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

Abstract

Abstract To save resources and reduce emissions, it is crucial to reduce weight of aircraft engines and further increase aerodynamic efficiency of gas and steam turbines. For turbine blades, these goals often lead to flutter. Thus, innovative flutter-tolerant designs are explored, where flutter induces limit cycle oscillations (LCOs) of tolerable yet nonzero levels. Flutter represents a self-excitation mechanism and, in the linear case, would lead to exponential divergence. Flutter-induced LCOs are therefore an inherently nonlinear phenomenon. The saturation of flutter-induced vibrations can be caused by nonlinear frictional contact interactions, e.g., in tip shroud interfaces. To develop flutter-tolerant designs, efficient methods are required which compute LCOs based on an appropriate modeling of elastic, inertia, aerodynamic, and contact forces. We recently developed a Frequency Domain Fluid-Structure Interaction (FD-FSI) solver for flutter-induced LCOs. The solver relies on the Harmonic Balance method 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 strong aerodynamic influence, a coupled analysis can significantly increase the accuracy of predicted LCOs compared to the current state-of-the-art 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 numerically validated against Time Domain Fluid-Structure Interaction (TD-FSI) simulations. As a test case, 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 make the test case challenging. Apart from a successful validation of the FD-FSI solver, we shed light on important advantages and disadvantages of both solvers. Due to the lack of robust phase-lag boundary conditions for time domain solvers, a full blade row must be simulated. Thus, the FD-FSI solver typically requires only a fraction of the computational costs. Moreover, the FD-FSI solver contributes to an increased physical understanding of the coupled vibrations: By analyzing the contribution of individual harmonics, we analyze why unexpected even harmonics appear in a certain LCO. On the other hand, the FD-FSI solver does not provide information on the asymptotic stability of the LCOs and is strictly limited to periodic oscillations. Indeed, quasi-periodic limit torus oscillations (LTOs) appear in our test case. Using the TD-FSI solver, we confirm the internal combination resonance, postulated recently as necessary condition for LTOs, for the first time, in a fully coupled analysis.