Kinetic theory derivation of transport equations for gases with internal energy

Abstract

Multitemperature models are widely used in the aerospace community to model atmospheric entry flows. In this paper, we propose a general description of the internal energy excitation of a molecular gas in thermal nonequilibrium by distinguishing between slow and fast collisions. A multiscale Chapman-Enskog method is used to study thermalization and derive Euler equations of conservation of mass, momentum, translational energy and internal energy. As opposed to conventional perturbation methods, the fast collision operator is expanded in the small parameter used to define the threshold for the net energy for fast collisions. We show that the role of the fast collisions is to thermalize the translational and internal energy modes, whereas the role of the slow collisions is to contribute to the thermal relaxation of the translational and internal energy modes.