曲线坐标系下水动力多层积分模型研究及应用
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摘要
环境污染与环境保护是当今世界所面临的严重问题之一。由于工业的发展，大量有害于人类和其它生物的工业废物(废水、废气、废渣)和生活污水、农业废水排入河流、湖泊、水库与海湾，使天然水体受到严重的污染。为了保护环境，防止污染的危害，必须了解这些污染物质的扩散输移规律，就是要探求当污染物投放于水体后，由于扩散、输移所造成的污染物浓度随空间和时间的变化规律。
本文基于现代紊流理论、现代数值计算方法建立适合描述水利工程中紊流规律的非线性数值模型，即曲线坐标系下的多层紊流水动力模型，旨在提高紊流精细模拟的实用性，以求有效地解决水利工程中的水流和输运现象的实际问题。因此，该研究既具有理论意义，又具有工程实用价值。
本文的主要研究内容：
1)对选题的目的和意义进行了论述；对水流与水质数值模拟发展的现状进行了系统的分析和评述，并提出了本文的研究问题；对现代紊流理论、数值计算方法进行了详细的综述、归纳和总结，并提出了本文采用的模型与方法；对紊流数值计算中的关键性技术问题(离散方法、自由表面位置的确定问题、复杂边界的处理方法等)进行了详细的综述和研究。
2)本文基于直角坐标系和非交错的网格系统，研究了一种模拟三维非恒定明渠紊流的沿层积分数值模型。通过将渠道的实验资料和计算结果的比较看出，多层模型辅助标准深度平均κ—ε模型，可以预测明渠中的时匀量和紊动量。水深校正方法可以用来获得自由表面形状，避免了“刚盖”假定，排除了非交错网格系统带来的计算振荡。
3)提出了一种生成边界处正交曲线网格的新方法，收敛速度快，在复杂边界流场区域的数值计算中，有很大的实用价值；
)为了克服复杂几何边界给数值计算带来的困难，提高通用性以及水流的预测精度，本文采用上述网格生成技术，在直角坐标系三维非恒定明渠紊流的沿层积分数值模型基础上，发展了曲线坐标系下的多层紊流水动力模型。一般的曲线坐标和非交错网格系统的应用增强了模型计算复杂边界三维流动的能力。
5)为了提高模拟具有自由表面、受显著曲率壁面影响的明渠水流的能力，本文对曲线坐标系下的多层紊流水动力模型进行了曲率修正，计入曲率效应的影响，在一定程度上考虑了紊流的各向异性效应，是一种很有工程实用价值的模型。
6)在上述紊流模型的基础上，建立三维水质模型；采用实例验证了所建立的三维非恒定沿层积分数值模型和三维水质模型，并应用于实际工程中。
Environmental pollution and protection is one of the big problems in the world. With the development of industry, a large amount of industry waste water and life polluted water harmful to people and other living things is discharged into river, lake, reservoir and ocean and make the natural water much more polluted. To protect environment, people must study the hydrodynamic and pollutant transport characteristics to obtain the distribution of the concentration.
In this paper, a three-dimensional multi-level hydrodynamic model with curvature correction in curvilinear coordinates has been developed based on the update turbulent theory and numerical method, which can effectively solve the practical problems of flows and water quality transportations in hydraulic engineering, and can strengthen the practical usage of the mathematical model. The research also has theoretical meanings and practical values in engineering.
The research details and results of this paper are as follows:
1.The purpose and meanings of the research has been discussed; the development of numerical simulation for flows and matter transportations have been analyzed and commenced, and the problem to be solved has been presented; the update turbulent theory , numerical method and the key techniques in turbulence numerical simulation( such as the discretization method, the method of determining free water surface, and treatment of complicated boundary, etc.) have been summarized.
2.A three-dimensional multi-level hydrodynamic model in Cartisn coordinates has been developed, and is solved numerically with a finite-volume method on an adaptive, nonstaggered grid.Comparisons between computed results and measured data in a straight open channel flow show that the multi-level hydrodynamic model with the standard layer averaged k-εturbulence model is capable of simulating turbulence flow, both the mean flow and the turbulence quantities. The water depth correction scheme can be used to obtain the free-surface elevation, avoiding the rigid-lid assumptions, and eliminating the oscillation of the calculations due to the non-staggered grid arrangement.
3.A new method for the generation of curvilinear grid has been proposed. Some curvilinear grid generation examples show that satisfactory grids can be generated for simple-connected regions and connected- regions with complex boundary by using the proposed adjusting factors. The curvilinear grid at boundaries is orthogonal and the interior grids can be adaptive to the variation of physical parameters of fluid.
