Control of fan broadband noise through wavy leading and trailing edge serrations

Abstract

The present study provides comprehensive experimental investigations into the use of wavy leading edge (LE) and trailing edge (TE) serrations as a passive means for augmenting the reductions of fan broadband noise. The findings clearly indicate that the wavy LE – TE serrated fan could yield greater noise reduction performance than the un-serrated and wavy LE serrated fan, over a wide range of frequencies. In general, the wavy LE-TE serrated fans offer a maximum noise reduction of about 10 - 6 dB and an average reduction of about 4 - 5 dB, over a broad range of frequencies. For the range of frequencies from about 3 to 8 kHz, the wavy LE – TE serrated fan delivers a notable additional noise reductions of about 1-2 dB as compared to LE serrated ones, which is observed for all rpm values. For all rpm values, the un-serrated and serrated fans exhibit maximum / minimum directivity at an emission angle of about 127.5^o / 77.5^o. The lower far-field acoustic emissions (i.e., interaction noise + self-noise) offered by the wavy LE-TE serrated fans arises due to intense far-field destructive interference as a result of the faster spanwise phase variation of the velocity/pressure as well as the higher spanwise de-coherence. Further, the wavy LE-TE serrations mitigate direct scattering at both the LE and TE by dispersing sound energy over a wider area, which results in less intense noise signature in the far field. Thus, it clearly demonstrates that the second generation wavy LE-TE serrations could provide the substantial reduction of the far-field noise as compared to first-generation wavy serrations over a broad range of frequencies.

Keywords

Leading edge and trailing edge serrations fan blade noise control airfoil airfoil noise

Introduction

The development of a nation mainly depends on industries since they fulfil all the manufacturing demands which are essential for the development of a country. For this we need to increase the production capacity of industries which increases the number of machineries that could result in immense noise pollution to the surrounding areas. The machines which have rotor devices namely, fans, turbine blades, propeller blades etc are generally producing higher level of noise out of those having no rotary components. The blades of the rotors are airfoil shaped to obtain better performance (drag reduction and lift enhancement) but they are highly noisy and broadband in nature. The dominant noise source in civil aviation sector is fan broadband noise except during the approach conditions. The noise emitted from such rotor devices can cause serious health issues such as vertigo, speech disturbance, hearing loss, heart ailments etc, to those who are working on machineries, living in the vicinity of airports, wind-farms etc and hence an immediate attention is needed to control it. Researchers have studied various passive means namely, dimples, wavy leading edge serrations, sawtooth / wavy trailing edge serrations, porous trailing edges etc for the control of fan broadband noise but the combined use of novel bio-inspired wavy leading edge (LE) and trailing edge (TE) serrations on the blades for achieving the enhanced reductions of overall fan broadband noise is still underway. Thus, the present study aimed at improving the reductions of total broadband noise over a broad range of frequencies by introducing the wavy serrations at the LE and TE of the airfoil simultaneously, inspired by the biomimicry of the barn owls. Further, the current study attempts to develop low noise ‘wavy LE-TE serrated airfoils’ of the next generation. Some of the key literatures relevant to the present study are given below:

Bachmann et al.¹ observed that the presence of leading edge serrations and trailing edge fringes makes the flight of the barn owl quieter than the pigeon. They also mentioned the possibility of developing bio-inspired low noise wing designs in the future based on the silent flight of the barn owl. Soderman² investigated the acoustic characteristics of two leading edge serrated rotors of different sizes. He noticed the significant reductions of the high frequency noise as compared to the low frequency ones. Further, he observed decrease in the level of the overall noise from 4 to 8 dB for 1.52 m rotor, while it is up to 4 dB for the 2.59 m.

Zhou et al.³ showed that the owl-inspired velvety coating modifies the boundary layer characteristics and the TE noise spectrum. Also, they found that the velvety structure reduces high frequency noise by decreasing the normal velocity gradient and turbulence intensities close to the wall.

Hersh et al.⁴ showed that the LE serrations act as an effective passive means in lessening the narrow band vortex shedding noise from stationary / spinning airfoils by about 4 to 8 dB. Also, they exemplified that the serrations decrease the generation of tones that arises due to the periodic oscillating forces near the trailing edge, by producing vortices which modifies the wake and alter the velocity fluctuations from periodic to random.

