Broadband Noise Reduction with Trailing Edge...

American Institute of Aeronautics and Astronautics

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Broadband Noise Reduction With Trailing Edge Brushes

Arthur Finez1, Emmanuel Jondeau 2 , Michel Roger3 Laboratoire de Mécanique des Fluides et d'Acoustique,

UMR CNRS 5509, Ecole Centale de Lyon, 69134 Ecully, France

and

Marc C. Jacob4 Laboratoire de Mécanique des Fluides et d'Acoustique,

UMR CNRS 5509, Ecole Centale de Lyon, 69134 Ecully, France - Université Claude-Bernard Lyon I F-69134 Ecully, France

Airfoil broadband trailing edge noise is reduced by modification of the trailing edge geometry. A brush made of a single row of flexible polypropylene fibers is integrated in the trailing edge of a cambered airfoil. Far field acoustic measurements show a noise reduction potential reaching 3 dB on a wide frequency range. Due to high curvature of the incident flow, a secondary acoustic source partly masks the trailing edge noise reduction. Hot wire correlation measurements in the very near wake of the airfoil show that longitudinal as well as transversal length scales are affected by the brush. Span wise coherence length of boundary layer eddies falls off by 25 % in the presence of a brush in the adequate frequency range, possibly explaining a 1.3 dB contribution to the noise reduction mechanism. Boundary layer turbulence exhibits a preferred coherence length ℓy

v on a wide frequency range. ℓyv/d ≈ 2, is considered a proper brush design law, d being

the diameter of the brush.

Nomenclature c = airfoil chord length (m) d = diameter of brush fiber (m) f = frequency (Hz) Guv = one-sided cross-spectrum of two time series u and v (u unit²/Hz) ℓy

p = span wise pressure-based coherence length scale (m) ℓy

v = span wise velocity-based coherence length scale (m) L = span of the airfoil (m) r = listener distance to the airfoil (m) x = coordinate in the chord wise direction (m) y = coordinate normal to the airfoil surface (m) z = coordinate in the span wise direction (m) R11(η,τ) = correlation coefficient for a spacing η and a delay τ St = Strouhal number Spp = Acoustic Pressure Spectral Density (Pa²/Hz) U = external flow velocity (m/s) Uc = eddy convection velocity (m/s) u'1 = fluctuating velocity component parallel to the flow measured by the first hot-wire (m/s) v'1 = fluctuating velocity component parallel to the flow measured by the second hot-wire (m/s)

1 Ph.D student, [email protected] 2 CNRS Engineer, LMFA, [email protected] 3 Professor, Laboratoire de Mécanique des Fluides et d'Acoustique, [email protected] 4 Assistant Professor, Laboratoire de Mécanique des Fluides et d'Acoustique, [email protected]

16th AIAA/CEAS Aeroacoustics Conference AIAA 2010-3980

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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α = geometric angle of attack (°) α* = effective angle of attack (°) γ = square root of the coherence function η = spacing between the two hot-wires (m) θ = angle between the axis of the incident flow and the listener position (°) τ = time delay (s) TBL = turbulent boundary layer TE = trailing edge

I. Introduction an broadband noise has become an important sound source during approach flights when engine power is reduced. Many broadband noise sources occur near an engine fan: turbulence interaction with the blade leading edge, boundary layer turbulence interaction with the trailing edge, tip vortex formation, tip leakage

vortex and wake interaction with the stator to point out a few of them. The broadband part of thin trailing edge noise is related to small size turbulence naturally developing in highly sheared zones of blade boundary layers leading to a relatively high frequency acoustic emission. As the turbulent boundary layer is swept past the trailing edge, the sudden pressure release causes a distortion of eddies which eventually results in the production of sound as an elastic response of the medium to this excitation. The turbulent field at the origin of the acoustic process can be modified through design parameters such as blade shape, whereas the radiation efficiency itself can be driven via the trailing edge geometry. These noise sources are located in the vicinity of the trailing edge, which is from an aerodynamic point of view of less importance than the leading edge and can be modified without severely damaging the aerodynamic performances as long as their drag is not significantly increased. Therefore the reduction of broadband trailing edge noise through trailing edge modification appears to be a fruitful strategy in the global goal of reducing aircraft noise. Numerous attempts to reduce blade broadband trailing edge noise have recently emerged. The idea of reducing the impedance jump between pressure and suction side in order to smooth out the transition to the free flow regime came to the fore in the early seventies1 and has been investigated both experimentaly2,3,4 and analytically5. Porous treatments were applied to the trailing edge region in wind tunnel experiments and trailing edge noise was substantially reduced. Another noise reduction technique consists in designing a serrated trailing edge. As noted by Howe6, the main idea is that acoustic radiation occurs efficiently for spatial Fourier components of the turbulent sheet whose wave number is normal to the local orientation of the trailing edge. The number of these components decreases rapidly as the angle of the trailing edge to the mean flow increases. This basic idea has been recently tested on a wind turbine e.g. by Oerlemans et al.7, together with an optimized blade shape strategy that aims at changing the structure of the boundary layer before it reaches the trailing edge. An average overall noise reduction of 3.2dB has been obtained for the serrated trailing edge. In his literature survey8, Casalino pointed out that sawtooth trailing edges proved to be more efficient than porous edges in full scale experimental campaigns9.

