Modeling the Effects of Viscosity and Thermal Conduction on Acoustic Propagation in Rigid Tubes with Various Cross-Sectional Shapes

When modeling acoustics with viscothermal effects included, typically of importance for narrow tubes and slits, one can often use the so-called low reduced frequency model. With this model a characteristic length is assumed for which the sound pressure is constant. For example for a circular cylindrical tube the characteristic length is the radius. A triangular cross-section does not have a characteristic length, but as will be shown in this paper the model can in fact be used as long as 1) the cross-sectional pressure is constant and 2) a characteristic impedance and propagation wavenumber can be established for the geometry. These parameters can be found for a tube with a triangular cross-section and an implementation of the low reduced frequency which can handle tubes with both circular, rectangular triangular cross-sections has been made in COMSOL Multiphysics. For the circular and the rectangular tube results found using this implementation have been compared to results from an analytical model, a so-called full Navier-Stokes implementation in COMSOL Multiphysics and the commercial package FFT ACTRAN which also uses the low reduced frequency model. The triangular tube implementation has been compared to the analytical case as well as the full Navier-Stokes implementation.