Alex et al.⁵ studied the effect of spanwise varying wavy LE serrations for the control of airfoil interaction noise. They found that the crucial factor which controls the noise reduction performance of the LE serrated airfoil is the ratio of LE amplitude to the oncoming gust wavelength. They observed considerable noise reductions when the ratio of LE amplitude to the gust wavelength surpasses 0.3. Further, they found that the rapid phase variation of the pressure along the spanwise varying LE causes the reduction of far-field noise as compared to the straight leading edge.

Tang et al.⁶ observed that the trailing edge (TE) serrations hamper the growth of the spanwise vortices and promotes the development of the streamwise vortices near the TE. They observed that the decrease of velocity fluctuations in the vertical cross section of the mainstream direction reduces the wall pressure fluctuations near the TE, thus decreases the far-field noise when compared with the baseline. They showed that the introduction of serrations upstream of the reattachment point could effectively decreases the strength of the sound source and provide considerable noise reduction. Lacagnina et al.⁷ studied the self noise performance of the LE serrated airfoils for low, moderate and high angles of attack. They observed that LE serrations are effectual in reducing the airfoil noise for low and high angles of attack.

Juknevicius et al.⁸ showed that the longer and wider serrations must be present in the serration design for achieving the trade-off between the aeroacoustic and aerodynamic performances. They revealed that the LE serration reduces airfoil interaction noise and delays the separation of boundary layer at high angles of attack.

Chaitanya et al.⁹ showed that the maximum noise reductions occur when the transverse turbulence integral length-scale is roughly one fourth of the wavelength of the LE serrations. Further, they found that at optimum wavelengths, the acoustic power radiated by the LE serrated airfoil varies inversely with the Strouhal number. They also demonstrated that the LE serrations are effective passive means in reducing the trailing edge self noise.

Howe et al.¹⁰ showed that the acoustic performance of the wavy TE serration follows 10 × log₁₀ [6h/λ] dB for the Strouhal number >>1, where h and λ are the amplitude and wavelength of the serration. Further, they showed that the serrations should be of the order of thickness of the boundary layer to achieve considerable acoustic benefits.

Dassen et al.¹¹ found that the TE serrated airfoils could provide acoustic benefit from 3 to 8 dB. For the range of frequencies from 1 to 6 kHz, the serrated flat plates provided notable noise reductions of up to 10 dB. They showed that the degree of noise reduction decreases when the plate is inclined at 10° with respect to the flow direction, while further increase in the inclination to 15° causes an increase in the radiated noise.

Sivakumar¹² studied six TE serration profiles for the range of chordwise Reynolds numbers from 1.8 × 10⁵ - 5.7 × 10⁵. They found that the triangle shaped serration with included angles <45^o showed large noise reduction of up to 6 dB. They also observed highest noise reductions at 5 kHz, where the TE noise starts to dominate over the LE one.

Chong et al.¹³ observed that the non-flat plate serrations gave considerable decrease in the broadband self-noise by eliminating the high-frequency noise present with flat plate type serrations. Also, they proposed a hybrid serration profile for the reduction of narrowband shedding noise which includes a non-flat plate type TE serration with woven wire mesh screen.

Very recently, Sushil et al.^14,15 showed that use of non-uniform sinusoidal as well as curved wavy trailing edge (TE) serrations could act as a the best passive means for augmenting the airfoil broadband noise reductions over traditional uniform wavy TE serrations particularly from mid to high frequency ranges.

Objectives of the present study

Previous studies have shown that the serrations applied individually on either at the leading edge (LE) or trailing edge (TE) of an airfoil can act as an effective passive means to control the broadband noise. The present study attempts to develop low noise airfoil by introducing wavy serrations at the LE and TE of a fan blade (or airfoil) simultaneously for enhancing the reductions of the overall broadband noise (interaction noise + self-noise) as compared to the serrations applied only at the LE, which is a new step in this direction. The experiments are conducted for three different rpm values of fan such as 1300, 1600, and 1900. The level of noise reductions obtained with wavy serrations applied on the LE and TE of a fan blade is expected to be higher when the serrations are present on the LE alone. The studies are conducted by measuring fan broadband noise having blades with (i) wavy LE serrations and (ii) wavy LE and TE serrations, which are compared with noise radiated from an un-serrated fan blade having the same parameters as that of the serrated ones. Further, the additional noise reduction benefit offered by the wavy LE and TE serrated fans are determined by comparing the noise reductions provided by the wavy LE serrated fans, to demonstrate its enhanced noise reduction performance over a broad range of frequencies. Thus, the present study leads to the development of novel wavy LE and TE serrated fan blades (or airfoils) of the next (i.e., second) generation for achieving the significant reductions of far-field noise which finds numerous potential practical applications namely, fans, propellers, wind turbines, wings and so on.

