Uncertainty analysis of airfoil wind tunnel tests with automatic differentiation

In order to obtain a deep understanding of the way that the perturbations from free stream influence the test results, based on finite volume algorithm, solving the Reynolds-averaged Navier-Stokes equations with Spalart-Allmaras turbulence model, we develop a set of computational fluid dynamics (CFD) program for 2 dimension problems and then build the corresponding process to compute sensitive derivatives with the method of automatic differentiation. With the transformed program, one computational course yields derivatives of all aerodynamic coefficients with respect to angle of attack, Mach number and Reynolds number. As the computational results show, in subsonic flow and transonic flow, surface pressure coefficients of the airfoil are the most sensitive to Mach number, to which the sensitivities are at least 8 order higher than that to Reynolds number. However, in subsonic flow, uncertainties caused by angle of attack perturbations is one order higher than that caused by Mach number perturbations, which means that wind tunnel accuracy of angle of attack would determine the accuracy of experimental results to a great extent, while transonic flow reverses the above results and conclusion. Furthermore, increased sensitivities to Mach number lead to the fact that uncertainties of pressure coefficients of the airfoil in transonic flow are one order higher than that in subsonic flow, which means, in transonic flow, wind tunnel accuracy of Mach number should be raised to guarantee the accuracy of the experimental results.