An industrial onsite methodology for combined acoustic-aerodynamic diagnostics of axial fans,involving the phased array microphone technique *

Abstract

A combined acoustic-aerodynamic diagnostics methodology is presented herein, involving the phased array microphone technique and an in-house rotating source identifier processing algorithm. The methodology makes possible the industrial onsite investigation of unducted or short-ducted rotor-only axial fans. Its application is illustrated in a case study of a free-inlet, free-exhausting fan, surveyed from the upstream direction. A methodology is outlined for guaranteeing the appropriateness of averaging of the phased array microphone records. A technique is proposed for eliminating the ambiguity of the angular position of the rotor noise sources. A complete set of noise source maps of various frequencies have been evaluated. Noise sources, such as tip leakage flow and suction side blade boundary layer flow, have been identified. Empirical correlations have been pointed out between indicators of aerodynamic noise and aerodynamic loss along the blade span. Such correlations may contribute to redesign guidelines for simultaneous reduction of noise and improvement of efficiency at prescribed fan performance.

Keywords

Phased array microphone beamforming rotating source identifier algorithm industrial axial fan onsite diagnostics fan noise aerodynamic loss

Introduction

Axial flow fans installed for real-life industrial applications occasionally generate more noise and aerodynamic loss than expected on the basis of the fan catalogue data. One possible reason is that, due to the industrial environment of the fan, the realized inlet flow to the rotor differs from the inlet condition assumed in design or realized in the measurements published in the catalogue. In order to elaborate a proposal for the improvement of the criticized axial fan, combined acoustic-aerodynamic onsite investigation is essential, incorporating the localization and identification of noise sources. The following demands are laid on behalf of the industry for the ad hoc onsite experiments and their evaluation.

Cost- and time-effectiveness → rapid measurements (avoiding the interference between the measurements and the industrial process – vice versa); minimization of costly instruments; rapid and effective proposal, based on straightforward guidelines;

Ergonomics demands → robust instrumentation; limited space demand; no special onsite preparation needed;

Data being relevant for guidelines of improvement → spatially well-resolved acoustic and aerodynamic data; distinction of fan noise sources from background noise, being due to the industrial environment.

The phased array microphone (PAM) technique, supplemented with the rotating source identifier (ROSI) PAM data processing algorithm,¹ gives a potential aid in fulfillment of the above demands. However, the experiences are still limited in this field. PAM is applied to axial flow turbomachinery mostly not on industrial sites but in laboratory experiments,^2–6 often involving immobile PAM equipment. The subjects of experimentation are mostly not industrial ventilating fans but aero-engine fans.^3,4,6–8 The ROSI algorithm is still rarely applied.^1,4 In the cases when multiple microphones are used in diagnostics of industrial ventilating fans, the supplement of acoustics measurements by aerodynamic experiments is either lacking⁵ or is usually confined to global data.^9–13 In Sturm and Carolus,¹⁴ pressure transducers are used on the rotor blade surface for detecting eddies impacting on fan noise. Very few papers are published on rotor noise sources measured locally along the blade span, and seeking their possible correlation with spanwise resolved aerodynamic characteristics.^9,10

The initiative of the authors is to extensively apply the PAM technique in onsite diagnostics of axial flow fans, e.g. in Benedek and Tóth.¹⁵ This paper adds to the literature from the following perspectives. It presents a combined acoustic-aerodynamic diagnostics and evaluation methodology, involving the PAM + ROSI technique, developed by the authors for a complete fulfillment of demands (a) to (c) listed above. The application of the methodology is illustrated herein in a case study of a short-ducted ventilating fan, investigated from the upstream direction. Guidelines are provided for the appropriateness of averaging of the PAM records, in order to minimize the duration of the PAM measurement—for fulfillment of demand (a)—whereas guaranteeing the proper quality of the PAM-based data under evaluation. A technique is proposed for eliminating the ambiguity in determining the angular position of the rotor noise sources. The dominant noise sources such as tip leakage flow and blade suction side (SS) boundary layer (BL) flow, are identified. To the authors’ best knowledge, the presented research campaign is the first one in which quantitative correlation is discovered between the measurement-based local indicators of sound pressure and aerodynamic loss, along the rotor blade span. Such correlation provides a basis for a customized redesign of the fan inlet section and / or the rotor, by straightforward means, for a simultaneous reduction of noise and loss, while retaining the required aerodynamic performance. Preliminary studies to this paper have been published in Benedek and Vad.^16–18

Fan of case study, diagnostics methodology

The sketch of the fan of the case study is presented in Figure 1. The fan is a rotor-only configuration with five forward-skewed blades, built in a short duct, and equipped with a short inlet cone. It is a wall-mounted free-inlet, free-exhausting ventilating fan, used e.g. for extraction of warmed-up air from a room incorporating heat exchangers. The static pressure rise performed by the fan is negligible in the case study. The main data of the fan are as follows: d_t = 300 mm, hub-to-tip diameter ratio: 0.30, tip clearance relative to the span: 0.066, rotor speed: 1430 r/min, global flow coefficient (annulus area-averaged axial velocity normalized by u_t): 0.316. Detailed data on the blade geometrical features and operational characteristics of the fan are documented in Benedek and Vad.¹⁶ Studies by Benedek and Vad^16,18 also serve with further details on the measurement technique, instrumentation, limitations, measurements errors, as well as on the data processing and evaluation methods.

