A study on the acoustic performance of array silencer combined with active noise control

Abstract

Array silencers are widely used in large airflow aerodynamic noise control due to their high flow-through ratio, low airflow resistance, and low regeneration noise. However, the acoustic performance of an array silencer in low frequencies is inadequate. To enhance the low-frequency transmission loss ( $T L$ ), this study combined array silencers with Active Noise Control (ANC) and the acoustic performance of active array silencers was investigated through simulations and experiments, which clarified the enhancement effect of ANC on the $T L$ of array silencers with different structural parameters (cross-sectional side length ( $a$ ) of anechoic columns, aspect ratio of anechoic column amount ( $A R$ ), flow-through ratio ( $r$ )). Results showed that when $r$ =0.56, $a$ =150 mm, $A R$ =1:4 and ANC was on, the increment of $T L$ was less than or equal to 0 dB at each 1/1 octave band with a center frequency greater than 1000 Hz. When there was no airflow, $T L$ increased by 200.0%, 148.4%, 55.4%, and 23.1%, respectively at each 1/1 octave band with a center frequency of 63 Hz-500 Hz. When airflow was present in the same direction as sound propagation, $T L$ increased by 14.3%, 88.3%, 25.3%, and 5.4%, respectively. When airflow was present in the direction opposite to sound propagation, $T L$ increased by 18.2%, 37.5%, 5.6%, and -15.2%, respectively. The active array silencer can be widely applied in situations with large airflow and high requirements for low-frequency noise reduction performance.

Keywords

array active noise control (ANC)silencer acoustic performance transmission loss (TL)

1. Introduction

Silencers are widely used in the field of aerodynamic noise control.^1–5 Silencers of various structural forms, such as sheet type, acoustic flow type, folded plate type, and labyrinth type, are widely employed in engineering. Compared with these silencers above, array silencers⁶ (see Figure 1) have advantages including high flow-through ratio, low airflow resistance, and low regeneration noise. Consequently, array silencers have gained extensive application for aerodynamic noise control in recent years.^7–10 However, since array silencers generally employ porous sound absorption materials or micro-perforated panel structures, their transmission loss ( $T L$ ) in the low frequency band are still inadequate and urgently needs to be improved.¹¹

Figure 1.

Schematic diagram of a resistive array silencer.

Active noise cancellation technology is also called Active Noise Control (ANC). It generates a series of secondary sounds with the same amplitude but opposite phase to the primary noise (the noise to be eliminated), and uses the destructive interference of sound waves to effectively reduce low-frequency noise.^12,13 Prevoius researches showed that introducing ANC systems into silencers with single or multiple independent airflow channels (uninterconnected airflow channels) can significantly improve the noise reduction performance in the low-frequency range.^14–16 However, there is still a lack of research on the coupled acoustic performance of array silencers featuring interconnected airflow channels with Active Noise Control (ANC) systems. A key unresolved question is how structural parameters affect the overall acoustic performance when array silencers with interconnected channels are integrated with ANC systems.

This study explored the construction methods of ANC and array silencer, and systematically studied the enhancement effect of ANC on the acoustic performance of array silencer with different structural parameters. The research results can provide a technical basis for the development and engineering application of active array silencer.

2. Construction of active array silencer

2.1. Construction of active array silencer

The active array silencer consists of two components: ANC systems and an array silencer. The ANC system includes secondary sources, reference microphones, error microphones, and a controller. As shown in Figure 1, the array silencer mainly includes several resistive anechoic columns distributed in an array pattern.

Taking the 1×4 array silencer as an example, its composite method with ANC is shown in Figure 2. Secondary sources are embedded in the air deflectors end of the anechoic column, facing the silencer outlet. The air deflector of each anechoic column uses a metal orifice plate with a perforation diameter of 5 mm and a perforation rate of more than 65%, to ensure that it does not affect the acoustic emission of the secondary sources.

Figure 2.

