An automatic differentiation method for uncertainty analysis due to airfoil configuration variation

Focused on the quantification of the uncertainties of areodynamics performance of airfoils with respect to geometry error, with a set of CFD program based on finite volume algorithm solving the Reynolds-Averaged Navier-Stokes equations with S-A turbulent model, adopting automatic differentiation method to reform the program simultaniously, all kinds of sensitive derivatives, uncertainties of all kinds of aerodynamic coefficients and pressure coefficients distribution resulting from geometry error could be obtained in one course of computation. As the computational results show, even if the geometry error is only 63 microns (while the length of chord is 1 meter), the pressure distribution of the walls could be influenced obviously with uncertainty quantity reaching 0.312 (taking dynamic pressure of the flow as reference) for an airfois in transonic flow, moreover, pressure attached to the place where shock wave stationed bears peak uncertainty. the results of method of automatic differentiation account for the dispersity of results of numeric simulations and wind tunnel experiments well.