Wall-pressure spectra, spanwise correlation, and far-ﬁeld noise measurements of a NACA 0008 airfoil under uniform and turbulent inﬂows

This paper discusses unique measurements of wall-pressure ﬂuctuations (WPFs), spanwise correlation length, and far-ﬁeld noise of a NACA 0008 airfoil subjected to uniform, non-turbulent and turbulent inﬂows. From these measurements, the near-ﬁeld characteristics of trailing-edge (TE) and leading-edge (LE) noise of a thin airfoil are analyzed. The competing nature of the LE and TE noise mechanisms of an airfoil subjected to a turbulent inﬂow is also investigated. Experiments were performed in the Aeroacoustic Wind Tunnel of the University of Twente for a chord-based Reynolds number ranging from 3 . 2 × 10 5 to 9 × 10 5 for a uniform inﬂow and a rod-generated turbulent inﬂow with a turbulence intensity of approximately 18%. The eﬀective angles of attack ranged from -5 ◦ to 5 ◦ . Measurements of the boundary layer at the TE, the WPFs along the chord and span, and the far-ﬁeld radiated noise were performed. For the uniform inﬂow case, laminar-boundary-layer noise, turbulent-boundary-layer (TBL) noise, and blunt TE noise sources are identiﬁed. The far-ﬁeld noise spectrum presents similar components in the frequency domain as the WPF spectrum and the spanwise correlation length at the TE. The angle of attack mainly aﬀects the WPF spectrum and spanwise correlation length for chord-based Strouhal numbers 𝑆𝑡 < 10 . The angle of attack slightly aﬀects the TE noise with a maximum variation of 3 dB for 10 < 𝑆𝑡 < 60 . For the turbulent inﬂow case, it is observed that the turbulence signiﬁcantly aﬀects the WPFs and spanwise correlation length along the chord, increasing considerably compared to the case of uniform inﬂow. The highest WPF spectral level and the larger spanwise correlation length occur at positions close to the LE. The results show that the turbulent inﬂow yields a higher WPF spectral level and larger spanwise correlation length at the TE, resulting in higher levels of TE noise. However, LE noise is still the dominant noise source for 𝑆𝑡 < 25 . 2 . For higher frequencies, the TE noise level is expected to become higher than the LE noise level.


Introduction
Flow-induced noise has attracted considerable research interest in the last decades because of its importance to engineering applications and its impact on the health of people and animals [1][2][3][4].The two main aerodynamic noise sources for foils are the trailing-edge (TE) and leading-edge (LE) noise [5].TE noise is generated by the interaction of the TE region of the foil blade with the boundary layer and near-wake flow [6].This noise source is relevant for wind turbines [7], aircraft, and noncavitating ship propellers [8].Depending on the flow conditions, different TE noise mechanisms are observed, for example, turbulent-boundary-layer (TBL) noise, laminar-boundarylayer (LBL) noise, and TE bluntness noise.For an overview of TE noise mechanisms, see Brooks et al. [6].LE noise becomes relevant when the * Corresponding author.E-mail address: f.l.dossantos@utwente.nl(F.L. dos Santos).inflow is turbulent.This noise is generated by the interaction of turbulent inflow with a foil LE [9].For the case of a foil exposed to a turbulent inflow, LE and TE noise become competing mechanisms, yet this has not been investigated extensively [10][11][12].LE noise is usually dominant for applications exposed to turbulent inflow [10][11][12], e.g., propellers [8] and fans [13].Botero-Bolívar et al. [14] investigated the influence of the inflow turbulence on the wall-pressure fluctuations (WPFs) at the TE of a NACA 0012 airfoil.They showed that the inflow turbulence increases the WPFs at the TE, which might affect the TE noise.Experimental studies focusing on the competitive nature of LE and TE noise generating mechanisms in the near field (such as WPFs and spanwise correlation lengths) are scarce.Thus, this paper presents an experimental investigation of TE and LE noise of a thin airfoil due to the importance of these noise sources to various applications and compethttps://doi.org/10.1016/j.apacoust.2023 Past studies often focused on the noise characteristics of NACA 4-digit series foils, such as the NACA 0012 [6,[14][15][16][17][18][19][20] and thicker foils [17,20,21], due to their symmetry and relevance for helicopter rotor and wind turbine aeroacoustics.However, foils used on ship propellers, outlet guiding vanes, and compressor cascades are generally thinner [22].The foil thickness is an important parameter for aeroacoustic studies since it affects the pressure gradient, directly impacting the radiated TE noise.Also, the inflow turbulence is distorted as it approaches a finite thick foil, affecting the radiated LE noise [13,21,23].Few studies have discussed the noise generated by thin airfoils.Paruchuri [12] experimentally investigated TE and LE noise for airfoils of different thicknesses, observing that the LE noise is dominant for low and mid frequencies.Gill et al. [24] performed a similar numerical study to analyze the effect of the airfoil geometry on the LE noise.Paruchuri [12] and Gill et al. [24] observed that LE noise decreases for high frequencies due to the airfoil thickness, which is attributed to turbulence distortion effects [24].Dos Santos et al. [23] investigated turbulence distortion effects on the LE noise prediction for a NACA 0008, showing that this effect is also relevant for thin airfoils.Juknevicius and Chong [22] experimentally studied the effects of straight and curved serrations on far-field noise generated by a NACA 0008 airfoil subjected to free-stream turbulence.The same authors [25] have also investigated the flow mechanism that results in TBL noise reduction when add-on saw-tooth serrations are used on a NACA 0008 using hot-wire anemometry and far-field noise measurements.Furthermore, the analysis of WPFs and spanwise correlation length in experimental investigations is limited due to difficulties in instrumenting a thin airfoil with surface microphones.
In this paper, an experimental investigation of TE and LE noise of a thin airfoil is carried out because of the importance of these noise mechanisms for various applications and their competing nature.The scope of the present study is to analyze and discuss unique measurements of WPFs, spanwise correlation length, and far-field noise of a thin airfoil subjected to uniform and turbulent inflows.From these measurements, we aim to gain insights into the near-field characteristics of TE and LE noise for a thin airfoil.Also, we aim to better understand the competing nature of LE and TE noise for a thin airfoil when subjected to a turbulent inflow.A NACA 0008 airfoil was chosen for this study because the instrumentation to measure the WPFs in an even thinner airfoil would be considerably more complex, and this geometry is considered a thin airfoil.The unique aspect of this work is the experimental analysis of the WPF spectra and the spanwise correlation length close to the airfoil LE and TE when subjected to uniform and turbulent inflows.Even for thicker airfoils, these types of measurements are challenging and scarce in the literature [26].

