Simplified Method of Simulating Double-Layer Micro-Perforated Panel Structure
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Abstract
The micro-perforated panel (MPP) structure has been widely used in various noise control applications, and thus its acoustic performance prediction has been receiving increasing attention. The acoustic performance of simple MPP structures, such as a MPP sound absorber, has been predicted using an analytical calculation method. However, this is not a suitable approach toward predicting the acoustic performance of complicated MPP structures, owing to the structural complexity of these structures. Moreover, the many perforations of submillimeter scale diameter render the MPP structures very difficult to analyze using numerical simulation. Thus, this study focused on two different simplified MPP simulation methods: the transfer admittance method and the equivalent fluid method, and their application on double-layer MPP structures. Based on the two simplified MPP simulation methods, the transmission loss value of the double-layer MPP mufflers with two sets of different structural parameters was calculated, respectively. The predicted results were compared with the impedance tube measurements. The results revealed that the two simplified MPP simulation methods could effectively predict the acoustic performance of double-layer MPP structures. Moreover, the prediction based on the transfer admittance method can outperform the two simplified simulation methods.
Keywords
Double-layer MPP structure Acoustic simulation Transfer admittance Porous material Experimental testList of symbols
- MPP
Micro-perforated panel
- FEM
Finite element method
- CFD
Computational fluid dynamics
- t
Panel thickness
- d
Perforation diameter
- p
Perforation ratio
- D_{1}, D_{2}
Cavity depth
- b
Perforation spacing
- TL
Transmission loss
- v_{n1}, v_{n2}
Normal particle velocity
- α_{1}, α_{2}, α_{3}, α_{4}, α_{5}, α_{6}
Transfer admittance coefficient
- p_{1}, p_{2}
Sound pressure
- β
Transfer admittance
- K
Diameter ratio
- Z
Specific acoustic impedance
- R
Specific acoustic resistance
- X
Specific acoustic reactance
- η
Dynamic viscosity
- ρ
Air density
- ω
Angular frequency
- f
Frequency
- φ
Porosity
- σ
Flow resistivity
- α_{∞}
Tortuosity
- ε_{e}
Correction length
- A_{v}
Viscous characteristic length
- A_{t}
Thermal characteristic length
1 Introduction
The micro-perforated panel (MPP) structure is very promising as the basis for the next generation of sound absorbing constructions. This structure has enough acoustic resistance and sufficiently low acoustic reactance to provide good absorption properties by reducing the perforation diameter to submillimeter scale. The MPP combined with a uniform air-back cavity and a rigid back wall can be used to construct conventional single-layer MPP sound absorbers, which were first proposed by Maa [1]. Based on Maa’s pioneering work, many theoretical methods have been proposed to predict the acoustic performance of MPP sound absorbers. The most common method is the acoustic-electric analogy method [2, 3, 4], which has been used to calculate the normal sound absorption coefficient of many different types of MPP sound absorbers. The transfer matrix method [5, 6] has also been used to predict the sound absorption performance of a single-layer MPP sound absorber or a multilayer MPP sound absorber. Additionally, the impedance transfer method [7, 8] has been used to calculate the surface acoustic impedance of MPP sound absorbers. In summary, the acoustic performance of simple MPP sound absorbers can be easily predicted based on the abovementioned analytical calculation methods. However, in practical applications, MPPs are more often applied to a complicated muffler, with a complex interior structural environment. Moreover, the incidence sound wave is also more frequently subject to an oblique incidence condition. Therefore, in these cases, it is not suitable to use any of the commonly used analytical calculation methods to predict the overall acoustic performance of the MPP structures.
To ensure the prediction accuracy, many scholars have used the acoustic finite element method (FEM) to simulate the acoustic performance of MPP structures. For example, Gerdes et al. [9] established a geometrical perforation model and adopted a computational fluid dynamics (CFD) approach to calculate the acoustic transfer impedance of a MPP. Subsequently, they used the acoustic transfer impedance results to describe the MPP layer in the finite element (FE) model of a MPP sound absorber. However, the large number of perforations in the MPP increased the difficulty of the geometrical modeling process, which in turn increased considerably the complexity of the entire simulation calculation.
