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多孔介质热弥散系数的分形模型

张杰 张赛 高伟业 胡世旺 汪振毅

张杰,张赛,高伟业,胡世旺,汪振毅. 多孔介质热弥散系数的分形模型 [J]. 应用数学和力学,2022,43(5):553-560 doi: 10.21656/1000-0887.420314
引用本文: 张杰,张赛,高伟业,胡世旺,汪振毅. 多孔介质热弥散系数的分形模型 [J]. 应用数学和力学,2022,43(5):553-560 doi: 10.21656/1000-0887.420314
ZHANG Jie, ZHANG Sai, GAO Weiye, HU Shiwang, WANG Zhenyi. A Fractal Model for Thermal Dispersion Coefficients of Porous Media[J]. Applied Mathematics and Mechanics, 2022, 43(5): 553-560. doi: 10.21656/1000-0887.420314
Citation: ZHANG Jie, ZHANG Sai, GAO Weiye, HU Shiwang, WANG Zhenyi. A Fractal Model for Thermal Dispersion Coefficients of Porous Media[J]. Applied Mathematics and Mechanics, 2022, 43(5): 553-560. doi: 10.21656/1000-0887.420314

多孔介质热弥散系数的分形模型

doi: 10.21656/1000-0887.420314
基金项目: 昆明理工大学省级项目(人培)(KKSY201601011);云南省科学技术厅青年基金(KKSQ201701008)
详细信息
    作者简介:

    张杰(1996—),男,硕士生(E-mail:jie_zh@163.com

    张赛(1987—),女,博士,硕士生导师(通讯作者. E-mail:sai_zh@163.com

  • 中图分类号: O357.5

A Fractal Model for Thermal Dispersion Coefficients of Porous Media

  • 摘要:

    热弥散系数是与流体的物性和多孔介质结构有关的,表征多孔介质传热传质强弱的重要参数。该文建立了分形多孔介质的孔喉结构模型,研究了在孔喉结构处流体由湍流状态变为层流状态的局部水头损失和速度弥散效应,在考虑微观孔喉结构和速度弥散效应的影响下,推导了热弥散系数关系式。研究表明,热弥散系数与孔喉比、孔喉结构个数和迂曲分形维数成正比,与孔隙率和面积分形维数成反比。进一步研究发现,孔喉比在1~150范围内对速度弥散效应有显著影响,流体在孔喉结构处存在局部水头损失,导致速度弥散效应增强,热弥散系数增大。

  • 图  1  孔喉结构流动模型

    Figure  1.  The flow model for the pore-throat structure

    图  2  孔道内流体流动模型

    Figure  2.  The fluid flow model in the channel

    图  3  热弥散系数分形模型与常规模型对比

    Figure  3.  Comparison between the fractal model for the thermal dispersion coefficient and the conventional model

    图  4  热弥散系数分形模型与实验值对比

    Figure  4.  Comparison between the fractal model for the thermal dispersion coefficient and experimental values

    图  5  孔喉比对速度弥散效应的影响

    Figure  5.  Influences of the pore-throat ratio on the velocity dispersion effect

    图  6  面积分形维数对热弥散系数的影响

    Figure  6.  Influences of the area fractal dimension on the thermal dispersion coefficient

    图  7  迂曲分形维数对热弥散系数的影响

    Figure  7.  Influences of the tortuous fractal dimension on the thermal dispersion coefficient

    图  8  孔喉结构个数对热弥散系数的影响

    Figure  8.  Influences of the number of pore-throat structures on the thermal dispersion coefficient

    表  1  分形模型中部分参数与数值

    Table  1.   Some parameters and values in the fractal model

    parametervalue
    pore diameter λ / m1×10−6~1×10−4
    minimum pore diameter λmin / m1×10−6
    solid particles dp / m1×10−4
    viscosityµ / (Pa·s)1.2×10−5
    density ρ / (kg·m−3)8.9×10−2
    specific heat capacity cp / (J·kg−1·K−1)1.43×104
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-10-18
  • 修回日期:  2021-12-08
  • 网络出版日期:  2022-04-07
  • 刊出日期:  2022-05-15

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