Acoustics
, Volume 2 (3) – Jul 23, 2020

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acoustics Article Applicability of Aeroacoustic Scaling Laws of Leading Edge Serrations for Rotating Applications 1 , 1 1 1 Till M. Biedermann * , Pasquale Czeckay , Nils Hintzen , Frank Kameier and C. O. Paschereit Institute of Sound and Vibration Engineering ISAVE, University of Applied Sciences, D-40476 Dusseldorf, Germany; pasquale.czeckay@hs-duesseldorf.de (P.C.); nils.hintzen@hs-duesseldorf.de (N.H.); frank.kameier@hs-duesseldorf.de (F.K.) Institute of Fluid Dynamics and Technical Acoustics ISTA, Technical University of Berlin, D-10623 Berlin, Germany; oliver.paschereit@tu-berlin.de * Correspondence: till.biedermann@hs-duesseldorf.de Received: 19 June 2020; Accepted: 21 July 2020; Published: 23 July 2020 Abstract: The dominant aeroacoustic mechanisms of serrated leading edges, subjected to highly turbulent inﬂow conditions, can be compressed to spanwise decorrelation eects as well as eects of destructive interference. For single aerofoils, the resulting broadband noise reduction is known to follow spectral scaling laws. However, transferring serrated leading edges to rotating machinery, results in noise radiation patterns of signiﬁcantly increased complexity, impeding to allocate the observed noise reduction to the underlying physical mechanisms. The current study aims at concatenating the scaling laws for stationary aerofoil and rotating-blade application and thus at providing valuable information on the aeroacoustic transferability of leading edge serrations. For the pursued approach, low-pressure axial fans are designed, obtaining identical serrated fan blade geometries than previously analyzed single aerofoils, hence allowing for direct comparison. Highly similar spectral noise reduction patterns are obtained for the broadband noise reduction of the serrated rotors, generally conﬁrming the transferability and showing a scaling with the geometrical parameters of the serrations as well as the inﬂow conditions. Continuative analysis of the total noise reduction, however, constrains the applicability of the scaling laws to a speciﬁc operating range of the rotors and motivates for a devaluation of the scaling coecients regarding additional rotor-speciﬁc eects. Keywords: axial fans; rotating machinery; leading edge serrations; noise reduction; rotor-turbulence- interaction noise; aeroacoustics; aerodynamics 1. Introduction For the single aerofoils under highly turbulent inﬂow conditions, the approaching turbulent structures cause pressure ﬂuctuations that propagate as acoustic waves into the far-ﬁeld [1], resulting in broadband noise radiation [2]. This broadband noise, mainly stemming from the leading edge of an aerofoil, can be drastically reduced by implementing a leading edge pattern of sinusoidal shape [3–5], called leading edge serrations. The general shape of these serrations is usually parametrized by the serration amplitude A and the serration wavelength (Figure 1), where the wavy shape of the serrations mainly results in three eects [6]. First, a cut-o of the acoustic sources along the oblique edges of the serrations [7–9], leading to weaker acoustic sources. Second, decorrelation eects [3,10] along the span of the aerofoil lead to reduced radiation due to phase dierences. Eventually, the third eect can be attributed to destructive interference between the serration peak and the root region [3,7,11], leading to an extensive decrease of noise at frequencies where the acoustic wavelength corresponds to Acoustics 2020, 2, 579–594; doi:10.3390/acoustics2030030 www.mdpi.com/journal/acoustics Acoustics 2020, 2 580 the Acoustics size of 2020 the , 3 FO serration R PEER Ramplitude. EVIEW A majority of the available studies concerning serrated leading 2 edges were carried out based on single stationary aerofoils [4,7,12], even though the ﬁnal application serrated leading edges were carried out based on single stationary aerofoils [4,7,12], even though the area is considered to be turbomachines, fans and blowers, or contra-rotating rotors, where only little final application area is considered to be turbomachines, fans and blowers, or contra-rotating rotors, research was carried out [13–15]. However, considering the acoustic sources of rotating machinery, where only little research was carried out [13–15]. However, considering the acoustic sources of it becomes apparent, that multiple additional noise sources are present (Figure 1). These include rotating machinery, it becomes apparent, that multiple additional noise sources are present (Figure among others (a) eects in the blade tip region due to interaction of the rotating blades and the 1). These include among others (a) effects in the blade tip region due to interaction of the rotating reverse ﬂow, (b) noise due to secondary ﬂows such as separated vortical structures interacting with blades and the reverse flow, (b) noise due to secondary flows such as separated vortical structures subsequent blades, and (c) rotor–stator interaction noise. This already complex aeroacoustic pattern interacting with subsequent blades, and (c) rotor–stator interaction noise. This already complex is bedevilled by radius-dependent inﬂow conditions of the blades in terms of the circumferential aeroacoustic pattern is bedevilled by radius-dependent inflow conditions of the blades in terms of velocity (and turbulence conditions) as well as varying inﬂow angles as a function of the fans’ throttling the circumferential velocity (and turbulence conditions) as well as varying inflow angles as a function state or operation point, respectively. Consequently, even at highly turbulent inﬂow conditions, of the fans’ throttling state or operation point, respectively. Consequently, even at highly turbulent the leading edge broadband noise not necessarily needs to represent the dominant noise source inflow conditions, the leading edge broadband noise not necessarily needs to represent the dominant since it can be masked by the aforementioned additional eects of tonal and/or broadband character. noise source since it can be masked by the aforementioned additional effects of tonal and/or Hence, when implementing leading edge serrations in rotating systems, the developer needs to deal with broadband character. Hence, when implementing leading edge serrations in rotating systems, the various eects, not yet considered for the single aerofoil investigations. To describe the transferability developer needs to deal with various effects, not yet considered for the single aerofoil investigations. of serrated leading edges, the current study focuses on directly comparing the aeroacoustic eect of To describe the transferability of serrated leading edges, the current study focuses on directly comparing the aeroacoustic effect of leading edge serrations for the single aerofoils and rotating leading edge serrations for the single aerofoils and rotating machinery through low-pressure axial machinery through low-pressure axial fans. The basic idea of the present study is to analyze the fans. The basic idea of the present study is to analyze the aeroacoustic noise reduction potential of aeroacoustic noise reduction potential of single stationary NACA 65(12)-10 aerofoils, which are also single stationary NACA 65(12)-10 aerofoils, which are also commonly used for rotating applications. commonly used for rotating applications. In a second step, the identical aerofoil type, including the In a second step, the identical aerofoil type, including the leading edge serrations, is scaled and leading edge serrations, is scaled and employed for the design of low-pressure axial fans, enabling a employed for the design of low-pressure axial fans, enabling a direct comparison between the two direct comparison between the two considered systems. considered systems. Figure 1. Juxtaposition of the sound pressure level SPL (Equation (6)) of a single NACA 65(12)-10 Figure 1. Juxtaposition of the sound pressure level SPL (Equation (6)) of a single NACA 65(12)-10 aerofoil vs. a 6-bladed axial fan, featuring the NACA 65(12)-10 as fan blades of span S [16]. Rotor blade aerofoil vs. a 6-bladed axial fan, featuring the NACA 65(12)-10 as fan blades of span S[16]. Rotor blade chord C, serration amplitude A and wavelength downscaled by factor 2 at comparable blade incidence. chord C, serration amplitude A and wavelength λ downscaled by factor 2 at comparable blade incidence. Figure 1 serves to emphasize the increased complexity of the acoustic