IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v574y2021ics0378437121001461.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121001461
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2021.125874?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carvalho, Filipe & Polewczak, Jacek & Silva, Adriano W. & Soares, Ana Jacinta, 2018. "Transport coefficients for the simple reacting spheres kinetic model I: Reaction rate and shear viscosity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1018-1037.
    2. Bisi, M. & Rossani, A. & Spiga, G., 2015. "A conservative multi-group approach to the Boltzmann equations for reactive gas mixtures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 603-611.
    3. Conforto, F. & Jannelli, A. & Monaco, R. & Ruggeri, T., 2007. "On the Riemann problem for a system of balance laws modelling a reactive gas mixture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 67-87.
    4. Silva, Adriano W. & Alves, Giselle M. & Kremer, Gilberto M., 2008. "Enskog’s kinetic theory of dense gases for chemically reacting binary mixtures. I. Reaction rate and viscosity coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 1733-1749.
    5. Silva, Adriano W. & Alves, Giselle M. & Marques, Wilson & Kremer, Gilberto M., 2009. "Enskog’s kinetic theory of dense gases for chemically reacting binary mixtures, II: Light scattering and sound propagation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 295-310.
    6. Bisi, Marzia & Cáceres, María J. & Spiga, Giampiero, 2010. "A Bhatnagar–Gross–Krook kinetic approach to fast reactive mixtures: Relaxation problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4528-4544.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:574:y:2021:i:c:s0378437121001461. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.