This paper develops a computational acoustic beamforming (CAB) methodology for identification of sources of small wind turbine noise. This methodology is validated using the case of the NACA 0012 airfoil trailing edge noise. For this validation case, the predicted acoustic maps were in excellent conformance with the results of the measurements obtained from the acoustic beamforming experiment. Following this validation study, the CAB methodology was applied to the identification of noise sources generated by a commercial small wind turbine. The simulated acoustic maps revealed that the blade tower interaction and the wind turbine nacelle were the two primary mechanisms for sound generation for this small wind turbine at frequencies between 100 and 630 Hz.
Noise is a critical issue affecting the continued development and use of small wind turbines, owing to the fact that small wind turbines are often installed in proximity of residential (populated) areas. However, similar to other emerging industries, noise issues are of secondary concern for small wind turbine manufacturers. Indeed, rightly or wrongly manufacturers still view the fabrication process and the total wind turbine cost (affordability) as the most important issues that need to be considered for the widespread use of small wind turbines [
In order to resolve the noise issues associated with the operation of small wind turbines, it is important to determine the locations of the primary sources of sound generation on a wind turbine. To this purpose, it is noted that application of a systematic methodology for noise source identification (NSI) would enable the localization of the sound sources on a wind turbine. This, in turn, would allow engineers to redesign the wind turbine (e.g., blades, hub, and tower) in order to reduce (or minimize) the noise generation. Currently, the NSI methodology for small wind turbines relies mainly on the use of acoustic beamforming measurements. This experimental methodology for noise source determination utilizes arrays of microphones in various geometric configurations for the measurement of the sound field generated by the wind turbine. Subsequently, these array-based microphone sound measurements are processed using high-resolution acoustic beamforming algorithms for the noise source identification. However, the cost of conducting an acoustic beamforming measurement campaign for the noise characterization of a wind turbine is high, especially when it is necessary to use a complex array involving a very large number of microphones. Furthermore, it is frequently difficult to deploy a microphone array at the optimal measurement location for the noise source identification, owing to some environmental limitations (obstacles such as trees, rocks, buildings, etc.). As a consequence, there are very few researchers that have conducted acoustic beamforming measurements for small wind turbines [
In view of the limitations arising from the use of experimental acoustic beamforming for the noise characterization of small wind turbines, we propose an alternative methodology in this paper. More specifically, we propose to use a computational acoustic beamforming (CAB) methodology for the identification of noise sources on a small wind turbine. The CAB methodology was first proposed by Li [
To resolve the discrepancies between the experiment and numerical results reported by Li [
This paper is organized as follows. In Section
The CAB methodology consists of three components: namely, the CFD, acoustic propagation and acoustic beamforming components. The CFD component is used to simulate the unsteady flow field containing the sound sources; the acoustic propagation component is used to simulate the sound propagation and calculate the acoustic signals at specified locations (e.g., microphone locations); and the acoustic beamforming component is used to generate the acoustic maps using the predicted acoustic (microphone) signals. A hybrid method is used in the CAB methodology for the simulation of the flow-generated noise. This approach decouples the flow simulations (CFD component) from the acoustic calculations (acoustic propagation component). Aerodynamic properties obtained from the CFD simulation can be used as inputs to the acoustic calculations. However, any changes in the noise simulation will not affect the flow field calculations. In this way, the same set of data (sound source information) obtained from the CFD simulation can be used for different arrangements of the receivers. The CFD simulation is the most computationally intensive component of the CAB methodology and, as a result, the use of a hybrid method increases the computational efficiency significantly. This is due to the fact that the CAB methodology can be applied to various cases using different microphone arrangements and/or different microphone array locations without having to redo the CFD calculations. However, the use of this hybrid method in the CAB methodology limits its principal application to flows at low Mach numbers (weakly compressible flows) [
In greater detail, Figure
Flowchart showing the three main components of the CAB methodology.
