A lattice Boltzmann model for reactive mixtures

Particles on demand method: Theoretical analysis, simplification techniques, and model extensions

The particles on demand method [Phys. Rev. Lett. 121, 130602 (2018)0031-900710.1103/PhysRevLett.121.130602] was recently formulated with a conservative finite-volume discretization and validated against challenging benchmarks. In this work, we focus on the properties of the reference frame transformation and its implications on the accuracy of the model. Based on these considerations, we propose strategies that simplify the scheme and generalize it to include a tunable Prandtl number via quasi-equilibrium relaxation. Finally, we adapt concepts from the multiscale semi-Lagrangian lattice Boltzmann formulation to the proposed framework, further improving the potential and the operating range of the kinetic model. Numerical simulations of high Mach compressible flows demonstrate excellent accuracy and stability of the model over a wide range of conditions.

Lattice Boltzmann modeling and simulation of velocity and concentration slip effects on the catalytic reaction rate of strongly nonequimolar reactions in microflows

A lattice Boltzmann (LB) interfacial gas-solid three-dimensional model is developed for isothermal multicomponent flows with strongly nonequimolar catalytic reactions, further accounting for the presence of velocity slips and concentration jumps. The model includes diffusion coefficients of all reactive species in the calculation of the catalytic reaction rates as well as an updated velocity at the reactive boundary node. Lattice Boltzmann simulations are performed in a catalytic channel-flow geometry under a wide range of Knudsen (Kn) and surface Damköhler (Da_{s}) numbers. Comparisons with simulations from a computational fluid dynamics (CFD) Navier-Stokes solver show good agreement in the continuum regime (Kn<0.01) in terms of flow velocity and reactive species distributions, while comparisons with direct simulation Monte Carlo results from the literature attest to the model's applicability in capturing the correct slip velocity at Kn as high as 0.1, even with a significantly reduced number of grid points (N=10) in the cross-flow direction. Theoretical and numerical results demonstrate that the term Da_{s}×Kn×A_{2} (where A_{2} is a function of the mass accommodation coefficient) determines the significance of the concentration jump on the catalytic reaction rate. The developed model is applicable for many catalytic microflow systems with complex geometries (such as reactors with porous networks) and large velocity/concentration slips (such as catalytic microthrusters for space applications).

Particles on demand for flows with strong discontinuities

Particles-on-demand formulation of kinetic theory [B. Dorschner, F. Bösch and I. V. Karlin, Phys. Rev. Lett. 121, 130602 (2018)0031-900710.1103/PhysRevLett.121.130602] is used to simulate a variety of compressible flows with strong discontinuities in density, pressure, and velocity. Two modifications are applied to the original formulation of the particles-on-demand method. First, a regularization by Grad's projection of particles populations is combined with the reference frame transformations in order to enhance stability and accuracy. Second, a finite-volume scheme is implemented which allows tight control of mass, momentum, and energy conservation. The proposed model is validated with an array of challenging one- and two-dimensional benchmarks of compressible flows, including hypersonic and near-vacuum situations, Richtmyer-Meshkov instability, double Mach reflection, and astrophysical jet. Excellent performance of the modified particles-on-demand method is demonstrated beyond the limitations of other lattice Boltzmann-like approaches to compressible flows.