WO2022067498A1 - 一种气液相变的介观模拟方法 - Google Patents

一种气液相变的介观模拟方法 Download PDF

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WO2022067498A1
WO2022067498A1 PCT/CN2020/118804 CN2020118804W WO2022067498A1 WO 2022067498 A1 WO2022067498 A1 WO 2022067498A1 CN 2020118804 W CN2020118804 W CN 2020118804W WO 2022067498 A1 WO2022067498 A1 WO 2022067498A1
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kinetic energy
distribution function
gas
density
total kinetic
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黄荣宗
蓝丽娟
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中南大学
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  • the invention relates to the fields of fluid mechanics, thermodynamics and kinetics, and more particularly to a mesoscopic simulation method of gas-liquid phase transition.
  • Gas-liquid transition is a fundamental thermophysical phenomenon that exists widely in nature and engineering applications.
  • the phase transition In the gas-liquid transition process, there is a phase interface between the gas-liquid two phases, the position of which is unknown and evolves dynamically with time. Within the gas-liquid interface, the phase transition is accompanied by the release/absorption of a large amount of latent heat.
  • the gas-liquid two phases usually have a great difference in density, and their physical parameters such as dynamic viscosity and thermal conductivity are also significantly different.
  • the gas-liquid phase transitions are extremely complex macroscopically, such as nucleation, superheating, supersaturation, evaporation, boiling, condensation, etc. The above characteristics make the numerical simulation of gas-liquid transition extremely challenging.
  • the gas-liquid phase transition is extremely complex in macroscopic terms, its microscopic mechanism is very simple. Physically, the gas-liquid phase transition and the complex phenomena related to it are the natural manifestations of microscopic intermolecular interactions.
  • Microscopic intermolecular interactions are usually composed of short-range repulsive effects and long-range attractive effects.
  • the short-range repulsive effect is a direct manifestation of the finite size of the molecule, which can be described by the dense gas Enskog theory, while the long-range attractive effect can be approximated by the mean field theory as Local point force. Therefore, numerical modeling of the gas-liquid phase transition from the physical point of view of microscopic intermolecular interactions has the unique advantages of clear concept and simple calculation, which can reflect the physical nature of the phase transition process.
  • Lattice Boltzmann method is a mesoscopic method of computational fluid dynamics, which originated from lattice gas automata and can also be regarded as a special discrete format of Boltzmann equation.
  • the lattice Boltzmann method has both the properties of mesoscopic particles and the theoretical background of kinetics, and can consider the interaction between microscopic particles. It is extremely suitable for physical modeling and numerical simulation of gas-liquid transition.
  • this mesoscopic simulation method uses the dense gas equation of state to describe the short-range repulsive effect between molecules, and uses paired interaction forces to simulate the long-range attraction effect between molecules.
  • this mesoscopic simulation method is based on the density distribution function to describe and solve the law of conservation of mass-momentum, and introduces the total kinetic energy distribution function to describe and solve the law of conservation of energy.
  • the mesoscopic simulation method of gas-liquid phase transition comprises the following steps:
  • S1 Select the actual gas state equation and parameters, determine the initial temperature, determine the saturation density of the gas and liquid phases, and set the surface tension and phase interface width between the gas and liquid phases;
  • S2 Set the grid space step size and the number of grids in the simulation area, and calculate the simulation parameters such as interaction strength, grid sound speed, time step size, and constant volume specific heat capacity;
  • f(x, ⁇ ,t) is the continuous density distribution function described by the Boltzmann equation in the kinetic theory
  • ⁇ is the molecular motion velocity
  • x is the spatial position
  • t is the time.
  • the physical essence of the internal potential energy in the present invention is: the internal potential energy ⁇ p is the energy possessed by a molecule due to the long-range attraction from other molecules.
  • the processing method of the internal potential energy of the present invention is as follows: the transport process of the internal potential energy ⁇ p can be realized by imitating the long-range attraction between molecules to do work.
