小Reynolds数下基于BJ滑移与分子滑移的n层多孔球体绕流分析
首发时间:2019-01-25
摘要:本文主要研究了小Reynolds数下均匀流体流经单个分层多孔球体的流动规律,考虑分层多孔球的结构,在多孔区域和纯流体区域分别采用了Darcy控制方程和Stokes控制方程,在流体和多孔球交界面处同时考虑了BJ滑移和分子滑移两种滑移条件,多孔球内部不同层之间则采用法向速度连续和压力连续的边界条件。通过理论分析推导出了整个流场的解析解,并对多孔球渗透率极小(可看做实心固体球)、仅考虑BJ滑移、仅考虑分子滑移三种特殊情况进行了对比验证,发现本文得到的解与其他学者的结果一致。在该解析解的基础上推导得到了无量纲阻力表达式,并绘制图表分析了BJ滑移系数、Kn数等对无量纲阻力的影响,最后得出结论,当多孔球渗透率较小时,Kn数对阻力系数的大小起决定性作用,而BJ滑移则可忽略;而在渗透率适中时,则需要重点考虑BJ滑移系数的选择;当渗透率很大时,分子滑移和BJ滑移对阻力系数的大小的影响都很小。
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Analysis of the flow at small Reynolds number over a layered porous sphere under the condition of BJ slip and molecular slip
Abstract:The uniform flow at small Reynolds number over a layered porous sphere has been studied. Considering the structure of the layered porous sphere, Darcy governing equation and Stokes governing equation are adopted separately in the porous region and fluid region. BJ slip and molecular slip are both considered at the interface of the porous region and fluid region. Normal velocity continuity and pressure continuity are used between the layers in the porous sphere. Analytic solutions have been derived and proved to be consistent with three special cases by contrast and verifying with other researchers’ result, which includes the cases that the permeability of the porous sphere is too small and the sphere can be considered as a solid sphere, only BJ slip is considered, and only molecular slip is considered. On the base of the analytic solutions, Dimensionless resistance coefficient is derived and the influence of BJ slip coefficient,Kn number and some other factors on it has been analyzed by figures. Figures and data shows that molecular slip play the decisive role in the influence of the resistance coefficient and BJ slip can be neglected when the permeability is small enough. But BJ slip coefficient is the key point when the permeability is moderate. Then impacts of BJ slip and molecular slip are both small when the permeability is large.
Keywords: Porous media molecular slip BJ slip Darcy model
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小Reynolds数下基于BJ滑移与分子滑移的n层多孔球体绕流分析
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