SIDLAB References 5
Optimization of Exhaust Systems to Meet the Acoustic Regulations and the Engine Specifications
Elsaadany, S., and Elnady, T., “Optimization of Exhaust Systems to Meet the Acoustic Regulations and the Engine Specifications,” ICSV18, Rio de Janeiro, 2011
Abstract
Mufflers for internal combustion engines should be carefully designed. The main objective of a muffler is to reduce the engine noise while maintaining the back pressure below a certain limit. A specific target acoustic performance has to be met under space constraints and allowable engine back pressure limit. Usually, the insertion loss of the exhaust system is required to satisfy a certain target performance curve. The insertion loss is most appropriate to describe the exhaust system acoustic performance since it is dependent on the engine acoustic impedance, which varies with the engine loading and rotational speed. In this paper, a muffler optimization problem is formulated so that several shape parameters are optimized under some space constraints with flow. Any combination of linear space constraints can be imposed. The allowable engine back pressure is introduced as a nonlinear constraint so that the optimum shape design will meet the engine back pressure specifications. The interior point optimization algorithm, which is available as a builtin MATLAB function “fmincon”, is used in this paper. The formulated problem is applied to a real case study, where a truck exhaust system consists of a diesel engine, two mufflers, intermediate pipes, and a tailpipe. The first muffler is a typical EUregulation compliant. The dimensions and location of the second muffler are to be optimized. A limit for the system back pressure is imposed by the engine manufacturer. An optimum design was investigated for different engine speeds and loadings. It was found that using the suggested formulation in this paper; one can obtain an applicable design of a muffler to meet both the acoustic regulations and the engine specifications.
Application
Under the continuous environmental demands to control noise emitted from ICengines, reduction of the exhaust system noise is an important task. Noise control can be accomplished at three locations – at the source, in the path between the source and the receiver and at the receiver. In this paper the noise is controlled in the path between the source and the receiver through the shape optimization of the exhaust system mufflers. The specific design of mufflers is driven by three paramount considerations which are: appropriate outer geometry, low pressure drop, and sufficient sound attenuation. It is thus important to get an optimal muffler design under space constraints while keeping the pressure drop below specific level, an area that is not yet so well developed.
The case study presented in this paper is a truck exhaust system consists of a diesel engine, two mufflers, intermediate pipes, and a tailpipe. The first muffler is a typical EUregulation compliant. The dimensions and location of the second muffler are to be optimized. A limit for the system back pressure is imposed by the engine manufacturer. An optimum design was investigated for different engine speeds and loadings.
The acoustic properties are calculated using SIDLAB software, which is a code to analyze low frequency sound propagation in complex duct networks based on the twoport theory. These acoustics properties calculation is conjugated with the optimization technique using “fmincon”, a function from the MATLAB optimization toolbox that finds the minimum of constrained nonlinear multivariable function. The optimization technique has been verified in earlier work. This optimization technique is implemented in SIDLAB, using the same solver of acoustics and flow simulation to find the optimum value of any chosen shape defining property, having the option to set the limit of engine back pressure as a nonlinear constraint.
Case Study
The case study presented is a truck exhaust system consisting of a diesel engine, two mufflers, intermediate pipes, and a tailpipe. The first muffler is a typical EUregulation compliant, the data for its transfer matrix is input to the system in the form of a twoport userdefined element. The dimensions and location of the second muffler are to be optimized, so that the insertion loss will be able to satisfy a certain target performance curve. Figure 1 shows a schematic diagram for this system.
A limit for the system back pressure is imposed by the engine manufacturer which equals to 21000 Pa for the whole exhaust system at 0.5 kg/sec inlet mass flow, and temperature of 490^{o}C. The outlet pipe from the engine has a diameter of 114 mm. The muffler to be optimized should not exceed 250 mm in diameter and 500 mm in length. The total length of the system after the EU muffler should not exceed 2 m.
An optimum design is to be investigated for 12 cases representing different engine source case for different speeds and loadings. The source impedance was measured for all these cases and used here to calculate the insertion loss. The source impedance is defined as a oneport user defined element in SIDLAB.
The first choice of the muffler to be optimized was a simple expansion chamber which was not enough to satisfy the target curve. Several configurations for the interior of this muffler were studied. First, a perforated pipe was introduced to construct a through flow muffler. Then, two resonators were added as extended inlet and outlet inside the muffler. Moreover, porous material was introduced to fill the cavity of the muffler. However, all these modifications could not meet the overall target insertion loss curve, especially at low frequencies up to 120 Hz.
It was then decided to reduce diameter of the intermediate pipe between the EU muffler and the muffler to be optimized to 90 mm. This would result in a larger area expansion ratio inside the muffler to be optimized which provides a better attenuation. However, reducing the diameter of the intermediate pipe than the diameter of the engine outlet will increase the pressure drop across the exhaust system. Therefore, it is important to include the pressure drop as a constraint in the optimization of the acoustic performance of exhaust system. The final exhaust system to be optimized is shown in Figure 2 and its associated SIDLAB network is shown in Figure 3. The SIDLAB model for this muffler was earlier verified in reference.
