Abstract
A new lattice Boltzmann model for reactive ideal gas mixtures is presented. The model is an extension to reactive flows of the recently proposed multi-component lattice Boltzmann model for compressible ideal gas mixtures with Stefan–Maxwell diffusion for species interaction. First, the kinetic model for the Stefan–Maxwell diffusion is enhanced to accommodate a source term accounting for the change in the mixture composition due to chemical reaction. Second, by including the heat of formation in the energy equation, the thermodynamic consistency of the underlying compressible lattice Boltzmann model for momentum and energy allows a realization of the energy and temperature change due to chemical reactions. This obviates the need for ad-hoc modelling with source terms for temperature or heat. Both parts remain consistently coupled through mixture composition, momentum, pressure, energy and enthalpy. The proposed model uses the standard three-dimensional lattices and is validated with a set of benchmarks including laminar burning speed in the hydrogen–air mixture and circular expanding premixed flame.This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.
Highlights
The lattice Boltzmann method (LBM) is a recast of fluid dynamics into a fully discrete kinetic system for the populations fi(x, t) of designer particles, which are associated with the discrete velocities ci fitting into a regular space-filling lattice
This is achieved by supplying a reaction source term to the kinetic equations for the species in such a way that the Stefan–Maxwell diffusion mechanism already implemented by the model stays intact
We proposed a lattice Boltzmann framework to simulate reactive mixtures
Summary
The lattice Boltzmann method (LBM) is a recast of fluid dynamics into a fully discrete kinetic system for the populations fi(x, t) of designer particles, which are associated with the discrete velocities ci fitting into a regular space-filling lattice. The strongly coupled formulation consists of kinetic equations for momentum, energy and species dynamics and was validated for a variety of test cases involving uphill diffusion, opposed jets and Kelvin–Helmholtz instability. This extends the LBM to realistic mixtures and opens the door for reactive flow applications with a fully kinetic approach, which is the subject of this paper. This is achieved by supplying a reaction source term to the kinetic equations for the species in such a way that the Stefan–Maxwell diffusion mechanism already implemented by the model stays intact.
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