Figure 1.

Sketch of the fan of the case study.¹⁷

In the discussion presented herein, the fan is subjected to combined acoustic-aerodynamic diagnostics from the upstream direction. Figure 2 outlines the methodology developed for this purpose. The acronyms applied in the figure are explained in this section. The upper part of the figure illustrates the instrumentation involved. Routine means—i.e. a thermometer for T₀ and a barometer for p₀—are applied for measuring the state of the ambient air on the site. The geometrical characteristics of the fan, FAN[GEOM(r)], incorporating the details of blade geometry along the span at representative locations,¹⁶ can be measured in its switched-off state. Robust, portable PAM equipment is installed upstream of the fan. The plate incorporating the microphones is to be set perpendicular to the axis of rotation and the center of the array is to coincide with the rotor axis. The microphone signals obtained on the operating fan, PAM[MIC SIGNS(t)], are recorded by means of the PAM data acquisition system. The noise sources are localized by means of a ROSI processing algorithm, necessitating the synchronization of the acoustic model with the source position. For this purpose, an index signal is to be obtained for each rotor revolution. This signal also provides a means for determining the rotor speed n(t). A non-contact (optical) angular encoder, adaptable to the onsite studies (e.g. a laser stroboscope and a light-reflecting sticker applied to one of the blades) is to be used.

Figure 2.

Scheme of the diagnostics and evaluation methodology.

For obtaining details on blade aerodynamics, the aforementioned experimentation is supplemented by a portable anemometer, being a routine instrument in industrial air technology. By means of the anemometer, the inlet axial velocity profile, v_ax(r), is measured. This is the sole aerodynamic measurement that is necessary in the diagnostics methodology outlined herein.

The lower part of Figure 2 presents the flowchart of data processing and evaluation. On the basis of the T₀ data, the speed of sound is calculated. It is used further on, together with the angular encoder data—rotor angular phase and n(t)—in processing the PAM records [MIC SIGNALS (t)], with application of the ROSI algorithm. By such means, the rotating noise sources are visualized for representative third-octave bands in the form of noise source maps (ROSI MAPS). It is noted that, e.g. with use of a classical frequency-domain-based Delay & Sum processing method,¹⁹ standing sources can also be localized. This is beyond the scope of the present paper. With knowledge of the rotor geometry [GEOM(r)], the image of the rotor is assigned to the ROSI maps in a phase-correct manner (ROSI MAPS + ROTOR PHASE). This enables a lifelike interpretation of the ROSI maps.

The ROSI maps represent the spatial distribution of P values. In order to quantify the generation of noise with respect to the radius, the P data are area-averaged along the circumference (CIRC. AVE.), resulting in P_M(r) profiles for each third-octave band under evaluation.

On the other hand, the aerodynamic properties of the blading along the span, [ADP(r)], are calculated. The obtainment of aerodynamic properties, including the momentum thickness parameter θ*, is discussed in sections “Aerodynamic characteristics along the blade span” and “Correlation between local indicators of noise and loss along the blade span”. The calculation procedure involves the measured v_ax(r) profile as well as the geometry of the elemental annular blade cascades along the span [GEOM(r)]. The aerodynamic properties are represented in dimensionless form, e.g. ϕ and ψ_is. For non-dimensionalization, u_t is calculated with use of d_t and n. Furthermore, ρ is approximated with use of T₀ and p₀. On the basis of the aerodynamic properties, θ*(r) is introduced as a representative indicator of aerodynamic loss along the span. A correlation (CORREL.) is sought between the local noise, represented by the P_M(r) profiles, and the local loss, represented by θ*(r). The established, case study-specific correlation functions [P_M = f(θ*)] provide a potential redesign guideline in simultaneous reduction of both rotor noise and loss.

The case study presented herein, demonstrating the application of the combined acoustic-aerodynamic diagnostics and evaluation methodology, is characterized by the following details.

A general purpose Optinav Inc., Array 24 PAM system, and an in-house ROSI processing algorithm¹⁵ have been applied. The microphones of the array are sunk into an octagonal aluminum plate, along a logarithmic spiral curve, in order to get good sidelobe characteristics. The diameter of the circle enveloping the octagonal plate is 3.17 d_t. The array was installed at a distance of 1.83 d_t from the outlet plane of the fan casing. Such distance made possible the detection of acoustic signals at a sufficiently high level, avoiding the overload of the microphones. Based on preliminary anemometer measurements, the impact of the PAM device on the flow field inlet to the fan was found negligible. The way of data sampling as well as forming the average of PAM records, providing the acoustic results presented in the paper, is detailed in subsection “Notes on averaging of PAM records”. The amplitude uncertainty of the PAM-measured noise source maps is influenced mainly by the uncertainty of the microphones, the sidelobe (ghost source) characteristics of the array, and the uncertainty of alignment of the PAM axis with the rotor axis. Based on anechoic chamber measurements in a worst-case study, the amplitude uncertainty has been estimated t ±1.0 dB. The uncertainty in detection of rotor angular position is estimated conservatively to ± 2.5°.