Trailing edge compliant brushes are also a promising mean for noise mitigation likely summing the effects of porosity and trailing edge geometry. The experimental work initiated by Herr et al.1010-11 concerned both a flat plate and a NACA 0012 airfoil. The study showed a suppression of vortex shedding noise due to blunt trailing edge together with a reduction potential of 10 dB of broadband trailing edge noise. A slight increase in high frequency noise components was observed, but this excess noise that is probably linked to micro-jets through the fibers, occurs close to the non-audible high frequency range and does not contribute significantly to overall sound levels. Moreover, the numerical study of Ortmann et al.12 showed that trailing edge thin slits geometrically comparable to brushes have little effect on steady aerodynamic performances. Therefore brush devices were considered to be effective noise reduction means. The suppression of vortex shedding noise could simply be brought to light by hot wire anemometry in the near wake of the flat plate: brushes disorganize the Von Karman vortex street and cancel the corresponding noise emission; the characteristic peak of the velocity fluctuation spectra in the wake disappears in the presence of brushes. The broadband turbulent boundary layer trailing edge noise reduction phenomenon is more pronounced. A first insight into the mechanism could be drawn from a parametric study: the effects of fiber length and diameter, as well as boundary layer thickness and external flow velocity influence have been studied. The broadband noise reduction appears to scale with the Strouhal number St = f.h/U0, h being a scale. Since no criterion for the choice of h has been found so far it was arbitrarily set to 1 mm. In these conditions, the noise reduction concerns a wide frequency range of 0.01<St<0.3. The reduced noise level follows a classical U0

5 scaling. The brush length has to be at least equal to the boundary layer

II. F


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thickness. Some brush configurations reveal to be optimal but a clear universal relation neither to h nor to the noise reduction levels could be identified. Moreover, current studies are limited to symmetrical configurations.

According to the promising noise reduction results, brushes have been applied on wind turbine trailing edges13. However the device yielded a reduction of only 0.5 dB possibly because the brushes were too short. Therefore a further investigation of the underlying physical phenomena is needed, so as to extract simple design rules when main aerodynamic quantities are known. The main goals of this study are manifold: - to extend the current database to the case of a cambered airfoil and to a new brush designs, - to cross-check the characteristics of the achieved noise reduction with former results, - to determine a approach suitable to investigate the physical phenomena resulting in broadband noise reduction. It should be noted that the range of technical applications of the concept is very large: high-lift devices, cooling fans, or wind turbines. The integration of such fragile devices on aircraft fan blades seems difficult if applied as such, but an equivalent (from an acoustic point of view) and more robust (from a mechanical point of view) solution may be found provided that main physical mechanisms are understood.

I. Acoustic measurements

A. Set-up The experiment is carried out in the small

anechoic room (6 m × 4 m × 5 m) of the Laboratoire de Mécanique des Fluides et d’Acoustique (LMFA), a joint CNRS-ECL-UCB Lyon-I laboratory located at the Ecole Centrale de Lyon. Air is supplied by a low speed subsonic anechoic wind tunnel at Mach numbers ranging up to 0.12. The set-up is shown in Figure 1.(a): before reaching the duct exit, the air is accelerated by a convergent nozzle from a 300 mm × 300 mm cross-section to the 150 mm wide and 300 mm high test section, where the flow develops into a semi open jet between two horizontal plates.

A NACA65(12)-10 airfoil (5% camber, 10% thickness) with a c = 130 mm chord and L = 300 mm span, is placed into the core of this jet between the two bounding plates one chord downstream of the nozzle. The airfoil is mounted onto an aluminum disk, which allows tuning the angle of attack α.