Experimental methodology
This section describes the experimental setups and the flow conditions for the measurements discussed in this paper.An overview of all measurements conducted is given in the supplementary material of this paper.

Wind tunnel facility
The experiments were conducted in the University of Twente AeroAcoustic Wind Tunnel, an open-jet, closed-circuit facility [27].The experiments were performed in the open test section of 0.7 m × 0.9 m (height x width).The turbulence intensity is below 0.08% [27].An anechoic chamber of 6 m × 6 m × 4 m encloses the test region with a cut-off frequency of 160 Hz [27].The flow temperature was controlled at approximately 20 • C. The reference coordinate system is shown in Fig. 1 with origin at the LE mid-span.The airfoil was installed vertically in the test section; see Fig. 2.

Airfoil geometry and instrumentation
A NACA 0008 airfoil with  = 300 mm chord and  = 700 mm span was used.The maximum thickness is 24 mm at ∕ = 0.30, and the TE thickness is  = 1 mm.The airfoil is instrumented with 82 pressure ports along the chord and span.The locations of all pressure ports are included in the supplementary material.The pressure ports allow the measurement of the static pressure and the WPFs, which were measured using remote microphone probes (RMPs) [28][29][30].The WPF measurements are discussed in Section 2.5.The RMP technique was chosen because it facilitates the instrumentation for WPF measurements in such a thin airfoil and results in a high spatial resolution, which is important to determine the spanwise correlation length of the turbulent structures on the airfoil surface.

Inflow turbulence
Measurements were performed for a uniform, non-turbulent inflow to investigate the near field at the TE region and the TE noise.In this case, the inflow turbulence corresponds to the wind tunnel turbulence, which is sufficiently low to consider the inflow non-turbulent.Experiments with a generated turbulent inflow were also conducted to evaluate the WPFs, the spanwise correlation length in the LE and TE regions, and the far-field noise.The turbulent inflow was generated by a rod of 40 mm diameter installed 0.68 m upstream of the airfoil LE; see Fig. 2. The width of the wake generated by the rod at the LE position is approximately 20 times larger than the airfoil maximum thickness.
Constant temperature hot-wire anemometry was used to measure the turbulence characteristics of the wake flow of the rod (discussed in ref. [23]).Table 1 lists the turbulence parameters at the LE location with the airfoil removed.  is the Reynolds number based on the airfoil chord length () and the streamwise velocity at the LE position without the airfoil in the test section ( LE ).For the case of uniform inflow, the free-stream velocity  ∞ is the same as  LE .However, for the rod-generated turbulent inflow, this is not the case because the airfoil LE is in the rod wake.  is the Reynolds number based on the rod diameter ( rod ) and the free-stream velocity ( ∞ ).Fig. 3 compares the velocity spectrum generated by the rod with the von Kármán spectrum combined with the dissipation range modeling proposed in ref. [31].The experimental spectrum agrees well with the von Kármán spectrum for higher frequencies, showing approximately the same decay.For low frequencies, it does not follow the von Kármán formulation, which is most probably because of the large turbulent structures due to the rod vortex shedding.The vortex shedding is observed at   rod ∕ ∞ ≈ 0.2, which corresponds to  ∕ LE ≈ 1.9.

Boundary layer measurements
The boundary layer at the airfoil TE was measured using hot-wire anemometry.A single-wire probe (Dantec Dynamics model 55P15) of 5 μm diameter and 1.25 mm wire length was used to measure the streamwise velocity.The probe translation was performed by a 3D traverse system with a resolution of 6.5 μm.The data was recorded for 20 s with a sampling frequency of 65,536 Hz and an anti-aliasing filter with a cut-off frequency of 30 kHz.The boundary layer was measured on the suction side at ∕ = 0.97 and mid-span.From the velocity profile, the boundary layer thickness is determined as the distance from the wall where the velocity corresponds to 99% of the edge velocity  e .The experimental boundary layer displacement  * and momentum  thicknesses are determined by performing a trapezoidal numerical integration of the velocity profile.The measured velocity profile is fitted to the law of the wall using the equation proposed by Coles [32].The friction velocity   is determined from this fitting with a coefficient of determination of 0.99.

Wall-pressure fluctuation measurements
The WPFs were measured using the RMP technique [28][29][30]33].This technique consists of microphones installed in a remote position, i.e., not directly flush with the airfoil surface.In this study, the microphones were installed at the end of tubes that guided the pressure fluctuations on the airfoil surface to the microphone.A total of 82 microphones (FG-23329-P07 Knowles) were used.The pressure ports on the airfoil surface had a diameter of 0.3 mm and were connected to stainless steel tubes of 1.5 mm inner diameter.An in-house plexiglas connection unit was manufactured and used to mount the stainless steel tube to the microphone and the anechoic termination, which consisted of polyurethane tubes with a 1.6 mm inner diameter.The end of these tubes was sealed.Each RMP sensitivity and frequency response was calibrated in situ using an in-house calibrator.More information about the RMP setup and the calibration is given in ref. [23,28].The data was acquired for 30 s at a sampling frequency of 65,536 Hz using PXIe-4499 Sound and Vibration modules installed in a NI PXIe-1073 chassis.The spanwise correlation length   quantifies the length scales in the spanwise direction present in the turbulent flow as a function of frequency.  is calculated as [9,10]: where the coherence ( 2 ) is computed between pairs of RMPs at the same chordwise position spaced in the spanwise direction by   .In this study,   is calculated at ∕ = 0.007 and 0.97.The trapezoidal method is used for the numerical integration of the coherence.Thirteen RPMs were distributed along the span following a logarithmic distribution.However, the spanwise position of some RMPs was adjusted to ensure that the distance between pairs of RMPs was different for all possible combinations of RMPs.This optimization was performed so that the integral used to compute the spanwise correlation length can be estimated more accurately.Thus, the distribution of 13 microphones resulted in 78 distinct distances between pairs of microphones.The minimum distance between a pair of microphones (  = 2.3 mm) was dictated by the minimum distance required to install two pressure ports side by side.The maximum distance (  | max = 82.3mm) was estimated to be roughly the integral length scale of the turbulent inflow tested.Fig. 4 shows the coherence between pairs of microphones at ∕ = 0.97 spaced by the minimum and maximum distances for different flow conditions.The coherence is almost zero in the entire frequency range for   | max = 82.9mm, indicating that the maximum distance between a pair of microphones is sufficiently large to ensure the decay of the coherence to zero.This distance   | max is the upper limit of the integral in Eq. ( 1).

