柱状珊瑚砂静水沉降试验研究

蒋超; 陈杰; 蒋昌波; 姚震; 梁海; 伍志元

doi:10.12284/hyxb2023043

柱状珊瑚砂静水沉降试验研究

doi: 10.12284/hyxb2023043

蒋超^1,,
陈杰^{1, 2, 3, ,},
蒋昌波^{1, 2, 3},
姚震¹,
梁海¹,
伍志元^{1, 2, 3}

1.
长沙理工大学水利与环境工程学院，湖南长沙 410114
2.
洞庭湖水环境治理与生态修复湖南省重点实验室，湖南长沙 410114
3.
水沙科学与水灾害防治湖南省重点实验室，湖南长沙 410114

基金项目: 国家重点研发计划（2021YFB2601100）；国家自然科学基金重点项目（51839002）；国家自然科学基金面上项目（51979014，52271257）；湖南省杰出青年科学基金项目（2022JJ10047）

详细信息

作者简介:
蒋超（1999-），男，湖南省邵阳市人，主要从事珊瑚砂运动特性研究。E-mail: 841072313@qq.com

通讯作者:
陈杰（1982-），男，广西壮族自治区桂林市人，博士，教授，主要从事河口海岸动力学及泥沙运动研究。E-mail: chenjie166@163.com

中图分类号: P736.21⁺3
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出版历程
- 收稿日期: 2022-02-08
- 修回日期: 2022-09-08
- 网络出版日期: 2023-04-03
- 刊出日期: 2023-03-31

Experimental study on settlement of rod coral sand in stagnant water

Jiang Chao^1
,,
Chen Jie^{1, 2, 3
, ,},
Jiang Changbo^{1, 2, 3},
Yao Zhen¹,
Liang Hai¹,
Wu Zhiyuan^{1, 2, 3}

1.
School of Hydraulic and Environmental Engineering, Changsha University of Science & Technology, Changsha 410114, China
2.
Laboratory of Dongting Lake Aquatic Eco-Environmental Control and Restoration of Hunan Province, Changsha 410114, China
3.
Key Laboratory of Water-Sediment Sciences and Water Disaster Prevention of Hunan Province, Changsha 410114, China

摘要

摘要: 沉降速度是珊瑚砂的一个重要物理参数。由于柱状珊瑚砂与其他形状的珊瑚砂有着明显的差异，套用现有珊瑚砂的沉速公式进行计算并不合适。本文选取柱状珊瑚砂进行单颗粒沉降试验，研究静水中柱状珊瑚砂沉降速度及其影响因素，通过讨论分析不同的等效粒径和形状系数对柱状珊瑚砂沉降速度的影响，发现柱状珊瑚砂的沉降速度与等容粒径和Corey形状系数密切相关，基于本文试验数据推求了适用于计算柱状珊瑚砂沉降速度的经验公式，丰富了海岸泥沙理论。
- 柱状珊瑚砂 /
- 沉降速度 /
- 阻力系数 /
- 形状系数
Abstract: The settling velocity is an important physical parameter of coral sand. Because of the rod coral sand is obviously different from other shapes of coral sand, it is not suitable to apply the settling velocity formula of the existing coral sand for calculation. The rod coral sand was selected to study the settling velocity and its influencing factors for single particle settlement experiment in stagnant water in this study. By analyzing the effects of different equivalent particle sizes and shape coefficients on the settling velocity of rod coral sand, it is found that the settling velocity of rod coral sand is strongly correlated with the diameter of the volume-equivalent sphere and Corey shape coefficient. Based on the experimental data, an empirical formula suitable for calculating the settling velocity of rod coral sand is deduced, which enriches the theory of coastal sediment.
- rod coral sand /
- settling velocity /
- drag coefficient /
- shape coefficient

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图 1 沉降试验布置图

Fig. 1 Schematic graph of settlement experiment

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图 2 获取形状参数流程图

Fig. 2 Flow chart of getting the shape factors

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图 3 颗粒形状分类图

Fig. 3 Graph of particle shape classification

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图 4 不同的等效粒径大小与形状系数分布

Fig. 4 Distribution graph of different equivalent particle sizes and shape coefficients

