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Article(id=1207627662512722553, tenantId=1146029695717560320, journalId=1205116964453384197, issueId=1207271180105499439, articleNumber=null, orderNo=null, doi=10.20040/j.cnki.1000-7709.2025.20241894, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1728403200000, receivedDateStr=2024-10-09, revisedDate=1731513600000, revisedDateStr=2024-11-14, acceptedDate=null, acceptedDateStr=null, onlineDate=1765850471380, onlineDateStr=2025-12-16, pubDate=1758729600000, pubDateStr=2025-09-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1765850471380, onlineIssueDateStr=2025-12-16, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1765850471380, creator=13701087609, updateTime=1765850471380, updator=13701087609, issue=Issue{id=1207271180105499439, tenantId=1146029695717560320, journalId=1205116964453384197, year='2025', volume='43', issue='9', pageStart='1', pageEnd='220', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1765765479351, creator=13701087609, updateTime=1765765681303, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1207272027254247478, tenantId=1146029695717560320, journalId=1205116964453384197, issueId=1207271180105499439, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1207272027254247479, tenantId=1146029695717560320, journalId=1205116964453384197, issueId=1207271180105499439, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=60, endPage=64, ext={EN=ArticleExt(id=1207627662768575108, articleId=1207627662512722553, tenantId=1146029695717560320, journalId=1205116964453384197, language=EN, title=Study on Bifurcation Flow Distribution Characteristics of Three-Branch River Channel, columnId=null, journalTitle=Water Resources and Power, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to meet the flood discharge and irrigation requirements of tributary channels, it is of great practical significance to master the water flow diversion characteristics of the three-branch river channel. Based on numerical simulation and physical model experiments, the water level changes, velocity distribution, and flow allocation characteristics at the mouth of three tributaries river under different branching angles were studied. The results show that for a three-branch river channel, the larger the branching angle, the smaller the flow velocity in the tributary is, and the flow allocation in the variable angle side gradually decreases, while the flow allocation in the fixed angle side and the main branch gradually increases. Based on dimensional analysis, a three-branch river flow diversion ratio calculation formula was obtained considering the Froude number at each branch inlet. The formula was verified, and it was found that the prediction accuracy of the formula for the flow diversion ratio of the tributary channels in a three-branch river system was good.

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为满足支汊河道泄洪和灌溉需求，掌握三分汊河道水流分流特性有重要实际意义。基于数值模拟和物理模型试验，对不同分汊角度下三分汊汊口的水位变化、流速分布和流量分配特性进行研究。结果表明，对于三分汊河道，分汊角度越大，支汊流速越小，变角度一侧的支汊分流量逐渐减小，固定角度一侧的支汊分流量和主汊分流量逐渐增大；基于量纲分析，得出考虑各汊进口弗劳德数的三分汊河道分流比计算式。经验证，计算式对三分汊河道支汊分流比的预测精度较好。

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李书芳（1981-），女，博士、副教授，研究方向为水力学及河流动力学，E-mail：
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杨杰（1998-），男，硕士研究生，研究方向为防洪及河道治理，E-mail：

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杨杰（1998-），男，硕士研究生，研究方向为防洪及河道治理，E-mail：

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杨杰（1998-），男，硕士研究生，研究方向为防洪及河道治理，E-mail：

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Catena, 2018, 166: 10-20., articleTitle=Experimental investigation of scour at a channel junctions of different diversion angles and bed width ratios, refAbstract=null), Reference(id=1207627673740873914, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207627662512722553, doi=null, pmid=null, pmcid=null, year=2022, volume=56, issue=null, pageStart=1914, pageEnd=1926, url=null, language=null, rfNumber=[7], rfOrder=6, authorNames=AL-ZUBAIDY R A, HILO A N, journalName=Materials today: Proceedings, refType=null, unstructuredReference=AL-ZUBAIDY R A, HILO A N. Numerical investigation of flow behavior at the lateral intake using Computational Fluid Dynamics (CFD)[J]. Materials today: Proceedings, 2022, 56: 1914-1926., articleTitle=Numerical investigation of flow behavior at the lateral intake using Computational Fluid Dynamics (CFD), refAbstract=null), Reference(id=1207627673807982779, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207627662512722553, doi=null, pmid=null, pmcid=null, year=2020, volume=35, issue=6, pageStart=600, pageEnd=608, url=null, language=null, rfNumber=[8], rfOrder=7, authorNames=ALOMARI N K, YUSUF B, AHMAD MOHAMMAD T, journalName=International journal of sediment research, refType=null, unstructuredReference=ALOMARI N K, YUSUF B, AHMAD MOHAMMAD T, et al. Influence of diversion angle on water and sediment flow into diversion channel[J]. 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Research programme

