三维紊流泥沙数学模型及其应用
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摘要
目前，紊流模型已被广泛应用于各种工程问题的水流计算，其中，K—ε双方程模型，以其有效性和精度，使用最为普遍。然而，由于它假定紊动粘滞性是各向同性的，在一些复杂的紊流运动计算中其应用受到限制。近年来，窦国仁发表了“紊流随机理论”，提出了新的各向异性紊动的Reynolds应力表达式，并改进了壁面律公式。这一理论具有广阔的应用前景。
本文在作者以往建立的二维紊流泥沙数学模型(2DTSM)基础上，根据窦国仁的紊流随机理论，建立了三维紊流泥沙数学模型。主要内容如下：
(1)开发了基于K—ε紊流模型的三维水流数值计算程序，并用于明渠丁坝绕流的流场计算。
(2)根据窦国仁的紊流随机理论，导出了各向异性紊流的Reynolds应力的数值格式，从而开发了基于紊流随机模型的三维水流计算程序，运用该程序计算了航槽内的三维流场，得到的结果与水槽试验资料吻合良好。
(3)在三维紊流模型的基础上，给出了描述三维悬沙运动及床沙级配的控制方程，建立了三维紊流泥沙数学模型(3DTSM)。用水槽冲淤试验含沙量沿垂线分布资料及葛洲坝水利枢纽建库前后水沙资料对该模型进行了检验，结果基本一致。
(4)将所建的三维紊流泥沙数学模型应用于三峡工程坝区泥沙冲淤问题的研究，预测了三峡工程建成后坝区上游河段泥沙冲淤发展过程及其分布、河床淤积物级配组成及不同时期、不同高程的流场、含沙场等，计算结果与清华大学、长江科学院、南京水利科学研究院物理模型试验值比较接近。
Turbulence models have been used extensively in flow calculation. The K-z model is the well known model for its efficiency and reasonable accuracy. However, the standard K-z model, because of the assumption of isotropic eddy viscosity, appears to be deficient in predicting flows of complex turbulent flow. Dou Guoren presented a Reynolds stress model for the anisotropic turbulent flow, in his study on "Stochastic Theory of Turbulence". Also, he improved the expressions of the Law of the Wall. His theory has wide application potential in the calculation of 3-D turbulent flow.
In this paper, based on the two-dimensional mathematical model of turbulent flow and sediment transport developed by author and Dou's stochastic theory of turbulent flow, a three-dimensional mathematical model of turbulent flow and sediment transport has been developed. The main contents of this work are as following:
(1) A 3-D mathematical model of turbulent flow, based on the K-e model, is developed to simulate the flow around the spur-dike, and the result shows that the model can predict the 3-D characteristic of flow.
(2) The 3-D turbulent flow model is further improved by using Dou's stochastic theory of turbulent flow and the 3-D flow fields in a navigation channel are calculated. The results is agreement with flume experiment data.
(3) Based on the 3-D turbulent flow model, by introducing the three-dimensional suspended-load transport and the bed material size
distribution equations, a 3-D turbulent flow and sediment transport mathematical model is developed. The water level is determined from a two-dimensional Poisson equation derived from two-dimensional depth-averaged momentum equations. The governing equations are solved numerically with a control method. The model was tested for channel flow situations with net entrainment from a loose bed and with net deposition, and the field data in the reach from Miaohe to Sandouping of the Yangtze river before and after the Gezhouba project was constructed. The calculated is agreement well with the measured data.
The model is applied to predict the sediment deposition of the Three Gorges Project. The computed deposition process and its distribution, the bed material size distribution and the flow velocity, the suspended sediment concentration in different term and elevations are in good agreement with the results of physical model by Tsinghua University, Research Institute of Yangtze River and Nanjing Hydraulic Research Institute.
本文在作者以往建立的二维紊流泥沙数学模型(2DTSM)基础上，根据窦国仁的紊流随机理论，建立了三维紊流泥沙数学模型。主要内容如下：
(1)开发了基于K—ε紊流模型的三维水流数值计算程序，并用于明渠丁坝绕流的流场计算。
(2)根据窦国仁的紊流随机理论，导出了各向异性紊流的Reynolds应力的数值格式，从而开发了基于紊流随机模型的三维水流计算程序，运用该程序计算了航槽内的三维流场，得到的结果与水槽试验资料吻合良好。
(3)在三维紊流模型的基础上，给出了描述三维悬沙运动及床沙级配的控制方程，建立了三维紊流泥沙数学模型(3DTSM)。用水槽冲淤试验含沙量沿垂线分布资料及葛洲坝水利枢纽建库前后水沙资料对该模型进行了检验，结果基本一致。
(4)将所建的三维紊流泥沙数学模型应用于三峡工程坝区泥沙冲淤问题的研究，预测了三峡工程建成后坝区上游河段泥沙冲淤发展过程及其分布、河床淤积物级配组成及不同时期、不同高程的流场、含沙场等，计算结果与清华大学、长江科学院、南京水利科学研究院物理模型试验值比较接近。
Turbulence models have been used extensively in flow calculation. The K-z model is the well known model for its efficiency and reasonable accuracy. However, the standard K-z model, because of the assumption of isotropic eddy viscosity, appears to be deficient in predicting flows of complex turbulent flow. Dou Guoren presented a Reynolds stress model for the anisotropic turbulent flow, in his study on "Stochastic Theory of Turbulence". Also, he improved the expressions of the Law of the Wall. His theory has wide application potential in the calculation of 3-D turbulent flow.
In this paper, based on the two-dimensional mathematical model of turbulent flow and sediment transport developed by author and Dou's stochastic theory of turbulent flow, a three-dimensional mathematical model of turbulent flow and sediment transport has been developed. The main contents of this work are as following:
(1) A 3-D mathematical model of turbulent flow, based on the K-e model, is developed to simulate the flow around the spur-dike, and the result shows that the model can predict the 3-D characteristic of flow.
(2) The 3-D turbulent flow model is further improved by using Dou's stochastic theory of turbulent flow and the 3-D flow fields in a navigation channel are calculated. The results is agreement with flume experiment data.
(3) Based on the 3-D turbulent flow model, by introducing the three-dimensional suspended-load transport and the bed material size
distribution equations, a 3-D turbulent flow and sediment transport mathematical model is developed. The water level is determined from a two-dimensional Poisson equation derived from two-dimensional depth-averaged momentum equations. The governing equations are solved numerically with a control method. The model was tested for channel flow situations with net entrainment from a loose bed and with net deposition, and the field data in the reach from Miaohe to Sandouping of the Yangtze river before and after the Gezhouba project was constructed. The calculated is agreement well with the measured data.
The model is applied to predict the sediment deposition of the Three Gorges Project. The computed deposition process and its distribution, the bed material size distribution and the flow velocity, the suspended sediment concentration in different term and elevations are in good agreement with the results of physical model by Tsinghua University, Research Institute of Yangtze River and Nanjing Hydraulic Research Institute.
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