  • the calculation method of density, velocity, total kinetic energy, temperature and pressure according to the present invention is as follows: density ⁇ and velocity u are calculated according to the density distribution function, total kinetic energy ⁇ e k is calculated according to the total kinetic energy distribution function, and physical quantities such as temperature and pressure are calculated according to the thermodynamic relationship The formula is completely determined by ⁇ , u and ⁇ ek .
  • the evolution equation described in the present invention satisfies: the density distribution function lattice Boltzmann equation should be able to recover the dense gas state equation and the paired interaction force.
  • the evolution equation described in the present invention satisfies: the total kinetic energy distribution function lattice Boltzmann equation should be able to recover dense gas pressure work, paired interaction force work, surface tension work and viscous heat dissipation.
  • the present invention relates to a mesoscopic simulation method of gas-liquid phase transition.
  • the method uses the equation of state of dense gas to describe the short-range repulsive effect between molecules, and uses paired interaction forces to simulate the long-range attraction effect between molecules.
  • the method is based on a double distribution function, where the density distribution function is used to describe and solve the law of conservation of mass-momentum, and the distribution function of total kinetic energy is used to describe and solve the law of conservation of energy.
  • the density distribution function lattice Boltzmann equation can recover the dense gas state equation and pairwise interaction force
  • the total kinetic energy distribution function lattice Boltzmann equation can recover the dense gas pressure work, pairwise interaction force work, surface tension work and viscous heat dissipation.
  • the method has a clear microscopic particle image and mesoscopic kinetic theory background, and has both conceptual and computational simplicity, and naturally satisfies thermodynamic consistency. It can realize direct numerical simulation of gas-liquid transition process, with wide applicability and reliability. high.
  • Fig. 1 is a calculation flow chart of the mesoscopic simulation method of gas-liquid phase transition of the present invention.
  • FIG. 2 is a schematic diagram of the two-dimensional space droplet evaporation according to the embodiment.
  • Fig. 3 is the evolution of the square of the dimensionless droplet diameter with dimensionless time, and the local density field and temperature field near the droplet at four times of the embodiment.
  • the mesoscopic simulation method of gas-liquid phase transition of the present invention includes the following steps, as shown in FIG. 1 :
  • S1 Select the actual gas state equation and parameters, determine the initial temperature, determine the saturation density of the gas and liquid phases, and set the surface tension and phase interface width between the gas and liquid phases;
  • S2 Set the grid space step size and the number of grids in the simulation area, and calculate the simulation parameters such as interaction strength, grid sound speed, time step size, and constant volume specific heat capacity;
  • f(x, ⁇ ,t) is the continuous density distribution function described by the Boltzmann equation in the kinetic theory
  • ⁇ is the molecular motion velocity
  • x is the spatial position
  • t is the time.
  • the physical essence of the internal potential energy in the embodiment of the present invention is: the internal potential energy ⁇ p is the energy possessed by a molecule due to the long-range attraction from other molecules.
  • the processing method of the internal potential energy in the embodiment of the present invention is as follows: the transport process of the internal potential energy ⁇ p can be realized by imitating the long-range attraction between molecules to do work.
  • the calculation methods of density, velocity, total kinetic energy, temperature and pressure in the embodiment of the present invention are as follows: density ⁇ and velocity u are calculated according to the density distribution function, total kinetic energy ⁇ e k is calculated according to the total kinetic energy distribution function, and physical quantities such as temperature and pressure are calculated according to thermodynamics The relation is completely determined by ⁇ , u and ⁇ ek .
  • the evolution equation in the embodiment of the present invention satisfies: the density distribution function lattice Boltzmann equation should be able to recover the dense gas state equation and the pairwise interaction force.
  • the evolution equation in the embodiment of the present invention satisfies: the total kinetic energy distribution function lattice Boltzmann equation should be able to recover dense gas pressure work, pairwise interaction force work, surface tension work and viscous heat dissipation.
