Coupled simulation of turbomachinery flutter and forced response blade vibrations using nonlinear frequency domain methods

Abstract

The central topic of this work is the simulation of nonlinear blade vibrations in turbomachinery. Two main causes of blade vibrations are flutter, denoting self-excited vibrations of the blades, and forced response due to e.g. aerodynamic rotor-stator interactions. During operation, the vibration levels of the blades must not exceed critical values in order to prevent high cycle fatigue or immediate failure of the engine. This motivates the development of numerical methods for the prediction of blade vibrations in order to evaluate the robustness of mechanical designs against flutter and forced response. In this work, the focus is laid on bladed turbine disks with interlocked shrouds, which represent a challenging task for numerical simulation. While interlocked shrouds introduce friction (and thus damping) into the structural system, possibly reducing the level of vibrations, they can alter the vibration shape and vibration frequency with increasing amplitude. This in turn makes the aerodynamic damping of the blade motion a nonlinear function of the vibration amplitude. Thus, the mechanical system is bidirectionally coupled, since the two physical domains (fluid and solid) interact with each other. Current numerical analysis tools like the energy method or the use of influence coefficients have deficits in resolving these nonlinear fluid-structure interactions. This motivates the development of improved numerical methods for the simulation of nonlinear blade vibrations. In this work, a refined energy method and a bidirectionally coupled fluid-structure solver are suggested for this purpose. For both approaches, the Harmonic Balance method is employed, which approximates a periodic motion of the blades very efficiently in the frequency domain. The novel methods are applied to numerical test cases of low pressure turbines to demonstrate the methods' capabilities and to investigate the potential influence of nonlinear contact forces on the blade vibrations. Here, the refined energy method allows to gain valuable insight on the impact of shroud contact interfaces on the aerodynamic damping. It is found, that the nonlinear structural contact forces can give rise to stable limit cycle oscillations as well as stability limits, which mark the amplitude level where blade vibrations become unstable if it is exceeded. Furthermore, the coupled solver reveals the complex interaction between a vibrating blade with shroud contact interfaces and a shock motion. For the analysis of forced response, the coupled solver is embedded into a path continuation procedure with a sequential and a parallel variant. The coupled method not only demonstrates the influence of nonlinear friction on the forced response but also reveals, that the superposition assumption regarding the aerodynamic wake excitation and the blade vibration induced aerodynamic forces can lead to inaccurate results.