4.A three-dimensional multi-level hydrodynamic model in curvilinear coordinates has been developed based on the proposed curvilinear grid generation method. The use of the curvilinear coordinates and non-staggered grid system increases the ability of the present model in computing complex 3D flows,
5.To increases the ability of the present model in computing complex 3D free surface flows in channel bands, the three-dimensional multi-level hydrodynamic model in curvilinear coordinates including effects of significant curvature has been developed.
本文基于现代紊流理论、现代数值计算方法建立适合描述水利工程中紊流规律的非线性数值模型，即曲线坐标系下的多层紊流水动力模型，旨在提高紊流精细模拟的实用性，以求有效地解决水利工程中的水流和输运现象的实际问题。因此，该研究既具有理论意义，又具有工程实用价值。
本文的主要研究内容：
1)对选题的目的和意义进行了论述；对水流与水质数值模拟发展的现状进行了系统的分析和评述，并提出了本文的研究问题；对现代紊流理论、数值计算方法进行了详细的综述、归纳和总结，并提出了本文采用的模型与方法；对紊流数值计算中的关键性技术问题(离散方法、自由表面位置的确定问题、复杂边界的处理方法等)进行了详细的综述和研究。
2)本文基于直角坐标系和非交错的网格系统，研究了一种模拟三维非恒定明渠紊流的沿层积分数值模型。通过将渠道的实验资料和计算结果的比较看出，多层模型辅助标准深度平均κ—ε模型，可以预测明渠中的时匀量和紊动量。水深校正方法可以用来获得自由表面形状，避免了“刚盖”假定，排除了非交错网格系统带来的计算振荡。
3)提出了一种生成边界处正交曲线网格的新方法，收敛速度快，在复杂边界流场区域的数值计算中，有很大的实用价值；
)为了克服复杂几何边界给数值计算带来的困难，提高通用性以及水流的预测精度，本文采用上述网格生成技术，在直角坐标系三维非恒定明渠紊流的沿层积分数值模型基础上，发展了曲线坐标系下的多层紊流水动力模型。一般的曲线坐标和非交错网格系统的应用增强了模型计算复杂边界三维流动的能力。
5)为了提高模拟具有自由表面、受显著曲率壁面影响的明渠水流的能力，本文对曲线坐标系下的多层紊流水动力模型进行了曲率修正，计入曲率效应的影响，在一定程度上考虑了紊流的各向异性效应，是一种很有工程实用价值的模型。
6)在上述紊流模型的基础上，建立三维水质模型；采用实例验证了所建立的三维非恒定沿层积分数值模型和三维水质模型，并应用于实际工程中。
Environmental pollution and protection is one of the big problems in the world. With the development of industry, a large amount of industry waste water and life polluted water harmful to people and other living things is discharged into river, lake, reservoir and ocean and make the natural water much more polluted. To protect environment, people must study the hydrodynamic and pollutant transport characteristics to obtain the distribution of the concentration.
In this paper, a three-dimensional multi-level hydrodynamic model with curvature correction in curvilinear coordinates has been developed based on the update turbulent theory and numerical method, which can effectively solve the practical problems of flows and water quality transportations in hydraulic engineering, and can strengthen the practical usage of the mathematical model. The research also has theoretical meanings and practical values in engineering.
The research details and results of this paper are as follows:
1.The purpose and meanings of the research has been discussed; the development of numerical simulation for flows and matter transportations have been analyzed and commenced, and the problem to be solved has been presented; the update turbulent theory , numerical method and the key techniques in turbulence numerical simulation( such as the discretization method, the method of determining free water surface, and treatment of complicated boundary, etc.) have been summarized.
2.A three-dimensional multi-level hydrodynamic model in Cartisn coordinates has been developed, and is solved numerically with a finite-volume method on an adaptive, nonstaggered grid.Comparisons between computed results and measured data in a straight open channel flow show that the multi-level hydrodynamic model with the standard layer averaged k-εturbulence model is capable of simulating turbulence flow, both the mean flow and the turbulence quantities. The water depth correction scheme can be used to obtain the free-surface elevation, avoiding the rigid-lid assumptions, and eliminating the oscillation of the calculations due to the non-staggered grid arrangement.
3.A new method for the generation of curvilinear grid has been proposed. Some curvilinear grid generation examples show that satisfactory grids can be generated for simple-connected regions and connected- regions with complex boundary by using the proposed adjusting factors. The curvilinear grid at boundaries is orthogonal and the interior grids can be adaptive to the variation of physical parameters of fluid.
4.A three-dimensional multi-level hydrodynamic model in curvilinear coordinates has been developed based on the proposed curvilinear grid generation method. The use of the curvilinear coordinates and non-staggered grid system increases the ability of the present model in computing complex 3D flows,
5.To increases the ability of the present model in computing complex 3D free surface flows in channel bands, the three-dimensional multi-level hydrodynamic model in curvilinear coordinates including effects of significant curvature has been developed.
引文
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