Transmission loss (TL) is often used to evaluate the acoustic attenuation performance of a silencer. In this work, a three-dimensional (3D) finite element method (FEM) is employed to calculate the TL of some representative silencers, namely, circular expansion chamber silencer and straight-through perforated pipe silencer. In order to account for the effect of mean flow that exists inside the silencer, the 3D FEM is used in conjunction with the Computational Fluid Dynamics (CFD) simulation of the flow field. More concretely, the 3D mean flow field is computed by firstly using CFD, and then the obtained mean flow data are imported to an acoustic solution undertaken using FEM. The data transfer between the two steps is accomplished by mesh mapping. The results presented demonstrate good agreement between present TL predictions and previously published experimental and numerical works. Also, the details of the flow inside the silencers may be studied. Furthermore, the effect of mean flow velocity on acoustic attenuation performance of the silencers is investigated. It is concluded that for the studied silencers, in general, increasing flow velocity increases the TL and decreases the resonance peaks.
It is common for silencing devices to be used to attenuate exhaust noise generated by vehicles and various fluid machines. It is well known that the silencer is always accompanied with mean gas flow in practical application. Many studies, including theoretical and experimental methods, had been conducted to investigate the acoustic attenuation performance of the silencer with mean flow during the past years [
FEM was initially applied to predict the acoustic performance of mufflers by Young and Crocker [
In the aforementioned works, the applications of FEM mainly focus on predicting TL in silencers without mean flow. Of course, FEM is capable of considering the effect of mean flow by assuming that the acoustic field is superimposed over the decoupled mean flow, but this mean flow must be imported from an external steady flow computation that is often performed by a simplified potential-flow approach [
In present work, the circle expansion chamber silencer with extended inlet used in [
Dimensions for the silencers considered (unit: mm).
Silencer |
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Expansion chamber | 108 | 40 | 208 | 52 | — | — |
Perforated pipe 1 ( |
110 | 32 | 200 | — | 4 | 4.7 |
Perforated pipe 2 ( |
110 | 32 | 200 | — | 6 | 9.0 |
Perforated pipe 3 ( |
110 | 32 | 200 | — | 8 | 14.7 |
Geometries of the silencers considered: (a) circle expansion chamber silencer and (b) straight-through perforated pipe silencer.
Tetrahedral mesh is chosen to discretize the computational field of the silencer due to its high flexibility. Two different meshes, namely, CFD mesh and acoustic mesh, will be used for the solution of mean flow and acoustic problems, respectively. For the expansion chamber silencer, the element sizes of CFD and acoustic meshes are 4 mm and 8 mm, respectively, and the CFD mesh is composed of 131111 nodes and 406204 elements; the acoustic mesh is composed of 51972 nodes and 35807 elements. For the straight-through perforated pipe silencer whose geometry is relatively complex, the computational model is split into several parts to generate mesh individually in order to decrease computational cost. An element size of 2 mm is used for the perforation area in both CFD and acoustic meshes, and the element sizes for the rest of the two meshes are 4 mm and 10 mm, respectively. Take silencer
Figures
Geometry of meshes for the expansion chamber silencer: (a) CFD mesh and (b) acoustic mesh.
Geometry of meshes for the straight-through perforated pipe silencer: (a) CFD mesh and (b) acoustic mesh.
In the CFD steady flow computation, the data type used is double precision, the solver implemented is a pressure-based implicit solver, SIMPLEC pressure-velocity coupling algorithm is chosen with second-order scheme for spatial discretisation, and the realizable
The data transfer between acoustic and mean flow problems is accomplished by mesh mapping function that Virtual.Lab provides. Because there is no one-to-one correspondence between nodes of generated CFD and acoustic meshes, an appropriate mapping algorithm should be employed. In this paper,
The transferred value on the target node is then
After finishing the data transfer, the acoustic response analysis is performed with 10 Hz spacing using FEM. For the sound field inside the silencer, the governing formulation is Helmholtz equation as [
Theory for TL calculation.
In the frequency range of interest for silencer analysis, these acoustic pressure waves typically travel through the inlet and outlet pipes as plane waves [
Following the calculation steps stated in Section
Counters of velocity-magnitude for the expansion chamber silencer with inlet flow velocity of
Counters of turbulent kinetic energy for the expansion chamber silencer with inlet flow velocity of
Velocity-vectors for the straight-through perforated pipe silencers: (a) silencer
Velocity-vector
Velocity-vector
Velocity-vector
Counters of turbulent kinetic energy for the straight-through perforated pipe silencers: (a) silencer
Turbulence kinetic energy
Turbulence kinetic energy
Turbulence kinetic energy
After importing the mean flow data to the acoustic field by mesh mapping, acoustic response analysis is performed to acquire acoustic pressure at the inlet and outlet as shown in Figures
Acoustic pressure level for the inlet and outlet of the expansion chamber silencer with inlet flow velocity of
Acoustic pressure level for the inlet and outlet of the straight-through perforated pipe silencers: (a) silencer
Figure
Measured and predicted TL for the expansion chamber silencer with inlet flow velocity of
In Figure
Measured and predicted TL for the straight-through perforated pipe silencers: (a) silencer
At present, with the development of computer performance, the full time-domain CFD method, such as that performed in [
Two main effects of mean flow on silencer acoustic performance can be distinguished: one is to affect the sound propagation in the silencer (stated in Section
Figure
Effect of flow velocity on TL of the expansion chamber silencer.
Effect of flow velocity on TL of the straight-through perforated pipe silencers: (a) silencer
In this paper, a 3D numerical method is employed to investigate the acoustic attenuation performance of a circular expansion chamber silencer with extended inlet and three straight-through perforated pipe silencers in the presence of mean flow. By decoupling the problem, the linear acoustics are away from the mean flow computation. CFD and FEM are employed to perform the steady flow computation and acoustic response analysis, respectively. The data transfer is accomplished by mesh mapping. A comparison between present results and previously published experimental and numerical results indicates that the present 3D numerical method is capable of delivering reasonable predictions. The major advantage of present method is that it is accessible and easy to use and avoids complex mathematical calculation with the help of simulation software, especially for the perforated pipe silencer, while the major drawback of this method lies in the considerable computational effort and cost that are required to acquire a complete and accurate solution in the 3D calculations.
Furthermore, the TL of studied silencers with different flow velocities is calculated. It is concluded that the presence of mean flow decreases the resonance peak and increases the acoustic attenuation at most frequencies for the expansion chamber silencer. For the straight-through perforated pipe silencer, mean flow has little influence on the acoustic attenuation in the plane wave range and remarkably decreases the resonance peak and increases the acoustic attenuation at higher frequencies.
The authors declare that there is no conflict of interests with regard to this study and the publication of this paper.
The authors are grateful for the grants from National Natural Science Foundation of China (51275082, 11272273), Fundamental Research Fund of Central Universities (N130403009), Research Fund for Doctoral Program of Higher Education (20100042110013), and Program for Liaoning Innovative Research Team in University (LT2014006).