An Extension of the Low Reduced Frequency Model for Viscothermal Acoustic Propagation Within Waveguides

Inside micro cavities, specific dissipative mechanisms influencing acoustic wave propagation occur due to viscous and heat-conducting nature of the fluid. This work focuses on a possible extension of the so called “Low Reduced Frequency” model for acoustic wave propagation in a thermoviscous fluid. This extension is built starting from geometrical and physical assumptions (boundary layer theory, straight waveguides) and consists in the incorporation of a stationary laminar and subsonic mean flow. The resulting equivalent fluid model provides a new damping coefficient which depends on the Mach number, the shear and thermal wave numbers and the cross-sectional profiles of axial velocity and temperature. The main application area is the study of acoustic attenuation within automotive catalytic converters or also thin fluid layers like cooling systems in small electronic devices. This formulation has been implemented for a simple one dimensional thin tube. Convergence to the original model in the absence of mean flow has been reached and comparisons with variational solutions given by Peat show good agreements.