Influence of blade skew on axial fan component noise

Abstract

Microphone arrays can be used to detect sound sources on rotating machinery. For this study, experiments with three different axial fans, featuring backward-skewed, unskewed, and forward-skewed blades, were conducted in a standardized fan test chamber. The measured data are processed using the virtual rotating array method. Subsequent application of beamforming and deconvolution in the frequency domain allows the localization and quantification of separate sources, as appear at different regions on the blades. Evaluating broadband spectra of the leading and trailing edges of the blades, phenomena governing the acoustic characteristics of the fans at different operating points are identified. This enables a detailed discussion of the influence of the blade design on the radiated noise.

Keywords

Microphone array rotating beamforming skewed fan blades

Introduction

The aeroacoustic design of fans is an ongoing challenge. In general, the fan geometry is dictated by the intended aerodynamic performance and the geometric boundaries. However, the design choices made also have an influence on the acoustic characteristics of the fan.

Mechanisms influencing the noise generation of axial fans are well described in the literature. Sharland¹ identified several aerodynamic phenomena, such as vortex shedding and interaction with incident turbulent flow, causing the generation of broad-band noise. Several studies investigated noise generation due to vortices at the blade tip region.^2–4 Considerable effort has been put into developing models to predict acoustic performance from the measurement of flow characteristics.^5–9

Aside from affecting the characteristics of the resulting flow field, the skew of the fan blades has a noise reducing influence. In their survey of existing models addressing this, Carolus and Beiler¹⁰ showed that the attribution of spectral characteristics to certain noise generating mechanisms, however, is still a matter of dispute. This is, in part, due to the fact that the experimental tools used for these investigations are limited to methods for characterizing the flow properties, while the acoustic properties are only evaluated through spectra for the respective fan as a whole. This makes it difficult to find effective measures to lower the overall noise emission or even address desired spectral characteristics of the fan through blade design.

Microphone array methods provide the possibility of localizing and quantifying multiple simultaneously emitting noise sources,¹¹ which makes them applicable as an acoustic design tool. Algorithms for processing array data are available in time domain and frequency domain. Delay-and-sum beamforming in the time domain can be applied for moving sources by continuously changing the focus distance.^12,13 However, the spatial resolution achievable with classic delay-and-sum beamforming is limited. Advanced frequency domain methods, on the other hand, allow a higher resolution, but can only be applied on stationary sources. In the case of rotating sources and with appropriate measuring setup, however, it is possible to transform the data such that these sources appear stationary, which allows subsequent processing in frequency domain.^14,15

In what follows, the aeroacoustic properties of three fans featuring backward-skewed, unskewed, and forward-skewed blades, respectively, are investigated experimentally. Measurements include different operating points, at which the aerodynamic and acoustic performance of the fans is evaluated. Major noise sources occurring on the fans are identified through the application of suitable microphone array data processing. Acoustic differences of the fan designs are discussed by means of leading and trailing edge (LE and TE, respectively) spectra. It will be shown that the noise generating mechanisms highly depend on the blade skew of the fan and its operating point.

Measurements and data processing

Experimental setup

Three generic fans featuring backward-skewed fan blades (fan B), unskewed fan blades (fan U), and forward-skewed fan blades (fan F) were investigated, see Figure 1. The fans were designed with a two-dimensional element blade method,^16–19 as outlined in Zenger et al.²⁰ To obtain comparable results, the fans were designed to have a similar operating point. Common fan design parameters are shown in Table 1.

Figure 1.

From left to right: backward-skewed fan, unskewed fan, and forward-skewed fan.

Table 1.

Common fan design parameters.

