The goal of this work was to determine the effect of grid topology and flow solver on the quantification of uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients, and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest for the RAE 2822 transonic airfoil. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-ω Model, and the Menter Shear-Stress Transport Model. Several structured and unstructured grid topologies were employed in the analysis. The Fun3D code, developed by NASA Langley Research Center, and the BCFD code, developed by The Boeing Company, were used as the flow solvers. The uncertainty quantification analysis employed stochastic expansions based on non-intrusive polynomial chaos as an efficient means of uncertainty propagation. Sobol indices were used to rank the relative contributions of each closure coefficient to the total uncertainty in the output flow quantities of interest. The results of this study are in good agreement with previously published results.