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清华大学学报(自然科学版)  2018, Vol. 58 Issue (10): 914-920    DOI: 10.16511/j.cnki.qhdxxb.2018.26.032
  水利水电工程 本期目录 | 过刊浏览 | 高级检索 |
垂向基于谱方法的三维弯道水流模型
杨飞, 傅旭东
清华大学 水利水电工程系, 北京 100084
3-D hydrodynamic model using the spectral method in the vertical direction for bend flow simulations
YANG Fei, FU Xudong
Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China
全文: PDF(3150 KB)  
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摘要 传统平面二维水动力模型模拟弯道水流时,将流速垂向分布固定化,不能随边界变化和二次流发展进行调整,而垂向完全自动调整的三维水动力模型计算效率低。该文采用谱方法将平面流速的垂向分布用正交多项式表示,通过加权余量法建立简易三维模型,对流项采用基于Gauss点的半Lagrangian法(semi-Lagrangian scheme,SLS)计算。由急弯弯道水流试验验证可知,多项式阶数大于1时模拟结果较好。弯道主流线位置预测整体误差不超过7%,精度和传统的三维水动力学模型相当。对涡黏性系数简单求解,但考虑了垂向和水平方向的差异性,能够得到合理的弯道水流结构。垂向基于谱方法建立的三维模型,无垂向网格离散,计算量明显减少,获得了与平面二维模型相当的计算效率。
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杨飞
傅旭东
关键词 谱方法三维水动力学模型二次流弯道水流各向异性    
Abstract:The traditional depth-averaged 2-D hydrodynamic models for bend flow simulations assume velocity profiles for the secondary flow terms in the momentum equations which are unable to adjust to dynamic conditions. More flexible three-dimensional models are not very efficient. A simplified 3-D model using a spectral method in the vertical direction was developed with the flow velocity components modeled by orthogonal polynomials in the vertical direction using polynomial coefficient equations obtained using the weighted residuals method with the advection terms defined at the vertical Gauss points by the semi-Lagrangian scheme. Simulated flow structures in a sharp bend open channel match well with measured data for polynomials having degrees larger than 1 with reasonable flow structures. The mean error of the predicted main flow location is less than 7%, equivalent to other 3-D hydrodynamic models. The eddy viscosity is solved in a simple way with consideration of the turbulence anisotropy between the vertical and horizontal directions. Since this method does not have a vertical grid, the calculational efficiency is proved to be to 2-D models.
Key wordsspectral method    3-D hydrodynamic model    secondary flow    bend flow    anisotropy
收稿日期: 2018-03-02      出版日期: 2018-10-17
基金资助:国家自然科学基金资助项目(51525901,91747207)
通讯作者: 傅旭东,教授,E-mail:xdfu@tsinghua.edu.cn     E-mail: xdfu@tsinghua.edu.cn
引用本文:   
杨飞, 傅旭东. 垂向基于谱方法的三维弯道水流模型[J]. 清华大学学报(自然科学版), 2018, 58(10): 914-920.
YANG Fei, FU Xudong. 3-D hydrodynamic model using the spectral method in the vertical direction for bend flow simulations. Journal of Tsinghua University(Science and Technology), 2018, 58(10): 914-920.
链接本文:  
http://jst.tsinghuajournals.com/CN/10.16511/j.cnki.qhdxxb.2018.26.032  或          http://jst.tsinghuajournals.com/CN/Y2018/V58/I10/914
  表1 水槽试验验证结果
  图1 文[3]的试验水槽形态
  图2 (网络版彩图)弯道垂向平均流速实测与模拟结果
  图3 (网络版彩图)水位平面分布图
  图4 主流线横向相对位置的沿程变化
  图5 (网络版彩图)断面纵向流速分布实测与N=6模拟对比
  图6 S90断面中心线纵向(右侧)与横向(左侧) 流速垂向分布的模拟与实测值
  图7 S180断面中心线纵向(右侧)与横向(左侧) 流速垂向分布的模拟与实测值
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