垂直坐标系对于水温分层流动模拟的影响研究
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摘要
随着高坝水库的建设和高性能计算机的出现,以往应用于大洋的三维模型正越来越多的应用于水库分层流动的模拟中。作为三维模型的建立基础,垂向坐标系对于小尺度区域模拟精度的影响研究目前尚不多见。基于物理水槽分层流动实验结果,评估了最常用的笛卡儿z坐标系和σ地形坐标系对于流场和温度场的模拟精度影响。结果显示两种垂直坐标系均适用于分层流模拟,但σ垂直坐标系模型模拟结果精度更高;与σ坐标系相比较,z坐标系由于底部阶梯水体静力不稳定和虚拟漩涡放大了垂向扩散能力,使得速度以及温度分层强度偏小;水平速度场显示,z坐标系对于底部的阶梯化处理会引起底部速度场的失真,等温线也呈相应的阶梯型变化趋势。
With the construction of high dam reservoirs and the appearance of high performance computers,increasingly more 3D models are used in the simulations of stratified flows in reservoirs.Influence of the vertical coordinate system on the accuracy in the simulations of small scale regions is essential to 3D modeling,but there are few previous studies on it.Based on the results of a stratified flow experiment,this study focuses on evaluation of the effects of the most commonly used Cartesian z coordinate system and the σ coordinate system on the accuracy in flow and temperature simulations.It is concluded that both systems are applicable but with different accuracy and the σ coordinate is better.Static instability and extra vortices caused by bottom step in the z coordinate exaggerate vertical diffusivity and lead to weaker velocity and vertical temperature stratification than those in the σ coordinate.Distribution of horizontal velocity shows small scale circulations near the bottom that are caused by a spurious water falling process produced numerically in the z coordinate modeling.The isothermals also show a stairstepping trend in the z coordinate system.
With the construction of high dam reservoirs and the appearance of high performance computers,increasingly more 3D models are used in the simulations of stratified flows in reservoirs.Influence of the vertical coordinate system on the accuracy in the simulations of small scale regions is essential to 3D modeling,but there are few previous studies on it.Based on the results of a stratified flow experiment,this study focuses on evaluation of the effects of the most commonly used Cartesian z coordinate system and the σ coordinate system on the accuracy in flow and temperature simulations.It is concluded that both systems are applicable but with different accuracy and the σ coordinate is better.Static instability and extra vortices caused by bottom step in the z coordinate exaggerate vertical diffusivity and lead to weaker velocity and vertical temperature stratification than those in the σ coordinate.Distribution of horizontal velocity shows small scale circulations near the bottom that are caused by a spurious water falling process produced numerically in the z coordinate modeling.The isothermals also show a stairstepping trend in the z coordinate system.
引文
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[2]龙圣海,黄廷林,李扬,等.基于MIKE3的金盆水库三维水温结构模拟研究[J].水力发电学报,2016,35(11):16-24.Doi:10.11660/slfdxb.20161103.LONG Shenghai,HUANG Tinglin,LI Yang,et al.Water temperature modeling for Jinpen Reservoir using MIKE3[J].Journal of Hydroelectric Engineering,2016,35(11):16-24.Doi:10.11660/slfdxb.20161103.(in Chinese)
[3]陈弘.大型水库分层取水下泄水温模型试验与数值模拟研究[D].天津:天津大学,2013.CHEN Hong.Experimental study and numerical simulation on water temperature released from the multilevel intake of large hydropower stations[D].Tianjin:Tianjin University,2013.(in Chinese)
[4]姜彬彬,韩龙喜,颜芬芬,等.基于三维水动力-水温耦合模型的水库水温预测及影响研究[J].河南科学,2016,34(12):2012-2019.JIANG Binbin,HAN Longxi,YAN Fenfen,et al.Reservoir water temperature prediction and impact analysis based on the 3D hydrodynamic water temperature coupling model[J].Henan Science,2016,34(12):2012-2019.(in Chinese)
[5]Cole T M,Buchak E M.CE-QUAL-W2:A twodimensional,laterally averaged,hydrodynamic and water quality model,Version 2.0.User Manual[M]//Civil and Environmental Engineering Faculty Publications and Presentations,1995.
[6]邓云,李嘉,罗麟.河道型深水库的温度分层模拟[J].水动力学研究与进展,2004,19(5):604-609.DENG Yun,LI Jia,LUO Lin.Simulation on thermal stratification of the river like deep reservoir[J].Chinese Journal of Hydrodynamics,2004,19(5):604-609.(in Chinese).
[7]任华堂.大型水库水温数值模拟研究[M].北京:海洋出版社,2010.REN Huatang.Study on temperature numerical simulation in large reservoirs[M].Beijing:Ocean Press,2010.(in Chinese)
[8]邱进生,邓云,颜剑波,等.水库水温数学模型适用性研究[J].环境影响评价,2017,39(2):57-62.QIU Jinsheng,DENG Yun,YAN Jianbo,et al.Study on applicability of mathematical models of reservoir water temperature[J].Environmental Impact Assessment,2017,39(2):57-62.(in Chinese)
[9]陈振华,夏长水,乔方利.钦州湾水交换能力数值模拟研究[J].海洋学报,2017,39(3):14-23.CHENG Zhenhua,XIA Changshui,QIAO Fangli.Numerical simulation of water exchange capacity in Qinzhou Bay[J].Acta Oceanologica Sinica,2017,39(3):14-23.(in Chinese).
[10]申霞.基于POM的近海三维水质模型研究及其应用[D].南京:河海大学,2006.SHEN Xia.Study and application of 3D offshore water quality model based on POM[D].Nanjing:Hohai University,2006.(in Chinese)
[11]夏长水.基于POM的浪流耦合模式的建立及其在大洋和近海的应用[D].青岛:中国海洋大学,2005.XIA Changshui.Establishment of wave coupling model Based on POM and its application in oceanic and offshore[D].Qingdao:Periodical of Ocean University of China,2005.(in Chinese)
[12]崔培.POM模型在台湾海峡潮波形态分布及污染物扩散研究中的应用[D].厦门:厦门大学,2008.CUI Pei.Applications of POM on tidal wave distribution and pollutant diffusion in the Taiwan strait[D].Xiamen:Xiamen University,2008.(in Chinese)
[13]DHI.MIKE3 coastal hydraulics and oceanography user guide[R].DHI,Denmark,2005.
[14]Backhaus J O.A three-dimensional model for the simulation of the shelf sea dynamics[J].Deutsche Hydrographische Zeitshrift,1985,38(4):165-187.
[15]Ben H,Chris D.Estuary,lake and coastal ocean model:ELCOM,v2.2.User Manual[R].Centre for Water Research,University of Western Australia,Australia,2007.
[16]Pacanowski R C,Griffies S M.The MOM3 manual[R].NOAA/Geophysical Fluid Dynamics Laboratory,USA,1999.
[17]Ezer T,Mellor G L.A generalized coordinate ocean model and a comparison of the bottom boundary layer dynamics in terrain-following and in z-level grids[J].Ocean Modelling,2004,6(3-4):379-403.
[18]Christopher J B,Scott A W,Robert A.Laurance lake temperature model[R].Unpublished doctoral dissertation,Maseeh College of Engineering and Computer Science Department of Civil and Environmental Engineering Portland State University,USA,2005.
[19]Chen C,Liu H,Beardsley R C.An unstructured grid,finite-volume,three-dimensional,primitive equations ocean model:Application to coastal ocean and estuaries[J].Journal of Atmospheric&Oceanic Technology,2003,20:159-186.
[20]George M S,Bertino L,Johannessen O M,Samuelsen A.Validation of a hybrid coordinate ocean model for the Indian Ocean[J].Journal of Operational Oceanography,2010,3(2):25-38.
[21]Bleck R.An oceanic general circulation model framed in hybrid isopycnic-cartesian coordinates[J].Ocean Modeling,2002,4(1):55-88.
[22]Mellor G L,Hakkinen S,Ezer T,Patchen R.A generalization of a sigma coordinate ocean model and an intercomparison of model vertical grids[C]//Pinardi N,Woods J D.Ocean forecasting:conceptual basis and applications.New York:Springer,2002:55-72.
[23]Ezer T.Entrainment,diapycnal mixing and transport in three-dimensional bottom gravity current simulations using the Mellor–Yamada turbulence scheme[J].Ocean Modelling,2005,9(2):151-168.
[24]Johnson B H.A review of numerical reservoir hydrodynamic modeling[R].US army engineer waterways experiment station,USA,1981.