Far-field noise measurements
A microphone phased array [18,34] was used to localize and quantify the TE and LE noise.A circular array with a 1 m diameter consisting of 62 GRAS 40 PH microphones distributed in a Vogel spiral arrangement was used; see Fig. 2. Each microphone was calibrated using the pistonphone GRAS 42AG Multifunction Sound Calibrator with a sound pressure level of 94 dB and frequency of 1 kHz.The microphone array plane was parallel to the - plane, with its center aligned with the airfoil center at 1.5 m distance.The far-field noise was acquired for 30 s at a sampling frequency of 65,536 Hz using PXIe-4499 Sound and Vibration modules installed in a NI PXIe-1073 chassis.
Noise localization and quantification were performed using an inhouse beamforming algorithm which has been benchmarked against an array benchmark database [35,36].Diagonal removal was applied to the cross-spectral matrix (CSM).Microphone weighting was not applied in the beamforming process.The frequency response of each microphone was accounted for in the CSM calculation.Conventional beam-

Measurement
× 10 forming in the frequency domain was performed on a searching grid ranging ∕ ∈ [−2, 3] and ∕ ∈ [−0.71, 0.71] in the plane composed of the airfoil chord-span lines.The grid resolution was 0.1  in each direction.Amiet's shear layer correction method [37] was applied following the procedure described by Bahr et al. [38].TE and LE noise were determined with the source power integration (SPI) technique [39].Different regions of integration (ROI) are analyzed to determine the appropriate ROI size.Fig. 5 shows the TE far-field noise for the case of turbulent inflow in the frequency range where the TE noise is observed.This case is chosen because two noise sources located in different regions are present, i.e., LE and TE noise.Three ROI sizes varying in the streamwise direction are investigated: a spanwise length of 0.6 and streamwise lengths of 0.2, 0.6, and 1.0, with the ROI centered at the TE mid-span.The maximum level difference between these ROI sizes is 3 dB, with the highest noise level occurring for an ROI extending 1.0 in the streamwise direction.This ROI size is relatively large and is likely to be contaminated with LE noise.The level difference between the ROI sizes 0.2 and 0.6 is less than 1 dB.An ROI size of 0.2 is chosen in order to minimize contamination from LE noise.Regarding the spanwise extent of the ROI, three sizes are analyzed: a streamwise length of 0.2 and spanwise lengths of 0.6, 0.7, and 0.8.The maximum level difference among these ROI sizes is approximately 1 dB.An ROI size of 0.6 is chosen to avoid contamination from the wind tunnel walls.A similar analysis was also performed for TE noise for uniform inflow and for LE noise.This analysis showed a difference of less than 1 dB for all ROIs investigated.Thus, the ROI used for TE noise evaluation was ∕ ∈ [0.9, 1.1] and ∕ ∈ [−0.3, 0.3]; see Fig. 5.For LE noise, the ROI was ∕ ∈ [−0.1, 0.1] and ∕ ∈ [−0.3, 0.3]; see Fig. 5.The power spectral density (PSD) of the SPI is given at the array center.The uncertainty of the sound power estimated by conventional beamforming in the frequency domain method is around 1 dB [36].

Flow conditions
Table 2 summarizes the flow conditions for the measurements performed.Some tests were conducted for different angles of attack.The effective angle of attack was determined from the wind tunnel correction [6]: where  geom is the geometric angle of attack and  WT is the wind tunnel height.Forced transition was induced by a zigzag strip installed at ∕ = 0.05.The height of the trip was chosen based on the flow condition, following the recommendations from dos Santos et al. [18].Thus, the trip height was between 50% and 100% of the boundary layer thickness at the trip location, which was determined from XFOIL [40,41].The trip height used for each measurement is given in the experimental campaign overview in the supplementary material.

Power spectral density and coherence determination
The PSD of the WPFs   , the CSM for the beamforming method, and the coherence  2 between a pair of microphones were calculated using Welch's method [42].The data was averaged using blocks of 8192 samples (125 ms) and windowed by a Hanning windowing function with 50% overlap, resulting in a frequency resolution of 8 Hz.This frequency resolution was chosen because it is sufficiently small for narrowband components to be visible in the spectrum but large enough for the resulting spectrum not to be noisy.The spectral levels are shown in dB.The reference values used to compute the spectral level in dB are  ref = 20 μPa and Δ ref = 1 Hz.

Boundary layer at the airfoil trailing edge
Fig. 6 shows the velocity and the turbulence intensity profiles at ∕ = 0.97 for   = 6×10 5 with forced transition for different effective angles of attack.The angle of attack directly affects the velocity and the turbulence intensity profiles, resulting in higher turbulence intensities as the angle of attack increases.The curves named "Fit."correspond to the law of the wall by Coles [32] fitted to the measured velocity profile.The friction velocity is determined from this fit and decreases as the angle of attack increases.Table 3 shows the boundary layer parameters determined from the velocity profile.The boundary layer thickens as the angle of attack increases.This occurs due to the stronger adverse pressure gradient the airfoil is subjected to at a higher angle of attack.
The boundary layer parameters are also determined using XFOIL [40] and compared with the experimental results; see Table 3. XFOIL is a two-dimensional panel method that allows steady-state viscous/inviscid analysis of an airfoil aerodynamic performance.The boundary layer

