LINEARIZED EULER PREDICTIONS OF UNSTEADY AERODYNAMIC LOADS IN CASCADES

A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and vibratory blade motion is presented. Using the linearized Euler technique, one decomposes the flow into a mean (or steady) now plus an unsteady, harmonically varying, small-disturbance flow. Linear variable coefficient equations describe the small-disturbance behavior of the now and are solved using a pseudotime time-marching Lax-Wendroff scheme. For the blade-motion problem, a harmonically deforming computational grid that conforms to the motion of vibrating blades eliminates large error producing mean flow gradient terms that would otherwise appear in the unsteady flow tangency boundary condition. Also presented is a new, numerically exact, nonreflecting far-field boundary condition based on an eigenanalysis of the discretized equations. Computed flow solutions demonstrate the computational accuracy and efficiency of the present method. The solution of the linearized Euler equations requires one to two orders of magnitude less computer time than solution of the nonlinear Euler equations using traditional time-accurate time-marching techniques. Furthermore, it is shown that the deformable grid technique significantly improves the accuracy of the solution.