Flow and Pressure Drop Calculation Using Two-Ports
Abosrea, A., ElSallamy, W., and Elnady, T., “Flow generated noise inside mufflers,” INTERNOISE, California, 2015.
One of the factors that can limit muffler performance is flow generated noise. If not designed carefully, mufflers can generate noise which limits the amount of reduction it can introduce to the exhaust system. There has been a lot of work done to measure and calculate the flow generated noise from flow constriction and bends using scaling laws. In this paper, a review of previous prediction models is done in literature or standards. These models are applied to calculate the flow generated sound inside several commercial mufflers. These models are formulated using the two-port theory to model 1D sound propagation in duct systems. Straight pipes and perforates are modeled as active two-port elements within the muffler network. The two-port network model is validated by comparing the calculated Transmission Loss to the measured one. The radiated sound power from the muffler outlet is calculated using tail pipe model as active one-port element and compared to the measured values. The radiated sound power is measured inside a reverberation room according to ISO 3741. The comparison shows good agreement within the valid frequency range of the measurements. This formulation can be used to predict the flow generated noise from any duct network.
The prediction of the flow generated noise is an important parameter for a complete muffler design and performance optimization. In the presence of flow, several muffler elements can be described as flow discontinuities that damp the acoustic noise coming from the source. These discontinuities produce disturbances in the fluid flow, which will result in noise generation. Holes in perforated pipes or baffles are good examples of the flow discontinuities that may produce broadband noise or tones “whistling” when subjected to flow. The flow generated noise will act as a dipole source inside the muffler elements that produce acoustic pressures in the region of flow separation in both directions. At higher flow speeds, the fluid movement can produce pressure amplitudes sufficiently large to generate enough noise to limit the effectiveness of the muffler.
In this paper, the prediction models in literature were integrated in SIDLAB software to predict the sound power levels due to flow generated noise in each element. A straight pipe and three mufflers were considered as case studies, simulated as a network of connected elements using the two-port transfer matrix method. Case studies’ simulations matched their measured acoustic parameter “Transmission loss” and pressure drop at different flow speeds to validate the simulation network. Active simulations were then performed at different flow speeds up to 50 m/s to predict the flow noise radiated from each muffler. ISO 3741 was used to measure the radiated sound power in a reverberation room where all sound waves from the noise source are measured (incident and reflected) and the sound power is uniformly distributed all over the room (diffuse field). Measurements are then compared to the flow noise simulation results.
The mufflers considered in the test cases were completely characterized, and the following parameters were measured: Transmission Loss, pressure drop and radiated Sound Power Level due to flow generated noise. The Transmission loss was measured using the platform developed, see Fig. 1. The two source technique is used where loudspeakers are placed upstream and downstream the muffler. The two microphone technique is used for the wave decomposition. Three microphones are used on each side of the muffler using two different microphone spacing to give wider valid frequency range. The pressure drop was measured using digital manometer at different flow speeds up to 36 m/s. The pressure taps are located just before and just after the tested muffler.
For the flow generated noise measurement, the output of the rig goes into a reverberation room and the radiated sound power is measured using the direct method described in ISO 3741. Eight microphones are placed inside the room to measure the Sound Pressure Level in a diffuse field. A pressure relief vent is used to prevent the reverberation room from over pressurizing. The microphones are connected to data acquisition system “LMS Scadas mobile”, controlled by LMS Test.Xpress. The measurements were conducted in third octave bands and filtered by A-weighting as the ISO procedures recommends. The measurement standard limits the frequency of interest for a reverberation room with 70 m3 volume to be 200 Hz and higher.
Case 1: Straight pipe
The first case is the case with no mufflers attached to the flow rig. The rig entrance consists of a few diffusers connected to a 6 m hard pipe and the outlet jet-mixing region. This simple case was just used to calibrate the system and the measurement technique and post-processing procedures.
Figures 4 and 5 show a comparison between the measured and simulated radiated Sound Power Level from the rig entrance at two different inlet flow speeds of 15 and 25 m/s. The agreement is good for the lower flow speed and better for the high flow speed. The main flow generated noise source here is the flow radiated noise due to the turbulence inside the 6 m pipe.