Schematic structure of the arrayed elements silencer combined with ANC. (a) Top view of silencer (b) A-A sectional view of silencer.

Considering the performance and volume of secondary sources, this study selected the full-band speakers as secondary sources in the active array silencer prototype, and their technical parameters are shown in Table 1. Reference microphones are arranged at the silencer inlet, and error microphones are arranged at the silencer outlet.^17,18 Previous researches showed that when error microphone is located downstream of the secondary source, the system is stable and its position selection is relatively flexible.^19,20 All components are connected via wires to an external ANC controller.

Table 1.

Speaker technical parameters.

Parameter	Rated impedance	Resonant frequency	Rated power	Maximum power	Sensitivity (2.83V/1m)	Moving mass	Equivalent air volume	Voice coil diameter
Value	8 Ω	69 Hz	15 W	30 W	82 dB	4.8 g	4.3 L	20 mm

As shown in Figure 2, the distance between the reference microphones and the secondary sources is approximately the effective silencing length of the anechoic columns. The propagation time for primary noise from reference microphones to secondary sources is represented by Eq. (1). The system delay is given by Eq. (2).

T_{1} = \frac{L}{c_{0}}

(1)

T_{2} = T_{e} + T_{f}

(2)

Where

T_{1}

is the propagation time,

T_{2}

is the system delay, L is the distance between the reference microphone and the secondary sound source, which is approximately the effective silencing length of the anechoic column,

c_{0}

is the sound speed,

T_{e}

is the delay of the A/D converter, D/A converter, filter, speaker, etc., in the peripheral circuit and

T_{f}

is the delay caused by the adaptive control algorithm.

To ensure the noise reduction performance and system stability of the active array silencer, the ANC must meet the causal condition ( $T_{1} > T_{2}$ ), that is, the secondary sound generated by the secondary source must propagate to this position before the primary noise reaches the error microphone.¹⁸ Consequently, distance L should satisfy Eq. (3).

L > c_{0} (T_{e} + T_{f})

(3)

As the number of ANC channels increases, the computational complexity grows exponentially.²¹ Thus, the array silencer can be divided into independent units with fewer airflow channels. Each unit includes an independent ANC. As Figure 2 shows, the 1×4 active array silencer is divided into two units. Each unit is independently controlled by an ANC system with two secondary sources.

2.2. Active noise control system algorithm

The ANC system generates anti-phase sound waves with equal amplitude and opposite phase to the original noise in real time based on adaptive algorithms. To balance the ANC system stability, computational complexity, and engineering practicality, this study adopted a composite algorithm including offline identification and online control approach. It significantly improved the convergence speed and stability of the system, reduced real-time computing load, ensured noise reduction performance, and provided the feasibility for embedded deployment of the system in actual ventilation environments. A detailed flowchart of the algorithm is shown in Figure 3.

Figure 3.

Flow chart of ANC system algorithm.

During the offline identification phase, the Least Mean Square Algorithm (LMS) is used to accurately model the secondary path. The specific method is as follows. A white noise excitation signal is applied to the secondary source, reaches the error microphone through the actual secondary path $S_{1} (z)$ , and generates a response signal. The formulas for the weight update of the adaptive filter are shown in Eq. (4) and Eq. (5). Through iterative updates, a secondary path estimation model $S_{2} (z)$ is ultimately formed, which can be used for online control.

e_{i} (n) = d_{s} (n) - y_{s} (n)

(4)

w (n + 1) = w (n) + μ \cdot e_{i} (n) \cdot x_{s} (n)

(5)

Where

e_{i} (n)

is the modeling error at the nth sampling moment,

d_{s} (n)

is the response signal,

y_{s} (n)

is the estimated output of the adaptive filter,

w (n)

is the adaptive filter weight vector during the offline identification phase,

μ

is the step parameter and

x_{s} (n)

is the input signal vector.

