Turbomachinery bladings typically have a high mass ratio of structure to air. As a consequence, the aerodynamic forces acting on the structure have a neglectable influence on the structural vibration modes and frequencies. Within the context of flutter analysis, this assumption justifies the usage of decoupled methods (i.e. energy method) in which only vacuum mode shape vibrations are taken into account to predict the blade aerodynamic damping (or excitation) at a fixed frequency. Furthermore, considering the structural damping as a conservative margin, this one is neglected and the blade aeroelastic stability is focused exclusively on the accurate prediction of the blade aerodynamic damping.

With the current trend for more aggressive engine design yielding higher blade loading, thinner profiles and general weight reduction, the blade mass ratio to air is significantly reduced. As a consequence, applying decoupled methods for flutter analysis might not be legitimate anymore, as they can yield a non-conservative statement in predicting the blade aeroelastic stability boundary of the next generation of turbomachinery bladings. In particular, the absence of friction dampers significantly reduces the blade structural damping and almost all vibrational damping has to be aerodynamic, thus the blades are prone to self-induced aerodynamic excitations.

Assuming small perturbations in the vicinity of flutter onset, vibrations can be treated by a linearized approach. Thus, aerodynamic responses are independent of the amplitude and the structural vibration can be expressed as a superposition of linear mode shapes.

The p-k method, which solves a coupled aeroelastic eigenvalue problem for frequency and damping resp. excitation of the multi-mode vibration, was adapted for turbomachinery application using aerodynamic responses computed in the frequency domain. Alongside the promise of reduced computational costs, choosing frequency domain over fully coupled time-marching methods allows a systematic assessment: the investigator gets a better insight into modal participation factors and into the sensitivity of modal coupling towards mass ratio or frequency separation.

A two-dimensional test case is validated against time-marching fluid-structure coupled simulations for subsonic and transonic conditions. A span of mass ratios is investigated showing that the adapted p-k method is able to predict the transition between aeroelastically stable and unstable cascades depending on the mass ratio. A good agreement of the predicted frequency and aerodynamic damping is obtained between the two approaches. The results further show that the strength of modal coupling is not equally distributed for all traveling wave modes. The inter-blade phase angles predicted to be the least stable by the energy method are becoming unstable first as the mass ratios is lowered and modal coupling has a significant impact. For even lower values of mass ratio, frequency coalescence is observed and the formerly most stable traveling wave modes also become unstable.

Finally, the p-k method is applied to a low mass ratio fan blade showing that the flutter-free operating range is significantly reduced when modal coupling effects are taken into account.


Coupled Mode Flutter Analysis of Turbomachinery Blades Using an Adaptation of the P-K Method

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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