河流水动力及水质模型研究
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摘要
湖泊、河流及河口水质的恶化已经成为我国一个突出的环境问题。在治理水体污染时，必须掌握污染物质随水流是如何掺混、迁移和分布的，以便进行预测及治理，这样才能有的放矢。本文根据前人研究工作的总结和本课题研究的需要，对一维河网、二维及三维曲线坐标变换、湍流模型、自由表面流动、水质模型进行了系统的文献综述。在此基础上，以研究一维河网及曲线坐标系下二维、三维河流水动力和水质模型作为本文的工作重点。一维河网模型基于以z、Q为变量的一维圣维南方程组，河流二维及三维的模型采用曲线坐标非正交网格，曲线网格可以精确地处理非规则边界，减少计算时间和计算机存储量，提高模型的计算精度。对于变量的布置，采用了B—交错网格系统。对具有实测资料的实验室弯道及天然河网、河流的水动力和水质分布进行了验证与分析。
本文建立了一维河网水动力及水质模型、ξ-η曲线坐标系下平面二维河流水动力及水质模型、ξ-η-(?)曲线坐标系下三维河流水动力及水质模型。推导了N-S方程的平面二维ξ-η坐标变换公式、三维ξ-η-(?)坐标变换公式。水质模型建立在WASP水质变量迁移、转化的理论基础之上，它考虑了10余个水质变量，分别为：浮游植物(PHYT)、氨氮(NH3)、硝酸盐氮(NO3)、无机磷(OPO4)、碳化需氧量(C-BOD)、化学需氧量(COD)、溶解氧(DO)、有机氮(ON)、有机磷(OP)、电导率、pH值、温度等，并考虑了它们之间的相互作用。
一维河网水动力及水质模型，是以一维连续、运动方程及水质扩散方程为基础，离散水动力方程组时采用了普列斯曼四点隐式差分格式，离散水质方程时采用隐式迎风差分格式，利用三级联解法求解水动力和水质方程。利用建立的一维河网水动力及水质模型对单一河道的洪水演进、复杂的树状和环状河网进行了数值模拟，给出了各断面的流量和水位变化过程，对水质模型也进行了相应的验证，给出了各个断面各水质变量的时间变化过程。计算结果表明，该模型能够反映河网水流的顺逆流动不定和输运物质浓度的非均匀变化过程，不仅可以用于单一河道和树状的河网，还可以用于复杂的环状河网。
平面二维河流水动力及水质模型，是建立在曲线坐标系下的，运用守恒性较好的控制体积法对方程进行离散，采用SIMPLEC程式求解离散的方程。以实验室弯道为例，对深度平均的二维水动力模型进行了验证，给出了各实测断面的流速及水位，并同实验结果进行对比，验证了水动力模型的可靠性。通过天然河道的实例对所建的水动力及水质模型进行验证和分析，给出了各水质变量的计算结果。
三维河流水动力及水质模型，是建立在曲线坐标系下的，自由表面的模拟采用压力Poisson方法，该方法基于二维动量方程，采用κ-ε双方程湍流模型封闭雷诺应力项，应用全坐标的坐标变换，划分完全的三维曲线网格，采用控制体积法离散方程，SIMPLEC程式求解离散方程。对实验室宽浅强弯道、天然河流的流场及弯曲漫滩流动进行模拟，给出了各个断面的水位、流速，并对具有实测资料的断面进行验证。对三峡库区蓄水前涪陵江段的水流、水质进行了数值模拟并进行了验证，并对三峡库区蓄水后万州江段及重庆两江汇流江段岸边排放的污染物扩散问题进行了预测。
The worsen environment of lake, river and estuary is one of the serious questions in our country. In treating the water pollution, we must hold how the pollutants mix, transfer and distribute along with the water flow in order to find the treatment method quickly. Based on the research work of former summarized and the need of the research task, the systemic review is made of one-dimensional river networks, two and three dimensional curvilinear coordinate transformation, turbulent model, free surface and water quality model. The research emphasis of this thesis is to study the hydrodynamic and water quality model of one dimension, two-dimension, three-dimension. Based on the Saint-Venant equations, the hydrodynamic and water quality model of one-dimension is set up. In calculating two-dimensional and three-dimensional models, the curvilinear coordinate system is used to treat the irregular boundary and improve the computed precision. At the same time, it can reduce the computed time and storage of computer. The staggered grid of B type is adopted to lay the variables. The hydrodynamic and water quality models are validated to simulate the river netwoks, the curved channel of laboratory, natural-river.