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研究方法方案来流量Q/（L·s-1）左支汊角度γ/（°）右支汊角度β/（°）不对称度α
数值模拟18.51530-0.5
 28.530300
 38.545300.33
 48.560300.5
 58.575300.6
模型试验64.530300
 75.530300
 87.030300
 98.530300
 1010.030300
), ArticleFig(id=1207627672352559264, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207627662512722553, language=CN, label=表1, caption=

研究方案

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研究方法方案来流量Q/（L·s-1）左支汊角度γ/（°）右支汊角度β/（°）不对称度α
数值模拟18.51530-0.5
 28.530300
 38.545300.33
 48.560300.5
 58.575300.6
模型试验64.530300
 75.530300
 87.030300
 98.530300
 1010.030300
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The comparison between the simulated results and the measured results

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断面测点模拟值/cm实测值/cm相对误差/%
03Ⅰ2.062.32-11.20
 Ⅲ2.913.33-12.60
 Ⅴ2.162.42-10.70
05Ⅰ'3.923.657.40
 Ⅲ'4.003.902.60
 Ⅴ'3.953.609.70
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测点水深模拟结果与实测结果对比情况

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断面测点模拟值/cm实测值/cm相对误差/%
03Ⅰ2.062.32-11.20
 Ⅲ2.913.33-12.60
 Ⅴ2.162.42-10.70
05Ⅰ'3.923.657.40
 Ⅲ'4.003.902.60
 Ⅴ'3.953.609.70
), ArticleFig(id=1207627672625189028, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207627662512722553, language=EN, label=Tab. 3, caption=

The branching ratio of each branch under different branching angle and incoming flow rate

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序号不对称度α来流量Q左支汊分流量Q1主汊分流量Q2右支汊分流量Q3左支汊分流比η1/%主汊分流比η2/%右支汊分流比η3/%
1-0.58.52.863.522.1033.7041.4924.80
208.52.194.102.2025.7848.2725.94
30.338.51.404.752.3416.5055.9527.55
40.508.50.565.382.556.6063.3730.04
50.608.50.365.482.654.2664.5331.21
604.51.092.291.0524.5651.6723.76
705.51.342.991.3223.6352.9423.43
807.01.63.841.622.7354.5522.73
908.52.064.412.1523.9151.1624.93
10010.02.345.082.4923.6351.2725.10
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不同分汊角度及来流量下各汊分流比

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序号不对称度α来流量Q左支汊分流量Q1主汊分流量Q2右支汊分流量Q3左支汊分流比η1/%主汊分流比η2/%右支汊分流比η3/%
1-0.58.52.863.522.1033.7041.4924.80
208.52.194.102.2025.7848.2725.94
30.338.51.404.752.3416.5055.9527.55
40.508.50.565.382.556.6063.3730.04
50.608.50.365.482.654.2664.5331.21
604.51.092.291.0524.5651.6723.76
705.51.342.991.3223.6352.9423.43
807.01.63.841.622.7354.5522.73
908.52.064.412.1523.9151.1624.93
10010.02.345.082.4923.6351.2725.10
), ArticleFig(id=1207627672771989672, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207627662512722553, language=EN, label=Tab. 4, caption=

Comparison of the calculated and simulated values of variable angle shunt ratio

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支汊不对称度α模拟值/%计算值/%相对误差/%
左支汊（计算值、相对误差由式（16）计算）-0.533.7031.45-6.68
025.7824.61-4.23
0.3316.5017.324.99
0.56.606.21-5.95
0.64.263.93-8.62
右支汊（计算值、相对误差由式（17）计算）-0.524.8024.38-1.71
025.9424.50-5.42
0.3327.5527.10-1.80
0.530.0429.46-2.11
0.631.2129.86-4.28
), ArticleFig(id=1207627672839098538, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207627662512722553, language=CN, label=表4, caption=

