Transmission matrix model of a quarter-wave-tube with gas temperature gradients

Abstract

A transmission matrix (also known as four pole) model is presented of a duct with anechoic terminations and a quarter-wave-tube, where each duct segment has a linear temperature gradient. The results from simulations conducted using the mathematical model show good agreement with results from finite element simulations using Ansys. Expressions are derived for the four pole analysis method that are relevant when conducting finite element simulations where an incident acoustic particle velocity is specified as the excitation source. A static thermal finite element analysis is conducted using thermal solid elements to determine the nodal temperatures. The nodal temperatures are transferred to the nodes of the acoustic elements and a harmonic analysis is conducted to determine the pressure within the duct.