Since the downstream end of the airfoil can be changed, several treated trailing edge types can easily be tested as shown in Fig.1(b). Brushes made of a single row of polypropylene fibers are inserted into a flexible resin extension. The reference brush used here is 10 mm long and the fiber diameter is 0.5 mm. Fibers are side to side with a linear fiber density of 19 fibers/cm. Acoustic observations are supported by various trailing edge designs with parameters listed in fig.1.

B. Measurements Measurements referred to in the present paper

include: - far field pressure measurements in the mid-

span plane obtained from a ½” Brüel & Kjær type 4191 microphone with a

Fiber length, mm

Fiber diameter, mm

Density (number of fibers per cm)

Brush n°1&2 32 0.5 18

Brush n°3 40 0.5 10

Brush n°4 37 0.5 18

Brush n°5 (ref.) 10 0.5 19

Brus Brush n°6 25 0.25 30 Table 1. Brush Parameters

(a)

(b) Figure 1. Experiment Pictures

a)Set-up, b)Brushes


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Brüel&Kjær type 2669 preamplifier, at a 2.0 m distance for an observer angle θ = 90° (θ = 0° being on the downstream jet axis); the analysis is made between 100 Hz and 10, 000 Hz with a 25, 600 Hz sampling frequency; a microphone wind foam protection has been applied to the head of the microphone so as to prevent the recirculation flow in the anechoic room to pollute the measurement in the low frequency range; preliminary tests have shown that this precaution improves data below 300Hz and that no absorption due to the foam occurs below 10 kHz;

- near field source localizations carried out with a linear array of twelve, 9 cm spaced Brüel & Kjær ¼” ICP microphones that are conditioned by a PXI system; the array is parallel to the jet wind tunnel axis 0.37 m away from the airfoil on the suction side;

- steady wall pressure measurements at mid-span measured with a Furness manometer; - hot wire two-point measurements in the near wake reported in section III.

C. Flow conditions The reference velocity at the exit of the wind tunnel varies from U0= 20 to 40 m/s, and the turbulence level

u’/U0 is about 0.1%. The corresponding chord-based Reynolds number Rec lies between 173, 000 and 347, 000. The reference geometric angle of attack α is set to 10°. Since the jet width is quite small compared to the airfoil chord, the flow is significantly deviated by the airfoil. As a result, the effective angle of attack α*, that is, the equivalent angle of attack in an unbounded uniform flow, is significantly smaller than the geometrical one.

D. Baseline airfoil results Measuring isolated broadband trailing edge noise requires checking the predominance of this noise source over others even in the idealized context of an anechoic wind-tunnel. Recently developed phased array beam-forming using deconvolution methods allow to discriminate acoustic power emanating from distinct sources. The CLEAN-SC algorithm proposed by Sijstma14 has been used here with the antenna described in section I.C. For a given frequency, the sources are first localized using a conventional beam-forming techique and assuming a free field propagation function for monopoles sources, and then the amplitude corresponding to the coherent contribution in the cross spectral matrix is attributed to this source location. The results between 2 kHz and 5 kHz are presented in Fig.2 for the non-treated airfoil in a uniform 30 m/s flow with a geometric angle of attack α = 10°. In this frequency range, three main sources are competing: one located at the end of the wind tunnel can be attributed to the wind tunnel turbulent boundary layer diffraction at the edge. Two other sources are located on the airfoil, one on the trailing edge and one in the vicinity of the leading edge. The former is obviously TBL-TE noise while the latter could be associated with a small recirculation bubble on the pressure side closed to the leading edge. This interpretation is based on following observations. - Leading edge - turbulence interaction noise is not believed to be an important source in this experiment since the incoming turbulence intensity u’/U0 that has been measured using hot wire anemometry is 0.1%. - As mentioned by Brooks et al.15 the finite-size of open wind tunnel causes curvature and deflection of the incident flow. This results in a reduction of the effective angle of attack with respect to the geometrical one. A rough estimate of this reduction is given by Brooks: for the present configuration, the effective angle of attack α* associated to α = 10° is 3.2°. - Moreover the geometric angle of attack α is defined as the angle between the chord and the axis of the wind tunnel; since the NACA 6512-10 is a cambered airfoil, the angle of the surface of the pressure side to the chord is

Figure 2. Acoustic sources locations as a function of frequency. Non-treated airfoil: U0 = 30 m/s; α = 10°. The linear grey scale is defined for source amplitude between 0 and 10-6 Pa².m²/Hz, from light to dark.


