Assessment of interaction potential in simulating nonisothermal multiphase systems by means of lattice Boltzmann modeling

Abstract

The pseudopotential lattice Boltzmann model (PP-LBM) is a very popular model for simulating multiphase systems. In this model, phase separation occurs via a short-range attraction between different phases when the interaction potential term is properly chosen. Therefore, the potential term is expected to play a significant role in the model and to affect the accuracy and the stability of the computations. The original PP-LBM suffers from some drawbacks such as being capable of dealing with low density ratios only, thermodynamic inconsistency, and spurious velocities. In this paper, we aim to analyze the PP-LBM with the view to simulate single-component (non-)isothermal multiphase systems at large density ratios and in spite of the presence of spurious velocities. For this purpose, the performance of two popular potential terms and of various implementation schemes for these potential terms is examined. Furthermore, the effects of different parameters (i.e., equation of state, viscosity, etc.) on the simulations are evaluated, and, finally, recommendations for a proper simulation of (non-)isothermal multiphase systems are presented.

Thermohydrodynamics of an evaporating droplet studied using a multiphase lattice Boltzmann method

“…By choosing a proper value for β, the thermodynamic inconsistency and magnitude of spurious currents reduce greatly [11,27]. For β = 1, the expression coincides with Eq.…”

“…(1), the exact difference method (EDM) is used [25]. The EDM is directly derived from the Boltzmann equation and has a great effect on numerical stability and accuracy of the solution [27,43,44]. In this scheme, the force term, the equilibrium velocity u eq , and the real fluid velocity U are calculated by…”

“…By decreasing the temperature (or increasing the density ratio), the magnitude of spurious velocities increases which indicates the deviation from the real physical situation. It has been shown that due to the existence of the spurious velocities, four unphysical symmetric hot and cold spots are formed around the interface when simulating a (non-)isothermal droplet [27].…”

“…For the sake of overcoming these drawbacks, various researchers tried to develop the PP-LBM for high density ratio and decrease the unphysical spurious velocities [10,[19][20][21][22][23][24][25][26]. In our previous paper [27] we analyzed the effects of various lattice Boltzmann parameters and showed how to reduce the spurious velocities when simulating a stationary droplet with high density ratio and with heat transfer. Reviews of the theory and applications of the PP-LBM for simulating multiphase flows with phase change during the past two decades have been presented in Refs.…”

Comparison of finite volume and lattice Boltzmann methods for multicomponent flow simulations

“…Use of this force scheme, however, also changes the composition of the phases. We do not consider here in further detail the reasons for the differences in behaviour of LB forcing schemes that are due to differences in higher order terms that affect the mass and momentum equations . Higher order terms, which were omitted in the FV implementation, are also the reason for the difference in interfacial tension between the LBM and FV results.…”