By means of a wool tuft probe, it has been confirmed that both the radial and tangential velocity components are negligible at the fan inlet. v_ax(r) has been measured by means of a calibrated Schiltknecht “Mini-Air” vane anemometer probe, connected to a Schiltknecht P670 encoder. The axial velocity distributions were measured along two diameters being perpendicular to each other, and were then averaged. The measurements were taken at the inlet plane of the fan casing, located at 70% of midspan axial chord length upstream of the blade leading edges at midspan. The fidelity of the vane anemometer in onsite measurement of the rotor inlet axial velocity profile has been confirmed via a preliminary hot-wire laboratory measurement. The estimated uncertainty of the geometrical and aerodynamic data is reported in Benedek and Vad.¹⁶

Acoustic characteristics

Noise spectra

Based on measurements and finite-element computations²⁰ on the mechanical behavior of the fan (e.g. blade eigenfrequencies), it has been concluded that the noise dedicated to the rotor is predominantly airborne noise. Figure 3 presents the noise spectra determined with use of the PAM-detected L_P peak values within the annulus region. The following observations are made on the basis of the figure. The fan noise dominates over the background noise in the case study. The noise is dominated by broadband noise sources (BNS), since no significant tonal noise peaks are observable. The base frequency of the classic rotor–stator interaction noise is the blade passing frequency n·N (119 Hz) multiplied by the number of stator elements (2 pieces of fan supporting struts located downstream), being 238 Hz in the present case study. Although some peaks appear near 1 × and 2 × 238 Hz in the spectra related to the fan, they cannot noticeably be distinguished from the peaks being also present in the spectra of background noise. The suppression of the tonal noise, i.e. rotor–stator interaction noise can be dedicated to the application of skewed blades.²¹

Figure 3.

Upper graph: noise spectra. Black line: fan in operation. Gray line: background noise. Lower graph: A-weighting across the frequency range.

For elaboration of the noise source maps, the third-octave frequency bands having middle frequencies of f_mid = 2000, 2500, 3150, 4000, 5000, and 6300 Hz have been selected. The lower limit of this frequency range corresponds to the limited spatial resolution of the beamforming technique.

The lower part of Figure 3 presents the A-weighting graph, representing the sensitivity of human audition as a function of the frequency.²² The selected f_mid frequencies are indicated in the diagrams by arrows. The A-weighting factors related to f_mid = 2000, 2500, and 3150 Hz are near the maximum value of the A-weighting graph. It is also noted that the noise spectrum of the fan slopes down with increasing frequency, i.e. the higher the frequency, the less significant of the related noise. Based on the above, the bands of f_mid = 2000, 2500, and 3150 Hz were judged as the most significant ones from the viewpoint of human audition, within this case study. Therefore, the paper focuses on establishing guidelines in modeling and moderation of BNS related to these bands. As demonstrated in Lowis and Joseph² and Sijtsma,⁴ the PAM technique is an effective means for localizing and identifying BNS.

Source maps, aspects of evaluation

The left column in Figure 4 presents the source maps, having the rotor in the center. The images of the blades are included in the source maps, for a picturesque explanation of the results. They are located in correspondence to the instantaneous angular position of the rotor, assigned to the source maps. The rotor annulus area is indicated using concentric circles (inner circle: at the hub of R = 0.30; outer circle: at the tip of R = 1.00). Circles are presented on the top left corner of the source maps the diameter of which corresponds to the resolution of the measurements.¹⁶ The resolution characterizes the spatial uncertainty of the source maps. It is the shortest distance within which two sources can be distinguished. The resolution can be theoretically estimated,²³ considering that it is proportional to the distance between the sources and the array, and is inversely proportional to the size of the array and to the frequency of interest.

Figure 4.

Left column: Source maps (L_P[dB]). Right column: comparative source maps obtained after reduction of the tip clearance of the blade indicated with arrows. f_mid increases from top to bottom.

Taking the noise source classification in Carolus²¹ and De Gennaro and Kuehnelt²⁴ as a basis, the source maps will be analyzed for a possible identification and localization of the following BNS, related to each blade.

Turbulence ingestion noise ← Turbulent inflow originating from the inlet cone at the highest radii, and impacting on the leading edge;

BL noise ← Interaction of the turbulent BL with the blade surface;

Trailing edge noise ← Interaction of the turbulent BL with the trailing edge;

Vortex shedding noise ← Interaction of the SS and pressure side BLs just downstream of the trailing edge (partly BNS);

Separation noise ← BL separation;

Leakage flow noise ← Turbulent tip leakage flow.

Inspired by the study of Bianchi et al.,^9,10 the authors have aimed to quantify the radial distribution of rotor noise. For this purpose, the P data in the source maps have been area-averaged along the circumference,¹⁶ resulting in P_M(R) profiles. The P_M(R) distributions are presented in Figure 5, in the form of logarithmic levels L_P_M. The hub radius at R = 0.3 is indicated with use of a dashed line. The L_P_M(R) distributions will give an aid in evaluating the source maps.

Figure 5.

L_P_M(R) distributions and their correlation with the momentum thickness level (upper three diagrams).

