Establishment of a Beamforming Dataset on Basic Models of Low-Speed Axial Fan Blade Sections

The paper presents wind tunnel experiments, supplemented with phased array microphone measurements, on 2D basic models of low-speed axial fan blade sections: a flat plate, a cambered plate, and a RAF6-E airfoil. It aims at documenting the establishment of an acoustic beamforming dataset for the three profiles. The phased array microphone measurements offer spatially resolved information on the generated noise. The measurement setup enables the correlation of the streamwise evolution of the blade boundary layer with the associated noise characteristics. The dataset incorporates a wide range of incidence and Reynolds-numbers investigated. The present paper is confined to reporting on experimental results for arbi trarily selected representative incidences, Reynolds numbers, frequency bands, and profiles. The paper outlines a methodol ogy for the evaluation and representation of the beamforming data in the following forms: source strength level based third-octave spectra obtained using background noise subtraction; maps presenting the loci of source strength level maxima; noise source maps for frequency bands of anticipated vortex shedding noise.


Introduction and objectives
Low-speed axial flow fans are widely used in human environment. Some examples are as follows: fans in heating, ventilating and air conditioning (HVAC) for residential buildings as well as for non-residential buildings with occasional human access, and fans of industrial air technology (e.g. air supply, ventilation, cooling) operating in the vicinity of human personnel. In order to moderate the environmental impact of emitted fan noise on humans, and to ensure a proper aerodynamic operation as well, a concerted aeroacoustic and aerodynamic investigation and improvement of low-speed axial fans is a timely issue in the turbomachinery community.
In order to correspond to the simultaneous user demands of limitation in space and in rotor speed -being a basis for noise reduction as well -, the elemental blade sections of the aforementioned fans are often characterized by moderate Reynolds numbers, even below the critical value of 1.5·10 5 [1]. For achieving the prescribed aerodynamic performance -flow rate, total pressure rise -even at moderate diameter, rotor speed, and rotor blade count, such fans are often of high design specific performance, i.e. the blade sections are designed for high load (high lift). This corresponds to pronounced streamwise adverse pressure gradient on the blade suction side downstream of the suction peak. Such adverse effect is amplified due to the fact that the fan frequently operates in a throttled state relative to the design point, i.e. the flow incidence to the blade sections is increased. The resultant thickening or even separation of the suction side boundary layer tends to increase the turbulentboundary-layer-trailing edge noise and the separation-stall noise [1][2]. The aeroacoustic investigation of highly loaded / high incidence blade sections is therefore a topic of great practical importance, with special regard to discovering the correlation between the streamwise evolution of the boundary layer thickness and the spatial distribution of the noise sources associated with the thickened / separated boundary layer. In [3][4][5], a correlation has been found between the loss generated in the suction side boundary layer -represented by the momentum thickness -and the radiated broadband noise. This implies that by the detailed investigation of the boundary layer, additional knowledge can be gained regarding the noise formation mechanisms, contributing to the continuation of the research documented in [3][4][5]. Beyond the practical relevance as outlined above, the investigation of blade boundary layers exposed to pronounced adverse streamwise gradients, potentially leading to boundary layer separation, pose a challenge from basic research point view, in terms of experimentation, Computational Fluid Dynamics (CFD) as well as Computational Aeroacoustics (CAA) simulation.
Simple, traditional blade section geometry is characteristic for a great variety of axial fans, enabling relatively easy and low-cost manufacturing. Blades manufactured from e.g. sheet metal are characterized by cambered plate sections. Traditional airfoil profiles of relatively simple geometry -e.g. the RAF6-E profile, with a plain pressure surface [6] -are also popular in low-speed fan applications. It is important to note that for moderate Reynolds numbers, a cambered plate blade section may exhibit a more favorable aerodynamic behavior -higher possible lift, higher lift-to-drag ratio -than a profiled airfoil blade section. Examples are given for Reynolds numbers below ≈7·10 4 in [1], on the basis of [7]. The aforementioned favorable trends make the application of cambered plate blade sections especially relevant for certain low-speed fans, such as in [8].
In basic aerodynamic modelling of fan operation, the twodimensional (2D) airfoil / cascade approach is widely accepted [1]. In addition, also the basic modelling of the aeroacoustic behavior frequently relies on a 2D basis even in recent research projects. For example, in reference [9], the 2D blade elements are modelled acoustically as flat plates. Even recent experiments [10] aim at investigating the detailed aerodynamic features of the flat plate, however, without delivering spatially resolved measurement data on the acoustic behavior. The above suggest the need for noise source localization for 2D basic models of blade sections, thus extending the benchmark database available in the literature for acoustic modelling of low-speed axial fans. The usage of phased array microphones (PAM) along with the beamforming technique is increasing in the field of noise source localization. Its advantage compared to measurements with individual microphones is that it offers a convenient way to spatially discretize the sound field. This recently emerging -and nowadays still relatively costly -technique, as such, has a number of applications e.g. in aerospace engineering, as e.g. in [11]. Only a few applications of PAM is reported in relationship with low-speed air-handling turbomachinery [12][13][14][15].