Total-to-static pressure coefficient $ψ_{ts}$	0.18
Flow-rate coefficient $Φ$	0.18
No. of fan blades $z_{b}$	9
Blade airfoil	NACA 4510
Fan diameter $d_{fan}$ in mm	495
Hub diameter $d_{hub}$ in mm	248
Tip gap s in mm	2.5

In Table 1, the total-to-static pressure coefficient $ψ_{ts}$ is calculated with

\begin{matrix} ψ_{ts} = \frac{2 Δ p_{ts}}{ρ (d_{fan} π n)^{2}} \end{matrix}

(1)

and the flow-rate coefficient

Φ

with

\begin{matrix} Φ = \frac{4 \overset{\cdot}{V}}{π^{2} d_{fan}^{3} n} \end{matrix}

(2)

In equations (1) and (2), $Δ p_{ts}$ is the total-to-static pressure difference, $\overset{\cdot}{V}$ is the volume flow rate, n is the rotational speed and ρ is the fluid density. The total-to-static efficiency $η_{ts}$ is calculated via

η_{ts} = \frac{\overset{\cdot}{V} Δ p_{ts}}{2 π nT}

(3)

with the shaft torque T.

The fans differ in the fan blade skew and in the fan blade loading distribution $r u_{2}$ , where r is the radius and $c_{u 2}$ is the circumferential component of the absolute velocity at the blade row exit. The fan blade loading distribution can be a free vortex design, with $r u_{2} = const .$ over the blade span, or a controlled vortex design with $r \cdot c_{u 2} = f (r)$ .^19–22 For fan U, a free vortex design was chosen with $r u_{2} = const .$ , whereas for fans B and F, a controlled vortex design with $r u_{2} = (3 r + 1.115 m)$ $\frac{m}{s}$ was chosen.²⁰

For fan U, no fan blade skew, i.e. no blade sweep or blade dihedral,^20,23,24 was applied. For fan B, the sweep angle was varied from 0° at the fan blade hub to −55° at the fan blade tip. Correspondingly for fan F, the sweep angle was varied from 0° at the fan blade hub to 55° at the fan blade tip. The dihedral angle of fans B and F was chosen as to minimize the axial installation space of the fans.

Aerodynamic and aeroacoustic measurements were conducted inside an ISO 5801 standardized inlet test chamber,²⁵ as shown in Figure 2. The chamber provided semi free-field conditions, with absorbing walls and ceiling. The fans were installed in a short duct with a diffusor on the pressure side and a bellmouth inlet on the suction side, see Figure 2. The drive motor was mounted outside the duct. The rotation of the fans was kept at a nominal rate of 1500 r/min during all measurements. When the fan is running, a certain operating point (i.e. volume flow and pressure difference) is reached. If a higher volume flow is desired, the auxiliary fan is turned on. If a lower volume flow than that caused by the fan itself is desired, the butterfly damper is closed.

Figure 2.

Schematic representation of the test chamber.²⁶

The microphone array (Figure 3) was positioned on the suction side of the fan, at a distance of 0.45 m from the fan. It consisted of 64 microphones, arranged evenly on a ring with a diameter of $d_{array} = 1$ m. In addition to the sound pressures, the rotation of the fan was recorded using a trigger-per-revolution signal.

Figure 3.

Microphone array position.²⁶

Virtual rotating array

Beamforming in frequency domain requires sources of interest to be stationary for a meaningful reconstruction. In this case, the major interest lies in the sources occurring on the fan blades, i.e. rotating with the same rate as the fan. One possibility to obtain data with the fan blades appearing stationary is to physically rotate the microphone array at the same rate as the fan, similar to the setup used by Heidelberg and Hall.²⁷ However, an implementation of such a technique is not always feasible. Alternatively, data can be measured with stationary microphones and transformed into the rotating domain prior to further processing.

Herold and Sarradj¹⁵ proposed implementing a virtual rotating microphone array via linear interpolation between adjacent microphones of a circular array in synchronization with the current angle of the fan. The axes of the array and the fan have to be aligned for this method. As the rotation of the fan is not necessarily constant throughout an actual measurement, the motion is tracked with a one-trigger-per-revolution signal. Assuming smooth transition of rotational rates, the current angle is determined via spline interpolation from several consecutive trigger events.