pattern when comparing a full rotor to an isolated stationary aerofoil at comparable operation conditions, which include Figure 1 serves to emphasize the increased complexity of the acoustic pattern when comparing (a) comparable inﬂow angles, (b) an identical aerofoil/blade geometry, and (c) comparable inﬂow a full rotor to an isolated stationary aerofoil at comparable operation conditions, which include (a) conditions using U and the turbulence intensity Tu. comparable inflow angles, (b) an identical aerofoil/blade geometry, and (c) comparable inflow As it is indicated by the grey hatching in Figure 1, the radiated noise increases signiﬁcantly at conditions using U0 and the turbulence intensity Tu. inﬂow conditions of elevated turbulence. In reverse conclusion, this low-to-mid-frequency region As it is indicated by the grey hatching in Figure 1, the radiated noise increases significantly at characterizes the maximum noise reduction potential when implementing e.g., serrated leading edges inflow conditions of elevated turbulence. In reverse conclusion, this low-to-mid-frequency region or any other device aecting the radiation of turbulence-ingested leading edge noise. characterizes the maximum noise reduction potential when implementing e.g., serrated leading edges or any other device affecting the radiation of turbulence-ingested leading edge noise. Acoustics 2020, 2 581 Speaking of broadband noise reduction due to leading edge serrations, the spectral sound power level reduction DPWL (Equation (6)) is obtained by subtracting the acoustic signature of a serrated aerofoil PWL from that of an aerofoil with a straight leading edge PWL . For isolated stationary Serr BSLN aerofoils, the resulting spectral noise reduction is known to continuously increase from low to high frequencies [6,17], where the maximum is reached at the point of intersection, at which aerofoil self-noise due to the turbulent boundary layer starts to become increasingly dominant, forcing a decreasing performance for frequencies beyond this point. On this basis, a recent study by Chaitanya et al. [6], extending initial studies by Kim et al. [7], provides a rudimentary scaling law by which the spectral noise reduction DPWL is stated to follow Equation (1), with the prefactor generally being a = 10. The upper limit of the possible noise reduction can be achieved with b = 10 at an optimum ratio of serration wavelength and transversal turbulence length scale /L 4 and takes place in the low-to-intermediate frequency range in the form of the amplitude-based Strouhal number Sr . Note that even though both constants a and b deﬁne the maximum noise reduction capability, the prefactor a controls the slope s s s of the trends, whereas b controls the parallel shift of the noise reduction: fA DPWL = PWL PWL = a lg(Sr ) + b with Sr = . (1) BSLN Serr S A S A Continuatively, the current study aims at answering the question if and how these aeroacoustic scaling laws also apply in the rotating context. This is of importance since it assists in assigning the causative mechanisms of the noise reduction for the tested rotors to the known mechanisms at isolated aerofoils. In a more general context, this analysis is expected to provide valuable information in assessing if the already known eects assigned to leading edge serrations still play the key role in reducing rotor noise or if there are eects that are more prominent. Prior extracting the spectral scaling in the rotating domain, a valid data basis for isolated aerofoils of the identical geometric design was generated by Biedermann et al. [18], who performed aeroacoustic (and aerodynamic) characterization of the chosen NACA 65(12)-10 aerofoils via an extensive aeroacoustic beamforming study. The main advantage of this speciﬁc setup, however, is the possibility to exclude all the unwanted and distracting noise sources stemming from the aerofoil trailing edge, the open jet, the turbulence grids installed or even from the turbulent boundary layer. More recently, a similar approach was also followed by Bampanis et al. [19] for ﬂat plate aerofoils, dierentiating between the spectral contributions of leading edge noise and trailing edge noise. For the current study, testing serrated aerofoils of varying serration amplitude A and serration wavelength by comparing the spectral noise composition to a straight leading edge baseline aerofoil, results in the spectral noise reduction pattern DPWL shown in Figure 2. Generally, the proposed spectral scaling law can be conﬁrmed, even though higher prefactors of a = 15 according to Equation (1) are obtained, which can be attributed to the absence of aerofoil self-noise, usually attenuating the maximum noise reduction in the mid-frequency Sr -range. The upper limits of noise reduction are obtained at maximum amplitudes (b = 8.5) and minimum wavelengths (b = 10) [18]. Most interestingly, s s the optimum /L -ratio deﬁned by Chaitanya et al. [3,6] is /L 2 for maximum decorrelation eects t t and /L 4 for maximum interference eects, enclosing the observed optimum of /L = 2.6 in t t Figure 2. Acoustics 2020, 2 582 Acoustics 2020, 3 FOR PEER REVIEW 4 Acoustics 2020, 3 FOR PEER REVIEW 4 (a) (b) (a) (b) Figure 2. Spectral noise reduction (500 Hz ≤ f ≤ 5.8 kHz, 6th order median filtered) obtained from the Figure 2. Spectral noise reduction (500 Hz f 5.8 kHz, 6th order median ﬁltered) obtained from Figure 2. Spectral noise reduction (500 Hz ≤ f ≤ 5.8 kHz, 6th order median filtered) obtained from the 2D integration the 2D integration area. ( ara ea. ) Varying serration amplitude A; ( (a) Varying serration amplitude b) Varying serration wavelength A; (b) Varying serration wavelength λ at Re = at 2D integration area. (a) Varying serration amplitude A; (b) Varying serration wavelength λ at Re = 350,000, AoA = Re = 350,000, AoA 0 deg, aerofo = 0 deg, aer il span S = ofoil span 0.35 S m, = 0.35 chord = 0 m, chor .15 d = m. Figure adopted from [18] 0.15 m. Figure adopted from . [18]. 350,000, AoA = 0 deg, aerofoil span S = 0.35 m, chord = 0.15 m. Figure adopted from [18]. 2. Materials and Methods 2. Materials and Methods 2. Materials and Methods To make ﬁrst steps towards rotating applications, a test rig (Figure 3a) according to the ISO 5136 To make first steps towards rotating applications, a test rig (Figure 3a) according to the ISO 5136 To make first steps towards rotating applications, a test rig (Figure 3a) according to the ISO 5136 standard [20] was developed which allows for simultaneous characterization of the aerodynamic standard [20] was developed which allows for simultaneous characterization of the aerodynamic and standard [20] was developed which allows for simultaneous characterization of the aerodynamic and and aeroacoustic performance of low-pressure axial fans with and without leading edge serrations. aeroacoustic performance of low-pressure axial fans with and without leading edge serrations. The aeroacoustic performance of low-pressure axial fans with and without leading edge serrations. The The rotor is designed according to the isolated aerofoil approach [21], where the NACA 65(12)-10 rotor is designed according to the isolated aerofoil approach [21], where the NACA 65(12)-10 fan rotor is designed according to the isolated aerofoil approach [21], where the NACA 65(12)-10 fan fan blades are twisted in the spanwise direction to meet optimum incidence for all circumferential bladeblade s ares t are wist tw ed ist in ed t in h t e sp he sp anwis anwis e edi di rect rection t ion too m meet eet opt optimum imum inc inc idence idence fo r fo alr l c alirc l c umf ircumf erenteia rent l ial sections at design conditions. The test rig, as well as the data acquisition procedure, is identical to sections at design conditions. The test rig, as well as the data acquisition procedure, is identical to sections at design conditions. The test rig, as well as the data acquisition procedure, is identical to previous studies by the authors and is described more detailed in [22,23]. However, the focus of the previous studies by the authors and is described more detailed in [22,23]. However, the focus of the previous studies by the authors and is described more detailed in [22,23]. However, the focus of the present as well as of previous studies is to provide a low-speed axial fan of minimum complexity, present as well as of previous studies is to provide a low-speed axial fan of minimum complexity, present as well as of previous studies is to provide a low-speed axial fan of minimum complexity, which, in