Length correction of 2D discontinuities or perforations at large wavelengths and for linear acoustics

TL;DR

This paper investigates the length correction for duct discontinuities and perforations in linear acoustics at large wavelengths, revealing negligible mode-coupling at low frequencies and proposing a unified correction model.

Contribution

It introduces a simplified, unified length correction model applicable to various geometries of duct discontinuities and perforations, excluding slit-like shapes.

Findings

Mode-coupling is negligible at low frequencies.

Models are similar when plotted against the square root of perforation rate.

A single approximate formula is proposed for practical use.

Abstract

This work focuses on the length correction due to radiation effect of a duct discontinuity or at the surface of a perforated plate in the linear acoustic domain and at large wavelengths. Two results are obtained from the comparison of models used in the literature for different geometries of duct discontinuities or perforations. First, the mode-coupling at the discontinuity between two ducts or a perforated plate and air is negligible for low frequencies. Second, all consistent models of the length correction proposed so far, for any geometries except slit-like, are similar when plotted as a function of the square root of the perforation rate (the ratio of the duct cross-section areas for ducts). These two results imply the effect of the thickness of the ducts or the perforated plate can be accounted for in the length correction expression independently from other geometric variables. A single approximate formulation for all geometries of perforations or duct discontinuities, except slit-like geometries, is proposed for practical uses.