Porous plates at incidence

Abstract

This paper investigates the effect of permeability on two-dimensional rectangular plates at incidences. The flow topology is investigated for Reynolds number (Re) values between 30 and 90, and the forces on the plate are discussed for \(Re=30\), where the wake is found to be steady for any value of the Darcy number (Da) and the flow incidence (\(\alpha \)). At \(Re=30\), for a plate normal to the stream and vanishing Da, the wake shows a vortex dipole with a stagnation point on the plate surface. With increasing Da, the separation between the vortex dipole and the plate increases; the vortex dipole shortens and is eventually annihilated at a critical Da. For any value of Da below the critical one, the vortex dipole disappears with decreasing \(\alpha \). However, at low Da, the two saddle-node pairs merge at the same \(\alpha \), annihilating the dipole; while at high Da, they merge at different \(\alpha \), resulting in a single recirculating region for intermediate incidences. The magnitudes of lift, drag, and torque decrease with Da. Nevertheless, there exists a range of Da and \(\alpha \), where the magnitude of the plate-wise force component increases with Da, driven by the shear on the plate’s pressure side. Finally, the analysis of the fluid impulse suggests that the lift and drag reduction with Da are associated with the weakening of the leading and trailing edge shear layer, respectively. The present findings will be directly beneficial in understanding the role of permeability on small permeable bodies.