Fully Coupled Analysis of Flutter Induced Limit Cycles: Frequency vs. Time Domain Methods

Abstract

In the field of turbomachinery mechanical designs strive for increased efficiency and lighter engines. For turbines however these goals often lead to flutter. Thus new and innovative flutter-tolerant designs are explored where the vibration amplitudes are limited due to nonlinear frictional contact interactions in e.g. tip shroud interfaces. As a result Limit Cycle Oscillations (LCOs) are expected which motivates the development of new numerical methods for their efficient analysis. In previous research a Frequency Domain Fluid-Structure Interaction (FD-FSI) solver for flutter induced LCOs was developed. Within this framework the harmonic balance method is applied to the structure as well as the fluid domain. It was shown that especially for long and slender blades with friction in shroud interfaces and a high aerodynamic damping and stiffness, a coupled analysis can significantly increase the accuracy of predicted LCOs compared to unidirectional methods. Conventional methods do not properly account for the nonlinear change of frequency and deflection shape, and the effect of these changes on the aerodynamic damping, and thus fail in predicting certain LCOs at all. In the current work the FD-FSI solver is validated against numerical Time Domain Fluid-Structure Interaction (TD-FSI) simulations. As a numerical testcase a shrouded low pressure turbine with friction in the shroud interfaces is considered. The point of operation is highly loaded and transonic in order to provoke a nonlinear aerodynamic behavior. For the TD-FSI simulations the coupled mechanical system (fluid and structure) is modeled as a full annulus avoiding the need for phase-lag boundaries. The FD-FSI simulations only require a single sector for both physical domains which requires only a fraction of the computational costs compared to TD-FSI simulations. Apart from a successful validation of the FD-FSI solver the comparison of the two solvers also sheds light on important advantages and disadvantages of both methods. It turns out that the FD-FSI solver not only constitutes an efficient tool for the calculation of flutter induced LCOs but also contributes to an increased physical understanding of the coupled vibrations, e.g. it is found that a strong coupling among fluid harmonics can enrich the frequency spectrum of the structural vibrations. On the other hand the TD-FSI solver is found to be beneficial when it comes to stability analysis or the investigation of limit torus oscillations (LTOs) which are quasi-periodic oscillations. To demonstrate this an LTO with two incommensurable frequencies is simulated. Its analysis confirms the internal combination resonance as a necessary condition which was discovered in previous research. This time however a state-of-the-art model with accurately resolved aerodynamic forces is used instead of aerodynamic influence coefficients.