59188 - Global Stability Analysis of an Academic Rotor/stator Cavity Subject to Periodic and Simple Wall Oscillations 

Complex unsteady phenomena can appear in turbomachinery components and result in the self-sustained oscillatory motion of the fluid as found in aeronautical engines or rocket turbopumps for example. The origin of these oscillations often results from the complex coupling between flow non linearities and structure motion generating major risks for the operation of the engine and even jeopardizing its components. Vibrations in turbomachinery can be split into two types: local vibration and machine vibration. The former refers to the vibration of local components such as the blades or discs of a turbine, whereas the latter involves widespread motion of the rotor and/or stator which induces periodic reactions at the bearings hence causing the static components to vibrate[1]. The origin of these vibrations can also be classified into two classes: imposed or self-excited; depending on whether the vibration is the result of an imposed disturbance such as a rotor experiencing a cyclic pressure fluctuation due to the rotation of the blades in a steady non-uniform field in the azimuthal direction[2], or the disturbance is the consequence of an instability such as flutter or aeroelastic instability which occurs at or near the natural frequency of the rotor blade. In the present investigation, the flow inside an academic rotor/stator cavity is studied by mean of Large Eddy Simulation (LES) and a global linear stability analysis. The objective is to understand the behavior of the flow when subject to a periodic forcing imposed by the rotor motion. This chosen cavity, also referred to as Tuliszka cavity, has been thoroughly studied from a hydrodynamic perspective through a local and global stability analysis by M. Quegineur[3] whereby successfully showing that the flow inside the cavity expresses a self-sustained oscillatory motion, an intrinsic phenomenon commonly found in enclosed rotating flows. Subsequently different unstable fluid modes were identified as the main driving factor of the reported phenomenon. Based on this knowledge, the effect of a vibrating rotor is assessed from multiple test cases where the frequency of the vibrations are imposed and correspond to the previously identified unstable modes inside the cavity. This is done by carrying Large Eddy Simulation (LES) of the aforementioned cases in conjunction to a bi-global linear stability analysis. Focus is here brought to the underlying pressure fluctuations found inside the cavity using spectral analysis complemented with the global stability analysis, demonstrating that such tools can address forced flow problems. It is also noted that the new fluid limit cycles present modes that shift or completely disappear compared to the unforced case, the forcing mechanism altering the stability of the entire system.

[1]D. M. Smith, Proceedings of the institution of mechanical engineers, 1965
[2]M. Baumgartner, F. Kameier, J. Hourmouziadis, Twelfth International Symposium on Airbreathing Engines, 1995 
[3]M. Queguineur, T. Bridel-Bertomeu, L. Gicquel, G. Staffelbach, Proceedings of ASME Turbo Expo 2018: Turbine Technical Conference and Exposition.