Simulation for High Density Ratio Gas-liquid System Through the Lattice Boltzmann Model Based on the Carnahan-Starling State Equation

Numerous multi-component and multi-phase fluid environments with high density ratios exist in nature, such as the water-air system with density ratios ρwater /ρair = ۸۳۰. Nevertheless, conventional Shan-Chen (SC) models for MCMP systems fail to maintain thermodynamic stability when the density ratio is beyond ρ* ~ O(۱۰²). Given this limitation, an enhanced Shan-Chen model is established in this study by incorporating the Carnahan-Starling equation of state (C-S EOS). In the enhanced model, multiple components are represented by distinct distribution functions. The phase separation for a single component is governed by the C-S EOS, and interactions between different components across all coexisting phases are modeled by the traditional pseudo-potential approach. The model is first validated through stationary droplet analysis, confirming compliance with surface tension and the Laplace law, as well as through Maxwell construction verification, which demonstrates agreement between the gas-liquid coexistence densities and thermodynamic theory. The proposed MCMP LBM method yields a linear variation between the droplet-wall contact angle θ and the difference in the repulsive force coefficient, ΔG. Simulations of Rayleigh-Taylor instability at Re = ۲۵۶ and ۲۰۴۸, and at density ratios up to ρ* ~ O(۱۰³), reveal bubble and spike amplitudes in excellent agreement with prior literature (Huang et al. ۲۰۱۵), with correlation coefficients of ۰.۹۹۷ and ۰.۹۹۸, respectively. Furthermore, simulations of a falling particle impacting an air-water interface have strong agreement with experimental data, with correlation coefficients of ۰.۹۸۵ and ۰.۹۱۹ for dimensionless height and velocity, respectively, validating the reliability of the proposed model.

کلیدواژه ها:

High density ratio ، Multiphase flow ، Carnahan-Starling equation of state (C-S EOS) ، Lattice Boltzmann method ، Gas-liquid interactions