# Applicability of Aeroacoustic Scaling Laws of Leading Edge Serrations for Rotating Applications

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## Abstract

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## 1. Introduction

_{0}and the turbulence intensity Tu.

_{Serr}from that of an aerofoil with a straight leading edge PWL

_{BSLN}. For isolated stationary 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 ΔPWL is stated to follow Equation (1), with the prefactor generally being a

_{s}= 10. The upper limit of the possible noise reduction can be achieved with b

_{s}= 10 at an optimum ratio of serration wavelength and transversal turbulence length scale λ/Λ

_{t}≥ 4 and takes place in the low-to-intermediate frequency range in the form of the amplitude-based Strouhal number Sr

_{A}. Note that even though both constants a

_{s}and b

_{s}define the maximum noise reduction capability, the prefactor a

_{s}controls the slope of the trends, whereas b

_{s}controls the parallel shift of the noise reduction:

_{s}= 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

_{A}-range. The upper limits of noise reduction are obtained at maximum amplitudes (b

_{s}= 8.5) and minimum wavelengths (b

_{s}= 10) [18]. Most interestingly, the optimum λ/Λ

_{t}-ratio defined by Chaitanya et al. [3,6] is λ/Λ

_{t}≈ 2 for maximum decorrelation effects and λ/Λ

_{t}≈ 4 for maximum interference effects, enclosing the observed optimum of λ/Λ

_{t}= 2.6 in Figure 2.

## 2. Materials and Methods

_{0}serves as the denominator of the turbulence intensity Tu to remain independent of the tested rotor design. Excessive preliminary measurements via hot wire 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. Circumferential averaging of the data obtained leads to more general profiles of the incoming Tu, the longitudinal velocity as well as the transversal integral length scale Λ

_{T}(Figure 4b), making apparent the strong influence of the duct boundary layer on the resulting profiles. Representative single number values are obtained by averaging over a radius of R

_{Duct}= 0.15 m to neglect influences of the wall boundary layer (Figure 4a). Preliminary studies on the power spectral density of the turbulent energy [23] showed it to scale-well with the turbulent cascade theory [25], resulting in scaling with f

^{−5/3}in the inertial range and with f

^{−7}in the dissipation range. Deviations from the model are, once again, observed close to the duct wall, though generally proving the turbulence conditions being of near-isotropic nature.

- A constant maximum blade chord results in only one baseline reference case for comparison as well as in a constant blade thickness for different serration geometries.
- Keeping constant maximum solidity σ
_{S}prevents amplitude-dependent interaction effects of successive blades at solidities σ_{S}≥ 0.7. - Pursuing a conservative approach that remains close to practical applications, in which serrations might be included as a substituting technology at limited installation space by simply replacing previously mounted straight blades.

^{−1}. Note that due to the specific setup and the location of the pressure sensors, the pressure coefficient ψ is defined by the static pressure rise Δp and the grid-dependent pressure loss Δp

_{Grid}(compare Figure 3a). The efficiency of the fan assembly η

_{System}in Equation (4) eventually serves to describe the relation of electric demand P

_{el}vs. the aerodynamic output P

_{aero}. The small amplitude-dependent differences in the blade surface area (see Figure 5) naturally affect the aerodynamic performance in terms of static pressure rise Δp as well as the flow rate $\dot{\mathrm{Q}}$. For comparison purposes, these differences require compensation. In contrast to the coefficients of lift and drag, for which a normalization by the wetted surface takes 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 chord are carried out by testing three different 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}= 0.83), intermediate (C/C

_{0}= 0.91), and no (C/C

_{0}= 1) serration amplitude. Testing these scaled baseline blades, instead of the serrated blades, prevents including possible flow-dependent effects of leading edge serrations, which might affect the flow rate or the pressure rise.

_{rot}(U

_{rot}*) in Equations (2) and (3), where the required rotor diameter is defined by the hub diameter D

_{Hub}plus the (representative) blade span S (S

_{Rep}). Consequently, the circumferential velocity U

_{rot}of the pressure coefficient ψ (Equation (3)) is defined according to an area-equivalent blade span S

_{Rep}(Equation (3) and Figure 5), which is a function of the removed serration area A

_{Serr}(Equation (5)) from the initial blade area A

_{Blade}:

_{RMS}being the effective sound pressure of the gathered signals and p

_{0}the reference value by means of the human threshold of audibility at 1 kHz. Continuatively, the overall 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

_{E}as well as compensating for varying ambient conditions in terms of fluid density ρ 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

_{E}. 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]:

## 3. Results

#### 3.1. Low-Pressure Axial Fans: Aerodynamic Performance

#### 3.2. Low-Pressure Axial Fans: Spectral Broadband Noise Reduction

_{0}is chosen instead of taking the circumferential rotor mid-span velocity U

_{rot}.

_{s}. This is followed by defining a common offset factor b

_{s}, controlling the parallel shift. Note that the b

_{s}is matched only at 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 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

_{s}, which extends the currently known trends for isolated stationary aerofoils since, in direct comparison, turbulence of significantly higher levels is generated for the rotating application. The prefactors show to continuously increase from a

_{s}= 10 for the lowest $\overline{Tu}$ = 2.6% (Figure 9a) to a

_{s}= 22 for the highest $\overline{Tu}$ = 12.1% (Figure 10c), leading to local reductions of the sound power level of up to ΔPWL = 14 dB. In conclusion, the common spectral logarithmic scaling (Equation (1)) for both isolated aerofoils and full rotors, indicates a reduction of leading edge broadband noise following the well-known aeroacoustic noise reduction mechanisms of serrated leading edges (compare Section 1). At least for the broadband noise, this enables a direct transfer from stationary aerofoils to rotating applications for operation conditions close to the design point φ ≈ 0.18.