These models are built in this thesis, the hydrodynamic and water quality model of one-dimension, the planar 2D k-εturbulent hydrodynamic and water quality model of river, the 3D k-εturbulent hydrodynamic and water quality model of river. The transform formula is deduced of Reynolds Averaged Navier Stokes(RANS) equation in planar 2Dξ-ηcoordinates, and fully 3Dξ-η-ζcoordinates at the same time. Based on the theory of WASP water quality model, the water quality model concludes twelve variables: PHYT, NH3, NO3, OPO4, CBOD, COD, DO, ON, OP, conductivity, pH and temperature and considers the variables transformation and affect each other.
Base on the Saint-Venant equations and the advection-dispersion equations of one dimension, the Preissmann implicit scheme and the implicit finite scheme are used to discrete the Saint-Venant equations and the water quality equation. The river-junction-river method is applied to resolve the hydrodynamic and water quality model for river networks. The one-dimensional model of hydrodynamic and water quality is applied to simulate flood routing of single-river, unsteady flow of tree-type, looped open channel networks and river networks. The results of levels, flows and discharge distribution between the branches are presented. The water quality is validated corresponsively and time course of contamination variables are given in this thesis. The simulated trends and magnitudes of water quality constituents were generally in good agreement with field observations. The calculated results show that this model can be used to simulate the concentration of water quality constituents in river networks with the flood tide and ebb tide, not only single-river and tree-type river networks but also complex looped river networks.
The two-dimensional model of hydrodynamic and water quality is set up in curvilinear coordinate, the control volume method is used to disperse the equations and the flow calculation adopts the SIMPLEC algorithm to acquire the coupling of velocity and pressure. The curved channel in laboratory is selected to validate the depth-averaged 2D model. The velocity and water level at all sections are presented and are compared with the data of experiment. This results show that this hydrodynamic model is credible. This model is applied to simulate the reservoir of Post Fall and these results validate the reliability of this model.
The 3D model of hydrodynamic and water quality is set up in curvilinear coordinate, the water level of this model is determined from 2D Poisson equation derived from 2D depth averaged momentum equations. The k-εturbulent mathematic model is used to calculate the reynold stress. The fully coordinate transformation is used to represent the free surface and bed topography. The control volume method is used to disperse the equations and the flow calculation adopts the SIMPLEC algorithm to acquire the coupling of velocity and pressure. This model is applied to simulate the channel bend in the laboratory, the part section of Fall river and the flows in the meander channel with straight flood plain banks, the results are given and validated with measurements. The model is applied to calculate the flow and water quality of the FuLing river and then the pollutant diffuseness of bank discharge is forecast in WanZhou river and ChongQing river.
本文建立了一维河网水动力及水质模型、ξ-η曲线坐标系下平面二维河流水动力及水质模型、ξ-η-(?)曲线坐标系下三维河流水动力及水质模型。推导了N-S方程的平面二维ξ-η坐标变换公式、三维ξ-η-(?)坐标变换公式。水质模型建立在WASP水质变量迁移、转化的理论基础之上，它考虑了10余个水质变量，分别为：浮游植物(PHYT)、氨氮(NH3)、硝酸盐氮(NO3)、无机磷(OPO4)、碳化需氧量(C-BOD)、化学需氧量(COD)、溶解氧(DO)、有机氮(ON)、有机磷(OP)、电导率、pH值、温度等，并考虑了它们之间的相互作用。
一维河网水动力及水质模型，是以一维连续、运动方程及水质扩散方程为基础，离散水动力方程组时采用了普列斯曼四点隐式差分格式，离散水质方程时采用隐式迎风差分格式，利用三级联解法求解水动力和水质方程。利用建立的一维河网水动力及水质模型对单一河道的洪水演进、复杂的树状和环状河网进行了数值模拟，给出了各断面的流量和水位变化过程，对水质模型也进行了相应的验证，给出了各个断面各水质变量的时间变化过程。计算结果表明，该模型能够反映河网水流的顺逆流动不定和输运物质浓度的非均匀变化过程，不仅可以用于单一河道和树状的河网，还可以用于复杂的环状河网。
平面二维河流水动力及水质模型，是建立在曲线坐标系下的，运用守恒性较好的控制体积法对方程进行离散，采用SIMPLEC程式求解离散的方程。以实验室弯道为例，对深度平均的二维水动力模型进行了验证，给出了各实测断面的流速及水位，并同实验结果进行对比，验证了水动力模型的可靠性。通过天然河道的实例对所建的水动力及水质模型进行验证和分析，给出了各水质变量的计算结果。
三维河流水动力及水质模型，是建立在曲线坐标系下的，自由表面的模拟采用压力Poisson方法，该方法基于二维动量方程，采用κ-ε双方程湍流模型封闭雷诺应力项，应用全坐标的坐标变换，划分完全的三维曲线网格，采用控制体积法离散方程，SIMPLEC程式求解离散方程。对实验室宽浅强弯道、天然河流的流场及弯曲漫滩流动进行模拟，给出了各个断面的水位、流速，并对具有实测资料的断面进行验证。对三峡库区蓄水前涪陵江段的水流、水质进行了数值模拟并进行了验证，并对三峡库区蓄水后万州江段及重庆两江汇流江段岸边排放的污染物扩散问题进行了预测。