Notes on averaging of PAM records

When detecting rotating sources, the appropriateness of averaging of PAM records is of great importance. This is due to the demand that the data processing method should resolve the acoustic effect of unsteady, rotating flow phenomena such as highly turbulent leakage flow. For industrial onsite measurements, the duration of PAM recording is to be possibly minimized—see demand (a) in the “Introduction” section. In addition, the proper spatial resolution and quantification of the sources is also to be achieved on the source maps. These demands are simultaneously to be fulfilled by means of a reasonable compromise in setting the parameters of averaging of PAM records. However, the literature is very limited in this regard. In particular case studies,^6–8 although the duration of averaging (recording) is reported,¹⁸ these cases are restricted to the use of conventional algorithms capable for detecting standing sources. No direct recommendations were found in the literature for the appropriateness of averaging of PAM records in application of the ROSI algorithm. Therefore, it became necessary to carry out own investigations from this point of view.

The authors were compelled to take guidelines in Koop,²⁵ valid in localizing standing sources, as a basis. On the basis of Koop,²⁵ the following parameters play a role in the averaging process: f_S, Δf, K_W, L_S, N_W, O_W, t_S. The relationship among these parameters is as follows

L_{S} = f_{S} \cdot t_{S}

(1a)

K_{W} = \frac{L_{S}}{(1 - O_{W}) \cdot N_{W}} - 1

(1b)

Δ f = \frac{f_{S}}{N_{W}}

(1c)

The PAM records have been averaged for various parameter settings, in application of the ROSI algorithm. The guidelines in Koop²⁵ have been supplemented by own experiences gathered in this campaign of investigations. It has been concluded that, for the appropriateness of averaging of PAM records, a sufficiently large value of K_W is to be ensured. In order to maximize K_W, a fixed PAM sampling frequency of f_S = 44,100 Hz, being the maximum frequency made available by the data acquisition system, has been applied. Based on past experiences, the ratio of overlap between the windows has been kept at a constant value of O_W = 0.5. The sampling time t_S as well as the window size N_W have been set to various values in a number of averaging scenarios. As indicated in equations (1a) and (1b), K_W can be increased: (a) by increasing t_S, (b) by reducing N_W. However, when reducing N_W, it is to be controlled by means of equation (1c) that the available frequency resolution, Δf, decreases. Given that BNS are investigated in the present study, there is no need to capture narrow-band phenomena, being anyway of importance in the investigation of sources of tonal noise. Therefore, a relatively coarse frequency resolution was judged to be sufficient. For the data presented herein, Δf = 43.1 Hz was eventually accepted.

For the assessment of appropriateness of averaging of PAM records, the following method was used. The experience gathered in the present case study will contribute to designing future onsite PAM experiments. The PAM data set related to the highest frequencies of f_mid = 6300 Hz was found as the most relevant indicator of appropriateness of averaging, since it represents mostly the unsteadiness due to turbulent fluctuations. For the various scenarios of parameter setting, the source maps were obtained. Couples of averaging scenarios related to certain K_W → 2K_W values were compared. For example, such couples can be obtained by fixing N_W, and having a certain t_S value as well as its multiplication by a factor of 2. The comparison between the coupled averaging scenarios was carried out by means of preparing subtractive source maps. Such ΔL_P maps were obtained by subtracting the map related to a certain 2K_W value from that related to K_W. As an example, the top of Figure 6 presents the subtractive source map of K_W = [1291 → 2583] for the band of f_mid = 6300 Hz. In the annulus region, the local ΔL_P values fall within the range of reported uncertainty of ±1 dB. Since the quantification of radial distribution of noise is also important in the studies, the evaluation of subtractive source maps has been supplemented by the following analysis. The local P values related to K_W as well as to 2K_W were circumferentially area-averaged, and then rewritten in logarithmic level form. Afterwards, the results related to 2K_W were subtracted from those related to K_W, resulting in ΔL_P_M(R) profiles. The bottom of Figure 6 presents an example. The ΔL_P_M(R) distribution is also within the range of reported uncertainty of ±1 dB with great confidence. On the basis of the above, it has been concluded that the averaging scenario corresponding to f_S = 44,100 Hz, Δf = 43.1 Hz, K_W = 1291, L_S = 661,500, N_W = 1024, O_W = 0.5, t_S = 15 s is appropriate from the viewpoints of both (a) the local L_P data in the source maps, as well as (b) the circumferentially averaged data in the L_P_M(R) profiles. A further increase of t_S = [15 s → 30 s] does not improve the quality of averaging. Therefore, the data presented in the paper are related to the aforementioned averaging scenario. The sampling time of t_S = 15 s—corresponding anyway to 358 rotor revolutions—is a reasonably low value for an onsite measurement. Furthermore, the corresponding moderation in L_S contributes to economical data storage and processing.

Figure 6.

Comparison between the couple of averaging scenarios related to t_S = [15 s → 30 s], corresponding to K_W = [1291 → 2583]. Common parameters: f_S = 44,100 Hz, Δf = 43.1 Hz, N_W = 1024, O_W = 0.5. Top: Subtractive source map of ΔL_P [dB]. Bottom: ΔL_P_M(R) profile.

