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Improved three-dimensional color-gradient lattice Boltzmann model for immiscible multiphase flows
In this paper, an improved three-dimensional color-gradient lattice Boltzmann
(LB) model is proposed for simulating immiscible multiphase flows. Compared
with the previous three-dimensional color-gradient LB models, which suffer from
the lack of Galilean invariance and considerable numerical errors in many cases
owing to the error terms in the recovered macroscopic equations, the present
model eliminates the error terms and therefore improves the numerical accuracy
and enhances the Galilean invariance. To validate the proposed model, numerical
simulation are performed. First, the test of a moving droplet in a uniform flow
field is employed to verify the Galilean invariance of the improved model.
Subsequently, numerical simulations are carried out for the layered two-phase
flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using
the improved model, the numerical accuracy can be significantly improved in
comparison with the color-gradient LB model without the improvements. Finally,
the capability of the improved color-gradient LB model for simulating dynamic
multiphase flows at a relatively large density ratio is demonstrated via the
simulation of droplet impact on a solid surface.Comment: 9 Figure
Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model
Owing to its conceptual simplicity and computational efficiency, the
pseudopotential multiphase lattice Boltzmann (LB) model has attracted
significant attention since its emergence. In this work, we aim to extend the
pseudopotential LB model to simulate multiphase flows at large density ratio
and relatively high Reynolds number. First, based on our recent work [Li et
al., Phys. Rev. E. 86, 016709 (2012)], an improved forcing scheme is proposed
for the multiple-relaxation-time pseudopotential LB model in order to achieve
thermodynamic consistency and large density ratio in the model. Next, through
investigating the effects of the parameter a in the Carnahan-Starling equation
of state, we find that the interface thickness is approximately proportional to
1/sqrt(a). Using a smaller a will lead to a wider interface thickness, which
can reduce the spurious currents and enhance the numerical stability of the
pseudopotential model at large density ratio. Furthermore, it is found that a
lower liquid viscosity can be gained in the pseudopotential model by increasing
the kinematic viscosity ratio between the vapor and liquid phases. The improved
pseudopotential LB model is numerically validated via the simulations of
stationary droplet and droplet oscillation. Using the improved model as well as
the above treatments, numerical simulations of droplet splashing on a thin
liquid film are conducted at a density ratio in excess of 500 with Reynolds
numbers ranging from 40 to 1000. The dynamics of droplet splashing is correctly
reproduced and the predicted spread radius is found to obey the power law
reported in the literature.Comment: 9 figures, 2 tables, accepted by Physical Review E (in press
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Three-dimensional micro-droplet collision simulation using the Lattice Boltzmann method
This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.The modelling of binary droplet collisions has important applications in many engineering problems, including spray coating and fuel injection. The Lattice Boltzmann method (LBM) is a well established technique for modelling multiphase fluids, and does so without the difficulties of explicit interface tracking found in other CFD methods. However, simulating droplet collisions under realistic conditions remains a complex problem. Challenges include reproducing the different collision outcomes observed experimentally (Qian and Law, 1997), and maintaining a stable simulation at sufficiently high Reynolds and Weber numbers, and with a high density ratio between the liquid and gas phases. Although previous studies have achieved these goals individually, they have not been successfully combined to simulate droplet collisions with realistic physical parameters. A number of different methods for extending the LBM for multiphase flow exist, with the Shan-Chen interparticle potential method (Shan and Chen, 1993) being the basic model used here. Many extensions to improve the original Shan-Chen method have been proposed, to improve achievable Reynolds number and density ratio. Using combinations of these, both coalescence and separation of two-dimensional droplets were successfully simulated at density ratios of order 1000, and high Weber numbers (Lycett-Brown et al., 2011). In this study, the developed methodologies in Lycett-Brown et al. (2011) are extended to simulate three dimensional micro-droplet collisions by making use of the LBM’s excellent scalability on massively parallel computers. These high-resolution simulations are also compared with low-resolution three-dimensional simulations using a multiple-relaxation-time LBM approach (Monaco and Luo, 2008).This study is funded by the Engineering and Physical Sciences Research Council for Grant No. EP/I000801/1 and a HEC Studentship
Comparison of multiphase SPH and LBM approaches for the simulation of intermittent flows
Smoothed Particle Hydrodynamics (SPH) and Lattice Boltzmann Method (LBM) are
increasingly popular and attractive methods that propose efficient multiphase
formulations, each one with its own strengths and weaknesses. In this context,
when it comes to study a given multi-fluid problem, it is helpful to rely on a
quantitative comparison to decide which approach should be used and in which
context. In particular, the simulation of intermittent two-phase flows in pipes
such as slug flows is a complex problem involving moving and intersecting
interfaces for which both SPH and LBM could be considered. It is a problem of
interest in petroleum applications since the formation of slug flows that can
occur in submarine pipelines connecting the wells to the production facility
can cause undesired behaviors with hazardous consequences. In this work, we
compare SPH and LBM multiphase formulations where surface tension effects are
modeled respectively using the continuum surface force and the color gradient
approaches on a collection of standard test cases, and on the simulation of
intermittent flows in 2D. This paper aims to highlight the contributions and
limitations of SPH and LBM when applied to these problems. First, we compare
our implementations on static bubble problems with different density and
viscosity ratios. Then, we focus on gravity driven simulations of slug flows in
pipes for several Reynolds numbers. Finally, we conclude with simulations of
slug flows with inlet/outlet boundary conditions. According to the results
presented in this study, we confirm that the SPH approach is more robust and
versatile whereas the LBM formulation is more accurate and faster
Three-Dimensional Multi-Relaxation Time (MRT) Lattice-Boltzmann Models for Multiphase Flow
In this paper, three-dimensional (3D) multi-relaxation time (MRT)
lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to
the Bhatnagar-Gross-Krook (BGK) model, a widely employed kinetic model, in MRT
models the rates of relaxation processes owing to collisions of particle
populations may be independently adjusted. As a result, the MRT models offer a
significant improvement in numerical stability of the LB method for simulating
fluids with lower viscosities. We show through the Chapman-Enskog multiscale
analysis that the continuum limit behavior of 3D MRT LB models corresponds to
that of the macroscopic dynamical equations for multiphase flow. We extend the
3D MRT LB models developed to represent multiphase flow with reduced
compressibility effects. The multiphase models are evaluated by verifying the
Laplace-Young relation for static drops and the frequency of oscillations of
drops. The results show satisfactory agreement with available data and
significant gains in numerical stability.Comment: Accepted for publication in the Journal of Computational Physic
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