Reduced-order aerodynamic models for aeroelastic control of turbomachines

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2000.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 138-143).Aeroelasticity is a critical consideration in the design of gas turbine engines, both for stability and forced response. Current aeroelastic models cannot provide high-fidelity aerodynamics in a form suitable for design or control applications. In this thesis low-order, high-fidelity aerodynamic models are developed using systematic model order reduction from computational fluid dynamic (CFD) methods. Reduction techniques are presented which use the proper orthogonal decomposition, and also a new approach for turbomachinery which is based on computing Arnoldi vectors. This method matches the input/output characteristic of the CFD model and includes the proper orthogonal decomposition as a special case. Here, reduction is applied to the linearized two-dimensional Euler equations, although the methodology applies to any linearized CFD model. Both methods make efficient use of linearity to compute the reduced-order basis on a single blade passage. The reduced-order models themselves are developed in the time domain for the full blade row and cast in state-space form. This makes the model appropriate for control applications and also facilitates coupling to other engine components. Moreover, because the full blade row is considered, the models can be applied to problems which lack cyclic symmetry. Although most aeroelastic analyses assume each blade to be identical, in practice variations in blade shape and structural properties exist due to manufacturing limitations and engine wear. These blade to blade variations, known as mistuning, have been shown to have a significant effect on compressor aeroelastic properties. A reduced-order aerodynamic model is developed for a twenty-blade transonic rotor operating in unsteady plunging motion, and coupled to a simple typical section structural model. Stability and forced response of the rotor to an inlet ow disturbance are computed and compared to results obtained using a constant coefficient model similar to those currently used in practice. Mistuning of this rotor and its effect on aeroelastic response is also considered. The simple models are found to inaccurately predict important aeroelastic results, while the relevant dynamics can be accurately captured by the reduced-order models with less than two hundred aerodynamic states. Models are also developed for a low-speed compressor stage in a stator/rotor configuration. The stator is shown to have a significant destabilizing effect on the aeroelastic system, and the results suggest that analysis of the rotor as an isolated blade row may provide inaccurate predictions.by Karen Elizabeth Willcox.Ph.D