曲线坐标系下水动力模型的修正研究及应用
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摘要
在水利建设和国民经济建设的许多领域中,研究水流和伴随着水流的热输运、物质输运都具有极其重要的意义。江、河、湖、海以及地下的水体昼夜不停地运动,携带着热量、泥沙、盐份和各类污染物质,改变着我们的生活环境。为了兴水利、除水害、作为水资源综合利用的第一步,必须探明水流运动的规律和伴随水流发生的热输运、物质输运的规律。对水流和输运现象进行预测,工程设计人员才能从大量的方案中选取最优设计方案,并保证其设计得以实现。准确地预测水流和输运现象,还能帮助我们预报乃至控制一些潜在的灾祸,如水体污染、洪水、潮汐等。
预测的实质,是在给定的物理条件下,求出控制着物理过程的若干变量在空间的分布和随时间的演变。预测的方法,基本上可分为两类：实验研究和理论计算。
本文采用理论计算的方法,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,即曲线坐标系下的二、三维紊流水动力模型,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)提出一种生成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。
3)基于正交曲线拟合坐标系,建立了一种模拟二维非恒定弯曲边界明渠紊流的深度平均模型,并对流速深度平均值和二次流流速分布之间的差异所带来的影响进行修正,使其计入二次流的影响。采用修正的紊流模型计算紊动应力项；采用正交曲线拟合坐标技术处理复杂的实际计算域边界；采用试验数据验证所建计算模型的准确性和适应性,计算结果都与实验值有很好的一致性,从而证明流速深度平均值和二次流流速分布之间的差异带来的弥散应力项是影响大曲率弯道流动的最主要的应力。
4)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,本文将采用上述网格生成技术,将直角坐标系三维非恒定明渠紊流的数值模型,发展成曲线坐标系系统的多层紊流水动力模型,即平面上采用曲线拟合坐标系,在垂直方向采用sigema坐标变换。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的三维流动的能力。
5)为了提高模拟具有自由表面,受显著曲率壁面影响的弯曲明渠水流的能力,本文对曲线坐标系下的紊流水动力模型进行了曲率效应修正,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)采用实例验证本文所建立的三维非恒定数值模型；并应用于三峡工程截流水流流态的数值计算中。
The prediction of flow and sediment transport is one of the most important tasks in river engineering and related areas. 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.
The prediction is very difficult because the flow in open channels is usually turbulent, the geometry is irregular and can vary with time, and sediment transport phenomena are very complex. Until now, predictions of flow and sediment transport in rivers usually neglect the influence of secondary flows. However, this influence is important for the main flow and the sediment transport and can only be accounted for realistically with a 3D model.
In this paper, a 2D depth-averaged model for simulating and examining flow patterns in channel bends has been proposed, which takes into account the influence of the secondary flow phenomenon through the calculation of the dispersion stresses arisen from the integration of the products of the discrepancy between the mean and the true velocity distributions. And a three-dimensional numerical hydrodynamic model with an orthogonal curvilinear coordinate in the horizontal direction and sigma coordinate in the vertical direction has been developed, and the model includes the effects of significant curvature. The two models 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 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.
3. A 2D depth-averaged model for simulating and examining flow patterns in channel bends has been proposed. In particular, this proposed 2D depth-averaged model takes into account the influence of the secondary flow phenomenon through the calculation of the dispersion stresses arisen from the integration of the products of the discrepancy between the mean and the true velocity distributions. The proposed model uses an orthogonal curvilinear coordinate system to efficiently and accurately simulate the flow field with irregular boundaries. Two sets of experimental data were used to demonstrate the model's capabilities. The simulations considering the secondary flow effect agree well with the measured data. Furthermore, an examination of the dispersion stress terms shows that the dispersion stresses play a major role in the transverse convection of the momentum shifting from the inner bank to the outer bank for flows in both mild and sharp bends.
4. A three-dimensional numerical hydrodynamic model with an orthogonal curvilinear coordinate in the horizontal direction and sigma coordinate in the vertical direction has been developed. The use of the curvilinear coordinates and non-staggered grid system increases the ability of the presented 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 hydrodynamic model in curvilinear coordinates including effects of significant curvature has been developed.
