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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 the change of 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.
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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 to extend the temperature dynamics to the reactive mixtures by merely including the enthalpy of formation in addition to the previously considered sensible energy. 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 new lattice Boltzmann model for multicomponent ideal gas mixtures is presented. The model development consists of two parts. First, a new kinetic model for Stefan- Maxwell diffusion amongst the species is proposed and realized as a lattice Boltzmann equation on the standard discrete velocity set. Second, a compressible lattice Boltzmann model for the momentum and energy of the mixture is established. Both parts are consistently coupled through mixture composition, momentum, pressure, energy and enthalpy whereby a passive scalar advection-diffusion coupling is obviated, unlike in previous approaches. The proposed model is realized on the standard three-dimensional lattices and is validated with a set of benchmarks highlighting various physical aspects of compressible mixtures. Stefan-Maxwell diffusion is tested against experiment and theory of uphill diffusion of argon and methane in a ternary mixture with hydrogen. The speed of sound is measured in various binary and ternary compositions. We further validate the Stefan-Maxwell diffusion coupling with hydrodynamics by simulating diffusion in opposed jets and the three-dimensional Kelvin-Helmholtz instability of shear layers in a two-component mixture. Apart from the multicomponent compressible mixture, the proposed lattice Boltzmann model also provides an extension of the lattice Boltzmann equation to the compressible flow regime on the standard three-dimensional lattice.
The squirmer is a simple yet instructive model for microswimmers, which employs an effective slip velocity on the surface of a spherical swimmer to describe its self-propulsion. We solve the hydrodynamic flow problem with the lattice Boltzmann (LB) method, which is well-suited for time-dependent problems involving complex boundary conditions. Incorporating the squirmer into LB is relatively straight-forward, but requires an unexpectedly fine grid resolution to capture the physical flow fields and behaviors accurately. We demonstrate this using four basic hydrodynamic tests: Two for the far-field flow---accuracy of the hydrodynamic moments and squirmer-squirmer interactions---and two that require the near field to be accurately resolved---a squirmer confined to a tube and one scattering off a spherical obstacle---which LB is capable of doing down to the grid resolution. We find good agreement with (numerical) results obtained using other hydrodynamic solvers in the same geometries and identify a minimum required resolution to achieve this reproduction. We discuss our algorithm in the context of other hydrodynamic solvers and present an outlook on its application to multi-squirmer problems.
In this paper, we develop and characterize the fully dissipative Lattice Boltzmann method for ultra-relativistic fluids in two dimensions using three equilibrium distribution functions: Maxwell-Juttner, Fermi-Dirac and Bose-Einstein. Our results stem from the expansion of these distribution functions up to fifth order in relativistic polynomials. We also obtain new Gaussian quadratures for square lattices that preserve the spatial resolution. Our models are validated with the Riemann problem and the limitations of lower order expansions to calculate higher order moments are shown. The kinematic viscosity and the thermal conductivity are numerically obtained using the Taylor-Green vortex and the Fourier flow respectively and these transport coefficients are compared with the theoretical prediction from Grads theory. In order to compare different expansion orders, we analyze the temperature and heat flux fields on the time evolution of a hot spot.
A rigorous free energy model for ternary fluid flows with density ratio up to of order $O(10^3)$ is presented and implemented using the entropic lattice Boltzmann scheme. The model is thermodynamically consistent and allows a broad range of surface tension ratios, covering both partial wetting states where Neumann triangles are formed, and full wetting states where complete encapsulation of one of fluid components is observed. We further demonstrate that we can capture the bouncing, adhesive and insertive regimes for the binary collisions between immiscible droplets suspended in air. Our approach opens up a vast range of multiphase flow applications involving one gas and several liquid components.
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