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approximately -3°. As a consequence, the pressure side surface is nearly at negative incidence to the effective incoming flow and a recirculation bubble is likely to appear. - Evidence for this is shown on Figure 3.(a) where the airfoil loading at U0 = 20 m/s and α = 10° is plotted. The two first probes located at x/c = 3% experience an almost equal loading while a large pressure drop is expected between the two sides of the airfoil for such angle of attack. Moreover a comparison with previous experiment for the same airfoil in a wider wind tunnel reveals that a geometrical angle of attack of 10° in the present experiment is aerodynamically equivalent to an angle of attack of 4° with a wider nozzle where the deflection was gentle. - Finally Figure 3.(b) presents a turbulent profile in the wake of the non-treated airfoil at a distance x/c = 9.2% from the trailing edge. The maximum turbulent intensity in the wake of the suction side boundary layer is 11% while it is 9.5% in the wake of the pressure side boundary layer. The relative importance of turbulence intensities on the pressure side could be linked to the history of the boundary layer, thus comforting the assumption of a

recirculation bubble on the pressure side near the leading edge. To summarize, in the reference configuration of α = 10°, U0 = 30 m/s, the airfoil trailing edge is a more efficient source than the wind tunnel edge. However, it is not the primary source between 2 kHz and 4 kHz because of the presence of a probable recirculation bubble on the pressure side leading edge of the airfoil. Array measurements show that TBL-TE is predominant between 4 kHz and 5 kHz but don't provide information for higher frequencies. However, it is reasonable to assume that TBL-TE noise will also be dominant at higher frequencies since the turbulent structures involved in the process are smaller than the ones present in the recirculation bubble. It is thus possible to analyze the effect of brushes on noise for the range 4 – 20 kHz.

Figure 4. Acoustic Pressure Spectral Density in the far field

U0 =30 m/s; α =10°; r =2 m; θ=90°

a) b) Figure 3. Aerodynamic performances of the non treated airfoil a) Pressure Coefficient, b)Turbulence level measured with a single hot wire probe in the near wake of the non treated airfoil.

α = 10°; x/c = 9.2 %; U0 = 21 m/s


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E. Noise reduction assessment The measured PSD for the baseline case of U0 = 30 m/s, α = 10° perpendicularly to the jet axis on the suction

side is compared to the same configuration with the reference brush mounted on the trailing edge. Background noise is defined as the noise made by all external sources, e.g. mainly jet noise and wind tunnel trailing edge noise. It has been estimated by removing the airfoil and keeping the same flow velocity. Since the leading edge source is due to the presence of the airfoil, it is not included in the measured background noise.

As can be seen on Fig.4, a maximum reduction of 3 dB is observed around 1, 000 Hz. It is believed that the maximum noise reduction is actually higher, since the noise reduction is limited between 2 kHz and 4 kHz by the strong emission of the leading edge source. It can be noted that no supplementary noise is measured in the high frequency range contrary to the study of Herr10.

In order to highlight general trends of the measured noise reduction, the Strouhal scaling mentioned by Herr is investigated in Fig. 5. Three different velocities have been tested: 20 m/s, 30 m/s, 40 m/s, all with a geometric angle of attack α = 10°. As noted by Herr, a constant reference length h arbitrarily set to 10-

3 m for comparison is used. Whereas Herr10 found an almost perfect Strouhal scaling for many brush parameters and a noise reduction in a 0.01 - 0.3 Strouhal range, the present study does not exhibit any shape similarity except at low Strouhal numbers in a 0.005 - 0.02 range. Moreover, a noise reduction is visible on a more limited frequency range. An explanation for these results could be that although the noise reduction phenomenon is the same as in previous studies, external acoustic sources might be responsible for this discrepancy.

Several brushes have been tested with various parameters: fiber length, diameter and spacing. The St scaling failed in all cases. Thus the St scaling seems inappropriate in our case. Even if the acoustic reduction could be neither fully measured nor scaled, the mechanisms responsible for it are present in the experiment and it can be investigated.

III. Wake coherence measurements

A. Motivations Several mechanisms are likely to explain the sound reduction by

brushes. In the presence of a brush, the situation is severely different from the simple solid edge: 1. The span wise uneven geometry of brush-type devices suggests

that eddies might be modified by a loss of span wise coherence. According to acoustic analogies (e.g. refs.16-20) far field pressure can be related to the fluctuating pressure field on the surface of the airfoil. In analytical models20,21, it is usually assumed that the pressure field on the surface can be described using turbulence quantities like the span wise coherence length scale ly. An experimental quantification of the effect of brushes on ly would allow predicting and assessing the noise reduction potential.

