格子Boltzmann方法在相变过程中的应用

Application of lattice Boltzmann method to phase transition process

提出了一种新的描述气液相变过程的单组分格子Boltzmann模型,利用该模型模拟水以及氨分别在R-K,RKS和P-R状态方程控制下的相变过程,发现相对于R-K和RKS状态方程,水以及氨在P-R状态方程控制下模拟结果均与实验值更接近;特别地,P-R状态方程更适合描述氨.为验证该模型处理两相问题的能力,利用该模型模拟不同温度下水以及氨在P-R状态方程控制下的界面密度梯度,所得的结果与经典的界面理论相符.为此,进一步探讨了气泡(液滴)与周围液体(气体)处于力平衡和热平衡时,气泡(液滴)内外压力差在不同温度下与其半径之间的关系,所得的结果满足Laplace定律,并得到了不同温度下水以及氨的表面张力,发现均与实验值符合得很好,且与表面张力临界理论甚为相符.

In this paper, a new single-component lattice Boltzmann method is proposed to describe liquid-vapor phase transition process. Water and ammonia phase transition process are simulated by using this new model for Redlich-Kwong, Redlich-Kwong Soave and Peng-Robinson equations of state. Compared with the experimental data of water and ammonia, the results show that the Peng-Robinson equation of state is more suitable to describe the phase transitions process of water, ammonia and other substance. In particularly, the simulation results of ammonia with Peng-Robinson equation of state are more close to the experimental data. In order to demonstrate the capability of this model for dealing with two-phase problems, the mass density profile across the interface of water or ammonia which is controlled by Peng-Robinson equation of state are simulated by this model for different temperatures. These simulation results agree with that of classical interface theory. Finally, the relationship between the bubble （droplet） inside and outside pressure difference and its radius is simulated when the bubble （droplet） is in equilibrium environment at different temperatures. The results agree with Laplace law. The surface tension of water and ammonia is obtained from simulation results at different temperature, which agree with experimental data and the critical theory of surface tension.