2D lattice-boltzmann method with detailed surface chemistry: conservation of geometrical surface

• Implementation of detailed surface chemistry into D2Q9 Lattice-Boltzmann code. • Staircase-shaped interfaces in LBM are always too large versus geometrical surfaces. • Error in surface size is quantified based on theoretical investigations. • An approach is developed to conserve geometrical surface in LBM. • Validation for flow around bodies with surface reaction shows perfect results. The paper discusses the coupling of detailed surface chemistry to the Lattice-Boltzmann Method and shows an approach on how the geometrical catalytic surface can be preserved. Results from calculations with the 2D LBM code MATRICS for formaldehyde conversion in a channel show good agreement compared to measurements under diffusion-controlled conditions, but not for a kinetically controlled system. Results fit for both modes of operation with results from a Finite-Volume code. Modeling of systems with surface chemistry requires the consideration of the exact geometrical surface. However, basis of LBM is a staircase approximation for interfaces between fluid and solid. Based on theoretical derivations, it was shown that the asymptotic discretization error for circles is 27%. The error of skew lines is maximal for an angle of α = 45° and shows the value of 41%. The discretization error for curvilinear interfaces cannot be diminished by grid refinement. An approach was developed, which allows the use of the exact geometric surface for calculation of surface chemistry. It consists of two steps: 1. Implementation of the species fluxes at surfaces as volumetric sources in wall bounded fluid cells. 2. Segmentation of the original geometrical surface and assignment of line segments to reactive wall cells located nearby. The validation of the approach by calculation of flows around circles and rotated squares shows the discretization errors predicted by theory and allows to suppress the errors due to the incorporation of the exact size of curvilinear or skew geometrical interfaces in the calculation.