Analysis of Friction-Saturated Flutter Vibrations With a Fully-Coupled Frequency Domain Method

Abstract

Flutter stability is a dominant design constraint of modern gas and steam turbines. Thus, flutter-tolerant designs are currently explored, where the resulting vibrations remain within acceptable bounds. In particular, friction damping has the potential to yield Limit Cycle Oscillations (LCOs) in the presence of a flutter instability. To predict such LCOs, it is the current practice to model the aerodynamic forces in terms of aerodynamic influence coefficients, derived for some normal modes of the linearized structural model and fixed oscillation frequency. However, this approach neglects that both the nonlinear contact interactions and the aerodynamic stiffness cause a change in the deflection shape and the frequency of the LCO. This, in turn, may have a substantial effect on the aerodynamic damping. The goal of this paper is to assess the technical importance of these neglected interactions. To this end, a state-of-the-art aero-elastic model of a low pressure turbine blade row is considered, undergoing nonlinear frictional contact interactions in the tip shroud interfaces. The LCOs are computed with a fully-coupled harmonic balance method, which iteratively computes the Fourier coefficients of structural deformation and conservative flow variables, as well as the a priori unknown frequency. The coupled algorithm was tested for various combinations of harmonics in both domains and found to provide excellent computational robustness and efficiency. Moreover, a refinement of the conventional energy method is developed and assessed, which accounts for both the nonlinear contact boundary conditions and the linearized aerodynamic influence. It is found that the conventional energy method may not predict a limit cycle oscillation at all while the novel approach presented here can. Furthermore the refined energy method provides deep understanding of the nonlinear aero-elastic interactions.

Multi Traveling Wave Flutter Onset in Tuned Bladed-Disks

“…On the other hand, in the case of strong nonlinear coupling effects (contact at the tip shroud), multi-TW states have been reported both in reduced models (Krack et al, 2017) and more realistic descriptions (Gross and Krack, 2019). Further analysis (Berthold et al, 2020) showed that nonlinear tip contact effects change the vibration modes and frequencies of the system with respect to those obtained by linearized contact conditions.…”

Investigation of a Methodology for Describing Fan Blade Flutter Limitations Induced by Non-Linear Friction at Blade Roots

“…Decoupled approaches have allowed to find Limit Cycle Oscillations (LCO) of the structure by using the HBM procedure, while modelling aerodynamic effects from Computational Fluid Dynamics (CFD) calculations [19,20]. More recently, a fully coupled method in the frequency domain has been established [21] in order to find LCO by using harmonic formulation in both flow and structure models, and iterating in a fixed point loop between the two physics.…”

Friction-induced traveling wave coupling in tuned bladed-disks

“…Here, it was shown that the inclusion of strong nonlinear coupling effects at the tip shroud can produce multi-TW final states. The analysis was continued in [2], to show that nonlinear tip contact effects change the vibration modes and frequencies of the system with respect to those obtained with linearized contact conditions. These changes in frequencies and mode shapes have to be considered in order to correctly estimate the amplitude of the resulting limit cycle oscillations.…”