_{s}when compared to the existing literature. However, the differences 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

_{s}. 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

_{s}for the rotating 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 effects on the prefactor a

_{s}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 b

_{s}. Accordingly, for the presented study a constant prefactor a

_{s}can be defined for each turbulent case where the second constant b

_{s}is controlled by the optimum serration amplitude A and an optimum ratio of serration wavelength and integral length scale λ/Λ

_{T}.

#### 3.3. Low-Pressure Axial Fans: Overall Acoustic Performance

#### 3.4. Low-Pressure Axial Fans: Broadband vs. Total Noise Reduction

_{s}as well as the offset b

_{s}results in a 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 effects, 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 affected by additional rotor effects 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.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**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 chord C, serration amplitude A and wavelength λ downscaled by factor 2 at comparable blade incidence.

**Figure 2.**Spectral noise reduction (500 Hz ≤ f ≤ 5.8 kHz, 6th order median filtered) obtained from the 2D integration area. (

**a**) Varying serration amplitude A; (

**b**) Varying serration wavelength λ at Re = 350,000, AoA = 0 deg, aerofoil span S = 0.35 m, chord = 0.15 m. Figure adopted from [18].

**Figure 3.**(

**a**) Aeroacoustic test rig according to ISO 5136 [23]; (

**b**) Analyzed serration designs for the tested rotors. Absolute values for amplitude A and wavelength λ are indicated in mm. Rotor blade span S = 0.098 m, rotor blade chord C = 0.075 m, duct radius R

_{Duct}= 0.2 m.

**Figure 4.**(

**a**) Local distribution of longitudinal velocity; (

**b**) Circumferentially averaged turbulent properties vs. the radial duct position for the tested turbulence grids at n = 2000 min

^{−1}, $\overline{Tu}=12.1\%,$ and measurement plane = rotor plane.

**Figure 5.**Schematic of leading edge design including measures of importance. Both blades exhibit 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.

**Figure 6.**Validation of scaling approach by varying the chord length C of the baseline blades with C

_{0}= 75 mm. (

**a**) Non-dimensional static pressure rise ψ; (

**b**) Aerodynamic efficiency η; (

**c**) Overall sound power level OAPWL (Equation (7)).

**Figure 7.**(

**a**) Example of a sound power level spectrum for the baseline rotor with applied filters, separating tonal and broadband effects; (

**b**) Boundary conditions of customized filters [16].

**Figure 8.**Characteristic curves of pressure vs. flow coefficient for different rotor configurations. (

**a**) Varying serration wavelength; (

**b**) Varying serration amplitude.

**Figure 9.**Spectral sound power level reduction ΔPWL of the tested rotors at maximum flow coefficient φ and varying Tu. 20th-order median-filtered signals of broadband components only. Additional indication of the λ/Λ

_{t}-ratio. (

**a**) $\overline{Tu}$ = 2.6%; (

**b**) $\overline{Tu}$ = 3.6%; (

**c**) $\overline{Tu}$ = 5.3%.

**Figure 10.**Spectral sound power level reduction ΔPWL of the tested rotors at maximum flow coefficient φ and varying Tu. 20th-order median-filtered signals of broadband components only. Additional indication of the λ/Λ

_{t}-ratio. (

**a**) $\overline{Tu}$ = 7.5%; (

**b**) $\overline{Tu}$ = 9.6%; (

**c**) $\overline{Tu}$ = 12.1%.

**Figure 11.**Spectral sound power level reduction ΔPWL at varying flow coefficient for two rotor designs (

**a**) A22λ13; (

**b**) A14λ4.

**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 $\overline{Tu}$ = 2.6%; (

**b**) Varying amplitude at $\overline{Tu}$ = 12.1%; (

**c**) Varying wavelength at $\overline{Tu}$ = 2.6%; (

**d**) Varying wavelength at $\overline{Tu}$ = 12.1%.

**Figure 13.**Juxtaposition of spectral noise reduction ΔPWL for broadband and total noise while varying the serration parameters as well as the point of operation. (

**a**) Broadband reduction at $\overline{\phi}$ = 0.233%; (

**b**) Total reduction at $\overline{\phi}$ = 0.233%; (

**c**) Broadband reduction at $\overline{\phi}$ = 0.203%; (

**d**) Total reduction at $\overline{\phi}$ = 0.203%.

**Figure 14.**Juxtaposition of spectral noise reduction ΔPWL at partial load conditions $\overline{\phi}$ = 0.17%. (

**a**) Broadband reduction; (

**b**) Total reduction.

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**MDPI and ACS Style**

Biedermann, T.M.; Czeckay, P.; Hintzen, N.; Kameier, F.; Paschereit, C.O.
Applicability of Aeroacoustic Scaling Laws of Leading Edge Serrations for Rotating Applications. *Acoustics* **2020**, *2*, 579-594.
https://doi.org/10.3390/acoustics2030030

**AMA Style**

Biedermann TM, Czeckay P, Hintzen N, Kameier F, Paschereit CO.
Applicability of Aeroacoustic Scaling Laws of Leading Edge Serrations for Rotating Applications. *Acoustics*. 2020; 2(3):579-594.
https://doi.org/10.3390/acoustics2030030

**Chicago/Turabian Style**

Biedermann, Till M., Pasquale Czeckay, Nils Hintzen, Frank Kameier, and C. O. Paschereit.
2020. "Applicability of Aeroacoustic Scaling Laws of Leading Edge Serrations for Rotating Applications" *Acoustics* 2, no. 3: 579-594.
https://doi.org/10.3390/acoustics2030030