Benjamin R. Bettis
Missouri University of Science and Technology
Advisor: Dr. Serhat Hosder

Abstract
In this study, computational fluid dynamics was utilized to examine the performance characteristics of the RAE2822 airfoil in transonic, viscous, turbulent flow when the angle of attack was treated as a uniform random variable. An initial grid convergence study was conducted in order to determine the optimum grid resolution in terms of accuracy and computational efficiency. From the results of the convergence study, the discretization error was determined for each grid. Once the optimum grid was found, the study was mainly focused on quantifying the uncertainty in the performance of the airfoil with the angle of attack treated as a random variable. A newly developed non-intrusive polynomial chaos method was then used to propagate this uncertainty to the resulting performance of the airfoil. This particular method is much less computationally expensive when compared to typical sampling methods. Furthermore, this method allows all of the airfoil’s relevant performance statistics to be calculated quite conveniently. The study showed that as the grid resolution was increased, the discretization error decreased. Also, the uncertainty in the angle of attack caused a considerable amount of variation in the drag performance of the airfoil. It was determined that the highest level of uncertainty in the pressure field was near the stagnation point towards the leading edge, and also in region of the transonic shock wave on the top surface of the airfoil. Overall, this study has shown that an uncertainty in operating conditions can have a drastic effect on the performance of the airfoil.