References [16][17][18][19] report on studies related to increased Reynolds numbers, i.e. being characteristic for the aeronautic industry, and related to moderate angles of attack. In [16][17][18][19], the PAM measurement planes were aligned either with the suction surface or with the pressure surface of the airfoils or fan blades. This configuration however does not provide acoustic information in correlation with the boundary layer as it evolves in chordwise and chord-normal direction, characterized e.g. by the boundary layer thickness.
In the beamforming measurement technique the evaluation of the measurement data is of great significance. Several deconvolution methods exist and the diagonal treatment of the cross spectral matrix can also be chosen. The diagonal removal was commonly used in recent studies [16][17]19], however reference [20] challenges this practice by presenting its drawbacks.
To the authors' best knowledge, the PAM-based beamforming dataset established by the authors, and outlined in the paper, adds to the open literature from the viewpoint of the following objectives.
• It has been aimed to establish a concerted aeroacousticaerodynamic benchmark database on 2D basic models of low-speed axial fan blade sections, with involvement of the PAM technique for obtaining spatially resolved information on noise. The applicability of the PAM technique to this field of application -its advantages, and limitshas been intended to be tested. • The wind tunnel measurement setup presented in the paper enables the PAM investigation of the planes normal to the spanwise direction, thus correlating the chordwiseresolved and chord-normal resolved aeroacoustic and aerodynamic features. • In the beamforming technique, instead of the diagonal removal method, the capabilities of another diagonal treatment method have been intended to be tested. More specifically, the original diagonal is retained, and optimized. • The subjects of PAM investigation are basic models of low-speed axial fan blade sections, represented by three profiles: a flat plate, a cambered plate of circular arc camber line, and a RAF6-E profile. The three profiles are of rectilinear geometry, being in correspondence with the 2D flow approximation applied herein. To the authors' best knowledge, none of these geometries have been examined with the PAM technique; although aerodynamic and individual microphone measurement data are accessible for them, e.g. [21]. • The investigated Reynolds number range significantly extends below the critical value of 1.5·10 5 . • The range of studied angles of attack significantly exceeds the range presented in the literature [16][17][18][19]. Regarding the full dataset, the range of angle of attack α is between -10° and 50°, which means that extreme values are included as well -although only the range from 0° to 30° has been evaluated so far in detail. This examination range offers the possibility to take into account the effect of the angle of attack and to model a wide range of working conditions for fans, also including deep-stalled conditions.
through the Kevlar wall. The profiles were placed to the middle of the test section, and were bounded by the wall of the test section from one side and by a Kevlar wall on the other side. The distance between the midspan of the profiles and the microphone array was 0.556 m. The test section of the wind tunnel ends at 4.5 c downstream of the TE of the profiles. The sketch of the measurement setup is shown in Fig. 2.

Fig. 2 Measurement setup from two perspectives
The Kevlar wall was placed between the test section and the microphone array as it imitates the aerodynamically impermeable side wall of the wind tunnel test section -being anyway a Plexiglass wall in routine applications of the wind tunnel, for optical access -, whereas it provides high acoustic transmission for the PAM experimentation. The Kevlar fabric was stretched on an aluminum frame evenly in all directions.
The turbulence intensity is 0.8% and the flow inhomogeneity is below 3% in the middle of the test section, with respect to the mean velocity in the test section. The turbulence intensity was calculated from one velocity component as the root-meansquare of the velocity fluctuation divided by the mean velocity. The properties of the flow field are presented in reference [24].
The uncertainty of setting the angle of attack α has been estimated to ± 0.5°. The inlet velocity in the test section, v, has been set with a conservatively estimated uncertainty of ± 1.0 %, as checked with use of a calibrated Pitot-static probe.