  • the droplet evaporation in the two-dimensional space shown in Figure 2 is taken as an example to simulate and calculate the change of droplet diameter with time during the droplet evaporation process, as well as the evolution of density field and temperature field with time.
  • T cr the critical temperature and p cr is the critical pressure.
  • the pressure is calculated according to the equation of state (1).
  • the formula for calculating the pairwise interaction force is
  • n eq is the equilibrium moment function of the total kinetic energy distribution function
  • ⁇ 2 -2/(1- ⁇ )
  • ⁇ h k ⁇ e k +p LBE
  • C ref is the reference heat capacity
  • ⁇ 1 and ⁇ 2 are coefficients related to thermal conductivity
  • ⁇ is a coefficient related to bulk viscosity.
  • L is the moment space relaxation matrix
  • the pairwise interaction force F pair (x,t+ ⁇ t ) is calculated according to equation (6). Calculate the velocity and specific total kinetic energy at the next moment
  • the boundary conditions of the four sides of the simulation area shown in Figure 2 are the outflow boundary condition, the constant pressure boundary condition, and the constant temperature boundary condition, from which the density, velocity, total kinetic energy, temperature, pressure and other physical quantities at the boundary grid points can be determined , the density distribution function and the total kinetic energy distribution function at the boundary grid points are constructed using the boundary condition processing scheme in the lattice Boltzmann method.
  • ⁇ g is the thermal diffusivity of the gas phase.
  • Figure 3 shows the evolution of the square of the dimensionless droplet diameter (D/D 0 ) 2 with the dimensionless time t * , as well as the local density and temperature fields around the droplet at four instants. It can be seen that the mesoscopic simulation method provided by the present invention can successfully capture the gas-liquid phase transition process. Furthermore, the droplet evaporation process given by the simulation satisfies the D2 - law very well. These results prove the feasibility and accuracy of the mesoscopic simulation method for gas-liquid transition provided by the present invention.

