Lattice Boltzmann model for thermal binary-mixture gas flows

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

A lattice Boltzmann model for multispecies flows with catalytic reactions is developed, which is valid from very low to very high surface Damköhler numbers (Da_{s}). 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 Da_{s} 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 (Da_{s}→∞). 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 Da_{s} (∼10^{9}) where the old model fails. Moreover, to achieve the same accuracy at moderate-to-high Da_{s} of O(1), the new model requires ∼2^{d}×N coarser grid than the original model, where d is the spatial dimension and N the number of species.

Extended Lattice Boltzmann Model

Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and the isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model also remains valid for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.

Multiple-relaxation-time discrete Boltzmann modeling of multicomponent mixture with nonequilibrium effects

A multiple-relaxation-time discrete Boltzmann model (DBM) is proposed for multicomponent mixtures, where compressible, hydrodynamic, and thermodynamic nonequilibrium effects are taken into account. It allows the specific heat ratio and the Prandtl number to be adjustable, and is suitable for both low and high speed fluid flows. From the physical side, besides being consistent with the multicomponent Navier-Stokes equations, Fick's law, and Stefan-Maxwell diffusion equation in the hydrodynamic limit, the DBM provides more kinetic information about the nonequilibrium effects. The physical capability of DBM to describe the nonequilibrium flows, beyond the Navier-Stokes representation, enables the study of the entropy production mechanism in complex flows, especially in multicomponent mixtures. Moreover, the current kinetic model is employed to investigate nonequilibrium behaviors of the compressible Kelvin-Helmholtz instability (KHI). The entropy of mixing, the mixing area, the mixing width, the kinetic and internal energies, and the maximum and minimum temperatures are investigated during the dynamic KHI process. It is found that the mixing degree and fluid flow are similar in the KHI process for cases with various thermal conductivity and initial temperature configurations, while the maximum and minimum temperatures show different trends in cases with or without initial temperature gradients. Physically, both heat conduction and temperature exert slight influences on the formation and evolution of the KHI morphological structure.

Lattice Boltzmann model for weakly compressible flows

We present an energy conserving lattice Boltzmann model based on a crystallographic lattice for simulation of weakly compressible flows. The theoretical requirements and the methodology to construct such a model are discussed. We demonstrate that the model recovers the isentropic sound speed in addition to the effects of viscous heating and heat flux dynamics. Several test cases for acoustics and thermal and thermoacoustic flows are simulated to show the accuracy of the proposed model.

Thermal multicomponent lattice Boltzmann model for catalytic reactive flows

Catalytic reactions are of great interest in many applications related to power generation, fuel reforming and pollutant abatement, as well as in various biochemical processes. A recently proposed lattice Boltzmann model for thermal binary-mixture gas flows [J. Kang, N. I. Prasianakis, and J. Mantzaras, Phys. Rev. E. 87, 053304 (2013)] is revisited and extended for the simulation of multispecies flows with catalytic reactions. The resulting model can handle flows with large temperature and concentration gradients. The developed model is presented in detail and validated against a finite volume Navier-Stokes solver in the case of channel-flow methane catalytic combustion. The surface chemistry is treated with a one-step global reaction for the catalytic total oxidation of methane on platinum. In order to take into account thermal effects, the catalytic boundary condition of S. Arcidiacono, J. Mantzaras, and I. V. Karlin [Phys. Rev. E 78, 046711 (2008)] is adapted to account for temperature variations. Speed of sound simulations further demonstrate the physical integrity and unique features of the model.