During the online control phase, the system uses the Filtered-x Least Mean Squares Algorithm (FxLMS). A primary signal is picked up by the reference microphone and propagates along the main path $P (z)$ to the error microphone, ultimately forming the primary noise signal. Meanwhile, the primary signal is fed into the adaptive filter to generate secondary control signal, as calculated in Eq. (6). The secondary control signal drives the secondary source to generate a sound wave. This wave propagates to the error microphone through the actual secondary path, where it is superimposed with the primary noise to form the residual error, as calculated as Eq. (7).

y (n) = W^{T} (n) \cdot x (n)

(6)

e (n) = d (n) + S_{1} (z) * y (n)

(7)

Where

y (n)

is the secondary control signal,

W (n)

is the adaptive filter weight vector during the online control phase,

x (n)

is the primary signal vector,

e (n)

is the residual error,

d (n)

is the primary noise signal and

S_{1} (z) * y (n)

is the secondary sound signal filtered by the actual secondary path

S_{1} (z)

To achieve effective noise cancellation, the controller weights need to be updated in real time. To this end, $x (n)$ is first filtered through $S_{2} (z)$ to obtain the filtered primary signal, as calculated as Eq. (8). The controller weight update formula is shown in Eq. (9).

x^{'} (n) = S_{2} (z) * x (n)

(8)

W (n + 1) = W (n) + μ \cdot e (n) \cdot x^{'} (n)

(9)

Where

x^{'} (n)

is the filtered primary signal.

Considering the characteristics of the secondary path, the ANC system controller optimizes the weight vector to drive the system to converge towards the direction of minimizing error, which can achieve effective noise cancellation.

3. Simulation and experimental methodology

3.1. Simulation methodology

Based on the COMSOL Multiphysics finite element analysis platform, a 3D acoustic simulation model of 1×4 active array silencer as shown in Figure 4 was constructed.

Figure 4.

Simulation model of 1×4 active array silencer.

3.1.1. Simulation of the array silencer

The array silencer was composed of four square anechoic column units with the same structure in parallel. The geometric parameters are shown in Table 2. COMSOL Pressure Acoustic module was used to study its acoustic performance. The anechoic column domain was set to porous medium acoustic conditions. The properties of the anechoic column material were characterized using the Delany-Bazley-Miki model,²² with a material density of 24 kg/m³, a fiber diameter of 6×10^-6 m, and constants

k_{1}

and

k_{2}

of 3.18×10^-9 and 1.53, respectively. According to Eq. (10),²³ the flow resistivity of the porous sound-absorbing material was 11425 Pa·s/m².

σ = k_{1} \cdot \frac{{ρ_{m}}^{k_{2}}}{{d_{m}}^{2}}

(10)

Where

ρ_{m}

is the material volume,

d_{m}

is the fiber diameter,

k_{1}

k_{2}

is constants and

σ

is the flow resistivity.

Table 2.

Structural parameters of simulation model for active array silencer.

Parameter	Value
Silencer width	850 mm
Silencer height	250 mm
Silencer length	1840 mm
Cross-sectional side length of anechoic columns	150 mm
Effective column length	1500 mm
Column spacing	50 mm
Column-to-shell spacing	50 mm
Column porosity	23%

The outer shell of the anechoic column was the boundary of the internal perforated plate with a 1 mm thickness, a 2.5 mm pore diameter, and 23% porosity. The rest of the parts were set as air medium attribute, the density ρ₀ was 1.25 kg/m³, and the sound speed c₀ was 343 m/s.

The surfaces of the walls and the inlet air deflectors used the internal hard sound field boundary. The surface of the outlet air deflectors was the internal perforated plate boundary with a 1 mm thickness, a 5 mm pore diameter, and porosity exceeding 65%. 1 Pa plane wave radiation was applied to the inlet, and a Perfectly Matched Layer (PML) was configured at the outlet. To simulate the influence of airflow, the ‘Laminar Flow’ interface defined a vertical inlet airflow velocity of 2 m/s–6 m/s. The acoustic model and the airflow model were coupled through “Acoustic-Structure Interaction”.