2. As noted by Herr, a brush can be considered as a porous extension of the trailing edge, whose porosity is a function of the distance from the actual trailing edge to the eddy. As a vortex travels along the airfoil, the pressure release condition in the wake is not applied

Figure 5. Acoustic Pressure Spectral Density in the far field

U0 =30 m/s; α = 10°; r = 2 m; θ = 90° (thin solid line) 20 m/s, (bold solid line) 30 m/s, (dashed line) 40 m/s

Figure 6. Picture of the hot wire set up, airfoil mounted with brush n°1

U0 = 30 m/s; α = 10°


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(a)

(b)

Figure 7. Isocorrelation contours plots in the wake of the airfoil a) baseline airfoil, b) treated airfoil

span

wis

e di

rect

ion

(y)

stream wise direction (x)

suddenly as for a solid edge, but the adaptation is made smoothly possibly resulting in a low interaction between the vortex and the trailing edge. This effect could be estimated by means of analytical models5

provided that equivalent impedance is measured or assumed for the brushes. The complex shape and porosity of the noise reduction device suggests that two effects combine to decrease noise radiation. One is that the brushes break up eddies of the airfoil boundary layer, whereas the other is due to the induced modification of the Green function by the trailing edge porosity. These two effects may be considered as independent and can be studied separately since the first is purely aerodynamic whereas the second is purely acoustic. Let us now consider merely the aerodynamic effect, which results statistically in a reduction of the span-wise coherence and possible also in a spectral redistribution of the wall pressure fluctuations. In order to evidence this mechanism one should ideally measure the wall pressure fluctuations next to the trailing edge both with and without trailing edge treatment, ideally with a remote microphone technique as described by in ref25. Unfortunately, this technique is not suitable in the vicinity of the brushes: because of manufacturing constraints, they could be placed sufficiently near the trailing edge to feel the influence of the brushes onto turbulence. Hot wire measurements could neither been carried out in the boundary layer above the brushes because of the fiber oscillations. Therefore hot wire measurements were carried out in the near wake. The main goal of these measurements is to quantify the relative importance of turbulence reorganization by different trailing edge geometries.

B. Set-up In order to obtain relevant information, two point measurements are carried out by placing two parallel hot wire probes in the near wake of the airfoil in a similar manner than in ref22 but with single wires. Figure 6 shows that the hot wire probes are placed as close as possible to the free extremity of the fibers. The length of the two hot wires is 1 mm long and their axis is normal to the surface of the airfoil. In the 5 mm wide wake of the suction side boundary layer, the length of the hot wire is considered to be small enough to capture the main coherent structures in the boundary layer wake. This orientation allows reaching small distances between the two wires (0.78 mm for the closest position). The single component u'1 of the fluctuating velocity parallel to the main flow is measured. Probes are mounted on a measuring carriage that allows a simultaneous displacement. Measurements are performed with a DANTEC anemometer with two 55P11 hot wire probes to allow span wise coherence and correlation length measurements. Velocity signals are sampled at 25, 600 Hz with enough points to carry out 600 averages of 6, 400 point DFT’s, leading to one-sided spectra with a 4 Hz resolution. The measurement location relatively to the solid part of the airfoil is the same for the configurations with- and without brush, that is, 12 mm away from the baseline trailing edge and 2 mm away from the end of the fibers.

C. Space-time correlations First, space-time correlations are computed. If the stream wise fluctuating velocity component measured by the first hot-wire is denoted u'1 and the one measured by the second hot wire is denoted v'1, the correlation coefficient R11(η,τ) for a separation distance η between the two wires is defined by23:

€

R11(η,τ ) =u1(y,t)v1(y +η,t +τ )

u1(y, t)u1(y,t) × v1(y +η,t +τ)v1(y +η,t +τ )


