Aeroacoustic calculations of a full scale Nordtank 500kW wind turbine

The Actuator Line/ Navier-stokes technique is used to compute the incompressible flow around a full scale Nordtank 500kW wind turbine under different complex flow conditions such as atmospheric turbulence and wind shear. The flow field is used as an input to aeroacoustic calculations based on; a semi empirical noise model; and a Navier-Stokes based computational aeroacoustic code (CAA). The Navier-Stokes based approach is solving acoustic perturbation equations and is capable of taking propagation and ground effects into account, but is limited to low frequency noise due to feasible mesh resolution, and due to the simplification in the actuator line method using body forces to represent the blade. Noise levels are compared to field measurements of a Nordtank 500kW wind turbine at different wind speeds and inflow profiles.


Introduction
Wind turbine noise has been identified by Megavind, a strategic partnership for the Danish wind industry, as the most important environmental impact of wind-energy systems [1]. The pace of growth of on-shore wind energy has led to turbines being placed closer to where people live. Placing the turbines close to residential areas creates social acceptance problems, especially in densely populated areas such as Europe. Consequently noise regulations have become stricter, particularly in Denmark. In the past decades mechanical noise has been a major issue, but due to improved components designs this has been lowered significantly. Therefore the focus is now on aerodynamic generated noise. Aeroacoustic noise can be divided into two major mechanisms: airfoil self-noise, and turbulent inflow noise. Turbulent inflow noise appears due to the interaction of incoming turbulent eddies in the atmospheric boundary layer with the blade. These eddies are rather big in comparison to the size of eddies in the boundary layer developing along the blade surface. Because of that turbulent inflow noise is the dominant noise source at lower frequencies. Airfoil self-noise is generated by of the boundary layer interaction on the pressure and suction side at the trailing edge. Vortices in the boundary layer on the pressure and suctiion side interact with the hard blade surface, especially at the sharp trailing edge, radiating acoustic waves. Since the boundary layer is relatively thin, the main contribution of airfoil self-noise is at higher frequencies.
The flow around a single wind turbine or a wind farm is very complex due to wind shear, yaw, atmospheric turbulence, and wake effects. Hence it is important to have high fidelity codes for the flow and the acoustics to be able to capture these flow conditions and their effect on wind turbine noise.

Methodology
A two-step approach is used to calculate aerodynamic noise of a wind turbine. The flow chart in Figure 1 gives an overview of the methodology. First the flow field around a wind turbine is simulated using Large Eddy Simulation (LES) with the Finite Volume Method, block structured, multi grid solver EllipSys3D, developed at Denmark Technical University [2] with the actuator line method [3]. In a second step the acoustic calculations are done based on the flow simulation as input. For the acoustic calculation two different methods are used, an acoustic model based on semi empirical scaling laws, and a high fidelity model based on solving the Navier-Stokes equations.

Actuator Line Technique
In the actuator line method forces mimicking the wind turbine blades are added by introducing additional source terms to the Navier-Stokes equations, with U i as velocity, P as incompressible pressure, ρ as density, ν as kinematic viscosity, c as chord length, C l (α, Re) and C d (α, Re) as lift and drag coefficient, f i as the added body forces, f 2D as the force per spanwise unit length, and U rel as the local relative flow velocity close to the blade segment. The forces f 2D are calculated using tabulated airfoil data and are then introduced as smeared body forces f i in the Navier-Stokes equations. Turbulent stresses are modelled by the mixed-scale turbulence model of Ta Phuoc [4]. Different flow conditions can be added to the flow simulation, such as wind shear , and atmospheric turbulence. Wind shear follows equation (4), with U ∞ as a reference wind speed at a specified height H and a shear exponent α. Atmospheric turbulence is introduced with a Mann box [5]. The Mann model assumes a constant shear based on a roughness length z 0 . Body forces are added in the flow calculations at a slice upstream the wind turbine, creating a velocity field with atmospheric turbulence.

Acoustic perturbation equations
To take propagation and ground effects into account and to study the development of aeroacoustic noise in the source region a high fidelity method is needed. A Navier-Stokes based approach, the acoustic splitting technique, developed by Shen and Sørensen [6] is used to capture those effects. The acoustic calculation is split into two steps: solving the incompressible flow field, and solving acoustic perturbation equations (5)(6)(7)(8). The acoustic perturbation equations are derived by introducing the compressible flow variables with a decomposition of an incompressible and an acoustic part.
Instantaneous incompressible velocities U i and pressure P are taken from the incompressible LES computation. The main source term in these equations is the fluctuating incompressible pressure ∂P ∂t . With this splitting it is possible to use different meshes for flow and acoustic simulation and to use different time steps for both calculations. Using different time steps is especially beneficial in low Mach number flows.

