Research on muffler performance control by arrangement of Helmholtz resonators

Abstract

The Helmholtz resonator is widely used as an effective way to reduce noise around the resonance frequency. But the resonator is a single degree of freedom and has a narrow resonance frequency band which determined by its geometry. This paper used three-dimensional finite element method to calculate the acoustic characteristics of different arrangement of the Helmholtz resonant. It is can be found that 2 Helmholtz resonators connected in parallel, the narrow-band not be changed and the performance of muffler is enhanced. As for the 2 degrees of freedom Helmholtz resonator has two resonance frequencies, and the narrow-band has been broaden. From the simulation, the performance of muffler has no significant change with distance change, but the effect of two Helmholtz resonators has been changed by the angle between the two Helmholtz resonators. Introduction Noise is the by-product of the industrial society, which is regarded as one of the three public hazards in the world today. The Helmholtz resonator (HR) is widely used as an effective way to reduce noise around the resonance frequency. While the disadvantage of HR is its effective frequency range is restricted by its resonance frequency, which is decided by the physical dimensions of neck area, neck length, and cavity volume. It is clear that the resonant frequency is fixed when the geometry of the resonator fixed. There are 2 method to optimize the effect of Helmholtz resonator, one is changing the geometry of the resonator or the arrangement of Helmholtz resonators, anther is designing a tuned Helmholtz resonator. This paper chooses the former, which using multiple Helmholtz resonator to optimize the performance by changing the arrangement of mufflers. Theoretical analysis Helmholtz resonator is widely used to attenuate the narrow-band low-frequency noise. In view of the low frequencies of interest in this paper, the geometrical dimensions of HR considered here are significantly smaller than the fluid wave length. The Physical dimensions is shown in table1. Then the model of Helmholtz resonator can be established by lumped parameter theory. The mass significant for oscillation of single Helmholtz resonator in air medium is concentrated in the neck of the resonator and the volume of resonator acts as a spring, and the mechanical-acoustical analogy for single Helmholtz resonator in air medium which is a mass-spring system. Assuming that flow can be neglected, and the wave field in the duct is isentropic. The resonant frequency of the resonator can be expressed as ∆ (1) where t and r are the thickness and the radius of the neck, respectively, Δt is the sum of the end correction at the inner and outer neck ends, 343m/ s is sound velocity in medium, and v is the cavity volume. 3rd International Conference on Machinery, Materials and Information Technology Applications (ICMMITA 2015) © 2015. The authors Published by Atlantis Press 1307 The tra representat matrix met input port network co matrix. The P-Q Where P i parameters If the te variable in And the tra Where the Dividin model can transfer ma contraction The mat where is area of the