﻿ 孔堰流分流点竖向位置实验探究
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 哈尔滨工程大学学报  2019, Vol. 40 Issue (4): 738-745  DOI: 10.11990/jheu.201711031 0

### 引用本文

CUI Zhen, FU Zongfu, MA Guanggang, et al. Experimental study onvertical position of diversion point of orifice-weir flow[J]. Journal of Harbin Engineering University, 2019, 40(4), 738-745. DOI: 10.11990/jheu.201711031.

### 文章历史

Experimental study onvertical position of diversion point of orifice-weir flow
CUI Zhen , FU Zongfu , MA Guanggang , JIANG Wen , MA Yonglin
College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China
Abstract: The position of diversion point is an important index to distinguish the orifice flow and weir flow pattern when they exist simultaneously.To obtain the vertical position of diversion point and better distinguish two kinds of flow states, physical tests were used, and the mathematical expression of the diversion point between orifice flow and weir flow was obtained through analysis and comparison of different parameters.First, based on the theory of hydraulics, Rayleigh method was used to obtain the dimensionless parameters affecting the vertical position of diversion point.The correlational relationship between the vertical position of diversion point and dimensionless parameters was obtained, and the sensitivities of parameters were compared.Then, five mathematical models were obtained based on the least square method using different parameters.The optimal model of the vertical position was obtained by comparing statistical indicators.Finally, the optimal model was examined and compared with the experimental result; it was found that the model can be used to accurately describe the vertical position of diversion point.The obtained model of the vertical position of diversion point can be used in practical engineering and can provide a basis for research on the discharge capacity of relevant water conservancy projects.
Keywords: orifice flow and weir flow    Rayleigh method    diversion point    least square method    multi-linear regression    sensitivity    statistical indexes    optimal model

1 实验装置及方法

2 实验结果分析 2.1 无因次分析

 $f\left( {y,L,e,a,H,{\rm{d}}H,g,u,V} \right) = 0$ (1)

 $Y = f\left( {\Delta H/H,e/a,L/a,\mathit{Re}} \right)$ (2)
2.2 各水力参数相关性分析

3 敏感性分析及公式推导验证 3.1 公式推导及因素敏感性分析

 $\begin{array}{l} {\rm{MOD}}\left( {\rm{a}} \right):\\ \;\;\;\;\;\;\;\;Y = f\left( {\Delta H/H,e/a,L/a,\lg\left( {\mathit{Re}} \right)} \right) \end{array}$ (3)
 $\begin{array}{l} {\rm{MOD}}\left( {\rm{b}} \right):\\ \;\;\;\;\;\;\;\;Y = f\left( {e/a,L/a,\lg\left( {\mathit{Re}} \right)} \right) \end{array}$ (4)
 $\begin{array}{l} {\rm{MOD}}\left( {\rm{c}} \right):\\ \;\;\;\;\;\;\;\;Y = f\left( {\Delta H/H,e/a,\lg\left( {\mathit{Re}} \right)} \right) \end{array}$ (5)
 $\begin{array}{l} {\rm{MOD}}\left( {\rm{d}} \right):\\ \;\;\;\;\;\;\;\;Y = f\left( {\Delta H/H,e/a,L/a} \right) \end{array}$ (6)
 $\begin{array}{l} {\rm{MOD}}\left( {\rm{e}} \right):\\ \;\;\;\;\;\;\;\;Y = f\left( {\Delta H/H,L/a,\lg\left( {\mathit{Re}} \right)} \right) \end{array}$ (7)

