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Forchheimer方程参数量化及达西—非达西转变临界点

刘建 杨巧艳 白雪 宋凯 骆成杰 洒永芳

刘建, 杨巧艳, 白雪, 宋凯, 骆成杰, 洒永芳. Forchheimer方程参数量化及达西—非达西转变临界点[J]. 西南交通大学学报, 2020, 55(1): 218-224. doi: 10.3969/j.issn.0258-2724.20180756
引用本文: 刘建, 杨巧艳, 白雪, 宋凯, 骆成杰, 洒永芳. Forchheimer方程参数量化及达西—非达西转变临界点[J]. 西南交通大学学报, 2020, 55(1): 218-224. doi: 10.3969/j.issn.0258-2724.20180756
LIU Jian, YANG Qiaoyan, BAI Xue, SONG Kai, LUO Chengjie, SA Yongfang. Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow[J]. Journal of Southwest Jiaotong University, 2020, 55(1): 218-224. doi: 10.3969/j.issn.0258-2724.20180756
Citation: LIU Jian, YANG Qiaoyan, BAI Xue, SONG Kai, LUO Chengjie, SA Yongfang. Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow[J]. Journal of Southwest Jiaotong University, 2020, 55(1): 218-224. doi: 10.3969/j.issn.0258-2724.20180756

Forchheimer方程参数量化及达西—非达西转变临界点

doi: 10.3969/j.issn.0258-2724.20180756
基金项目: 国家自然科学基金(41602241,U1734205)
详细信息
    作者简介:

    刘建(1982—),男,副研究员,研究方向为工程水环境效应及其控制,E-mail:liukai-102@163.com

  • 中图分类号: TU458

Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow

  • 摘要: 为探究岩体裂隙中水流的运动规律,基于真实岩体材料建立裂隙渗流模型,对裂隙中的渗流状态及渗流参数进行了研究. 区别于水泥、玻璃、亚克力、钢材等常见非石材类材质,选用天然大理石岩块为基材构建单裂隙渗流模型,开展不同隙宽(0.77、1.18、1.97、2.73 mm)的渗流试验,考察压力损失与流量的关系,探讨达西—非达西流转变的临界点及Forchheimer方程的参数量化问题. 研究结果表明:隙宽为0.77 mm时压力梯度与流量基本呈线性达西关系,随着隙宽和流量的增大,二者呈现出明显的非达西特征,可用Forchheimer方程描述;Forchheimer方程的粘滞项和惯性系数均可表达为隙宽的幂函数,引入雷诺数对惯性项系数进行修正可以减少误差;提出以压力梯度-流量曲线的斜率变化特征来判断达西—非达西流临界点的方法,并在本试验中得到了验证.

     

  • 图 1  试验装置

    Figure 1.  Experimental configurations

    图 2  压力梯度随流量的变化曲线

    Figure 2.  Variation of pressure gradient with flow rate

    图 3  实验值与计算值($- \nabla {P_{1i}} $)比较

    Figure 3.  Comparison between experimental value and calculated value ($ - \nabla {P_{1i}} $)

    图 4  $ - \nabla {P_{1i}} $相对误差分布

    Figure 4.  Relative error distribution of model $ - \nabla {P_{1i}} $

    图 5  试验值与计算值($ - \nabla {P_{2i}}$)比较

    Figure 5.  Comparison between experimental value and calculated value ($- \nabla {P_{2i}} $)

    图 6  $- \nabla {P_{2i}} $相对误差分布

    Figure 6.  Relative error distribution of model $- \nabla {P_{2i}} $

    图 7  不同隙宽K-Q曲线

    Figure 7.  Curves of K-Q for different fracture widths

    表  1  压力梯度与流量的拟合关系式

    Table  1.   Fitted formulas between pressure gradient and flow rate

    类别隙宽/mm拟合方程R2
    线性方程0.77$ { {\rm{ - } }\nabla P_1 = 22.539\;6Q}$0.997 3
    1.18$ { {\rm{ - } }\nabla P_2 = 8.793\;7Q}$0.879 3
    1.97$ { {\rm{ - } }\nabla P_3 = 2.918\;2Q}$0.864 9
    2.73$ { {\rm{ - } }\nabla P_4 = 1.079\;3Q}$0.887 1
    Forchheimer方程0.77$ { {\rm{ - } }\nabla P_1 = 20.722\;7Q + 0.090\;8{Q^2} }$0.999 1
    1.18$ { {\rm{ - } }\nabla P_2 = 1.739\;6Q + 0.176\;1{Q^2} }$0.995 6
    1.97$ { {\rm{ - } }\nabla P_3 = 0.477\;7Q + 0.032\;9{Q^2} }$0.999 6
    2.73$ { {\rm{ - } }\nabla P_4 = 0.310\;9Q + 0.009\;8{Q^2} }$0.997 3
    下载: 导出CSV

    表  2  $ - \nabla {P_{{\rm{1}}i}}$模型参数计算结果

    Table  2.   Calculated parameters of model $ - \nabla {P_{{\rm{1}}i}}$

    c1n1c2n2
    6.848 4−3.091 10.177 1−2.718 7
    下载: 导出CSV

    表  3  $ - \nabla {P_{{\rm{2}}i}}$模型参数计算结果

    Table  3.   Calculated parameters of model $ - \nabla {P_{{{\rm{2}}i}}}$

    c3n3c4n4
    9.112 2−2.819 10.000 12−3.452 6
    下载: 导出CSV

    表  4  不同隙宽的临界流量及雷诺数

    Table  4.   Values of critical flux and critical Reynolds number for different fracture widths

    隙宽/mm${E_{P{_ {i} } } }$/%临界流量/(ml•s−1临界雷诺数
    0.771823.07614.55
    1.182028.44741.30
    1.972842.111 054.30
    2.733354.091 304.72
    下载: 导出CSV
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出版历程
  • 收稿日期:  2018-09-04
  • 修回日期:  2018-10-08
  • 网络出版日期:  2018-12-21
  • 刊出日期:  2020-02-01

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