Blade Row Interaction Effects on Flutter and Forced Response

Abstract

A procedure to calculate intrablade row unsteady aerodynamic interactions is developed that relies upon results from isolated blade row unsteady aerodynamic analyses. Using influence coefficients that express the unsteady forces on one blade row due to the motion of another, an aeroelastic model is obtained that accounts for the coupling of the vibratory responses of multiple blade rows. The model is applied to two model config- urations, each consisting of three blade rows. The flutter analysis shows that interaction effects can be desta- bilizing, and the forced response analysis shows that interaction effects can result in a significant increase in the resonant response of a blade row. N the flutter analysis of a turbomachine blade row, the blade row is commonly assumed to be isolated—distur- bances created by the vibrating blades are free to propagate away from the blade row without being disturbed. Therefore, any reflections of these outgoing waves by other structural members or nonuniformiti es in the mean-flowfield are ne- glected. Although the forced response problem is typically concerned with blade row interaction, forced response anal- yses also generally neglect any reflections of outgoing waves. However, in an engine environment, structural elements such as neighboring blade rows or struts and nonuniformities in the mean-flowfield will reflect some of this wave energy back toward the vibrating blades, causing additional unsteady forces on them. Whether or not these reflected waves can signifi- cantly affect the aeroelastic stability or forced response of a blade row is a question of fundamental importance. Several investigations have focused on the unsteady aero- dynamic interaction between two rigid blade rows. Kaji and Okazaki1 investigated the interaction of two blade rows for the purpose of predicting rotor-stator interaction noise. They obtained a simultaneous solution to the unsteady lift distri- butions on both of the blade rows. Hanson2 modified Smith's3 isolated blade row unsteady aerodynamic analysis to predict rotor-stator interaction noise, essentially extending Kaji and Okazaki's work to include effects of frequency scattering and mean-flow turning by the blade rows. For a counter-rotati ng propfan in incompressibl e flow, Chen and Williams4 used a panel method to determine the unsteady loads on rigid pro- peller blades. From the point-of-view of the present investi- gation, all of these investigations are somewhat limited be- cause they did not delve into the aeroelastic problem and they were limited to two blade rows. One investigation that did consider the aeroelastic effects of interactions of a vibrating blade row and an adjacent struc- ture was that of Williams et al. 5 A three-dimensio nal linear- ized compressible panel method was used to calculate the unsteady aerodynamics of a ducted fan. The aeroelastic anal- ysis allowed flexibility of both the fan and the duct. The duct was found to have a destabilizing effect on the fan. A number of time-accurate solutions to the Euler and Na- vier-Stokes equations for rotor-stator interaction have been