Experimental test models

The present study is performed on a fan made by ORIENT ELECTRIC (Model STAND-32 OF series 4467679215595127). The experiments are performed with six fan blades having the same dimensions for the rpm values of 1300, 1600, and 1900. The span of all fan blades is kept as 0.36 m for uniform comparison of the acoustic performance. The photographs showing the details of the wavy serrations cut on leading edge (LE) and leading and trailing edge (LE-TE) of the fanblades are shown in Figure 1. The serrations are introduced in the spanwise direction (i.e., Y-direction) at the distance of 15 mm from the tip and root on LE of the fan blade to make the LE serrated blade. Similarly, the serrations are also provided at the same distance of 15 mm from the tip and root of the blade to make the LE - TE edge serrated fan blades. A distance of 15 mm is provided from the root and tip of the blade to lessen its vibration while rotating. The serrations are introduced over a length of 95 mm in both the cases. For both the LE and LE-TE edge serrated fan blades, the serrations are introduced at the same locations to obtain uniform comparison of the noise reduction performance.

The dimensions of amplitude (2h) and wavelength (l) in mm of the serrations introduced on the LE and LE-TE serrated fan blades are kept constant as LE (Ll10, 2h20), while the dimensions of the serrations provided on TE are varied to make different LE-TE serrated fan blades, where Ll10, 2h20 indicates leading edge with a wavelength of 10 mm and an amplitude of 20 mm. The parameters of the LE-TE serrated fan blades used in the present study are (i) L110, 2h20-Tl5,2h15 (ii) Ll10,2h20 - Tl10,2h15 (iii) Ll10,2h20 - Tl0,2h10 (vi) variable l and 2h where L and T represent leading and trailing edges, respectively. For variable l and 2h serrated fan blades, the wavelength of the TE serration is varied between 8.5 and 19.25 mm and the amplitude is varied from 14 to 32 mm. The photographs of typical baseline (un-serrated), wavy LE serrated and wavy LE-TE serrated fan blades are shown in Figure 2.

Design of wavy LE and LE-TE serrations on fan blades

The wavy serrations provided at the LE of an airfoil is made using MATLAB. The mainframe equation used for producing wavy serration profile on a variable chord fan blade airfoil is given in equation (1). The wavy serration profile possesses an amplitude h and a wavelength l is based on the equation given below:

C (y) = C_{o y} + h \sin (2 π y / l)

(1)

where C_oy is the variable chord of the fan blade and y is the spanwise variation of the wavy LE serration profile. The variations in the C_oy are not significant since the wavy LE serrations provided on the fan blade airfoil are small and are introduced over a small spanwise distance of 95 mm. The modified form of the above equation when the wavy serrations are introduced at both the leading edge (LE) and the trailing edge (TE) of the fan blade airfoil is as follows:

C (y_{1}) = C_{o y 1} / 2 + h_{1} \sin (2 π y_{1} / l_{1}) for LE modification

(2)

C (y_{2}) = C_{o y 2} / 2 + h_{2} \sin (2 π y_{2} / l_{2}) for TE modification

(3)

where C_oy1 and C_oy2 are the spanwise locations of the chord at which the wavy LE and TE serrations are provided. The wavy serrations introduced at the LE / TE of the variable chord fan blade are small and are provided over a spanwise distance of 95 mm and hence the variations of the chord at LE and TE of the fan blade airfoil C_oy1 and C_oy2 are not significant.

The equation for the LE and TE serrated airfoil is given below (Equation (4))

C (y_{1}, y_{2}) = C (y_{1}) + C (y_{2})

(4)

where y₁ and y₂ are variations in the spanwise variation of the airfoil section for the leading and trailing edges, respectively (Figure 1). The serration inclination angles at the LE and TE θ_SLE and θ_STE of the fan blade are determined from Figure 3 as follows:

{\tan θ}_{S L E} = \frac{l_{1}}{4 h_{1}}

(5)

{\tan θ}_{S L E} = \frac{l_{2}}{4 h_{2}}

(6)

where l₁, l₂ are the wavelengths and h₁, h₂ are the amplitudes of the LE and TE serrations respectively. The LE serration inclination angle θ_SLE of the fan blade is kept fixed as 14.036^o for all the cases. The TE serration inclination angles θ_STE of the fan blades are varied as follows: 4.769^o, 9.462^o, 14.036^o and 18.434^o to make different LE-TE serrated airfoils.