 $\begin{array}{l} {\rm{MOD}}\left( {\rm{a}} \right):\\ \;\;\;\;\;\;\;\;\begin{array}{*{20}{c}} {Y = 1.73 + 0.372\frac{e}{a} + 0.014\frac{L}{a} + }\\ {3.94\frac{e}{a} \cdot \frac{{\Delta H}}{H} - 0.34\lg \left( {\mathit{Re}} \right)} \end{array} \end{array}$ (8)
 $\begin{array}{l} {\rm{MOD}}\left( {\rm{b}} \right):\\ \;\;\;\;\;\;\;\;Y = 1.594 + 0.494\frac{e}{a} + 0.009\frac{L}{a} - 0.298\lg \left( {\mathit{Re}} \right) \end{array}$ (9)
 $\begin{array}{l} {\rm{MOD}}\left( {\rm{c}} \right):\\ \;\;\;\;\;\;\;\;\begin{array}{*{20}{c}} {Y = 1.74 + 0.371\frac{e}{a} + 3.899\frac{e}{a} \cdot \frac{{\Delta H}}{H} - }\\ {0.335\lg \left( {\mathit{Re}} \right)} \end{array} \end{array}$ (10)
 $\begin{array}{l} {\rm{MOD}}\left( {\rm{d}} \right):\\ \;\;\;\;\;\;\;\;Y = 0.101 + 0.363\frac{e}{a} + 0.013\frac{L}{a} + 3.903\frac{e}{a} \cdot \frac{{\Delta H}}{H} \end{array}$ (11)
 $\begin{array}{l} {\rm{MOD}}\left( {\rm{e}} \right):\\ \;\;\;\;\;\;\;\;Y = 0.492 + 0.005\frac{L}{a} + 0.505\frac{{\Delta H}}{H} - 0.024\lg \left( {\mathit{Re}} \right) \end{array}$ (12)

 ${R^2} = \frac{{\sum\nolimits_{k = 1}^K {{{\left( {{Y_{k{\rm{ - pre}}}} - \bar Y} \right)}^2}} }}{{\sum\nolimits_{k = 1}^K {{{\left( {{Y_{k{\rm{ - exp}}}} - \bar Y} \right)}^2}} }}$ (13)
 ${A_{{\rm{MCC}}}} = {R^2} - \frac{{J \times \left( {1 - {R^2}} \right)}}{{K - J - 1}}$ (14)
 ${R_{{\rm{MSE}}}} = \sqrt {\frac{{\sum\limits_{k = 1}^K {{{\left( {{Y_{k{\rm{ - exp}}}} - {Y_{k{\rm{ - pre}}}}} \right)}^2}} }}{{K - J - 1}}}$ (15)
 ${Z_{{\rm{R}}{{\rm{E}}_k}}} = \frac{{{Y_{k{\rm{ - exp}}}} - {Y_{k{\rm{ - pre}}}}}}{{\hat \sigma }}$ (16)

 $\begin{array}{*{20}{c}} {Y = 1.73 + 0.372\frac{e}{a} + 0.014\frac{L}{a} + }\\ {3.94\frac{e}{a} \cdot \frac{{\Delta H}}{H} - 0.34\lg \left( {Re} \right)} \end{array}$

 Download: 图 7 Y的理论值与实验值散点分布 Fig. 7 Comparison between theoretical value and experimental value of the Y
3.2 公式验证

 $F = \frac{{\sum\limits_{k = 1}^K {{{\left( {{Y_{k{\rm{ - pre}}}} - \bar Y} \right)}^2}/K} }}{{\sum\limits_{k = 1}^K {{{\left( {{Y_{k{\rm{ - exp}}}} - {Y_{k{\rm{ - pre}}}}} \right)}^2}/\left( {K - J - 1} \right)} }}$ (17)
 ${D_W} = \frac{{\sum\limits_{t = 2}^K {\left( {{e_t} - {e_{t - 1}}} \right)} }}{{\sum\limits_{t = 2}^K {e_t^2} }}$ (18)
 ${V_{IFi}} = {\left( {1 - R_i^2} \right)^{ - 1}}$ (19)

 Download: 图 8 MOD(a)残差分布直方图(平均值=0，标准差=0.989，N=178) Fig. 8 MOD(a) Residual distribution histogram(mean=0, standard deviation=0.989, N=178)

4 结论

1) 分流点的竖向位置与上下游水位差与上游水位的比值(ΔH/H)，孔口高度与孔堰高度(e/a)、孔堰结构体型(L/a)以及雷诺数(Re)有关，并随着4种无因参数的不同，呈现不同的规律：分流点受结构体型长度的变化影响不大；随着孔口开度以及水位差的变化影响较明显，并呈现正相关关系；雷诺数对分流点位置的影响随着孔口高度的变化发生变化。

2) 通过5种不同的参数模型，分别对4种无量纲因子对分流点竖向位置影响的敏感性进行了分析，得到影响分流点位置的因子敏感性大小排列为e/a、ΔH/H、lg(Re)以及L/a

3) 通过5种模型统计指标的比较，得到预测分流点位置的最优模型MOD(a)(AMCC=0.921，RMSE=0.051和ZRE=0.989)，并进一步验证了模型的正确性以及合理性，该公式拟合度高、结构简单、通用性强，可对分流点的竖向位置进行描述。

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