A Numerical MFS Model for Computational Analysis of Acoustic Horns

Godinho, L.; Amado-Mendes, Paulo; Ramis, J.; Cárdenas, William; Carbajo, J.

doi:10.3813/aaa.918575

Cited by 7 publications

(1 citation statement)

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“…21 A semi-analytical solution for acoustic wave propagation in ducts with arbitrary CSA variations and temperature gradient in the presence of non-isentropic mean flow is developed by Yeddula and Morgans. 22 For waveguides with more general CSA variations, Webster's horn equation can be solved by numerical methods 23,24 or perturbation methods. 25 In this work, we build on these existing solutions for ducts with a polynomial, sinusoidal or exponential variation in the longitudinal direction, with the important difference that we focus on deriving exact solutions for the acoustic impedance of the side-branch required for spatial localization of traveling and standing waves.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions for Side-branch Impedance Producing Spatial Localization of Acoustic Waves in Ducts with Varying Cross Sections

Xiao¹,

Lu²,

McFarland³

et al. 2021

The International Journal of Acoustics and Vibration

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Analytical mathematical models and solutions for spatial localization of acoustic waves through an impedance discontinuity produced by an intermediate damped side branch are studied in stationary media in ducts with varying cross sections. Three specific geometries, namely, with polynomial, sinusoidal, and exponential longitudinal variations, are investigated. The sound fields inside the ducts are modeled by Webster's horn equation. Traveling-wave solutions are obtained by appropriate transformations. The side-branch impedances required for spatial localization (confinement) of traveling and standing waves are found analytically and verified numerically using three-dimensional finite element analysis. The impact of the longitudinal variation of the duct's cross-sectional area (CSA) on the side-branch impedance is examined. It was found that the required side-branch resistance changes more than the reactance with the variation of the duct CSA. A measure of a traveling wave is defined to quantitatively examine the spatial localization of acoustic waves. It was found that the CSA corrections on the side-branch impedances are important. The results of this study reveal the quantitative relationships between the side-branch impedance and the CSA variations for zero reflection from the impedance discontinuity. The mathematical approach presented is potentially helpful for a design of a full anechoic termination and energy localization in duct systems.

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