Lattice Boltzmann model with generalized wall boundary conditions for arbitrary catalytic reactivity

Abstract

A lattice Boltzmann model for multispecies flows with catalytic reactions is developed, which is valid from very low to very high surface Damköhler numbers (Das). The previously proposed model for catalytic reactions [S. Arcidiacono, J. Mantzaras, and I. V. Karlin, Phys. Rev. E 78, 046711 (2008)PLEEE81539-375510.1103/PhysRevE.78.046711], which is applicable for low-to-moderate Das and encompasses part of the mixed kinetics and transport-controlled regime, is revisited and extended for the simulation of arbitrary kinetics-to-transport rate ratios, including strongly transport-controlled conditions (Das→∞). The catalytic boundary condition is modified by bringing nonlocal information on the wall reactive nodes, allowing accurate evaluation of chemical rates even when the concentration of the deficient reactant at the wall becomes vanishingly small. The developed model is validated against a finite volume Navier-Stokes CFD (Computational Fluid Dynamics) solver for the total oxidation of methane in an isothermal channel-flow configuration. CFD simulations and lattice Boltzmann simulations with the old and new catalytic reaction models are compared against each other. The new model demonstrates a second order accuracy in space and time and provides accurate results at very high Das (∼109) where the old model fails. Moreover, to achieve the same accuracy at moderate-to-high Das of O(1), the new model requires ∼2d×N coarser grid than the original model, where d is the spatial dimension and N the number of species.