Simulating Gas–Liquid Flows by Means of a Pseudopotential Lattice Boltzmann Method

Abstract

Dispersed gas (vapor)–liquid flow through an inclined microchannel with bends has successfully been simulated, that is, without numerical difficulties, by means of a two-phase Lattice Boltzmann method. Combining in this method the Shan-Chen pseudopotential interaction model with the Yuan and Schaefer proposal for dealing with nonideal equations of state makes high density ratios achievable. This approach also allows simulation of gas–liquid flows without explicitly having to track the phase interfaces. Rather, a potential function related to the equation of state for vapor–liquid equilibrium, a coupling strength representing attraction or repulsion between species, and a relaxation time scale take care of microscale and mesoscale phenomena such as phase separation and interfacial tension as well as interphase transport and multiphase flow. In addition, fluid–wall interaction (contact angle) is taken into account by selecting proper potential functions and coupling strengths. As far as the phase behavior is concerned, we assessed our method by studying the phase separation process and by validating against Maxwell’s equilibrium rule. Qualitative validation of our approach of gas–liquid flow has been done with a comparison against experimental data on a single bubble rise. Detailed simulations were carried out for an individual Taylor bubble in a channel, the results of which compared favorably to literature data.

Droplet–turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions

“…A few examples are simulations of binary droplet collisions and coalescence at different density ratios (Inamuro et al 2004a), inertial droplet collision dynamics (Inamuro, Tajima & Ogino 2004b;Sun, Jia & Wang 2014;Moqaddam, Chikatamarla & Karlin 2016;Montessori et al 2017) and droplet breakup in Stokes (Liu, Valocchi & Kang 2012) and inertial (Komrakova et al 2015b) shear flows. Some examples of the PP-LB method in particular are simulations of multiple bubble dynamics (Gupta & Kumar 2008), droplet deformation and breakup in shear flow (Xi & Duncan 1999;Biferale et al 2011), droplet collision (Lycett-Brown, Karlin & Luo 2011) and impact (Gupta & Kumar 2010) at high Weber numbers, droplet formation and breakup (Liu & Zhang 2011;Wang et al 2011) and gas-liquid flow (Kamali & Van den Akker 2013) in micro-channels. Chen et al (2014) gives an extensive review of the application of PP-LB to various physical problems involving droplets or bubbles.…”

“…Additionally, multiphase LB simulations suffer from spurious currents (u sp ) which are velocities arising from anisotropy in the discretization of inter-particle forces. While it has been shown that u sp can be kept small in the PP-LB method (Kamali & Van den Akker 2013;Zarghami, Looije & Van den Akker 2015), also lower than in comparison to conventional finite volume techniques like the volume-of-fluid method (Mukherjee et al 2018), in the free-energy LB method spurious current were found strong enough to dominate the multiphase kinetic energy spectra at high wavenumbers (Komrakova et al 2015a). Further, in LB, the characteristic fluid velocity (here the large-scale velocity U) should be kept smaller than the lattice speed of sound c s , such that the flow Mach number Ma = U/c s is low (where traditionally Ma < 0.3 is considered incompressible) and hence the flow being simulated obeys the incompressible Navier-Stokes equations.…”

“…2011), droplet collision (Lycett-Brown, Karlin & Luo 2011) and impact (Gupta & Kumar 2010) at high Weber numbers, droplet formation and breakup (Liu & Zhang 2011; Wang et al. 2011) and gas–liquid flow (Kamali & Van den Akker 2013) in micro-channels. Chen et al.…”

“…Additionally, multiphase LB simulations suffer from spurious currents ( ) which are velocities arising from anisotropy in the discretization of inter-particle forces. While it has been shown that can be kept small in the PP-LB method (Kamali & Van den Akker 2013; Zarghami, Looije & Van den Akker 2015), also lower than in comparison to conventional finite volume techniques like the volume-of-fluid method (Mukherjee et al. 2018), in the free-energy LB method spurious current were found strong enough to dominate the multiphase kinetic energy spectra at high wavenumbers (Komrakova et al.…”

Multiphase lattice Boltzmann simulations for porous media applications

“…These techniques include incorporating a realistic equation of state into the model [111,112], increasing the isotropy order of the interactive force [113,114], improving the force scheme [115][116][117][118], and using the Multi-Relaxation Time (MRT) scheme [109,119] instead of the BGK approximation. These techniques have been demonstrated to be effective in reducing the magnitude of spurious velocities, eliminating the unphysical dependence of equilibrium density and interfacial tension on viscosity (relaxation time), and increasing the viscosity and density ratios in simple systems [120][121][122][123][124]. As shown by Porter et al [120], the fourth-order isotropy in the interactive force results in stable bubble simulations for a viscosity ratio of up to 300, whereas the tenth-order isotropy result is in stable bubble simulations for a viscosity ratio of up to 1050.…”