Noise Elimination of a Multi-tone Broadband Noise with Hybrid Helmholtz Mufflers Using a Simulated Annealing Method

Abstract

Noise control is essential in an enclosed machine room where the noise level has to comply with the occupational safety and health act. In order to overcome a pure tone noise with a high peak value that is harmful to human hearing, a traditional reactive muffler has been used. However, the traditional method for designing a reactive muffler has proven to be time-consuming and insufficient. In order to efficiently reduce the peak noise level, interest in shape optimization of a Helmholtz muffler is coming to the forefront.Helmholtz mufflers that deal with a pure tone have been adequately researched. However, the shape optimization of multi-chamber Helmholtz mufflers that deal with a broadband noise hybridized with multiple tones within a constrained space has been mostly ignored. Therefore, this study analyzes the sound transmission loss (STL) and the best optimized design for a hybrid Helmholtz muffler under a spaceconstrained situation. On the basis of the plane wave theory, the four-pole system matrix used to evaluate the acoustic performance of a multi-tone hybrid Helmholtz muffler is presented. Two numerical cases for eliminating one/two tone noises emitted from a machine room using six kinds of mufflers (muffler A∼F) is also introduced. To find the best acoustical performance of a space-constrained muffler, a numerical assessment using a simulated annealing (SA) method is adopted. Before the SA operation can be carried out, the accuracy of the mathematical model has been checked using the experimental data. Eliminating a broadband noise hybridized with a pure tone (130 Hz) in Case I reveals that muffler C composed of a onechamber Helmholtz Resonator and a one-chamber dissipative element has a noise reduction of 54.9 (dB). Moreover, as indicated in Case II, muffler F, a two-chamber Helmholtz Resonator and a one-chamber dissipative element, has a noise reduction of 69.7 (dB). Obviously, the peak values of the pure tones in Case I and Case II are efficiently reduced after the muffler is added.Consequently, a successful approach in eliminating a broadband noise hybridized with multiple tones using optimally shaped hybrid Helmholtz mufflers and a simulated annealing method within a constrained space is demonstrated.Keywords: multiple tones, hybrid, Helmholtz, four-pole transfer matrix method, SA method. p -acoustic pressure (Pa), p% -the porosity of the perforated tube in the dissipative element, Q -volume flow rate of venting gas (m 3 s −1 ), r k -the radius of the resonating tube in the Helmholtz resonator (m), Rres -the acoustic resistance, SA -simulated annealing, S i -the section area at the i-th node (m 2 ), Archives of Acoustics -Volume 37, Number 4, 2012 S k -the section area of the resonating tube in the Helmholtz resonator (m 2 ), STL -sound transmission loss (dB), SWL T -overall sound power level inside the muffler's output (dB), T * ij -components of a four-pole transfer system matrix, TS ij , TSC ij , TSE ij , THR ij -components of four-pole transfer matrices for an acoustical mechanism with a s...

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