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Moment method for the Boltzmann equation of reactive quaternary gaseous mixture

Author

Listed:
  • Sarna, Neeraj
  • Oblapenko, Georgii
  • Torrilhon, Manuel

Abstract

We are interested in solving the Boltzmann equation of chemically reacting rarefied gas flows using the Grad’s-14 moment method. We first propose a novel mathematical model that describes the collision dynamics of chemically reacting hard spheres. Using the collision model, we present an algorithm to compute the moments of the Boltzmann collision operator. Our algorithm is general in the sense that it can be used to compute arbitrary order moments of the collision operator and not just the moments included in the Grad’s-14 moment system. For a first-order chemical kinetics, we derive reaction rates for a chemical reaction outside of equilibrium thereby, extending the Arrhenius law that is valid only in equilibrium. We show that the derived reaction rates (i) are consistent in the sense that at equilibrium, we recover the Arrhenius law and (ii) have an explicit dependence on the scalar fourteenth moment, highlighting the importance of considering a fourteen moment system rather than a thirteen one. Through numerical experiments we study the relaxation of the Grad’s-14 moment system to the equilibrium state.

Suggested Citation

  • Sarna, Neeraj & Oblapenko, Georgii & Torrilhon, Manuel, 2021. "Moment method for the Boltzmann equation of reactive quaternary gaseous mixture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
  • Handle: RePEc:eee:phsmap:v:574:y:2021:i:c:s0378437121001461
    DOI: 10.1016/j.physa.2021.125874
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    References listed on IDEAS

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    1. Silva, Adriano W. & Alves, Giselle M. & Kremer, Gilberto M., 2007. "Transport phenomena in a reactive quaternary gas mixture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 533-548.
    2. Rossani, A & Spiga, G, 1999. "A note on the kinetic theory of chemically reacting gases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(3), pages 563-573.
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