In Figure 2, D_{p1} is the diameter of the engine exhaust pipe, D_{p2} is the diameter of the intermediate pipe, D_{m} is the diameter of the muffler to be optimized, L_{1} is the length of the intermediate pipe, L_{2} is the length of the muffler to be optimized, L_{3} is the length of the tailpipe, LR is the length of the inlet resonator and RR is the length of the outlet resonator.
The optimization was carried out for 9 parameters. These are: L_{1}, L_{3}, LR, RR, perforate parameters [thickness (t), hole diameter (d), porosity (σ), and length (l)], flow resistivity of the porous material inside the cavity (φ). Table 1 summarizes the constraints on the optimization variables.
Table 1. The constraints of the optimization problem.
Bounds  Linear Constraints  Nonlinear Constraints 
900 mm ≤ L_{1} ≤ 1400 mm.
300 mm ≤ L_{3} ≤ 500 mm. 10 mm ≤ RR ≤ 400 mm. 10 mm ≤ LR ≤ 400 mm. 200 mm ≤ l ≤ 500 mm. 0 rayl/m ≤ f ≤ 10000 rayl/m. 1 mm ≤ t ≤ 2 mm. 1 mm ≤ d ≤ 5 mm. 4% ≤ s ≤ 10%. 
L_{0} = L_{1}+L_{2}+L_{3}+L_{horn} = 2000 mm
L_{2 }= l + LR + RR. Pipe 7 length = pipe 8 length. Pipe 9 length = pipe 10 length.

Overall Pressure Drop ≤ 21000 Pa 
Figure 4 to Figure 8 show the insertion loss results for several iterations of the internal design configuration of the muffler to be optimized at one source case (1200 rpm at 25% loading). In all the figures, the dashed red curve represents the target curve to be achieved (exceeded). Figure 4 shows the insertion loss of the exhaust system with the EU muffler only. Although the insertion loss curve satisfies the target curve at low frequencies (at the slope), it has a few antipeaks at higher frequencies. The next step was to choose a simple expansion chamber, which does not enhance the performance too much, as shown in Figure 5. When a perforated pipe is fitted inside the expansion chamber to form a through flow muffler, it enhances the insertion loss performance at high frequencies but the rising slope at low frequencies is not satisfied, as shown in Figure 6. When adding extended inlet and outlet acting as quarter wavelength resonators, it increases the slope of the insertion loss at low frequencies, but not enough to exceed the slope of the target curve, as shown in Figure 7.
One basic rule in muffler design to achieve higher attenuation through expansion cavities, is to increase the ratio between the area of the cavity and the area of the inlet pipe and not only the value of the cavity area. In our case, we are bounded by a maximum diameter for the cavity, and therefore we have to reduce the diameter of the inlet pipe in order to achieve a high expansion ratio.
A horn (diffuser) was added after the EU muffler to reduce the diameter of the intermediate pipe from 114 mm to 90 mm. This change resulted in an increase of the insertion loss curve above the target curve at all frequencies, as shown in Figure 8. Therefore, it can be concluded that this internal configuration is possible to satisfy the target curve under the dimensional constraints and the engine specification for the backpressure limitation.
The next step is to find an optimum design for the exhaust system at other source cases 1200 rpm, 1400 rpm, 1600 rpm and 1800 rpm and at different three loadings 25%, 50% and 100%. We now have 12 optimum designs, one for each source case. Six variables are the same for all the cases, and three are different from case to case. The variables that remain the same are the perforate dimensions [t = 1.99 mm, d = 1 mm, σ= 4 %, and l = 300 mm], and the lengths of the resonators [LL = 189 mm and LR = 10 mm]. The variables which differ are the flow resistivity of the porous material inside the cavity and the lengths of the intermediate and tailpipes which determine the location of the second muffler along the exhaust system. The flow resistivity of the porous material varies from 4750 to 9900 rayl/m, the length of intermediate pipe varies from 300 to 500 mm, and the length of the tailpipe varies from 900 to 1100 mm. It is worth noting that the pressure drop across the whole system is almost the same and is below the allowable limit.
The challenge is to choose which of these designs to implement in the exhaust system. We need to find out which design satisfies the target insertion loss at other source cases at the same time. One strategy is to choose the source case which corresponds to a critical operating condition; e.g. during the passby noise test. In this paper, we did an exercise to predict the insertion loss of the exhaust muffler for each of the 12 optimum designs at all source cases resulting in 144 calculations. It was found that the optimum design at the source case of 1200 rpm and 50% loading provides best performance at other source cases. Figure 9 shows the insertion loss results using this optimum design at all source cases.
The last step is to round of the optimized values for different variables in order to make it easier for the workshop drawing. It was found that rounding off the variables does not affect the insertion loss optimized curve.