不可逆热力学理论在多孔介质渗流问题中的应用研究
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摘要
不可逆特性是多孔介质渗流问题的本质特征。本文针对多孔介质渗流过程中的不可逆行为，尝试将不可逆热力学的研究思路和方法引入多孔介质渗流问题的研究中，取得了一些积极的成果。
由于多孔介质本身的复杂性，多孔介质渗流问题的分析理论往往需要在多孔介质连续介质方法的基础上进行。本文基于流体粘滞流动过程的熵产表达，研究提出了多孔介质连续介质方法下多孔介质渗流过程的熵产表达形式，并在平直管模型中验证了两者的统一性。多孔介质体系往往具有复杂的宏观几何结构，本文提出了多孔介质宏观几何分类的思想，使得在具有复杂宏观几何结构的系统中可以建立简化的分析方法。另外，宏观几何分类方法亦有助于针对特定问题建立相应的输运模型，这对多孔介质渗流问题更广泛、深入的应用具有重要意义。
本文分析了多孔介质渗流过程的耗散规律，提出了不可逆特性是多孔介质渗流问题的本质特征。提出并推导了多孔介质渗流问题最小能量耗散原理，以该原理作为多孔介质渗流问题的变分原理的理论基础，具有很好的适应性和可操作性。文中在综合分析了多孔介质渗流问题各类边界条件和源(汇)条件的基础上，提出将渗流问题的水力条件划分为三类边界条件和三类源(汇)条件；基于最小能量耗散原理推导了渗流问题中各类水力条件的变分表达，丰富并发展了渗流问题变分原理。
研究了最小能量耗散原理在不同宏观几何分类多孔介质体系中的应用；列举若干应用问题，展示了最小能量耗散原理的较好的应用价值。为了进一步展示多孔介质宏观几何分类方法及最小能量耗散原理的应用，文中还尝试采用具有一维性质的管道介质与具有三维性质的块体介质组合体系进行了土体管涌破坏发展过程的模拟。
在多孔介质对流扩散问题的熵产规律的研究中，分析了最小熵产原理在这一问题中的不适应性的原因。在二组元稀薄浓度问题中，通过构造扩散过程的强制对流项并结合伴随算子的有关理论推导了二组元稀薄浓度问题的伴随变分原理及其有限元方法，同时讨论了扩散问题的各类动力条件及其变分表达式。本文的工作体现了不可逆热力学理论和方法在多孔介质多过程不可逆输运问题中应用的价值，为同类问题的研究提供了新的思路和方法。基于多孔介质宏观几何分类方法和二组元稀薄浓度问题系统分析理论，提出了建立多孔介质输运模型的思路。
The irreversibility is the essential characteristic of porous media seepage problems. In allusion to the irreversible behavior of porous media seepage process, the research thought and method of irreversible thermodynamics are attempted to introduce in the research on porous media seepage system, and some positive conclusions have been achieved.
Due to the complexity of porous media, the analytical theory about porous media seepage must be based on the method of porous media continuum hypothesis. On the basis of the entropy expression of viscous flow, the entropy expression of porous media seepage under porous media continuum hypothesis is studied and put forward, and their unification is verified in pipe model.
Porous media systems usually have complex macroscopical geometric structure. The idea of macroscopical geometric classification of porous media is brought forward in this paper, which enables the simplified analytical method to be established in the system with complex macroscopical geometric structure. In addition, this method also helps to establish corresponding transportation model aiming at specific problems, which has much importance to wider and deeper application of porous media seepage theory.
In the paper, the dissipation behavior of porous media seepage process is analyzed, and it is presented that irreversibility is the essential characteristic of porous media seepage process. The minimum energy dissipation principle of seepage problem is put forward and deduced, which is so adaptive and maneuverable that is used as the theoretical basis for the viariational principle of porous media seepage. After the integrated study of various boundary hydraulic conditions and field hydraulic conditions, a new method that the hydraulic conditions of seepage can be classified as three boundary conditions and three field conditions is presented. The variational expressions of various hydraulic conditions in seepage problems are deduced based on minimum energy dissipation principle, and the variational principles of seepage problems are enriched and developed.
The application of minimum energy dissipation principle in different
microscopical porous media systems is studied, some application problems are listed, and the preferable application value of minimum energy dissipation is laid out. In order to exhibit the application of the method of porous media macroscopical geometric classification and minimum energy dissipation, the combination system between one-dimension pipeline media and three-dimension block media is tried to simulate the destroying and developing process of soil piping erosion.
In the study of entropy expression of porous media convection-diffusion process, the reason why minimum entropy production principle is uncomformable is analyzed. In the two-substance attenuate consistency problem, by means of constituting the compulsive convection function of diffusion process, as well as integrating adjoint function, the adjoint variational principle and its finite element method of two-substance attenuate consistency are deduced, and all kinds of dynamic conditions and their variational expressions are discussed. The application value of irreversible thermodynamics in multi-process irreversible transportation problem in the process of porous media seepage is embodied in this paper, and provides new idea and method for the research of kin problems. Based on the method of porous media macroscopic geometric classification and the analytical theory of two-substance attenuate consistency problem, the idea of establishing transportation model of porous media is put forward.
