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<p>This research presents the detailed investigation of coupled-mode flutter and non-synchronous
vibration in turbomachinery. Coupled-mode flutter and non-synchronous vibration are
two aeromechanical challenges in designing turbomachinery that, when present, can
cause engine blade failure. Regarding flutter, current industry design practices
calculate the aerodynamic loads on a blade due to a single mode. In response to these
design standards, a quasi three-dimensional, reduced-order modeling tool was developed
for identifying the aeroelastic conditions that cause multi-mode flutter. This tool
predicts the onset of coupled-mode flutter reasonable well for four different configurations,
though certain parameters were tuned to agree with experimentation. Additionally,
the results of this research indicate that mass ratio, frequency separation, and solidity
have an effect on critical rotor speed for flutter. Higher mass-ratio blades require
larger rotational velocities before they experience coupled-mode flutter. Similarly,
increasing the frequency separation between modes and raising the solidity increases
the critical rotor speed. Finally, and most importantly, design guidelines were generated
for defining when a multi-mode flutter analysis is required in practical turbomachinery
design. </p><p>Previous work has shown that industry computational fluid dynamics
can approximately predict non-synchronous vibration (NSV), but no real understanding
of frequency lock-in and blade limit-cycle amplitude exists. Therefore, to understand
the causes of NSV, two different reduced-order modeling approaches were used. The
first approach uses a van der Pol oscillator to model a non-linear fluid instability.
The van der Pol model is then coupled to a structural degree of freedom. This coupled
system exhibits the two chief properties seen in experimental and computational non-synchronous
vibration. Under various conditions, the fluid instability and the natural structural
frequency will lock-in, causing structural limit-cycle oscillations. This research
shows that with proper model-coefficient choices, the frequency range of lock-in can
be predicted and the conditions for the worst-case, limit-cycle-oscillation amplitude
can be determined. This high-amplitude limit-cycle oscillation is found at an off-resonant
condition, i.e., the ratio of the fluid-shedding frequency and the natural-structural
frequency is not unity. In practice, low amplitude limit-cycle oscillations are acceptable;
this research gives insight into when high-amplitude oscillations may occur and suggests
that altering a blade's natural frequency to avoid this resonance can potentially
make the response worse.</p><p>The second reduced-order model uses proper orthogonal
decomposition (POD) methods to first reconstruct, and ultimately predict, computational
fluid dynamics (CFD) simulations of non-synchronous vibration. Overall, this method
was successfully developed and implemented, requiring between two and six POD modes
to accurately predict CFD solutions that are experiencing non-synchronous vibration.
This POD method was first developed and demonstrated for a transversely-moving, two-dimensional
cylinder in cross-flow. Later, the method was used for the prediction of CFD solutions
for a two-dimensional compressor blade, and the reconstruction of solutions for a
three-dimensional first-stage compressor blade. </p><p>This research is the first
to offer a van der Pol or proper orthogonal decomposition approach to the reduced-order
modeling of non-synchronous vibration in turbomachinery. Modeling non-synchronous
vibration is especially challenging because NSV is caused by complicated, unsteady
flow dynamics; this initial study helps researchers understand the causes of NSV,
and aids in the future development of predictive tools for aeromechanical design engineers.</p>
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