On the effect of viscosity and thermal conductivity on sound power transmitted in uniform circular ducts

Abstract

The present paper investigates the effect of fluid viscosity and thermal conductivity on the time-averaged acoustic power transmitted in the fundamental mode of a uniform circular duct. The topic has some theoretical ramifications, since there is no unequivocal mathematical definition of acoustic intensity in a duct carrying a Newtonian fluid with non-negligible viscosity and thermal conductivity. In this paper, the mathematical definition of acoustic intensity is based on the view that, in most practical duct-acoustics applications, the metric for ‘acoustic energy’ is the mechanical part of the total acoustic energy associated with the presence of a sound wave. The time-averaged acoustic power transmitted in the duct is formulated by using the exact solution for the wave modes in the duct in the proposed definition of acoustic intensity. Numerical results are given to show the characteristics of the time-averaged acoustic power transmitted in the fundamental mode for a wide range of problem parameters, displaying some phenomena not reported previously. The paper also includes a comparison of the present results with those based on the low reduced frequency approximation for the fundamental mode.