Table 3
Boundary layer parameters at ∕ = 0.97 on the suction side for different effective angles of attack,   = 6×10 5 ,  = 0.087, and forced transition at ∕ = 0.05.The values between curly brackets correspond to the boundary layer parameters for  ef f = {0 shape factor  , displacement thickness  * , and momentum thickness  are output from XFOIL from which the boundary layer thickness is calculated as [41]: The friction velocity   is determined from the skin friction coefficient   , which is also obtained from XFOIL: Table 3 shows that the XFOIL simulation results present similar tendencies as the experimental data; i.e., as the angle of attack increases, the boundary layer thickens and the friction velocity decreases.The simulations predict ,  * , and  with a difference from the experimental values up to 27%, which is satisfactory in view of the limitations of the flow model used in XFOIL and the many factors that can influence the boundary layer measured, such as the determination of the distance from the wall, the resolution of the measurement points, and the tripping device used.For example, dos Santos et al. [18] showed that the boundary layer thickness varies significantly with the trip height used.They showed that  could increase by as much as 35% as the trip height increased, even though the trip height used was smaller than the boundary layer thickness at the trip location for all cases.The difference between the simulation and measurement results decreases for higher angles of attack.The agreement of the experimental and simulated friction velocity is good for  ef f = 0 • , but it significantly worsens as the angle of attack increases.This analysis shows that using XFOIL to estimate the boundary layer parameters is reasonable, mainly for an angle of attack close to zero, because then the friction velocity presents a reasonable agreement with the measurements.XFOIL results are used in the next sections to scale the WPF spectrum because XFOIL estimates the boundary layer parameters fairly well, and boundary layer measurements are not available for all flow velocities investigated.

Wall-pressure fluctuation spectrum and spanwise correlation length
Fig. 7 shows the WPF spectrum   and the spanwise correlation length   at ∕ = 0.97 on the suction side for natural transition for different Reynolds numbers and angles of attack.In Fig. 7a, a hump and a peak are observed for   = 2 ×10 5 in the low-frequency range.They are due to the laminar structures still present in the boundary layer, such as Tollmien-Schlichting (TS) waves [14].No pressure fluctuations are observed for frequencies higher than 1 kHz because the boundary layer is still laminar.As the Reynolds number increases to   = 4 × 10 5 , a broadband component is observed, indicating that turbulent structures with various sizes have developed.However, the boundary layer is not yet fully turbulent because the hump with peaks is evidence of the presence of laminar structures.Thus, the boundary layer is under transition.By increasing the Reynolds number, the hump amplitude decreases until only a broadband component is observed (  ≥ 9 × 10 5 ).This occurs because the laminar structures in the boundary layer cease to exist at the TE as the Reynolds number increases due to the upstream movement of the transition.Similar behavior is observed for the spanwise correlation length, with the hump and peaks occurring at the same fre-quencies as observed for the WPF spectra; see Fig. 7c.As the Reynolds number increases, the laminar instabilities are broken down into turbulent structures resulting in a decrease in the spectral hump level and its eventual disappearance.This breakdown also results in a broadband spectral content since flow structures of various sizes are formed.
Fig. 7b shows the WPF spectrum for different angles of attack for   = 6 × 10 5 .As highlighted before, for  ef f = 0 • , a hump with peaks is observed, indicating that the boundary layer is under transition.As the angle of attack increases, the spectrum is only composed of a broadband component, indicating that the boundary layer is turbulent.This behavior occurs because the adverse pressure gradient becomes stronger for higher angles of attack, triggering an earlier transition on the suction side.For low frequencies and a turbulent boundary layer ( ef f ≥ 3 • ), the WPF spectral level increases with the angle of attack because the boundary layer becomes thicker as the angle of attack increases, resulting in a higher energy level for large turbulent structures, i.e., low frequencies.Similar results are observed for the spanwise correlation length; see Fig. 7d.This figure shows that the laminar structures in the boundary layer are no longer present for higher angles of attack.Also, it shows that the large turbulent structures increase with the angle of attack, which is associated with the thickening of the boundary layer.
To analyze the WPF spectrum for a TBL, a tripping device is used to hasten the laminar-turbulent transition.Fig. 8 shows the WPF spectrum at ∕ = 0.97 for  ef f = 0 • with forced transition for different Reynolds numbers.The spectrum for the different Reynolds numbers mainly consists of a broadband component, indicating that the boundary layer at the TE is turbulent (no peaks due to laminar instabilities) and that turbulent eddies with various sizes are present in the boundary layer.Hence, the tripping device successfully triggered a faster transition, resulting in the development of a TBL at the airfoil TE.The spectrum scaling is investigated following the scaling in Glegg and Devenport [5]; see Figs. 8b and 8d.The parameters for the scaling are taken from XFOIL [40,41] results because experimental data is unavailable for all velocities tested.Different scalings are used in the low-and high-frequency ranges.At low frequencies, the pressure fluctuations are essentially generated by the large turbulent structures in the outer part of the boundary layer.However, Fig. 8b shows that the spectra curves do not collapse with the scaling using the outer boundary layer parameters, i.e.,  e and .To understand why the low-frequency range does not scale with the outer variables, the velocity scaling of the spectrum is analyzed since the only variable changing is the velocity.For simplicity, it is assumed that the TBL has developed as for a zero-pressure-gradient flat plate following the one-seventh-power law [43].The scaling of  e , , and   with the free-stream velocity is [43]: Therefore, the outer variable scaling ( e ∕(( 2  ) 2 )) should scale with the velocity to the 2.4 th power.Fig. 8c shows that the spectrum for low frequencies ( ∕ ∞ < 0.4) scales with the velocity to the 2 nd power.The reason why the spectra do not scale with the outer variables might be associated with the tripping device effects on the transition process and on the boundary layer thickness, which would directly impact the scaling with .Dos Santos et al. [18] showed that the boundary layer thickness depends on the ratio of the trip height to the boundary layer thickness at the location of the trip.The input values used in the scaling of Fig. 8b were obtained from XFOIL, where the tripping device influence on the boundary layer thickness is not considered.Thus, the fact that the WPF spectra do not scale with the outer variables is likely due to the effect of the tripping device on the boundary layer thickness.
The small eddies close to the wall are governed by the viscosity  and the wall shear stress   =  2   from which the high-frequency scaling of the WPF spectra is defined [5].Fig. 8d shows that the scaling for high frequencies ( ∕ 2  > 0.02) presents a good collapse of the spectral curves.As the tripping device does not significantly influence the friction velocity [44], it is expected that it also does not greatly affect this scaling.Fig. 9 shows the WPF spectrum and the spanwise correlation length at ∕ = 0.97 for   = 6 ×10 5 with forced transition for different angles of attack.The WPF spectral level and the spanwise correlation length increase for low frequencies as the angle of attack increases, as was also observed for natural transition (Figs.7b and 7d).This increase occurs because the boundary layer becomes thicker with the angle of attack (see Table 3).As the large structures in the boundary layer are of the order of magnitude of  [5], the thickening of the boundary layer results in larger turbulence length scales inside the boundary layer.At stall, a significant increase in the spectral level is observed in the lowfrequency range.This is associated with the large vortices formed when the flow is separated.This observation is supported by the spanwise correlation length results, where a considerable increase in the correlation length is observed for low frequencies, indicating the formation of large turbulent structures.