reverse conclusion, allows analyzing and identifying the net-noise-reduction potential of which, in reverse conclusion, allows analyzing and identifying the net-noise-reduction potential of which, in reverse conclusion, allows analyzing and identifying the net-noise-reduction potential of serrated blades in the rotating frame. Therefore, complex blade geometries such as blade skew and serrated blades in the rotating frame. Therefore, complex blade geometries such as blade skew and serrated blades in the rotating frame. Therefore, complex blade geometries such as blade skew and blade dihedral are intentionally avoided. blade dihedral are intentionally avoided. blade dihedral are intentionally avoided. (a) (b) Figure 3. (a) Aeroacoustic test rig according to ISO 5136 [23]; (b) Analyzed serration designs for the Figure 3. (a) Aeroacoustic test rig according to ISO 5136 [23]; (b) Analyzed serration designs for the (a) (b) tested rotors. Absolute values for amplitude A and wavelength λ are indicated in mm. Rotor blade tested rotors. Absolute values for amplitude A and wavelength are indicated in mm. Rotor blade span S = 0.098 m, rotor blade chord C = 0.075 m, duct radius RDuct = 0.2 m. span S = 0.098 m, rotor blade chord C = 0.075 m, duct radius R = 0.2 m. Figure 3. (a) Aeroacoustic test rig according to ISO 5136 [23]; (b) Analyzed serration designs for the Duct tested rotors. Absolute values for amplitude A and wavelength λ are indicated in mm. Rotor blade Implementing coarse biplane square grids [24] upstream of the rotor allows to vary the level of Implementing coarse biplane square grids [24] upstream of the rotor allows to vary the level of the span S = 0.098 m, rotor blade chord C = 0.075 m, duct radius RDuct = 0.2 m. the incoming turbulence in a range of 2.6% ≤ Tu ≤ 12.1% for the rotor plane, where the mean incoming turbulence in a range of 2.6% Tu 12.1% for the rotor plane, where the mean longitudinal longitudinal velocity U0 serves as the denominator of the turbulence intensity Tu to remain velocity U serves as the denominator of the turbulence intensity Tu to remain independent of the Implementing coarse biplane square grids [24] upstream of the rotor allows to vary the level of independent of the tested rotor design. Excessive preliminary measurements via hot wire tested rotor design. Excessive preliminary measurements via hot wire anemometry were carried the incoming turbulence in a range of 2.6% ≤ Tu ≤ 12.1% for the rotor plane, where the mean out by employing a rotating duct and the hot wire anemometry [22], resulting in the spatial velocity longitudinal velocity U0 serves as the denominator of the turbulence intensity Tu to remain independent of the tested rotor design. Excessive preliminary measurements via hot wire Acoustics 2020, 3 FOR PEER REVIEW 5 Acoustics 2020, 2 583 anemometry were carried out by employing a rotating duct and the hot wire anemometry [22], resulting in the spatial velocity distribution for the rotor plane as can be seen from Figure 4. distribution Circumferent for ial aver the r ag otor ing plane of the dat as a can obta be ined seen lead fr s t om o more gener Figure 4. al pro Circumfer files ofential the incoming averaging Tu, the of the longitudinal velocity as well as the transversal integral length scale ΛT (Figure 4b), making apparent data obtained leads to more general proﬁles of the incoming Tu, the longitudinal velocity as well the strong influence of the duct boundary layer on the resulting profiles. Representative single as the transversal integral length scale L (Figure 4b), making apparent the strong inﬂuence of the number values are obtained by averaging over a radius of RDuct = 0.15 m to neglect influences of the duct boundary layer on the resulting proﬁles. Representative single number values are obtained by wall boundary layer (Figure 4a). Preliminary studies on the power spectral density of the turbulent averaging over a radius of R = 0.15 m to neglect inﬂuences of the wall boundary layer (Figure 4a). Duct energy [23] showed it to scale-well with the turbulent cascade theory [25], resulting in scaling with Preliminary studies on the power spectral density of the turbulent energy [23] showed it to scale-well −5/3 −7 f in the inertial range and with f in the dissipation range. Deviations from the model are, once 5/3 7 with the turbulent cascade theory [25], resulting in scaling with f in the inertial range and with f again, observed close to the duct wall, though generally proving the turbulence conditions being of in the dissipation range. Deviations from the model are, once again, observed close to the duct wall, near-isotropic nature. though generally proving the turbulence conditions being of near-isotropic nature. (a) (b) Figure 4. (a) Local distribution of longitudinal velocity; (b) Circumferentially averaged turbulent Figure 4. (a) Local distribution of longitudinal velocity; (b) Circumferentially averaged turbulent −1 1 properties vs. the radial duct position for the tested turbulence grids at n = 2000 min , = 12.1%, properties vs. the radial duct position for the tested turbulence grids at n = 2000 min , Tu = 12.1%, and measurement plane = rotor plane. and measurement plane = rotor plane. For the design of the serrated leading edges, the maximum chord C of the blades was kept For the design of the serrated leading edges, the maximum chord C of the blades was kept constant, resulting in different amplitude-dependent wetted surfaces of the fan blades as can be seen constant, resulting in dierent amplitude-dependent wetted surfaces of the fan blades as can be seen in in Figure 5. An alternative approach would be to keep the mean chord constant, resulting in an Figure 5. An alternative approach would be to keep the mean chord constant, resulting in an extension extension of the local blade chord by A/2. The choice for the former design approach mainly serves of the local blade chord by A/2. The choice for the former design approach mainly serves three reasons: three reasons: 1. A constant maximum blade chord results in only one baseline reference case for comparison as 1. A constant maximum blade chord results in only one baseline reference case for comparison as well as in a constant blade thickness for dierent serration geometries. well as in a constant blade thickness for different serration geometries. 2. Keeping constant maximum solidity prevents amplitude-dependent interaction eects of 2. Keeping constant maximum solidity σS prevents amplitude-dependent interaction effects of successive blades at solidities 0.7. successive blades at solidities σS ≥ 0.7. 3. Pursuing a conservative approach that remains close to practical applications, in which serrations 3. Pursuing a conservative approach that remains close to practical applications, in which might be included as a substituting technology at limited installation space by simply replacing serrations might be included as a substituting technology at limited installation space by simply previously mounted straight blades. replacing previously mounted straight blades. The aerodynamic performance is described via the non-dimensional ﬂow coecient ' in Equation (2) and the pressure coecient (Equation (3)) at iso-speed n = 2000 min . Note that due to the speciﬁc setup and the location of the pressure sensors, the pressure coecient is deﬁned by the static pressure rise Dp and the grid-dependent pressure loss Dp (compare Figure 3a). Grid The eciency of the fan assembly in Equation (4) eventually serves to describe the relation of System electric demand P vs. the aerodynamic output P . The small amplitude-dependent dierences aero el in the blade surface area (see Figure 5) naturally aect the aerodynamic performance in terms of static pressure rise Dp as well as the ﬂow rate Q. For comparison purposes, these dierences require compensation. In contrast to the coecients of lift and drag, for which a normalization by the wetted surface takes place for single aerofoils, the ﬂow and pressure coecients of rotating machines oer no 𝑇𝑢 Acoustics 2020, 2 584 such compensation mechanisms. Therefore, preliminary measurements for straight blades of a varying chord are carried out by testing three dierent rotors with straight leading edges [23]. The surface of the three sets of rotor blades equals the wetted surface of the serrated blades with maximum (C/C = 0.83), intermediate (C/C = 0.91), and no (C/C = 1) serration amplitude. Testing these scaled baseline blades, 0 0 instead of the serrated blades, prevents including possible