The interpolated data can then be processed as if the fan is in fact not moving. However, in the rotating reference frame of the virtual array, the medium features a swirl centered at the axis of the fan. This has to be accounted for in the model for the sound propagation from the fan to the array microphones. In particular, the sound travel times from any point of interest on the fan to each microphone are affected by this. Depending on the rotational rate and the respective emitting and receiving positions, the effective sound travel times deviate from those in a resting medium.

Beamforming and deconvolution

Beamforming in the frequency domain relies on the evaluation of the cross-spectral matrix (CSM). Based on the virtual rotating data, the CSM can be estimated using Welch’s method.²⁸ For this, each signal is divided into K blocks, onto which an Fast Fourier Transformation (FFT) is applied. The resulting complex sound pressures are stored in a vector $p_{k} \in ℂ^{M}$ , with the number of microphones M. For every block, the cross-spectra between the channels are calculated, and finally, the CSM by averaging all cross-spectra

\begin{matrix} C = \frac{1}{K} \sum_{k = 1}^{K} p_{k} p_{k}^{H} \end{matrix}

(4)

For further processing, the main diagonal of the CSM is removed, since the autospectra hold no information on phase differences between the microphones but may contain self-noise of the channels. The squared sound pressure radiated by a source at a focus point $x_{t}$ is calculated with

\begin{matrix} b (x_{t}) = h^{H} (x_{t}) C h (x_{t}), t = 1 \dots N \end{matrix}

(5)

where N is the number of focus points chosen to discretize an area where sources are expected. The steering vector

h

contains the sound propagation model and the weighting of the microphones. Assuming a monopole model, its entries are calculated with

h_{m} = \frac{1}{r_{t, 0} r_{t, m} \sum_{l = 1}^{M} r_{t, l}^{- 2}} e^{- j k (r_{t, m} - r_{t, 0})}, m = 1 \dots M

(6)

where

r_{t, m}

denotes the distance from one focus point to the mth of M microphones and

r_{t, 0}

the distance from the focus point to a reference position at which the sound pressure levels are evaluated. It may be noted that several formulations for steering vectors exist in literature. As has been shown, the formulation used in equation (6) allows a correct reconstruction of the pressure amplitudes with a small error in the radial positioning of the sources.²⁹

The sound source map calculated with equation (5) features artifacts that reduce the spatial resolution of the map. Further processing with deconvolution methods allows a higher resolution of the final result. For this purpose, the CLEAN-SC method³⁰ is applied here. It enhances the resolution through identifying correlated portions in the map and only retaining the respective maximum values for the final result. It has to be noted that the method can only be successfully applied as long as the assumption of the major sources being uncorrelated holds. While this method can be efficiently applied on broadband noise, it might not perform satisfactory on multiple sources emitting tonal noise, as these are not uncorrelated.

For the purpose of this study, the three-dimensional focus region is chosen to fully encompass the fan blades with

r_{min} = 0.1

r_{max} = 0.35

m and a resolution of 0.01 m normal to the fan axis. The resolution in axial direction is 0.02 m, with

x_{min} = 0.45

m and

x_{max} = 0.55

m. For display and further processing, the reconstructed sound pressures are summed in x-axis direction. The array measurement and processing parameters are summarized in Table 2. Similar setups were employed in earlier studies.^26,31,32 The calculations including beamforming and deconvolution were done with the help of the microphone array signal processing library Acoular.³³

Table 2.

Data acquisition and processing parameters.