Trailing-edge noise
Fig. 10 shows the measured far-field noise for different Reynolds numbers for natural transition.The far-field noise is shown for frequencies where the background noise is not dominant.The far-field noise spectrum has similar components as the WPF spectrum shown in Fig. 7a.The similarity between the components in the WPF spectrum and the far-field noise can be explained because the WPFs are the source for the far-field noise [10].For   = 2 × 10 5 , tones are observed in the far-field noise for low frequencies, with the spectral level decaying rapidly with frequency.The peak observed in the WPF spectrum at 440 Hz is also observed in the far-field noise.In addition, the WPF spectral level rapidly decays after this peak, which is also observed in the far-field noise spectrum.When the Reynolds number increases to   = 4 ×10 5 , the far-field noise consists of a broadband component and a broadband hump with discrete tones.These spectral components are also observed in the WPF  spectrum and spanwise correlation length shown in Fig. 7 for similar frequency ranges.The tonal noise is known as LBL noise and is observed for low-and moderate-Reynolds number flows.The broadband component is due to the incoherent eddies with various sizes reaching the TE [45].The WPF spectrum for these flow conditions (Fig. 7a) shows a broadband component, confirming the existence of eddies with various sizes at the TE.According to Arbey and Bataille [46], the broadband hump results from the diffraction by the TE of TS instabilities.Analyzing the WPF spectrum in Fig. 7a, it is clear that TS instabilities are present at the TE since the TS instabilities are responsible for the spectral hump observed in the WPF spectrum.This hump ceases to exist in the WPF spectrum and spanwise correlation length at   = 9 × 10 5 (see Figs. 7a and 7c), which is the same Reynolds number at which the spectral hump and tonal noise cease to exist in the far-field noise (see Fig. 10).This observation corroborates the statement of Arbey and Bataille [46] because the spectral hump with tones in the far-field noise is only observed when TS waves are present at the TE.The mechanism responsible for generating the tones is based on an aeroacoustic feedback loop between the acoustic waves diffracted at the TE and a point upstream of the airfoil where the TS waves are amplified by the acoustic waves [46,47].By increasing the Reynolds number, the level of the hump and tones decreases because the point where the aeroacoustic feedback loop closes moves further upstream, making the feedback loop more difficult to sustain.For   = 9 × 10 5 , the spectrum is broadband without tones because the aeroacoustic feedback loop is ceased.A hump in the high-frequency range becomes noticeable for   ≥ 6 × 10 5 , which is blunt TE noise.This noise source is discussed in more detail below.
Fig. 11a shows the scaling of the far-field noise measured for  ef f = 0 • with forced transition for different Reynolds numbers.The background noise for the different Reynolds numbers is also shown in this figure.The noise is shown for frequencies where the background noise is not dominant and the TE noise is visible in the beamforming maps.The -axis shows the Strouhal number based on the boundary layer thickness at the TE, which is taken from XFOIL results.No tones are observed in the spectrum, indicating that the tripping device eliminated the LBL noise.This figure shows that the TE noise level scales with the velocity to the 3 rd power when the frequency is scaled with the Strouhal number based on .However, the scaling of the TE noise level with velocity depends on the frequency scaling used.Fig. 11b shows the TE noise spectrum with the frequency scaled with the TE thickness  and the level scaled with the velocity to the 4 th power.This scaling results in a good overlap of the curves for  ∕ ∞ > 0.1.Roger and Moreau [48] observed a good overlap of TE noise by scaling the frequency as  ∕ ∞ and the level with the velocity to the 5 th power.These different velocity scaling powers are observed most likely because in one scaling ( ∕ ∞ ) the velocity dependence is considered in both  and  ∞ terms, whereas in the other scaling ( ∕ ∞ ) the velocity dependence is only considered in the  ∞ term.In addition, two TE noise mechanisms are present, i.e., TBL noise and blunt TE noise, which might also affect the scaling.These noise mechanisms are discussed in the next paragraph.The overall sound pressure level (OSPL) is shown in Fig. 12 so that a scaling of the TE noise level that does not depend on the frequency scaling can be obtained.The OSPL is plotted as a function of the Mach number  =  ∞ ∕ 0 , where  0 is the speed of sound in air at the ambient condition of 20 • C. The experimental OSPL is fitted to a curve as a function of  , resulting in an exponential value of 5.3.Zhu et al. [49] also performed a similar analysis for the case where TBL noise and blunt TE noise were observed, as it is the case in the current study.Their results scale with the Mach number to the 5.7 th power, which is close to the value encountered in this research.
The spectrum in Fig. 11a presents a hump at  ∕ ∞ ≈ 0.8, which is attributed to the blunt TE of the NACA 0008 because it generates a turbulent vortex street, resulting in a peak or hump in the noise spectrum [50].According to Blake [51], blunt TE noise is negligible if the TE is sufficiently sharp, such that the bluntness parameter ∕ * < 0.3 is satisfied.This parameter is 0.56 < ∕ * < 0.67 for the Reynolds numbers tested, where  * was obtained from XFOIL.Thus, blunt TE noise contribution to the far-field noise is expected.Brooks and Hodgson [52] performed measurements with a NACA 0012 with blunt TE thicknesses of 2.5, 1.9, and 1.1 mm and a sharp TE.They observed blunt TE noise at  ∕ ∞ ≈ 0.1.Moreau and Doolan [53] and Herr and Dobrzynski [54] conducted measurements on a flat plate with blunt TE and observed blunt TE noise at 0.08 < ∕ ∞ < 0.11 and  ∕ ∞ ≈ 0.1, respectively.Fig. 11b shows that by scaling the frequency as  ∕ ∞ a hump is observed at 0.085 < ∕ ∞ < 0.09, which is close to the values observed in the other studies.The broadband component is likely due to TBL noise because the boundary layer is turbulent at the TE for these flow conditions.Also, this is expected because the blunt TE noise adds a hump to the broadband noise originating from the TBL noise [6,49].
Fig. 13 shows noise levels for different angles of attack relative to the zero-angle-of-attack results.A positive angle of attack indicates that  the airfoil suction side was toward the microphone array, whereas a negative angle of attack indicates that the pressure side was directed toward the microphone array.The angle of attack slightly influences the radiated TE noise in the frequency range analyzed with a maximum difference of 3 dB for both suction and pressure sides.Hutcheson and Brooks [55] analyzed the effect of the angle of attack on the TE noise for a NACA 63-215.They observed that the angle of attack mainly affected the TE noise for low frequencies.Even though TE noise for frequencies lower than 1 kHz is not clearly visible in the beamforming maps, an increase in the far-field noise would be expected for low frequencies because the WPF spectral level and the spanwise correlation length increase with the angle of attack (see Fig. 9), which, according to Amiet's theory [10], would result in an increase in the radiated noise.Hutcheson and Brooks [55] observed that the noise for high frequencies was hardly affected, as is also found in this study.The small effect of the angle of attack on the TE noise for high frequencies is in accordance with the WPF spectra for the different angles of attack; see Fig. 9.

