Lattice-Boltzmann model for van der Waals fluids with liquid-vapor phase transition. (November 2021)

• Record Type: Journal Article
• Authors: Zhang, Chunhua; Liang, Hong; Yuan, Xiaolei; Liu, Gaojie; Guo, Zhaoli; Wang, Lianping
• Is Part Of: International journal of heat and mass transfer. Volume 179(2021)
• Publication Date: 2021-11
• Subjects: Lattice Boltzmann model -- Phase transition -- Two-phase flows -- van der Waals fluids -- Nucleate boiling; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2021.121741
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: Two kinds of LBE models for the momentum equations derived from the van der Waals theory have been proposed. A new thermal LBE method with a modified the equilibrium distribution function is proposed. The thermal boundary conditions, including the Dirichlet and adiabatic boundaries, have been analyzed by Maxwell iteration. Abstract: A lattice Boltzmann model (LBM) for two-phase flows with liquid-vapor phase transition based on a dynamic van der Waals theory [Phys. Rev. Lett. 94, 054501 (2005)] is proposed. The proposed model consists of two lattice Boltzmann equations (LBE): one for the Navier-Stokes-Korteweg (NSK) equations and the other for the temperature equation. In the thermal LBE, the equilibrium distribution function is redesigned by introducing a reference temperature, which is used to reduce the numerical errors of velocity divergence in the thermal LBE. A free-energy-based LBE is developed for the hydrodynamic equations and a novel force term is used to correctly recover the NSK equations. Several numerical simulations, including the liquid-vapor coexistence curve, phase separation, stationary droplet, droplet on partially wetting surface, droplet evaporation and bubble nucleate and departure, are conducted to validate the capability and performance of the present model. The numerical results of the proposed model are found to be in excellent agreement with the results of theoretical and/or the hybrid method. It is also shown that numerical stability and accuracy of the present models can be greatly improved by adjusting the reference temperature. The present models provide an effective predictive tool for two-phase flows involving phase change.