Acoustics Array Systems: Paper ICA2016-122

Composite aeroacoustic beamforming of an axial fan

Jeoffrey Fischer(a), Con Doolan(b)

(a)School of Mechanical and Manufacturing Engineering, UNSW Australia, Sydney, NSW 2052,Australia, jeoffrey.fischer@unsw.edu.au

(b)School of Mechanical and Manufacturing Engineering, UNSW Australia, Sydney, NSW 2052,Australia, c.doolan@unsw.edu.au

Abstract

As part an effort to more completely understand fan noise, this paper is concerned with the mea-surement of axial fan noise using beamforming acoustic arrays. Measurements were obtainedusing a large axial fan rig, located in UNSW’s aerospace research laboratory. The rig containsan axial fan, containing 8 rotors and 8 stators. The diameter of the fan is 0.9 m and the rotorsare contained in a duct with a flared inlet. The fan operates at 1900 RPM. Further, the input shaftis mounted upstream of the rotor and is housed within a central nacelle. This rather complicatedarrangement means that an acoustic array cannot be placed directly upstream of the fan, nor canit be placed parallel to it. Also, the external duct and central nacelle prevent line-of-sight of anarray to parts of the fan. To overcome these difficulties, a composite beamforming methodologyhas been devised. In this method, beamforming images are obtained from two (or more) view-ing angles and the sound maps are corrected for to account for the geometrical viewing angle.Two resulting beamforming outputs are then superimposed to obtain composite beamformingsound maps that reveal the sound sources more completely. The results show the various soundsources such as rotor stator interaction and blade self noise as a function of frequency. The influ-ence of the duct and nacelle on the beamforming output was determined by placing an acousticsource on a single blade and measuring the response on the array for multiple angular positionsof the fan. Overall, the composite beamforming methodology was found to work well and it is ableto overcome the difficulties presented by the axial fan design.

Keywords: experimental aeroacoustics - acoustic array - beamforming.

Composite aeroacoustic beamforming of an axial fan

1 IntroductionAxial fans are used in many industries, for mine ventilation systems, automotive cooling sys-tems and within aerospace propulsion systems. Understanding broadband noise generation ofthese devices is becoming a more and more important topic of research [1] but still remainsan engineering challenge.

For axial induct fans, the broadband noise is created by the interaction of the duct wall bound-ary layer with the trailing edge tip vortex structures of the fan blades. Noise sources on aninduct fan have been investigated by Sijtsma [2] with beamforming. Two arrays were used,located upstream (rotor side) and downstream (stator side) of the fan. The results obtainedseemed to indicate that the noise sources were distributed along the span rather than beingconcentrated in the tip region. Tip clearance noise was studied by Fukano et al. [3]. Thisnoise consists of a discrete frequency noise due to periodic velocity fluctuation and a broad-band noise due to velocity fluctuation in the blade passage.

The present work aims to perform acoustic array measurements on an axial induct fan wherethe array could not be aligned parallel to the fan. An improved beamforming technique, called“composite aeroacoustic beamforming” herein, has been devised which improves the resultsand assists in their interpretation.

2 Experimental set-upAcoustic array measurements were performed on an axial fan in the UNSW Aerospace Lab-oratory. Fig. 1(a) shows a sketch of the fan. The outer diameter of the impeller is D = 900mm and consists of 8 equally spaced NACA 4412 blades Fig. 1(b). The fan can operate at amaximum rotational speed of 1,900 RPM, corresponding to a fan inflow speed of Ui = 20 m/s,where Ui is the flow velocity just upstream of the fan blades. The tip speed at this flow speedis Utip = πDΩ = 90 m/s, where Ω =RPM/60. The experiments were obtained for several flowspeeds Ui = 5,10,15 and 20 m/s.

The fan noise was measured using an acoustic array to locate noise sources through beam-forming to gain a better understanding of the noise sources close to the blades. For thispurpose, a 64-channel array (7 circles of 9 microphones each and one microphone in the cen-tre), shown in Figure 2(a), was used. The design of the array has been optimized to provide agood compromise between the beamwidth and the maximum side-lobe level in the frequencyrange of interest [4]. The array, which could not be aligned properly due to the presence ofthe input shaft, was placed at the inlet of the fan at an angle of α = 19 to the plane of bladerotation as shown in Figure 2(b). Each 1/4 inch GRAS 40PH CCP free-field array microphonewas connected to a PXIe-4499 24bit simultaneous sample and hold data acquisition card. Theacoustic pressure signals were recorded at a sampling frequency of fs = 65,536 Hz over 60 s.