Results for a turbulent inflow
In this section, the measurements for the case of a turbulent inflow generated by a rod are discussed and compared with the case of uniform inflow.

Wall-pressure fluctuations and spanwise correlation length
Fig. 14 shows the WPF spectrum at ∕ = 0.007 for  ef f = 0 • and different Reynolds numbers.The frequency is shown as the Strouhal number for the rod, i.e.,   rod ∕ ∞ .A hump is observed for low frequencies.It collapses well at   rod ∕ ∞ ≈ 0.24 for the different Reynolds numbers.The Strouhal number for the vortex shedding of a bluff body is approximately 0.2 (Sharma et al. [20] found 0.23, and Schlichting and Gersten [56] found 0.21).Thus, the hump in Fig. 14 is most probably due to the periodic Kármán vortices shed by the upstream rod interacting with the airfoil LE.
Fig. 15a shows the WPF spectrum for   = 4.8 × 10 5 and  ef f = 0 • at different chordwise positions.The highest energy level is observed closest to the LE at ∕ = 0.007, where the inflow turbulence is directly impinging on the surface.The spectrum level decreases with the chordwise position.The low-frequency hump is clearly observed up to ∕ = 0.73, showing that the rod vortex shedding affects the low-frequency WPFs along the airfoil chord.Fig. 15b shows the spanwise correlation length, which decreases with the chordwise direction.A hump is observed in the spanwise correlation length at the same frequency (rod Strouhal number) for which the vortex shedding is observed.This hump is also observed at ∕ = 0.97, showing that the rod vortex shedding affects the WPFs up to the TE.Similar results were also obtained for the other Reynolds numbers tested.
To gain insight into the near field of the competing nature of LE and TE noise mechanisms, the WPF spectra and spanwise correlation lengths for uniform and turbulent inflows are compared.Fig. 16 shows the WPF spectrum and spanwise correlation length at ∕ = 0.97 for the cases of uniform and turbulent inflows.In addition, the results at ∕ = 0.007 for the case of turbulent inflow are shown.The WPFs near the LE are approximately 18 dB higher (at  = 304 Hz) than at ∕ = 0.97 for the turbulent inflow case.The spectral level near the TE (∕ = 0.97) increases when the inflow is turbulent.The WPFs very close to the LE, i.e., at ∕ = 0.007, are only due to the impingement of the turbulent inflow on the surface since the boundary layer is barely developed yet.In this case, the WPF spectrum decays with frequency to the power -2.For turbulent inflow and 200 <  < 1600 Hz, the WPF spectrum at ∕ = 0.97 decays with frequency to the power -1.5, which is relatively close to the spectral decay observed at ∕ = 0.007 but considerably different from the decay of the spectrum for the case of uniform inflow (decay with frequency to the power -0.9).This indicates that the turbulent inflow strongly influences the large scales of the developed boundary layer, resulting in a spectral decay that resembles that of a WPF spectrum induced by the pure interaction of the turbulent inflow with the surface.Previous research [57][58][59] investigated the penetration of the free-stream turbulence in the boundary layer, showing that the turbulent inflow penetrates the outer part of the boundary layer and, for sufficiently high turbulence levels, it can penetrate up to locations very close to the wall, i.e., down to the small scales, resulting in an amplitude modulation of the smaller length scales.Similar trends are also observed in the current research.The WPF spectrum at ∕ = 0.97 shows higher levels in the entire frequency range, indicating the penetration of the free-stream turbulence for all scales measured.Interestingly, the decay with frequency of the WPF spectrum at ∕ = 0.97 changes to a power of -0.9 at approximately  = 1600 Hz, yielding a level decay with frequency more comparable to the case of a TBL for the uniform flow case  but with a higher spectral level.These results suggest that the turbulent inflow penetrates the boundary layer, strongly affecting the large turbulent structures (low frequencies) associated with the outer boundary layer part and resulting in higher spectral levels for the small structures (high frequencies) located near the wall.The effect of the turbulent inflow is not only limited to the WPF spectral levels.The spanwise correlation length is considerably larger at the TE for low frequencies when the inflow is turbulent.This is a consequence of the penetration of the inflow turbulence in the boundary layer, resulting in larger turbulent structures in the spanwise direction.Note that, even though the spanwise correlation length increases close to the TE when the inflow is turbulent, this correlation length is still larger close to the LE.According to Amiet's theory [9,10], LE and TE noise are proportional to the spanwise correlation length at the LE and TE region, respectively.Thus, LE noise is expected to be dominant for low frequencies because of the larger spanwise turbulence length scales and the higher level of WPFs, which is the source of LE and TE noise.This hypothesis is confirmed in Section 4.3.As the WPF spectral level and the spanwise correlation length at the TE increase when the inflow is turbulent, the TE radiated noise is expected to have higher noise levels when the inflow is turbulent compared to the TE noise levels for a uniform, non-turbulent flow.This hypothesis is investigated in Section 4.3.

