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

Abstract The interaction between an unsteady aerodynamic instability with a natural mode of vibration causes large, undesired vibration 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. If the aerodynamic event occurs at frequencies away 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. That leaves NSV as the most important issue to tackle for the need of an industry design tool is great. This paper is a conclusion of multiple papers on utilizing a reduced-order model for NSV. For a pitching airfoil model, the first degree-of-freedom is the structure, while the second is the oscillating vortex shedding, captured using a Van der Pol and Duffing oscillator equation. These coupled equations create a fluid-structure interaction model which is tuned to replicate the experimental results of a wind tunnel airfoil exhibiting NSV. For the three-degree-of-freedom model, the compressor blade is given the motions of plunge and pitch, which the third degree is again the fluid. The tuned model is compared to experimental turbomachinery data. For both models, phase shift and work done per cycle are calculated and analyzed; the former depicts times for constructive and deconstructive interference, the latter demonstrates the dominant contributors to work. Finally, a framework for a full NSV design tool for industry is described including next steps for the eventually implementation of it within the research stages of turbomachinery geometry. Immediate next steps as well as long term future work are also described for this tool.