Modal Analysis of Vertical-Axis Darrieus Wind Turbine Blade with a Troposkein Shape

摘要

Darrieus wind turbines with troposkein shaped blades are an important type of vertical axis wind turbines. When designing these turbines it is important to consider how vibrations may affect blade failure. In order to avoid resonance, the blade natural frequencies need to be determined. The goal of this research is to determine the blade free vibration mode shapes and modal frequencies, neglecting the variation of the upstream wind speed for simplicity. The blade modal vibration is studied numerically using ANSYS WORKBENCH software, and analytically using thin-beam theory and an assumed modes method. Firstly, the analysis is performed on a 17 m diameter Sandia blade with a simplified troposkein shape with a NACA 0015 airfoil. The first ten modes and the corresponding natural frequencies were calculated using ANSYS. The analysis was done for stationary and spinning blade at 54 rpm. The spin case compared very well to previous Sandia results. The same analysis was then applied to an ideal troposkein shaped blade, and a slightly modified cross section. Results show consistency across the blade shapes. The Sandia blade shape was studied analytically using thin-beam theory and an assumed modes method. Kinetic and potential energies were derived. Mass and stiffness matrices are formulated for the discretized model, to which modal analysis is applied. The natural frequencies were calculated analytically for same simplified Sandia blade shape used for finite element model under stationary condition. The results of the two methods were compared for consistency.