Coupled Mode Flutter of Turbomachinery Blades

Abstract

With new turbomachinery designs, especially for the fan stage of aero engines, the ratio of blade mass to the surrounding air is significantly reduced. As the aerodynamic forces become relevant in relation to the inertial forces of the structure, aeroelastic coupling cannot be neglected anymore. The classically used decoupled methods for flutter analysis, such as Carta's energy method also known as the work-per-cycle approach, yield a non-conservative statement in predicting the aeroelastic stability boundary. The resulting aeroelastic system of structural dynamics and aerodynamics leads to the aeroelastic stability equation, which itself is a generalized eigenvalue problem depending on an aeroelastic frequency. In fixed-wing analysis, different methods to solve the stability equation were introduced over the decades. The most prominent technique used nowadays is the p-k method as described by Hassig. Within this thesis, the p-k method is adapted for the usage in turbomachinery with respect to the specific numeric setups, such as cyclic symmetry, or the change of mode shapes and natural frequencies over rotor speed and throttling state. Assuming small perturbations in the vicinity of flutter onset, vibrations can be handled by a linearized approach so that aerodynamic responses are independent of the amplitude and allow a superposition. Thus, the unsteady aerodynamic forces are gained from a set of frequency domain forced motion simulations and interpolated at the aeroelastic frequency. The goal of this thesis is to verify and validate the adapted p-k method for coupled-mode flutter in turbomachinery. The results are compared against time-marching fluid/structure-coupled simulations and show good agreement. An intensive investigation of the influencing parameters, i.e. mass ratio, frequency separation and solidity, is performed. Applying the herein established process to a low mass ratio fan blade, it is shown that the flutter-free regime is significantly reduced in comparison to the classical energy method approach.