The worsen environment of lake, river and estuary is one of the serious questions in our country. In treating the water pollution, we must hold how the pollutants mix, transfer and distribute along with the water flow in order to find the treatment method quickly. Based on the research work of former summarized and the need of the research task, the systemic review is made of one-dimensional river networks, two and three dimensional curvilinear coordinate transformation, turbulent model, free surface and water quality model. The research emphasis of this thesis is to study the hydrodynamic and water quality model of one dimension, two-dimension, three-dimension. Based on the Saint-Venant equations, the hydrodynamic and water quality model of one-dimension is set up. In calculating two-dimensional and three-dimensional models, the curvilinear coordinate system is used to treat the irregular boundary and improve the computed precision. At the same time, it can reduce the computed time and storage of computer. The staggered grid of B type is adopted to lay the variables. The hydrodynamic and water quality models are validated to simulate the river netwoks, the curved channel of laboratory, natural-river.
These models are built in this thesis, the hydrodynamic and water quality model of one-dimension, the planar 2D k-εturbulent hydrodynamic and water quality model of river, the 3D k-εturbulent hydrodynamic and water quality model of river. The transform formula is deduced of Reynolds Averaged Navier Stokes(RANS) equation in planar 2Dξ-ηcoordinates, and fully 3Dξ-η-ζcoordinates at the same time. Based on the theory of WASP water quality model, the water quality model concludes twelve variables: PHYT, NH3, NO3, OPO4, CBOD, COD, DO, ON, OP, conductivity, pH and temperature and considers the variables transformation and affect each other.
Base on the Saint-Venant equations and the advection-dispersion equations of one dimension, the Preissmann implicit scheme and the implicit finite scheme are used to discrete the Saint-Venant equations and the water quality equation. The river-junction-river method is applied to resolve the hydrodynamic and water quality model for river networks. The one-dimensional model of hydrodynamic and water quality is applied to simulate flood routing of single-river, unsteady flow of tree-type, looped open channel networks and river networks. The results of levels, flows and discharge distribution between the branches are presented. The water quality is validated corresponsively and time course of contamination variables are given in this thesis. The simulated trends and magnitudes of water quality constituents were generally in good agreement with field observations. The calculated results show that this model can be used to simulate the concentration of water quality constituents in river networks with the flood tide and ebb tide, not only single-river and tree-type river networks but also complex looped river networks.
The two-dimensional model of hydrodynamic and water quality is set up in curvilinear coordinate, the control volume method is used to disperse the equations and the flow calculation adopts the SIMPLEC algorithm to acquire the coupling of velocity and pressure. The curved channel in laboratory is selected to validate the depth-averaged 2D model. The velocity and water level at all sections are presented and are compared with the data of experiment. This results show that this hydrodynamic model is credible. This model is applied to simulate the reservoir of Post Fall and these results validate the reliability of this model.
The 3D model of hydrodynamic and water quality is set up in curvilinear coordinate, the water level of this model is determined from 2D Poisson equation derived from 2D depth averaged momentum equations. The k-εturbulent mathematic model is used to calculate the reynold stress. The fully coordinate transformation is used to represent the free surface and bed topography. The control volume method is used to disperse the equations and the flow calculation adopts the SIMPLEC algorithm to acquire the coupling of velocity and pressure. This model is applied to simulate the channel bend in the laboratory, the part section of Fall river and the flows in the meander channel with straight flood plain banks, the results are given and validated with measurements. The model is applied to calculate the flow and water quality of the FuLing river and then the pollutant diffuseness of bank discharge is forecast in WanZhou river and ChongQing river.
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