Experimental facility and procedure

Measurement system and instrumentation

Experiments are conducted in an in-house built anechoic chamber which has a dimension of 2.6 m × 1.7 m x 2.20 m (tip-to-tip). Photograph and schematic of a fan test setup kept inside an anechoic chamber for measuring fan broadband noise is shown in Figure 4(a) and (b). Fan noise measurements are made using an array of six-quarter-inch free-field condenser microphones (Make: GRAS, Model: 40PH 277,551). During the acoustic measurements, the fan is placed at the centre of the microphone array to include all the microphones which are positioned in the semi-circular arc of radius 0.65 m. The emission angle of the microphone varies from 60^o to 135^o. The noise is simultaneously measured with six microphones for 10 seconds at a sampling frequency of 50 kHz. Data acquisition was done using a four-channel simultaneous sampling NI chassis (CDAQ 9174) and module (NI 9222). The acoustic data is amplifying using an amplifier (Make: PCB PIEZOTRONICS, MODEL: 482C SERIES). The data is transferred to a PC using NI 15 LABVIEW software. The time history of the acoustic data is transformed to frequency domain using MATLAB scripts. The microphones are calibrated using sound calibrator (Make: Larson Davis, Model no. CAL 200) prior to each measurement which showed an uncertainty of $\pm$ 0.2 dB with a maximum of $\pm$ 0.5 dB in one or two cases. From the calibration, the uncertainty in the measurement of sound pressure is within $\pm$ 0.2 dB with a maximum $\pm$ 0.5 dB, including repeatability factors. The velocity fluctuations near the wavy LE-TE serrated airfoil are acquired using a hotwire (MAKE: SUNSHINE, MODEL: HWCTA AMB-717) in our open jet anechoic wind tunnel setup. The velocity fluctuations are measured at the tip / oblique / root of the wavy TE serration as well as the tip of the wavy LE serration in the spanwise direction to explain the noise reduction mechanism.

The sound power reduction level (∆PWL) and additional sound power reduction level and (ΔPWL_additional) of the wavy LE and TE serrated airfoils over baseline and LE serrated airfoil are determined using the Eqs. (7) and Eq. (10) given below:

Δ P W L (f) = {P W L}_{B a s e l i n e a i r f o i l} - P W L_{L E - T E s e r r a t e d a i r f o i l}

(7)

P W L (f) = 10 \times \log_{10} (W (f) / W_{r e f})

(8)

\begin{array}{l} Δ {P W L (f)}_{a d d i t i o n a l} = {P W L}_{L E s e r r a t e d a i r f o i l} - P W L_{L E - T E s e r r a t e d a i r f o i l} \\ = 10 \times \log_{10} ({W (f)}_{L E s e r r a t e d a i r f o i l} / {W (f)}_{L E - T E s e r r a t e d a i r f o i l}) \end{array}

(9)

W (f) = \frac{L R}{ρ a} {\sum_{i = 1}^{N - 1} (\frac{Φ p p (θ_{i}) + Φ p p (θ_{i + 1})}{2}) Δ θ}

(10)

where, PWL is the sound power level given in Eq. (8), and W( f ) is determined using equation (10), which represents the acoustic power radiated between the emission angles [60^o to 135^o], W_ref = 10⁻¹² W,

Φ p p (θ_{i})

and

Φ p p (θ_{i + 1})

represent the spectral density of the sound pressure at the measurement angles

θ_{i}

and

θ_{i + 1}

, N represents the number of microphones (N = 6), L is the span of the fan blade (0.36 m), R is the radius of the array over which microphone are placed (0.65 m),

Δ θ

is the angle between the two subsequent microphones (15°), ρ denotes the ambient air density (kg/m³), and a is sound speed in the air (m/s).