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This definition assumes the turbulent quantities to be stationary and homogeneous in the span wise direction i.e. there is no dependence of this quantity with respect to the x and t variables. It is a fair assumption as long as the measurement is made close to the mid-span plane where end effects are negligible since the aspect ratio of the airfoil is L/c = 2.3. This correlation coefficient of the stream wise velocity component between different span wise locations can be plotted in terms of contours maps in the (x,y) plane. Assuming the Taylor hypothesis of frozen turbulence, the time-dependence of R11 can be investigated by means of the spatial variable τ.Uc where Uc is the eddy convection velocity which is well estimated by the local mean velocity. In our case Uc ~ 19 m/s. Figure 7.(a) and (b) contain iso-correlation contour plots obtained at U0 = 30 m/s and α = 10° in the wake of the baseline airfoil and the treated airfoil respectively. Figure 7.(a) which corresponds to the solid trailing-edge, shows that for small separations (η < 3 mm) the iso-correlation curves are quasi elliptic with a main axis aligned onto the stream wise direction. With this scaling correlations are elongated in x-axis. When probe spacing increases, a sudden correlation drop is observed around η = 2.5 mm which corresponds to the mean span wise extent of convected eddies. Following the τ.Uc = 0 axis, it can be seen that after the correlation drop at η = 2.5 mm, the coefficient re-increases up to a value of 12 %. This suggest that other structures with a larger extent in the span wise direction are present but weakly coherent. The correlation deficit near η = 2.3 mm can be explained by phase lag between the two velocities as will be seen here in section III.D. A negative high frequency contribution cancels a positive low frequency contribution of eddies. At larger span wise separation distances, the correlation rapidly decays to zero. Figure 7.(b) shows the same plot (with the same axis and grey scale) at the same location relative to the solid part of the airfoil in the presence of the reference brush. The main trends observed in the non-treated case are still valid with a treated trailing edge except that the values decay faster both in the span wise direction and in time. For instance the 30 % auto-correlation level is reached at τ.Uc = 2.5 mm in the presence of the brush and at τ.Uc = 5 mm without brush. In other words the life time is divide by two by the brush. Similarly, the span wise extent associated to the 12 % correlation level is now about η =1.8 mm instead of 2.5 mm. It is not surprising since the fiber diameter and separation are 0.5 mm. The brush has also an influence on larger eddies because correlation for large probe separations is slightly weaker in the presence of the brush. However weak values of the correlation coefficient prevent to draw a more robust conclusion at this stage of the study. Nevertheless a first partial conclusion is that the brush is an effective device to de-correlate both span wise and time correlation of vortical structures.

D. Coherence measurements The analysis of the correlation coefficient gives an overall frequency independent view of the trailing edge physics. A more detailed analysis can be made by computing the coherence function γ2 between two time signals u and v, corresponding to a separation distance η:

€

γ 2(η, f ) =Gu,v (η, f )

2

Gu,u( f )Gv,v ( f )

where u is the cross-stream velocity compnent taken at an arbitrary y location along the airfoil trailing edge and v is the same component taken at y+η. This quantity is linked to the previous spatial correlation coefficient for a zero delay by:

€

R11(η,0) =Gu,v (η, f )df0

∞

∫Gu,u( f )df0

∞

∫ Gv,v ( f )df0

∞

∫

The zero-delay correlation coefficient can thus be seen as an energy-weighted integral of the γ function. Let us first consider the velocity auto-spectrum at the measurement location in Fig. 8. In the baseline configuration, it exhibits a large hump between 50 Hz and 200 Hz; in the 200 Hz - 2, 000 Hz frequency range, the spectrum is nearly frequency independent. Above 2, 000 Hz, a spectral decay indicates that energy is transferred from large eddies to smaller ones, but the classical inertial turbulence Kolmogorov law is not recovered which is not surprising since the wake is not developed near the trailing edge. This holds for both configurations which have the same trends. However, the turbulence intensity of the u'1 component is slightly reduced by the presence of the brush. This might partly be explained by an energy transfer to other velocity components and partly by a reduction of the turbulent energy in the near wake. However, this reduction is too small to explain the 3 dB noise reduction at 1 kHz (see Fig. 2). To summarize, Fig. 8 tells us that the turbulence is not isotropic at this location, that its intensity is independent of the frequency in the range [200 Hz, 2, 000 kHz] and that it is slightly reduced


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by the TE-treatment. Let us consider now the coherence as a function of the frequency for typical probe separation distances η, as shown in Fig.9. The velocity based coherence function does not depend on frequency as simply as a pressure based coherence function. For the baseline configuration, three frequency ranges can be identified:

1. 50 Hz < f < 200 Hz – low frequency range: highly coherent structures with a hump centered around 100 Hz. The coherence decays slowly with increasing separation,

2. 200 Hz < f < 2, 000 Hz – mid frequency range: the structures are less coherent. The coherence is almost frequency independent, but the coherence decreases rapidly against the separation distance,

3. 2, 000 Hz < f – high frequency range: the exponential decay is somewhat recovered both with frequency and separation. For more than ten tested values of η, the coherence functions follow this classification.

