A fundamental thermodynamic correction to existing theory in quasi-equilibrium gas dynamics

Abstract

To satisfy fundamental thermodynamic requirements and in contrast to the conventional mathematical procedure, a small finite molecular sample is considered as the essential basis for a theoretical structure in gas dynamics. With molecular flux gradients present the conventional particle velocity used in the Euler-Lagrange relationship is then necessarily modified. Further corrections appear in the momentum and energy conservation equations; and it follows that the entropy increment for conventional isentropic conditions is not zero. Although the procedures are developed, with a number of simplifying approximations, for conventional adiabatic non-viscous, one-dimensional flow of a perfect gas at moderate Mach numbers, more complex conditions may be included, and do not fundamentally affect the principles involved. Quantitatively the corrections are significant when gradients are severe. For unsteady flow in a duct it is indicated, contrary to existing theory, that multi-values of the variables do not arise as a pressure wave progresses; and that attenuation of the peak amplitude does occur. It is suggested that the proposed structure provides an improved physical basis for the appraisal of phenomena in gas dynamics.