WO2022067498A1 - 一种气液相变的介观模拟方法 - Google Patents
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- 238000005315 distribution function Methods 0.000 claims abstract description 81
- 230000008569 process Effects 0.000 claims abstract description 28
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- 230000003993 interaction Effects 0.000 claims description 24
- 238000005381 potential energy Methods 0.000 claims description 16
- 239000007788 liquid Substances 0.000 claims description 12
- 230000005012 migration Effects 0.000 claims description 8
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- 239000012071 phase Substances 0.000 claims description 8
- 230000005501 phase interface Effects 0.000 claims description 6
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- 230000002452 interceptive effect Effects 0.000 abstract 3
- 230000003278 mimic effect Effects 0.000 abstract 1
- 230000008020 evaporation Effects 0.000 description 5
- 238000001704 evaporation Methods 0.000 description 5
- 230000009878 intermolecular interaction Effects 0.000 description 3
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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
Description
Claims (9)
- 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。
- 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。
- 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。
- 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。
- 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。
- 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。
- 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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