工程科学与技术   2020, Vol. 52 Issue (4): 176-183

1. 四川大学 水力学与山区河流开发保护国家重点实验室，四川 成都 610065;
2. 黄埔区水务设施管理所，广东 广州 510700

Numerical Simulation of Sediment Transport and Variation Based on the Braided River of Yalu Tsangpo River
MENG Wenkang1, AN Ruidong1, LI Jia1, LI Fang2, YOU Jinghao1
1. State Key Lab. of Hydraulics and Mountain River Eng., Sichuan Univ., Chengdu 610065, China;
2. Waterworks Management of Huangpu District, Guangzhou 510700, China
Abstract: Based on the shape of the braided river in the middle reaches of the Yalu Tsangpo River, the study established a mathematical model for the simulation of sediment transport in braided rivers. The numerical calculation used a two-dimensional hydrodynamic and non-viscous sediment coupling model to simulate the sediment transport in the braided river. The model is based on the incompressible Reynolds average N–S equation, which included continuous equations, momentum equations, riverbed deformation equations, and total sand transport equations. The mathematical model calculated the suspended sediment and the sediment transport rate through the theory of total sediment transport. When simulating flood peak flow, the peak of the sediment concentration process and the suspended sediment transport rate of the braided river lags was behind the inflow process, causing a phase difference. The smaller the sediment particle, the smaller the phase difference. The phase difference of sands, whose particle sizes were 0.01 mm and 0.02 mm, was about 0, and the phase difference caused by the rate of exit suspension sediment transport was less than that caused by sediment concentration. The sedimentation of 0.30 mm, 0.20 mm and 0.10 mm particle size in the braided river exceeded 50%. In the calculation of sediment transport, the topographic renewal caused by sediment start-up and sedimentation was considered, and the influence of the sediment flow on the topographic changes during the movement of the braided river was analyzed, which established a numerical simulation example for the research prediction of the natural braided river.
Key words: braided river    sediment transport    Yalu Tsangpo River    numerical simulation

Griffiths等[6]认为辫状砾石河流的推移质输运能力随着下游水力学条件的变化而发生改变，受洪水期间推移质输运的影响，推移质输运能力的差异会导致河床物质的改变；反过来，河床物质的改变会使床面产生不规律的波动及泥沙输运波动，这些波动是辫状河流中推移质输运的作用机制。在辫状河流中，泥沙输运尤其是推移质输运对地形的动态变化至关重要[4]，河床发生泥沙运输和地形变化的区域被定义为活动宽度，是辫状河形态动力学研究非常有用的要素，可通过辫状强度、浸湿宽度等参数求得活动宽度，并用于预测推移质输沙量[7]。Yang等[8]采用水动力和泥沙输运数值模型，模拟了在理想河流中悬移质控制的辫状河流的演变过程，模拟了天然辫状河中常见的河道节点和演变过程，如心滩；采用多级泥沙组分的方法模拟了泥沙粗化和细化对新塘和辫状河道演化的影响。

1 数学模拟方法 1.1 模型简介

1.2 水动力控制方程

1）连续性方程：

 $\frac{\partial h}{\partial t}+\frac{\partial h \bar{u}}{\partial x}+\frac{\partial h \bar{v}}{\partial y}=0$ (1)

2）动量方程组：

 \begin{aligned}[b] \frac{{\partial h\overline u }}{{\partial t}} +& \frac{{\partial h{{\overline u }^2}}}{{\partial x}} + \frac{{\partial h\overline {uv} }}{{\partial y}} = - gh\frac{{\partial \eta }}{{\partial x}}- \\ &\frac{h}{{{\rho _0}}}\frac{{\partial {p_{\rm{a}}}}}{{\partial x}} - \frac{{g{h^2}}}{{2{\rho _0}}}\frac{{\partial \rho }}{{\partial x}} - \frac{{{\tau _{{\rm{b}}{x}}}}}{{{\rho _0}}} + \\ &\frac{\partial }{{\partial x}}\left( {2h{\nu _{\rm{t}}}\frac{{\partial \overline u }}{{\partial x}}} \right) + \frac{\partial }{{\partial y}}\left( {h{\nu _{\rm{t}}}\Bigg(\frac{{\partial \overline u }}{{\partial y}} + \frac{{\partial \overline v }}{{\partial x}}\Bigg)} \right) \end{aligned} (2)
 \begin{aligned}[b] \frac{{\partial h\overline v }}{{\partial t}} + & \frac{{\partial h{{\overline v }^2}}}{{\partial y}} + \frac{{\partial h\overline {uv} }}{{\partial x}} = - gh\frac{{\partial \eta }}{{\partial y}}- \\ &\frac{h}{{{\rho _0}}}\frac{{\partial {p_{\rm{a}}}}}{{\partial y}} - \frac{{g{h^2}}}{{2{\rho _0}}}\frac{{\partial \rho }}{{\partial y}} - \frac{{{\tau _{{\rm{b}}y}}}}{{{\rho _0}}} + \\ &\frac{\partial }{{\partial y}}\left( {2h{\nu _{\rm{t}}}\frac{{\partial \overline v }}{{\partial y}}} \right) + \frac{\partial }{{\partial x}}\left( {h{\nu _{\rm{t}}}\Bigg(\frac{{\partial \overline u }}{{\partial y}} + \frac{{\partial \overline v }}{{\partial x}}\Bigg)} \right) \end{aligned} (3)

