A COUPLED-MODE ANALYSIS OF UNSTEADY MULTISTAGE FLOWS IN TURBOMACHINERY

A computational method is presented for predicting the unsteady aerody namic response of a vibrating blade row that is part of a multistage t urbomachine. Most current unsteady aerodynamic theories model a single blade row isolated in an infinitely long duct. This assumption neglec ts the potentially important influence of neighboring blade rows. The present ''coupled mode'' analysis is an elegant and computationally ef ficient method for modeling neighboring blade row effects. Using this approach, the coupling between blade rows is modeled using a subset of the so-called spinning modes, ie., pressure, vorticity, and entropy w aves, which propagate between the blade rows. The blade rows themselve s are represented by reflection and transmission coefficients. These c oefficients describe how spinning modes interact with, and are scatter ed by, a given blade row. The coefficients can be calculated using any standard isolated blade row model; here we use a linearized full pote ntial flow model together with rapid distortion theory to account for incident vortical gusts. The isolated blade row reflection and transmi ssion coefficients, interrow coupling relationships, and appropriate b oundary conditions are all assembled into a small sparse linear system of equations that describes the unsteady multistage flow. A number of numerical examples are presented to validate the method and to demons trate the profound influence of neighboring blade rows on the aerodyna mic damping of a cascade of vibrating airfoils.