Number of microphones	64
Diameter of ring array	1 m
Distance from fan to array	0.45 m
Measurement time	30 s
Sampling rate	48 kHz
FFT block size	2048 samples
FFT window	von Hann, 50% overlap
Circular focus grid	r_min=0.1 m, r_max= 0.35 m
	x_min=0.45 m, x_max= 0.55 m
Resolution of focus grid	$Δ yz = 0.01 m$ , $Δ x = 0.02 m$
CLEAN-SC iterations	500
CLEAN-SC damping	0.6

Results

The aerodynamic characteristic curves are shown in Figure 4. The data presented here have partly been discussed in previous studies.^20,26 The curves of the pressure coefficient $ψ_{ts}$ show the expected extended stall-free operating range of fan F at lower flow-rate coefficients than the design point flow-rate coefficient of $Φ = 0.18$ .^23,34 In general, the pressure coefficient of the forward-skewed fan F is higher than the pressure coefficient of the unskewed fan U and the backward-skewed fan B in the region from $0.1 \leq Φ \leq 0.22$ , i.e. in the typical operating range of the fans. The pressure coefficient curves for the unskewed and backward-skewed fan show a similar progression, with the backward-skewed fan having slightly higher values at $Φ > 0.18$ .

Figure 4.

Pressure coefficient $ψ_{ts}$ (left) and efficiency $η_{ts}$ (right) at different flow-rate coefficients $Φ$ for fans B, U, and F. The gray bars mark the coefficients for which the soundmaps (Figure 5) and the spectra (Figure 6) are evaluated.

A similar trend is observable for the efficiency curves. The forward-skewed fan F has a higher efficiency in the region of $0.12 \leq Φ \leq 0.25$ . The backward-skewed fan B has the lowest efficiency over a broad range from $0.075 \leq Φ \leq 0.21$ . For $Φ < 0.11$ , the unskewed fan U has the highest efficiency of the three fans. For $0.11 \leq Φ \leq 0.225$ , efficiency values of fan U are between the values of the backward- and forward-skewed fan, and for $Φ > 0.225$ , the unskewed fan has the lowest efficiency.

It is obvious that the fan blade design has a great impact on the aerodynamic properties. With the current test setup, the forward-skewed fan features the best aerodynamic properties.

Figure 5 shows the source distribution in terms of the sound pressure level at the exemplary 5 kHz one-third octave band for the three fans at the flow-rate coefficients $Φ = 0.105, Φ = 0.18$ , and $Φ = 0.22$ . The maps include sources with a 30-dB dynamic range. Most of the maps feature a number of source levels at focus points that lie effectively outside the ducted region. While these are believed to represent actual sources, their radial localization might be distorted by reflections on the duct wall and the positioning error introduced by the steering vector formulation as mentioned earlier.

Figure 5.

Sound maps at 5000 Hz one-third octave band for fan B (backward-skewed), U (unskewed), and F (forward-skewed) at different flow-rate coefficients $Φ$ .

For all depicted fan geometries and flow rates, the dominant source regions appear towards the blade tips. This effect is to be expected in view of the higher relative flow velocities towards higher radii.

At the lowest considered flow-rate coefficient $Φ = 0.105$ , the fans are operating in the stall region. Here, fan B features a line of sources along the blade chord, with decreasing level towards the TE. This can be caused by flow separation at the LE or the interaction of the LEs with turbulences of the inflow. Also visible are source regions at the LEs at the duct wall, which commends the appearance of tip clearance noise. Fan U shows similar noise structures, albeit with a higher level. In addition to that, sources along the whole span of the LE and TE are visible here. It appears that for this fan, the flow separates at the LEs of the blades, and generated turbulences interact with the TEs, causing vortex shedding noise. For fan F, the noise radiation due to flow separation at the LE is much more pronounced. In this case, this does not lead to increased noise at the TE. The map does indicate, however, tip clearance noise at the LE as well as at the TE.

At the design flow-rate coefficient $Φ = 0.18$ , no flow separations are expected. Thus, the occurring sources near the LEs can most likely be attributed to turbulent ingestion noise. While at this frequency band, the source patterns of fans B and U are similar if a little more distinct to the case at the lower flow rate, the major sources on fan F are contained to a smaller region originating at the LE and proceeding to the blade center. This indicates noise due to interaction of the LE with turbulent flow and possible build-up of further turbulence on the blade.

