Pd. Silkowski et Kc. Hall, A COUPLED-MODE ANALYSIS OF UNSTEADY MULTISTAGE FLOWS IN TURBOMACHINERY, Journal of turbomachinery, 120(3), 1998, pp. 410-421
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.