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Abstract

一种气液相变的介观模拟方法。方法采用稠密气体状态方程刻画分子间短程排斥效应，采用成对相互作用力模仿分子间长程吸引效应。方法基于双分布函数，其中密度分布函数用于描述并求解质量-动量守恒定律，总动能分布函数用于描述并求解能量守恒定律。密度分布函数格子Boltzmann方程可恢复稠密气体状态方程和成对相互作用力，总动能分布函数格子Boltzmann方程可恢复稠密气体压力功、成对相互作用力做功、表面张力做功和粘性热耗散。方法拥有明确的微观粒子图像和介观动理学理论背景，兼具概念及计算简洁性，并自然地满足热力学一致性，可实现气液相变过程的直接数值模拟，适用性广、可靠性高。

Description

一种气液相变的介观模拟方法 技术领域
本发明涉及流体力学、热力学和动理学领域，更具体地涉及一种气液相变的介观模拟方法。
背景技术
气液相变是一种基本的热物理现象，广泛存在于自然界和工程应用中。气液相变过程气液两相之间存在相界面，其位置未知且随时间动态演化。在气液相界面内，相态转变伴随着大量潜热的释放/吸收。气液两相通常存在极大的密度差异，其动力粘度、热导率等物性参数亦显著不同。气液相变在宏观上表现极为复杂，如成核、过热、过饱和、蒸发、沸腾、冷凝等。上述特征使得气液相变的数值模拟极具挑战，现有的宏观数值方法必须依赖于复杂的相界面捕捉与追踪算法，且在处理气液相变过程时唯象地采用了大量假设、近似及简化，无法反映气液相变过程底层的基本物理规律，数值方法的普适性和模拟结果的真实性亦难以保证。
气液相变虽然在宏观上表现极为复杂，但其微观机理则十分简单。从物理上讲，气液相变及与之相关的复杂现象均是微观分子间相互作用的自然体现。微观分子间相互作用通常由短程排斥效应和长程吸引效应构成，其中短程排斥效应为分子有限体积大小的直接体现，可采用稠密气体Enskog理论进行描述，而长程吸引效应则可利用平均场理论近似为局部点力。因此，从微观分子间相互作用的物理角度，对气液相变进行数值建模，具有概念清晰、计算简洁的独特优势，可反映相变过程的物理本质。格子Boltzmann方法是一种计算流体力学的介观方法，它起源于格子气自动机，亦可视为Boltzmann方程的一种特殊离散格式。格子Boltzmann方法兼具介观粒子属性和动理学理论背景，可考虑微观粒子间的相互作用，极为适用于气液相变的物理建模和数值模拟。
发明内容
基于格子Boltzmann方法的理论框架，本发明提供了一种气液相变的介观模拟方法。从物理上讲，该介观模拟方法采用稠密气体状态方程刻画分子间短程排斥效应，采用成对相互作用力模仿分子间长程吸引效应。从数值上讲，该介观模拟方法基于密度分布函数描述并求解质量-动量守恒定律，引入总动能分布函数描述并求解能量守恒定律。
本发明提供的气液相变的介观模拟方法包括如下步骤：
S1：选定实际气体状态方程及参数，确定初始温度，确定气相和液相的饱和密度， 设定气液两相间的表面张力和相界面宽度；
S2：设定网格空间步长和模拟区域网格数，计算相互作用强度、格子声速、时间步长、定容比热容等模拟参数；
S3：初始化网格点处的密度、速度、总动能、温度、压力等物理量，根据密度场计算成对相互作用力，初始化密度分布函数和总动能分布函数；
S4：执行密度分布函数格子Boltzmann方程的局部碰撞过程，得到碰撞后的密度分布函数；执行总动能分布函数格子Boltzmann方程的局部碰撞过程，得到碰撞后的总动能分布函数；
S5：执行密度分布函数格子Boltzmann方程的线性迁移过程，得到下一时刻的密度分布函数；执行总动能分布函数格子Boltzmann方程的线性迁移过程，得到下一时刻的总动能分布函数；
S6：计算下一时刻的密度，根据密度场计算成对相互作用力，计算下一时刻的速度、总动能、温度、压力等物理量；
