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Register a new userA thermodynamically consistent pseudo-potential lattice Boltzmann model for multi-component, multiphase, partially miscible mixtures
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Current multi-component, multiphase pseudo-potential lattice Boltzmann models have thermodynamic inconsistencies that prevent them to correctly predict the thermodynamic phase behavior of partially miscible multi-component mixtures, such as hydrocarbon mixtures. This paper identifies these inconsistencies and attempts to design a thermodynamically consistent multi-component, multiphase pseudo-potential lattice Boltzmann model that allows mass transfer across the phase interfaces and is capable to predict the phase behavior of typically partially miscible hydrocarbon mixtures. The designed model defines the total interaction force for the entire phase and split the force into individual components. Through a properly derived force split factor associated with the volatility of each component, the model can achieve precise thermodynamic consistency in multi-component hydrocarbon mixtures, which is described by the iso-fugacity rule.
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In this brief report, a thermal lattice-Boltzmann (LB) model is presented for axisymmetric thermal flows in the incompressible limit. The model is based on the double-distribution-function LB method, which has attracted much attention since its emergence for its excellent numerical stability. Compared with the existing axisymmetric thermal LB models, the present model is simpler and retains the inherent features of the standard LB method. Numerical simulations are carried out for the thermally developing laminar flows in circular ducts and the natural convection in an annulus between two coaxial vertical cylinders. The Nusselt number obtained from the simulations agrees well with the analytical solutions and/or the results reported in previous studies.
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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.
In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard D2Q9 lattice is developed in the framework of the double-distribution-function (DDF) approach in which the viscous heat dissipation and compression work are considered. In the model, a density distribution function is used to simulate the flow field, while a total energy distribution function is employed to simulate the temperature field. The discrete equilibrium density and total energy distribution functions are obtained from the Hermite expansions of the corresponding continuous equilibrium distribution functions. The pressure given by the equation of state of perfect gases is recovered in the macroscopic momentum and energy equations. The coupling between the momentum and energy transports makes the model applicable for general thermal flows such as non-Boussinesq flows, while the existing DDF LB models on standard lattices are usually limited to Boussinesq flows in which the temperature variation is small. Meanwhile, the simple structure and basic advantages of the DDF LB approach are retained. The model is tested by numerical simulations of thermal Couette flow, attenuation-driven acoustic streaming, and natural convection in a square cavity with small and large temperature differences. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature.
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