The vibration level of aerodynamically unstable low-pressure-turbine rotor blades has been assessed for the first time using two-different approaches. Both methods assume that the aerodynamic forcing is due solely to the self-excitation of the airfoil and that the vibration amplitude is saturated due to the non-linearity associated to the fir-tree dry friction, which is modeled using a simplified approach. To compensate for the limitations of the friction model several hypotheses need to be done, among them, the geometric similarity of the different configurations and that the aspect ratio of the rotor blades is high. The first approach, which is novel, assumes that the vibration amplitude is small enough and the unsteady aerodynamics associated to the airfoil motion may be computed using a frequency domain linearized Navier-Stokes solver. The vibration amplitude is obtained posing the energy balance between the energy exerted by the most unstable aerodynamic mode and the energy dissipated by dry friction. The second approach time marches simultaneously the Reynolds-Average Navier Stokes equations and a simple mass-spring non-linear model consistent with the mechanical model used in the first approach. This fully coupled non-linear, both in the aerodynamic and structural sides, flutter analysis is considered unique in its kind. It is demonstrated by means of a simplified, but consistent with typical low-pressure-turbine bladed-disk, model that both methods are equivalent. The first approach has been applied to several bladed-disks and the comparison with experimental data is good in overall.

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