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图 5 沉降速度与形状系数分布

Fig. 5 Distribution graph of settling velocitys and shape coefficients

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图 6 本文沉降速度与前人研究沉速降速度对比

Fig. 6 Comparison of particle settling velocitys of the present study with those of previous studies

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图 7 不同雷诺数与阻力系数的关系

Fig. 7 Relationships between different Reynolds numbers and drag coefficients

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图 8 沉降速度预测值和实测值对比

Fig. 8 Comparison of calculated and tested settling velocity

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图 9 沉降速度预测值和实测值拟合

Fig. 9 The fitting relationship between the predicted value and the measured value of the settling velocity

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表 1 不同等效粒径和形状系数方案设计

Tab. 1 Programmes of different equivalent particle sizes and shape coefficients

组次	等效粒径	形状系数
1	轴平均粒径	Corey形状系数
2	轴平均粒径	Wang形状系数
3	等容粒径	Corey形状系数
4	等容粒径	Wang形状系数
5	投影粒径	Corey形状系数
6	投影粒径	Wang形状系数

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表 2 Corey形状系数离散程度

Tab. 2 Dispersions of Corey shape coefficient

粒径大小	D_n<0.20	D_n <0.25	D_n <0.30	D_n <0.35
第25百分位数	0.635	0.637	0.623	0.511
第75百分位数	0.685	0.685	0.684	0.680
四分位差	0.050	0.048	0.059	0.169
注：D_n单位：cm。

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表 3 不同形状系数与沉降速度相关系数

Tab. 3 Correlation coefficients of shape coefficients and settling velocitys

形状系数	粗颗粒沉降速度/（cm·s⁻¹）	细颗粒沉降速度/（cm·s⁻¹）
Corey形状系数	0.634	0.277
Wang形状系数	0.562	0.238

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表 4 柱状珊瑚砂不同等效粒径和形状参数拟合公式对照

Tab. 4 Comparison of fitting formulas for rod coral sand with different equivalent particle sizes and shape coefficients

组次	V/A拟合公式	R²	沉降速度拟合公式
1	${\dfrac{V}{ { {A_p} } } = 0.381S_{ f}^{0.434}{D_n} }$	0.735	${ {\omega ^2} = 0.762\dfrac{ {\left( { {\rho _s} - \rho } \right)g} }{ {\rho {C_d} } }S_{ f}^{0.434}{D_n} }$
2	$ {\dfrac{V}{{{A_p}}} = 0.366{\psi ^{0.243}}{D_n}} $	0.726	$ {{\omega ^2} = 0.732\dfrac{{\left( {{\rho _s} - \rho } \right)g}}{{\rho {C_d}}}{\psi ^{0.243}}{D_n}} $
3	${\dfrac{V}{ { {A_p} } } = 0.473S_{ f}^{0.428}{D_v} }$	0.897	${ {\omega ^2} = 0.946\dfrac{ {\left( { {\rho _s} - \rho } \right)g} }{ {\rho {C_d} } }S_{ f}^{0.428}{D_v} }$
4	$ {\dfrac{V}{{{A_p}}} = 0.452{\psi ^{0.234}}{D_v}} $	0.886	$ {{\omega ^2} = 0.904\dfrac{{\left( {{\rho _s} - \rho } \right)g}}{{\rho {C_d}}}{\psi ^{0.234}}{D_v}} $
5	${\dfrac{V}{ { {A_p} } } = 0.380S_{ f}^{0.765}{D_p} }$	0.735	${ {\omega ^2} = 0.760\dfrac{ {\left( { {\rho _s} - \rho } \right)g} }{ {\rho {C_d} } }S_{ f}^{0.765}{D_p} }$
6	$ {\dfrac{V}{{{A_p}}} = 0.355{\psi ^{0.435}}{D_p}} $	0.708	$ {{\omega ^2} = 0.710\dfrac{{\left( {{\rho _s} - \rho } \right)g}}{{\rho {C_d}}}{\psi ^{0.435}}{D_p}} $