变角度分流比计算值与模拟值对比

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支汊不对称度α模拟值/%计算值/%相对误差/%
左支汊（计算值、相对误差由式（16）计算）-0.533.7031.45-6.68
025.7824.61-4.23
0.3316.5017.324.99
0.56.606.21-5.95
0.64.263.93-8.62
右支汊（计算值、相对误差由式（17）计算）-0.524.8024.38-1.71
025.9424.50-5.42
0.3327.5527.10-1.80
0.530.0429.46-2.11
0.631.2129.86-4.28
), ArticleFig(id=1207627672910401708, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207627662512722553, language=EN, label=Tab. 5, caption=

Comparison between the calculated value and the test value of the variable flow shunt ratio

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支汊来流量Q/（L·s-1）试验值/%计算值/%相对误差/%
左支汊（计算值、相对误差由式（16）计算）4.524.5621.91-10.79
5.523.6322.39-5.25
722.7324.497.74
8.523.9125.516.68
1023.6326.1410.63
右支汊（计算值、相对误差由式（17）计算）4.523.7624.503.10
5.523.4324.504.55
722.7324.50-7.74
8.524.9324.50-1.74
1025.1024.50-2.40
), ArticleFig(id=1207627672981704878, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207627662512722553, language=CN, label=表5, caption=

变流量分流比计算值与试验值对比

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支汊来流量Q/（L·s-1）试验值/%计算值/%相对误差/%
左支汊（计算值、相对误差由式（16）计算）4.524.5621.91-10.79
5.523.6322.39-5.25
722.7324.497.74
8.523.9125.516.68
1023.6326.1410.63
右支汊（计算值、相对误差由式（17）计算）4.523.7624.503.10
5.523.4324.504.55
722.7324.50-7.74
8.524.9324.50-1.74
1025.1024.50-2.40
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三分汊河道汊口分流特性研究
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杨杰 1 , 王心宇 1 , 李书芳 1, 2, 3 , 师帅 1
水电能源科学 | 水力学 2025,43(9): 60-64
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水电能源科学 | 水力学 2025, 43(9): 60-64
三分汊河道汊口分流特性研究
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杨杰1 , 王心宇1, 李书芳1, 2, 3 , 师帅1
作者信息
  • 1.河北工程大学水利水电学院，河北 邯郸 056038
  • 2.河北省智慧水利重点实验室，河北 邯郸 056038
  • 3.河北省水利水电虚拟仿真实验教学中心，河北 邯郸 056038

    • 杨杰（1998-），男，硕士研究生，研究方向为防洪及河道治理，E-mail：

通讯作者:

李书芳（1981-），女，博士、副教授，研究方向为水力学及河流动力学，E-mail：
Study on Bifurcation Flow Distribution Characteristics of Three-Branch River Channel
Jie YANG1 , Xin-yu WANG1, Shu-fang LI1, 2, 3 , Shuai SHI1
Affiliations
  • 1.School of Water Conservancy and Hydroelectric Power, Hebei University of Engineering, Handan 056038, China
  • 2.Key Laboratory of Intelligent Water Resources of Hebei Province, Handan 056038, China
  • 3.Hebei Water Resources and Hydropower Virtual Simulation Experiment Teaching Center, Handan 056038, China
出版时间: 2025-09-25 doi: 10.20040/j.cnki.1000-7709.2025.20241894
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摘要
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为满足支汊河道泄洪和灌溉需求，掌握三分汊河道水流分流特性有重要实际意义。基于数值模拟和物理模型试验，对不同分汊角度下三分汊汊口的水位变化、流速分布和流量分配特性进行研究。结果表明，对于三分汊河道，分汊角度越大，支汊流速越小，变角度一侧的支汊分流量逐渐减小，固定角度一侧的支汊分流量和主汊分流量逐渐增大；基于量纲分析，得出考虑各汊进口弗劳德数的三分汊河道分流比计算式。经验证，计算式对三分汊河道支汊分流比的预测精度较好。

三分汊河道  /  分流特性  /  水流结构  /  数值模拟

In order to meet the flood discharge and irrigation requirements of tributary channels, it is of great practical significance to master the water flow diversion characteristics of the three-branch river channel. Based on numerical simulation and physical model experiments, the water level changes, velocity distribution, and flow allocation characteristics at the mouth of three tributaries river under different branching angles were studied. The results show that for a three-branch river channel, the larger the branching angle, the smaller the flow velocity in the tributary is, and the flow allocation in the variable angle side gradually decreases, while the flow allocation in the fixed angle side and the main branch gradually increases. Based on dimensional analysis, a three-branch river flow diversion ratio calculation formula was obtained considering the Froude number at each branch inlet. The formula was verified, and it was found that the prediction accuracy of the formula for the flow diversion ratio of the tributary channels in a three-branch river system was good.

