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’.

A new lattice Boltzmann model (LBM) for chemically reactive mixtures is presented. The approach capitalizes on the recently introduced thermodynamically consistent LBM for multicomponent mixtures of ideal gases. Similar to the non-reactive case, the present LBM features Stefan–Maxwell diffusion of chemical species and a fully on-lattice mean-field realization of the momentum and energy of the flow. Besides introducing the reaction mechanism into the kinetic equations for the species, the proposed LBM also features a new realization of the compressible flow by using a concept of extended equilibrium on a standard lattice in three dimensions. The full thermodynamic consistency of the original non-reactive multicomponent LBM enables us to extend the temperature dynamics to the reactive mixtures by merely including the enthalpy of formation in addition to the sensible energy considered previously. Furthermore, we describe in detail the boundary conditions to be used for reactive flows of practical interest. The model is validated against a direct numerical simulation of various burning regimes of a hydrogen/air mixture in a microchannel, in two and three dimensions. Excellent comparison in these demanding benchmarks indicates that the proposed LBM can be a valuable and universal model for complex reactive flows.

A kinetic model based on the particles on demand method is introduced for gas phase detonation hydrodynamics in conjunction with the Lee–Tarver reaction model. The proposed model is realized on two- and three-dimensional lattices and is validated with a set of benchmarks. Quantitative validation is performed with the Chapman–Jouguet theory up to a detonation wave speed of Mach 20 in one dimension. Two-dimensional outward expanding circular detonation is tested for isotropy of the model as well as for the asymptotic detonation wave speed. Mach reflection angles are verified in setups consisting of interacting strong bow shocks emanating from detonation. Spherical detonation is computed to show the viability of the proposed model for three-dimensional simulations.

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