A Framework for Analyzing the Dynamics of Flexibly-Bladed Turbomachines

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Abstract
A framework for analyzing the nonlinear dynamic behavior of flexibly-bladed turbomachines is presented. The analytical description is based on matching a two dimensional, incompressible flow field across a semi-actuator disk representation of a flexible rotor and a rigid stator. The aerodynamic loading on the rotor is derived using control volume formulations applied to discrete blade passages allowing consideration of finite interblade phase angles. Depending on operating parameters, the model exhibits behaviors classified as surge, rotating stall, and stall flutter which are qualitatively consistent with experimentally observed results. The formulation provides a tractable, nonlinear, state-space description of the dynamics responsible for surge, rotating stall, flutter, and their interaction. An analysis is performed for system parameters representative of a fan in a modern high-bypass ratio aeroengine. The behavior of the operability limiting instability modes is examined using time simulations, eigenvalues plots and two-parameter stability diagrams.

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