A lattice Boltzmann model for reactive mixtures

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’.

Consistent lattice Boltzmann model for reactive mixtures

“…The species densities and the partial momenta are defined accordingly as while partial momenta sum to the mixture momentum, Following Sawant et al. (2021 a , b ), the kinetic equations for the species can be written as where are Stefan–Maxwell binary diffusion coefficients, while the reaction source term satisfies the following conditions, consistent with (2.4): We now proceed with specifying the equilibrium , the quasi-equilibrium and the reaction source term .…”

“…Furthermore, unlike previous realizations (Sawant et al. 2021 a ; Sawant, Dorschner & Karlin 2021 b ), we use the extended LBM (Saadat, Dorschner & Karlin 2021 a ; Saadat et al. 2021 b ) for the mean-field model.…”

Particles on Demand for flows with strong discontinuities

“…Let us consider a reference frame λ defined by a reference temperature T and frame velocity u, λ = {u, T }. (12) Discrete velocities relative to the reference frame λ (12) are defined as,…”

“…In order to keep the notation simple, we shall consider f -populations (g-populations are considered in the same fashion). A key element of PonD is the transformation of populations f λ i , defined with respect to a λ-reference (12), to a different reference frame λ ,…”

“…, Q − 1, fitting into a regular space-filling lattice, with the kinetic equation for the populations f i (x, t) following a simple algorithm of "stream along links c i and collide at the nodes x in discrete time t". Since its inception [1,2], LBM has evolved into a versatile tool for the simulation of complex flows including transitional flows [3], flows in complex moving geometries [4], thermal and convective flows [5][6][7], multiphase and multicomponent flows [8][9][10][11], reactive flows [12] and rarefied gas [13], to mention a few recent instances; see [14][15][16] for a discussion of LBM and its application areas.…”