微尺度流动与传热传质的格子Boltzmann方法
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摘要
气体在微机械装置、燃料电池、微燃烧器等系统中的流动、传热与传质等问题已经成为国际社会共同关注的话题。由于气体在这些系统中的输运过程一般发生在微米量级,通常表现出一些反常现象,比如：非连续效应、热蠕动效应以及扩散滑移效应等。需要指出的是最近发展起来的介观方法-格子Boltzmann方法(LBM),由于其微观粒子本质和介观特性,该方法已经被用来研究微尺度气体流动问题,但是对于微尺度传热传质方面的研究十分缺乏。并且我们也注意到不管是宏观大尺度还是微观尺度问题,LBM本身仍然存在众多理论不足。另外,在微尺度传热传质问题的研究中,LBM刚刚起步,还存在两个关键问题需要解决,即松弛时间与Knudsen数之间的关系以及LBM的边界处理问题。本文正是基于以上几个方面开展了相关的研究,并且基于多松弛格子Boltzmann模型的思想完善了LBM在传热、传质方面的相关理论。在此基础上对微尺度传热传质的LBM的两个关键问题进行了研究并且对微尺度传热传质的前沿问题进行了有益的探索。论文的主要工作包括以下两个方面：
首先,在LBM的理论方面有如下几个方面的创新：
(1)提出了耦合多松弛热格子Boltzmann模型,该模型通过对能量通量进行修正彻底克服了现有多速度模型中Prandlt数唯一以及粘性系数不一致的不足；
(2)基于Boltzmann方程提出了两类轴对称热格子Boltzmann模型：无粘性耗散和压缩功的轴对称热LBM模型；含粘性耗散和压缩功的轴对称热LBM模型,有效克服现有热格子Boltzmann模型存在复杂外力梯度项等不足,完善了格子方法在轴对称流动中的理论；
(3)基于单流体模型,本文提出了两组分多松弛格子Boltzmann模型有效克服了现有模型在处理不同分子质量时采用两套网格等不足。这些理论的完善和发展为推动LBM在传热传质领域的应用奠定了必要的基础。
其次,在微尺度传热传质方面做出了如下几个方面的工作：
(1)提出了两种边界处理格式,即：平衡态与镜面反射的组合边界条件以及平衡态与反弹的组合边界条件。
(2)详细的分析了二维或三维微管道流动与传热传质的LBM边界处理格式并发现了离散效应,同时也给出相应的正确处理格式；
(3)基于理论方面提出的基本模型成功捕捉了微尺度反常热蠕动现象,并且发现非耦合热模型不能捕捉热蠕动现象。最后对微尺度Kramer以及Poiseuille流随组分浓度变化的传质问题进行了初步的研究。
The fluid flow, heat and mass transfer in the Micro-electro-mechanical systems (MEMS), Fuel Cell and Micro-combustion have been obtained much more attentions in the world. Owing to the micro/nanometer scales appearing in such systems, the researches on the transports of gases should be considered such small scales effects. Recently, own to its kinetic background, the lattice Boltzmann method (LBM) has been applied to micro-scopic gas flows, however, the study of microscopic gas heat and mass transfer is quite rare. It is also observed that the LBM still has many fundamental problems at the macroscopic or microscopic gas flows. In addition, the application of LBE to the microscopic gas flows still has two critical problems, that is, the relation between relaxation time and Knudsen number, another is the boundary treatment of LBE. In sight of the above mentioned problems, this thesis will study such problems as following aspects:Firstly, we improve the theory of LBE in the field of heat and mass transfer, and then have a try to apply LBE models to investi-gating the microscopic heat and mass transfer problems. The contents of this thesis can be classified to two main aspects:
(1) Theory of the LBE:First, a coupled multiple relaxation times (MRT) thermal LBE model is proposed, which overcome the fixed Prandt number and the inconsistent of the viscous coefficient in the existing multispeed LBE models; Second, two kinds of the ax-isymmetric thermal LBE models are introduced, which overcome the complex external force terms in the existing axisymmetric thermal LBE models; Then, under the single fluid assumption, a binary mixtures LBE model with MRT is proposed, which overcome the Schmidt and the viscosity problems in the existing LBE models; These theoretical works have provided a solid foundation for LBE to investigate the field of heat and mass transfer.