6. The modified three-dimensional hydrodynamic model was used to predict the hydraulic characteristics of Three Gorge river flow when the left river is being closed and water has to pass only through the right channel.The important hydraulic parameters such as velocity and water level have been obtained very easily, and the computed results are in agreement with experimental data under different practical conditions.
预测的实质,是在给定的物理条件下,求出控制着物理过程的若干变量在空间的分布和随时间的演变。预测的方法,基本上可分为两类：实验研究和理论计算。
本文采用理论计算的方法,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,即曲线坐标系下的二、三维紊流水动力模型,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)提出一种生成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。
3)基于正交曲线拟合坐标系,建立了一种模拟二维非恒定弯曲边界明渠紊流的深度平均模型,并对流速深度平均值和二次流流速分布之间的差异所带来的影响进行修正,使其计入二次流的影响。采用修正的紊流模型计算紊动应力项；采用正交曲线拟合坐标技术处理复杂的实际计算域边界；采用试验数据验证所建计算模型的准确性和适应性,计算结果都与实验值有很好的一致性,从而证明流速深度平均值和二次流流速分布之间的差异带来的弥散应力项是影响大曲率弯道流动的最主要的应力。
4)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,本文将采用上述网格生成技术,将直角坐标系三维非恒定明渠紊流的数值模型,发展成曲线坐标系系统的多层紊流水动力模型,即平面上采用曲线拟合坐标系,在垂直方向采用sigema坐标变换。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的三维流动的能力。
5)为了提高模拟具有自由表面,受显著曲率壁面影响的弯曲明渠水流的能力,本文对曲线坐标系下的紊流水动力模型进行了曲率效应修正,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)采用实例验证本文所建立的三维非恒定数值模型；并应用于三峡工程截流水流流态的数值计算中。
The prediction of flow and sediment transport is one of the most important tasks in river engineering and related areas. 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.
The prediction is very difficult because the flow in open channels is usually turbulent, the geometry is irregular and can vary with time, and sediment transport phenomena are very complex. Until now, predictions of flow and sediment transport in rivers usually neglect the influence of secondary flows. However, this influence is important for the main flow and the sediment transport and can only be accounted for realistically with a 3D model.
In this paper, a 2D depth-averaged model for simulating and examining flow patterns in channel bends has been proposed, which takes into account the influence of the secondary flow phenomenon through the calculation of the dispersion stresses arisen from the integration of the products of the discrepancy between the mean and the true velocity distributions. And a three-dimensional numerical hydrodynamic model with an orthogonal curvilinear coordinate in the horizontal direction and sigma coordinate in the vertical direction has been developed, and the model includes the effects of significant curvature. The two models 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 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.
3. A 2D depth-averaged model for simulating and examining flow patterns in channel bends has been proposed. In particular, this proposed 2D depth-averaged model takes into account the influence of the secondary flow phenomenon through the calculation of the dispersion stresses arisen from the integration of the products of the discrepancy between the mean and the true velocity distributions. The proposed model uses an orthogonal curvilinear coordinate system to efficiently and accurately simulate the flow field with irregular boundaries. Two sets of experimental data were used to demonstrate the model's capabilities. The simulations considering the secondary flow effect agree well with the measured data. Furthermore, an examination of the dispersion stress terms shows that the dispersion stresses play a major role in the transverse convection of the momentum shifting from the inner bank to the outer bank for flows in both mild and sharp bends.
4. A three-dimensional numerical hydrodynamic model with an orthogonal curvilinear coordinate in the horizontal direction and sigma coordinate in the vertical direction has been developed. The use of the curvilinear coordinates and non-staggered grid system increases the ability of the presented 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 hydrodynamic model in curvilinear coordinates including effects of significant curvature has been developed.
6. The modified three-dimensional hydrodynamic model was used to predict the hydraulic characteristics of Three Gorge river flow when the left river is being closed and water has to pass only through the right channel.The important hydraulic parameters such as velocity and water level have been obtained very easily, and the computed results are in agreement with experimental data under different practical conditions.
引文
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