Slow sound in lined flow ducts

TL;DR

This paper investigates how reactive liners in flow ducts can slow sound propagation, affecting acoustic and hydrodynamic modes, with implications for controlling sound in low Mach number flows.

Contribution

It develops an approximate 1D model from the exact 2D formulation to analyze acoustic wave scattering in lined ducts with varying impedance, highlighting mode interactions.

Findings

Identification of four propagating modes at low frequencies

Transition to two propagating modes above a critical frequency

Significance of negative energy waves and mode interactions

Abstract

We consider the acoustic propagation in lined flow duct with a purely reactive impedance at the wall. This reacting liner has the capability to reduce the speed of sound, and thus to enhance the interaction between the acoustic propagation and the low Mach number flow ($M\simeq0.3$). At the lower frequencies, there are typically 4 acoustic or hydrodynamic propagating modes, with 3 of them propagating in the direction of the flow. Above a critical frequency, there are only 2 propagating modes that all propagate in the direction of the flow. From the exact 2D formulation an approximate 1D model is developed to study the scattering of acoustic waves in a straight duct with varying wall impedance. This simple system, with a uniform flow and with a non-uniform liner impedance at the wall, permits to study the scattering between regions with different waves characteristics. Several situations are characterized to show the importance of negative energy waves, strong interactions between acoustic and hydrodynamic modes or asymmetric scattering.