three distributaries river channel  /  diversion characteristic  /  flow structure  /  numerical simulation
杨杰, 王心宇, 李书芳, 师帅. 三分汊河道汊口分流特性研究. 水电能源科学, 2025 , 43 (9) : 60 -64 . DOI: 10.20040/j.cnki.1000-7709.2025.20241894
Jie YANG, Xin-yu WANG, Shu-fang LI, Shuai SHI. Study on Bifurcation Flow Distribution Characteristics of Three-Branch River Channel[J]. Water Resources and Power, 2025 , 43 (9) : 60 -64 . DOI: 10.20040/j.cnki.1000-7709.2025.20241894
正文
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1 引言
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分汊河道是一种常见的河流平面形态，对于天然河道，冲击河流在水流泥沙作用下，形成树枝状的多分汊河流，分汊河道各汊分流比的大小和变化将直接决定分汊河道各支汊的兴衰，影响航道变迁，防洪布局等。在人工河道工程中，为满足防洪、航运、引水及排水等需求，常通过开挖形成多处分汊结构。合理设计分水渠分流角度和分水渠的结构尺寸对于调节控制分水流量至关重要[1-2]，掌握分汊河道分流特性有重要工程参考意义。目前，关于分汊河道的研究主要集中在对二分汊河道的研究。现有研究表明，影响汊口处水沙分配的因素主要包括汊道的坡度、分汊角的角度、分汊河道的弯曲程度，以及河床形态、糙率等[3-5]。分汊河道的几何特性，尤其是分汊角度，对分汊口水流结构影响显著。分汊角度不同导致汊口附近的流速分布、水位变动及涡量大小也存在较大差异，进而影响汊口冲淤特性和水流分配[6]。小分汊角是增加分汊河道流量、减少分汊河道含沙量和降低分汊尖端冲刷深度的最佳方案[7]。汊口分流使得流线发生弯曲，易在汊口区域形成涡旋、二次流等复杂水力现象，导致泥沙冲刷和淤积，进而影响河道稳定性和生态功能[8]。为满足分洪或引水需求，往往需在二分汊河道（渠道）的基础上开挖新的分洪渠或引水渠，使二分汊变为三分汊形式。尽管三分汊河道水流特性与二分汊有一定相似之处，但因三分汊河道分汊形式的多样性和复杂性，在分洪、引水及泥沙输运等相关计算方面与二分汊存在一定差异，二分汊河道的研究成果不能直接应用于三分汊河道的计算。目前，关于三分汊河道的研究尚不多见，本研究基于数值模拟和物理模型试验，开展三分汊河道水流特性和分流特性研究，以期为类似工程的设计、维护提供参考。
2 方案设计
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三分汊河道概化模型示意图见图1。模型主河道长5.00 m，宽0.30 m，左右支汊长度均为2.00 m，宽0.15 m。共设计10个研究方案，其中数值模拟方案5个，固定主河道来流量Q=8.5 L/s，右支汊分汊角β=30°不变，改变左支汊分汊角度γ=15°、30°、45°、60°、75°。模型试验方案5个，固定左右支汊角度分别为γ=β=30°不变，改变来流流量Q=4.5、5.5、7.0、8.5、10.0 L/s。方案见表1。数值模拟采用CFD软件进行模拟，模型试验在河北工程大学水利馆进行。为量化河道分汊形式并区分左支汊不同分汊角度，采用不对称度α来表示各方案，α计算式[3]为：
式中，α为不对称度；γ、β分别为左、右支汊分汊角度；max（γ，β）为左右支汊角度最大值。
3 数值模拟方法
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3.1 控制方程
采用基于有限体积的CFD软件进行数值模拟，控制方程采用N-S方程，简化后的矩形河道分汊口处的水流状态为湍流，因此选用RNGκ-ε模型，自由液面采用VOF方法进行处理。
连续性方程为：
动量方程为：
式中，u、v、w分别为流体在x、y、z三个方向上的速度分量；Ax、Ay、Az分别为x、y、z三个方向上可流动流体的面积分数；VF为可流动流体的体积分数；ρ为流体密度；p为流体上的压强；Gx、Gy、Gz分别为x、y、z三个方向上的重力加速度；fx、fy、fz分别为x、y、z三个方向上的粘滞加速度。