The CFD component involves conducting the CFD simulations to determine the flow field quantities that embody the sound source information, such as the flow velocity, density, and pressure. In the NACA 0012 airfoil and WINPhase 10 wind turbine cases (described later), the flow field around the airfoil or the small wind turbine is simulated in the CFD component.
The CFD simulations are conducted using a commercial CFD package, namely, STAR CCM+®. To this purpose, the flow field around the NACA 0012 airfoil (described in Section
The sound source information provided by the CFD component is used by the acoustic propagation component to calculate the sound signals at a set of prescribed locations for the microphone. The acoustic propagation component was conducted using an in-house code that implements the FW-H integral method [
where
When the permeable integration surface coincides with the solid surface, the body and fluid velocities are related by
The sound signals calculated with the acoustic propagation component are transferred to the acoustic beamforming component. Within the CAB methodology, the latter component is used to generate the acoustic maps for the identification of the possible sound sources.
The acoustic beamforming calculation is conducted using an in-house code that implements the time-domain delay-and-sum acoustic beamforming algorithm [
The diagonal removal technique, which is widely used to improve the signal-to-noise ratio (SNR) for large microphone arrays mounted on wind-tunnel wall surfaces (e.g., for the removal of turbulent boundary layer wall-pressure fluctuations) [
The experimental aeroacoustic data for the NACA 0012 airfoil provided by the National Renewable Energy Laboratory (NREL) was used for the validation of the CAB methodology. The objective of this experiment was to understand the aeroacoustic performance of six different airfoils that are candidates for use in small wind turbines [
The computational domain used for the aerodynamic simulation of the NACA 0012 airfoil has dimensions of
Twenty prism layers were generated around the airfoil with a layer stretch ratio of 1.2. The resulting nondimensional wall distance had the value of
Computational mesh used for the aerodynamic simulation of the NACA 0012 airfoil: (a) mesh for the whole computational domain and (b) mesh around the airfoil trailing edge.
The aerodynamic simulation of the flow around the NACA 0012 airfoil was based on LES with the Smagorinsky subgrid-scale model [
A uniform velocity distribution was prescribed at the inlet of the computational domain with an inlet Mach number of 0.12. The pressure at the outlet boundaries of the domain was set to atmospheric pressure. The airfoil surfaces were treated as no-slip smooth walls. The top and bottom boundaries of the computational domain were treated as symmetric planes. Periodic boundary conditions were applied at the front and back surfaces of the computational domain.
The impermeable integration surface used for the aeroacoustic simulation coincides with the airfoil wall boundary. The acoustic propagation calculation used the sound source data which was obtained by periodically extending the original sound source data derived from the CFD simulation by five times in the spanwise direction. The impermeable formulation of the FW-H equation is employed for the aeroacoustic simulation. The central-differencing scheme was used to approximate the time derivatives in the acoustic propagation calculations.
The spherical wave incidence acoustic beamformer was used for the acoustic beamforming calculations. Owing to the fact that the microphone array geometry employed in the NACA 0012 airfoil experiment [
Two microphone arrays used for aeroacoustic simulation for the NACA 0012 airfoil: an Archimedean spiral array (a) and a star array (b).
Sketch showing the location of the microphone array and the source plane used for the aeroacoustic simulation of the NACA 0012 airfoil.
The acoustic images were computed at the source plane with 3 mm spatial resolution in the spanwise direction and 7 mm spatial resolution in the streamwise direction, in conformance with those measured in the wind-tunnel experiment [
The predicted lift
Lift and drag coefficients comparison for the NACA 0012 airfoil at zero degree angle-of-attack.
Experiment [ |
Simulation (time-averaged) | |
---|---|---|
|
0 | 0.0105 |
|
(0.0062, 0.0082) | 0.0065 |
Figure
Mean airfoil surface pressure coefficient at zero degree angle-of-attack: predicted results (a) and experimental data (b). The upper triangle symbols correspond to the experimental data from [
Predicted velocity magnitude contours and streamlines around the NACA 0012 airfoil: (a) velocity magnitude (m s−1) contours and (b) velocity streamlines around the trailing edge region of the airfoil.