由于多孔介质本身的复杂性，多孔介质渗流问题的分析理论往往需要在多孔介质连续介质方法的基础上进行。本文基于流体粘滞流动过程的熵产表达，研究提出了多孔介质连续介质方法下多孔介质渗流过程的熵产表达形式，并在平直管模型中验证了两者的统一性。多孔介质体系往往具有复杂的宏观几何结构，本文提出了多孔介质宏观几何分类的思想，使得在具有复杂宏观几何结构的系统中可以建立简化的分析方法。另外，宏观几何分类方法亦有助于针对特定问题建立相应的输运模型，这对多孔介质渗流问题更广泛、深入的应用具有重要意义。
本文分析了多孔介质渗流过程的耗散规律，提出了不可逆特性是多孔介质渗流问题的本质特征。提出并推导了多孔介质渗流问题最小能量耗散原理，以该原理作为多孔介质渗流问题的变分原理的理论基础，具有很好的适应性和可操作性。文中在综合分析了多孔介质渗流问题各类边界条件和源(汇)条件的基础上，提出将渗流问题的水力条件划分为三类边界条件和三类源(汇)条件；基于最小能量耗散原理推导了渗流问题中各类水力条件的变分表达，丰富并发展了渗流问题变分原理。
研究了最小能量耗散原理在不同宏观几何分类多孔介质体系中的应用；列举若干应用问题，展示了最小能量耗散原理的较好的应用价值。为了进一步展示多孔介质宏观几何分类方法及最小能量耗散原理的应用，文中还尝试采用具有一维性质的管道介质与具有三维性质的块体介质组合体系进行了土体管涌破坏发展过程的模拟。
在多孔介质对流扩散问题的熵产规律的研究中，分析了最小熵产原理在这一问题中的不适应性的原因。在二组元稀薄浓度问题中，通过构造扩散过程的强制对流项并结合伴随算子的有关理论推导了二组元稀薄浓度问题的伴随变分原理及其有限元方法，同时讨论了扩散问题的各类动力条件及其变分表达式。本文的工作体现了不可逆热力学理论和方法在多孔介质多过程不可逆输运问题中应用的价值，为同类问题的研究提供了新的思路和方法。基于多孔介质宏观几何分类方法和二组元稀薄浓度问题系统分析理论，提出了建立多孔介质输运模型的思路。
The irreversibility is the essential characteristic of porous media seepage problems. In allusion to the irreversible behavior of porous media seepage process, the research thought and method of irreversible thermodynamics are attempted to introduce in the research on porous media seepage system, and some positive conclusions have been achieved.
Due to the complexity of porous media, the analytical theory about porous media seepage must be based on the method of porous media continuum hypothesis. On the basis of the entropy expression of viscous flow, the entropy expression of porous media seepage under porous media continuum hypothesis is studied and put forward, and their unification is verified in pipe model.
Porous media systems usually have complex macroscopical geometric structure. The idea of macroscopical geometric classification of porous media is brought forward in this paper, which enables the simplified analytical method to be established in the system with complex macroscopical geometric structure. In addition, this method also helps to establish corresponding transportation model aiming at specific problems, which has much importance to wider and deeper application of porous media seepage theory.
In the paper, the dissipation behavior of porous media seepage process is analyzed, and it is presented that irreversibility is the essential characteristic of porous media seepage process. The minimum energy dissipation principle of seepage problem is put forward and deduced, which is so adaptive and maneuverable that is used as the theoretical basis for the viariational principle of porous media seepage. After the integrated study of various boundary hydraulic conditions and field hydraulic conditions, a new method that the hydraulic conditions of seepage can be classified as three boundary conditions and three field conditions is presented. The variational expressions of various hydraulic conditions in seepage problems are deduced based on minimum energy dissipation principle, and the variational principles of seepage problems are enriched and developed.
The application of minimum energy dissipation principle in different
microscopical porous media systems is studied, some application problems are listed, and the preferable application value of minimum energy dissipation is laid out. In order to exhibit the application of the method of porous media macroscopical geometric classification and minimum energy dissipation, the combination system between one-dimension pipeline media and three-dimension block media is tried to simulate the destroying and developing process of soil piping erosion.
In the study of entropy expression of porous media convection-diffusion process, the reason why minimum entropy production principle is uncomformable is analyzed. In the two-substance attenuate consistency problem, by means of constituting the compulsive convection function of diffusion process, as well as integrating adjoint function, the adjoint variational principle and its finite element method of two-substance attenuate consistency are deduced, and all kinds of dynamic conditions and their variational expressions are discussed. The application value of irreversible thermodynamics in multi-process irreversible transportation problem in the process of porous media seepage is embodied in this paper, and provides new idea and method for the research of kin problems. Based on the method of porous media macroscopic geometric classification and the analytical theory of two-substance attenuate consistency problem, the idea of establishing transportation model of porous media is put forward.
引文
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