1.3 泥沙输运模型及方程

 \begin{aligned}[b] \frac{{\partial h\overline C }}{{\partial t}} \!+\! \frac{{\partial h\overline u \overline C }}{{\partial x}} \!+\! \frac{{\partial h\overline v \overline C }}{{\partial y}} = h\bigg(\frac{\partial }{{\partial x}}\bigg(\frac{{{\nu _{\rm{t}}}}}{{{\sigma _{\rm{t}}}}}\frac{\partial }{{\partial x}}\bigg)+ \frac{\partial }{{\partial y}}\bigg(\frac{{{\nu _{\rm{t}}}}}{{{\sigma _{\rm{t}}}}}\frac{\partial }{{\partial y}}\bigg)\bigg)\overline C + \Delta S \\ \end{aligned} (4)

Engelund–Hansen泥沙输移计算公式[10]

 $\phi = \frac{S}{{\sqrt {(s - 1)g{d^3}} }}$ (5)

 ${S\!_{{\rm{tl}}}} = 0.05\frac{{{C^2}}}{g}{\theta ^{2.5}}\sqrt {(s - 1)gd_{50}^3}$ (6)
 ${S\!_{{\rm{bl}}}} = {k_{\rm{b}}}{S\!_{{\rm{tl}}}}$ (7)
 $S\!_{{\rm{sl}}}=k_{{\rm{s}}} S\!_{{\rm{tl}}}$ (8)
 $\theta=\frac{\tau}{({\rm{s}}-1) \rho g d_{50}}$ (9)

 $-(1-n) \frac{\partial {\textit{z}}}{\partial t}=\frac{\partial S\!_{x}}{\partial x}+\frac{\partial S\!_{y}}{\partial y}-\Delta S$ (10)
 ${{\textit{Z}}_{{\rm{new}}}} = {{\textit{Z}}_{{\rm{old}}}} + \frac{1}{{1 - n}}\frac{{\partial {\textit{Z}}}}{{\partial t}}\Delta {t_{{\rm{HD}}}}$ (11)

1.4 模型参数设置

2 工况设置及地形模型 2.1 工况设置

 图1 典型河段水样粒径级配曲线 Fig. 1 Water sample size grading curves of typical river sections

2.2 辫状河流地形模型

 图2 辫状河流地形数学模型 Fig. 2 Mathematical model of braided river topography

3 辫状河流输沙特征及变异分析 3.1 泥沙输运特征

 图3 洪峰流量过程中河床高程变化 Fig. 3 Changes of river bed elevation during flood peak

 图4 入口及下游的冲淤变化 Fig. 4 Changes of sediment erosion and siltation at the entrance and downstream

 图5 洪峰流量过程中总水深变化 Fig. 5 Changes of total water depth during flood peak

 图6 洪峰流量过程中流场变化 Fig. 6 Changes of flow field during flood peak

3.2 输沙变异分析

 图7 辫状河流出口流量过程线 Fig. 7 Outflow discharge process of the braided river

 图8 不同中值粒径泥沙进口来沙量和出口悬移质输沙率对比 Fig. 8 Comparison of inlet sediment content and outlet suspended sediment transport rate of different median particle size

3.3 试验模型验证

 图9 试验与模拟进出口流量对比 Fig. 9 Comparison of experimental flow and simulated flow in inlet and outlet

 图10 各中值粒径泥沙出口悬移质含沙量试验值与模拟值相关性 Fig. 10 Correlation between experimental values and simulated values of suspended sediment concentration of different median particle sizes

4 结论与展望

1）水槽试验中，本文采用中值粒径较大的泥沙进行试验，得到较好的试验结果，但是更小颗粒泥沙在辫状河流中的输运仍需探究；

2）模型中只能计算单一粒径泥沙，与天然辫状包含各级粒径泥沙的混合沙有所差别，下一步计算中可考虑混合沙的计算。

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