The model was meshed with free tetrahedral elements. To ensure the accuracy of acoustic calculations, the mesh size was set according to the highest frequency of interest. This study calculated the 1/1 octave noise reduction in the range of 63 Hz to 4000 Hz. To ensure the simulation calculation accuracy in this frequency band, the mesh was divided according to the higher frequency of 5680 Hz (corresponding to the minimum wavelength λ_min is 0.0604), and the maximum element size was set to be λ_min/8 (7.55 mm).

3.1.2. Active noise control system

The ANC system was implemented through COMSOL-MATLAB LiveLink. The structure of the ANC system is shown in Figure 4. Four monopole secondary sources were embedded in the exit guide head of the anechoic column, and their initial amplitude and phase were preset to 0.01 and 180°, respectively. The virtual reference microphones were set up 75 mm in front of the entrance plane to collect incident noise, the virtual error microphones were set up 75 mm behind the exit plane to monitor the residual sound pressure in real time. The system control goal was to minimize the sound pressure amplitude at the error point to 0 Pa. The system used a reference signal as input and an error signal as feedback. In each iteration, the system calculated the sound pressure deviation based on the residual error and continuously adjusted the amplitude and phase of the secondary source. This process continued until the preset iteration count was reached or the error signal dropped to an acceptable level. Ultimately, a stable noise control could be achieved.

During the offline identification phase, the system generated 10,000 samples of standard white noise as the excitation signal. A 22nd-order low-pass filter was used as the identification of the actual secondary path and measurement noise with a variance of 0.1 was superimposed on the output to simulate actual environment disturbance. A 31st-order LMS adaptive filter with a step size of 0.01 was employed to perform a correlation analysis between the input and output signals and estimated the transfer function of the secondary path. During the online control phase, the primary noise signal was composed of a narrowband signal and a wideband signal. The narrowband signal was made up of three sine waves of specific frequencies, while the wideband signal was white noise with unit variance. A 42nd-order low-pass filter was used for main path identification. Measurement noise with a variance of 0.1 was superimposed on the output, and 1% sensor noise was introduced into the reference signal to simulate actual sensing conditions. The controller used a 21st-order adaptive FIR filter and set a step size of 0.0005 to balance system convergence speed and stability. To reduce the interference of random factors in a single simulation, this study repeated the simulation 40 times and averaged the resulting mean square error curves.

3.2. Experimental methods

A silencer prototype that is consistent with the structural parameters of the simulation model shown in Figure 4 was produced. Figure 5 shows the active array silencer prototypes. The anechoic columns were filled with porous sound-absorbing material with a flow resistivity of 11,425 Pa·s/m², and the acoustic performance of its static working conditions (no airflow) and dynamic working conditions (with airflow) were measured respectively. Under static conditions, used the white noise in the frequency range of 50 Hz-1000 Hz as the sound source. Under dynamic conditions, the fan was connected to the upstream of the test pipeline through a diameter-reducing pipe, and a silencer was installed in the fan pipeline to eliminate its noise interference. Then, the airflow speed was adjusted to 2 m/s, 4 m/s and 6 m/s. The same white noise was applied as the sound source after the airflow became stable. The data acquisition system synchronously recorded real-time noise signals with no obvious external noise interference and a duration of about 30 s at 0.5 m away from the center of the inlet and outlet ends. The sampling process strictly eliminated environmental noise interference.

Figure 5.

A photo of the active array silencer prototype. (a) Experimental prototype. (b) Engineering prototype.

Measurement equipment included BSWA MA231 microphones, an ArtemiS DATaRec multichannel data acquisition system (Head Acoustics, Germany), and a laptop running ArtemiS 10.00 software (Head Acoustic, Germany).