These data were then processed using the conventional beamforming (CBF) technique which

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(a) 0.55 D 2.5 D 1.9 D 0.88 D 1.28 D 1.11 D

2.06

D2.06

D

MotorTurbine

D = 900 0.84 DFlow

Grid

(b)

180

120

27

240

Figure 1: (a) Sketch of the axial fan in the UNSW Aerospace Laboratory. (b) Sketch of oneNACA 4412 blade. Dimensions in mm.

is a very popular technique for the location of noise sources in aeroacoustics. The CBF methodproduces an acoustic sound map in a plane parallel to the array. It is based on an optimizationof the time-delay between each microphone. For more information about the technique, pleaserefer to Mueller [5] and Brooks et al. [6].

3 Composite beamforming3.1 Conventional beamforming

Consider a set of M microphones where the mth microphone is located at rm. The acousticpressure field from any given source of noise is then recorded using these microphones andprojected in the frequency domain using a Fourier transform. The obtained vectors, P(rm, f ),are used to create the Cross-Spectral Matrix (CSM) defined as:

C(rm,r′m, f ) = P∗(rm, f )P(r′m, f ) (1)

where the superscript X denotes the Welch’s periodogram applied to X with the use of a Han-ning window function.

3

(a) (b)

1.31D2.3D

19

Acousticarray

Motor

Rotating blades

Shaft

D=9000.86D

2.44D

Figure 2: Photo of the 64 microphones acoustic array (left) and sketch of the experimentwith the acoustic array in front of the fan seen from above (right). Dimensions in mm.

The CBF seeks the position of the acoustic source in a so-called focusing plane. The beam-former output at a given frequency is generally defined by:

Z(rn, f ) =eTCe

M(M−1), (2)

where e(rm,rn, f ) = exp(− jk||rm− rn||)/4π||rm−rn|| is the free-field Green’s function (also calledsteering vector) between the microphone located at rm and the focusing point at rn, and k = 2π fdenotes the wavenumber at frequency f . Note that the diagonal elements of the CSM are setto 0 to improve the resolution on the beamforming map [5].

3.2 Composite beamforming

As the CBF algorithm locates sound sources in a plane parallel to the array plane, an anglecorrection has been applied to the obtained sound maps, as shown in Figure 3. If we considera point F(xF ,yF ,zF ) in the initial focusing plane, its coordinates in the corrected plane afterrotating by an angle α will be:

(x′Fz′F

)=

(cosα −sinα

sinα cosα

)(xF

zF

)(3)

Note that the y coordinate does not change as the altitude of the microphones remains thesame after rotating.

The array measurement were performed on both sides of the shaft as shown in Figure 4 fortwo reasons: first, the central shaft is hiding some regions when the array is set-up on one side

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of the fan. Thus, performing array measurement on the other side enlarges the noise region.The second reason is that the sound maps obtained from each sides can be superimposed asthey are estimated in the same plane. This technique helps to recreate the map that would beobtained if the array was placed in front of the fan (α = 0).

Corrected focusing plane

Initial focusing plane

α~x

~z ~y

Acousticarray

Figure 3: Display of the initial and corrected focusing plane for the CBF application.

Arrayposition 1

Arrayposition 2

~x

~z ~y

Figure 4: Position of the array for the acoustic measurements.

4 Results4.1 Speaker measurements

In order to better understand how the acoustic waves propagate from the blades to the array,some preliminary experiments were performed with a speaker attached to one of the blade and

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no flow. The speaker was located at 8 azimuthal locations equally spaced around the rotationalcentre of the fan. The sum of the acoustic maps obtained with the array in position 2 (seeFigure 4) are shown in Figure 5(a) at f = 3,175 kHz with a third-octave band integration andusing the angle correction described in Eq.3. The green cross indicates the speaker locationand the black curves show the positions of the shaft (inner circle) and duct (outer circle),respectively. Even though the speaker level was the same for each measurement, the noiseintensity is higher when the speaker is located on the lower part of the duct. The reason forthis is due to the internal geometry of the fan, which does not scatter sound uniformly.

To investigate the influence of all 8 sources, the level on the maps has been normalised inFigure 5(b). This beamforming map show that when the speaker is at the same side as thearray, the sources are reasonably well recovered. Otherwise, the source is located out of thetunnel, most likely due to the presence of the shaft and bell mouth inlet. Reflections and prop-agation through the inlet overestimate the time-delay between the source and the microphonesand thus an error is record in the location and amplitude of the source.

(a) (b)

Figure 5: Sum of the CBF maps for each of the 8 positions at f = 3,175 Hz. The array is atposition 2, f = 3,175 Hz. (a) No level correction and (b) same level imposed.

