Computation of the Stability Limit of Nonlinear Bladerow Flutter with a Fully Coupled Frequency Domain FSI Solver

Abstract

To guarantee a safe operation of turbomachinery components engineers need to consider the aeroe- lastic behavior of the mechanical design. Due to increasing demands with respect to e�ciency and fuel consumption components need to be further optimized. However conventional computational analysis meth- ods for aeroelasticity which are commonly used in industry during the design phase have uncertainties since they are often based on linearization or neglect interactions between physical nonlinear e�ects in the solid and �uid domain. Thus large safety margins for conventional methods need to be considered resulting in restrictive design guidelines. Furthermore the nonlinear behavior of blade vibrations and the interaction with the surrounding nonlinear �ow is only rarely analyzed and therefore not yet fully understood. Time accurate methods can deliver higher accuracy but the computational costs are prohibitive for the industrial design pro- cess. In this study a fully coupled �uid-structure interaction (FSI) solver in the frequency domain is presented to provide a computationally e�cient simulation tool which is able to consider nonlinear solid and �uid e�ects of blade limit cycle oscillations (LCOs) in turbo engines. It can compute stable LCOs as well as unstable LCOs (stability limit) which can occur e.g. due to dry nonlinear friction in shrouded blades and is based on the Harmonic Balance method. The fourier components of the blade vibration and the frequency are passed to the �ow solver and the aerodynamic forces are returned to the strucure solver. Because the frequency of self excited vibrations is not known a priori the FSI solver considers the frequency as part of the sought solution. Furthermore a linearization of the aerodynamic forces inside the structure solver is introduced to improve the convergence of the coupled solver and countermeasures are implemented to prevent the solver from converging to the trivial solution (zero amplitude). To further reduce the computational costs the structural model is reduced with the Craig-Bampton approach. During the reduction the degrees of freedom in the solid contact regions of the bladerow are retained to model dry friction. To initialize the solver the energy method is extended to approximately determine the nonlinear behavior with a one-way coupling approach. The novel method is applied to a bladerow which is aerodynamically stable for small vibration amplitudes. With in- creasing amplitude the modeshape as well as the frequency change due to nonlinear friction in the joints of the shrouded rotor. This has an e�ect on the aerodynamic response and for large amplitudes the oscillations are aerodynamically unstable. The coupled solver is able to determine the limit of stability and the frequency of the coupled problem while conventional energy methods are not able to detect a stability boundary at all.