Impact of turbulence models and shape parameterization on robust aerodynamic shape optimization

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

Impact of Turbulence Models and Objective Function on Three-Dimensional Robust Aerodynamic Optimization

The objective of this paper was to investigate the impact of two commonly used turbulence models in Reynolds-averaged Navier–Stokes simulations (Spalart–Allmaras and Menter\u27s shear stress transport models) on the three-dimensional optimum wing design obtained with the gradient-based deterministic and robust aerodynamic shape optimization in transonic, viscous, turbulent flow. In particular, the main contribution of this study to aerodynamic design area is to evaluate the impact of turbulence models and different weight distributions in the multi-objective function (equal, mean biased, and variance biased) on the computational cost, optimal shape, and its performance under Mach-number uncertainty obtained with robust optimization. The results of the study show that the effect of weight distribution in the objective function is more significant than the effect of turbulence model on the final shape obtained with robust design at lower off-design Mach numbers. Robust design tends to mitigate the impact of the turbulence model selection on the optimum shape and performance over the uncertain Mach-number range, whereas the choice of the turbulence model becomes significant at off-design conditions for the optimal shapes obtained with deterministic design. This study also demonstrates the effectiveness of using stochastic expansions in robust aerodynamic shape optimization of three-dimensional wings