Improved Brooks, Pope, Marcolini model
Based on experimental data and acoustic scaling laws semi empirical acoustic formulas for airfoils were developed by Brook, Pope, and Marcolini [7] and by Lowson [8]. Those semi empirical noise models have been combined and extended to wind turbine level by Zhu et al. [9]- [10] in the Improved Brooks, Pope, Marcolini (IBPM) model, which takes into account the detailed blade shapes and the consideration of trailing edge shapes in the new blunt trailing edge noise model. In Figure 2 sketches of airfoil self noise mechanisms are shown (left), and the methodology of the IBPM model (right). The blade is divided into airfoil sections. At each section the noise of an airfoil is calculated based on local angle of attack, and local relative flow velocity. Those quantities are input from the incompressible flow solution at each time step. The noise levels for each airfoil segment at each blade are summed up in 1/3 octave band with respect to a specified observer position. Due to the input of the incompressible LES actuator line model computation, noise calculations can be done for any flow condition around the wind turbine, such as atmospheric turbulence, and wind shear.

Results
Aeroacoustic calculations are done for a Nordtank 500kW wind turbine with a blade radius of R = 20.5m and a hub height of H = 1.8R = 36m. The computations are compared to The tip speed ratio is set to λ = 10, 7.5, 6.0 leading to a wind speed of 6, 8, and 10m/s at hub height. Atmospheric turbulence is introduced by a Mann box at a distance of 6R in front of the wind turbine. For each wind speed a turbulent box was created, with a surface roughness of z 0 = 0.1m. The average turbulent intensity is about 11% in the stream-wise direction for all three boxes. 9% is reported for the measurements. The Mann box has a dimension of [12R; 12R; 380R].

Actuator line solution
In Figure 3 the stream-wise velocity field for a wind speed of 10m/s is shown. The wind turbine is placed at Z = 5R; Y = 1.8R, and its position is indicated as a black vertical line. Atmospheric turbulence is introduced at Z = −1R and has a significant influence on the incoming flow facing the wind turbine, as well as on the wake development. In particular it has an influence on local angel of attack and local relative velocity, that are inputs to the semi empirical noise calculation.
To validate the loading, integral values are compared against measurements. In Figure 4 thrust coefficient C T = T 1/2ρAV 2 , and power coefficient C P = P 1/2ρAV 3 are compared against measured values [12]. The agreement is fairly good. The slope of C T curve is slightly higher than the measured one, with a maximum difference ∆C T = 0.05. The shape of the power coefficient is matched, with a peak at v = 8m/s or a tip speed ratio of λ = 7.5. The maximum deviation ∆C P   The local forces along the blades cause a fluctuating incompressible pressure ∂P ∂t that acts as a source term in the acoustic perturbation equations and can be seen in Figure 5. On the left (a) the local normalized forces at selected span wise sections are shown. They are oscillating with blade passing frequency, but have a superposed fluctuation due to the atmospheric turbulence. The loading is highest at the outer part of the blade and so are the force fluctuations. From this it can be expected that the acoustic sources are strongest in the outer part of the blade. On the right (b) the power spectral density (PSD) of the normalized forces are plotted. The highest spectral energy is in the lower frequencies and decays to higher frequencies. The sampling frequency is 300Hz.