Elimination of noise source ambiguity; evaluation of source maps

As illustrated by the left-hand side column in Figure 4, the source maps show a repetition of the noise source patterns in the pitchwise direction, in accordance with the periodicity of the rotor blade passages. Such repetition is especially well-visible at the higher frequencies of f_mid ≥ 4000 Hz, where spots of sound pressure peaks appear near the blade tip region. Taking the direction of rotation as a basis, it is ambiguous whether a given noise peak is associated with phenomena related to (a) the blade preceding the peak, e.g. leakage flow noise originating from the preceding blade, or (b) the blade following the peak, e.g. turbulence ingestion noise at the leading edge of the following blade. For a comprehensive understanding of the underlying physics of noise generation, such ambiguity is to be eliminated.

For this purpose, the following technique has been proposed, as an extension of the presented onsite diagnostics methodology. A single blade has been elongated, i.e. the tip clearance of it has been reduced to 30% of the original value, by means of a narrow cardboard plate, having a camber geometry being identical with that of the blade tip, and attached to the blade tip with use of a sticker tape. The plate was judged by the authors to be sufficiently light-weight to avoid any additional noise and vibration due to rotor imbalance. Furthermore, the attachment was considered to be sufficiently rigid to avoid any flow-induced vibration. The PAM measurements have been repeated. The right-hand side column of Figure 4 presents the resultant source maps, in which the blade of reduced tip clearance is indicated with arrows. These source maps have been compared to those of uniform tip clearance (left column). The source maps under comparison are of identical scaling. Figure 7 gives an aid in explanation of the results of the qualitative comparison. It has been investigated how the reduction of tip clearance influences the values of the sound pressure maxima in the vicinity of the tip clearance-reduced blade. The qualitative changes observed consequently for each frequency band are presented in Figures 4 and 7, and are discussed herein. (+) and (–) signs in Figure 4 (right column) and in Figure 7 indicate an amplification or attenuation in the local maximum, respectively. The loci of well-visible changes of (+) and (–) are indicated by pointers in Figure 4. The pitchwise-averaged representative position of a local maximum is the mid-pitch position between the blades preceding and following the maximum. Therefore, the (+) and (–) signs represent the maxima at mid-pitch position between the leading edges in Figure 7.

Figure 7.

Sketch for explanation of the effects due to tip clearance reduction.

The zones of local maxima of upstream-radiated noise, being the subjects of the present discussion, are labeled in Figures 4 and 7 as follows. Label 1: the blade passage following the blade of reduced tip clearance. Label 2: the second blade passage following the blade of reduced tip clearance. Label 3: the blade passage preceding the blade of reduced tip clearance. Figures 4 and 7 suggest the following qualitative trends for which the following explanations are given.

Label 1: The reduction of tip clearance, i.e. attenuation of tip leakage flow, tends to attenuate the upstream-radiated noise in the blade passage following the blade of reduced clearance. The local maxima in the source maps are associated with flow phenomena related to the blade preceding the peak. As such, Figure 4 suggests the presence of the following noise sources:

SS BL noise, dominating in the entire annulus region: on the maps of f_mid ≤ 3150 Hz. The SS of the rotor blades, exposed to pronounced BL growth, “faces” toward the upstream field, as illustrated in Figures 1 and 7. This suggests that in the case of a rotor being free from any upstream obstacles, i.e. “free-inlet”, the rotor noise radiated toward the upstream field is dominated by the “self-noise”²¹ of BNS related to the SS BL.

Leakage flow noise, dominating near the tip: on the maps of f_mid ≥ 4000 Hz. Fukano and Jang²⁶ and Corsini et al.²⁷ confirm that the tip leakage flow noise may dominate within the rotor under certain conditions.

Label 2: The attenuation of leakage flow tends to attenuate also the noise maximum related to the second blade passage following the blade of reduced clearance. This symptom appears to be a circumstantial evidence for the presence of the double leakage phenomenon. Double leakage²⁸ means that the tip leakage flow intersects the pressure surface of the adjacent blade, and leaks across again. Double leakage is assumed by the authors as the exclusive means how the tip clearance reduction may impact on the second adjacent blade passage, from aerodynamics as well as from acoustics points of view. As extension of the noise class of leakage flow noise, the concept of double-leakage flow noise is therefore introduced herein. By attenuating the tip leakage flow due to reducing the clearance, the double-leaked flow is also assumed to attenuate, leading apparently to local noise reduction.

Label 3: The reduction of tip clearance tends to amplify the noise values at the blade passage preceding the blade of reduced clearance. Based on the previous conclusions, the following explanation is given. Leakage flow originates from the blade tip preceding the blade of reduced clearance. Such leakage flow is amplified by the double-leakage phenomenon. The leakage flow impacts on the pressure surface of the blade of reduced clearance, and tends to stagnate there since its leakage across the reduced clearance is restricted. Such stagnating, highly turbulent fluid is assumed to be a source of increased noise. Furthermore, the pressure surface at which the fluid is stagnating acts as a source of noise radiation. Due to the elongation of the blade tip, the pressure surface area is increased, contributing also to locally increased noise.

