Lattice Boltzmann method for the simulation of miscible gases


In general, mass transport and diffusion process involve complex geometries and complicated non-linear interactions between components. Analytical models are usually inappropriate and experiments are not always possible. Numerical simulations are often the only way to understand the underlying mechanics of mixing dynamics. The lattice Boltzmann method (LBM) is an alternative method for simulating fluid flows. With its mesoscopic features, simple algorithm and great performance in parallel computing, the LBM can be a powerful tool for the simulation of multicomponent flows. The first approach for the simulation of mixtures is the single-fluid approach which assumes as unknowns the species densities and the whole mixture velocity. The second strategy is called multi-fluid because it involves solving the equations for the conservation of mass and momentum for each species (species densitiesand species velocities are unknown). The latter is often preferred when the properties of the components differ greatly and is adopted in number of multicomponent lattice Boltzmann models [1, 2, 3, 4]. The model proposed here is derived from an alternative theory of multicomponent fluid diffusion by Kerkhof [5] based on an expansion of the legacy theory of Hirschfelder, Curtiss and Bird [6]. In contrast with previous lattice Boltzmann models, the diffusion force is directly added to the momentum equation through a Guo’s forcing scheme [7]. In addition, the corresponding transport coefficients, viscosity and diffusion coefficients for each species, are given according to the molecular properties of the components. Then, some numerical simulations are presented for validation purposes. First, a simple diffusion test is performed and measured diffusion coefficients from a decay of a sinusoidal density wave agree well with theoretical values. Finally, more challenging mixture dynamics are simulated through the viscous fingering instability which occurs when a less viscous fluid displaces a more viscous one. Macro-scale and pore scale dynamics of such an instability are simulated and analyzed in the framework of the proposed lattice Boltzmann model.

Jun 25, 2018 — Jun 29, 2018
Worcester, USA