Multiple-relaxation-time discrete Boltzmann modeling of multicomponent mixture with nonequilibrium effects

Abstract

A multiple-relaxation-time discrete Boltzmann model (DBM) is proposed for multicomponent mixtures, where compressible, hydrodynamic, and thermodynamic nonequilibrium effects are taken into account. It allows the specific heat ratio and the Prandtl number to be adjustable, and is suitable for both low and high speed fluid flows. From the physical side, besides being consistent with the multicomponent Navier-Stokes equations, Fick's law, and Stefan-Maxwell diffusion equation in the hydrodynamic limit, the DBM provides more kinetic information about the nonequilibrium effects. The physical capability of DBM to describe the nonequilibrium flows, beyond the Navier-Stokes representation, enables the study of the entropy production mechanism in complex flows, especially in multicomponent mixtures. Moreover, the current kinetic model is employed to investigate nonequilibrium behaviors of the compressible Kelvin-Helmholtz instability (KHI). The entropy of mixing, the mixing area, the mixing width, the kinetic and internal energies, and the maximum and minimum temperatures are investigated during the dynamic KHI process. It is found that the mixing degree and fluid flow are similar in the KHI process for cases with various thermal conductivity and initial temperature configurations, while the maximum and minimum temperatures show different trends in cases with or without initial temperature gradients. Physically, both heat conduction and temperature exert slight influences on the formation and evolution of the KHI morphological structure.

Droplet evaporation in finite-size systems: Theoretical analysis and mesoscopic modeling

“…The LB method can be viewed as a mesoscopic "computational fluid dynamics" approach that simulates complex fluids by solving a specific discrete Boltzmann equation for the density distribution function (DDF) f i [20,[33][34][35][36][37][38][39][40]. A standard LB algorithm consists of two steps: (i) the collision step, representing the time relaxation towards the local equilibrium state due to molecular collisions, and (ii) the streaming step, standing for molecular free streaming.…”

Discrete Boltzmann modeling of detonation: Based on the Shakhov model

“…At present, there are mainly two methods to overcome this defect: (i) using the Multiple Relaxation Time (MRT) model 16,51,[56][57][58] , and (ii) reasonably modifying the framework of the Single Relaxation Time (SRT) BGK-like model 54,55,59 , and both of them have their own advantages and strengths. At present, in the DBM modeling including chemical reactions, the previous works to solve the problem of fixed Pr numbers are mainly based on the first idea 51,56 . In this paper, we propose a discrete Boltzmann model for detonation based on the Shakhov model, so that the Pr number can be adjusted in the SRT framework.…”

A Lattice-Boltzmann study of premixed flames thermo-acoustic instabilities

“…Note that another class LB methods is available for compressible flows -usually referred to as Discrete Boltzmann Methods -with increased focus on the thermodynamic non-equilibrium behaviors [23,24]. They have been applied successfully to multiphase [25], multicomponent flows [26], as well as detonations [27,28].…”