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arXiv 2409.19652physics.flu-dyn
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从达西流到对流流：多孔介质中密度驱动流的孔隙尺度研究

From Darcy flow to convective flow: pore-scale study of density-driven currents in porous media

Junyi Li, Yantao Yang, Chao Sun

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AI总结：

本文通过孔隙尺度数值模拟研究多孔介质中密度驱动对流，揭示随瑞利数增大流动从达西型状态向RB型状态转变的机制、临界条件及标度律变化，并阐明达西模型的有效范围。

摘要：

我们对多孔介质中的对流流动进行了一系列孔隙尺度数值模拟，固定施密特数为400，瑞利数范围很宽。多孔介质采用瑞利-贝纳德（RB）系统中规则排列的方形障碍物建模。随着瑞利数增大，流动从达西型状态过渡到RB型状态，相应的$Sh-Ra_D$关系从亚线性标度转变为RB对流的经典0.3标度。这里，$Sh$和$Ra_D$分别表示舍伍德数和瑞利-达西数。对于不同孔隙率，过渡大约在$Ra_D = 4000$时开始，此时流场的特征水平尺度与单个障碍物单元的尺寸相当。当浓度边界层厚度小于约孔间距的六分之一时，流动最终进入RB状态。在达西状态下，$Sh$与$Ra_D$的标度指数随孔隙率增大而减小。基于Grossman-Lohse理论（J. Fluid Mech., vol. 407, 2000; Phys. Rev. Lett., vol. 86, 2001），我们对各状态下的标度律给出解释，并强调边界层内机械弥散效应的显著影响。我们的发现为达西模型的有效范围提供了一些新的认识。

英文摘要：

We conducted a series of pore-scale numerical simulations on convective flow in porous media, with a fixed Schmidt number of 400 and a wide range of Rayleigh numbers. The porous media are modeled using regularly arranged square obstacles in a Rayleigh-Bénard (RB) system. As the Rayleigh number increases, the flow transitions from a Darcy-type regime to an RB-type regime, with the corresponding $Sh-Ra_D$ relationship shifting from sublinear scaling to the classical 0.3 scaling of RB convection. Here, $Sh$ and $Ra_D$ represent the Sherwood number and Rayleigh-Darcy number, respectively. For different porosities, the transition begins at approximately $Ra_D = 4000$, at which point the characteristic horizontal scale of the flow field is comparable to the size of a single obstacle unit. When the thickness of the concentration boundary layer is less than about one-sixth of the pore spacing, the flow finally enters the RB regime. In the Darcy regime, the scaling exponent of $Sh$ and $Ra_D$ decreases as porosity increases. Based on the Grossman-Lohse theory (J. Fluid Mech., vol. 407, 2000; Phys. Rev. Lett., vol. 86, 2001), we provide an explanation for the scaling laws in each regime and highlight the significant impact of mechanical dispersion effects within the boundary layer. Our findings provide some new insights into the validity range of the Darcy model.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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