The above discussion implies that the majority of the upstream-radiated noise is associated with the SS BL, and with the leakage flow, in this case study. The other noise classes listed in subsection “Source maps, aspects of evaluation” appear to be of minor importance. Turbulence ingestion noise is negligible since it has been pointed out that the noise peaks near the tip are related not to the leading edges of the blades. The trailing edge noise and the vortex shedding noise are anticipated to be noticeable rather in the downstream-radiated noise—being a subject of further studies. Finally, considering the moderate load of the blading (D ≤ 0.45, see the next section), separation noise is generally assumed to be negligible herein.

Guidelines are to be provided on the possible moderation of the detected noise sources. As far as the leakage flow noise is concerned, it can be attenuated e.g. by means of passive noise control features.^9,10,13,27 In what follows, it is studied how the noise due to the SS BL can potentially be controlled by straightforward means.

Aerodynamic characteristics along the blade span

The electric motor driving the fan is embedded in the hub. As the L_P_M(R) distributions in Figure 5 suggest for the bands of higher frequencies of f_mid ≥ 4000 Hz, the noise radiated by the electric motor (at R ≤ 0.3) is comparable with or even dominates over the aerodynamic noise dedicated to the rotor (at R > 0.3). According to the limited spatial resolution of the PAM technique, the pronounced noise of the electric motor affects the L_P_M(R) distributions also in the annulus region at lower radii. Furthermore, as noted before, the noise of the tip leakage flow is dominant in these frequency bands. The tip leakage flow is highly three-dimensional (3D) in nature.^9,10,13,27 Therefore, the possibility for its characterization by simple means of blade cascade aerodynamic analysis is limited. Based on the above, it was found unreasonable to seek any straightforward correlation between the noise and the aerodynamic characteristics of the rotor for the bands of f_mid ≥ 4000 Hz.

For the bands of f_mid ≤ 3150 Hz—being anyway the most significant ones with respect to the human audition in the studied range—the noise due to the SS BL flow was suggested to dominate in the annulus region. For characterizing the annular flow incorporating the SS BL, a brief aerodynamic modeling approximation of 2D blade cascade flow is reasonable. As discussed in detail in Vad,²⁹ supported by a literature survey incorporating e.g. Carolus²¹ and Dixon,³⁰ the simplified 2D cascade flow approach is widely used in preliminary aerodynamic design and analysis of axial flow rotors. This applies even for rotors of non-free vortex operation associated with 3D interblade flow phenomena. Therefore, in what follows, a 2D cascade flow analysis is applied. The details are documented in Benedek and Vad,¹⁶ so only a brief account is given here.

Sturm and Carolus¹⁴ suggest that the flow inlet to the rotor may significantly influence not only the aerodynamic but also the acoustic behavior of the fan. This supports the importance of supplementing the acoustic experiments by measuring the inlet flow, as described in section “Fan of case study, diagnostics methodology”. Figure 8 presents the aerodynamic properties along the span, including the inlet axial velocity profile ϕ(R) measured by means of the anemometer. The inlet axial velocity distribution, realized in this industrial layout, significantly differs from the uniform axial inlet condition used often in fan design.²¹

Figure 8.

Aerodynamic properties along the blade span.

For obtaining further aerodynamic characteristics along the span, 2D empirical cascade correlations established by Howell, and cited in Dixon,³⁰ were taken as basis. As an approximation suggested in Carolus,²¹ the change of the axial velocity profile ϕ(R) was neglected through the rotor, in accordance with the 2D approach. The angle of flow inlet to the elemental cascades was calculated along the span. The fictitious nominal cascade conditions, guaranteeing a favorable aerodynamic behavior according to Howell, were computed, with knowledge of the blade geometry. As a brief approximation, Howell’s tangent-difference rule and deviation rule were applied for determining the nominal outlet flow angle and deviation angle, respectively. On the basis of the above, nominal characteristic angles (outlet and inlet blade angles, incidence angle) were determined. Given that the blade geometry generally differs from the nominal one, the outlet flow angle has been corrected, relative to the preliminarily calculated nominal value. This was carried out on the basis of the “off-design performance” graph by Howell,³⁰ using the linear approximation suggested by the graph, and considering the comments in Lewis³¹ on cascade correlations. With knowledge of the outlet flow angle and the axial velocity, the outlet tangential velocity, the Euler work, and the isentropic total pressure rise were calculated. The aerodynamic effects of non-radial stacking have been considered on the basis of Ramakrishna and Govardhan.³² Figure 8 shows the isentropic total pressure distribution ψ_is(R), following a spanwise increasing trend. Such “non-free vortex”²⁹ behavior is dedicated partly to the non-uniformity of the inlet axial velocity profile, and is often characteristic for axial fans operating in a real industrial environment.

Correlation between local indicators of noise and loss along the blade span

The measurements reported in the literature are mostly confined to correlating the global axial fan noise with global aerodynamic performance characteristics.^21,24,33,34 In the classic view, the fan noise strongly correlates with the global aerodynamic loss of the fan. This view is incorporated in the Regenscheit method, cited in Carolus,²¹ and applied in the standard,³³ as well as confirmed in Daly.³⁴ The intention of the authors is to seek a correlation between experiment-based indicators of local noise and loss, along the blade span. The SS BL, appearing as the dominant BNS in the bands of f_mid ≤ 3150 Hz, plays a major role also in generation of aerodynamic loss, as noted in Vad³⁵ on the basis of literature references. Some recent techniques in BNS computation²⁴ relate the noise to the BL thickness. As discussed e.g. in Lieblein,³⁶ the BL thickness is an indicator of the total pressure loss.

