Sensitivity analysis of unsteady aerodynamic loads in cascades

Abstract

A method for computing the effect perturbations in the shape of airfoils in a cascade have on the steady and unsteady flow through the cascade is presented. First, the full potential equation is used to describe the behavior of the nonlinear steady flow and the small disturbance unsteady flow through the cascade. The steady flow and small disturbance unsteady flow versions of the full potential equation are then discretized on a computational grid of quadrilateral cells using a variational finite element technique. The resulting discretized equations describing the nonlinear steady flow are solved using Newton iteration with lower-upper decomposition at each iteration. Similarly, the discretized unsteady small disturbance equations, which are linear, are solved using a single lower-upper decomposition. Next, a sensitivity analysis is performed to determine the effect small changes in cascade and airfoil geometry have on the steady and unsteady flowfields. The sensitivity analysis makes use of the nominal steady and unsteady flow lower-upper decompositions so that no additional matrices need to be factored. Hence, the present method is computationally very efficient.