Leading-edge far-field noise
Fig. 17a shows the nondimensionalized PSD of the LE noise generated by the airfoil when subjected to inflow turbulence generated by the rod for different Reynolds numbers.The far-field noise is shown for frequencies where the background noise is not dominant, i.e., 100 <  < 2500 Hz with the upper limit varying slightly with the Reynolds number.The normalization follows the approach in ref. [5].The curves collapse well for  ∕ LE > 6.For this range and this scaling, the LE noise level scales with the velocity to the 3 rd power (if we consider that  rms ∝  LE ).However, the level scaling with the velocity depends on the frequency scaling.Fig. 17b shows the LE noise level scaled with the velocity to the 5 th power and the frequency as the Strouhal number based on the turbulence integral length scale.A good overlap of the data is observed for  Λ  ∕ ∞ > 0.6.These results demonstrate that the velocity scaling of the LE noise levels depends on the scaling parameters used to normalize the frequency, as also observed for the TE noise.With frequency scaling  Λ  ∕ ∞ , the velocity dependence is present in the variable  ∞ but also in the Λ  term since the length scale also depends on the flow velocity; see Table 1.For the turbulent inflow investigated in this research, the integral length scale shows a dependence with the velocity to the 1 st or 2 nd power (the exact absolute power could not be deduced accurately).The low-frequency range does not overlap with the scaling laws shown in Figs.17a and 17b.This is investigated next.
Fig. 17c shows the LE noise level scaled with the velocity to the 5 th power and the frequency scaled with the rod Strouhal number, presenting a good overlap of the noise for low frequencies.The low-frequency hump collapses with this scaling, occurring at   rod ∕ ∞ ≈ 0.185, which is close to the Strouhal number for the rod vortex shedding.To verify if the low-frequency hump is due to the interaction of the vortex shedding with the airfoil LE, the airfoil noise is compared with the background noise.Fig. 17d shows the far-field noise from a single microphone aligned with the airfoil mid-chord and mid-span at 1.5 m distance.The background noise is measured without the airfoil in the test section with the wind tunnel on and with the rod in the flow.The hump centered at  = 180 Hz for the background noise is due to the noise generated by the Kármán vortices shed by the rod.This same hump is also observed for the airfoil noise.However, there is a difference of 4.3 dB between the airfoil noise and the background noise at  = 180 Hz.Thus, the low-frequency hump for the airfoil noise is attributed to the interaction of the Kármán vortices shed by the rod with the airfoil LE.In previous works [20,60], it was also observed that the LE noise due to the interaction of vortex shedding with an airfoil scales with the velocity to the 5 th power.

Leading-and trailing-edge noise competing characteristics
Fig. 18 shows the source maps obtained from beamforming for the case of inflow turbulence generated by the rod.The noise generated by the airfoil LE interacting with the inflow turbulence, i.e., LE noise, is dominant for frequencies up to 2520 Hz.For higher frequencies, no noise sources from the airfoil are observed.In Fig. 16, it was shown that the WPF energy content at the TE for the measurements with inflow turbulence increased for low frequencies, which might increase the TE noise.However, despite this trend, Fig. 18 clearly shows that the LE noise is the dominant noise source for this airfoil up to 2520 Hz ( ∕ LE = 31.5, =  ∕ ∞ = 25.2).For this frequency, two distinct    Fig. 19 shows LE and TE noise for the case of turbulent inflow (TI) and also shows the TE noise for the case of uniform, non-turbulent inflow (UI).For a turbulent inflow, LE and TE noise cannot be distinguished for frequencies below 800 Hz because the microphone array resolution is not optimal to localize low-frequency noise precisely.It is expected that the noise levels in this frequency range are due to LE noise since this noise source is known to be dominant for low frequencies [10,13].For frequencies above 800 Hz, LE and TE noise are distinguishable, with LE noise levels about 5 dB higher than TE noise levels on average.This confirms that LE noise is dominant up to approximately 2600 Hz.As seen from Fig. 16, the turbulent inflow results in higher levels of the WPF spectrum and a larger spanwise correlation length at the airfoil TE compared to a uniform, non-turbulent inflow.Thus, as the WPFs and the spanwise correlation length at the TE are directly linked to the TE noise [10], TE noise levels for a turbulent inflow are expected to be higher than for a uniform inflow.Comparing the TE noise for a uniform inflow and a turbulent inflow in Fig. 19, it is observed that the TE noise level for a turbulent inflow is higher than for a uniform inflow for 800 <  < 2000 Hz, with a difference of 10 dB at  = 1000 Hz.These results confirm that the TE noise level increases when the inflow is turbulent.However, for the case studied here, the LE noise is dominant for the frequencies investigated.noise for the case of turbulent inflow presents a broadband character, which is most likely TBL noise since the turbulent inflow induces a faster transition and thickening of the layer [59], which likely results in the suppression of TE noise.As in Section 3.3, the hump in the spectrum for uniform inflow at  = 2200 Hz is blunt TE noise, and the broadband component is TBL noise.