In order to introduce a relevant indicator for the local loss of the elemental blade cascades, dominated by the loss in the SS BL, the following procedure has been applied.

Based on the theory detailed in De Gennaro and Kuehnelt,²⁴ it is generally assumed that the pressure of radiated noise at a given radius is proportional to the displacement thickness of the blade boundary layer at the trailing edge—being approximately equal to the displacement thickness in the wake: P ∝ δ*. The shape factor is defined as H = δ*/θ.³⁷ According to Lieblein,³⁶ H is usually less than 1.2, and the approximation of H ≈ 1 can be applied in conventional unstalled configurations. The above read the following assumption for the radiated noise at a given radius

P \propto θ

(2)

Lieblein³⁶ established a strong correlation between the D diffusion factor^21,30,37 and the wake momentum thickness θ normalized by the blade chord c. In Vad,³⁵ the following empirical formula has been proposed for this correlation

θ / c = F (D) = 6.2 \times 1 0^{- 3} + 3 \times 1 0^{- 4} \times exp (6.34 D)

(3)

With use of equation (3), the normalized momentum thickness F is obtained as function of D, and the wake momentum thickness is calculated as θ=c·F(D). Substituting this formula into the relationship (2) reads the assumed correlation P ∝ c·F(D). With the knowledge of the spanwise distribution of the D and c characteristics, the θ (R) = [c·F(D)](R) profile can be calculated for the rotor.

For the case study presented herein, the Lieblein diffusion factor D^21,30,36,37 was calculated from the formerly determined cascade solidity as well as inlet and outlet flow angles. Afterwards, using the c(R) data, θ (R) has also been computed. In order to make possible a non-dimensional representation of the θ data and to scale them into the order of magnitude of 0–1, the following momentum thickness parameter θ* is introduced

θ^{*} = (c / c_{t}) \cdot F (D) \times 100

(4)

Figure 8 shows the calculated D(R) and θ*(R) distributions.

The combination of formulae (2) to (4) reads the following assumption

P \propto θ^{*}

(5)

In addition to the trend expressed by formula (5), it is also considered that, according to Lieblein,³⁶ the total pressure loss is proportional to the wake momentum thickness. These two proportionalities formulate the assumptions that (a) a correlation exists between the local loss and local noise, (b) the momentum thickness parameter θ* is a simultaneous indicator of both local loss and local noise. In order to experimentally justify these assumptions, correlations between P_M (presented in Figure 5 in logarithmic level) and the momentum thickness parameter θ* have been sought. A test function of P_θ_* = A₁·θ* has been constructed for representation of the assumed linear trend of formula (5). In order to make possible a direct comparison with the logarithmic L_P_M level, the test function P_θ_* has been logarithmized and multiplied by 20 (the factor also being present in the definition of the sound pressure level), resulting in L_P_θ_* = 20·log₁₀P_θ_*. The momentum thickness level has been introduced as L_θ_* = log₁₀(θ*). Considering the above, and introducing a further parameter A (originating from A₁), L_P_θ_* can be written in the following form

L_{P θ^{*}} = A + 20 \cdot L_{*}

(6)

If the frequency-dependent parameter A can be set by such means that a fair agreement occurs between the measurement-based L_P_M(R) and the approximate L_P_θ_*(R) distributions for the bands of f_mid ≤ 3150 Hz, the correlation between local spanwise-resolved loss and noise data is justified.

The L_P_M(R) distributions presented in Figure 5 were approximated along the entire span with functions L_P_θ_*(R) of suitably chosen A parameters. The L_P_θ_*(R) distributions, performing the best fits to the L_P_M(R) profiles, are presented in Figure 5 for f_mid ≤ 3150 Hz, using dot symbols. The A parameter values, set for the best fits with use of a least-squares method, are as follows: A = 106.3 dB for f_mid = 2000 Hz; A = 105.0 dB for f_mid = 2500 Hz; A = 98.2 dB for f_mid = 3150 Hz. The figure suggests that the agreement is fair between the L_P_M(R) and the L_P_θ_*(R) profiles, considering also the uncertainty of the acoustic measurement.

The θ*(R) as well as the frequency-dependent L_P_θ_*(R) profiles, determined by such means for this specific case study, offer the following potential in elaborating redesign guidelines. Such guidelines form the subject of future work. The inlet section can be redesigned for a more appropriate inlet axial velocity profile, and / or the rotor can be redesigned for a better aerodynamic behavior, while retaining the required aerodynamic performance. At a given radius, the aerodynamic improvement is controlled by the moderation of θ*, leading to local improvement of blade efficiency. The moderation of θ* is assumed to lead also to the attenuation of the local noise emission toward the upstream field. The attenuation of noise can be controlled in redesign with use of the experimentally determined L_P_θ_*(R) functions. When using these functions, it is to be assumed that the frequency-dependent A parameters remain unchanged in the redesign process.

For other fans, the same diagnostics and evaluation methodology is proposed to be applied. The result is a generally different set of case study-specific A parameters for the approximate functions in equation (6).