The overall sound power level OAPWL (f) is determined by integrating the sound power for the range of frequencies from 1 to 10 $kHz$ using the equation given:

O A P W L (f_{j}) = 10 \times \log_{10} [\frac{\sum_{N_{i}}^{N_{i + 1}} W (f_{j})}{W_{r e f}}] 1 < f_{j} < 10 kHz

(11)

where N_i and N_i+1 are the first two subsequent microphones for i = 1 and next two for i = 2 up to i = 5

W (f_{j})

is the sound power in Watts and

W_{r e f}

= 10⁻¹² W

Source decomposition of wavy LE-TE serrated airfoils

The mean square pressure radiated by the baseline airfoil ( $\bar{{p_{B a s e l i n e}}^{2}} (f)$ ) kept in the turbulent stream may be written as the sum of the background noise ( $\bar{{p_{B G}}^{2}} (f)$ ), interaction-noise ( $\bar{{p_{I N}}^{2}} (f)$ ) and airfoil self-noise $\bar{{p_{S N}}^{2}} (f)$ ), that is,

\bar{{p_{B a s e l i n e}}^{2}} (f) = \bar{{p_{B G}}^{2}} (f) + \bar{{p_{I N}}^{2}} (f) + \bar{{p_{S N}}^{2}} (f)

(12)

Once the leading edge and trailing edge serrations are introduced on the airfoil, the interaction noise and self-noise are reduced by the factors α_{LE-TE IN} ( f ) and β_{LE-TE SN} ( f ), respectively. The mean square pressure radiated by the wavy LE - TE serrated airfoil is given by (Equation (13))

\bar{{p_{L E - T E s e r r a t i o n}}^{2}} (f) = \bar{{p_{B G}}^{2}} (f) + α_{L E - T E I N} \bar{{p_{I N}}^{2}} (f) + β_{L E - T E S N} \bar{{p_{S N}}^{2}} (f)

(13)

The overall mean square pressure reduction γ_{LE-TE Total} ( f ) is therefore given by (Eq. (14))

γ_{L E - T E o v e r a l l} = \frac{\bar{{p_{B a s e l i n e}}^{2}} (f)}{\bar{{p_{L E - T E s e r r a t i o n}}^{2}} (f)} = \frac{\bar{{p_{B G}}^{2}} (f) + \bar{{p_{I N}}^{2}} (f) + \bar{{p_{S N}}^{2}} (f)}{\bar{{p_{B G}}^{2}} (f) + α_{L E - T E I N} \bar{{p_{I N}}^{2}} (f) + β_{L E - T E S N} \bar{{p_{S N}}^{2}} (f)}

(14)

γ_{L E - T E o v e r a l l} = \frac{\bar{{p_{B a s e l i n e}}^{2}} (f)}{\bar{{p_{L E - T E s e r r a t i o n}}^{2}} (f)} = \frac{1 + ((\bar{{p_{I N}}^{2}} (f) + \bar{{p_{S N}}^{2}} (f)) / \bar{{p_{B G}}^{2}} (f))}{1 + ((α_{L E - T E I N} \bar{{p_{I N}}^{2}} (f) + β_{L E - T E S N} \bar{{p_{S N}}^{2}} (f)) / \bar{{p_{B G}}^{2}} (f))}

(15)

The sound power can also be written in the similar form. The reduction in sound power level is therefore given below in equation (16)

Δ P W L (f) = 10 \times \log_{10} ({γ_{L E - T E}}_{o v e r a l l})

(16)

Uncertainty in measurements

The uncertainty in the rpm of fan is within $\pm 1$ %. The variation of surrounding temperature inside the anechoic chamber is within $\pm$ 1^o C. The uncertainty in the measurement of sound pressure is within $\pm$ 0.2 dB with a maximum of $\pm$ 0.5 dB including repeatability factors. The resolution of the frequency spectra is 48.83 Hz.

Results and discussions

Acoustic spectra comparison of un-serrated and serrated fans

The far-field acoustic spectra of the un-serrated fan, wavy LE serrated fan, wavy LE-TE serrated fans and wavy LETE (variable l and 2h in mm), are shown in Figure 5 for different rpm values of 1300, 1600 and 1900. As the fan speed increases, the sound power emission level increases for all the fans. For all rpm values, the un-serrated fan radiates higher acoustic emissions as compared to the wavy LE and wavy LE-TE serrated fans over the wide range of frequencies from 300 Hz to 10 kHz. However, the acoustic emissions from the un-serrated fan show significant decrease with increase in frequency from about 8 to 10 kHz and similar behavior is observed for both the wavy LE serrated and wavy LE-TE serrated fans. For all r.p.m values (Figure 5(a)-(c)), wavy LE as well as wavy LE-TE edge serrated fans produce lower sound radiation than un-serreted fan over the entire range of frequencies.