(2) Application of the LBE to microscopic problems:Firstly, two different boundary conditions have been proposed, i.e, one is the combination of the equilibrium distribution and the specular refection scheme, and another is the combination of the equilibrium distribution and the bounce back scheme. Then, the heat and mass transfer problems in two or three dimensional microscopic pipe flows have been investigated, and a detailed analysis for the discrete effects on the boundary conditions is discussed, and correct treatment schemes are proposed; Finally, we applied the proposed models in (1) to investigating the microscopic gas flow of heat transfer problems, and mass transfer in Kramer or Poiseuille flows, and found that the MRT thermal model could capture the thermal creep phenomena;
首先,在LBM的理论方面有如下几个方面的创新：
(1)提出了耦合多松弛热格子Boltzmann模型,该模型通过对能量通量进行修正彻底克服了现有多速度模型中Prandlt数唯一以及粘性系数不一致的不足；
(2)基于Boltzmann方程提出了两类轴对称热格子Boltzmann模型：无粘性耗散和压缩功的轴对称热LBM模型；含粘性耗散和压缩功的轴对称热LBM模型,有效克服现有热格子Boltzmann模型存在复杂外力梯度项等不足,完善了格子方法在轴对称流动中的理论；
(3)基于单流体模型,本文提出了两组分多松弛格子Boltzmann模型有效克服了现有模型在处理不同分子质量时采用两套网格等不足。这些理论的完善和发展为推动LBM在传热传质领域的应用奠定了必要的基础。
其次,在微尺度传热传质方面做出了如下几个方面的工作：
(1)提出了两种边界处理格式,即：平衡态与镜面反射的组合边界条件以及平衡态与反弹的组合边界条件。
(2)详细的分析了二维或三维微管道流动与传热传质的LBM边界处理格式并发现了离散效应,同时也给出相应的正确处理格式；
(3)基于理论方面提出的基本模型成功捕捉了微尺度反常热蠕动现象,并且发现非耦合热模型不能捕捉热蠕动现象。最后对微尺度Kramer以及Poiseuille流随组分浓度变化的传质问题进行了初步的研究。
The fluid flow, heat and mass transfer in the Micro-electro-mechanical systems (MEMS), Fuel Cell and Micro-combustion have been obtained much more attentions in the world. Owing to the micro/nanometer scales appearing in such systems, the researches on the transports of gases should be considered such small scales effects. Recently, own to its kinetic background, the lattice Boltzmann method (LBM) has been applied to micro-scopic gas flows, however, the study of microscopic gas heat and mass transfer is quite rare. It is also observed that the LBM still has many fundamental problems at the macroscopic or microscopic gas flows. In addition, the application of LBE to the microscopic gas flows still has two critical problems, that is, the relation between relaxation time and Knudsen number, another is the boundary treatment of LBE. In sight of the above mentioned problems, this thesis will study such problems as following aspects:Firstly, we improve the theory of LBE in the field of heat and mass transfer, and then have a try to apply LBE models to investi-gating the microscopic heat and mass transfer problems. The contents of this thesis can be classified to two main aspects:
(1) Theory of the LBE:First, a coupled multiple relaxation times (MRT) thermal LBE model is proposed, which overcome the fixed Prandt number and the inconsistent of the viscous coefficient in the existing multispeed LBE models; Second, two kinds of the ax-isymmetric thermal LBE models are introduced, which overcome the complex external force terms in the existing axisymmetric thermal LBE models; Then, under the single fluid assumption, a binary mixtures LBE model with MRT is proposed, which overcome the Schmidt and the viscosity problems in the existing LBE models; These theoretical works have provided a solid foundation for LBE to investigate the field of heat and mass transfer.
(2) Application of the LBE to microscopic problems:Firstly, two different boundary conditions have been proposed, i.e, one is the combination of the equilibrium distribution and the specular refection scheme, and another is the combination of the equilibrium distribution and the bounce back scheme. Then, the heat and mass transfer problems in two or three dimensional microscopic pipe flows have been investigated, and a detailed analysis for the discrete effects on the boundary conditions is discussed, and correct treatment schemes are proposed; Finally, we applied the proposed models in (1) to investigating the microscopic gas flow of heat transfer problems, and mass transfer in Kramer or Poiseuille flows, and found that the MRT thermal model could capture the thermal creep phenomena;
引文
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