Figure
Acoustic maps for the NACA 0012 airfoil obtained from experimental measurements [
Despite the differences in the sizes and coordinates (different locations were chosen for the origins in the simulation and experiment, resp.) of the acoustic maps shown in Figures
It is noted that the acoustic maps obtained from the numerical simulation provide a much larger dynamic range than those obtained from the experimental measurements. This implies that the acoustic maps obtained from the numerical simulations using the CAB methodology have a higher signal-to-noise ratio (SNR) than those obtained from the experimental measurements. This is not surprising given the fact that the experimental data are subject to various sources of noise (e.g., background noise) that is absent in the numerical data.
In order to evaluate the effect of the periodic expansion of the sound source information in the spanwise direction on the resulting acoustic maps, Figure
Predicted acoustic maps for the NACA 0012 airfoil obtained using the original sound source data (a) and using a periodic extension of the original sound source data in the spanwise direction (b).
Continuing with the validation of the CAB methodology using the NACA 0012 airfoil, we study the effect of the inclusion of the diagonal removal process in the acoustic beamforming calculations on the generation of the acoustic maps. Figure
Predicted acoustic maps for the NACA 0012 airfoil obtained without (a) and with (b) the inclusion of the diagonal removal process in the acoustic beamforming calculations.
Furthermore, the areas of the region of maximum SPL on the acoustic maps with the inclusion of the diagonal removal technique are slightly larger at the higher frequencies than those obtained without the inclusion of the diagonal removal technique. This shows that the diagonal removal process might worsen the acoustic beamforming spatial resolution while increasing the dynamic range. Although most of the investigations reported that the use of the diagonal removal technique improved the dynamic range on the acoustic maps, some investigators [
Next, we investigate the effect of different microphone array geometries on the generation of acoustic maps. Figure
Predicted acoustic maps for the NACA 0012 airfoil obtained using an Archimedean spiral array (a) and a star array (b).
It is stressed that there is no “universal” microphone array geometry that would produce optimal results vis-à-vis the acoustic beamforming for every case. For the current application involving the identification of trailing edge noise from the NACA 0012 airfoil, an Archimedean spiral array generally resulted in a better spatial resolution, but a star array yielded a higher SNR at frequencies above 1000 Hz. However, it is not possible to conclude that one array performs better than the other because both arrays were found to provide correct predictions of the locations of the sound source for the various frequencies examined. In consequence, both array geometries will be used to generate acoustic maps for the identification of the source of wind turbine noise described in the next section.
The flow field simulation and acoustic propagation calculations for the WINPhase 10 small wind turbine have been conducted previously by Ma et al. [
The WINPhase 10 wind turbine is a three-bladed upwind-arranged small wind turbine. The field measurements of the sound pressure level for this wind turbine were conducted by Intertek Testing Services Ltd. [
Figure
Computational domain used for the aerodynamic simulation of the WINPhase 10 small wind turbine.
The dimensions of the computational domain were as follows:
The mesh used for the discretization of the computational domain for the WINPhase 10 wind turbine aerodynamic simulation: (a) front view of the three blades and (b) seven prism layers surrounding a turbine blade.
As mentioned earlier, the CFD simulation for the WINPhase 10 wind turbine applied the DDES methodology using the S-A turbulence model [
A set of reference wind speeds in the range from 9 to 11 m s−1 with a one-seventh power-law dependence on height above the ground surface was used to prescribe the wind speed profile at the computational domain inlet for the DDES simulations. The turbulence viscosity ratio was set to a value of 10 at the inlet boundary [
In accordance with the American Wind Energy Association (AWEA) and the International Electrotechnical Commission (IEC) standards [
Standard configuration for microphone measurement positions (plan view).
