Shape optimization on mufflers within a limited space volume is essential for industry, where the equipment layout is occasionally tight and the available space for a muffler is limited for maintenance and operation purposes. To proficiently enhance the acoustical performance within a constrained space, the selection of an appropriate acoustical mechanism and optimizer becomes crucial. A multi-chamber side muffler hybridized with reverse-flow ducts which can visibly increase the acoustical performance is rarely addressed; therefore, the main purpose of this paper is to numerically analyze and maximize the acoustical performance of this muffler within a limited space.

In this paper, the four-pole system matrix for evaluating the acoustic performance - sound transmission loss (STL) - is derived by using a decoupled numerical method. Moreover, a simulated annealing (SA) algorithm, a robust scheme in searching for the global optimum by imitating the softening process of metal, has been used during the optimization process. Before dealing with a broadband noise, the STL's maximization with respect to a one-tone noise is introduced for the reliability check on the SA method. Moreover, the accuracy check of the mathematical models with respect to various acoustical elements is performed.

The optimal result in eliminating broadband noise reveals that the multi-chamber muffler with reverse-flow perforated ducts is excellent for noise reduction. Consequently, the approach used for the optimal design of the noise elimination proposed in this study is easy and effective.

Recently, there has been research on high frequency dissipative mufflers. However, research on shape optimization of hybrid mufflers that reduce broadband noise within a constrained space is sparse. In this paper, a hybrid muffler composed of a dissipative muffler and a reactive muffler within a constrained space is assessed. Using the eigenvalues and eigenfunctions, a coupling wave equation for the perforated dissipative chamber is simplified into a four-pole matrix form. To efficiently find the optimal shape within a constrained space, a four-pole matrix system used to evaluate the acoustical performance of the sound transmission loss (STL) is evaluated using a genetic algorithm (GA).

A numerical case for eliminating a broadband venting noise is also introduced. To verify the reliability of a GA optimization, optimal noise abatements for two pure tones (500 Hz and 800 Hz) are exemplified. Before the GA operation can be carried out, the accuracy of the mathematical models has been checked using experimental data. Results indicate that the maximal STL is precisely located at the desired target tone. The optimal result of case studies for eliminating broadband noise also reveals that the overall sound power level (SWL) of the hybrid muffler can be reduced from 138.9 dB(A) to 84.5 dB(A), which is superior to other mufflers (a one-chamber dissipative and a one-chamber reactive muffler). Consequently, a successful approach used for the optimal design of the hybrid mufflers within a constrained space has been demonstrated.