At $Φ = 0.22$ , the noise originating from TE of fan B becomes more prominent. At this flow rate, the boundary layer is increasingly turbulent, causing noise generation by vortex shedding. In comparison, TE noise of fan U is more pronounced than for fan B. This may be explained by the vortex shedding being significantly dependent on the flow velocity component normal to the TE,¹⁰ which is decreased in case of a backward skew of the blade.³⁵ In contrast, no significant noise generation at the TEs of fan F can be observed at 5 kHz, even though the velocity normal to the TE of this fan is expected to be increased compared to the other fans.

A possible explanation is that the interaction of emerging larger turbulent structures with the TEs is only minor, but that these structures cause noise when dissipating in the wake of the blade and when interacting with the LEs of the following blade. This is in line with the observation of mapped sources that appear to protrude from the LEs towards the direction of rotation. In a less distinct shape, similar structures are also visible in the other sound maps. Noise generation due to turbulences generated at the preceding blade has been observed in an earlier study.¹⁵ However, the exact mechanisms causing this noise emission have to be studied further, since it is plausible for the turbulent structures to be convected downstream, not being able to interact with the following LE.

In this case, what might be visible is noise caused by dissipating turbulences downstream of the fan. A further explanation might be that with increasing volume flow, separations on the fan hub occur, which may also lead to increased turbulence ingestion noise. As has been shown previously,²⁰ in terms of noise emission, forward-skewed fans are more susceptible to distorted inflow conditions than backward-skewed fans. Hence, this effect would be more pronounced for fan F.

In contrast to lower flow rates, the tip clearance noise is reduced here. While the unskewed fan features visible sources that can be attributed to tip clearance, such sources are not apparent in case of the fans with skewed blades.

Figure 6 shows integrated spectra of the three fans at different operating points. They are obtained through summation of the mapped sound pressure levels over the respective fan blade LE and TE sub-regions. For clarity, the TE and LE are not depicted separately for each blade but summed for the respective sub-regions of all blades. This can be done since the spectra do not deviate considerably between the blades.²⁶

Figure 6.

One-third octave spectra of the backward-, non-, and forward-skewed fans at three different operating conditions. The sound pressure levels integrated over the leading edge sub-regions are plotted in dark red, those of the trailing edges in light green, and the spectra summed over the whole focus area are indicated by the black curve. Also, the total sound pressure level (sum of all spectral bands) is noted in each sub-plot.

For the flow-rate coefficient of $Φ = 0.105$ , fan B has the lowest total sound pressure level with $L_{p, total} = 80.7$ dB. Spectra of the LE and TE sub-regions have similar values for frequencies below 2 kHz; hence, no dominant noise generating mechanism can be identified. As has been shown in a previous study,²⁶ a reliable reconstruction of sources below 1 kHz is generally difficult with the employed measuring setup. For higher frequencies, the noise generation at the LEs tends to be slightly higher than at the TE for this fan. The overall sound pressure levels of fans U and F are substantially higher: 5.4 dB for the unskewed fan and 6.2 dB for the forward-skewed fan. Also, the dominance of LE noise is more pronounced for these fans at frequencies f > 1.4 kHz. Hence, although all fans are operating in the stall region, the radiated sound is still dependent on the fan blade geometry. In a previous study,²⁰ it was shown that LE noise is less pronounced for the backward-skewed fan at the design point, as there is a less energetic interaction mechanism of the fan blade LEs with the inflow. Obviously, the same applies for off-design operating points.

