Effect of the medium viscosity on sound propagation and attenuation in ducts

Abstract

The viscosity of the medium plays an important role in defining the characteristics of sound wave propagation in ducts. This effect, due to the difficulty of analysis, has been either completely neglected in the literature or considered only approximately. One common assumption has been that viscosity would affect the inviscid acoustic wave indirectly through its effect on the mean flow. In this study, a mathematical model is constructed to describe the physical problem in its general form without imposing assumptions a priori. The set of equations describing the model are solved in a two-dimensional duct. The losses due to thermal conductivity of the medium are neglected in order to focus on that due to viscosity. The physical quantities have been conveniently expressed in only two nondimentional quantities, a frequency or wave number bK and a Reynolds number Re. The effect of these two parameters on the propagation and attenuation constants was studied in detail for a wide range of bK and Re. Results were obtained for the zeroth- and higher-order modes. The huge amount of numerical results obtained led to rather interesting conclusions.