State-specific transport coefficients with varying molecular diameters using machine learning methods

Abstract

One of the important issues in modern non-equilibrium gas dynamics is the correct modeling of all possible molecular distributions over internal energy levels, taking into account a varying collision diameter. This is important for the accurate calculation of physical properties, transport coefficients, and flux terms. In particular, it is significant for the modeling of thermal protection systems for re-entry spacecraft and hypersonic vehicles. This work is devoted to modeling various non-equilibrium vibrational distributions for molecular species that differ significantly from the well-known Boltzmann and Treanor distributions, taking into account the effect of varying collision diameters of vibrationally excited molecules. The obtained distributions are implemented in the problem of calculating state-specific transport coefficients, and, in particular, for the calculation of the thermal conductivity coefficient using machine learning methods. To accelerate the calculation speed, the developed accurate state-to-state approach is combined with different machine learning methods: linear regression, decision tree, random forest, as well as a neural network (multilayer perceptron). It is shown that, in terms of Shapley values for the neural network regression of thermal conductivity, the molar fraction of vibrationally excited states (taking into account the varying collisional diameter) is of the same order of magnitude as other input parameters. It is demonstrated that, in terms of generalization ability, the neural network represents the most appropriate technique.