4.2 Fan noise

First, the acoustic spectra obtained for several fan speeds are shown in Figure 6(a). Theseshow that the fan noise is broadband in nature but starts containing peaks at the highestspeed U∞ = 20 m/s which correspond to the blade passing frequency (BPF). The BPF of the8 blades fan can be obtained from BPF = Ω× 8 = 1,900/60× 8 = 253 Hz. When using anhydrodynamic reference pre f = 1/2ρU2

∞ with ρ = 1.2 kg/m3 being the air density, the broadbandspectra collapse as shown in Figure 6(b).

The noise of the fan running at Ui = 15 m/s is measured with the acoustic array positioned onboth sides of the tunnel inlet. The results are shown in Figure 7 for f = 2,4 and 8 kHz in thirdoctave band integration, in three columns. The left and central columns show the beamformingresults obtained from the left and right positioned arrays, respectively. Composite beamforming

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(a) (b)

Figure 6: Spectra of the central microphone for several wind speeds with reference (a)acoustic pressure and (b) hydrodynamic pressure.

results are displayed in the right column. The first observation is that the location of the noisesources is more accurate at higher frequencies; at f = 8 kHz, all the sources are located at thetip of the blades while at f = 2 kHz most of the sources are located outside of the duct due tothe presence of the shaft and bell mouth inlet geometries.

However, the sources are only located on the top and bottom parts of the duct. Again, thereason for that is that these regions are the only one that are directly visible from the array.Figure 8 shows a picture of the blades as seen by the acoustic array: the visible parts aredisplayed in bold line while the invisible ones are in dashed line. When compared to the actualmaps in Figure 7, the source regions do not exactly match. This is because the image inFigure 8 was taken from the centre microphone using a camera whose optical aperture isquite different from the acoustic aperture of the array.

5 ConclusionsThe noise of a large axial fan rig located in UNSW’s aerospace research laboratory was studiedusing acoustic array techniques. As the array could not be aligned with the blades, a compositebeamforming technique was introduced. This method enabled a better understanding of thenoise sources on the fan.

Measurements were first conducted using a speaker located at each blade position with noflow. The location on the acoustic maps was accurate when the source was located at thesame side as the array. Otherwise, the maps show a source out of the boundaries of the ductdue to the presence of the shaft and inlet. The fan geometry distorts the direct field and leadsto sources that are recorded at different locations to what is expected.

When the fan was turned on, the noise sources appeared clearly at the blade tips, but only onthe top and bottom parts of the duct. Again, the fan geometry obscures these regions from thearray. To improve the accuracy of the composite beamforming method, accurate reconstruction

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Left array Right array Composite

Figure 7: CBF maps with the fan turned at Ui = 15 m/s for each array position and their sum.f = 2, 4 and 8 kHz.

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Figure 8: Photo of the experiment as seen by the acoustic array in position 1. The whitesolid and dashed lines show the region where the blades tip are visible and hidden respec-tively.

of the Greens function that describes the propagation from each fan blade to the array isneeded. Such a Greens function can replace the free field model used in the beamformingalgorithm and remove the distorting effects of the fan duct and inlet shaft. Further, the use ofdeconvolution methods will improve the localisation of noise sources, and should form part offuture developments of the model.

Acknowledgements

Financial support from the Australian Research Council, Project DP130103136, is gratefully ac-knowledged.

References

[1] Abdelhamid, Y.A., Ng, L.L., Hanson, D.B. and Zlavog, G., Fan Broadband Noise Generationand Propagation, 44th AIAA, 2006, Reno, Nevada.

[2] Sijtsma, P., Using phased array beamforming to identify broadband noise sources in a tur-bofan engine, NLR report, 2009.

[3] Fukano, T., and Jang, C.M., Tip clearance noise of axial flow fans operating at design andoff-design condition, Journal of Sound and Vibration. Vol. 275, 2004, pp. 1027-1050.

[4] Prime, Z., Doolan, C., and Zajamsek, B., Beamforming array optimisation and phase av-eraged sound source mapping on a model wind turbine, INTER-NOISE and NOISE-CONCongress and Conference Proceedings, Vol. 249, Institute of Noise Control Engineering,2014, pp. 1078-1086.

[5] Mueller, T.J., Aeroacoustic measurements, Springer,2002.

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[6] Brooks, T.F. and Humphreys, W.M., A deconvolution approach for the mapping of acous-tic sources (DAMAS) determined from phased microphone arrays, Journal of Sound andVibration. Vol. 294, 2006, pp. 856-879.

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