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表 5 不同等效粒径和形状参数拟合公式对照

Tab. 5 Comparison of fitting formulas for rod coral sand with different equivalent particle sizes and shape coefficients

组次	阻力系数C_d拟合公式	沉降速度ω拟合公式
1	$ {{C_d} = {\left( {\dfrac{{ - 403 \nu }}{{D_n^{1.5} \times {g^{0.5}}}} + 3.34} \right)^{ - 4.58}} + {\left( {\dfrac{{ - 205 \nu }}{{D_n^{1.5} \times {g^{0.5}}}} + 1.13} \right)^{0.405}}} $	${ {\omega ^2} = 0.762\dfrac{ {\left( { {\rho _s} - \rho } \right)g} }{ {\rho {C_d} } }S_{ f}^{0.434}{D_n} }$
2	$ {{C_d} = {\left( {\dfrac{{ - 725 \nu }}{{D_n^{1.5} \times {g^{0.5}}}} + 4.82} \right)^{ - 2.77}} + {\left( {\dfrac{{ - 226 \nu }}{{D_n^{1.5} \times {g^{0.5}}}} + 1.14} \right)^{0.416}}} $	$ {{\omega ^2} = 0.732\dfrac{{\left( {{\rho _s} - \rho } \right)g}}{{\rho {C_d}}}{\psi ^{0.243}}{D_n}} $
3	$ {{C_d} = {\left( {\dfrac{{ - 108 \nu }}{{D_v^{1.5} \times {g^{0.5}}}} + 2.39} \right)^{ - 11.60}} + {\left( {\dfrac{{ - 74.5 \nu }}{{D_v^{1.5} \times {g^{0.5}}}} + 1.03} \right)^{0.601}}} $	${ {\omega ^2} = 0.946\dfrac{ {\left( { {\rho _s} - \rho } \right)g} }{ {\rho {C_d} } }S_{ f}^{0.428}{D_v} }$
4	$ {{C_d} = {\left( {\dfrac{{ - 172 \nu }}{{D_v^{1.5} \times {g^{0.5}}}} + 2.95} \right)^{ - 13.50}} + {\left( {\dfrac{{ - 95.3 \nu }}{{D_v^{1.5} \times {g^{0.5}}}} + 1.05} \right)^{0.486}}} $	$ {{\omega ^2} = 0.904\dfrac{{\left( {{\rho _s} - \rho } \right)g}}{{\rho {C_d}}}{\psi ^{0.234}}{D_v}} $
5	$ {{C_d} = {\left( {\dfrac{{ - 210 \nu }}{{D_p^{1.5} \times {g^{0.5}}}} + 2.00} \right)^{ - 15.70}} + {\left( {\dfrac{{ - 182 \nu }}{{D_p^{1.5} \times {g^{0.5}}}} + 1.09} \right)^{0.533}}} $	${ {\omega ^2} = 0.760\dfrac{ {\left( { {\rho _s} - \rho } \right)g} }{ {\rho {C_d} } }S_{ f}^{0.765}{D_p} }$
6	$ {{C_d} = {\left( {\dfrac{{ - 778 \nu }}{{D_p^{1.5} \times {g^{0.5}}}} + 4.57} \right)^{ - 14.12}} + {\left( {\dfrac{{ - 249 \nu }}{{D_p^{1.5} \times {g^{0.5}}}} + 1.14} \right)^{0.436}}} $	$ {{\omega ^2} = 0.710\dfrac{{\left( {{\rho _s} - \rho } \right)g}}{{\rho {C_d}}}{\psi ^{0.435}}{D_p}} $

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表 6 沉降速度计算误差表

Tab. 6 Calculation error of the settling velocity

	E_ave	RMSE
Wang公式^[18]	0.1346	3.1869
本文公式训练组	0.0714	1.7608
本文公式验证组	0.1191	2.6018

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