Consistent lattice Boltzmann model for multicomponent mixtures

Abstract

Abstract

A lattice Boltzmann model for reactive mixtures

“…Combined with the equation of state (2.2), the partial pressure Pa takes the form Pa=ρaRaT, where Ra=RU/ma is the specific gas constant of the component. A kinetic model for the Stefan–Maxwell diffusion in the non-reactive mixture was introduced in [11]. Here, we extend the formulation [11] to include the reaction.…”

“…A kinetic model for the Stefan–Maxwell diffusion in the non-reactive mixture was introduced in [11]. Here, we extend the formulation [11] to include the reaction. To that end, we write the kinetic equation for the populations fai, a=1,…,M, of the component a , corresponding to the discrete velocities bold-italicci, i=0,…,Q−1, ∂tfai+bold-italicci⋅normal∇fai=∑b≠aMPXaXbDab[(faieq−faiρa)−(fbieq−fbi∗ρb)]+f˙aic. Here scriptDab are the binary diffusivity coefficients.…”

“…The species’ densities ρa and partial momenta ρaua are, respectively, ρa=∑i=0Q−1fai1emand1emρaua=∑i=0Q−1faibold-italicci. The momenta of the components sum up to the mixture momentum, At variance with the non-reactive mixture [11], kinetic equation (2.3) includes a source term f˙aic which implements the rate of change of ρa due to the reaction and satisfies the following conditions, ∑i=0Q−1f˙aic=ρ˙ac1emand1em∑i=0Q−1f˙aicbold-italicci=ρ˙acbold-italicu. The kinetic model (…”

“…Derivation of the lattice Boltzmann equation from the kinetic model (2.3) proceeds along the lines of the non-reactive case [11]. Upon integration of (2.3) along the characteristics and application of the trapezoidal rule, we arrive at a fully discrete lattice Boltzmann equation faifalse(x+bold-italicciδt,t+δtfalse)=faifalse(x,tfalse)+2βafalse[faieqfalse(x,tfalse)−faifalse(x,tfalse)false]+δtfalse(βa−1false)Faifalse(x,tfalse)+δtf˙aic. The discrete equation (2.12) is used in the actual numerical implementation.…”

Progress in mesoscale methods for fluid dynamics simulation

“…[1] discuss a GPU implementation of pseudo potential lattice Boltzmann models for three-dimensional immiscible Rayleigh–Taylor turbulence. Sawant et al [2] present a new LB models for reactive mixtures and validate it for the case of laminar burning processes and propagation of circular flames. Li et al [3] present the application of reactive LB methods electro-kinetic fluids in porous media and assess the corresponding conversion efficiency.…”