3.2 RNG κ-ε方程
控制方程包括湍动能κ方程和湍动能耗散率ε方程。湍动能κ方程为：
湍动能耗散率ε方程：
其中
式中，ui、uj均为流场的速度分量；μ为湍动黏滞系数；σκ、σε分别为湍动能和湍动能耗散率所对应的普朗特数，取1.39；C1ε、C2ε均为经验系数，分别取1.42、1.68；η为无量纲参数；η0、β分别取4.377、0.012。
3.3 网格无关性分析及边界条件
采用有限体积法生成正矩形网格进行网格划分。网格无关性验证表明单元格边长为0.01 m时断面01上平均流速实测值与模拟值的相对误差为4.16%，当单元格边长为0.008 m时相对误差为3.36%。两者相对误差较为接近，但后者网格数量与计算时间几乎翻倍，鉴于时间和计算资源有限，最终单元格边长选择为0.01 m。在模型边界条件设置中，主河道进口边界设定为流量进口，主槽和支汊边壁设定为滑移固体边壁，自由水面与空气交界面设为Symmetry边界，出口边界为自由出流。
4 模型验证
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4.1 验证断面
为验证数值模拟结果的准确性，在模型尺寸和来流条件完全相同的条件下，对模拟方案2和试验方案9的结果进行对比。选择典型断面对流速和水深的数值模拟结果与物理模型试验结果进行对比验证。图2为主支汊河道对比断面及测点布置图，由于汊口附近水流流态复杂，验证断面选择主河道中部断面03和左汊进口断面05。主河道的断面自主河道左岸至右岸每间隔0.06 m等间距布置一个测点，断面05自左支汊左岸至右岸每间隔0.03 m布置一个测点。定义w0为测线Ⅰ、Ⅴ之间的横向距离；l1为断面01至断面04的纵向距离。
4.2 流速对比
流速是评估水流动力特性重要的参数。分析两断面各点位的流速模拟值与实测值的相对误差，以验证数值模拟结果的精准性。结果表明，各典型断面流速模拟值和试验值较为接近，流速最大相对误差为10.3%，其余点位误差均小于15%，证明利用RNGκ-ε模型对三分汊河道流速进行模拟的方法可行。
4.3 水深对比
进一步对比验证断面的水深模拟结果和实测结果，表2中列出两个断面六个典型测点的数值模拟结果与实测结果对比情况。测点水深数值模拟结果的最大相对误差为-12.6%。说明所采用的数值模拟方法对三分汊河道的水深模拟结果可信度较高。
5 结果与讨论
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5.1 主河道纵向及横向水面线分布
图3为主河道纵向水面线分布图。同一来流量下，不同分汊角度下的主河道纵向水面线变化规律呈现出一定相似性，具体而言，测线Ⅰ、Ⅲ、Ⅴ纵向水面线分布均表现为在进入汊口附近时水面开始显著降低，在汊口中部断面03下游附近，水位降至最低，自l1/B>1.0开始水位迅速回升，并逐渐趋于平稳。稳定后各工况的水位高度与不对称度成正比，不对称度越大，平稳后的水面越高。当一侧支汊角度发生变化时，靠近变支汊角度的一侧，最低水位受分汊角影响变化较为明显，左汊分汊角较小时，即γ≤45°时，最低水位位置几乎不受分汊角变化影响，当左侧分汊角γ>45°时，分汊角增大，最低水位增大，最低水位位置比小分汊角时向上游偏移。
分析其原因为，水流在沿主河道向下游流动过程中，一部分水流向支汊发生分流，另一部分水流在惯性力作用下仍然沿主流方向流动，向支汊分流的流速大小取决于支汊角度和来流流速，分汊角度越大，支汊分流流速越小，相应的水位越高。
5.2 汊口流速分布特性
对于含沙河道，在低流速区容易造成泥沙淤积，高流速区易导致局部冲刷[9]。掌握三分汊河道分汊口附近流速分布情况，可以初步预估在分汊口附近的分流情况、泥沙输移规律和对岸边的冲淤影响。
各工况三汊口附近流速矢量图和流速云图见图4。由图4可知，当左支汊角度γ=15°时，右支汊进口断面出现一小范围高流速区，左支汊进口断面下游靠近左侧岸边存在一小的低流速区，随左支汊分汊角增大，左支汊低流速区逐渐沿侧壁向下游发展，当γ增至75°时，左支汊进口断面下游几乎全部变为低流速区；当左右支汊分汊角相等时，右支汊的右侧壁出现与左支汊左侧壁相似的低流速区，整个三汊口流速以主河道中轴线为对称轴呈对称分布，且在左、右支汊进口断面出现对称的高流速区，三分汊汊口附近流速矢量同样呈对称分布；当左支汊分汊角大于右支汊分汊角，左支汊进口断面的高流速区较右支汊明显减小；当γ>60°，左支汊进口断面高流速区消失，右支汊进口断面的高流速区大小和范围趋于稳定。
