Modeling of trailing edge noise on the rotor blade of a wind turbine
Background
Wind power is a common source of renewable energy. However, noise from wind turbines is a significant problem for wider use in the onshore sector, as the highly intermittent noise source is perceived as more disturbing than other noise sources with comparable sound pressure levels (such as cars or aircraft) due to the continuous rotation. Trailing edge noise is considered the largest noise source in this regard. However, the physical mechanisms for the generation of trailing edge noise have not yet been conclusively clarified. Therefore, the aim of this research project is to develop a model and a detailed understanding of the generation mechanisms of trailing edge noise, which are related to coherent structures in the turbulent boundary layer and in the wake of the rotor blade, in order to develop control and influencing solutions for reducing the noise in the long term. Such coherent structures are visualized exemplarily on the right. Contours of instantaneous flow velocity are shown in a generic turbulent plate boundary layer from a direct numerical simulation (from publication 1, see below).
Methods
In this project, data-driven methods such as spectral proper orthogonal decomposition (SPOD) are used to identify the dominant coherent structures in highly turbulent experimental and numerical flows. The SPOD modes are correlated with the sound pressure level by linear stochastic estimation to identify those coherent fluctuations that contribute most to the trailing edge noise. Linear stability analysis (LSA) and resolvent analysis (RA) are used to model the coherent structures to predict the pressure fluctuations on the wing surface that are responsible for the trailing edge noise. The model is validated against the coherent fluctuations extracted empirically using SPOD. Subsequently, the far-field noise is calculated using the Curle equation with the LSA and RA modes as the noise sources.
On the one hand, the reduced-order model is useful for data assimilation. It can be used to estimate the intensity of coherent fluctuations and noise at an early stage of the design process, where only the mean flow and at least one time-resolved pressure signal need to be known (e.g., using a simple pressure sensor). This saves sophisticated numerical simulations such as LES or DNS or a complex experimental setup. On the other hand, quantitative identification and modeling of the noise-generating coherent modes provides new insights into the physical mechanisms leading to trailing edge noise. This can be used to improve existing methods of passive and active flow control for noise reduction or even to develop novel approaches.
Results
The figure below illustrates the methodology used in the LowNoise project, applied to the flow around a NACA0012 airfoil. First, the span-time-averaged flow field (left) is obtained from either Reynolds Averaged Navier-Stokes (RANS) simulations or Large Eddy simulations (LES). In the case presented, the mean field was obtained from an implicit LES using the open-source PyFR library, with the flow going from left to right. Then, the relevant coherent structures within the boundary layer and wake (middle) are extracted using a linear stability analysis about the turbulent mean flow. Here, stream-wise velocity fluctuations obtained from an incompressible resolvent analysis are shown. Due to the moderate angle of attack, an adverse pressure gradient occurs on the (upper) suction side of the airfoil, leading to the development the coherent structures via shear layer instabilities of the boundary layer. The coherent structures create pressure fluctuations on the surface of the airfoil, which are used as input to an acoustic analogy to reconstruct the radiated sound. Here, Curle's solution to Lighthill analogy is used to obtain pressure fluctuations away from the surface of the airfoil (right).