S7：根据实际边界条件确定边界网格点处的密度、速度、总动能、温度、压力等物理量，采用格子Boltzmann方法中的边界条件处理格式构造边界网格点处的密度分布函数和总动能分布函数；
S8：重复步骤S4～S7，直至气液相变结束或到达指定时刻。
本发明所述的总动能的热力学定义为：总动能ρe k为内动能ρò k和宏观动能
Figure PCTCN2020118804-appb-000001
之和，即
Figure PCTCN2020118804-appb-000002
内动能ρò k和内位能ρò p共同构成内能ρò，即ρ蝌＝ρ k+ρ？ p；内能ρò和宏观动能
Figure PCTCN2020118804-appb-000003
共同构成总能ρe，即
Figure PCTCN2020118804-appb-000004
其中，ρ为密度、u为速度、e k为比总动能、ò k为比内动能、ò p为比内位能、ò为比内能、e为比总能。
本发明所述的总动能在介观层面的物理意义为：密度ρ、速度u、内动能ρò k、总动能ρe k在介观层面的物理意义为ρ＝òf(x,ξ,t)dξ、ρu＝òf(x,ξ,t)ξdξ、
Figure PCTCN2020118804-appb-000005
此处，f(x,ξ,t)为动理学理论中Boltzmann方程所描述的连续型密度分布函数，ξ为分子运动速度、x为空间位置、t为时间。
本发明所述的内动能满足：内动能ρò k与温度T之间的关系为ρò k＝ρc vT，其中c v为 定容比热容。
本发明所述的内位能的物理本质为：内位能ρò p是由于分子受到来自于其它分子的长程吸引力而拥有的能量。
本发明所述的内位能的处理方式为：内位能ρò p的输运过程可通过模仿分子间长程吸引力做功实现。
本发明所述的密度、速度、总动能、温度、压力的计算方式为：密度ρ和速度u根据密度分布函数计算，总动能ρe k根据总动能分布函数计算，温度、压力等物理量依据热力学关系式由ρ、u和ρe k完全确定。
本发明所述的演化方程满足：密度分布函数格子Boltzmann方程应可恢复稠密气体状态方程和成对相互作用力。
本发明所述的演化方程满足：总动能分布函数格子Boltzmann方程应可恢复稠密气体压力做功、成对相互作用力做功、表面张力做功和粘性热耗散。
本发明的有益效果：本发明涉及一种气液相变的介观模拟方法。该方法采用稠密气体状态方程刻画分子间短程排斥效应，采用成对相互作用力模仿分子间长程吸引效应。该方法基于双分布函数，其中密度分布函数用于描述并求解质量-动量守恒定律，总动能分布函数用于描述并求解能量守恒定律。密度分布函数格子Boltzmann方程可恢复稠密气体状态方程和成对相互作用力，总动能分布函数格子Boltzmann方程可恢复稠密气体压力功、成对相互作用力做功、表面张力做功和粘性热耗散。该方法拥有明确的微观粒子图像和介观动理学理论背景，兼具概念及计算简洁性，并自然地满足热力学一致性，可实现气液相变过程的直接数值模拟，适用性广、可靠性高。
附图说明
图1是本发明的气液相变的介观模拟方法的计算流程图。
图2是实施例二维空间液滴蒸发示意图。
图3是实施例二维空间液滴蒸发无量纲液滴直径的平方随无量纲时间的演化，以及四个时刻液滴附近的局部密度场和温度场。
具体实施方式
为使本发明的目的、技术方案和优点更加清楚明白，以下结合具体实施例，并参照附图，对本发明作进一步的详细说明。
更具体地，本发明的气液相变的介观模拟方法，包括如下步骤，如图1所示：
S1：选定实际气体状态方程及参数，确定初始温度，确定气相和液相的饱和密度，设定气液两相间的表面张力和相界面宽度；
S2：设定网格空间步长和模拟区域网格数，计算相互作用强度、格子声速、时间步长、定容比热容等模拟参数；
S3：初始化网格点处的密度、速度、总动能、温度、压力等物理量，根据密度场计算成对相互作用力，初始化密度分布函数和总动能分布函数；
S4：执行密度分布函数格子Boltzmann方程的局部碰撞过程，得到碰撞后的密度分布函数；执行总动能分布函数格子Boltzmann方程的局部碰撞过程，得到碰撞后的总动能分布函数；
S5：执行密度分布函数格子Boltzmann方程的线性迁移过程，得到下一时刻的密度分布函数；执行总动能分布函数格子Boltzmann方程的线性迁移过程，得到下一时刻的总动能分布函数；
S6：计算下一时刻的密度，根据密度场计算成对相互作用力，计算下一时刻的速度、总动能、温度、压力等物理量；
S7：根据实际边界条件确定边界网格点处的密度、速度、总动能、温度、压力等物理量，采用格子Boltzmann方法中的边界条件处理格式构造边界网格点处的密度分布函数和总动能分布函数；
S8：重复步骤S4～S7，直至气液相变结束或到达指定时刻。
