A kinetic model of polyatomic gas with resonant collisions

Abstract

We propose a kinetic model describing a polyatomic gas undergoing resonant collisions, in which the microscopic internal and kinetic energies are separately conserved during a collision process. This behaviour has been observed in some physical phenomena, for example in the collisions between selectively excited CO2 molecules. We discuss the model itself, prove the related H-theorem and show that, at the equilibrium, two temperatures are expected. We eventually present a numerical illustration of the model and its main properties.

Navier–Stokes Equations and Bulk Viscosity for a Polyatomic Gas with Temperature-Dependent Specific Heats

“…In this section, we show some numerical results for the three gases mentioned in Section 6.2, i.e., CO 2 , SF 6 , and CH 4 . The shock-wave structure based on the two-temperature NS equations ( 18) is compared with that based on the ordinary NS equations (14). For CO 2 gas, it is also compared with the result based on the original ES model (2) taken from [41].…”

“…However, it follows from (15) that large µ b /µ means small θ. Therefore, for the gases with large µ b /µ, the appropriate fluid-dynamic equations are not (14), derived under the assumption θ = O(1), but (18), derived under (17). This fact was already pointed out in [36] for a gas with constant specific heats.…”

“…Therefore, we need the principal equations governing T tr and T int , which are given by the system (18). The transition from (18) to (14) for θ such that O( ) θ O(1) can be shown by following the procedure in [44], as in the case of a gas with constant specific heats (see Appendix B in [46]).…”

“…The gas at upstream infinity (X 1 → −∞) is in an equilibrium state with density ρ − , flow velocity v − = (v − , 0, 0), and temperature T − , while the gas at downstream infinity (X 1 → +∞) is in another equilibrium state with density ρ + , flow velocity v + = (v + , 0, 0), and temperature T + . We investigate the steady behavior of the gas under the following assumptions: (i) the specific heat at constant volume c v is a known function of the temperature T; (ii) the behavior of the gas is described by the Navier-Stokes equations with a single temperature (14) or those with two temperatures (18); (iii) the problem is spatially one dimensional, so that the physical quantities are independent of X 2 and X 3 .…”

“…The basis of the study of such flows is kinetic theory of gases based on the Boltzmann Equation [3,[5][6][7][8]. However, since the Boltzmann equation has a complicated structure particularly for polyatomic gases, simplified Boltzmann equations for a polyatomic gas, in which the internal states are represented by a single variable associated with the energy of internal modes, have been proposed [9][10][11][12][13][14]. It should be mentioned that recent progress in the mathematical study of these Boltzmann equations is remarkable [12,[14][15][16][17].…”