Case 2: Muffler Type A
The first muffler is a combined resistive-reactive muffler. The resistive behavior is achieved through perforations in the inlet, outlet and intermediate pipes. The reactive behavior is achieved through resonators. Each perforated pipe section is 95 mm long, with 156 holes of 3.2 mm diameter. One of the baffles has 4 holes, each of 15 mm diameter. Figure 6 shows the schematic and 3D drawings for this muffler, and Fig. 7 shows the associated SIDLAB network.
Figures 8 and 9 show a comparison between the measured and simulated Transmission Loss of muffler Type A at no flow and at inlet flow speed of 25 m/s. The acoustic attenuation with flow of this muffler is very good with an almost constant Transmission Loss above 25 dB. Figure 10 shows the pressure drop curve vs. inlet mass flow. All these results show very good agreement between the measurements and the simulations. This is an initial validation test to make sure that we have a good two-port network description for the muffler and it works well for acoustics and flow.
Figures 11 and 12 show a comparison between the measured and simulated radiated Sound Power Level from muffler Type A at two different inlet flow speeds of 15 and 25 m/s. The comparison show that both curves have the same trend but the simulated sound power is under estimated. The main flow generated noise source inside this muffler is the flow constriction inside the perforated pipes.
Case 3: Muffler Type B
The second muffler has the same outer casing as muffler type A. It is a modified version of type A with the aim of reducing the production cost by removing all the perforated pipe sections. The inlet and outlet pipes are located in the same places but without the perforated sections. The muffler is now completely reactive with no dissipation. The perforated baffles are also the same and located in the same position. The removal of the intermediate pipe and the cut of the inlet and outlet pipes result in two extra holes in each baffle of 45 mm in diameter. This makes the outer cavities working as Helmholtz resonators. Figure 13 shows the schematic and 3D drawings for this muffler, and Fig. 14 shows the associated SIDLAB network.
Figures 15 and 16 show a comparison between the measured and simulated Transmission Loss of muffler Type B at no flow and at inlet flow speed of 25 m/s. The acoustic attenuation with flow of this muffler has several resonances and anti-resonances in the frequency spectrum. Figure 17 shows the pressure drop curve vs. inlet mass flow. The simulated Transmission Loss at no flow show good agreement with the measurement result, whereas the simulated Transmission Loss with flow does not show the same agreement. The reason is that the resonances of the Helmholtz resonators are damped with flow, which is not properly captured by the 1D flow model.
Figures 18 and 19 show a comparison between the measured and simulated radiated Sound Power Level from muffler Type B at two different inlet flow speeds of 15 and 25 m/s. The comparison show that both curves have the same trend but the simulated sound power is under estimated. The main flow generated noise source inside this muffler is the sudden area expansion and contraction inside this muffler.
Case 4: Muffler Type C
The third muffler has a different internal structure. It is divided into two chambers, the first with two perforated pipes and the second with one perforated pipe surrounded by rock wool with density 14 kg/m3. The area of the chambers varies due to the wavy shape of the outer shell that is implemented for structural integrity. The inlet pipe has 120 holes, and the first section of the outlet pipe has 78 holes, whereas the other section has 156 holes. All the holes are 3 mm in diameter. Figure 20 shows the schematic and 3D drawings for this muffler, and Fig. 21 shows the associated SIDLAB network.
Figures 22 and 23 show a comparison between the measured and simulated Transmission Loss of muffler Type C at no flow and at inlet flow speed of 25 m/s. The internal configuration of this muffler is similar to Type A except that the second chamber is filled with absorbing material. This results in more attenuation at higher frequencies whereas the attenuation at lower frequencies is lower. Figure 24 shows the pressure drop curve vs. inlet mass flow. All these results show very good agreement between the measurements and the simulations. The two-port model of this muffler is properly built.
Figures 25 and 26 show a comparison between the measured and simulated radiated Sound Power Level from muffler Type C at two different inlet flow speeds of 15 and 25 m/s. The comparison show that both curves have the same trend, but again, the simulated sound power is under estimated. The main flow generated noise source inside this muffler is the flow constriction inside the perforated pipes.