Conclusions
Measurements of WPFs, spanwise correlation length, and far-field noise for a NACA 0008 airfoil for the cases of uniform and turbulent inflows are analyzed and discussed in this study.For the uniform inflow case, LBL noise, TBL noise, and blunt TE noise are identified.For natural transition, the hump with discrete tones present in the far-field noise spectrum is also observed in the WPFs and spanwise correlation length at the TE at the same frequencies, showing that the near field in the airfoil suction side has a direct relation to the LBL noise.For forced transition, the TE noise is a combination of blunt TE noise and TBL noise, with the blunt TE noise resulting in a hump centered at  ∕ ∞ ≈ 0.087.The WPF spectral level and the spanwise correlation length at ∕ = 0.97 increase with the angle of attack for  < 10 due to the thickening of the boundary layer with the angle of attack.A considerable WPF spectral level and spanwise correlation length increase occur at the stall condition due to the large vortices formed when the flow is separated.The WPFs scale with the velocity to the 2 nd power for low frequencies and with the inner variables for high frequencies.TE noise is slightly influenced by the angle of attack with a maximum difference of 3 dB for 10 <  < 60.The scaling of TE noise levels with the velocity depends on the frequency scaling.By scaling the frequency with the boundary layer thickness, the TE noise levels scale with the velocity to the 3 rd power.In contrast, the TE noise levels scale with the velocity to the 4 th power when the frequency is scaled with the airfoil TE thickness.The overall sound pressure level scales with the velocity to the 5 th power, agreeing with the literature.
Measurements with a rod-generated turbulent inflow are analyzed to investigate the LE noise generation and the competing nature of LE and TE noise.The results show that the inflow turbulence generated by the rod has a significant effect on the WPFs along the chord and on the spanwise correlation length up to the airfoil TE.The WPF spectral level along the chord increases considerably when the inflow is turbulent, mainly in the low-frequency range.A hump in the WPFs is observed at rod Strouhal number of approximately 0.24 due to the rod vortex shedding interaction with the airfoil.This hump is observed up to the TE.The WPF level close to the LE is the highest, with a difference of approximately 18 dB at  = 304 Hz compared to the level at the TE.The spanwise correlation length also increases when the inflow is turbulent, showing a hump at rod Strouhal number of approximately 0.2.This correlation length is larger at the LE than at the TE, with a difference of approximately 0.02 at  = 304 Hz.The LE noise is shown to be dominant for frequencies up to  ∕ LE = 31.5( =  ∕ ∞ = 25.2), which occurs due to the higher WPF spectral level and larger spanwise turbulence correlation length at the LE region.LE noise scales with the 5 th power of the free-stream velocity for  Λ  ∕ ∞ > 0.6 when the frequency is scaled as  Λ  ∕ ∞ .The low-frequency hump due to the rod

Fig. 1 .
Fig. 1.Schematic view of the NACA 0008 profile with the pressure ports along the chord and spanwise directions.

Fig. 2 .
Fig. 2. Experimental setup for far-field noise measurements for the case of rodgenerated turbulent inflow.

Fig. 3 .
Fig. 3. Turbulence spectrum at the LE position with the airfoil removed for a turbulent inflow generated by the rod for   = 6.4 × 10 5 .

Fig. 5 .
Fig. 5. (a) TE far-field noise spectrum calculated for the case of turbulent inflow at   = 4.8 × 10 5 considering different ROI sizes.(b) Source map for 1/3-octave band with center frequency of 1,587 Hz for   = 4.8×10 5 with the rod generating the inflow turbulence.Decibel reference value:  ref = 20 μPa.

Fig. 6 .
Fig. 6.Boundary layer profiles at ∕ = 0.97 on the suction side for   = 6×10 5 with forced transition for different effective angles of attack.

Fig. 12 .
Fig. 12. Overall sound pressure level (OSPL) of the TE far-field noise for  ef f = 0 • with forced transition for different Mach numbers. ref = 20 μPa.

Fig. 13 .
Fig. 13.Relative noise level for different angles of attack for two different Reynolds numbers with forced transition.The noise level is in relation to the noise level for  ef f = 0 • . ref = 20 μPa, Δ ref = 1 Hz.Frequency resolution of 64 Hz.

Fig. 14 .
Fig. 14.PSD of the WPFs at ∕ = 0.007 for the case of inflow turbulence generated by a rod for  ef f = 0 • and different Reynolds numbers. ref = 20 μPa, Δ ref = 1 Hz.

Fig. 19 .
Fig. 19.Leading-edge (LE) and trailing-edge (TE) far-field noise comparison.UI -uniform, non-turbulent inflow at   = 5 × 10 5 ; TI -rod-generated turbulent inflow at   = 4.8 × 10 5 . ref = 20 μPa, Δ ref = 1 Hz.noise sources are observed: one at the LE and another at the TE.TE noise is not visible at 2520 Hz because of the level scale.Fig.19showsLE and TE noise for the case of turbulent inflow (TI) and also shows the TE noise for the case of uniform, non-turbulent inflow (UI).For a turbulent inflow, LE and TE noise cannot be distinguished for frequencies below 800 Hz because the microphone array resolution is not optimal to localize low-frequency noise precisely.It is expected that the noise levels in this frequency range are due to LE noise since this noise source is known to be dominant for low frequencies[10,13].For frequencies above 800 Hz, LE and TE noise are distinguishable, with LE noise levels about 5 dB higher than TE noise levels on average.This confirms that LE noise is dominant up to approximately 2600 Hz.As seen from Fig.16, the turbulent inflow results in higher levels of the WPF spectrum and a larger spanwise correlation length at the airfoil TE compared to a uniform, non-turbulent inflow.Thus, as the WPFs and the spanwise correlation length at the TE are directly linked to the TE noise[10], TE noise levels for a turbulent inflow are expected to be higher than for a uniform inflow.Comparing the TE noise for a uniform inflow and a turbulent inflow in Fig.19, it is observed that the TE noise level for a turbulent inflow is higher than for a uniform inflow for 800 <  < 2000 Hz, with a difference of 10 dB at  = 1000 Hz.These results confirm that the TE noise level increases when the inflow is turbulent.However, for the case studied here, the LE noise is dominant for the frequencies investigated.noise for the case of turbulent inflow presents a broadband character, which is most likely TBL noise since the turbulent inflow induces a faster transition and thickening of the layer[59], which likely results in the suppression of TE noise.As in Section 3.3, the hump in the spectrum for uniform inflow at  = 2200 Hz is blunt TE noise, and the broadband component is TBL noise.

Table 1
Rod-generated turbulence parameters (root-mean-square of the velocity fluctuations  rms and integral length scale   ) at the LE position with the airfoil removed.