ﬂow-dependent eects of leading edge Acoustics 2020, 3 FOR PEER REVIEW 6 serrations, which might aect the ﬂow rate or the pressure rise. (a) (b) Figure 5. Figure 5. Sc Schematic hematic of l of leading eading ed edge ge d desig esign n including including meas measur ures es of i of importance. mportance. B Both oth bl blades ades exhi exhibit bit equal NACA 65(12)-10 properties. (a) Baseline case with a straight leading edge; (b) Serrated design, equal NACA 65(12)-10 properties. (a) Baseline case with a straight leading edge; (b) Serrated design, where grey hatching indicates reduced wetted area of the blade. where grey hatching indicates reduced wetted area of the blade. The results shown in Figure 6 indicate the (wetted) surface of the blades to contribute linearly to the The aerodynamic performance is described via the non-dimensional flow coefficient φ in static pressure riseDp. The individual share of each semi-inﬁnite radial element, however, scales with the −1 Equation (2) and the pressure coefficient ψ (Equation (3)) at iso-speed n = 2000 min . Note that due circumferential velocity U (U *) in Equations (2) and (3), where the required rotor diameter is deﬁned rot rot to the specific setup and the location of the pressure sensors, the pressure coefficient ψ is defined by by the hub diameter D plus the (representative) blade span S (S ). Consequently, the circumferential Hub Rep the static pressure rise Δp and the grid-dependent pressure loss ΔpGrid (compare Figure 3a). The velocity U of the pressure coecient (Equation (3)) is deﬁned according to an area-equivalent rot efficiency of the fan assembly ηSystem in Equation (4) eventually serves to describe the relation of electric blade span S (Equation (3) and Figure 5), which is a function of the removed serration area A Rep Serr demand Pel vs. the aerodynamic output Paero. The small amplitude-dependent differences in the blade (Equation (5)) from the initial blade area A : Blade surface area (see Figure 5) naturally affect the aerodynamic performance in terms of static pressure rise Δp as well as the flow rate Q. For comparison p . urposes, these differences require compensation. In contrast to the coefficients of lift and drag, for which a normalization by the wetted surface takes ' = , U = n(D + 2S), (2) rot Hub U (A A /2) rot Blade Serr place for single aerofoils, the flow and pressure coefficients of rotating machines offer no such compensation mechanisms. Therefore, preliminary measurements for straight blades of a varying (Dp + Dp )/ SC A Grid Serr chord are carrie d out by testi = ng three dif , U ferent rotors = n(D with straight + 2S ), S leading = edges [23]. The sur , face of (3) rot Rep Rep Hub U /2 rot the three sets of rotor blades equals the wetted surface of the serrated blades with maximum (C/C0 = 0.83), intermediate (C/C0 = 0.91), and no (C/C0 = 1) serration amplitude. Testing these scaled baseline P DpQ aero = = , (4) system blades, instead of the serrated blades, prevents including possible flow-dependent effects of leading P U A el el el edge serrations, which might affect the flow rate or the pressure rise. 2S The results shown in Figure 6 indicate the (wetted) surface of the blades to contribute linearly to A = Asin(2/x) dx. (5) Serr the static pressure rise Δp. The individual share of each semi-infinite radial element, however, scales In terms of acoustics, a microphone arrays at the discharge side of the fan unit enables gathering with the circumferential velocity Urot (Urot*) in Equation (2) and Equation (3), where the required rotor diameter reliable and is stable definedata, d by t non-a he hub diameter ected by the grid DHubself-noise plus the on(re the present suction ativside. e) blade This sp array an S consists (SRep). of three one-quarter inch wall-mounted condenser microphones, distributed circumferentially at the Consequently, the circumferential velocity Urot of the pressure coefficient ψ (Equation (3)) is defined accord duct wall. ing toNot an ar e that ea-equ noiv beamforming alent blade span is applied SRep (Equ to ation ( the r 3otating ) and Figure application 5), whic but h is a that funct the iospectral n of the average of the microphone signals is used for further processing towards the local sound pressure removed serration area ASerr (Equation (5)) from the initial blade area ABlade: level SPL (Equation (6)) with p being the eective sound pressure of the gathered signals and p RMS 0 the reference value by means of the human threshold of audibility at 1 kHz. Continuatively, the overall (2) 𝜑= ,𝑈 =𝜋 ∙ 𝑛 ∙ (𝐷 +2∙ 𝑆), 𝑈 ∙ (𝐴 − 𝐴 ⁄) 2 sound pressure level OASPL is deﬁned according to Equation (7) in the given frequency band 10 Hz f 10 kHz. Eventually, normalization by the enveloping surface of the noise sources A ( + Δ𝑝 )/𝜌 𝑆∙ 𝐶 − 𝐴 𝜓= ,𝑈 =𝜋 ∙ 𝑛 ∙ (𝐷 +2∙𝑆 ), 𝑆 = , (3) 𝑈 /2 𝑃 Δ𝑝 ∙ 𝑄 (4) 𝜂 = = , 𝑃 𝑈 ∙ 𝐴 2𝑆 𝐴 = 𝐴 ∙𝑠𝑖𝑛 (2𝜋/𝜆 ∙ 𝑥 ) 𝑑𝑥 . (5) 𝛥𝑝 Acoustics 2020, 2 585 as well as compensating for varying ambient conditions in terms of ﬂuid density and speed of sound c, allows deﬁning the local sound power level PWL (Equation (6)). This is followed by the overall sound power level OAPWL (Equation (7)). Note that for a ducted fan, the duct radius R Duct limits the enveloping acoustic surface A . Concerning the previously discussed compensation of the amplitude-dependent blade surface, also the sound power levels of the fan are monitored in Figure 6. Unlike for the aerodynamic properties, highly similar results are obtained for the OAPWL, indicating the wetted surface of the blades being only of secondary importance for the aeroacoustic signature. This is meaningful insofar as the level-dominant noise sources of the blades are the blade-tip region, the trailing edges, and the leading edges. Since the radial extension of the blades does not change with or without applying serrations or while varying the blade chord, also no dierences in the noise radiation are obtained [2,23]: 2 2 0 1 " ! !# > A = R , A = 1m > E 0 Duct p > c B C B C < E RMS B C PWL = SPL + 10lg 10lg , SPL = 10lgB C > p = 210 Pa , (6) @ A > A c > 0 0 0 p c = 400 Ns/m 0 0 0 1 " ! !# i= f max B X C c B C E B C 2 2 B C OAPWL = OASPL + 10lg 10lg , OASPL = 10lgB p /p C. (7) B 0C @ A A c 0 0 0 i= f min Acoustics 2020, 3 FOR PEER REVIEW 7 (a) (b) (c) Figure 6. Validation of scaling approach by varying the chord length C of the baseline blades with C0 Figure 6. Validation of scaling approach by varying the chord length C of the baseline blades with = 75 mm. (a) Non-dimensional static pressure rise ψ; (b) Aerodynamic efficiency η; (c) Overall sound C = 75 mm. (a) Non-dimensional static pressure rise ; (b) Aerodynamic eciency ; (c) Overall power level OAPWL (Equation (7)). sound power level OAPWL (Equation (7)). To gain deeper insights into the noise reduction mechanisms, resolving the spectral pattern of In terms of acoustics, a microphone arrays at the discharge side of the fan unit enables gathering the data is required. Based on preliminary analysis of the signals [16], partitioning of the spectral reliable and stable data, non-affected by the grid self-noise on the suction side. This array consists of content into its broadband and its discrete components proved to be meaningful since the underlying three one-quarter inch wall-mounted condenser microphones, distributed circumferentially at the noise generation mechanisms are of dierent physical origin [26]. To split the rotor-speed-dependent duct wall. Note that no beamforming is applied to the rotating application but that the spectral components from those of broadband character, a customized one-dimensional median ﬁlter of the average of the microphone signals is used for further processing towards the local sound pressure 30th order is applied to the original signal. In doing so, a frequency band of 7.5 Hz around the rotor ’s level SPL (Equation (6)) with pRMS being the effective sound pressure of the gathered signals and p0 fundamental speed, or an integer multiple thereof, is replaced by its median, thus neglecting peaks the reference value by means of the human threshold of audibility at 1 kHz. Continuatively, the with high slopes, which, in this case, are representing the tonal components. This procedure results in overall sound pressure level OASPL is defined according to Equation (7) in the given frequency band a broadband signal without loss of spectral energy (Figure 7a). The tonal ﬁlter is speciﬁed vice versa, 10 Hz ≤ f ≤ 10 kHz. Eventually, normalization by the enveloping surface of the noise sources AE