Discrete Boltzmann modeling of multiphase flows: hydrodynamic and thermodynamic non-equilibrium effects

A discrete Boltzmann model (DBM) is developed to investigate the hydrodynamic and thermodynamic non-equilibrium (TNE) effects in phase separation processes. The interparticle force drives changes and the gradient force, induced by gradients of macroscopic quantities, opposes them. In this paper, we investigate the interplay between them by providing detailed inspection of various non-equilibrium observables. Based on the TNE features, we define a TNE strength which roughly estimates the deviation amplitude from the thermodynamic equilibrium. The time evolution of the TNE intensity provides a convenient and efficient physical criterion to discriminate the stages of the spinodal decomposition and domain growth. Via the DBM simulation and this criterion, we quantitatively study the effects of latent heat and surface tension on phase separation. It is found that, the TNE strength attains its maximum at the end of the spinodal decomposition stage, and it decreases when the latent heat increases from zero. The surface tension effects are threefold, to prolong the duration of the spinodal decomposition stage, decrease the maximum TNE intensity, and accelerate the speed of the domain growth stage.Comment: 10 pages, 10 figure

Lattice BGK kinetic model for high speed compressible flows: hydrodynamic and nonequilibrium behaviors

We present a simple and general approach to formulate the lattice BGK model for high speed compressible flows. The main point consists of two parts: an appropriate discrete equilibrium distribution function (DEDF) $\mathbf{f}^{eq}$ and a discrete velocity model with flexible velocity size. The DEDF is obtained by $\mathbf{f}^{eq}=\mathbf{C}^{-1}\mathbf{M}$, where $\mathbf{M}$ is a set of moment of the Maxwellian distribution function, and $\mathbf{C}$ is the matrix connecting the DEDF and the moments. The numerical components of $\mathbf{C}$ are determined by the discrete velocity model. The calculation of $\mathbf{C}^{-1}$ is based on the analytic solution which is a function of the parameter controlling the sizes of discrete velocity. The choosing of discrete velocity model has a high flexibility. The specific heat ratio of the system can be flexible. The approach works for the one-, two- and three-dimensional model constructions. As an example, we compose a new lattice BGK kinetic model which works not only for recovering the Navier-Stokes equations in the continuum limit but also for measuring the departure of system from its thermodynamic equilibrium. Via adjusting the sizes of the discrete velocities the stably simulated Mach number can be significantly increased up to 30 or even higher. The model is verified and validated by well-known benchmark tests. Some macroscopic behaviors of the system due to deviating from thermodynamic equilibrium around the shock wave interfaces are shown.Comment: accepted for publication in EP

Droplet coalescence kinetics: thermodynamic non-equilibrium effects and entropy production mechanism

The thermodynamic non-equilibrium (TNE) effects and the relationships between various TNE effects and entropy production rate, morphology, kinematics, and dynamics during two initially static droplet coalescence are studied in detail via the discrete Boltzmann method. The temporal evolutions of the total TNE strength ($D^*$) and the total entropy production rate ($\dot S$) can both provide concise, effective and consistent physical criteria to distinguish the stages of droplet coalescence. Specifically, when $\bar D^*$ and $\dot S$ reach their maxima, it corresponds to the time when the liquid-vapor interface length changes the fastest; when $D^*$ and $\dot S$ reach their valleys, it corresponds to the moment of the droplet being the longest elliptical shape. During the merging process, the force contributed by surface tension in the coalescence direction acts as the primary promoting force for droplet coalescence and reaches its maximum concurrently with coalescent acceleration. In contrast, the force contributed by non-organized momentum fluxes (NOMFs) in the coalescing direction inhibits the merging process and reaches its maximum at the same time as $D^*$. For the coalescence of two unequal size droplets, the smaller droplet exhibits larger values for TNE intensity, merging velocity, driving force contributed by surface tension, and resistance contributed by NOMFs. Moreover, these values gradually increase with the initial radius ratio of the large and small droplets due to larger curvature. However, non-equilibrium components and forces related to shear velocity in the small droplet, are all smaller than those in the larger droplet and gradually decrease with the radius ratio

Thermodynamic non-equilibrium effects in bubble coalescence: A discrete Boltzmann study

The Thermodynamic Non-Equilibrium (TNE) effects in the coalescing process of two initially static bubbles under thermal conditions are investigated by a Discrete Boltzmann Model (DBM). The spatial distributions of the typical none-quilibrium quantity, i.e., the Non-Organized Momentum Fluxes (NOMF) during evolutions are investigated in detail. The density-weighted statistical method is used to highlight the relationship between the TNE effects and the morphological or kinetics characteristics of bubble coalescence. It is found that the $xx$-component and $yy$-component of NOMF are anti-symmetrical; the $xy$-component changes from an anti-symmetric internal and external double quadrupole structure to an outer octupole structure during the coalescing process. More importantly, the evolution of the averaged $xx$-component of NOMF provides two characteristic instants, which divide the non-equilibrium process into three stages. The first instant corresponds to the moment when the mean coalescing speed gets the maximum and at this time the ratio of minor and major axes is about $1/2$. The second instant corresponds to the moment when the ratio of minor and major axes gets $1$ for the first time. It is interesting to find that the three quantities, TNE intensity, acceleration of coalescence and negative slope of boundary length, show a high degree of correlation and attain their maxima simultaneously. Surface tension and heat conduction accelerate the process of bubble coalescence while viscosity delays it. Both surface tension and viscosity enhance the global non-equilibrium intensity, whereas heat conduction restrains it. These TNE features and findings present some new insights into the kinetics of bubble coalescence