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Measurement and Simulation of Two-Inlet Single-Outlet Mufflers
Elsahar, W. and Elnady, T., “Measurement and Simulation of Two-inlet Single-Outlet Mufflers,” SAE Int. J. Passeng. Cars – Mech. Syst. 8(3):2015, doi:10.4271/2015-01-2316

Abstract

In several applications, two-inlet single-outlet mufflers are possible to encounter in exhaust systems. They are usually used to merge two exhaust streams from two similar engines or from two sides of an engine. They have an advantage of reducing the back pressure on the engine(s). There is a lot of published research on the analysis of single-inlet single-outlet mufflers acting as a two-port. On the other hand, there are a few publications on the analysis of two-inlet single-outlet mufflers due to their complexity representing a three-port. A three-port is characterized by a 3×3 Scattering Matrix. The nine elements of this matrix represent the 3 reflection coefficients at each port, and the 6 transmission coefficients between the 3 ports in both directions. In this work, a two-inlet single-outlet muffler is studied. The elements of the scattering matrix were measured using the two-source two-microphone technique with and without flow. These elements were also calculated from 1D simulation using a set of two-port elements representing the internal dimensions of the muffler, and compared to those obtained from the measurement. A similar 1D simulation was performed using Flow two-ports in order to analyze the flow distribution inside the muffler and the pressure drop across both flow paths. The flow distribution is crucial to obtain accurate acoustic predictions. For all cases, there was a very good agreement between the measurement and the simulations.

Introduction

The two-inlet single-outlet muffler configuration, is one of the common muffler forms used in exhaust systems. This configuration is usually used with V-type engines, where each bank of cylinders is connected to a separate exhaust pipe. This allows merging two streams of exhaust gas, while introducing low engine back pressure. The introduced back pressure is usually lower than the back pressure caused by other merging approaches such as using a Y-type junction. Moreover, this is a good alternative to a dual exhaust system, having a separate muffler connected to each of the two exhaust pipes.In this work, a two-inlet single-outlet muffler was studied. The acoustic performance of the muffler was defined by a multi-port scattering matrix. The elements of the scattering matrix were determined experimentally using a set of two-source two microphone measurements with and without mean flow. Similarly, the scattering matrix of this muffler was calculated from a set of 1D acoustic two-port simulations and the results were compared to measurements. A similar 1D simulation was performed using Flow two-ports in order to analyze the flow distribution inside the muffler and the pressure drop across both flow paths, as the flow distribution is crucial to obtain accurate acoustic predictions for the with flow case study.

Two-Inlet Muffler Two-Port Model

For this three-port element, the elements of the 3×3 scattering matrix can be obtained using a combination of measurement steps, where the pressure values are measured simultaneously at two ports only and the third port is connected to a long pipe extension to reduce the reflections at this port. A two-port model was constructed for each of the measurement steps described before. SIDLAB, which is a software based on the two-port theory and implements the formulism developed by Glav and Åbom, was used for these simulations. Figure 1 shows a detailed section view for the muffler considered for this study.

Figure 1 Detailed section view of the studied muffler.

The two-port network is the same for all the steps, but the terminations of the two-port network were reconfigured for each study step. Different volumes inside the muffler were discretized into acoustic two-ports as shown in Figure 2.

Figure 2 Schematic showing the studied two-inlet muffler divided into volumes, to be represented as two-port elements.

For step 1 the two-port network is shown in Figure 3. The elements are indexed according to the corresponding volumes numbered in Figure 2. Consider the muffler to be divided into three main chambers, the first chamber from the left where inlet A is extended into, the last chamber to the right where inlet B is extended into and the middle chamber where the outlet pipe is extended from. The three chambers are separated by two perforated plates represented by elements 10 and 12.For study step 1 as shown in Figure 3, the upstream point of the two-port network was set to node number 1 (inlet A), the downstream was set to node number 11 (inlet B) and node 15 from the outlet pipe was connected to the pipe extension element number 16 and the one port open end termination element number 1. Similarly, study steps 2 and 3 were configured as shown in Figure 4 and Figure 5.

Figure 3 Two-port network representation for the two-inlet muffler in study step 1.

 

Figure 4 Two-port network representation for the two-inlet muffler in study step 2.

Figure 5 Two-port network representation for the two-inlet muffler in study step 3.

Experimental setup

The two source two-port measurement technique was used to extract the scattering matrices from the 3 study steps described earlier. SIDLAB Acquisition software and SIDLAB Rig hardware configuration was used for these measurements. The measured two-port element is mounted between two measurement sections, upstream and downstream. Each measurement section consists of a 25 mm hard walled pipe, to this pipe three ¼ inch (6.35 mm) microphones are mounted flushed to the internal diameter of the pipe and a loudspeaker is mounted after these microphones. The end of this pipe is connected to a muffler to reduce end reflections.For each of the proposed configurations, measurements were performed with both inlets of the muffler (A and B) connected to a silent flow source with similar flow speed of 0.01 kg/sec supplied to each inlet. The speed of the supplied air flow was measured using two in-duct flow meters. Figure 6 shows a picture of the test rig used for measurements.

Figure 6 Two-inlet muffler two-port measurement test rig. The figure shows the setup configuration used for measurement.

Results

For this case study, the 9 elements of the scattering matrix were considered for comparison between two-port simulations and measurements. Figures 7, 8, 9 show the reflection and transmission coefficients obtained from different measurement steps, comparing measurements to two-port simulations with no mean flow. For the same case study, the transmission loss for each study step was calculated using FEM (Finite Element Method). FEM software COMSOL was used to obtain these results. FEM results are also included in this comparison.Figure 7 shows the reflection coefficient (R1) at inlet A, calculated from the first measurement step. The measurements agree well with the two-port simulation using SIDLAB within the plane wave range. The plane wave limit is indicated by the vertical red dotted line.Figure 8 shows the reflection coefficient (R2) at inlet B, calculated from the first measurement step. The measurements agree well with the two-port simulation using SIDLAB within the plane wave range.


