range considered as the uncertain operating condition in this study. The results of the 2-D study show that the shape parameterization technique has a larger impact on the computational cost than the turbulence models in both deterministic and robust design. The results of the 3-D study show that the effect of the weight distribution in the objective function is more significant than the effect of turbulence model on the final design obtained with robust optimization below the design Mach number value. In general, robust optimization tends to reduce the impact of the turbulence model selection on the optimum shape and performance over the uncertain Mach number range considered, whereas the effect of the turbulence model becomes significant at off-design conditions for the optimal shapes obtained with deterministic design --Abstract, page iii
