We perform direct numerical simulations of turbulent flow at friction Reynolds number \(Re_\tau \approx 500{-}2000\) grazing over perforates plates with moderate viscous-scaled orifice diameter \(d^+\approx 40-160\) and analyse the relation between permeability and added drag. Unlike previous studies of turbulent flows over permeable surfaces, we find that the flow inside the orifices is dominated by inertial effects, and that the relevant permeability is the Forchheimer and not the Darcy one. We find evidence of a fully rough regime where the relevant length scale is the inverse of the Forchheimer coefficient, which can be regarded as the resistance experienced by the wall-normal flow. Moreover, we show that, for low porosities, the Forchheimer coefficient can be estimated with good accuracy using a simple analytical relation.

我们对摩擦雷诺数\(Re_\tau \约 500{-}2000\)的湍流进行直接数值模拟，掠过具有中等粘性尺度孔直径\(d^+\约 40-160\)的穿孔板并分析渗透率与附加阻力的关系。与之前对可渗透表面湍流的研究不同，我们发现孔口内的流动受惯性效应支配，相关渗透率是 Forchheimer 而不是 Darcy。我们发现了一个完全粗糙状态的证据，其中相关的长度尺度是 Forchheimer 系数的倒数，可以将其视为壁法向流动所经历的阻力。此外，我们表明，对于低孔隙率，可以使用简单的分析关系以良好的精度估计 Forchheimer 系数。