Figure 7 Reflection coefficient at inlet A (R1). A comparison between two-port simulation and measurements.

 

Figure 8 Reflection coefficient at inlet B (R2). A comparison between two-port simulation and measurements.

Figure 8 Reflection coefficient at inlet B (R2). A comparison between two-port simulation and measurements.

Figure 9 shows the reflection coefficient (R3) at the outlet pipe, calculated from the second measurement step. The measurements agree well with the two-port simulation using SIDLAB within the plane wave range.

Figure 9 Reflection coefficient at the outlet (R3). A comparison between two-port simulation and measurements.

Figures 10 to 11 show the transmission loss between different ports of the two-inlet muffler. Figure 12 shows the transmission loss between inlet A and Inlet B, comparing measurements to two-port simulations with no mean flow. The FEM results are also included in this comparison. The measurements and FEM results matches well within the plane wave range. On the other hand, the two-port simulation showed a shift in frequency between the first peak from 620 to 735 Hz and shift in the preceding trough from 850 to 910 Hz. Otherwise, the two-port results follow the same transmission loss profile as the other cases.

Figure 10 Transmission loss between inlet A and Inlet B. A comparison between two-port simulation, FEM and measurements.

Figure 11 Transmission loss between inlet A and outlet. A comparison between two-port simulation, FEM and measurements.

Figure 12 Transmission loss between inlet B and outlet. A comparison between two-port simulation, FEM and measurements.

Figure 10 shows the transmission loss between inlet A and the outlet. The measurements and FEM results matches well within the plane wave range. However, the level of the transmission loss between 380 and 1260 Hz is slightly lower for the FEM results. Again in this step, the two-port simulation showed a shift in frequency. There is a frequency shift in the first trough from 380 to 520 Hz. Otherwise, the two-port results follow the same transmission loss profile as the other cases.Figure 12 shows the transmission loss between inlet B and the outlet. The measurements and FEM results matches well within the plane wave range. However, the peak at 710 Hz does not appear in both the FEM and two-port models. Instead, there is another peak around 990 Hz that does not exist in the measurements. Similar to the previous transmission loss values, the two-port simulation showed a shift in frequency. There is a frequency shift in the first trough from 380 to 520 Hz.The results shown earlier were conducted with no mean flow inside the muffler. The following shows similar results, where simulations and measurements were conducted at inlet flow rate 0.01 kg/sec supplied to each inlet. Figure 13 shows the reflection coefficient (R1) at inlet A, calculated from the first measurement step. The measurements agree well with the two-port simulation using SIDLAB within the plane wave range.

Figure 13 Reflection coefficient at inlet A (R1). A comparison between two-port simulation, FEM and measurements at inlet mass flow 0.01 kg/sec.

Figure 14 shows the reflection coefficient (R2) at inlet B, calculated from the first measurement step. The measurements agree well with the two-port simulation using SIDLAB within the plane wave range.

Figure 14 Reflection coefficient at inlet B (R2). A comparison between two-port simulation and measurements at inlet mass flow 0.01 kg/sec.

Figure 15 shows the reflection coefficient (R3) at the outlet, calculated from the second measurement step. The measurements agree well with the two-port simulation using SIDLAB within the plane wave range.

Figure 15 Reflection coefficient at the outlet (R3). A comparison between two-port simulation and measurements at inlet mass flow 0.01 kg/sec.

Figures 16, 17, 18 show the transmission loss between different ports of the two-inlet muffler. Figure 16 shows the transmission loss between inlet A and Inlet B comparing measurements, two-port and FEM results. The transmission loss measurements agree well with the two-port simulation using SIDLAB up to 800 Hz. FEM results agree well slightly more in the frequency range.

Figure 16 Transmission loss between inlet A and Inlet B. A comparison between two-port simulation, FEM and measurements at inlet mass flow 0.01 kg/sec.

Figure 17 shows the transmission loss between inlet A and outlet comparing measurements, two-port and FEM results. The transmission loss measurements agree well with the two-port simulation for configuration 2 up to 1200 Hz.

Figure 17 Transmission loss between inlet A and outlet. A comparison between two-port simulation, FEM and measurements at inlet mass flow 0.01 kg/sec.

Figure 18 shows the transmission loss between inlet A and outlet comparing measurements, two-port and FEM results.

Figure 18 Transmission loss between inlet B and outlet. A comparison between two-port simulation, FEM and measurements at inlet mass flow 0.01 kg/sec.

In all with flow cases the measurements tend to be incoherent above 900Hz. Starting from this limit the flow generated noise inside the duct is much higher than the source noise produced from the exciting loudspeakers. The loudspeakers used in this setup are more powerful in the low frequency range and they fail to produce sound pressure levels that are sufficient to mask the flow generated noise at higher frequencies.

In Figures 17 and 18, the FEM results seem to be over predicting the transmission loss within the range from 200 to 1200Hz. These higher transmission loss values are caused by the over estimation of the flow speed going through some perforated areas in FEM flow calculations. This resulted in overestimating the acoustic impedance at some regions of the perforated areas and thus increasing the transmission loss at this frequency range. Otherwise, the transmission loss measurements agree well with the two-port simulations for configuration 3 up to 900 Hz.

Observing several transmission coefficient values in both no flow and with flow cases. It can be noticed that, the frequency shift in the simulated transmission coefficients disappeared when flow was introduced to the system. When flow is introduced, the acoustic impedance of the perforates increases and dominates the acoustic behavior of the muffler, masking the shift in frequency. In similar muffler case studies were conducted showing similar behavior.