Randomization to Tackle Mid-Frequency Acoustic Tones in Wind Turbines
Wind turbine towers can often become modal if matched closely in frequency with the excitation associated with rotating components in the drive train, such as gearboxes and generators. When these conditions are met, the modal response is greatly amplified due to the very low structural damping of the steel structure resulting in undesired audible tones. Furthermore, the steel structures have large surface areas making them very efficient at radiating tonal noise. Tonal noise can have adverse effects on neighboring residences and its emissions can result in strong regulatory penalties that can include the closure of wind farms.
At frequencies below ~200 Hz the modality of with turbines and the resultant tonal acoustic output can be readily modeled using a combination of structural dynamics, acoustic finite elements, and boundary element methods in COMSOL Multiphysics®. At frequencies above ~1 kHz the modal density of the turbine towers and blades become very high and the problem is better approached using a statistical energy approach (SEA). However, the excitation forces related to gearbox and direct-drive generates commonly fall between 200 Hz and 1 kHz; this zone is sometimes referred to as the mid-frequency problem in vibro-acoustic modeling.
COMSOL Multiphysics’® Methods in the Application Builder has been employed to model the mid-frequency tones radiated by wind turbines. The wind turbine was represented in the Structural Mechanics module using shell elements to model the tower with a series of added-masses used to represent the nacelle components, blades and hub. The model coupled structural Mechanics with the Acoustics Module and used the Boundary Element Method to calculate the far-field sound pressure level. A series of Methods were written in the Application Builder to randomize the key design elements such as the tower’s mass distribution and damping, the foundation stiffness and the mass of the nacelle and rotor components. The LiveLink™ for Matlab® was used to batch process and solve randomized models ~1000 times. Statistical methods used on the resultant model output show the distribution of the tower’s response as a function of frequency. The results show that the mid-frequency range in wind turbine towers is dominated by bending modes with significant contributions from panels modes at higher frequency.
