Analysis of experimental results of turbomachinery flutter using an asymptotic reduced order model

Abstract

Flutter of bladed disks is an instability mechanism where the aerodynamic flow pumps energy into the blade vibration. This energy is dissipated through dry friction, normally at the blade-disk attachment, and this balance defines the blade vibration amplitude that sets in. The magnitude of this final vibration amplitude is crucial to correctly estimate the blade fatigue life. In the context of the European project FUTURE, a series of flutter experiments were carried out for a realistic low-pressure turbine with different intentional mistuning patterns. To analyze the results, a simple 3 degrees of freedom per sector mass-spring model is set up with the experimental configuration parameters. This mass-spring system still requires very long integration times due to: (i) the large difference between the fast elastic oscillation time and the slow time associated with the aerodynamic instability, friction, and mistuning, and (ii) the presence of many aerodynamically unstable modes with very similar growth rates. A multiple-scale method is applied to further simplify the mass-spring system. The blade elastic oscillation is filtered out, and the resulting asymptotic reduced order model reduces considerably the integration time required to reach a converged solution. It is found that the final vibration state of the mistuned problem depends on the selected initial conditions, so the model is run for a large number of random initial conditions to explore the possible final states. The asymptotic model gives results that show a good agreement with the experimental measurements, and it also allows to explain the origin of the peaks in the travelling wave content of the final solution found in the experiment for the intentionally mistuned configurations.