The acoustic propagation solver (second component of the CAB methodology) used the data (sound source information) obtained from the aerodynamic simulation of three complete revolutions of the WINPhase 10 wind turbine blades. The permeable formulation of the FW-H equation was used for the sound propagation calculation. The Stirling scheme [
Figure
Sketch showing the locations of the microphone (MC) arrays used for the acoustic beamforming for the WINPhase 10 wind turbine.
Two microphone array geometries (namely, an Archimedean spiral array and a star array) were used for the acoustic beamforming calculations for the WINPhase 10 wind turbine. Three scenarios, which were determined by the lowest frequency of interest and by the focusing capabilities of the array, were applied for each array geometry:
Figure
WINPhase 10 wind turbine power predictions compared with field measurement data.
Figure
Spectra of the A-weighted sound pressure level (SPLA) for an inflow velocity of 9 m s−1 at hub height. The continuous lines show the narrow-band SPLA spectra. The bars correspond to the SPLA spectra frequency averaged over one-third octave bands (blue bar: numerical results; black bar: experimental data (EXP)).
The acoustic maps for three inflow wind speeds (9 m s−1, 10 m s−1, and 11 m s−1 at the wind turbine hub height) were generated from the predicted sound signals at the microphones for two array geometries. Owing to similarities of the acoustic maps obtained for the three inflow velocities, we present only the acoustic maps generated for a 9 m s−1 inflow velocity. These maps were computed in the frequency range from 100 to 800 Hz for one-third octave bands (the same bands as displayed in Figure
Predicted acoustic maps for the WINPhase 10 wind turbine for an Archimedean spiral array: 8 m × 8 m horizontal array at ground level (a); 20 m × 20 m horizontal array at ground level (b); 20 m × 20 m vertical array parallel to the wind turbine rotor plane (c). The inflow velocity is 9 m s−1 at the turbine hub height. The wind turbine rotates in the counter-clockwise direction.
Predicted acoustic maps for the WINPhase 10 wind turbine for a star array: 8 m × 8 m horizontal array at ground level (a); 20 m × 20 m horizontal array at ground level (b); 20 m × 20 m vertical array parallel to the wind turbine rotor plane (c). The inflow velocity is 9 m s−1 at the turbine hub height. The wind turbine rotates in the counter-clockwise direction.
According to (
For the NACA 0012 airfoil case investigated in Section
For the two different microphone array geometries employed, the area of the identified sound source in the acoustic maps obtained for the vertical microphone array (Figures
An examination of Figures
However, at frequencies below 200 Hz, the noise source location is difficult to identify because this source appears to cover a relatively large area in the acoustic maps. It is anticipated that the use of more advanced acoustic beamforming techniques can potentially be used to improve the spatial resolution and, hence, to better localize the noise sound source in the acoustic maps for frequencies less than 200 Hz. Two examples of super-resolution techniques for acoustic beamforming are the nonnegative least squares and the deconvolution approaches for noise source identification. It has been reported that these super-resolution techniques can improve the spatial resolution of the acoustic maps by a factor typically between three and ten [
To better localize the noise sources in the acoustic maps for frequencies above 800 Hz for this small wind turbine, a finer mesh and a smaller time step will need to be used in the CFD simulations. If this is done, it is anticipated that the high-frequency noise source information (for frequencies greater than about 800 Hz) can be encapsulated in the flow field calculations. This information can subsequently be passed onto the aeroacoustic calculations which can then be used in the generation of acoustic maps that will provide better localization of noise sources from the wind turbine that are associated with frequencies greater than about 800 Hz.
