Acoustic analysis and structural optimization of dual-chamber reactive muffler

Abstract: The existing studies of the acoustic performance of reactive mufflers are mainly based on the numerical method or the transfer matrix method. But the numerical methods like the finite element method or the boundary element method mean plenty of time needed, and the transfer matrix method is only useful below the cutoff frequency of the expansion chamber. This paper use two-dimensional analytical method to study the acoustic behaviors of dual-chamber reactive muffler. This method is based on the sound wave equations in the muffler. Firstly the sound pressure and particle velocity in the air domains of the dual-chamber reactive muffler are expressed according to the Helmholtz equation, in which there are some unknown variables to be solved. Secondly the expressions are used to construct an equation set according to the boundary conditions at the interfaces of different domains of the muffler. The conditions are that the sound pressure and particle velocity are continuous at the interfaces. That means the sound pressures expressed in adjacent domains are equal at the interface, which is the same way for the particle velocity. At last the amplitudes of the sound pressure of all domains are solved according to the equation set. Then the transmission loss can be calculated based on the sound pressure amplitudes of the inlet and outlet of the muffler. A dual-chamber reactive muffler is manufactured for the experiment. The transmission loss of the muffler was measured by the two-load method. The impedance tube is used for the experiment. The result shows that the calculated transmission loss agrees well with the measured one below 3 000 Hz. On the contrary, the transfer matrix method is accurate only below 1 299 Hz for this muffler. This means the two-dimensional analytical model is effective for the analysis and design of dual-chamber reactive muffler. Then the effects of several parameters on the transmission loss of the dual-chamber reactive muffler are analyzed. The analysis shows that the dual-chamber reactive muffler performs better than the one-chamber reactive muffler with the same outer dimensions. The muffler with two chambers attenuates much more noise on a wider frequency band than that with only one chamber. It also shows that the clapboard hole radius and its position in the baffle have an obvious influence on the acoustic behavior of the dual-chamber reactive muffler. As the radius of the clapboard hole increases, the acoustic behavior becomes worse. Then the paper uses the genetic algorithm for the optimal design of the dual-chamber reactive muffler. The variables of the optimization include the clapboard radius, the radii of inlet/outlet and expansion chambers and the lengths of the expansion chambers. The denoising objective is the noise between 1 000 and 3 000 Hz. The constraint condition is that the outer dimension of the muffler could not become larger. The optimization leads to a wonderful result. After optimization, the average value of transmission loss between 1 000 and 3 000 Hz increases from 17.2 to 39.5 dB, with a growth of 130%. The study in this paper demonstrates that the proposed theoretical model of dual-chamber reactive muffler can be used for the analysis and design of the muffler effectively and efficiently, which is really helpful in the industrial application.