An Analytical Solution for Acoustic Wave Propagation in a Narrow Duct with Mean Temperature Gradient

Abstract

A method to compute the acoustic behavior of a compressible fl uid in the vicinity of rigid walls and with a mean temperature gradient along the main propagation direction is presented. Due to the wall interaction viscous dissipation and thermal diffusion are not neglected. For a given mean temperature distribution T(x) = (ax+ b) n , an analytical solution is provided. This solution is compared to an existing solution for one dimensional acoustic fields in ducts with a similar temperat ure profile from Kumar and Sujith. 1 The deviation from their results with decreasing cross section of the observed duct and increasing importance of viscosity and thermal conductivity is presented. Additionally the fir st eigenfrequency behavior is considered and interpreted. Finally a scattering matrix for the system is set up and compared to a compact element approximation for a duct with included losses and a temperature jump.