as solely showing the chopped-o peaks of the signal. Adding up the tonal and the broadband level well as compensating for varying ambient conditions in terms of fluid density ρ and speed of sound yields exactly the original signal. c, allows defining the local sound power level PWL (Equation (6)). This is followed by the overall sound power level OAPWL (Equation (7)). Note that for a ducted fan, the duct radius RDuct limits the enveloping acoustic surface AE. Concerning the previously discussed compensation of the amplitude- dependent blade surface, also the sound power levels of the fan are monitored in Figure 6. Unlike for the aerodynamic properties, highly similar results are obtained for the OAPWL, indicating the wetted surface of the blades being only of secondary importance for the aeroacoustic signature. This is meaningful insofar as the level-dominant noise sources of the blades are the blade-tip region, the trailing edges, and the leading edges. Since the radial extension of the blades does not change with or without applying serrations or while varying the blade chord, also no differences in the noise radiation are obtained [2,23]: 𝐴 =𝜋 ∙ 𝑅 , 𝐴 =1𝑚 𝐴 𝑝 𝑃𝑊𝐿 = 𝐿 + 10𝑙𝑔 − 10𝑙𝑔 , SPL = 10 lg 𝑝 =2 ∙ 10 𝑃𝑎 , (6) 𝐴 𝜌 𝑐 𝑝 𝜌 𝑐 = 400 𝑁 ∙ 𝑠/𝑚 = + 10 𝑙𝑔 − 10𝑙𝑔 , 𝐿𝑂 = 10𝑙𝑔 𝑝 𝑝 . (7) 𝐴 𝜌 𝑐 To gain deeper insights into the noise reduction mechanisms, resolving the spectral pattern of the data is required. Based on preliminary analysis of the signals [16], partitioning of the spectral content into its broadband and its discrete components proved to be meaningful since the underlying noise generation mechanisms are of different physical origin [26]. To split the rotor-speed-dependent components from those of broadband character, a customized one-dimensional median filter of the 30th order is applied to the original signal. In doing so, a frequency band of ± 7.5 Hz around the rotor's fundamental speed, or an integer multiple thereof, is replaced by its median, thus neglecting peaks with high slopes, which, in this case, are representing the tonal components. This procedure 𝐴𝑆𝑃 𝑂𝐴𝑆𝑃𝐿 𝑂𝐴𝑃𝑊𝐿 𝜌𝑐 𝑆𝑃 𝜌𝑐 Acoustics 2020, 3 FOR PEER REVIEW 9 Acoustics 2020, 2 586 Acoustics 2020, 3 FOR PEER REVIEW 9 (a) (b) (a) (b) Figure 7. (a) Example of a sound power level spectrum for the baseline rotor with applied filters, Figure 7. Figure 7. (a (a) )E Example xample of a so of a sound und power level spe power level spectr ctru um m for the baseline for the baselinerotor with applied f rotor with applied ﬁlters, ilters, separating tonal and broadband effects; (b) Boundary conditions of customized filters [16]. separating separating tonal and broa tonal and broadband dband effect eects; s; ( (b b) ) Bou Boundary ndary conditions conditions of of cu customized stomized fi ﬁlters lters [1 [16 6]. ]. 3. Results 3. Results 3. Results 3.1. Low-Pressure Axial Fans: Aerodynamic Performance 3.1. Low-Pressure Axial Fans: Aerodynamic Performance 3.1. Low-Pressure Axial Fans: Aerodynamic Performance Figure 8 shows the overall performance of the tested rotors in terms of aerodynamics at (a) Figure 8 shows the overall performance of the tested rotors in terms of aerodynamics at (a) varying Figure 8 shows the overall performance of the tested rotors in terms of aerodynamics at (a) varying serration wavelength and (b) serration amplitude. For brevity, the fan characteristic curves serration wavelength and (b) serration amplitude. For brevity, the fan characteristic curves of the varying serration wavelength and (b) serration amplitude. For brevity, the fan characteristic curves of the serration configurations tested as well as the baseline case are presented only at low turbulence serration conﬁgurations tested as well as the baseline case are presented only at low turbulence of the serration configurations tested as well as the baseline case are presented only at low turbulence intensity. Even though the full characteristic curves are analyzed, the fan design point can be stated intensity. Even though the full characteristic curves are analyzed, the fan design point can be stated to intensity. Even though the full characteristic curves are analyzed, the fan design point can be stated to be at maximum efficiency, corresponding to φ = 0.20. In terms of aerodynamics, the results be at maximum eciency, corresponding to ' = 0.20. In terms of aerodynamics, the results obtained to be at maximum efficiency, corresponding to φ = 0.20. In terms of aerodynamics, the results obtained are highly comparable to those of previously investigated single aerofoils [23], showing are highly comparable to those of previously investigated single aerofoils [23], showing maximum obtained are highly comparable to those of previously investigated single aerofoils [23], showing maximum performance for small serration amplitudes and high wavelengths. Serrations with low performance for small serration amplitudes and high wavelengths. Serrations with low wavelengths maximum performance for small serration amplitudes and high wavelengths. Serrations with low wavelengths and high amplitudes tend to show poorer performance, which can be attributed to the and high amplitudes tend to show poorer performance, which can be attributed to the continuous wavelengths and high amplitudes tend to show poorer performance, which can be attributed to the continuous increase in drag due to the vortex-generating and crossflow effects of the serrations. increase in drag due to the vortex-generating and crossﬂow eects of the serrations. continuous increase in drag due to the vortex-generating and crossflow effects of the serrations. (a) (b) (a) (b) Figure Figure 8. 8. C Characteristic haracteristic cu curves rves of of pre prssu essur re e vsvs. . flow ﬂow coeffi coeci ent for cient diff for di erent rotor erent rotor config conﬁgurations. urations. (a) Figure 8. Characteristic curves of pressure vs. flow coefficient for different rotor configurations. (a) (Varying serration wavelength; ( a) Varying serration wavelength; b) Varying serration amplitude. (b) Varying serration amplitude. Varying serration wavelength; (b) Varying serration amplitude. Acoustics 2020, 2 587 Acoustics 2020, 3 FOR PEER REVIEW 10 3.2. Low-Pressure Axial Fans: Spectral Broadband Noise Reduction 3.2. Low-Pressure Axial Fans: Spectral Broadband Noise Reduction To compare the broadband noise reduction between single aerofoils and the rotating application, To compare the broadband noise reduction between single aerofoils and the rotating application, the gathered signals are ﬁltered in the frequency domain according to Section 2 and only the resulting the gathered signals are filtered in the frequency domain according to Section 2 and only the resulting broadband spectra are further processed towards the spectral noise reduction as was done for Figure 2. broadband spectra are further processed towards the spectral noise reduction as was done for Figure Once again, the frequency is normalized via the Strouhal number (Equation (1)), based on the serration 2. Once again, the frequency is normalized via the Strouhal number (Equation (1)), based on the amplitude. serration a Tomcomply plitude. To withcompl the deﬁnition y with the def of the Tiuni , tion of for the the Strouhal Tu, for number the St , the rouhal numb longitudinaler, the velocity at longit the rotor udin plane al velocit U y is at chosen the rot instead or plane ofU taking 0 is chosen instea the circumfer d of ta ential king the ci rotor mid-span rcumferentia velocity l rotoU r mi.d- 0 rot span velocity Urot. Figures 9 and 10 show the spectral noise reduction at varying turbulence intensities for the Figures 9 and 10 show the spectral noise reduction at varying turbulence intensities for the serrated rotors tested. According to the scaling of the spectral noise reduction discussed in Section 1, serrated rotors tested. According to the scaling of the spectral noise reduction discussed in Section 1, the results of the post-processed broadband signals are ﬁtted via the least-squares minimization the results of the post-processed broadband signals are fitted via the least-squares minimization approach to the scaling laws by adapting the slope-determining prefactor a . This is followed by approach to the scaling laws by adapting the slope-determining prefactor as. This is followed by deﬁning a common oset factor b , controlling the parallel shift. Note that the b is matched only at s s defining a common offset factor bs, controlling the parallel shift. Note that the bs is matched