Acoustic Perturbation Equation
As mentioned in the last section the forces on the blade generate a pressure change with respect to time ∂P ∂t . This acts as a source term in equation (8) leading to an acoustic pressure change. The instantaneous acoustic pressure field due to the wind turbine can be seen in Figure 6 for a wind speed of 10m/s. Acoustic waves are formed by the blades and propagate away from the wind turbine. The blade position of one blade is at an azimuthal angle of 180%, which corresponds to the blade being in the plane plotted, at bottom position. The highest instantaneous acoustic pressure is at the outboard section of the plane, since the aerodynamic forces are highest in this region (see Figure 5) and almost no noise is generated at the root part of the blade. Atmospheric turbulence adds fluctuations to the acoustic waves, that are modulated on a acoustic pressure change with the blade passing frequency. The influence of the ground can also be seen. An acoustically hard wall has been set, so that acoustic waves hitting the ground are fully reflected. In Figure 7 the narrowband sound pressure level at a position 2.2R downstream of the turbine is compared to data from measurements for wind speeds of v = 6, 8, 10m/s. The grey solid lines are measurements data with the turbine in operation, the grey dashed lines are background noise measurements data with the turbine turned off. The coloured solid lines represent the acoustic pressure calculated with the acoustic perturbation equations. The comparison shows a mismatch between the spectrum of the acoustic pressure with the spectrum from the measurements. The sound pressure level decays too fast for frequencies above 10Hz. We conclude that this is due to the fact, that the geometry of the blades as solid walls and the boundary layers of the blades are not resolved in the actuator line method. The mechanism of small turbulent eddies in the boundary layer interacting with the solid blade generating aerodynamic noise is not captured by modelling the blades with the actuator line technique. In future work additional noise sources out of the semi empirical IBPM model will be introduced along the blades in the acoustic perturbation equations to capture this.

IBPM
In Figure 8 the calculated A-weighted sound pressure level at 45m behind the wind turbine and ground level can be seen for wind speeds of 6, 8, and10m/s for a 2min period. The sound pressure level changes periodically with the blade passing frequency and is about 2dB(A). This is usually referred as amplitude modulation noise (AM). Atmospheric turbulence adds fluctuations to the local angle of attack, and directivity. Due to the random appearance of the none-periodic change in sound pressure level people are usually more annoyed by the perceived sound. Hence being able to calculate this contribution is important for wind turbine noise prediction tools.
In Figure 9 A-weighted sound pressure level in 1/3 octave bands out of the semi empirical model improved BPM model is compared to data from measurements. A comparison with the microphone in downwind position is shown. The semi empirical noise model is in good agreement with the experiment, especially for wind speeds of 8m/s and 10m/s. The peak in the experiments at ca. 50Hz is due to mechanical noise and cannot be captured with the aeroacoustic noise model. Background noise has been added to the computations to make a fairer comparison to the experimental data. As can be seen in Figure 7 the background noise is almost as high as the wind turbine noise between 60 − 160Hz. For 10m/s the calculated noise level show for frequencies below 200Hz up to 4dB deviation to the measurements. In this range the wind turbine noise is dominated by turbulent inflow noise. One explanation is, that a fixed value of 11% turbulence intensity is used in the model for the turbulent inflow noise. These 11% are the mean turbulent intensity of the Mann box. Due to the shear turbulent intensity varies with height and is higher at lower levels above ground and hence TI noise levels could be under predicted. At frequencies above 5kHz the IBPM model over predicts the noise levels for wind speeds of 6m/s and 8m/s. In this region trailing edge bluntness noise dominates. This behavior has been observed before and a new bluntness model was recently published [10]. Highest A-weighted sound pressure level of ca. 40dB(A) appear at 600Hz. The semi empirical noise model predicts lower levels at lower wind speeds. The measurements almost collapse at this frequency, while usually a decrease in sound pressure levels is seen for lower wind speeds.
Overall the semi empirical noise model predicts the sound pressure levels of the Nordtank 500kW wind turbine well.

Conclusions
Aerodynamic noise computations of a full scale Nordtank 500kW for wind speeds of 6, 8, and 10m/s were presented. Two methods are used to compute the noise: a Navier-Stokes based approach solving acoustic perturbation equations; and a semi empirical noise model. With the acoustic perturbation calculation ground, and propagation effects are included. Acoustic pressure is calculated in the whole domain and hence it is possible to get the acoustic response as a 3D field. An acoustical hard surface was used, and the influence of it was shown in a slice, cut through the wind turbine origin in the stream-wise direction. Compared to measurements the spectrum of the acoustic pressure at 45m behind the turbine at ground level shows a mismatch in amplitude for frequency above 10Hz.
In the flow computation, that is used as an input for the acoustic perturbation equation calculation, the blade is modelled with body forces in the actuator line technique. Hence the blade geometry and the boundary layers of the blades are not resolved. Noise due to the interaction of the blade geometry and the boundary layer is not fully captured. In future work the semi empirical IBPM noise model will be used to introduce additional noise sources in the acoustic perturbation equations along the blade to capture noise at higher frequencies.
The comparison with the semi empirical noise model shows good agreement. It could be shown that OAM appears due to the atmospheric boundary layer and its effect on change in local angle of attack and relative flow velocity. Sound pressure levels in 1/3 octave bands fit well with the