Lattice Boltzmann model for axisymmetric multiphase flows

Abstract

In this paper, a lattice Boltzmann (LB) model is presented for axisymmetric multiphase flows. Source terms are added to a two-dimensional standard lattice Boltzmann equation (LBE) for multiphase flows such that the emergent dynamics can be transformed into the axisymmetric cylindrical coordinate system. The source terms are temporally and spatially dependent and represent the axisymmetric contribution of the order parameter of fluid phases and inertial, viscous and surface tension forces. A model which is effectively explicit and second order is obtained. This is achieved by taking into account the discrete lattice effects in the Chapman-Enskog multiscale analysis, so that the macroscopic axisymmetric mass and momentum equations for multiphase flows are recovered self-consistently. The model is extended to incorporate reduced compressibility effects. Axisymmetric equilibrium drop formation and oscillations, breakup and formation of satellite droplets from viscous liquid cylindrical jets through Rayleigh capillary instability and drop collisions are presented. Comparisons of the computed results with available data show satisfactory agreement.

Axisymmetric multiphase lattice Boltzmann method

“…The idea to model the 3D axisymmetric LBM with a 2D LBM supplemented with appropriate source terms has already been employed in a number of studies, for single-phase axisymmetric LBM models [4,5,17,18] and for the multiphase LBM as well [10,11]. Here we will develop an axisymmetric version of the Shan-Chen model [12,13].…”

“…(9) and NS Eqs. (10) by means of a Chapman-Enskog (CE) expansion in the long-wavelength and long-time-scale limit. In order to derive such a model we start from the 2D LBM with the addition of appropriate space-and time-varying microscopic sources h i (see also [4,5,17,18]).…”

“…In recent years several implementations of the axisymmetric LBM for single-phase systems have been proposed [4][5][6][7][8][9], while, in comparison, relatively little attention has been devoted to the case of the multiphase flow [10,11].…”

A study of pressure-driven displacement flow of two immiscible liquids using a multiphase lattice Boltzmann approach

“…φ 1 and φ 2 are minimum and maximum values of the index function; in the present study, φ 1 and φ 2 are given values of 0.02381 and 0.2508, respectively. 42 We use the following expression of ψ(φ) using the Carnahan-Starling fluid equation of state, which describes the process of phase separation for non-ideal gases and fluids: [51][52][53][54][55] …”

FFT-LB Modeling of Thermal Liquid-Vapor System

“…The aforementioned models have been successfully applied to a wide variety of multiphase and/or multicomponent flow problems, including drop breakup [25,26], drop collisions [27], wetting [28,29], contact line motion [30,31], chemically reactive fluids [32], phase separation and phase ordering phenomena [19,21,23,33], hydrodynamic instability [34,35], etc.…”