only at optimum design conditions of the serrations. The obtained trends reveal a quite similar logarithmic optimum design conditions of the serrations. The obtained trends reveal a quite similar logarithmic scaling as for single aerofoils, where maximum serration amplitudes and small serration wavelengths scaling as for single aerofoils, where maximum serration amplitudes and small serration wavelengths show the highest potential for reducing rotor-turbulence interaction noise. Modulating the incoming show the highest potential for reducing rotor-turbulence interaction noise. Modulating the incoming turbulence reveals the noise reduction capability to be scaling with the slope-determining prefactor a , turbulence reveals the noise reduction capability to be scaling with the slope-determining prefactor which extends the currently known trends for isolated stationary aerofoils since, in direct comparison, as, which extends the currently known trends for isolated stationary aerofoils since, in direct turbulence of signiﬁcantly higher levels is generated for the rotating application. The prefactors show comparison, turbulence of significantly higher levels is generated for the rotating application. The to continuously increase from a = 10 for the lowest Tu = 2.6% (Figure 9a) to a = 22 for the highest s s prefactors show to continuously increase from as = 10 for the lowest = 2.6% (Figure 9a) to as = 22 Tu = 12.1% (Figure 10c), leading to local reductions of the sound power level of up to DPWL = 14 dB. for the highest = 12.1% (Figure 10c), leading to local reductions of the sound power level of up to In conclusion, the common spectral logarithmic scaling (Equation (1)) for both isolated aerofoils and full ΔPWL = 14 dB. In conclusion, the common spectral logarithmic scaling (Equation (1)) for both isolated rotors, indicates a reduction of leading edge broadband noise following the well-known aeroacoustic aerofoils and full rotors, indicates a reduction of leading edge broadband noise following the well- noise reduction mechanisms of serrated leading edges (compare Section 1). At least for the broadband known aeroacoustic noise reduction mechanisms of serrated leading edges (compare Section 1). At noise, this enables a direct transfer from stationary aerofoils to rotating applications for operation least for the broadband noise, this enables a direct transfer from stationary aerofoils to rotating conditions application close s for operat to the design ion condit point ions ' cl ose t 0.18. o the design point φ ≈ 0.18. (a) (b) (c) Figure 9. Spectral sound power level reduction ΔPWL of the tested rotors at maximum flow Figure 9. Spectral sound power level reduction DPWL of the tested rotors at maximum ﬂow coecient coefficient φ and varying Tu. 20th-order median-filtered signals of broadband components only. ' and varying Tu. 20th-order median-ﬁltered signals of broadband components only. Additional Additional indication of the λ/Λt-ratio. (a) = 2.6%; (b) = 3.6%; (c) = 5.3%. indication of the /L -ratio. (a) Tu = 2.6%; (b) Tu = 3.6%; (c) Tu = 5.3%. The obtained scaling laws for the broadband noise reduction hint at relatively high prefactors a when compared to the existing literature. However, the dierences to previous studies can be attributed to the fact that, ﬁrst, previous studies are focusing on rigidly mounted single aerofoils in turbulent streams. For these setups, it is not possible to generate conditions of homogeneous turbulence of Tu > 6% using passive turbulence generators as e.g., coarse grids. Consequently, the isolated stationary aerofoils are tested at moderately low turbulence intensities, which might be an argument for the lower prefactor a . In reverse conclusion, testing at similar Tu level for both isolated aerofoil and the full rotor is expected to lead to a comparable spectral scaling. Second, the high prefactors a for the rotating 𝑇𝑢 𝑇𝑢 𝑇𝑢 𝑇𝑢 𝑇𝑢 Acoustics 2020, 2 588 applications result from substantially higher Tu-Levels investigated, when compared to the isolated aerofoils. The initial spectral scaling law was deﬁned by Chaitanya et al. [6] who did not investigate eects on the prefactor a since in their study the Tu and thus the integral length scales were not varied in wide margins. Varying the serration wavelength and the amplitude mainly showed eects on the parallel shift of the noise reduction, as it can be described by the constant b . Accordingly, for the presented study a constant prefactor a can be deﬁned for each turbulent case where the second constant b is controlled by the optimum serration amplitude A and an optimum ratio of serration Acoustics 2020, 3 FOR PEER REVIEW 11 wavelength and integral length scale /L . (a) (b) (c) Figure 10. Spectral sound power level reduction ΔPWL of the tested rotors at maximum flow Figure 10. Spectral sound power level reduction DPWL of the tested rotors at maximum ﬂow coefficient φ and varying Tu. 20th-order median-filtered signals of broadband components only. coecient ' and varying Tu. 20th-order median-ﬁltered signals of broadband components only. Additional indication of the λ/Λt-ratio. (a) = 7.5%; (b) = 9.6%; (c) = 12.1%. Additional indication of the /L -ratio. (a) Tu = 7.5%; (b) Tu = 9.6%; (c) Tu = 12.1%. AtThe obt o-design ained condi scaling tions, law however s for the broadb , the brand oadband noise leading reduction h edge intnoise at rela not tively necessarily high prefr act epr ors esents as when compared to the existing literature. However, the differences to previous studies can be the dominant acoustic source. With reducing ﬂow coecients, rotor-speciﬁc acoustic eects such as attributed to the fact that, first, previous studies are focusing on rigidly mounted single aerofoils in separation noise and reverse ﬂow eects from the tip-gap region as well as rotor speed-dependent turbulent streams. For these setups, it is not possible to generate conditions of homogeneous tonal eects increase in relevance. Consequently, these eects also aect and attenuate the overall noise turbulence of Tu > 6% using passive turbulence generators as e.g., coarse grids. Consequently, the reduction potential of serrated rotors. This is evidenced in Figure 11, which shows the comparison of isolated stationary aerofoils are tested at moderately low turbulence intensities, which might be an the spectral noise reduction capability at dierent on-design and o-design conditions at iso-speed argument for the lower prefactor as. In reverse conclusion, testing at similar Tu level for both isolated of the rotor. At ﬂow coecients ' > 0.18, the grid-generated broadband noise is eciently reduced, aerofoil and the full rotor is expected to lead to a comparable spectral scaling. Second, the high whereas at partial loading of the fan at ' 0.17 signiﬁcantly stronger low-frequency components are prefactors as for the rotating applications result from substantially higher Tu-Levels investigated, Acoustics 2020, 3 FOR PEER REVIEW 12 induced and reduced. when compared to the isolated aerofoils. The initial spectral scaling law was defined by Chaitanya et al. [6] who did not investigate effects on the prefactor as since in their study the Tu and thus the integral length scales were not varied in wide margins. Varying the serration wavelength and the amplitude mainly showed effects on the parallel shift of the noise reduction, as it can be described by the constant bs. Accordingly, for the presented study a constant prefactor as can be defined for each turbulent case where the second constant bs is controlled by the optimum serration amplitude A and an optimum ratio of serration wavelength and integral length scale λ/ΛT. At off-design conditions, however, the broadband leading edge noise not necessarily represents the dominant acoustic source. With reducing flow coefficients, rotor-specific acoustic effects such as separation noise and reverse flow effects from the tip-gap region as well as rotor speed-dependent tonal effects increase in relevance. Consequently, these effects also affect and attenuate the overall noise reduction potential of serrated rotors. This is evidenced in Figure 11, which shows the comparison of the spectral noise reduction capability at different on-design and off-design conditions at iso-speed of the rotor. At flow coefficients φ > 0.18, the grid-generated broadband noise is efficiently reduced, whereas at partial loading of the fan at φ ≈ 0.17 significantly strong er low- frequency components are ind (a u) ( ced and reduced. b) Minimum flow coefficients again show