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Permeability and turbulence over perforated plates

We perform direct numerical simulations of turbulent flow at friction Reynolds number $Re_τ\approx 500-2000$ grazing over perforates plates with moderate viscous-scaled orifice diameter $d^+\approx40$--$160$ and analyse the relation between permeability and added drag. Unlike previous studies of turbulent flows over permeable surfaces, we find that 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.