Impact of the Stabilized Finite Element Method On Acoustic and Vortical Perturbations in Thermoacoustic Systems

This paper seeks to advance linear stability analyses of thermoacoustic systems conducted with the stabilized Finite Element Method (sFEM). Specifically, this work analyzes and quantifies the impact of the Streamline-Upwind-Petrov-Galerkin (SUPG) artificial diffusion scheme on (eigen)mode shapes and damping rates of the isentropic Linearized Euler Equations (LEE) in frequency space. The LEE (eigen)mode shapes are separated into acoustic and vortical perturbation components via a Helmholtz decomposition and their sensitivity on the employed stabilization scheme is investigated separately. The regions where numerical stabilization mainly acts on the perturbation types are identified and explanations for the observations are provided. A methodology is established, which allows the quantification of the impact of artificial diffusion on the acoustic field in terms of a damping rate. This non-physical damping rate is used to determine the physically meaningful, acoustic LEE damping rate, which is corrected by the contribution of artificial diffusion. Hence, the presented method eliminates a main shortcoming of LEE eigenfrequency analyses with the sFEM and, as a result, provides more accurate information on the stability of thermoacoustic systems.

Impact of the Stabilized Finite Element Method on Acoustic and Vortical Perturbations in Thermoacoustic Systems

This paper seeks to advance linear stability analyses of thermoacoustic systems conducted with the stabilized Finite Element Method (sFEM). Specifically, this work analyzes and quantifies the impact of the Streamline-Upwind-Petrov-Galerkin (SUPG) artificial diffusion scheme on (eigen)mode shapes and damping rates of the isentropic Linearized Euler Equations (LEE) in frequency space. The LEE (eigen)mode shapes are separated into acoustic and vortical perturbation components via a Helmholtz decomposition and their sensitivity on the employed stabilization scheme is investigated separately. The regions where numerical stabilization mainly acts on the perturbation types are identified and explanations for the observations are provided. A methodology is established, which allows the quantification of the impact of artificial diffusion on the acoustic field in terms of a damping rate. This non-physical damping rate is used to determine the physically meaningful, acoustic LEE damping rate, which is corrected by the contribution of artificial diffusion. Hence, the presented method eliminates a main shortcoming of LEE eigen-frequency analyses with the sFEM and, as a result, provides more accurate information on the stability of thermoacoustic systems.

A Vibration Damping Analysis Method of Turbine Blade Shroud Dampers Based on a Given Eigen-Mode

High cycle fatigue damage caused by resonance and forced vibration can significantly affect the life and reliability of turbine rotor blades in aero-engines. The friction damper has been widely used to reduce the resonant stress of blades, on which the turbine blade shroud dampers are highly used. In order to solve the problems of vibration damping analysis and design of shrouded blades dampers, an analytical method without complex and time-consuming nonlinear vibration response has been proposed based on a given eigen-mode in this paper. For the serrated shrouded damper, two typical friction models, namely macro-slip model, and micro-slip model, have been introduced. Additionally, a complete set of damping analysis method has been introduced by the energy method, based on the vibration dynamics principle and eigen-mode analyzed by finite element method. Combined with the analysis of the natural vibration characteristics of the shrouded turbine blade, the law of the damping ratio with the relevant design parameters, such as the vibration stress, the pre-twist angle, the friction coefficient and the nodal diameter, was obtained through a calculation example. The method can also provide an important reference for the parameterized design of dampers.

Theoretical study to calculate the vibration modes of a wind turbine blade with a new composite material

A precise understanding of the dynamics of a blade is essential for its design, especially in the development of new structures and the resolution of noise and vibration problems. This understanding involves the study of experimental and/or theoretical modal analysis. These latter present effective tools for describing, understanding and modelling the dynamic aspect of each structure, in the present work, we are going to establish the Eigen-mode of a wind turbine blade made by a new composite material ‘hemp fibre’ using theoretical calculation for flap-wise, edge-wise and torsional mode using the finite element method applied to a structure consisting of a beam embedded at one end, based on the Euler-Bernoulli hypothesis and the equation of beam’s motion. Furthermore; we compare the obtained results with those of composite material made by fibreglass. Keywords: Blade, Eigen-mode, hemp fibre, flap-wise, edge-wise, torsional, fibreglass.