The effect of mass transfer on sound propagation in cylindrical tubes using the low reduced frequency approximation

The theory for sound propagation in a gas/vapor mixture contained in a cylindrical tube is investigated. The tube is assumed to have a rigid wall covered by a thin film of water. This thin film of water acts as a source/sink for the mass and the heat associated with the vapor. This problem has been previously solved in the high‐ and low‐frequency limits using the Rayleigh eigenmode method [Y. Mao and J. M. Sabatier, J. Acoust. Soc. Am. 96, 3254(A) (1994)]. However, the interpretation of these results is limited by their complexity. This formulation of the problem parallels the low reduced frequency approximation work of Tijdeman [J. Sound Vib. 39, 1–33 (1975)]. In contrast to the earlier results an easily interpreted analytical solution for the propagation constant is obtained. The parameters governing the propagation of the sound waves are the shear wave number, Prandtl number, Schmitt number, and the reduced frequency. The limits of small and large shear wave number provide useful insight into the behav...