We have proposed the CAB methodology for identification of noise sources generated by a small wind turbine. This predictive method was validated using the NACA 0012 airfoil trailing edge noise case. The predicted acoustic maps obtained using the methodology were in excellent agreement with the corresponding observed acoustic maps obtained from wind-tunnel experiments. We found that the spatial resolution of the CAB methodology for the acoustic maps increases with increasing frequency. Furthermore, we found that an Archimedean spiral array has a better spatial resolution than a star array for all frequencies of interest. Finally, an Archimedean spiral microphone array exhibits better SNR at frequencies below 1000 Hz, but poorer SNR at frequencies above 1000 Hz when compared to the performance of a star microphone array.
The good agreement with the experimental data for the NACA 0012 airfoil case provides the confidence to apply the CAB methodology on a commercial small wind turbine (WINPhase 10 wind turbine). Despite the coarse grid and large time step used in the CFD simulations, the simulated aerodynamic results (wind turbine power output) and aeroacoustic results (A-weighted SPL spectra) were in good agreement with some field measurements for this wind turbine. The simulated acoustic maps revealed that the blade tower interaction and the wind turbine nacelle were two possible noise generation mechanisms in the range of frequencies between 200 and 630 Hz for this small wind turbine.
The agreement between the numerical results obtained using the CAB methodology and the corresponding experimental data for both the NACA 0012 airfoil and the WINPhase 10 wind turbine suggests that the methodology proposed herein can be used to obtain deeper insights for the noise generation issue for other types of wind turbines and turbomachinery. This is especially true for applications where it would be difficult and expensive to conduct a comprehensive set of acoustic beamforming measurements. The CAB methodology can also be applied in cases that require large-sized microphone arrays and/or large numbers of microphones. In particular, it is anticipated that the CAB methodology will be less expensive to apply in these cases owing to the increasing availability of cheap high-performance computing. In addition, the CAB methodology can also be applied as a virtual proving ground for optimization of microphone array geometries and acoustic beamforming algorithms for noise source identification that can take the user through the complete development cycle from design to evaluation. Finally, the use of the CAB methodology provides not only the acoustic maps for the noise source identification, but also the associated flow field which embodies the sound source information. This additional flow field information, which cannot be provided by the traditional acoustic beamforming experiments, can help researchers to gain deeper physical insights into the causes of the noise generated by turbomachinery (e.g., wind turbines, airfoils, etc.).
Time-domain beamforming at time
Time-domain beamforming at grid point
Airfoil chord length
Speed of sound
Time-averaged airfoil lift coefficient
Time-averaged airfoil drag coefficient
Wind turbine rotor diameter
Wind turbine hub height
Measurement distance for the acoustic beamforming
Component of vector defined in (
Magnitude of local Mach number vector for the source
Component of local Mach number vector for the source defined in Equation (
Mach number for the source in the direction of the radiation,
Mach number
Total number of microphones
Component of unit outward normal vector to surface
Local force intensity
Gauge pressure
Pressure signal for microphone
Distance between the microphone array center and the wind turbine
Spatial resolution for the acoustic beamforming
Reynolds number
Distance between the observer and the source
Component of unit vector in the direction of the radiation propagation
Distance between the assumed source and the microphone array center
Distance between the assumed source and microphone
Observation time
Nondimensional time step
Components of vector defined in (
Reference velocity at the computational domain inlet
Component of local fluid velocity
Fluid velocity in the normal direction to the body
Friction velocity
Kinematic viscosity of the fluid
Component of local velocity on the body
Local velocity on the body in the direction normal to the body surface
Reference velocity for power-law inlet boundary condition prescription
Weighting coefficient for microphone
Observation position vector
Distance normal to the wall
Dimensionless wall normal distance (
Source position vector
Time average
Generalized function
Source time differentiation.
Grid point
Wavelength
Density of fluid
Density perturbation,
Source time
Propagation time from source plane grid point
Time delay associated with microphone
Microphone array diameter.
Fluid variable in quiescent medium
Loading noise component
Thickness noise component.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors would like to thank WINPhase Energy Inc. for making their wind turbine power and acoustic field measurements available to them. The authors would also like to thank Natural Sciences and Engineering Research Council of Canada (NSERC). This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: