三峡水库近坝区三维流场温度场数值模拟
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摘要
从不可压缩流动的 N-S 方程出发,建立了三维非恒定流的水流水温耦合数学模型,本文模型由连续方程和动量方程导出关于压力的泊桑方程来求解压力分布,根据动量方程求解三个流速分量;取消了静水压力假定,适合于对复杂流态及其有密度分层流动的数值模拟。本文数值离散采用正交网格的有限体积方法,模型具有计算速度快的特点,能够应用于实际工程问题;模型除了在动量方程中考虑浮力项外,还采用大涡模拟紊流模型,使得流动与水温耦合计算;模型考虑了水面散热及其太阳辐射的影响因素。
应用美国陆军工程公司于 1980 年在水库试验水槽上进行的温差异重流试验来验证数学模型,计算结果与实验资料以及前人的计算结果符合较好,说明论文所采用的数学模型和数值计算方法能够预测温差异重流的特性。
水面热交换是引起水库水温分层的主要原因之一。本文分析了水面热交换的几种方式,在计算水面热交换时考虑了太阳辐射、湿度、气温、云量、风速等气象条件。并采用了一个直观的矩形试验水池,分别计算了两种不同气象条件的工况。结果表明水体中热传递符合客观规律,验证了在气象条件的影响下温度场计算的正确性。
应用所建立的数学模型对三峡近坝区从庙河至坝前约 18km 水域的三维流场及温度场进行了数值模拟。采用入口断面的流量水温等实测资料作为入流边界条件,大坝孔口为出流边界条件,计算了从 2003 年 6 月至 2004 年 6 月的实际工况。计算所得的流场与河道地形相比可以看出,水面狭窄的江段水流流速较大,江段突扩段附近有明显回水区,流速的横向分布受河道弯曲及水下地形和河道主槽影响。计算出的水温分布与坝前观测的水温分布符合良好,而且同一层水体温度相差不大,表层受气象条件影响较小,垂向没有温度分层现象的出现。由于在蓄水初期,最高水位为 139m,水深相对较浅,而且在汛期虽然气温较高,但流量很大,难以形成水温分层,这与计算的结果相符。
A three-dimension model coupled with flow and temperature is developed basedon Navier-Stokes equations for incompressible flows. The continuum-derivedPoisson equations are used to solve the pressure distribution and the momentumequations are used to solve the velocity components. Because the assumption of staticpressure of water is canceled, the model is appropriate for complex flows and densitylayered flows. The Finite Volume Method is adopted as the numerical discretizationmethod, the model has a fast computing velocity and it is applicable to engineering.Besides the buoyancy components considered in the momentum equations,anisotropic turbulent model is adopted in the model, such as Smagorinsky-DeardorffLarge Eddy Simulation, which enables the coupled flow and temperature can becomputed. The influence of the weather conditions is also considered in the model.
The channel experiment which was made in 1980 by U.S Army EngineeringCorporation is adopted to investigate the validity and the reliability of the model. Theresults show that the computational results agree well with the results of theexperiments. It illustrates that the numerical model and the numerical methods cancorrectly predict the characteristics of thermal temperature flows.
Some modes of heat exchange at the surface are considered. The radiant heat,humidity, air temperature, cloudage and wind speed are considered when computingthe heat exchange at the surface. Two conditions with different weather workingconditions are computed in a rectangle pool. The results show that the transfer of heatin the water agrees well with rules.
The numerical model is applied to simulate the 3D-flow and temperature fieldsnear the Dam Area of Three Gorges Reservoir. The measured data is used as theboundary conditions in the entrance. Many different working conditions aresimulated from June 2003 to June 2004. The results show that the velocity of the flowbecomes larger at the narrow areas, the breadthwise distribution of the velocity isinfluenced by the underwater landform and the riverway. The computational water
temperature near the dam agrees well with the measured data. The temperature of thesame layer has little difference and the weather conditions have little influence on thetop layer. The layered temperature of the vertical did not occured. During thereservoir impoundment period with a 139m water level, although the air temperatureis high, it is difficult to form the layered temperature. It agrees well with thecomputational results.
应用美国陆军工程公司于 1980 年在水库试验水槽上进行的温差异重流试验来验证数学模型,计算结果与实验资料以及前人的计算结果符合较好,说明论文所采用的数学模型和数值计算方法能够预测温差异重流的特性。
水面热交换是引起水库水温分层的主要原因之一。本文分析了水面热交换的几种方式,在计算水面热交换时考虑了太阳辐射、湿度、气温、云量、风速等气象条件。并采用了一个直观的矩形试验水池,分别计算了两种不同气象条件的工况。结果表明水体中热传递符合客观规律,验证了在气象条件的影响下温度场计算的正确性。
应用所建立的数学模型对三峡近坝区从庙河至坝前约 18km 水域的三维流场及温度场进行了数值模拟。采用入口断面的流量水温等实测资料作为入流边界条件,大坝孔口为出流边界条件,计算了从 2003 年 6 月至 2004 年 6 月的实际工况。计算所得的流场与河道地形相比可以看出,水面狭窄的江段水流流速较大,江段突扩段附近有明显回水区,流速的横向分布受河道弯曲及水下地形和河道主槽影响。计算出的水温分布与坝前观测的水温分布符合良好,而且同一层水体温度相差不大,表层受气象条件影响较小,垂向没有温度分层现象的出现。由于在蓄水初期,最高水位为 139m,水深相对较浅,而且在汛期虽然气温较高,但流量很大,难以形成水温分层,这与计算的结果相符。
A three-dimension model coupled with flow and temperature is developed basedon Navier-Stokes equations for incompressible flows. The continuum-derivedPoisson equations are used to solve the pressure distribution and the momentumequations are used to solve the velocity components. Because the assumption of staticpressure of water is canceled, the model is appropriate for complex flows and densitylayered flows. The Finite Volume Method is adopted as the numerical discretizationmethod, the model has a fast computing velocity and it is applicable to engineering.Besides the buoyancy components considered in the momentum equations,anisotropic turbulent model is adopted in the model, such as Smagorinsky-DeardorffLarge Eddy Simulation, which enables the coupled flow and temperature can becomputed. The influence of the weather conditions is also considered in the model.
The channel experiment which was made in 1980 by U.S Army EngineeringCorporation is adopted to investigate the validity and the reliability of the model. Theresults show that the computational results agree well with the results of theexperiments. It illustrates that the numerical model and the numerical methods cancorrectly predict the characteristics of thermal temperature flows.
Some modes of heat exchange at the surface are considered. The radiant heat,humidity, air temperature, cloudage and wind speed are considered when computingthe heat exchange at the surface. Two conditions with different weather workingconditions are computed in a rectangle pool. The results show that the transfer of heatin the water agrees well with rules.
The numerical model is applied to simulate the 3D-flow and temperature fieldsnear the Dam Area of Three Gorges Reservoir. The measured data is used as theboundary conditions in the entrance. Many different working conditions aresimulated from June 2003 to June 2004. The results show that the velocity of the flowbecomes larger at the narrow areas, the breadthwise distribution of the velocity isinfluenced by the underwater landform and the riverway. The computational water
temperature near the dam agrees well with the measured data. The temperature of thesame layer has little difference and the weather conditions have little influence on thetop layer. The layered temperature of the vertical did not occured. During thereservoir impoundment period with a 139m water level, although the air temperatureis high, it is difficult to form the layered temperature. It agrees well with thecomputational results.
引文
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[18] 王玲玲,金忠青. 利用二、三维嵌套技术数值模拟复杂边界下的流场[J]. 南京航空航天大学学报,1999,31(2):133~137
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[22] 张修忠,王光谦. 方腔回流区水流运动特性三维数值分析. 水科学进展, 2003,14(1):1~8
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[30] 董文军,李世森,白玉川. 三维潮流和潮流输沙问题的一种混合数值模拟及其应用[J]. 海洋学报,1999,21(2):108~114
[31] 李 炜. 黏性流体的混合有限分析解法[M]. 北京:科学出版社,2000
[32] 李 炜,赵毅山. 三维方腔流的混合有限分析解[J]. 水动力学研究与进展(A辑),1994,9(3):308~317
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[35] 杨辅政,代数应力模型在水轮机转轮内部紊流计算中的应用,清华大学水利水电工程系硕士论文,1997.5
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[37] 章梓雄,董曾南. 粘性流体力学. 清华大学出版社,1998.4
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[2] 黄耀华,黄煜龄. 天然河道长河段一维非恒定流数模研究. 长江科学院院报,1994,11(2):10~17
[3] 叶闽,陈惠敏. 一维垂向水温分布模型在隔河岩水库中的应用与检验. 水质源保护, 2001,(2):19~22
[4] D.Cokljat and B.A.Younis. Second-corder Closure Study of Open-channel Flows. Journal of Hydraulic Engineering, p94-106,1992.2
[5] Leschizner M.A.,Rodi W., Calculation of annular and thin parallel jaets using various discretization an turbulence model variations, J. of Fluid Eng., Vol.103,p353-360,June 1981
[6] 陈小红,刘美南,林艳珊. 水库垂向二维水质分布研究[J]. 水利学报,1997(4):9~16
[7] 江春波,张庆海,高忠信. 河道立面二维非恒定水温及污染物分布预报模型[J]. 水利学报,2000.9:20~24
[8] 黄胜,卢启苗编著. 河口动力学[M]. 北京: 水利电力出版社,1995
[9] 冯民权,周孝德,郑邦民. 糯扎渡水电站垂向二维非恒定流的数值模拟. 水力发电学报,2003(3):88~94
[10] 韩国其,许协庆. 天然水流三维数值模拟的进展. 河海大学科技情报,1989.9(1):13~22
[11] 刘桦,何友声. 河口三维流动数学模型研究进展[J]. 海洋工程,2000,18(2):87~93
[12] Weare T J. Recent advances in computational hydraulics[A]. Jayawardena A W, Lee J H W, Wang Z Y. Environmental Hydraulics[C]. Netherlands: Balkema A A, 1998:13~22
[13] 韩国其. 天然水流三维数值模拟[D]. 南京:河海大学,1989
[14] 白玉川,于天一. 分步分层拟三维水流数学模型及其在廉州湾潮流计算中的应用[J]. 海洋学报,1998,20(5):126~135
[15] Vincenzo Casulli, Guus S Setlling. Numerical simulation of 3D quasi-hydrostatic free-surface flows[J]. Journal of Hydraulic Engineering, 1998,124(7):678~686
[16] Shankar N J, Chan E S, Zhang Q Y. Three-dimensional simulation for an open channel flow with a constriction[J]. Journal of Hydraulic Research, 2001,39(2):187~201
[17] Jin X, Kranenburg C. Quasi-3D numerical modeling of shallow water circulation[J]. Journal of Hydraulic Engineering, 1993,119(4):458~472
[18] 王玲玲,金忠青. 利用二、三维嵌套技术数值模拟复杂边界下的流场[J]. 南京航空航天大学学报,1999,31(2):133~137
[19] Onyx W. H. Wai, Qimiao Lu and Y. S. Li, Multi-layer Modeling of Three-Dimensional Hydrodynamic Transport Process, Department of Civil and Structural Engineering, The HongKong Polytechnic University, 1995
[20] O. W. H. Wai, Q. Lu, Y. C. Chen and Y. S. Li, Multi-Layer Finite Element Formulateion For Suspended Sediment Transport in Tidal Flow, Department of Civil and Structural Engineering, The HongKong Polytechnic University, 1996
[21] 刘昭伟.斜分层有限元模型及其在三峡库区水流模拟中的应用:[硕士学位论文],清华大学水利水电工程系,2000
[22] 张修忠,王光谦. 方腔回流区水流运动特性三维数值分析. 水科学进展, 2003,14(1):1~8
[23] 韩国其等. 取水池内三维流场的数值计算[J]. 河海大学学报,1992,20(1):23~29
[24] 胡维平,濮陪民,秦伯强. 太湖水动力学三维数值试验研究. 风生流和风涌增减水的三维数值模拟[J]. 湖泊科学,1998,10(4):17~25
[25] Sanjiv K Sinha, Fotis Sotiropoulos, A Jacob Odgaard. Three-dimensional numerical model for flow through natural rivers[J]. Journal of Hydraulic Engineering, 1998, 124(1):13~24
[26] 魏文礼,王玲玲,金忠青. 曲线网格生成技术研究[J]. 河海大学学报,1998,26(3):92~96
[27] Thompson Joe F, Warsi Z U A, C Wayne Mastin. Numerical grid generation: foundations and applications[M]. New York: North-Holland,1985.
[28] 孔祥谦. 有限单元法在传热学中的应用[M]. 北京:科学出版社,1998:45~78
[29] 白玉川. 海岸三维潮流数学模型的研究及应用[J]. 海洋学报,1998,20(6):87~100
[30] 董文军,李世森,白玉川. 三维潮流和潮流输沙问题的一种混合数值模拟及其应用[J]. 海洋学报,1999,21(2):108~114
[31] 李 炜. 黏性流体的混合有限分析解法[M]. 北京:科学出版社,2000
[32] 李 炜,赵毅山. 三维方腔流的混合有限分析解[J]. 水动力学研究与进展(A辑),1994,9(3):308~317
[33] 彭文启,李 炜. 三维 N-S 方程混合有限分析多重网格方法[J]. 水科学进展,1997,8(1):9~15
[34] W. Rodi, Simulation of Turbulence in Practical Flow Calculations, ECCOMAS 2000, 2000.9
[35] 杨辅政,代数应力模型在水轮机转轮内部紊流计算中的应用,清华大学水利水电工程系硕士论文,1997.5
[36] 金忠青,N-S 方程的数值解和紊流模型,河海大学出版社,1989.6
[37] 章梓雄,董曾南. 粘性流体力学. 清华大学出版社,1998.4
[38] 余常昭,环境流体力学导论,清华大学出版社,1992
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