Summary

The experimentation presented in the literature for noise source localization of axial fans, incorporating the PAM technique, has been supplemented by an easily executable aerodynamic investigation method. This method relies on the measurement of the inlet axial velocity profile as well as on empirical cascade correlations. On this basis, a combined acoustic-aerodynamic diagnostics methodology has been developed. This methodology enables the survey on the PAM-based sound pressure, the indicator of aerodynamic loss, and their correlation, along the rotor blade span. The diagnostics methodology makes possible the industrial onsite investigation of unducted or short-ducted rotor-only fans, even if they are accessible for diagnostics only from the upstream direction. The application of the methodology was demonstrated in a case study of a free-inlet, free-exhausting fan.

An in-house ROSI processing algorithm has been adapted to the PAM beamforming technique. By such means, upstream source maps related to representative third-octave bands were obtained. When detecting rotating noise sources in industrial onsite survey, the following demands are laid with regard to averaging of the PAM records. (a) The duration of recording is to be minimized. (b) The proper spatial resolution and quantification of the sources is to be guaranteed. As an extension of the literature-based guidelines to cases involving the ROSI algorithm, a methodology has been developed for testing and guaranteeing the appropriateness of averaging of the PAM records. This methodology incorporates the following new features. The PAM data set related to the highest frequencies of f_mid = 6300 Hz was proven as the most relevant indicator of appropriateness of averaging, since it represents mostly the unsteadiness due to turbulent fluctuations. The effect of various scenarios of averaging was visualized and interpreted in the form of subtractive source maps.

In evaluating the source maps, it was found ambiguous whether a detected noise peak is associated with flow phenomena related to the blade preceding or following the peak with reference to the direction of rotation. The following method, adaptable to industrial onsite measurements, has been introduced for eliminating such “noise source ambiguity”. The tip clearance for a single blade was reduced. A narrow plate was attached to the tip, as an extrusion of the tip camber geometry. The PAM measurement was repeated, and the resultant source maps were compared to those related to uniform tip clearance. It was found that the source maps of higher frequencies of f_mid ≥ 4000 Hz are especially representative from the viewpoint of comparative changes. The reason is that the highly turbulent tip leakage flow—influenced by the modified tip clearance—was identified as the dominant aerodynamic noise source in this high-frequency range. The qualitative changes in the local noise levels—attenuation, amplification—observed consequently for each frequency band were interpreted. As a conclusion, the noise source ambiguity has been eliminated. The noise peaks were concluded to be associated with flow phenomena related to the blades preceding the peaks, in this particular case study. The interpretation necessitated the establishment of the new concept of double-leakage flow noise.

The complementary characteristics of the source maps have been pointed out. The maps over the entire studied frequency range were found necessary to be involved in the comprehensive evaluation process. (a) As noted above, the aerodynamic noise due to the highly unsteady, turbulent, 3D tip leakage flow was found to dominate the source maps of higher frequencies of f_mid ≥ 4000 Hz. These maps were therefore utilized in judging the appropriateness of averaging of PAM results, Point 2, and in eliminating the noise source ambiguity, Point 3. (b) The source maps related to the bands of lower frequencies of f_mid ≤ 3150 Hz were found to be dominated by the noise due to the SS BL flow, for which a 2D aerodynamic modeling approximation can be considered. Therefore, these maps were utilized for seeking an empirical correlation between the aerodynamic loss modeled in a 2D approach, and the circumferential area-average of the sound pressure data, along the blade span.

The momentum thickness parameter θ* has been established as a representative indicator of both loss and upstream-radiated aerodynamic noise, along the span. The local θ* values are calculated by simple arithmetical means, taking input data easily available from rotor geometry as well as from preliminary 2D rotor design and analysis, such as c and D. The momentum thickness level has been introduced, making possible a direct comparison with the logarithmic sound pressure level. The literature has been extended by comparing experiment-based, spanwise-resolved distributions of (a) the level of circumferentially averaged, upstream-radiated sound pressure, and (b) the momentum thickness level. The comparison regarded the bands of frequencies of f_mid ≤ 3150 Hz, being the most significant ones from the viewpoint of human audition within the investigated frequency range. Case study-specific, frequency-dependent linear correlations of P_M(R) ∝ θ*(R) were pointed out along the entire span. These empirical correlations are to be quantified for each individual fan of case study, using the methodology presented herein, e.g. by means of industrial onsite diagnostics. The momentum thickness parameter and the aforementioned correlations provide a basis for elaborating straightforward guidelines for redesign of the fan inlet and / or the rotor, for simultaneous reduction of noise and loss, at a prescribed aerodynamic performance.

Footnotes

Acknowledgement

Gratitude is expressed to Mr Csaba HORVÁTH, Mr Bence TÓTH, and Mr Péter TÓTH, for their useful comments and assistance.

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

This work has been supported by the Hungarian National Fund for Science and Research under contract OTKA K 112277. The work relates to the scientific program of the project “Development of quality-oriented and harmonized R + D + I strategy and the functional model at BME”, supported by the New Hungary Development Plan (Project ID: TÁMOP-4.2.1/B-09/1/KMR-2010-0002). It is also supported by the project “Talent care and cultivation in the scientific workshops of BME” project (Project ID: TÁMOP-4.2.2/B-10/1-2010-0009).

Appendix

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