Modeling the Impedance of Sound Waves Passing through a Roughness Pipe using COMSOL Multiphysics

This work examines, both theoretically and statistically, the acoustic impedance behavior of sound waves traveling through cylindrical pipes having smooth or rough interior surfaces. The study's main goal is to ascertain how pipe design, frequency, and medium characteristics affect impedance and to examine these effects using simulation in the COMSOL Multiphysics framework. The classical wave equation was used to discuss the propagation of acoustic waves, and the ideas of input impedance and characteristic impedance were developed. Specifically, when the wavelength was large in relation to the pipe diameter, the model was simplified using the plane wave approximation. In the simulations, a 4 m long, 2.5 cm diameter closed-end pipe was used to study the propagation of sound waves at a frequency of 171.5 Hz. The findings unequivocally show how standing waves form and how pressure is distributed inside the pipe. Impedance achieves its greatest values at locations where particle velocity approaches zero, according to an analysis of the impedance distribution. Energy losses were found to be minimal in pipes with smooth surfaces; nevertheless, impedance is impacted by increased viscous and thermal losses as roughness increases. For the modeling and experimental investigations of in-pipe acoustic systems, this work offers a solid theoretical and numerical basis.