A high‐order phase‐field based lattice Boltzmann model for simulating complex multiphase flows with large density ratios. (3rd August 2020)

• Record Type: Journal Article
• Authors: Li, Qiao‐Zhong; Lu, Zhi‐Liang; Zhou, Di; Niu, Xiao‐Dong; Guo, Tong‐Qin; Du, Bing‐Chen
• Is Part Of: International journal for numerical methods in fluids. Volume 93:Number 2(2021)
• Page Start: 293
• Page End: 313
• Publication Date: 2020-08-03
• Subjects: complex interface -- high‐order model -- large density ratios -- lattice Boltzmann model -- multiphase flows -- phase field method; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4883
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: Based on phase‐field theory, we develop a simple and robust single relaxation time (SRT) lattice Boltzmann (LB) model for simulating complex multiphase flows with large density ratios (up to 2000). The approach utilizes two LB equations (LBE), one is used to describe the interface behavior and the other is used to calculate the hydrodynamic properties. To improve the accuracy and stability in capturing interface, the high‐order LB model derived through the fourth‐order Chapman‐Enskog expansion analysis is applied to Cahn‐Hilliard equation. For solution of the flow field, a modified particle distribution function in the pressure‐velocity formulation is constructed to correctly consider the effect of local density variation and continuous pressure field. With such improvement, the proposed multiphase LB model is able to maintain numerical stability for the problem with very large density ratio, lower relaxation parameter and complex interface. For validation, a series of benchmark cases are carried out. Specially, the full potential of the proposed model is validated by bubble bursting at a free surface, bubble rising and droplet splashing with a density ratio of 2000. In all test cases, the obtained numerical results agree well with the reference data or the analytical solutions. Abstract : In this article, a high‐order phase‐field based multiphase LB model for the simulation of complex multiphase flow is constructed. Several challenging multiphase problems, including Rayleigh‐Taylor instability, bubble rising, bubble bursting at a free surface, and droplet splashing, are simulated to validate the model. Numerical results indicate that the model could effectively simulate complex multiphase problems with more complicated interaction between different fluids, larger density ratios (up to 2000), and at higher Reynolds number.