Investigation into Modeling of Multi-Perforated Mufflers
Elnady, Tamer, Elsaadany, Sara, and Åbom, Mats, 16th International Congress of Sound and Vibration, Krakow (2009),
There is a strong competition among automotive manufacturers to reduce the radiated noise levels. One main source is the engine where the main noise control strategy is by using efficient mufflers. Resistive mufflers are now widely used to attenuate IC-Engine noise due to its better performance over the reactive ones. Resistive damping can be achieved either by using absorbing material or perforates in the form of tubes or sheets. Perforates mufflers have an increased performance with flow when the acoustic impedance is increased by introducing flow through the perforate holes. On the other hand, perforates can deteriorate the engine performance, if badly designed, by increasing the flow back pressure. Modeling of perforated mufflers started in the seventies when simple geometries were used. There were two approaches to analyze two tubes connected with a perforate (i.e. four-port), segmentation and distributed. Both approaches were limited to a few specified geometries. Recently, the authors published a new technique based on the segmentation approach where four ports can be replaced by a number of two-ports so that it can be used in general two-port codes. This paper investigates the use of these techniques in modeling complex perforated muffler geometries. Fifteen different configurations were modeled and compared to measurements. There are some limitations to the use of these models in some configurations because of strong 3D effects that limits the validity of these models to almost half the plane wave region. These configurations are mainly the double plug flow muffler and the parallel tube mufflers.
Perforates tubes are commonly used inside automotive mufflers. They can be found in the form of perforated tubes to confine the mean flow in order to reduce the back-pressure to the engine and the flow generated noise inside the muffler. They can also be used to provide resistive damping to enhance the acoustic performance. On the other hand, if the flow is forced through the perforates, this provides a significant back pressure on the engine. Being able to theoretically model these mufflers enables car manufacturers to optimize their performance and increase their efficiency in attenuating engine noise, and at the same time minimize the back pressure exerted on the engine. Therefore, there has been a lot of interest to model the acoustics of two ducts coupled through a perforated plate or tube.
This paper presents new technique uses a two-port transfer matrix to model both the perforated branches and the intermediate hard pipe segments. This new technique is more flexible as it facilitates the modeling of perforated pipes with an arbitrary configuration within a muffler. The calculations were done using SIDLAB computer software for modeling low frequency sound propagation in complex duct networks.
In order to achieve acceptable accuracy, we need to have more segments which results in an increased number of two-ports that must be added to the network. Within the work done in this paper, the technique is coded into SIDLAB so that the associated two port network for each four or six port elements is generated automatically and all the element properties are calculated accordingly.
The objective of this paper is to try this technique on a verity of muffler types and configurations in order to determine its limitations, if any. A number of 15 different muffler configurations were tested and some limitations were identified in some complex muffler geometries due to 3D effects that start to deteriorate the plane wave assumption. These cases were verified by comparison to Finite Element results.
Two parameters were measured for each muffler:
- The Acoustic Transmission Loss This is done using six microphones, two on each side of the muffler in order to cover wider frequency range. The two-source technique was used and the wave decomposition inside each duct was done using the two-microphone technique. Transmission Loss was measured at no flow and at a few flow speeds.
- The flow-pressure drop curve or the characteristic flow curve of the muffler. This is done by measuring the static pressure drop across the muffler and plotting it against the inlet flow speed. The pressure drop is measured through two tubes that are connected to a digital manometer. The flow speed is measured using a Pitot tube.
Several muffler types were tested where perforates are used in different configurations. Some parameters for a few of these mufflers could be changed; e.g. porosity, flow direction …etc. The following perforated mufflers were tested:
- Through flow muffler:
Three configurations of through flow mufflers were tested. Two of them had the same overall dimensions but with different perforate porosity [Length = 0.2 m, Diameters = 0.057/0.197 m, perforate thickness = 1.4 mm, perforate hole diameter = 4 or 5 mm resulting in porosity 5.5 or 12%]. The third configuration had different overall dimensions and was tested twice; one with absorbing material in the cavity and one without [Length = 0.31 m, Diameters = 0.057/0.197 m, perforate thickness = 1.5 mm, perforate hole diameter = 5 mm, porosity 28%].