At lower frequency range (<1 kHz) radiation from the wavy LE-TE serrated fan is slightly higher than the wavy LE serrated fan. For the range of frequency from about 2 to 3 kHz both wavy LE as well as wavy LE-TE edge serrated fans produce nearly same acoustic radiation except for the LETE variable case. The multi-frequency TE serrations are combined with single frequency LE serration to obtain the LETE variable case. It showed higher emissions when compared to other wavy LE serrated and LE-TE serrated fans for the entire range of frequencies, however reduced emissions are observed as compared to the unserrated one. In general, the wavy LE-TE serrated fan with parameters Ll10, 2h20 and Tl5, 2h15 produces much reduced acoustic emission levels in the interaction noise dominated zone (i.e., 1-2 kHz) and self-noise dominated zone (i.e., 3-8 kHz) than LE one. Thus, it clearly demonstrates that the wavy LE-TE serrated fan could produce lower acoustic emissions as compared to the wavy LE serrated fans for a particular range of frequencies.

Sound power reduction level comparison of LE and LE-TE serrated fans

Figure 6(a)-(c) shows the sound power reduction level (∆PWL) comparisons of wavy LE and wavy LE-TE serrated fans with respect to the un-serrated fan for different rpm values. At lower frequency range (<1 kHz), the noise reductions provided by the wavy LE-TE serrated fans are about 6 to 8 dB while LE serrated fan showed a reduction of about 5 to 13 dB in general. It indicates that the maximum ∆PWL provided by LE serrated fan is higher than that of all LE-TE serrated fans when the frequency is less than 1 kHz. The wavy LE-TE serrated fan (Ll10, 2h20 - Tl5, 2h15) shows the highest ∆PWL of about 9 dB from mid to high frequency range (i.e., 5 – 10 kHz), while LE serrated fan shows about 8 dB for all rpm values. Similarly the wavy LE-TE serrated fan (Ll10, 2h20 - Tl10, 2h15) also shows a maximum reduction of about 8 dB for the range of frequencies from 5 to 8 kHz. Earlier studies by Narayanan et al.¹⁶ showed that the self-noise limits the achievable noise reductions provided by the LE serrations from mid to high frequencies but the presence of wavy LE-TE serrations could even provide significant noise reduction from mid to high frequencies by shifting the dominant self-noise zone to frequencies above 10 kHz. The variable LE-TE serrated fan gave lowest reduction as compared to the other LE-TE serrated for the entire range of frequencies. Thus, it clearly demonstrates that the wavy LE-TE serrated fans with parameters (Ll10, 2h20 - Tl5, 2h15, Ll10, 2h20 - Tl10, 2h15) could act as an effective passive means to achieve significant noise reduction in the self-noise dominated zone (i.e., 5 to 10 kHz) by shifting the limiting tendency of self-noise to higher frequencies (i.e., >10 kHz). The study also revealed that the wavy LE and TE serration inclination angles which gave greater noise reductions over a wide range of frequencies are 14.036 and 9.462°.

Additional sound power reduction level comparison of LE-TE serrated fans

The additional noise reductions benefit provided by the wavy LE-TE serrated fan with respect to wavy LE serrated fan for different rpm values are shown in Figure 7(a)-(c). For all rpm values, the wavy LE-TE serrated fan shows a maximum additional noise reduction benefit of about 2 dB and an average of about 1 dB from about 4 to 10 kHz, which indicates the superior noise reduction performance of the LE-TE serrated fan over LE serrated one. The noise reductions are mentioned in decibel (dB), which is a logarithmic scale and hence the reductions of about 1-2 dB cannot be considered as small since it plays a significant role in reducing the overall noise levels in the practical applications. The additional noise reductions offered by the wavy LE-TE serrated fans (Ll10, 2h20 - Tl5, 2h15, Ll10, 2h20 - Tl10, 2h15) from mid to high frequency range (i.e., 4 – 10 kHz) may be due to the reduced scattering intensity as a result of the decreased wall pressure fluatuations near the TE as well as the enhanced far-field destructive interference. Thus, the present study sufficiently demonstrates that the wavy LE-TE serrated fans could be considered as an effective passive noise control means for achieving the enhanced reductions of airfoil broadband noise over wavy LE serrated fans particularly from mid to high range of frequencies.

Noise reduction mechanism

The noise reduction mechanism is explained based on the hotwire measurements performed in our anechoic open jet wind tunnel facility for the wavy LE-TE serrated airfoil. The second generation wavy LE-TE pattern promotes rapid spanwise phase variation in velocity/pressure fluctuations as well as the higher spanwise de-coherence as shown in Figure 8(a) and (b), which strengthens the destructive interference of sound waves. Due to this wavy LE-TE geometry mitigates direct scattering at both the LE and TE by dispersing sound energy over a wider area that results in softer and less intense noise signature in the far field when compared to the first generation serrated airfoils.