根据上述步骤，本发明实施例中的总动能的热力学定义为：总动能ρe k为内动能ρò k和宏观动能
Figure PCTCN2020118804-appb-000006
之和，即
Figure PCTCN2020118804-appb-000007
内动能ρò k和内位能ρò p共同构成内能ρò，即ρ蝌＝ρ k+ρ？ p；内能ρò和宏观动能
Figure PCTCN2020118804-appb-000008
共同构成总能ρe，即
Figure PCTCN2020118804-appb-000009
其中，ρ为密度、u为速度、e k为比总动能、ò k为比内动能、ò p为比内位能、ò为比内能、e为比总能。
本发明实施例中的总动能在介观层面的物理意义为：密度ρ、速度u、内动能ρò k、总动能ρe k在介观层面的物理意义为
Figure PCTCN2020118804-appb-000010
ρu＝òf(x,ξ,t)ξdξ、
Figure PCTCN2020118804-appb-000011
此处，f(x,ξ,t)为动理学理论中Boltzmann方程所描述的连续型密度分布函数，ξ为分子运动速度、x为空间位置、t为 时间。
本发明实施例中的内动能满足：内动能ρò k与温度T之间的关系为ρò k＝ρc vT，其中c v为定容比热容。
本发明实施例中的内位能的物理本质为：内位能ρò p是由于分子受到来自于其它分子的长程吸引力而拥有的能量。
本发明实施例中的内位能的处理方式为：内位能ρò p的输运过程可通过模仿分子间长程吸引力做功实现。
本发明实施例中的密度、速度、总动能、温度、压力的计算方式为：密度ρ和速度u根据密度分布函数计算，总动能ρe k根据总动能分布函数计算，温度、压力等物理量依据热力学关系式由ρ、u和ρe k完全确定。
本发明实施例中的演化方程满足：密度分布函数格子Boltzmann方程应可恢复稠密气体状态方程和成对相互作用力。
本发明实施例中的演化方程满足：总动能分布函数格子Boltzmann方程应可恢复稠密气体压力做功、成对相互作用力做功、表面张力做功和粘性热耗散。
具体应用实施例
1)本实施例以图2所示的二维空间液滴蒸发为例，模拟计算液滴蒸发过程液滴直径随时间的变化，以及密度场和温度场随时间的演化。
2)采用如下Carnahan-Starling状态方程
Figure PCTCN2020118804-appb-000012
其中
Figure PCTCN2020118804-appb-000013
T cr为临界温度，p cr为临界压力。参数选定为
Figure PCTCN2020118804-appb-000014
R＝1，初始温度取为T 0＝0.8T cr，则液相和气相的密度分别为ρ l＝0.307195682和ρ g＝0.0217232434。气液两相间的表面张力设置为σ＝0.01，相界面宽度设置为W＝10，则比例因子K EOS＝0.479820。
3)对于二维情形，采用标准D2Q9离散速度集，9个离散速度为
Figure PCTCN2020118804-appb-000015
其中c＝δ x/δ t为格子速度。网格空间步长为δ x＝1，网格数为N x×N y＝1024×1024，液滴的初始直径为D 0＝256δ x。相互作用强度设置为
Figure PCTCN2020118804-appb-000016
格子声速设置为
Figure PCTCN2020118804-appb-000017
其中比例因子K INT＝2.294922。格子速度与格子声速之间的关系式为
Figure PCTCN2020118804-appb-000018
则时间步长为δ t＝δ x/c。定容比热容设置为c v＝0.005ρ lh fg/[ρ g(T 1-T 0)]，其中h fg为气化潜热，T 1＝0.85T cr为计算区域四边的加热温度。
4)网格点处的密度初始化为
Figure PCTCN2020118804-appb-000019
其中x c＝(512δ x,512δ x) T为模拟区域的中心。网格点处的速度、温度、总动能分别初始化为u＝0、T＝T 0、
Figure PCTCN2020118804-appb-000020
压力根据状态方程(1)计算得到。成对相互作用力的计算式为
Figure PCTCN2020118804-appb-000021
其中
Figure PCTCN2020118804-appb-000022
密度分布函数f i和总动能分布函数g i初始化为
Figure PCTCN2020118804-appb-000023
其中
Figure PCTCN2020118804-appb-000024
