Uncertainties in multi-temperature nonequilibrium partition functions and application to CO2

Abstract

Multi-temperature models are often used as a simplified way to describe nonequilibrium gases. These models assume Boltzmann distributions within each energy mode, which is useful for reducing the number of parameters in computations. This assumption requires that the energy modes are properly separated (which is valid, for instance, for vibration and rotation in low-lying rovibrational levels of diatomic molecules). For polyatomic molecules, several limitations arise. First, certain energy modes are often grouped together to further reduce the number of parameters, which requires additional hypotheses, and sometimes arbitrary grouping schemes. Moreover, the rovibrational levels of polyatomic molecules are often strongly coupled, and the assignment of the coupling terms to one or another energy mode is arbitrary. In this work, we present a method to quantify the influence of assignment or grouping schemes on nonequilibrium spectral models by comparing their impact on nonequilibrium partition functions, and we apply it to the CO2 molecule. We show that significant differences arise when reducing the nonequilibrium model to two temperatures only, as often done in CFD or spectroscopy applications. In particular, one should carefully justify whether the vibrational bending mode is in equilibrium with the rotational mode or with the other vibrational modes. We then determine the nonequilibrium range where a simple Uncoupled Vibrating Rotor model is sufficient, where the coupling term assignment scheme becomes important, and where the uncertainty induced by the assignment of the coupling terms can no longer be neglected. This approach can be extended to other molecules.