Normalized sound power reduction level of wavy LE-TE serrated fans: modified Strouhal number scaling law

The variation of normalized sound power reduction level ( $Δ P W L^{'} = \frac{Δ P W L}{{Δ P W L}_{\max}}$ ) of the wavy LE-TE serrated fans with modified Strouhal number (S_tm) is shown in Figure 9 for different rpm values of the fan. A modified Strouhal number (S_tm) scaling law is proposed to elucidate the noise reduction performance of the wavy LE-TE serrated fans from mid to high frequencies (i.e., from about 4 to 10 kHz) for all the rpm values. The modified Strouhal number (S_tm) is defined by scaling the parameters f, h_eq, and U in such a way that the $Δ P W L^{'}$ show good coalesce from mid to high frequencies (i.e., about 4 – 10 kHz) for all rpm values. The modified Strouhal number ( ${S t}_{m}$ ) is defined as ${S t}_{m} = \frac{f h_{e q}}{U}$ , where $h_{e q} = 0.6 \times \sqrt{h_{l E} \cdot h_{T E}}$ , $h_{l E} a n d h_{T E}$ are the serration amplitudes at the LE and TE of the wavy LE-TE serrated fans. The presence of good coalesces observed at higher S_tm values for all the rpm values represents the effectiveness of the wavy LE-TE serrations in providing greater noise reductions from mid to high frequencies. For all rpm values, the $Δ P W L^{'}$ show good coalesce for ${S t}_{m}$ lying between 5 and 8 which represents achievement of significant noise reductions performance of the wavy LE-TE serrated fans in the self-noise dominated zone. It also shows that $Δ P W L^{'}$ follows a linear behaviour for the range of ${S t}_{m}$ values from about 5 to 8. Mathematically, the normalized noise reduction performance of the wavy LE-TE serrated fans can be written as

Δ P W L^{'} = a {S t}_{m} + b

(17)

where a and b are constants

Sound power level directivity comparison of un-serrated and serrated fans

The directivity comparison of un-serrated and serrated fans is shown in Figure 10 for different rpm values. The overall sound power level directivity is obtained by integrating the sound pressures for the range of frequency from 1 to 10 kHz. It indicates that the un-serrated fan exhibits higher directivity, while LE-TE serrated one shows the lowest one for all the rpm values. For both the un-serrated and serrated fans, the highest directivity is observed in the downstream direction of the fan at an emission angle of about 127.5^o, while the lowest is observed in the upstream direction at an angle of 77.5^o− for all rpm values. The lowest directivity exhibited by the wavy LE-TE serrated fans may be due to the reduced scattering intensity and strong far-field destructive interference as compared to the un-serrated and LE-serrated fans. However, the variable LE-TE shows higher directivity than the uniform wavy LE-TE fans although its level is much lower than the un-serrated one. Thus, the study reveals that the use of uniform wavy LE-TE serrations could be preferred over the LE / variable LE-TE serrations to achieve lowest overall emission levels for all emission angles and rpm values.

Conclusions

The present study clearly indicates that the wavy LE – TE serrated airfoil could provide higher noise reduction performance than wavy LE serrated airfoil, over a wide range of frequencies. The wavy serrations provided on the LE and TE of the fan blades could provide significant broadband noise reductions of about 9 to 5 dB from mid to high frequency range with respect un-serrated fan of same-size and shape and are observed for all fan rpm values. In general, the wavy LE-TE serrated airfoils provide an average noise reduction of about 7 dB with respect to the un-serrated one, over the entire range of frequencies. For all rpm values, wavy LE – TE serrated fan provide an extra maximum noise reduction benefit of about 2 dB and an average of about 1 dB as compared to wavy LE serrated ones, for the range of frequencies from about 3 to 8 kHz. The un-serrated and serrated fans show highest directivity at an emission angle of about 127.5^o in the downstream direction, while it is lowest at an angle of 77.5^o in the upstream direction and these are observed for all the rpm values. The lower far-field acoustic emissions / greatest noise reductions provided by the wavy LE-TE serrated fans might be due to strong far-field destructive interference as a result of the rapid spanwise phase variation of the velocity/pressure as well as the reduced spanwise coherence. Owing to this the wavy LE-TE serrations lessen the direct scattering at both the LE and TE by spreading the acoustic energy over a broader area that results in lower acoustic radiations in the far field. Thus, the present study demonstrates that the ‘wavy LE-TE serrations’ introduced on airfoils such as fan blades, propellers, wings etc., could act as an effective passive means for achieving significantly enhanced reductions of broadband noise over a wide range of frequencies.

