Propagation of Sound Waves in a Rarefied Medium

Gilad Oskar
Work towards an M.Sc. degree under the supervision of Asst. Prof. Avshalom Manela
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology

Sound wave propagation in rarefied gases has been studied since the 1950s and evolved till our days, 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 near the location of acoustic wavefronts, where relatively sharp flow-field variations result in an effective increase in the value of local Knudsen number.

The talk will be given in Hebrew

Wed, 01-01-2014, 16:30 (Gathering at 16:00)

Classroom, ground floor, library, Aerospace Eng.

Light refreshments will be served before the lecture

Propagation of Sound Waves in a Rarefied Medium