Abstract
This paper builds upon a two-degree-of-freedom Van der Pol oscillator-based reduced-order model for studying the mechanisms around nonsynchronous vibrations (NSV) in turbomachinery. One degree tracks the fluid motion utilizing a combination of a traditional Van der Pol oscillator and a Duffing oscillator; the other degree of freedom is a mass on a spring and a damper, in this case, a cylinder. Thus, this model can be considered one of fluid–structure interaction. The cubic stiffening from the Duffing oscillator proved to improve the match to experimental data. Using this model to study the time history of the fluid and the structure oscillation, additional parameters are extracted to understand the underlying mechanisms of frequency lock-in and limit cycle oscillation. First, the phase shift between the vortex shedding and the structural motion is calculated when it locks-in and then unlocks. Second, the work done per cycle is analyzed from the contributions of the mass, spring, and damping forces to determine the dominant contributor when locking-in versus unlocking. Third, the phase portrait is plotted on a Poincaré map to further study the locked-in versus unlocked responses. This model is then validated against not only experimental data but also computational simulation results and previous reduced-order models. The finalized model can now serve as a preliminary design tool for turbomachinery applications. For more realistic and accurate modeling, the third degree of freedom in the form of an airfoil pitching motion will be added in a separate paper as well.