为平衡态密度分布函数，F v,i＝(M -1F m) i为离散力项，
Figure PCTCN2020118804-appb-000025
为平衡态总动能分布函数，q v,i＝(M -1q m) i为离散源项。此处，M为速度空间到矩空间的正交变换矩阵
Figure PCTCN2020118804-appb-000026
m eq为密度分布函数的平衡态矩函数
Figure PCTCN2020118804-appb-000027
F m为矩空间离散力项
Figure PCTCN2020118804-appb-000028
n eq为总动能分布函数的平衡态矩函数
Figure PCTCN2020118804-appb-000029
q m为矩空间离散源项
Figure PCTCN2020118804-appb-000030
此处，
Figure PCTCN2020118804-appb-000031
β 2＝-2/(1-ω)、
Figure PCTCN2020118804-appb-000032
ρh k＝ρe k+p LBE、
Figure PCTCN2020118804-appb-000033
C ref为参考热容，γ 1和γ 2为与热导率有关的系数，ω为与体积粘度有关的系数。p LBE中的内置变量η由关系式
Figure PCTCN2020118804-appb-000034
计算。不考虑其它外力，合力为F＝F pair，合力做功为q＝F·u。
5)在矩空间执行密度分布函数格子Boltzmann方程的局部碰撞过程
Figure PCTCN2020118804-appb-000035
其中m＝M[f 0,f 1,…,f 8] T为密度分布函数的矩，
Figure PCTCN2020118804-appb-000036
为碰撞后的矩，S为矩空间松弛矩阵
Figure PCTCN2020118804-appb-000037
Q m为用于补偿三阶离散格子效应的源项
Figure PCTCN2020118804-appb-000038
此处，k＝1-ω、h＝6ω(1-ω)/(1-3ω)、b＝(1-ω)/(1-3ω)，松弛因子需满足的关系式为
Figure PCTCN2020118804-appb-000039
碰撞后的密度分布函数为
Figure PCTCN2020118804-appb-000040
在矩空间执行总动能分布函数格子Boltzmann方程的局部碰撞过程
Figure PCTCN2020118804-appb-000041
其中n＝M[g 0,g 1,…,g 8] T为总动能分布函数的矩，
Figure PCTCN2020118804-appb-000042
为碰撞后的矩，L为矩空间松弛矩阵
Figure PCTCN2020118804-appb-000043
Y用于恢复粘性热耗散
Figure PCTCN2020118804-appb-000044
碰撞后的总动能分布函数为
Figure PCTCN2020118804-appb-000045
6)在速度空间执行密度分布函数格子Boltzmann方程的线性迁移过程，得到下一时刻的密度分布函数
Figure PCTCN2020118804-appb-000046
在速度空间执行总动能分布函数格子Boltzmann方程的线性迁移过程，得到下一时刻的总动能分布函数
Figure PCTCN2020118804-appb-000047
7)计算下一时刻的密度
Figure PCTCN2020118804-appb-000048
根据方程(6)计算成对相互作用力F pair(x,t+δ t)。计算下一时刻的速度和比总动能
Figure PCTCN2020118804-appb-000049
根据关系式
Figure PCTCN2020118804-appb-000050
和ρò k＝ρc vT计算下一时刻的温度T(x,t+δ t)，根据状态方程(1)计算下一时刻的压力p EOS(x,t+δ t)。
8)图2所示的模拟区域四边的边界条件为外流出边界条件、恒压边界条件、恒温边界条件，由此可确定边界网格点处的密度、速度、总动能、温度、压力等物理量，采用格子Boltzmann方法中的边界条件处理格式构造边界网格点处的密度分布函数和总动能分布函数。
9)重复步骤5～8，直至无量纲时间
Figure PCTCN2020118804-appb-000051
到达100。此处，α g为气相的热扩散率。