At the design flow-rate coefficient of $Φ = 0.18$ , fan F has a substantial lower total sound pressure level with $L_{p, total} = 75.2$ dB, compared to fan U ( $L_{p, total} = 85.3$ dB) and fan B ( $L_{p, total} = 83.6$ dB). Throughout the whole spectrum, sound pressure levels of fan F are lower than those of fan U. In comparison with fan B, the spectral curve of the fan F shows significantly lower levels for f ≤ 1 kHz. As mentioned, the exact location of the sources causing the spectral differences at low frequencies remains unknown. For an identification of the aeroacoustic effects causing the better performance at lower frequencies, further investigations with an array setup featuring a larger aperture are necessary. Also, the application of deconvolution methods capable of evaluating correlated sources might prove to be beneficial for this frequency range.

The LE and TE spectra of fan B at $Φ = 0.18$ show similar characteristics throughout the whole frequency range, except for the 2.5 kHz third-octave band, where LE noise is about 10 dB below TE noise. This relation is different for fans U and F. While TE and LE spectra in the low-frequency range are similar, noise from the LE sub-region is more dominant at frequencies between 1.6 kHz and 4 kHz for fan U and between 3.15 kHz and 6.3 kHz for fan F. At higher frequencies, noise from the TE sub-region is of higher magnitude. Hence, depending on the blade skew, dominant noise sources occur at different sub-regions and at different frequencies.

At the highest considered flow-rate coefficient of $Φ = 0.22$ , the total sound pressure levels of fan B ( $L_{p, total} = 73 dB$ ) and fan F ( $L_{p, total} = 73.2 dB$ ) are nearly identical. However, the details of the spectral characteristics of LE and TE noise differ visibly. While for fan B, TE noise is dominant for the most part of the spectrum, for fan F, LE noise dominates for several spectral bands, most noticeably at 2, 4, and 5 kHz. Fan U has the highest total sound pressure level with $L_{p, total} = 75.4$ dB. This is especially due to higher third-octave levels at frequencies of f ≤4 kHz. As previously observed,^18,35 TE noise is dependent on the velocity perpendicular to the TE. This velocity is significantly reduced by the TE geometry of skewed fans, which explains the reduced TE noise emission in comparison with the unskewed fan.

Conclusion

The influence of the skew of fan blades on the noise emission has been studied based on microphone array measurements conducted with three generic axial fans. With the help of the virtual rotating array method and subsequent beamforming and deconvolution algorithms, sound maps were generated. These allowed the detailed evaluation of acoustic source mechanisms occurring on backward-skewed, unskewed, and forward-skewed fans by means of localizing major sources and generating blade LE and TE spectra.

Several noise generating mechanisms, such as turbulence ingestion, vortex shedding, and tip clearance could be identified by acoustic source mapping. Some of the phenomena observed suggest that regions of turbulence generation do not necessarily coincide with the location of related noise generation.

It has been shown that, although the forward-skewed fan has an extended operating range below the design point, the noise emission at a very low flow rate is much higher due to extensive flow separations at the LE. At a high flow rate, the unskewed fan exhibits higher noise generation at the TEs than the skewed fans.

Independent of the operation point, the noise generation at the LEs of the forward-skewed fan is shown to dominate the spectrum at certain frequency bands. This is not the case for the backward- and unskewed fans, where the dominating part depends on the flow rate. In general, TE noise is more dominant at high flow rates and at higher frequencies.

At the design flow rate, the forward-skewed fan exhibits the least noise generation. Aside from comparatively low TE noise at medium frequencies, the major differences to the other fans can be found at the lower part of the spectrum. As has been discussed, the certain identification of the phenomena occurring at low frequencies requires further experiments with adapted array geometry and data processing.

This study has shown that noise generation mechanisms that have been discussed theoretically or measured indirectly can be verified with direct acoustic measurements. As the dominant source regions differ depending on the fan geometry and the operating point, an efficient noise reduction approach necessitates accurate knowledge of the location and strength of multiple sources. With the setup at hand, more insight into aeroacoustic phenomena occurring with rotating machinery can be gained, allowing the development of tailored measures for noise reduction.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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