To avoid the geometry modeling of massive perforations, Zuo et al. [10] first obtained the acoustic impedance of a MPP according to Maa’s formula and then simulated the MPP by defining the transfer admittance relationships between both of its sides such that the transmission loss of a single-layer MPP muffler could be predicted. From a different perspective, Atalla [11] proposed that a rigid perforated plate could be modeled as an equivalent fluid by following the Johnson–Allard approach, given that the equivalent tortuosity is appropriately defined. Thus, it becomes possible to use the existing finite element models of rigid porous materials to model rigid MPPs. On the basis of Atalla’s idea, Hou [12, 13] further expanded the modeling method and demonstrated that a flexible MPP can be modeled in a similar manner by using poro-elastic finite elements, which allow the prediction of the panel’s structural resonances. The two abovementioned simplified MPP simulation methods have been applied to the acoustic prediction of single-layer MPP structures. However, this application has not yet been investigated for complicated MPP structures, such as a double-layer MPP muffler. Moreover, many studies have focused only on one of these two simplified MPP simulation methods, and little effort has been put into investigating them simultaneously and comparing their accuracy. To fill this research gap, the two abovementioned simplified MPP simulation methods were used, respectively, to predict the acoustic performance of double-layer MPP mufflers with a wide silencing bandwidth.
In this study, first, the double-layer MPP structures were introduced. Then, the transmission loss of one double-layered MPP muffler was predicted using the transfer admittance method and the equivalent fluid method, respectively. The muffler was tested with an impedance tube to validate the predicted results. Additionally, the other muffler with different structural parameters was treated in a similar manner to further validate the results.
2 Double-Layer MPP Structures
2.1 Double-Layer MPP Sound Absorber
2.2 Double-Layer MPP Muffler
Muffler’s MPP structural parameters and cavity depths
t (mm) | d (mm) | p (%) | D_{1} (mm) | D_{2} (mm) |
---|---|---|---|---|
0.5 | 0.58 | 8.26 | 9 | 1.8 |
The transmission loss is determined by the structure of the muffler and is often used to evaluate its acoustic performance [17, 18, 19]. Thus, we focused on the transmission loss. The transmission loss value of the double-layer MPP muffler was calculated and measured, as will be discussed below.
3 Numerical Simulation Using Transfer Admittance Method
3.1 Transfer Admittance of MPP
3.2 Transmission Loss Calculation
Acoustic impedance of MPP
Frequency (Hz) | Acoustic resistance | Acoustic reactance |
---|---|---|
10 | 11.8196 | 1.0791 |
20 | 12.4082 | 2.1553 |
30 | 12.8730 | 3.2286 |
… | … | … |
6990 | 64.9178 | 674.9958 |
7000 | 64.9616 | 675.9426 |
4 Numerical Simulation by Equivalent Fluid Method
4.1 Porous Material Model
A porous material consists of a frame and a fluid medium. Johnson-Champoux-Allard porous material models are categorized into three types according to frame stiffness; namely the rigid model, limp model, and elastic model [21].
The rigid porous material model ignores the frame deformation, and its acoustic performance depends on the fluid parameters (sound velocity, mass density, specific heat ratio, Prandtl number, and dynamic viscosity) and the pore parameters (porosity, flow resistivity, tortuosity, and viscous and thermal characteristic lengths). In this case, sound absorption was produced by the air’s viscous resistance, which is similar to the sound absorption principle of the MPP. Based on the rigid porous material model, the limp porous material model considers the influence of the inertial load on the acoustic wave. Thus, it has an additional characteristic parameter (frame density), which refers to that of a rigid porous material model. Among the three models, the elastic porous material model is the most complicated. Considering the frame vibration effect under acoustic loading, the elastic model has three additional characteristic parameters (frame density, Young’s modulus, and Poisson’s ratio), which refer to those of the rigid porous material model.
4.2 MPP Equivalent Porous Material Model
The three porous material models correspond to three MPP equivalent porous material models, respectively [12, 13]. An appropriate MPP equivalent porous material model was selected based on the material properties of the MPP. During the parameter conversion, the panel density was considered in the limp MPP equivalent porous material model, and the panel density, Young’s modulus, and Poisson’s ratio were considered in the elastic MPP equivalent porous material model.
4.3 Transmission Loss Calculation
Parameters of MPP equivalent porous material model
φ (%) | σ (Pa·s· m^{−2}) | α _{∞} | A_{v} (mm) | A_{t} (mm) |
---|---|---|---|---|
8.26 | 20,959.71 | 1.66 | 0.29 | 0.29 |
5 Experimental Verification
Second muffler’s MPP structural parameters and cavity depths
t′ (mm) | d′ (mm) | p′ (%) | D_{1}′ (mm) | D_{2}′ (mm) |
---|---|---|---|---|
0.5 | 0.5 | 4.91 | 9 | 1.8 |
6 Conclusions
- (1)
The transfer admittance method and the equivalent fluid method both provide an easy and efficient approach toward predicting the acoustic performance of double-layer MPP structures.
- (2)
Acoustic prediction based on the transfer admittance method may be more accurate than that based on the equivalent fluid method at the peaks and dips of TL curve.
Notes
Acknowledgements
This study was supported by the National Key Laboratory Open Foundation of Tractor Power System (Grant No. SKT2017012) and the National Natural Science Foundation of China (Grant No. 51575410).
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