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

Ind. Eng. Chem. Res. Volume: 52   Issue: 33   Pages: 11365-11377, (2013).

Kamali, M. R.; Van den Akker, H. E. A.

Department of Chemical Engineering, Delft University of Technology, Delft, Netherlands

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-Chen1 pseudopotential interaction model with the Yuan and Schaefer2 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.

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Additional Information: 

The 2013 paper due to Kamali and Van den Akker reports on the use of the pseudo-potential Lattice Boltzmann Method (LBM) for simulating gas(vapour)-liquid flows. This method was originally proposed by Shan & Chen (1993) and later on modified and improved with the view of dealing with various equations of state and higher density ratios.

In general, LBMs offer an interesting approach to chemical reactor modeling. Rather than by solving for the usual continuum variables as in conventional CFD methods, in LBMs mesoscopic fluid particles containing a distribution of molecules are allowed to move in specified directions and collide at lattice nodes. By allowing the fluid particles to relax towards the Maxwell-Boltzmann equilibrium distribution, dynamic fluid flow is mimicked macroscopically. LBMs are well-suited for chemical engineering applications due to its close connection to kinetic theory, ease of implementation, computational efficiency, and ability to introduce multiple physical and chemical phenomena locally. The two movies illustrate the capability of the LB code under development in predicting the motion of a liquid droplet in an inclined micro-channel with different wetting properties (see also Figure 3 of the paper).

The 2013 paper due to Kamali and Van den Akker is part of a larger endeavour aimed at computationally simulating two-phase chemical reactors. The eventual goal is to develop a robust LB code capable of carrying out meso-scale simulations quantitatively reproducing the dynamic interplay of  convective transport of heat and chemical species which under two-phase flow conditions take part in a bulk or surface chemical reaction with a complex (non-trivial) reaction scheme. The choice of the parameter values should reflect operating conditions representative of industrial chemical reactors. A preliminary exercise for a strongly simplified case without flow and without thermal effects can be found in a 2012 paper due to Kamali¸ Sundaresan, Van den Akker and Gillissen:  A multi-component two-phase LB method applied to a 1-D Fischer-Tropsch reactor:  Chem. Eng. J.  207, 587-595.

Further papers resulting from Kamali’s PhD thesis are a 2011 paper on contact line motion without slip (see: Chem. Eng. Sci. 66, 3452-3458) and a 2013 paper on a novel two-phase thermal LB model (in  Phys. Rev. E 88).

 

Movie: reproduces the motion of a liquid slug in an inclined channel for the case of a non-wetting liquid

Movie: relates to wetting liquid.