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Phenomenological Theory of the Translational Relaxation Times in GasesThe exact solution to the classical equations governing the translational dispersion and absorption of sound in a gas obscures its relaxational character because of its mathematical complexity. The approach taken here is to solve the secular equation by the method of Pade approximants, which even to the relatively low order R(sub 11) yields a remarkably close approximation to the exact solution over a wide range of frequency/pressure (f/P) ratios. As a result, translational relaxation can be formulated in terms of a conventional relaxation process with well-defined relaxation times, relaxation strength, collision numbers, additivity relations, etc. To extend the theory to high values of f/P ratio, a model is proposed to account for the noncontinuum behavior of the transport coefficients (viscosity and thermal conductivity) as the molecular mean free path approaches the acoustical enclosure dimensions. The theoretical dispersion and absorption show good agreement with measurements in argon over the classical and transition regions of f/P, but a discrepancy appears at higher values of f/P, where collective propagating modes, assumed in the theory, give way to single-particle modes, prevailing in the experiments.
Document ID
19990040596
Acquisition Source
Langley Research Center
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Zuckerwar, Allan J.
(NASA Langley Research Center Hampton, VA United States)
Date Acquired
August 19, 2013
Publication Date
April 1, 1999
Publication Information
Publication: Journal of Acoustical Society of America
Volume: 104
Issue: 4
Subject Category
Acoustics
Distribution Limits
Public
Copyright
Other

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