Composite aeroacoustic beamforming of an axial fan

Transcription

1 Acoustics Array Systems: Paper ICA 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, (b) School of Mechanical and Manufacturing Engineering, UNSW Australia, Sydney, NSW 2052, Australia, Abstract As part an effort to more completely understand fan noise, this paper is concerned with the measurement of axial fan noise using beamforming acoustic arrays. Measurements were obtained using a large axial fan rig, located in UNSW s aerospace research laboratory. The rig contains an axial fan, containing 8 rotors and 8 stators. The diameter of the fan is 0.9 m and the rotors are contained in a duct with a flared inlet. The fan operates at 1900 RPM. Further, the input shaft is mounted upstream of the rotor and is housed within a central nacelle. This rather complicated arrangement means that an acoustic array cannot be placed directly upstream of the fan, nor can it be placed parallel to it. Also, the external duct and central nacelle prevent line-of-sight of an array to parts of the fan. To overcome these difficulties, a composite beamforming methodology has been devised. In this method, beamforming images are obtained from two (or more) viewing 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 beamforming sound maps that reveal the sound sources more completely. The results show the various sound sources such as rotor stator interaction and blade self noise as a function of frequency. The influence of the duct and nacelle on the beamforming output was determined by placing an acoustic source on a single blade and measuring the response on the array for multiple angular positions of the fan. Overall, the composite beamforming methodology was found to work well and it is able to overcome the difficulties presented by the axial fan design. Keywords: experimental aeroacoustics - acoustic array - beamforming.

2 Composite aeroacoustic beamforming of an axial fan 1 Introduction Axial fans are used in many industries, for mine ventilation systems, automotive cooling systems and within aerospace propulsion systems. Understanding broadband noise generation of these devices is becoming a more and more important topic of research [1] but still remains an engineering challenge. For axial induct fans, the broadband noise is created by the interaction of the duct wall boundary layer with the trailing edge tip vortex structures of the fan blades. Noise sources on an induct 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 obtained seemed to indicate that the noise sources were distributed along the span rather than being concentrated in the tip region. Tip clearance noise was studied by Fukano et al. [3]. This noise consists of a discrete frequency noise due to periodic velocity fluctuation and a broadband noise due to velocity fluctuation in the blade passage. The present work aims to perform acoustic array measurements on an axial induct fan where the array could not be aligned parallel to the fan. An improved beamforming technique, called composite aeroacoustic beamforming herein, has been devised which improves the results and assists in their interpretation. 2 Experimental set-up Acoustic array measurements were performed on an axial fan in the UNSW Aerospace Laboratory. Fig. 1(a) shows a sketch of the fan. The outer diameter of the impeller is D = 900 mm and consists of 8 equally spaced NACA 4412 blades Fig. 1(b). The fan can operate at a maximum rotational speed of 1,900 RPM, corresponding to a fan inflow speed of U i = 20 m/s, where U i is the flow velocity just upstream of the fan blades. The tip speed at this flow speed is U tip = πdω = 90 m/s, where Ω = RPM/60. The experiments were obtained for several flow speeds U i = 5,10,15 and 20 m/s. The fan noise was measured using an acoustic array to locate noise sources through beamforming to gain a better understanding of the noise sources close to the blades. For this purpose, a 64-channel array (7 circles of 9 microphones each and one microphone in the centre), shown in Figure 2(a), was used. The design of the array has been optimized to provide a good compromise between the beamwidth and the maximum side-lobe level in the frequency range of interest [4]. The array, which could not be aligned properly due to the presence of the input shaft, was placed at the inlet of the fan at an angle of α = 19 to the plane of blade rotation as shown in Figure 2(b). Each 1/4 inch GRAS 40PH CCP free-field array microphone was connected to a PXIe bit simultaneous sample and hold data acquisition card. The acoustic pressure signals were recorded at a sampling frequency of f s = 65,536 Hz over 60 s. These data were then processed using the conventional beamforming (CBF) technique which 2

3 2.06 D Motor Turbine Flow 2.06 D D = D Grid (a) 0.55 D 2.5 D 1.9 D 0.88 D 1.28 D 1.11 D (b) Figure 1: (a) Sketch of the axial fan in the UNSW Aerospace Laboratory. (b) Sketch of one NACA 4412 blade. Dimensions in mm. is a very popular technique for the location of noise sources in aeroacoustics. The CBF method produces an acoustic sound map in a plane parallel to the array. It is based on an optimization of the time-delay between each microphone. For more information about the technique, please refer to Mueller [5] and Brooks et al. [6]. 3 Composite beamforming 3.1 Conventional beamforming Consider a set of M microphones where the mth microphone is located at r m. The acoustic pressure field from any given source of noise is then recorded using these microphones and projected in the frequency domain using a Fourier transform. The obtained vectors, P(r m, f ), are used to create the Cross-Spectral Matrix (CSM) defined as: C(r m,r m, f ) = P (r m, f )P(r m, f ) (1) where the superscript X denotes the Welch s periodogram applied to X with the use of a Hanning window function. 3