4. Results and analysis

4.1. Acoustic performance of active array silencer

4.1.1. Static transmission loss

Figure 6 presents the simulated static $T L$ results for the active array silencer. After combining ANC, at the center frequency of 63 Hz –500 Hz in each 1/1 octave band, the increments of $T L$ ( $Δ T L$ ) were 1.8 dB, 9.2 dB, 12.8 dB, and 7.7 dB respectively. These values corresponded to $T L$ improvements of 200.0%, 148.4%, 55.4%, and 23.1%. For the octave bands centered at 1000 Hz, 2000 Hz, and 4000 Hz, the $T L$ decreased by 0.7 dB, 3.5 dB and 4.2 dB, respectively. These results show that ANC enhances $T L$ in the low and middle frequency band but reduces it at high frequencies. The degradation of high-frequency performance occurs because the acoustic wavelength shortens as frequency increases. This demands higher response speed and calculation efficiency from the control system. Limited by existing algorithms and hardware, the active system’s time delay ( $T_{2}$ ) exceeds the critical threshold ( $T_{1}$ ), thereby causing noise reduction failure.

Figure 6.

Simulated values of static $T L$ of active array silencer.

Figure 7 presents the measured static $T L$ results for the active array silencer. The effective noise reduction band was concentrated between 90 Hz and 900 Hz. In this frequency band, the $T L$ increased by 7.5 dB to 24.5 dB, and the corresponding $T L$ increments of the unit length ( ${Δ T L}_{ul}$ ) was 5 dB/m to 16.3 dB/m. Both $Δ T L$ and ${Δ T L}_{ul}$ reached their maximum values at 309 Hz.

Figure 7.

Measured values of static $T L$ of active array silencer.

Table 3 lists the simulation values, measured values and absolute errors of static

Δ T L

and

{Δ T L}_{ul}

at the center frequency of each 1/1 octave band from 63 Hz to 500 Hz. Data shows that the simulation values of each frequency band are higher than the actual measured values, and the absolute error is less than 1.0 dB. This shows good agreement between simulation and experimental results.

Table 3.

Simulation values of static $Δ T L$ and ${Δ T L}_{ul}$ for active array silencer at each 1/1 octave band.

1/1 octave band center frequency (Hz)	Simulation values (dB)		Measured values (dB)		Absolute errors (dB)
1/1 octave band center frequency (Hz)	$Δ T L$	${Δ T L}_{ul}$	$Δ T L$	${Δ T L}_{ul}$	$Δ T L$	${Δ T L}_{ul}$
63	1.8	1.2	1.1	0.7	0.7	0.5
125	9.2	6.1	8.3	5.5	0.9	0.6
250	12.8	8.5	12.1	8.1	0.5	0.5
500	7.7	5.1	7.4	4.9	0.3	0.2

4.1.2. Dynamic transmission loss

Figure 8 presents the simulated velocity distribution cloud map within the array silencer at airflow velocities of 2 m/s, 4 m/s, and 6 m/s. Results indicate that the airflow velocity only changes the numerical size of the flow field and does not affect the overall shape of the flow field. This phenomenon is consistent with Wan’s conclusion²⁴ on the flow field analysis of exhaust silencer based on COMSOL acoustic flow coupling. This behavior stems from the principle that in geometrically similar systems, different flow velocities produce similar flow patterns.²⁵

Figure 8.

Velocity distribution cloud map.