The low frequency range coherence suggests the presence of large eddies occurring mainly around 100 Hz (see Fig.7). The brush does not efficiently weaken or disorganize such coherent structures: a benefit is found for small separations (η < 1 mm) but is compensated by a loss at higher separation values (η > 1 mm). Low frequency structures have a wider extent in the presence of the brush but are less correlated. Eddies associated to the mid-frequency range have a span wise extent of about 1.5 mm in the experiment and are efficiently disorganized by the brush (50 % coherence loss). The brush can efficiently disorganize these eddies because the characteristic fiber spacing of the brush is about 3 times smaller than (i.e of the same order as) their span wise

Figure 8. Fluctuating velocity spectrum in the wake of the airfoil

U0 =30m/s; α=10°; x=12mm

(a) (b)

(c) (d)

Figure 9. Coherence function for several hot-wire spacings in the wake of the baseline and treated airfoils U0 = 30 m/s ; α = 10°; x =1 2 mm, (bold line) baseline airfoil, (thin line) treated airfoil

a) η = 0.78 mm, b) η = 1.01 mm, c) η = 2.08 mm, d) η = 6.08 mm


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extent. It may not be the case for eddies that are smaller the fiber spacing but for practical reasons, hot wires could not come close enough to characterize such details. This effect of the brush is of particular interest since it occurs in the frequency range at which the brush is most efficient. For the highest frequencies, the brush effect could not be assessed due to the low coherence levels. The spatial dependence of low- and mid –frequency coherence is investigated in Fig. 10 for two typical

frequencies f = 100 Hz (Fig. 10.(a)) and f = 1, 000 Hz (Fig 10.(b)). For low frequency range, two domains can be identified:

0 < η < 2.5 mm: the coherence decreases steeply until it reaches a value of 0.45 for a 2.5 mm probe spacing. The classical exponential decay fits well the data.

2.5 mm < η: coherence is nearly independent on the separation. Coherence levels are much higher than expected with exponential fitting. A small test for a very large separation (100 mm) exhibited still a high coherence level (10 %). This cannot be attributed to vortical structures but rather to an installation effect like a global low amplitude oscillation of the wake.

The brush reduces small separation coherence levels but has no effect for large separations. As a consequence, it is believed that the resulting span wise coherence length at 100 Hz is unaffected by the presence of the brush. It is worth mentioning that a correct definition of a span wise coherence length based on velocity measurements is an open question since the coherence levels do not vanish for tested separations up to 40 mm.

(a)

(b) Figure 11. Coherence amplitude and interspectrum phase of the velocity time series for a hot wire separation of 3mm in the wake of the non treated airfoil U0 = 30 m/s; α =10°; x =12 mm, a) Coherence b) Cross-spectrum phase in degrees, phase data above 1, 500 Hz have been erased since phase is not meaningful for incoherent signals

(a) (b) Figure 10. Coherence as a function of hot-wire probe spacing in the wake of baseline and treated airfoils U0 = 30 m/s; α = 10°; x = 12 mm. Solid line with dot symbols: baseline airfoil measurements; dashed line with square symbols: treated airfoil measurements; thin solid line: exponential decay fitted curve to experimental data between 1 and 2.5 mm. a) f = 100 Hz, b) f = 1, 000 Hz


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For the f = 1, 000 Hz case, coherence values decrease rapidly and reach negligible values at η = 1.8 mm. Figure 10.(b) shows that the brush significantly disorganizes and reduces the size of the eddies associated with the mid-frequency range for separations lower than 1.8 mm. Reductions of the coherence up to 50 % in coherence are observed which may affect the values of the span wise coherence length. For the 2 mm < η < 4 mm separation distances a slight hump is observed in coherence reaching values around 5 %. This hump is present between 200 Hz and 1, 500 Hz for a 3 mm separation as shown in Fig.11.(a) for the non-treated trailing edge. On Fig. 11.(b) the two probes appear to be in antiphase in the 200 Hz – 1, 000 Hz frequency range. A possible scenario would be that for this separation distance, the signals originate statistically from two sides of some cross-stream oriented vortical structures. So far no physical mechanism has been found to account for such vortical structures in the airfoil boundary. However it should be kept in mind that in some very organized wakes, such as a cylinder wakes, the span wise coherence changes discontinuously along with sudden phase lags, introducing cross-stream shear components where vortex dislocations occur. Between these sudden phase lags, these wakes are phase locked into so-called cells as discussed by several authors for low and sub-critical Reynolds number cylinder flows26-28: nevertheless such an encounter in a fully turbulent flow is unusual. A second explanation could be that probes record signal related to the two counter-rotating branches of a same structure like horseshoe vortices. This antiphase contributes negatively to the correlation coefficient and is held responsible for the lack of correlation at η = 3 mm observed in Fig. 7.(a). This feature is characteristic of the 200 Hz – 1, 000 Hz frequency range since below 200 Hz signals are in phase. The brush does not have any influence onto this phenomenon. The values presented in Fig. 10.(b) allow to compute a span wise coherence length based on velocity measurements ℓy

