A MODEL FOR SOUND-PROPAGATION IN CAPILLARY DUCTS WITH MEAN FLOW

A theoretical formulation is carried out of acoustic wave propagation in a narrow capillary tube with steady gas flow. The transverse variat ions of the particle velocity, temperature, and viscosity are consider ed. A fully developed laminar steady flow is assumed and the concept o f a complex propagation constant is introduced in the formulation. The final equation form reduces to a Kummer-type differential equation an d its solution is obtained in terms of confluent hypergeometric functi ons. The dispersion equation for the complex propagation constants tak es on a recursive form. A simplified form of the analysis permits comp arison with previous results dealing with visco-thermal effects and in cludes the features of Poiseuille-type laminar steady flow for low and medium shear wave numbers. Numerical simulation results show that the effect of steady flow is very significant for the backward traveling waves, and the assumption of a parabolic velocity profile for shear wa ve numbers less than four should be used carefully when the flow Mach number is greater than about 0.1. The present theory is applicable for shear wave numbers up to 10 or more, with the non-parabolic axial vel ocity fluctuations included, which encompasses almost all the possible practical situations of capillary duct dimension, temperature, and fl ow velocity. The theory would be useful as an approximation in solving the acoustic problems of the monolith in catalytic converters for aut omotive exhaust systems and of the propagation of sound in a porous me dium (C) 1996 Academic Press Limited