Figure 9 compares simulated dynamic and static $T L$ of the active array silencer under 2 m/s co-flow (the direction of airflow is the same as sound propagation) and contra-flow (the direction of airflow is opposite to sound propagation) conditions. Compared to the no-flow condition, the upper frequency limit of the effective ANC noise reduction band decreased to 592 Hz under co-flow and to 261 Hz under contra-flow conditions. Table 4 shows $T L$ and ${Δ T L}_{ul}$ values at each 1/1 octave band with a center frequency of 63 Hz-500 Hz for the array silencer and active array silencer under 2 m/s airflow conditions. The data shows that after compounding ANC, under co-flow condition, the $T L$ of the array silencer increased by 42.9%, 88.3%, 25.3%, and 5.4% at the respective center frequencies, corresponding to ${Δ T L}_{ul}$ values of 0.2 dB/m, 3.5 dB/m, 3.9 dB/m, and 1.2 dB/m, respectively, and under contra-flow condition, the $T L$ increased by 18.2%, 37.5%, 5.6% and -15.2%, corresponding to ${Δ T L}_{ul}$ values of 0.1 dB/m, 1.6 dB/m, 0.9 dB/m, and -3.4 dB/m, respectively.

Figure 9.

Simulated values of dynamic $T L$ for active array silencer.

Table 4.

Simulation values of dynamic $T L$ and ${Δ T L}_{ul}$ for active array silencer at each 1/1 octave band.

1/1 octave band center frequency (Hz)	Array silencer $T L$ (dB)		Active array silencer $T L$ (dB)		${Δ T L}_{ul}$ (dB/m)
1/1 octave band center frequency (Hz)	Co-flow	Contra-flow	Co-flow	Contra-flow	Co-flow	Contra-flow
63	0.7	1.1	1	1.3	0.2	0.1
125	6	6.4	11.3	8.8	3.5	1.6
250	22.9	23.2	28.7	24.5	3.9	0.9
500	33.3	33.5	35.1	28.4	1.2	-3.4

This indicates that the airflow affects the propagation of sound waves and changes their dissipation pattern within the duct. When there is no flow, the propagation path of the sound wave is stable, and high-frequency sound waves are easily attenuated effectively; when there is airflow, high-frequency sound waves are scattered in the dynamic airflow due to the short wavelength, resulting in a decrease in the upper limit frequency of the effective noise reduction band. At the same time, airflow regeneration noise interferes with reference/error signal acquisition, reduces coherence and affects system stability, thereby reducing noise attenuation. Under contra-flow condition, the sound waves are affected by reverse airflow and aggravate the scattering attenuation,²⁶ further diminishing $T L$ .

Figure 10 shows measured $T L$ results when the air flow rate at the inlet end of the silencer is 2 m/s. The effective noise reduction frequency band of the ANC was 100 Hz-150 Hz. After compounding ANC, the $T L$ increased by 5 dB-10 dB, and ${Δ T L}_{ul}$ reached 3.3 dB/m-6.7 dB/m, peaking at 125 Hz for both. Compared to static conditions, in addition to background white noise, the flow regeneration noise leads to more complex time-frequency characteristics of the sound field, resulting in a reduced coherence between the reference signals and the error signals, ultimately weakening the effect of ANC.

Figure 10.

Measured values of dynamic $T L$ of active array silencer. (v = 2 m/s).

4.2. Influence of structural parameters on acoustic performance

Simulation studies based on the parameters in Table 2. Investigated the impact of flow-through ratio ( $r$ ), silencer column cross-sectional size ( $a$ ), and aspect ratio of anechoic column amount ( $A R$ ) on $Δ T L$ at each 1/1 octave band with a center frequency of 63 Hz-500 Hz. In the simulation, $r$ is 0.4 –0.75; $a$ is 0.1 m-0.3 m; $A R$ is typical values 1/12, 1/3 and 3/4. The simulation results are shown in Figures 10–12.

Figure 11 demonstrates that when $a$ and $A R$ are the same, $Δ T L$ shows a linear downward trend with increasing $r$ . Under the same $r$ , the $Δ T L$ reaches its maximum at 250 Hz octave band and minimum at 63 Hz octave band. This phenomenon occurs because reducing $r$ decreases the cross-sectional area of the effective airflow channel within the silencer, which is equivalent to an increase in the number of secondary sources per unit flow area, and thereby enhancing the ANC efficacy.