图5为断面03流速等值线分布图。由图5可知，随着左支汊分汊角增大，左支汊流速逐渐减小，整个断面上左支汊所在区域为低流速区。这种流速分布情况会影响各汊流量分配。
5.3 汊口分流特性
汊口流速分布影响各支汊的流量分配，分析各工况下各汊流量分配情况。各汊分流比ηi为：
式中，ηi为各汊分流比；Qi为各汊的分流流量，下角标i=1、2、3分别代表左支汊、主汊和右支汊的物理量；Q为主河道来流量。
表3为不同分汊角度下各汊分流比变化情况。由表3可知，随着α增大，右支汊和主汊分流比逐渐增大，左支汊分流比呈减小趋势；当α<0时，左支汊分流比大于右支汊；当α=0，两支汊的分流比几乎相等，主汊分流流量接近来流总流量的1/2；当α>0时，左支汊分流比开始小于右支汊分流比。由此可见，较小的分汊角度使得水流向支汊流动的偏转角度较小，从而减弱了水流惯性，水流更易于进入支汊。随着α的增大，水流进入左支汊的偏转角度增大，水流进入支汊的难度也相应增加。因此，三分汊河道可以通过调整分汊角度从而调节各支汊和主汊分流量。
分析分流比与来流参数和汊口结构参数之间的影响关系。各汊分流比ηi与进口断面平均流速Vi、平均水深h，支汊宽度b，主河道宽度B、左、右支汊分汊角度γ和β、水流运动粘滞系数ν、水体密度ρ以及重力加速度g有关：
对式（11）进行量纲分析并对无量纲参数进行组合，可得：
其中f（β）、f（γ）分别为β、γ的无量纲函数，对式（12）进行改写：
在实际工程中所遇到的水流多为阻力平方区的湍流，该区沿程阻力系数与雷诺数Re无关，因此计算分流比时可以忽略雷诺数的影响。式（13）可进一步简化为：
参考童朝锋[2]的动量平衡公式形式，在其基础上增加各支汊弗劳德数Fri的影响，将分流比计算式优化为：
式（15）中，χi在i=1时；χi在i=3时，，ni、ki、ci均为未知参数。根据改变角度的数值模拟结果和改变来流量的物理试验结果，利用数据拟合软件拟合得出左右支汊的ni、ki值。得到左支汊和右支汊的分流比经验计算式为：
表4、5均为分流比计算结果和测量结果对比。结果表明，式（16）、（17）对改变分汊角度的左右支汊分流比计算误差均在10%以内，精度较好；分析计算结果与物理试验结果，可知式（16）、（17）对改变来流量的左右汊分流比计算误差均在15%之内，精度良好。
6 结论
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a. 对于三分汊河道，支汊分汊角度与流速及分流量呈负相关关系；即支汊角度增大，其对应的流速和分流量减小。
b. 随着不对称度增大，变角度的支汊分流量逐渐减小，相应的另一不变角度的支汊分流量则缓慢增大，主汊分流量逐渐增大。
c. 考虑支汊进口断面弗劳德数，结合量纲分析和既有研究成果，得出包含进口断面弗劳德数的分流比计算式，计算值和测量值相对误差较小。
基金
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  • 国家重点研发计划(2023YFC3209402)
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doi: 10.20040/j.cnki.1000-7709.2025.20241894
  • 接收时间：2024-10-09
  • 首发时间：2025-12-16
  • 出版时间：2025-09-25
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  • 收稿日期：2024-10-09
  • 修回日期：2024-11-14
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    1.河北工程大学水利水电学院，河北 邯郸 056038
    2.河北省智慧水利重点实验室，河北 邯郸 056038
    3.河北省水利水电虚拟仿真实验教学中心，河北 邯郸 056038

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李书芳（1981-），女，博士、副教授，研究方向为水力学及河流动力学，E-mail：
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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