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Experimental Determination of a Reflective Muffler Scattering Matrix for Single-Mode Excitation

Gorazd Łukasz

Archives of Acoustics

2021

Vol. 46, No. 4

667--675

The aim of the paper is to experimentally determine the scattering matrix S of an example reflective muffler of cylindrical geometry for Helmholtz number exceeding the plane wave propagation. Determining the scattering matrix of an acoustic systems is a new and increasingly used approach in the assessment of reduction of noise propagating inside duct-like elements of heating, ventilation and air conditioning systems (HVAC). The scattering matrix of an acoustic system provides all necessary information on the propagation of wave through it. In case of the analysed reflective silencer, considered as a two-port system, the noise reduction was determined by calculating the transmission loss parameter (TL) based on the scattering matrix (S). Measurements were carried out in two planes of the cross-section of pipes connected to the muffler. The paper presents results of the scattering matrix evaluation for the wave composed of the plane wave (mode (0,0)) and the first radial mode (0,1), each of which was generated separately using the self-designed and constructed single-mode generator. The gain of proceeding measurements for single modes stems from the fact that theoretically, calculation of the S-matrix does not require, as will be presented in the paper, calculation of the measurement data inverse matrix. Moreover, if single mode sound fields are well determined, it ensures error minimization. The presented measurement results refer to an example of a duct like system with a reflective muffler for which the scattering matrix S was determined. The acoustic phenomena inside such a system can be scaled by the parameter ka.

Simulation of a single mode wave generation in cylindrical systems applying numerical methods

Gorazd Łukasz, Snakowska Anna

Vibrations in Physical Systems

2019

Vol. 30, nr 1

art. no. 2019118

The paper presents simulations of a selected single mode generation in systems containing duct-like elements applying the finite element method (FEM). Simulations were carried out for values of the Helmholtz number exceeding the plane-wave propagation, i.e. for a multimode wave. The presented results constitute the first step to analyse propagation of the multimode wave through more complicated systems such as mufflers, even in a form of a cascade. Propagation of the incident wave in the form of a single mode greatly simplifies solutions of many problems, to mention only derivation of the transmission or the scattering matrices. The results obtained can be applied to analyse the effectiveness of attenuation of acoustic silencers or elements of heating, ventilation and air conditioning systems (HVAC) at the design stage. Results of simulations are compared with already published experimental data obtained in a measurement set-up containing the self-designed single mode synthesizer.