Figure 11.

Influence of r on $Δ T L$ .

Figure 12 demonstrates that when $r$ and $A R$ remain constant, $Δ T L$ exhibits a linear increase with decreasing $a$ . Under the same $a$ , the $Δ T L$ reaches its maximum at 250 Hz octave band and minimum at 63 Hz octave band. This phenomenon occurs because reducing $a$ decreases the effective airflow cross-sectional area within the silencer, which increases the number of secondary sources per unit flow area and thereby enhancing the ANC efficacy. It should be noted that adjusting $r$ or $a$ only changes $Δ T L$ magnitude and does not affect the frequency band where the maximum of $Δ T L$ ( ${Δ T L}_{\max}$ ) is located.

Figure 12.

Influence of a on $Δ T L$ .

Figure 13 demonstrates that with constant $r$ and $a$ , increasing $A R$ elevates $Δ T L$ in 63 Hz and 125 Hz octave band but reduces it at 250 Hz and 500 Hz octave band. As $A R$ decreases, ${Δ T L}_{\max}$ shows an upward trend, and the frequency band it is located moves toward the high frequency. This indicates that a greater difference between the number of rows and columns in the array of acoustic columns results in a higher optimal noise reduction frequency band for ANC. This frequency shift occurs because reducing $A R$ amplifies the width and height difference of the silencer cross-section, resulting in tighter packing of silencing units along the width/height directions, thereby enhancing $Δ T L$ . In actual engineering, large active array silencers can be divided into several rectangular active array silencers to increase their $T L$ .

Figure 13.

Influence of AR on $Δ T L$ .

5. Conclusions

This study constructed an active array silencer and quantitatively investigated its acoustic performance through simulations and experiments. The influence of key structural parameters, such as cross-sectional side length ( $a$ ) of anechoic columns, aspect ratio of anechoic columns amount ( $A R$ ) and flow-through ratio ( $r$ ), on the acoustic performance of the active array silencer was clarified. When $A R$ is 1/4, the results show that ANC enhances the static transmission loss per unit length of the passive array silencer by 5 dB-16.3 dB in the 90 Hz-900 Hz frequency range. Under co-flow at 2 m/s, ANC enhances the dynamic transmission loss per unit length by 3.3 dB-6.7 dB in the 100 Hz-150 Hz frequency range. Reducing $r$ , $a$ , or $A R$ consistently enhances transmission loss in the low frequency band, and adjusting $A R$ can directionally optimize the target noise reduction band. Active array silencers are suitable for scenarios with high airflow and high requirements for low-frequency noise reduction performance. Accordingly, the aerodynamic performance of the active array silencer can be further studied.

Footnotes

Acknowledgements

The authors acknowledge Professor Liu Bilong and Fengyan An of Qingdao University of Technology for providing experimental support for this work.

ORCID iD

Guoqing Di

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was funded by the scientific and technological project of State Grid Shaanxi Electric Power Co., Ltd., grant number 5226KY20001J.

Declaration of conflicting interests

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

Data Availability Statement

The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.*

References

Wang

Tang

. Transmission loss prediction on SIDO and DISO expansion-chamber mufflers with rectangular section by using the collocation approach. Int J Mech Sci 2007; 49: 872–877. https://doi.org/10.1016/j.ijmecsci.2006.11.007

Jie

. Ultra-broadband asymmetric acoustic transmission in a straight open duct. Appl Phys Express 2020; 13(6): 066501.

Kumar

Sharma

Singh

, et al. Development of muffler design and its validation. Appl Acoust 2021; 180: 108125.

Gao

Hou

, et al. Ventilation duct silencer design for broad low-frequency sound absorption. Appl Acoust 2023; 206: 109307.

Jin

Fang

, et al. Reconfigurable origami-inspired window for tunable noise reduction and air ventilation. Build Environ 2023; 227: 109808.