10)图3给出了无量纲液滴直径的平方(D/D 0) 2随无量纲时间t *的演化，以及四个时刻液滴附近的局部密度场和温度场。可以看出，本发明提供的介观模拟方法可成功地捕捉气液相变过程。此外，模拟给出的液滴蒸发过程极好地满足D 2-定律。这些结果证明了本发明提供的气液相变的介观模拟方法的可行性及精度。
以上所述是本发明在二维情形下的一种实施方式，应当指出，对于本领域的技术人员来说，在不脱离本发明精神和原则的前提下，还可以做出若干修改、替换和改进等， 这些修改、替换和改进也视为本发明的保护范围。

Claims (9)

  1. 一种气液相变的介观模拟方法，其特征在于：采用稠密气体状态方程刻画分子间短程排斥效应、成对相互作用力模仿分子间长程吸引效应，基于密度分布函数描述并求解质量-动量守恒定律，引入总动能分布函数描述并求解能量守恒定律；包括如下步骤：
    S1、选定实际气体状态方程及参数，确定初始温度，确定气相和液相的饱和密度，设定气液两相间的表面张力和相界面宽度；
    S2、设定网格空间步长和模拟区域网格数，计算相互作用强度、格子声速、时间步长、定容比热容；
    S3、初始化网格点处的密度、速度、总动能、温度、压力，根据密度场计算成对相互作用力，初始化密度分布函数和总动能分布函数；
    S4、执行密度分布函数格子Boltzmann方程的局部碰撞过程，得到碰撞后的密度分布函数；执行总动能分布函数格子Boltzmann方程的局部碰撞过程，得到碰撞后的总动能分布函数；
    S5、执行密度分布函数格子Boltzmann方程的线性迁移过程，得到下一时刻的密度分布函数；执行总动能分布函数格子Boltzmann方程的线性迁移过程，得到下一时刻的总动能分布函数；
    S6、计算下一时刻的密度，根据密度场计算成对相互作用力，计算下一时刻的速度、总动能、温度、压力；
    S7、根据实际边界条件确定边界网格点处的密度、速度、总动能、温度、压力，采用格子Boltzmann方法中的边界条件处理格式构造边界网格点处的密度分布函数和总动能分布函数；
    S8、重复步骤S4～S7，直至气液相变结束或到达指定时刻。
  2. 根据权利要求1所述的气液相变的介观模拟方法，其特征在于：总动能ρe k的热力学定义为内动能ρò k和宏观动能
    Figure PCTCN2020118804-appb-100001
    之和，即
    Figure PCTCN2020118804-appb-100002
    内动能ρò k和内位能ρò p共同构成内能ρò，即
    Figure PCTCN2020118804-appb-100003
    内能ρò和宏观动能
    Figure PCTCN2020118804-appb-100004
    共同构成总能ρe，即
    Figure PCTCN2020118804-appb-100005
    其中，ρ为密度、u为速度、e k为比总动能、ò k为比内动能、ò p为比内位能、ò为比内能、e为比总能。
  3. 根据权利要求2所述的气液相变的介观模拟方法，其特征在于：密度ρ、速度u、 内动能ρò k、总动能ρe k在介观层面的物理意义为ρ＝òf(x,ξ,t)dξ、ρu＝òf(x,ξ,t)ξdξ、
    Figure PCTCN2020118804-appb-100006
    此处，f(x,ξ,t)为动理学理论中Boltzmann方程所描述的连续型密度分布函数，ξ为分子运动速度、x为空间位置、t为时间。
  4. 根据权利要求3所述的气液相变的介观模拟方法，其特征在于：内动能ρò k与温度T之间的关系为ρò k＝ρc vT，其中c v为定容比热容。
  5. 根据权利要求2所述的气液相变的介观模拟方法，其特征在于：内位能ρò p是由于分子受到来自于其它分子的长程吸引力而拥有的能量。
  6. 根据权利要求5所述的气液相变的介观模拟方法，其特征在于：内位能ρò p的输运过程可通过模仿分子间长程吸引力做功实现。
  7. 根据权利要求1所述的气液相变的介观模拟方法，其特征在于：步骤S6中的密度ρ和速度u根据密度分布函数计算，总动能ρe k根据总动能分布函数计算，温度、压力依据热力学关系式由ρ、u和ρe k完全确定。
  8. 根据权利要求1所述的气液相变的介观模拟方法，其特征在于：密度分布函数格子Boltzmann方程应可恢复稠密气体状态方程和成对相互作用力。
  9. 根据权利要求1所述的气液相变的介观模拟方法，其特征在于：总动能分布函数格子Boltzmann方程应可恢复稠密气体压力做功、成对相互作用力做功、表面张力做功和粘性热耗散。
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