Modeling of Chemical Reactions in Rarefied Gas Flows by the Kinetic Fokker-Planck Method

Abstract

Flows encountered in space applications, like atmospheric reentry or thruster plume expansion and interactions, can be described by the well-known Boltzmann equation. A common approach to numerically solve it is the Direct Simulation Monte-Carlo (DSMC) [1]. The method is very efficient for high Knudsen numbers but becomes increasingly computationally intensive when approaching the continuum limit. In this regime the Boltzmann equation can be numerically solved using the kinetic Fokker-Planck method [2] which, like DSMC, relies on simulated particles to transport mass, momentum and energy through the flow domain, but does not resolve individual collisions. While this approach has been extended to mixtures [3, 4] and diatomic [5, 6] as well as polyatomic gases [7, 8], the modeling of chemical reactions remains a open research topic. Many problems arise from the fact that properties of the reactants need to be considered to evaluate a chemical reaction. This contradicts the Fokker-Planck approach that achieves its linear scaling in terms of particle numbers by forgoing the creation of interaction pairs.

We propose a novel approach to model chemical reactions in the Fokker-Planck framework which aims to conserve mass, energy and momentum while retaining the performance advantages in areas of high density [9]. In this presentation we show an extension of the model for recombination and exchange reactions as well as verification results obtained from code-to-code comparisons.