M.Sc Thesis


M.Sc StudentGilad Oskar
SubjectPropagation of Sound Waves in a Rarefied Medium
DepartmentDepartment of Aerospace Engineering
Supervisor Assistant Professor Manela Avshalom
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

Studies on sound wave propagation in rarefied gases have evolved since the 1950s, motivated by fundamental and practical applications. Notably, common to all existing works is a one-dimensional setup, where sound is generated by sinusoidal small-amplitude motion of an infinite boundary in the normal direction. The purpose of the present research is to extend existing knowledge by considering the response of a confined gas to instantaneous non-periodic motion of its boundaries, thus allowing for a relaxation process within the gas. The problem is formulated using the Bhatnagar, Gross and Krook (BGK) kinetic model, and solved for the entire range of gas rarefaction factor, the Knudsen (Kn) number. Analysis combines analytical (collisionless and continuum-limit) solutions with numerical (linearized BGK) calculation. Gas rarefaction is shown to have a “damping effect" on equilibration process, with the time required for re-achieving equilibrium shortening with increasing Kn. Oscillations in hydrodynamic quantities, characterizing gas response in the continuum limit, vanish rapidly in collisionless conditions. Comparison between analytical and numerical solutions indicates that the collisionless description predicts the system behavior exceptionally well for all systems of the size of the mean free path and somewhat larger. The continuum-limit solution, however, should be considered with care at early times in the vicinity of acoustic wavefronts, where relatively sharp flow-field variations result in an effective increase in the value of the local Knudsen number.