Footnotes

Acknowledgments

The authors thankfully acknowledge that the current work (No. CRG/2021/000508) was supported by Anusandhan National Research Foundation (ANRF) [Science and Engineering Research Board (SERB)], Department of Science and Technology, Government of India.

Declaration of conflicting interests

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

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Science and Engineering Research Board (CRG/2021/000508).

ORCID iDs

Subramanian Narayanan

Sushil Kumar Singh

References

Bachmann

Klän

Baumgartner

, et al. Morphometric characterization of wing feathers of the barn owl Tyto alba pratincola and the pigeon Columba livia. Front Zool 2007; 4: 1–15. DOI: 10.1186/1742-9994-4-23.

Soderman

. Leading edge serrations which reduce the noise of low-speed rotors. Washington, DC: NASA, 1973. Report No. NASA TN D- 7371.

Zhou

Zhong

Zhang

. On the effect of velvet structures on trailing edge noise: experimental investigation and theoretical analysis. J Fluid Mech 2021; 919: A11. DOI: 10.1017/jfm.2021.374.

Hersh

Soderman

Hayden

. Investigation of acoustic effects of leading edge serrations on airfoils. J Aircraft 1974; 11(4): 197–202.

Lau

ASH

Haeri

Kim

. The effect of wavy leading edges on aerofoil-gust interaction noise. J Sound Vib 2013; 332: 6234–6253.

Tang

Lei

. Noise reduction mechanisms of an airfoil with trailing edge serrations at low Mach number. Appl Sci 2019; 9: 3784. DOI: 10.3390/app9183784.

Lacagnina

Chaitanya

Kim

J-H

, et al. Leading edge serrations for the reduction of aerofoil self-noise at low angle of attack, pre-stall and post-stall conditions. Int J Aeroacoustics 2021; 20(1–2): 130–156.

Juknevicius

Chong

Woodhead

. Leading edge noise reduction of thin aerofoil by the straight and curved serrations of the add-on type. 23rd AIAA/CEAS Aeroacoustics Conference, Denver, Colorado, 5-9 June 2017; 1–17. DOI: 10.2514/6.2017-3491.

Chaitanya

Joseph

Narayanan

, et al. Performance and mechanism of sinusoidal leading-edge serrations for the reduction of turbulence-aerofoil interaction noise. J Fluid Mech 2017; 818: 435–464. DOI: 10.1017/jfm.2017.141.

10.

Howe

. Aerodynamic noise of a serrated trailing edge. J Fluid Struct 1991; 5: 33–45. DOI: 10.1016/0889-9746(91)80010-B.

11.

Dassen

Parchen

Bruggeman

, et al. Results of a wind tunnel study on the reduction of airfoil self-noise by the application of serrated blade trailing edges. https://reports.nlr.nl/xmlui/handle/10921/1359 (accessed 27 March 2021).

12.

Sivakumar

Porteous

Mimani

, et al. An experimental investigation of turbulent boundary-layer interaction with different serrated trailing-edge configurations. In: ACOUSTICS 2015 (Annual Conference of the Australian Acoustical Society). Hunter Valley, NSW, Australia, November 2015. https://dspace.nal.gov.au/xmlui/handle/123456789/363 (accessed 27 March 2021).

13.

Chong

Joseph

Gruber

. Airfoil self-noise reduction by non-flat plate type trailing edge serrations. Appl Acoust 2013; 74: 607–613. DOI: 10.1016/j.apacoust.2012.11.003.

14.

Singh

Narayanan

. Control of airfoil broadband noise through non-uniform sinusoidal trailing-edge serrations. Phys Fluids 2023; 35: 025139. DOI: 10.1063/5.0133556.

15.

Singh

Narayanan

. On the reductions of airfoil–turbulence noise by curved wavy serrations. Phys Fluids 2023; 35: 075140. DOI: 10.1063/5.0152637.

16.

Narayanan

Chaitanya

Haeri

, et al. Airfoil noise reductions through leading-edge serrations. Phys Fluids 2015; 27. DOI: 10.1063/1.4907798.