Incorporation of O2 and N2 vibrational relaxation into the nonlinear fluid dynamic equations and into an acoustic energy conservation theorem
Abstract
A formulation of fluid dynamic equations for air is given based on concepts of irreversible thermodynamics. An explicit expression for the instantaneous entropy function is derived from statistical physical principles and is approximated for the case when only O2 and N2 internal vibrations are not in internal equilibrium. The fluid model includes an entropy balance equation based on this instantaneous entropy function. An acoustic energy conservation theorem is derived which includes a nonnegative expression for acoustic energy dissipation per unit time and volume. The latter is shown to a lowest order approximation of temperature times the irreversible entropy production term in the entropy balance equation, even though this term does not appear in the linear acoustic equations. An independent derivation of the absorption coefficient of plane waves is given utilizing the energy theorem.
 Publication:

American Institute of Aeronautics and Astronautics Conference
 Pub Date:
 October 1977
 Bibcode:
 1977aiaa.confQ....P
 Keywords:

 Aeroacoustics;
 Energy Conversion Efficiency;
 Molecular Oscillations;
 Molecular Relaxation;
 Nitrogen;
 Oxygen;
 Conservation Equations;
 Energy Dissipation;
 Entropy;
 Irreversible Processes;
 Nonlinear Equations;
 Thermodynamics;
 Thermodynamics and Statistical Physics