List of symbols Latin letters A Empirical spectral shape based on the Strouhal number (dB) C Airfoil chord (m) D h Directivity function, high-frequency noise () f Frequency (Hz) K 1 SPL level experimental correction factor (dB) L Span of the airfoil (m) M Mach number () OASPL Overall sound pressure level (dB) Re C Reynolds number, based on airfoil chord () r e Effective observer distance (m) SPL 1/3 Sound pressure level for a 1/3 octave band (dB) SPL p, 1/3 Sound pressure level for a 1/3 octave band, at pressure side (dB) St Strouhal number, fδ * /U () St p , St 1 Strouhal number, peak frequency () TU Turbulence intensity (% of U) U Local mean velocity (m/s) U ∞ Uniform flow velocity (m/s) Y + Wall coordinate, dimensionless distance to wall () Greek letters α Angle of attack (°) δ * Boundary layer displacement thickness (m) δ * p Boundary layer displacement thickness, pressure side (m)
Turbulent inflow (TI) noise is reported as an important source of wind turbine (WT) broadband aeroacoustic noise, coexistent with many other sources (e.g., the airfoil self-noise). This manuscript intends to elucidate the discussion on TI noise by providing an alternative prediction method based on the rapidly distorted anisotropic turbulent velocity energy spectrum. A review on turbulent inflow noise prediction is presented, followed by the discussion on turbulence modeling and the derivation of a modified TI noise prediction expression, which allows a more detailed assessment of wind turbine noise sources. This can contribute for WT blade optimization, once it is implemented in design codes that consider noise as a constraint. Criteria for the turbulent velocity spectrum to be characterized by the rapid distortion theory (RDT) are established, and the validation methodology is carried through comparisons between the novel semi-empirical prediction method and data gathered from recent literature for a flat-plate airfoil with 3% relative thickness and a NACA 0008 airfoil. The RDT-modified turbulent inflow noise prediction method shows better agreement with the measured data, when compared to predictions that adopt an isotropic model for the turbulent velocity energy spectrum, a condition only achieved in the absence of the airfoil in the test section of aeroacoustic facilities.
This paper summarizes the determination of more realistic local Reynolds and Mach flow numbers at the blades of a largediameter, horizontal-axis wind turbine designed specifically for this purpose with the aid of the blade element momentum method, and the subsequent effort to extend the validation range of the modified-BPM airfoil trailing edge noise method against a single high Reynolds number acoustic dataset available. The validation extension effort proved unfruitful, and the reasons are discussed in detail in relation to the dataset employed. After coupling the BPM model to a hybrid boundary layer solver, the resultant modified method, called PNoise, was embedded into the TU Berlin (HFI) wind turbine design, open code environment, QBlade, available under General Public License. During the time period past since the release of the first integrated version (v0.95), the open-source code has been downloaded by users more than 20,000 times, prompting the trial for further validation of the proposed method. Although the validation extension is not sanctioned based on this preliminary investigation, the calculation of more realistic flow conditions over the blades of current utility-size wind turbines could be helpful to other researchers. Also, this effort highlighted the significant uncertainties associated with methods employed to obtain acoustic spectra from one specific aeroacoustic wind tunnel, especially when the acoustic signal obtained experimentally is later subjected to transforming algorithms. The findings also stress the fact that more reliable experimental data is needed under high Reynolds numbers (notice: all Reynolds numbers described in the text are local, chord-based Reynolds numbers.) in order to support TE and other airfoil self-noise model development and validation. Keywords Wind turbine noise • Airfoil trailing edge noise • PNoise • BPM model • QBlade List of symbols Latin letters c Airfoil chord (m) C p Power coefficient () cl Lift coefficient for the airfoil section () cd Drag coefficient for the airfoil section ()
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