Discrete Boltzmann multi-scale modelling of non-equilibrium multiphase flows

Abstract

The aim of this paper is twofold: the first aim is to formulate and validate a multi-scale discrete Boltzmann method (DBM) based on density functional kinetic theory for thermal multiphase flow systems, ranging from continuum to transition flow regime; the second aim is to present some new insights into the thermo-hydrodynamic non-equilibrium (THNE) effects in the phase separation process. Methodologically, for bulk flow, DBM includes three main pillars: (i) the determination of the fewest kinetic moment relations, which are required by the description of significant THNE effects beyond the realm of continuum fluid mechanics; (ii) the construction of an appropriate discrete equilibrium distribution function recovering all the desired kinetic moments; (iii) the detection, description, presentation and analysis of THNE based on the moments of the non-equilibrium distribution ( $f-f^{(eq)}$ ). The incorporation of appropriate additional higher-order thermodynamic kinetic moments considerably extends the DBM's capability of handling larger values of the liquid–vapour density ratio, curbing spurious currents, and ensuring mass/momentum/energy conservation. Compared with the DBM with only first-order THNE (Gan et al., Soft Matt., vol. 11 (26), 2015, pp. 5336–5345), the model retrieves kinetic moments beyond the third-order super-Burnett level, and is accurate for weak, moderate and strong THNE cases even when the local Knudsen number exceeds $1/3$ . Physically, the ending point of the linear relation between THNE and the concerned physical parameter provides a distinct criterion to identify whether the system is near or far from equilibrium. Besides, the surface tension suppresses the local THNE around the interface, but expands the THNE range and strengthens the THNE intensity away from the interface through interface smoothing and widening.

Lattice Boltzmann modelling of isothermal two-component evaporation in porous media

“…2016; Gan et al. 2022; Huang, Li & Adams 2022). Compared with PNMs, the LBM is a more accurate pore-scale method since the bounce-back type of boundary schemes in the LBM is very suitable for realistic and complex pore structures (Liu et al.…”

“…Different from the continuum models, the LBM is a solver of a specific discrete Boltzmann equation, designed to recover the Navier-Stokes equations in the low-Mach-number limit (Qiand, d'Humières & Lallemand 1992;Shan 2006;Guo & Shu 2013;Succi 2018). The mesoscale nature of the LBM allows the natural incorporation of micro-and mesoscale physics, leading to straightforward treatment of multiphase interface dynamics, such as phase separation and breakup and/or merging of phase interfaces (Shan & Chen 1993, 1994Succi 2015;Li et al 2016;Gan et al 2022;Huang, Li & Adams 2022). Compared with PNMs, the LBM is a more accurate pore-scale method since the bounce-back type of boundary schemes in the LBM is very suitable for realistic and complex pore structures (Liu et al 2016;Chen et al 2022), discarding the need for large simplification of real geometries.…”

Gas‐kinetic unified algorithm for two‐dimensional planar and axisymmetric nozzle flows

“…Direct numerical solutions of the Boltzmann equation for gas flows involves the calculation of the molecular distribution function as well as the collision integral at each velocity ordinate point in a three‐dimensional infinite velocity space 34 . Over the past decades, various kinetic methods have been developed to model and simulate the complex non‐equilibrium flows over a wide range of Knudsen numbers 35‐38 . In order to study aerodynamic problems covering various flow regimes, Li et al 4,39‐43 presented a unified computable modeling on the collision integral of the Boltzmann equation, in which the molecular collision relaxing parameter and the local equilibrium distribution function can be integrated with the macroscopic flow variables, the gas viscosity transport coefficient, the thermodynamic effect, the molecular power law, molecular models, and the flow state controlling parameter from various flow regimes and the gas‐kinetic unified algorithm (GKUA) has been presented and used to simulate the gas flows from highly rarefied free‐molecule flow to continuum flow regimes with the whole range of Knudsen numbers, specially to research the aerodynamic behaviors for the uncontrolled Tiangong‐1 target spacecraft, the controlled Tiangong‐2 space laboratory successively during the reentry and microscale flows in MEMS devices.…”

Molecular kinetic modelling of non-equilibrium transport of confined van der Waals fluids

“…Therefore, a multiscale model is required to capture both molecular and continuum effects. Kinetic theory relates the molecular-scale dynamics to the continuum-scale flow properties, serving as a bridge between the continuum and atomistic worlds (Kogan 1973;Guo & Shu 2013;Gan et al 2022). The fundamental equation in kinetic theory is the Boltzmann equation for ideal gases (Takata & Noguchi 2018).…”