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ABSTRACT
Previous two-fluid lattice Boltzmann (LB) models for multicomponent fluids are limited to mixtures with a low molecular weight ratio (i.e., below 9). In this paper, a finite difference-based two-fluid LB model is developed for mixtures with larger molecular weight ratios, which can be widely found in real applications. The basic idea is to use the finite difference scheme to discretize the discrete velocity LB equations derived from the two-fluid theory. The corresponding macroscopic hydrodynamic and diffusion equations are obtained by multiscale expansions. The adjusting strategy of model parameters significantly influencing the accuracy and stability of the LB model is discussed in detail. It is demonstrated that the present LB method is able to model multicomponent fluids with a high molecular weight ratio (e.g., 32). Further, the present model is applied to the simulation of multicomponent fluids in porous media.
Nomenclature
| cs | = | speed of sound |
| Dij | = | diffusion coefficient between species i and species j |
| = | discrete velocity set for species i | |
| f | = | density distribution function |
| = | equilibrium distribution function for species i | |
| Fα | = | forcing term |
| J | = | molar flux |
| Jσσ | = | self-collision term |
| Jσs | = | cross-collision term |
| M | = | molecular weight |
| p | = | pressure |
| R | = | gas constant |
| t | = | time |
| T | = | temperature |
| u | = | velocity |
| α | = | discrete velocity direction |
| ν | = | viscosity |
| ρ | = | density |
| τ | = | relaxation time for self-collision term |
| τD | = | relaxation time for cross-collision term |
| ωα | = | weighting function |
Nomenclature
| cs | = | speed of sound |
| Dij | = | diffusion coefficient between species i and species j |
| = | discrete velocity set for species i | |
| f | = | density distribution function |
| = | equilibrium distribution function for species i | |
| Fα | = | forcing term |
| J | = | molar flux |
| Jσσ | = | self-collision term |
| Jσs | = | cross-collision term |
| M | = | molecular weight |
| p | = | pressure |
| R | = | gas constant |
| t | = | time |
| T | = | temperature |
| u | = | velocity |
| α | = | discrete velocity direction |
| ν | = | viscosity |
| ρ | = | density |
| τ | = | relaxation time for self-collision term |
| τD | = | relaxation time for cross-collision term |
| ωα | = | weighting function |