Permeability and turbulence over perforated plates

TL;DR

This study uses direct numerical simulations to explore how permeability and turbulence interact over perforated plates, revealing inertial effects dominate flow inside orifices and identifying a fully rough regime characterized by the Forchheimer coefficient.

Contribution

It demonstrates that inertial effects dominate flow inside orifices and that the Forchheimer permeability better describes turbulent flow over perforated plates than Darcy permeability.

Findings

Flow inside orifices is dominated by inertial effects.

A fully rough regime is identified where the inverse of the Forchheimer coefficient is the relevant length scale.

The Forchheimer coefficient can be accurately estimated with a simple analytical relation for low porosities.

Abstract

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 $d^+\approx40$--$160$ 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.