Sound waves in gaseous mixtures induced by vibro-thermal excitation at arbitrary rarefaction and sound frequency

Abstract

Sound waves due to vibro-thermal excitation propagating through a binary mixture of rarefied gases in a gap between source and receptor are investigated by applying the McCormack model to the Boltzmann equation. The sound waves are induced by mechanical vibration and temperature variation of one plate, while the other plate being fixed at a constant temperature, acts as a receptor of sound waves. The oscillatory gas mixture flow is considered as fully established and all its macroscopic quantities depend on time harmonically. The discrete velocity method is used to solve the coupled kinetic equations in wide ranges of both rarefaction and oscillation parameters. The former is defined as the ratio of the distance between the plates to the equivalent free path, while the latter is the ratio of the intermolecular collision frequency to sound frequency. Analytical solutions in the free molecular and hydrodynamic regimes have been obtained too. Two mixtures, namely, HeliumArgon and HeliumXenon, are considered with a molar fraction equal to 0.1, 0.5 and 0.9. The amplitudes and phases of all macroscopic characteristics of the gas mixture flow are calculated as functions of the rarefaction and oscillation parameters so that the free molecular, transitional and hydrodynamic regimes are covered. The results are compared to those obtained in the limit of a single gas in order to investigate the influence of the molar fraction and molecular masses of species on the problem solution. The reciprocal relations between cross phenomena are obtained and verified numerically.