a log-dependent scaling of the noise reduction, albeit at Figure 11. Spectral sound power level reduction ΔPWL at varying flow coefficient for two rotor Figure 11. Spectral sound power level reduction DPWL at varying ﬂow coecient for two rotor designs a considerably lower level. This void in the validity of the spectral scaling laws for flow coefficients designs (a) A22λ13; (b) A14λ4. (a) A2213; (b) A144. φ ≤ 0.18 serves as a strong indicator that the mechanisms of the noise reduction differ from the hitherto known effects of leading edge serrations. More specifically, for the aerodynamic instability region of the fan characteristic curves, distinct aerodynamic effects such as a serration-induced delay in the onset of stall are considered being the key-effects in obtaining the significant overall noise reduction shown in Figure 12. The known aeroacoustic effects of decorrelation and interference are only of secondary importance for φ ≤ 0.18. (a) (b) (c) (d) Figure 12. OAPWL of rotor equipped with leading edge serrations of varying serration amplitude, serration wavelength λ, and incoming Tu. Grey hatching indicates the aerodynamic optimum range of operation. (a) Varying amplitude at = 2.6%; (b) Varying amplitude at = 12.1%; (c) Varying wavelength at = 2.6%; (d) Varying wavelength at = 12.1%. 𝑇𝑢 𝑇𝑢 𝑇𝑢 𝑇𝑢 𝑇𝑢 𝑇𝑢 𝑇𝑢 Acoustics 2020, 3 FOR PEER REVIEW 12 Acoustics 2020, 2 589 Minimum ﬂow coecients again show a log-dependent scaling of the noise reduction, albeit at a considerably lower level. This void in the validity of the spectral scaling laws for ﬂow coecients ' 0.18 serves as a strong indicator that the mechanisms of the noise reduction dier from the hitherto known eects of leading edge serrations. More speciﬁcally, for the aerodynamic instability region of the fan characteristic curves, distinct aerodynamic eects such as a serration-induced delay in the onset (a) (b) of stall are considered being the key-eects in obtaining the signiﬁcant overall noise reduction shown Figure 11. Spectral sound power level reduction ΔPWL at varying flow coefficient for two rotor in Figure 12. The known aeroacoustic eects of decorrelation and interference are only of secondary designs (a) A22λ13; (b) A14λ4. importance for ' 0.18. (a) (b) (c) (d) Figure Figure 12. 12. OAPWL OAPWLof of rotor equipped with rotor equipped with leading edge se leading edge serrations rrations of var of varying ying serration serration amplitude, amplitude, serration wavelength λ, and incoming Tu. Grey hatching indicates the aerodynamic optimum range serration wavelength , and incoming Tu. Grey hatching indicates the aerodynamic optimum range of operation. (a) Varying amplitude at = 2.6%; (b) Varying amplitude at = 12.1%; (c) Varying of operation. (a) Varying amplitude at Tu = 2.6%; (b) Varying amplitude at Tu = 12.1%; (c) Varying wavelength at = 2.6%; (d) Varying wavelength at = 12.1%. wavelength at Tu = 2.6%; (d) Varying wavelength at Tu = 12.1%. 3.3. Low-Pressure Axial Fans: Overall Acoustic Performance To assess the applicability of the spectral scaling laws for leading edge serrations requires a more general analysis of the aeroacoustic noise reduction pattern of the investigated low-pressure axial fans. In terms of acoustics, the overall eect of the tested rotors with and without leading edge serrations in Figure 12 shows that the baseline rotor radiates higher noise at all operation points. For maximum ﬂow coecients, the overall noise reduction is DOAPWL 2.5 dB. The most distinct dierences to the baseline rotor, however, occur in the transition region from pre-stall (' 0.18) towards instability (0.13 ' 0.18) leading to an increase of the noise reduction potential up to DOAPWL 6 dB for the high turbulent case (Figure 12b). Here, the serrations are supposed to shift the onset of the (aeroacoustic) 𝑇𝑢 𝑇𝑢 𝑇𝑢 𝑇𝑢 Acoustics 2020, 2 590 stall towards smaller ﬂow coecients when compared to the baseline rotor. Given the fact that this shift is less distinct for the aerodynamic performance (Figure 8) leads to the hypothesis that small-scale separation at single blades is suppressed, not-yet aecting the overall pressure rise of the full fan. The underlying eect is suspected to be an ecient reduction in small-scale separation due to the leading edge contour. This takes place via the vortex-generating character of the leading edge serrations [27,28], resulting in increased stability of the blades’ boundary layer as well as in an ecient shift of coherent structures in the blade tip region towards lower ﬂow coecients, as described in previous studies of the authors [16]. The known decorrelation and interference eects of the leading edge serrations [3] are still present though play a minor role in terms of the overall noise reduction. In consequence, for the instability region, the overall noise reduction results from a combination of aerodynamic and aeroacoustic eects of the leading edge serrations. The observed aeroacoustic shift tends to be more distinct at high turbulence, clearly scaling with the serration amplitude (Figure 12b). For the low turbulent case (Figure 12a,c), the shift beneﬁts from the maximum noise reduction potential at maximum serration amplitudes, though generally showing a reduced extend. However, the resulting acoustic dierences to the baseline case exceed those at high turbulence, resulting in an improved noise reduction potential (Figure 12b,d). This is meaningful insofar as the aeroacoustic onset of the stall is more distinct for the low turbulent case compared to the already high OAPWL at pre-stall and high incoming turbulence. The eect of the serration wavelength , illustrated in Figure 12c,d, is of reduced impact when compared to the serration amplitude. Small wavelengths lead to a slight attenuation of the radiated noise which is particularly true for the pre-stall region at high ﬂow coecients. Generally, the reduced eect of the serration wavelength is in close agreement with recent literature for isolated aerofoils [3,4,17]. 3.4. Low-Pressure Axial Fans: Broadband vs. Total Noise Reduction Based on the overall sound power level in Figure 12, it is dicult and intricate to conclude on the broadband leading edge noise reduction potential of serrated rotors as well as the underlying physical mechanisms, in particular, once again highlighting the need to take into account the spectral composition of the noise reduction. In this context, the spectral composition of the noise reduction is extracted separately for the broadband components and the total noise signature. The results are presented in Figures 13 and 14, showing the contrasting juxtaposition for three dierent operating points within the optimum range of operation (compare Figure 12). At ﬂow coecients ' 0.18, assigned to the pre stall region (Figure 13), where no relevant separation takes place, the spectral noise reduction for both broadband noise as well as total noise can be derived using the previously deﬁned scaling functions. This hints at the dominance of the aeroacoustic working principles of leading edge serrations in this region. Analysis of the slope-determining prefactor a as well as the oset b results in a s s clear devaluing when comparing broadband and total noise reduction. The reduction of low-frequency broadband noise (Figure 13a,c) is equalized by rotor noise of discrete character, resulting in only little total noise reduction for the low-frequency region (Figure 13b,d). Moreover, the presence of blade tip eects, scaling with the rotational speed further attenuate the noise reduction for the mid-frequency region. The resulting total noise reduction still is of signiﬁcant order even though the initially deﬁned reduction potential shows to be aected by additional rotor eects of both aerodynamic and acoustic nature. In terms of serration parameters, highly similar trends are observed for the broadband as well as the total noise reduction, enabling general statements of beneﬁcial parameter combinations for maximum noise reduction. Acoustics 2020, 3 FOR PEER REVIEW 14 trends are observed for the broadband as well as the total noise reduction, enabling general Acoustics 2020, 2 591 statements of beneficial parameter combinations for maximum noise reduction. (a) (b) (c) (d) Figure 13. Juxtaposition of spectral noise reduction ΔPWL for broadband and total noise while Figure 13. Juxtaposition of spectral noise reduction DPWL for broadband and total noise while varying varying the serration parameters as well as the point of operation. (a) Broadband reduction at 𝜑 = the