Session: 24-04 Forced response

Paper Number: 80481

80481 - Aerodynamic Forcing Models for Compressor Aeromechanics 

Unsteady aerodynamic forces on axial compressor blades determine blade vibration amplitudes. High-amplitude vibrations, both at design and off-design conditions, are unacceptable because they pose a high safety and reliability cost. To mitigate this cost, the unsteady aerodynamic forces must be better understood. Current understanding is obscured because the complex flow field within a compressor is affected by a multitude of basic physical mechanisms. These forcing mechanisms are distinguished from one another in the literature using terms such as forced response, flutter, buffeting, rotating instability, separated flow vibration, and non-synchronous vibration. An extensive literature review will be provided to outline the current and often ambiguous use of these terms.

The ambiguity in the literature often results from presenting such terms without a clear link to their mathematical form in the governing equations. Before discussing mathematical models for the aerodynamic forcing, the governing equations must first be put into a tractable form. Thus, this paper begins with a detailed derivation of transforming rotor vibration equations of motion into modal coordinates. Due to the rotor's periodic nature, the full-rotor mode shapes can be described by (1) blade-alone shapes and (2) nodal diameters. While this convention is used ubiquitously in the literature, a formal mathematical derivation using block-circulant linear operators will be provided to demonstrate such modes exactly decouple the governing equations into independent, second-order systems. Each second-order system is forced by the spatial integral of the mode's shape function with one discrete, circumferential Fourier component of the unsteady pressure on the airfoil's surface; this integral is known as the modal force.

The space-time characteristics of this aerodynamic modal force are implicitly present in measurements of rotor vibration. It is plausible these characteristics could be inferred from engine or rig test data by solving an inverse problem. However, the solution of this inverse problem lacks physical interpretation unless each of the above-mentioned physical mechanisms is explicitly connected to a mathematical description. Thus, the goal of this paper is to create a taxonomy of aerodynamic forcing functions, linking physical mechanisms to modal force characteristics. The forcing mechanisms are broadly defined into three categories: (i) unsteady pressure resulting from boundary conditions to the rotor, (ii) unsteadiness due to the aerodynamics of the rotor itself, and (iii) unsteadiness resulting from blade motion. It will be shown that each category has distinct space-time characteristics as a modal force.

Presenting Author: Valerie Hernley University of Notre Dame

Presenting Author Biography: Valerie is a 3rd-year graduate student at the University of Notre Dame Turbomachinery Lab. Interested in fluid-structure interactions, her main research focus is on developing novel data-processing techniques for learning about aerodynamic forcing from measurements of compressor blade vibrations.

Authors:

Valerie Hernley University of Notre Dame
Aleksandar Jemcov University of Notre Dame
Scott Morris University of Notre Dame