Fang

. Array Silencer. Chinese Patent CN200810066387.5, 2008.

Fang

. The application of array silencer performance curve in subway tunnel ventilation system. J Railw Sci Eng 2022; 19: 1794–1800 (In Chinese).

Zhao

Jiang

, et al. Calculation model of transmission loss for arrayed elements dissipative silencers. J Appl Acoust 2023; 42: 1264–1270 (In Chinese).

Boulandet

Meng

Goudé

. Optimization of a silencer design using an helmholtz resonators array in grazing incident waves for broadband noise reduction. Appl Acoust 2022; 201: 109131.

10.

Seo

Kim

. Design of silencer using resonator arrays with high sound pressure and grazing flow. Appl Acoust 2018; 138: 188–198. https://doi.org/10.1016/j.apacoust.2018.04.001

11.

. Handbook of Noise and Vibration Control Engineering. China Machine Press, 2002.

12.

Jabben

Verheijen

. Options for assessment and regulation of low frequency noise. J Low Freq Noise Vibration Active Control 2012; 31: 225–238. https://doi.org/10.1260/0263-0923.31.4.225

13.

Chen

. Active Noise Control. National Defense Industry Press, 2014.

14.

Papini

Pinto

Medeiros

, et al. Hybrid approach to noise control of industrial exhaust systems. Appl Acoust 2017; 125: 102–112. https://doi.org/10.1016/j.apacoust.2017.03.017

15.

Krüger

Castor

Jebasinski

. Active Exhaust Silencers - Current Perspectives and Challenges. SAE Tech Pap 2007; 1: 2204.

16.

Laugesen

. Active control of multi-modal propagation of tonal noise in ducts. J Sound Vib 1996; 195: 33–56. https://doi.org/10.1006/jsvi.1996.0402

17.

Chen

Liu

, et al. Optimization of Secondary Sources Configurations and Directivity Patterns for Active Noise Control in a Helicopter Cabin. In: Proceedings of the InterNoise 2017, Hong Kong, China, 27-30 August 2017, pp. 1996–2005.

18.

Larsson

Johansson

Håkansson

, et al. Microphone windscreens for turbulent noise suppression when applying active noise control to ducts. In: Proceedings of the 12th International Congress on Sound and Vibration, Lisbon, Portugal, 11-14 July 2005.

19.

Chang

Shyu

. A self-tuning fuzzy filtered-U algorithm for the application of active noise cancellation. IEEE Trans Circuits Syst I 2002; 49: 1325–1333. https://doi.org/10.1109/tcsi.2002.802350

20.

Liu

Qiu

. Position optimization for secondary speaker and error sensor of duct active noise control system. J Tsinghua Univ (Sci Technol) 2011; 51: 382–389.

21.

Shen

Guo

, et al. Multi-channel adjoint least mean square algorithm with momentum factor applied on active noise control. Mech Syst Signal Process 2025; 228: 112415. https://doi.org/10.1016/j.ymssp.2025.112415

22.

Delany

Bazley

. Acoustical properties of fibrous absorbent materials. Appl Acoust 1970; 3(2): 105–116. https://doi.org/10.1016/0003-682x(70)90031-9

23.

Bies

Hansen

. Flow resistance information for acoustical design. Appl Acoust 1980; 13(5): 357–391. https://doi.org/10.1016/0003-682x(80)90002-x

24.

Wan

. Structural Analysis of Automotive Exhaust Silencer Based on Acoustic-Flow-Thermal Multiphysics Coupling. Master’s Thesis, East China Jiaotong University, 2020.

25.

Duan

. Similarities of flow and heat transfer around a circular cylinder. Symmetry 2020; 12: 658. https://doi.org/10.3390/sym12040658

26.

Piana

Carlsson

Lezzi

, et al. Silencer design for the control of low frequency noise in ventilation ducts. Designs 2022; 6: 37. https://doi.org/10.3390/designs6020037