23 research outputs found
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)
and a discrete velocity model with flexible velocity size. The DEDF is obtained
by , where is a set of
moment of the Maxwellian distribution function, and is the matrix
connecting the DEDF and the moments. The numerical components of
are determined by the discrete velocity model. The calculation of
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 () and the total entropy production rate () can both
provide concise, effective and consistent physical criteria to distinguish the
stages of droplet coalescence. Specifically, when and reach
their maxima, it corresponds to the time when the liquid-vapor interface length
changes the fastest; when and 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 . 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 -component and -component of NOMF are anti-symmetrical; the
-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 -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 . The second instant corresponds to the moment when the
ratio of minor and major axes gets 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