大压力梯度下多孔介质中启动流动的相似性
Similarity of start-up flow in porous media for large pressure gradients
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中文总结 AI 辅助
研究大压力梯度下有序多孔介质启动流动，发现非线性效应由无粘时间τ_inv统一控制，确立其为强加速多孔介质流动非线性 onset 的统一度量，对非定常输运建模有直接意义。
中文摘要 AI 辅助
本文通过直接数值模拟研究有序多孔介质（六方最密堆积、面心立方和体心立方球体堆积）中的启动流动。流动从静止状态启动，由恒定压力梯度驱动，使我们能够在宽范围的哈根数（Hagen number）内研究瞬态发展。量纲分析确定了两个相关的时间尺度：粘性扩散时间τ_visc和无粘时间τ_inv。短时间行为遵循Johnson等人[《流体力学杂志》176卷，379页（1987年）]的粘性渐近理论，随后非线性效应的出现由无粘时间τ_inv统一控制，而非任何临界雷诺数。在孔隙尺度上，瞬态演化的特征是球体表面薄涡层的生长，这些涡层在t≈τ_inv时脱离到孔隙空间中，并形成惯性核心。尽管几何结构存在差异，但所有三种堆积的这些过程都以极为相似的序列发生。涡量大小表现出与哈根数相关的层流边界层标度，而在体心立方球体堆积的情况下，观察到向湍流型标度的转变。这些结果确立τ_inv为强加速多孔介质流动中非线性 onset 的统一度量，对自然和工程系统中非定常输运的建模具有直接意义。
英文摘要
We investigate the start-up flows through ordered porous media (hexagonal close-packed, face-centred cubic and body-centred sphere packs) by means of direct numerical simulations. The flows are initiated from rest and driven by a constant pressure gradient, allowing us to examine the transient development across a wide range of Hagen numbers. Dimensional analysis identifies two relevant time scales: the viscous diffusion time $τ_\mathrm{visc}$ and the inviscid time $τ_\mathrm{inv}$. While the small-time behaviour follows the viscous asymptotics of Johnson et al. [J. Fluid. Mech. 176, 379 (1987)], the subsequent emergence of nonlinear effects is universally governed by the inviscid time $τ_\mathrm{inv}$, rather than by any critical Reynolds number. At the pore scale, the transient evolution is characterised by the growth of thin vorticity layers on the sphere surfaces, their detachment into the pore space around $t \sim τ_\mathrm{inv}$, and the formation of inertial cores. Despite geometric differences, these processes occur in a remarkably similar sequence across all three packings. Vorticity magnitude exhibits laminar boundary-layer scaling with Hagen number, while in the body-centred cubic sphere pack case a transition towards turbulent-type scaling is observed. These results establish $τ_\mathrm{inv}$ as a unifying measure for the onset of nonlinearity in strongly accelerated porous media flows, with direct implications for the modelling of unsteady transport in natural and engineered systems.
