凝固前沿和气泡相互作用的大密度比格子玻尔兹曼方法模拟

Modeling of the interaction between solidification interface and bubble using the lattice Boltzmann method with large density ratio

建立了二维双组分两相流的大密度比格子玻尔兹曼方法(lattice Boltzmann method,LBM)模型.该模型基于改进的Shan-Chen伪势多相流LBM模型,结合采用不同时间步长的方法,实现密度比达800以上的气液两相流模拟.为了对模型进行验证,模拟了在不同气液相互作用系数和密度比条件下气泡内外压力差与其半径之间的关系,其结果满足Laplace定律.将所建立的大密度比LBM与介观尺度的元胞自动机(cellul arautomaton,CA)和有限差分法(FDM)相耦合,用LBM模拟气液两相流,用CA方法模拟固相生长,用有限差分法模拟温度场,采用LBM-CA-FDM耦合模型对定向凝固过程中凝固前沿的气泡与液-固界面之间的相互作用进行模拟研究.结果表明,绝热气泡的存在影响了温度场分布,使得凝固前沿接近气泡时,液-固界面凸起,在不同的固相生长速度条件下,出现凝固前沿淹没气泡或气泡脱离凝固前沿的不同情况,模拟结果与实验结果符合良好.

A two-dimensional （2D） two-component and two-phase lattice Boltzmann method （LBM） with large density ratio is developed based on a modified Shan-Chen pseudopotential model combined with the deferent time step method. The present LBM model can simulate the gas-liquid two-phase flow with density ratio up to around 800. To validate the model, the pressure difference between the inside and outside of a bubble varying with its radius is simulated with different gas-liquid interact parameters and density ratios. The results are found to obey the Laplace law. Then, the LBM is coupled with the cellular automaton （CA） method used for simulating the solid phase growth, and the finite difference method （FDM） used for calculating the temperature field. The LBM-CA-FDM coupled model is used to simulate the interaction between bubble and the solidification interface. The results show that the existence of adiabatic bubble influences the distribution of temperature field in front of solidification interface, which leads to a bulge of the solid- liquid interface when it is close to the bubble. Under the conditions of different growth rates, the bubble is either engulfed or pushed away by the growing solid-liquid interface. The simulation results agree reasonably well with those observed experimentally.