AN APPROXIMATE DISPERSION EQUATION FOR SOUND WAVES IN A NARROW PIPE WITH AMBIENT GRADIENTS

There is some interest on the effect of temperature gradient on sound propagation in a catalytic monolith. Some results are available in the literature for the effect of a constant temperature gradient on non-isentropic propagation in a narrow pipe modelling a monolith pore, but the effect of mean flow is neglected in these solutions. This paper presents an approximate solution in which the presence of a mean flow, which is assumed to have a uniform velocity profile, is taken into account. The solution also includes the effect of a constant pressure gradient. A dispersion equation is derived by assuming that the spatial variations of the ambient variables can be lumped by using their average values. This approximation limits the range of application of the solution to small ambient gradients or relatively high frequencies. For typical catalytic monolith cylinder dimensions, the present solution can be used to predict the mean flow effects over a useful frequency range.