v(f).

€

yv ( f ) = γ( f ,η)dη

0

∞

∫ It should be noted that even in the frozen turbulence hypothesis, this quantity may be significantly lower than the pressure-based coherence length ℓy

p(f) estimated from unsteady wall-pressure probes mounted near the traling edge, say, at 95 % chrod. This is because pressure is an integral quantity and its coherence sums all coherent contributions of surrounding eddies. Following this definition and integrating over all separation distances at a given frequency yields ℓy

v(f = 1, 000 Hz) = 0.92 mm for the baseline airfoil and ℓyv(f = 1, 000 Hz) = 0.75 mm for

the treated airfoil. This value is constant over the whole mid-frequency range both with and without brush because coherence is not a function of frequency in this case (see Fig.9). No experimental data are available the first experimental value raises some uncertainty especially because γ²(η) reaches its maximum at η = 0 mm which does not fit the “natural” extrapolation of the measured coherence. Therefore, interpolation of γ²(η) must be carefully examined and improved in future measurement campaigns for a more precise evaluation of ℓy

v.

IV. Conclusion Compliant single-row brushes have been applied to the trailing edge of a cambered airfoil in the small

anechoic wind tunnel facility at ECL in order to mitigate broadband trailing edge noise due to the scattering of the aerodynamic wall pressure waves by the edge. Previous studies have shown that brushes are efficient noise reduction tools for the standard cases of a flat plate and NACA 0012 airfoil with incidence. It has been seen here that it is the case as well for a cambered NACA 65(12)-10 airfoil. Noise reduction performances reach 3 dB in the [600 Hz – 2, 000 Hz] frequency range.

A possible explanation of the noise reduction process has been investigated: the fine span wise fibers of brush might disorganize turbulent structures before they radiate sound. Measurements in the very near wake of the suction side boundary layer have been performed. A space-time correlation analysis proved that the time as well as the span wise length scales are both reduced the brush fibers. A coherence study lead to identifying characteristics of the turbulent eddies in the [200 Hz - 2, 000 Hz] range. It is remarkable that these structures are of the same type and all have span wise extent of 1.8 mm or slightly less with the reference brusch. Higher separations exhibit a slow level coherence hump. This hump is associated to two-point velocities varying in phase opposition. The brush severely reduces span wise coherence of these structures. This effect leaves its footprint on the velocity based coherence length ℓy

v since it switches from 0.92 mm to 0.75 mm in the presence of the brush. The corresponding reduction on the pressure based coherence length ℓy

p has still to be assessed. If it drops by 25 % as well, it may explain a far-field noise reduction of 1.3 dB.

A good indicator for a future design rule would be the ratio ℓyv/d where d stands for fiber diameter, which

must be equal to several unities for a proper brush design.


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The relatively high chord-o-windtunnel width of the experimental set-up is responsible for a strong deviation of the jet flow by the airfoil. It results in an important reduction in the effective angle of attack, which in turn is responsible for a pressure side recirculation bubble in the vicinity of the leading edge. This appears to be a powerful noise source in the [2, 000 Hz – 5, 000 Hz] frequency range. In this range, it tends to dominate the trailing edge noise and introduces a flaw in the far field microphone measurements. In future investigations, far field acoustic measurements will be made at a higher angles of attack (15° or 20°) in order to overcome this flaw and to isolate more efficiently the trailing edge noise contribution. A theoretical link between ℓy

v and ℓyp might also help evaluating the reduction of span wise coherence and its benefit for noise

reduction. In order to rule out the modification of the Green function by the brushes, a new airfoil surface treatment on the suction side of the airfoil could be designed, that mimicks the uneven geometry of the brush in the span wise direction with negligible changes of the airfoil Green’s function. Technically, this could be achieved by implementing chord-wise ribblets on the downstream part of the airfoil.

References

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