Advances in the Numerical Analysis of Linearized Unsteady Cascade Flows

This paper describes two new developments in the numerical analysis of linearized unsteady cascade flows, which have been motivated by the need for an accurate analytical procedure for predicting the onset of flutter in highly loaded compressors. In previous work, results were determined using a two-step or single-pass procedure in which a solution was first determined on a rectilinear-type cascade mesh to determine the unsteady flow over an extended blade-passage solution domain and then on a polar-type local mesh to resolve the unsteady flow in high-gradient regions. In the present effort a composite procedure has been developed in which the cascade-and local-mesh equations are solved simultaneously. This allows the detailed features of the flow within the local mesh region to impact the unsteady solution over the entire domain. In addition, a new transfinite local mesh has been introduced to permit a more accurate modeling of unsteady shock phenomena. Numerical results are presented for a two dimensional compressor-type cascade operating at high subsonic inlet Mach number and high mean incidence to demonstrate the impact of the new composite- and local-mesh analyses on unsteady flow predictions.