4 0.86D Acoustic array Rotating blades 19 D = 900 (a) (b) Motor Shaft 1.31D 2.3D 2.44D Figure 2: Photo of the 64 microphones acoustic array (left) and sketch of the experiment with 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 beamformer output at a given frequency is generally defined by: Z(r n, f ) = et Ce M(M 1), (2) where e(r m,r n, f ) = exp( jk r m r n )/4π r m r n is the free-field Green s function (also called steering vector) between the microphone located at r m and the focusing point at r n, and k = 2π f denotes the wavenumber at frequency f. Note that the diagonal elements of the CSM are set to 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 angle correction has been applied to the obtained sound maps, as shown in Figure 3. If we consider a point F(x F,y F,z F ) in the initial focusing plane, its coordinates in the corrected plane after rotating by an angle α will be: ( x F z F ) = ( cosα sinα sinα cosα )( xf z F ) (3) Note that the y coordinate does not change as the altitude of the microphones remains the same after rotating. The array measurement were performed on both sides of the shaft as shown in Figure 4 for two reasons: first, the central shaft is hiding some regions when the array is set-up on one side 4

5 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 as they are estimated in the same plane. This technique helps to recreate the map that would be obtained if the array was placed in front of the fan (α = 0 ). Acoustic array Corrected focusing plane z x y α Initial focusing plane Figure 3: Display of the initial and corrected focusing plane for the CBF application. Array position 1 Array position 2 z x y Figure 4: Position of the array for the acoustic measurements. 4 Results 4.1 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 5

6 no flow. The speaker was located at 8 azimuthal locations equally spaced around the rotational centre of the fan. The sum of the acoustic maps obtained with the array in position 2 (see Figure 4) are shown in Figure 5(a) at f = 3,175 khz with a third-octave band integration and using the angle correction described in Eq.3. The green cross indicates the speaker location and 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 noise intensity is higher when the speaker is located on the lower part of the duct. The reason for this 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 in Figure 5(b). This beamforming map show that when the speaker is at the same side as the array, the sources are reasonably well recovered. Otherwise, the source is located out of the tunnel, most likely due to the presence of the shaft and bell mouth inlet. Reflections and propagation through the inlet overestimate the time-delay between the source and the microphones and 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 at position 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). These show that the fan noise is broadband in nature but starts containing peaks at the highest speed U = 20 m/s which correspond to the blade passing frequency (BPF). The BPF of the 8 blades fan can be obtained from BPF = Ω 8 = 1, 900/60 8 = 253 Hz. When using an hydrodynamic reference p re f = 1/2ρU 2 with ρ = 1.2 kg/m 3 being the air density, the broadband spectra collapse as shown in Figure 6(b). The noise of the fan running at U i = 15 m/s is measured with the acoustic array positioned on both sides of the tunnel inlet. The results are shown in Figure 7 for f = 2,4 and 8 khz in third octave band integration, in three columns. The left and central columns show the beamforming results obtained from the left and right positioned arrays, respectively. Composite beamforming 6

7 (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 noise sources is more accurate at higher frequencies; at f = 8 khz, all the sources are located at the tip of the blades while at f = 2 khz most of the sources are located outside of the duct due to the 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, the reason 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 are displayed in bold line while the invisible ones are in dashed line. When compared to the actual maps in Figure 7, the source regions do not exactly match. This is because the image in Figure 8 was taken from the centre microphone using a camera whose optical aperture is quite different from the acoustic aperture of the array. 5 Conclusions The noise of a large axial fan rig located in UNSW s aerospace research laboratory was studied using acoustic array techniques. As the array could not be aligned with the blades, a composite beamforming technique was introduced. This method enabled a better understanding of the noise sources on the fan. Measurements were first conducted using a speaker located at each blade position with no flow. The location on the acoustic maps was accurate when the source was located at the same side as the array. Otherwise, the maps show a source out of the boundaries of the duct due to the presence of the shaft and inlet. The fan geometry distorts the direct field and leads to 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 on the top and bottom parts of the duct. Again, the fan geometry obscures these regions from the array. To improve the accuracy of the composite beamforming method, accurate reconstruction 7

8 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. 8

9 Figure 8: Photo of the experiment as seen by the acoustic array in position 1. The white solid and dashed lines show the region where the blades tip are visible and hidden respectively. of the Greens function that describes the propagation from each fan blade to the array is needed. Such a Greens function can replace the free field model used in the beamforming algorithm and remove the distorting effects of the fan duct and inlet shaft. Further, the use of deconvolution methods will improve the localisation of noise sources, and should form part of future developments of the model. Acknowledgements Financial support from the Australian Research Council, Project DP , is gratefully acknowledged. References [1] Abdelhamid, Y.A., Ng, L.L., Hanson, D.B. and Zlavog, G., Fan Broadband Noise Generation and Propagation, 44th AIAA, 2006, Reno, Nevada. [2] Sijtsma, P., Using phased array beamforming to identify broadband noise sources in a turbofan engine, NLR report, [3] Fukano, T., and Jang, C.M., Tip clearance noise of axial flow fans operating at design and off-design condition, Journal of Sound and Vibration. Vol. 275, 2004, pp [4] Prime, Z., Doolan, C., and Zajamsek, B., Beamforming array optimisation and phase averaged sound source mapping on a model wind turbine, INTER-NOISE and NOISE-CON Congress and Conference Proceedings, Vol. 249, Institute of Noise Control Engineering, 2014, pp [5] Mueller, T.J., Aeroacoustic measurements, Springer,

10 [6] Brooks, T.F. and Humphreys, W.M., A deconvolution approach for the mapping of acoustic sources (DAMAS) determined from phased microphone arrays, Journal of Sound and Vibration. Vol. 294, 2006, pp