serration parameters as well as the point of operation. (a) Broadband reduction at ' = 0.233%; 0.233%; (b) Total reduction at 𝜑 = 0.233%; (c) Broadband reduction at 𝜑 = 0.203%; (d) Total reduction (b) Total reduction at ' = 0.233%; (c) Broadband reduction at ' = 0.203%; (d) Total reduction at at 𝜑 = 0.203%. ' = 0.203%. Entering the instability region at φ = 0.17 (Figure 14) shows a deviating pattern, making the Entering the instability region at ' = 0.17 (Figure 14) shows a deviating pattern, making the hitherto known scaling laws obsolete. A significant increase in low-frequency noise reduction is hitherto known scaling laws obsolete. A signiﬁcant increase in low-frequency noise reduction is observed for the broadband noise but also being present for the total noise reduction. This supports observed for the broadband noise but also being present for the total noise reduction. This supports the the initial statement of predominantly aerodynamic effects being present for the increase of the initial statement of predominantly aerodynamic eects being present for the increase of the acoustic stall acoustic stall margin. These effects in the form of a prevented flow separation mainly take place in margin. These eects in the form of a prevented ﬂow separation mainly take place in the low-frequency the low-frequency range, resulting in high absolute noise reduction. range, resulting in high absolute noise reduction. Acoustics 2020, 2 592 Acoustics 2020, 3 FOR PEER REVIEW 15 (a) (b) Figure 14. Juxtaposition of spectral noise reduction ΔPWL at partial load conditions 𝜑 = 0.17%. (a) Figure 14. Juxtaposition of spectral noise reduction DPWL at partial load conditions ' = 0.17%. Broadband reduction; (b) Total reduction. (a) Broadband reduction; (b) Total reduction. 4. Conclusions 4. Conclusions The conducted study provides detailed insights into the turbulence-induced broadband noise The conducted study provides detailed insights into the turbulence-induced broadband noise reduction capability of low-pressure axial fans equipped with leading edge serrations. A special focus reduction of t capability he conducteof d stlow-pr udy is on essur the appl e axial icabilit fans y of pr equipped eviously de with fined spect leading ral scedge aling la serrations. ws for the nois A e special reduction of single aerofoils. In consequence, a coherent transfer analysis from single and rigidly focus of the conducted study is on the applicability of previously deﬁned spectral scaling laws for mounted aerofoils towards a full axial fan was carried out by featuring identical aerofoil shapes, the noise reduction of single aerofoils. In consequence, a coherent transfer analysis from single and allowing to directly concluding on the transferability of the scaling laws from the rigid to the rotating rigidly mounted aerofoils towards a full axial fan was carried out by featuring identical aerofoil domain. In terms of aeroacoustics, significant noise reduction is observed for various tested rotors shapes, allowing to directly concluding on the transferability of the scaling laws from the rigid to the with serrated leading edges where high amplitudes and, to a lesser degree, small wavelengths are rotating domain. In terms of aeroacoustics, signiﬁcant noise reduction is observed for various tested found to be most beneficial. For the investigated rotors, a differentiation between the specific points of operation through the flow coefficients is inevitable. The classic broadband noise reduction due to rotors with serrated leading edges where high amplitudes and, to a lesser degree, small wavelengths spanwise decorrelation and destructive interference is observed for intermediate to high flow are found to be most beneﬁcial. For the investigated rotors, a dierentiation between the speciﬁc coefficients, corresponding to optimal and blade-congruent inflow conditions. For the instability points of operation through the ﬂow coecients is inevitable. The classic broadband noise reduction region at partial load conditions, the dominant noise reduction mechanisms are proposed to be due to spanwise decorrelation and destructive interference is observed for intermediate to high ﬂow predominantly due to aerodynamic effects of the leading edge serrations, leading to a reduction of coecients, corresponding to optimal and blade-congruent inﬂow conditions. For the instability level-dominant low-to-mid-frequency noise. To assess the applicability of the spectral scaling laws region at concerning th partial load e overall no conditions, ise reduct the ion re dominant quires for noise an add rieduction tional differentiation b mechanisms etween the hitherto are proposed to be analyzed broadband noise reduction and the total noise reduction of leading edge serrations. For the predominantly due to aerodynamic eects of the leading edge serrations, leading to a reduction of pre stall region, the spectral scaling laws were found to describe, the relevant noise reduction to a level-dominant low-to-mid-frequency noise. To assess the applicability of the spectral scaling laws reasonable level even though a devaluation of the broadband scaling laws is required to compensate concerning the overall noise reduction requires for an additional dierentiation between the hitherto for perturbations due to additional rotor-specific aeroacoustic effects. For the instability region of the analyzed broadband noise reduction and the total noise reduction of leading edge serrations. For the fan, showing the maximum overall noise reduction, no such broadband scaling laws apply since pre stall aerod region, ynam the ic serr spectral ation scaling effects, res laws ultinwer g ine an foun onset d to of t describe, he aeroacou thestric elevant stall ent noise ry, caruse t eduction he to a predominant noise reduction. Especially for fans operating close to the instability region, the reasonable level even though a devaluation of the broadband scaling laws is required to compensate interaction of aerodynamic and aeroacoustic effects of the serrations is considered highly important for perturbations due to additional rotor-speciﬁc aeroacoustic eects. For the instability region of and is expected to assist in the future design of low-noise serrated rotors. the fan, showing the maximum overall noise reduction, no such broadband scaling laws apply Author Contributions: Conceptualization, T.M.B., P.C. and N.H.; methodology, T.M.B.; software, T.M.B. and since aerodynamic serration eects, resulting in an onset of the aeroacoustic stall entry, cause the P.C.; validation, T.M.B. and N.H.; formal analysis, T.M.B., P.C. and N.H.; investigation, T.M.B., P.C. and N.H.; predominant noise reduction. Especially for fans operating close to the instability region, the interaction resources, T.M.B.; data curation, T.M.B., P.C. and N.H.; writing—original draft preparation, T.M.B.; writing— review and editing, T.M.B., P.C., N.H., F.K., C.O.P.; visualization, T.M.B., P.C., N.H.; supervision, F.K. and of aerodynamic and aeroacoustic eects of the serrations is considered highly important and is expected C.O.P.; project administration, T.M.B.; funding acquisition, T.M.B. All authors have read and agreed to the to assist in the future design of low-noise serrated rotors. published version of the manuscript. Author Contributions: Conceptualization, T.M.B., P.C. and N.H.; methodology, T.M.B.; software, T.M.B. and P.C.; validation, T.M.B. and N.H.; formal analysis, T.M.B., P.C. and N.H.; investigation, T.M.B., P.C. and N.H.; resources, T.M.B.; data curation, T.M.B., P.C. and N.H.; writing—original draft preparation, T.M.B.; writing—review and editing, T.M.B., P.C., N.H., F.K., C.O.P.; visualization, T.M.B., P.C., N.H.; supervision, F.K. and C.O.P.; project administration, T.M.B.; funding acquisition, T.M.B. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acoustics 2020, 2 593 Acknowledgments: The authors gratefully acknowledge the kind support of Daniel and David Delgado Hernandez in setting up the test rig and conducting the experiments. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. Devenport, W.J.; Staubs, J.K.; Glegg, S.A. Sound radiation from real airfoils in turbulence. 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Acoustics – Multidisciplinary Digital Publishing Institute

**Published: ** Jul 23, 2020

**Keywords: **axial fans; rotating machinery; leading edge serrations; noise reduction; rotor-turbulence-interaction noise; aeroacoustics; aerodynamics

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