Session: 40-09 Fan and Compressor Vibrations

Paper Number: 129201

129201 - Utilizing a Multi-Degree of Freedom Reduced-Order Model for Identifying Non-Synchronous Vibrations in Turbomachinery 

The interaction between an unsteady aerodynamic instability with a natural mode of vibration causes large, unwanted motion in turbomachinery. In a simple form, an unsteady instability might be von Karman vortex shedding; on the other hand, it might be as complex as tip gap flow, jet core flow, or even a rotating stall. Then this aerodynamic event occurs at frequencies different from shaft rotational harmonics, it is described as non-synchronous. Thus, an unsteady aerodynamic instability occurring at a frequency which excites a natural bending or torsional blade mode can be described as Non-Synchronous Vibrations (NSV), or often referred to as Vortex-Induced Vibrations (VIV).

Compared to other aeroelastic phenomena, NSV has no industry accepted design tool. Forced Response, a phenomenon where a frequency related to shaft speed and number of blades directly excites a natural frequency, has computational tools to measure the forces. A self-excited phenomenon in which aerodynamic damping falls below zero, flutter, as has computational tools to determine its envelope of occurrence. Separated Flow Vibration, a third phenomenon has little design tool, but occurs at low mass flow rates and exhibits low amplitudes of vibration, thus is of little concern for turbomachinery. That leaves NSV as the most important issue to tackle for the need of an industry design tool is great.

A framework for creating an industry design tool for search for and understanding NSV in engines is presented. The first step is to collect experimental data, whether it is of a cylinder, airfoil, or turbomachinery case, ideally as a function of frequency or rotational speed versus limit cycle oscillation (LCO) amplitude. Next, the coefficients are generated and tuned, whether through a manual guess and check method or computationally using Proper Orthogonal Decomposition (POD) [Clark 2013]. Once the coefficients are generated, then can be plugged into the Reduced Order Model (here titled the Van der Pol based Reduced Order Model for Non-Synchronous Vibrations), which would plot the limit cycle oscillations as a function of frequency or rotational speed. Then an iterative process begins to improve the fit, whether by tuning the coefficients [Clark 2013] or using a system identification tuning method [Hollenbach 2021]. Finally, when the fit is sufficient for the rotational speed versus LCO plot, then the following parameters can be extracted and studied: phase shift between fluid, linear motion, angular motion, as well as work done per cycle for parameters including stiffness, damping, inertia, and cross coupling terms.

In conclusion, a reduced-order model for non-synchronous vibrations will one day become part of the industry design tool for engine manufacturers to use. A 2 DOF model is used to compare against a pitching airfoil experimental LCO data to extrapolate additional insight into the underlying flow physics through phase shift and work done per cycle. In addition, expanding upon the previous suggested 3 DOF model represents the most realistic case for turbomachinery. In matching up experimental compressor data, the ROM provides insight into the phase shift and work done per cycle for a much more complicated system. These ROMs are cheaper and easier to use than large amounts of wind tunnel testing or large-scale computational fluid dynamics for studying NSV.

In the future, these ROMs should be compared against other turbomachinery cases to further develop them. In addition, they should be compared to CFD cases rather than simply wind tunnel testing data. The best scenario would be to partner up with an engine manufacturer to further this design tool using engine data and near instant feedback from them to finalize this industry design tool. Finally, this tool needs to be thoroughly tested and validated by multiple engine manufacturers.

Presenting Author: Richard Hollenbach Exponent

Presenting Author Biography: Dr. Hollenbach demonstrates his aptitude in mechanical engineering to provide technical consulting involving aeroelasticity, aerodynamics, vibrations, fluid-structure interaction, and turbomachinery. He applies the fundamentals of mechanics, aerospace engineering, physics, and mathematical modeling to investigate performance and failures within thermal fluid systems. He earned his Ph.D. in mechanical engineering from Duke University in May 2022, working under Dr. Bob Kielb. He also earned his B.S. in mechanical engineering from the University of Pittsburgh. Currently, as a Thermal Science Engineer at Exponent, Richard assist clients as an engineering and scientific consultant, where he is a licensed professional mechanical engineer in the state of North Carolina.

Authors:

Richard Hollenbach Exponent