- Muffler with perforated plate filled with absorbing material:
This type is the only one where the perforates are introduced as a baffle and not as a perforated tube, the overall dimensions are as follows [Length = 0.3 m, Diameters = 0.057/0.197 m, perforate thickness = 1.5 mm, perforate hole diameter = 5 mm, porosity 32%]. This muffler was measured in both flow directions.
- Plug flow muffler with one perforated pipe: In this type, there is a plug in the flow path in order to force the flow to enter through the perforates, two configurations were tested with the same overall dimensions but with different perforate porosities. The overall dimensions are as follows [Length = 0.2 m, Diameters = 0.057/0.197 m, perforate thickness = 1.4 mm, perforate hole diameter = 5 mm, porosity 32%].
- Two plugs flow muffler with one perforated pipe: This type is very similar to the previous one except that there are two plugs in the flow path forcing the flow through the perforate twice (Figure 4). Two configurations were tested with different perforate porosities. The overall dimensions are as follows [Length = 0.257 m, Diameters = 0.057/0.197 m, perforate thickness = 1.2 mm, perforate hole diameter = 4 mm, porosity 14 or 28%].
- Eccentric muffler with two perforated pipes:
This type has two parallel perforated pipes, where flow is forced to exit from the inlet pipe to enter into the outlet pipe through the perforates (Figure 5). Two configurations were tested with the same overall dimensions and different perforate porosities [Length = 0.257 m, Diameters = 0.057/0.197 m, perforate thickness = 1.4 mm, perforate hole diameter = 5 or 8 mm resulting in porosity 4.8 or 5.4%].
- Eccentric muffler with plugs:
This type is the most complex one. It has two eccentric perforated pipes plus two chambers with plugs at the end of the pipes (Figure 6). The overall dimensions are as follows [Length = 0.504 m, Diameters = 0.057/0.197 m, perforate thickness = 1.4 mm, perforate hole diameter = 5 mm, porosity 24%].
Two results are shown for each muffler configuration, pressure drop curve and transmission loss. The transmission loss will be shown at no flow and at one flow speed. The vertical dotted line shows the plane wave limit for the shown muffler.
The acoustic simulations were performed using SIDLAB Simulation, whereas the flow simulations were done using the SIDLAB Flow module. The acoustic measurements were calculated from the raw transfer functions between the microphones using SIDLAB Measurement.
Figure 8 Comparison between the measured Transmission Loss for selected mufflers at zero flow and that simulated using SIDLAB Acoustics.
The main results of this study are presented in Figures 7 to 9. Figure 7 compares the flow pressure drop curve for the muffler with that calculated by SIDLAB Flow. Figure 8 and Figure 9 compares the Transmission Loss to that calculated by SIDLAB Acoustics at zero flow and at M = 0.1 flow, respectively. The vertical line in the TL plots indicates the plane wave region.
Figure 9 Comparison between the measured Transmission Loss for selected mufflers with flow [M = 0.1] and that simulated using SIDLAB Acoustics
The flow-pressure drop curves for all the shown muffler configurations show good agreement with the simulations. There are some limitations with when comparing the Transmission Loss. For the first three cases where the muffler geometry is relatively simple: the through flow muffler, the perforated plate muffler, and the on-plug flow muffler, the technique works very well up to the plane wave region until the first higher order mode is cut-on. This fact applies with or without flow, empty or filled with absorbing material. For the two plugs flow muffler, the TL simulation at no flow shows discrepancy with the measurement. This is due to strong 3D effects that occur at the end of the first chamber that affect the sound propagation in the second chamber. The no flow case is however of less interest. When flow is introduced, the acoustic resistance of the perforates increases, dominates the acoustic behavior, and masks the previously mentioned effects resulting in a good agreement. For eccentric mufflers, the first higher order mode is cut-on much earlier resulting in higher discrepancy in the plane wave region. It can be concluded that the proposed technique always works well up to half the plane wave region in the case of flow.