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Evaluation of equations of state in multiphase lattice Boltzmann method with considering surface wettability effects

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  • Ezzatneshan, Eslam
  • Vaseghnia, Hamed

Abstract

A two-dimensional lattice Boltzmann method (LBM) is applied to investigate the use of various equations of state (EoS) for the simulation of liquid–vapor two-phase flow systems with considering the wetting properties, namely the hydrophilic and hydrophobic characteristics, for solid surfaces. The pseudo-potential single-component multiphase Shan–Chen model is used to resolve inter-particle interactions and phase change between the liquid and its vapor. Several EoSs, including the Redlich–Kwong (R–K), Carnahan-Starling (C–S), and Peng–Robinson (P–R) in comparison with the Shan–Chen (S–C) model are considered to study their effects on the numerical simulation results in terms of density ratios, spurious velocities and the contact angle of the two-phase flow with the solid wall. Accuracy and performance of the multiphase LBM by incorporating various EoSs are examined by solving two-phase flow systems at different conditions. Herein, three test cases considered are an equilibrium state of a droplet suspended in the vapor phase, a liquid droplet located on the solid surface, and a liquid droplet motion through a grooved channel with different wetting conditions. The results obtained demonstrate that implementation of the wall boundary condition with the wettability effects significantly impacts the numerical stability of the LBM with the EoSs employed for simulation of liquid–vapor flow problems, particularly at high-density ratio. Simulation of the equilibrium state of a droplet on a surface with considering wettability effects shows that the S–C model, R–K, P–R and C–S EoSs are stable for the maximum density ratio up to ρl∕ρv=74.6, 78.9, 4904.4 and 147, respectively. It is defined that the parasitic currents do not increase significantly due to imposing the wetting condition on the solid wall, however, the numerical solutions with considering wettability effects are more sensitive at high-density ratios. The present study demonstrates that the P–R EoS is more stable for simulation of high-density ratio liquid–vapor systems with reasonable spurious currents in the interfacial region for the flow problems with the periodic computational domain. However, with considering the wetting wall boundary condition, the C–S EoS produces less spurious velocity in the interface region, which leads to more precise and stable numerical simulations in comparison with the other EoSs applied for the equilibrium state of a liquid droplet on the solid surface. The results obtained also demonstrate the capability of the multiphase LBM for predicting practical flow characteristics with different EoSs implemented.

Suggested Citation

  • Ezzatneshan, Eslam & Vaseghnia, Hamed, 2020. "Evaluation of equations of state in multiphase lattice Boltzmann method with considering surface wettability effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    • Handle: RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119318229
    DOI: 10.1016/j.physa.2019.123258
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    References listed on IDEAS

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