| Lattice Boltzmann equation(LBE) method, also known as Lattice Boltzmann method(LBM), has attracted a significant attention due to its potential to solve problems at the mesoscopic scale. From its origins in lattice gas automation method, it has been developed into a numerical method to simulate fluid flows and other nonlinear problems. One promising application of LBE method is multiphase flow simulation. Due to its kinetic nature, a well-developed theoretical basis, and the ability of selfcapturing the interface, LBE method has many advantages when simulating multiphase problems. Several LBE multiphase models have thus been developed. Among them, the pseudo-potential models first proposed by Shan and Chen are most widely used because of their simplicity and stability. Moreover, recent research of pseudo-potential model has show that they have great potential to solve the large density ratio problems. However, these models still suffer some drawbacks such as untunable surface tension and spurious velocities, also their application on the phase change problem is very limited.To solve this problems, here we first theoretically and numerically analyzed the pseudo-potential model proposed by Kupershtokh, based on the analysis, several improvement methods are proposed. Secondly, to improve the stability of the pseudopotential model when the solid surface influence is considered, we proposed a new contact angle adjustment method. Finally, several thermal lattice Boltzmann simulation method are discussed and a new phase change simulation model is established based on the improved pseudo-potential model. The details of the present work are given as follows.① Isothermal pseudo-potential model improvement.a. The general equations of state(EOS) are applied in Kupershtokh et al.’s model to replace the reduced EOS, and a simple way to adjust these EOS is proposed. After change the EOS, the stability and application range of Kupershtokh et al.’s model are both improved.b. The interpaticle interaction force calculation method in Kupershtokh et al.’s model is theoretically and numerically analyzed. Moreover, three popular LB force methods are compared, and the force method proposed by Guo et al. is applied the model to improve the accuracy of the model based on the comparison results. To evaluate the performance of the improved model, we further compar it with Li et al.’s similar model on the aspects of accuracy and relaxation time’s effects. Based on the theoretical analysis and simulation results, two methods are proposed to further improve the accuracy and reduce the relaxation time’s influence.c. We theoretically analyzed the surface tension of improved Kupershtokh et al.’s model. Based on the analysis results, two surface tension adjustment methods are proposed and numerically compared. Moreover, the influence of relaxation time on the surface tension adjustment methods is numerically analyzed.d. A new contact angle adjustment method is proposed based on the geometrical analysis. Compared with the original contact angle adjustment method, the proposed model is much more stable and it also avoids the uncontrollable influence on the density distribution.② Thermal pseudo-potential model.a. Several thermal lattice Boltzmann equation are theoretically and numerically discussed, and compared with the finite difference method. Based on the results, the finite difference method of the thermal equation is applied in the multiphase pseudopotential model to eliminate the error caused by the thermal lattice Boltzmann equation, and improve the accuracy of the temperature calculation.b. To overcome the drawbacks of the traditional phase change lattice Boltzmann model, whose temperature field does not satisfy the bubble dynamics theory, we here propose a new phase change model based on the pressure-driven phase change mechanism and theoretically obtained its thermal equation. Simulation results show that the temperature distribution obtained by the new model is more reasonable than the existed models. |
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