An OptiNav Inc. Array24 general purpose PAM was used for noise recording. It consists of 24 microphones, arranged along a logarithmic spiral. The diameter of the PAM's aperture is 0.95 m. A camera is situated in the center of the array, which takes pictures of the sound source while the microphones are recording the sound data. As the Kevlar wall blocks the view of the camera, the pictures had to be taken separately from the noise measurements without the Kevlar wall. The analogous signals of the microphones were amplified and converted to digital signals, which were then analyzed with a computer software. The imageJ image processing program with Beamform Interactive plug-in of OptiNav was used for the evaluation of the measurements. As reported in [5], the amplitude uncertainty of the source strength obtained by the PAM experiments has been estimated to ± 1 dB. The duration of the measurements were 14s, with a sampling frequency of 44 100 Hz. Frequency domain beamforming was performed on the microphone data. The diagonal of the cross spectral density matrix was optimized. Beamforming was applied on a 2D grid at the midspan of the profiles.
The effect of the Kevlar wall was first investigated by measuring its sound attenuation at various frequencies. For this purpose the profiles were replaced with a point-like sound source which could emit sound at discrete frequencies. The measurement was made while the wind tunnel was turned off. The attenuation levels in the function of sound frequency (indicated with the center frequencies of the third octave bands) are shown in Fig. 3. The sound attenuation was defined by the difference between the source strength level (SSL) maxima detected by the PAM for the two cases: with and without the Kevlar wall. SSL is the output of the beamforming process [25], written in level form. The minimum of the investigated frequency range is in accordance with [5], while the maximum was adjusted to the capabilities of human audition. The attenuation of the Kevlar wall is frequency dependent, however comparison of the sound levels on the same frequencies are still possible without any compensation for the various profiles and flow conditions. 0.8-1 for profile vortex shedding. Such approximation has been refined on the basis of the experiences gathered in evaluating the beamform results for Re max , documented in [26]. For blunt trailing edge vortex-shedding, St is approximated as 0.2 [22]. With the approximate knowledge of St, the third octave bands were identified within which vortex shedding is anticipated. At α = 0° both types of vortex shedding may occur. The estimated third octave band center frequencies for the cambered plate are 1.6 kHz for both types of vortex shedding. For the RAF6-E the center frequencies are 2 kHz and 4 kHz respectively, for the profile vortex shedding and the for blunt trailing edge vortex-shedding. At α = 10° only the profile vortex shedding may occur, at a center frequency of 800 Hz, however the resolution of the PAM technique at this low frequency, together with the high background noise, make it impossible to distinguish this noise source on the beamforming source maps.
The signatures of vortex shedding were sought in the aforementioned third octave bands. The results are shown in Fig. 6. In the frequency regions indicated on the maps visible signs of vortex shedding noise was found. An attempt has been made to increase the quality of the source maps by choosing a suitable ROI for each case. For the cambered plate (top graph), the two types of vortex shedding cannot be distinguished from each other on the basis of the source map, as their estimated frequencies are in the same third octave band. In case of the RAF6-E profile the two types could be separated. For the graph related to the blunt trailing edge vortex-shedding noise (middle graph), the SSL maximum is detected near the leading edge, and is associated with a source being different from vortex shedding. However, the local peak related to the vortex shedding noise is still visible near the trailing edge. The map regarding the profile vortex shedding noise of the RAF6-E airfoil (bottom graph) indicates the peak near the TE, in accordance with the assumption of occurrence of vortex shedding.

Summary and future remarks
This paper serves as a starting reference for the related future research. It aims at documenting the establishment of an acoustic beamforming dataset on representative 2D basic models of low-speed axial fan blade sections: a flat plate, a cambered plate, and a RAF6-E airfoil. The wind tunnel experiments, supplemented with a PAM measuring technique, are documented in detail.
To the authors' best knowledge, the established benchmark dataset adds to the open literature from the following perspectives: a) PAM-based, spatially resolved information on the noise generated by the aforementioned low-speed 2D blade sectional models. b) Offering the possibility for correlating the streamwise evolution of the blade boundary layer with the associated noise characteristics. c) Extension of the ranges of Reynolds number and flow incidence under investigation, being especially relevant for low-speed axial fan blades.
The methodology for data processing and representation, to be used in future evaluation of the results, is outlined herein. The methodology is illustrated by means of representative examples on the following: a) Comparative spectra based on the detected SSL maxima. b) Maps presenting the loci of the SSL maxima in narrowband beamforming. c) Noise source maps.
In future work, the following steps of acoustic data processing are envisaged, with regard to evaluating the results over the entire dataset. a) Elaboration and application of a Fourier analysis-based technique for enhancement of the remarkable noise sources within specific frequency bands, and for effective removal of perturbations (e.g. background noise, sidelobes). b) Fuzzy clustering for identification of dominant noise sources that extend spatially as well as in frequency. c) Quantification of the broadband noise sources of various origin, thus contributing to the extension and refinement of semi-empirical acoustic models available in the literature for low-speed axial fans.