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多孔介质内黏弹性流体的热对流稳定性研究

康建宏 谭文长

康建宏, 谭文长. 多孔介质内黏弹性流体的热对流稳定性研究[J]. 力学学报, 2018, 50(6): 1436-1457. doi: 10.6052/0459-1879-18-309
引用本文: 康建宏, 谭文长. 多孔介质内黏弹性流体的热对流稳定性研究[J]. 力学学报, 2018, 50(6): 1436-1457. doi: 10.6052/0459-1879-18-309
Kang Jianhong, Tan Wenchang. THERMAL INSTABILITY OF VISCOELASTIC FLUIDS IN POROUS MEDIA[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1436-1457. doi: 10.6052/0459-1879-18-309
Citation: Kang Jianhong, Tan Wenchang. THERMAL INSTABILITY OF VISCOELASTIC FLUIDS IN POROUS MEDIA[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1436-1457. doi: 10.6052/0459-1879-18-309

多孔介质内黏弹性流体的热对流稳定性研究

doi: 10.6052/0459-1879-18-309
基金项目: 1) 国家重点研发计划项目(2018YFC0808100) 和国家自然科学基金重点项目(11732001) 资助.
详细信息
    作者简介:

    null

    2) 康建宏,副教授,主要从事瓦斯资源开发与利用、非牛顿流体力学等研究. E-mail: jhkang@cumt.edu.cn;
    3) 谭文长,教授,主要从事生物力学、非牛顿流体力学等研究. E-mail: tanwch@pku.edu.cn

  • 中图分类号: O357.3;

THERMAL INSTABILITY OF VISCOELASTIC FLUIDS IN POROUS MEDIA

  • 摘要: 基于修正的Darcy模型, 介绍了多孔介质内黏弹性流体热对流稳定性研究的现状和主要进展. 通过线性稳定性理论, 分析计算多孔介质几何形状(水平多孔介质层、多孔圆柱以及多孔方腔)、热边界条件(底部等温加热、底部等热流加热、底部对流换热以及顶部自由开口边界)、黏弹性流体的流动模型(Darcy-Jeffrey, Darcy-Brinkman-Oldroyd以及Darcy-Brinkman -Maxwell模型)、局部热非平衡效应以及旋转效应对黏弹性流体热对流失稳的临界Rayleigh数的影响. 利用弱非线性分析方法, 揭示失稳临界点附近热对流流动的分叉情况, 以及失稳临界点附近黏弹性流体换热Nusselt数的解析表达式. 采用数值模拟方法, 研究高Rayleigh数下黏弹性流体换热Nusselt数和流场的演化规律,分析各参数对黏弹性流体热对流失稳和对流换热速率的影响.主要结果:(1)流体的黏弹性能够促进振荡对流的发生;(2)旋转效应、流体与多孔介质间的传热能够抑制黏弹性流体的热对流失稳;(3)在临界Rayleigh数附近,静态对流分叉解是超临界稳定的, 而振荡对流分叉可能是超临界或者亚临界的,主要取决于流体的黏弹性参数、Prandtl数以及Darcy数;(4)随着Rayleigh数的增加,热对流的流场从单个涡胞逐渐演化为多个不规则单元涡胞, 最后发展为混沌状态.

     

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  • 收稿日期:  2018-09-17
  • 刊出日期:  2018-11-18

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