Porous plates at incidence

This paper investigates the effect of permeability on two-dimensional rectangular plates at incidences. The flow topology is investigated for Reynolds number (<i>Re</i>) values between 30 and 90, and the forces on the plate are discussed for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi> <mml:mi>e</mml:mi> <mml:mo>=</mml:mo> <mml:mn>30</mml:mn></mml:mrow> </mml:math> , where the wake is found to be steady for any value of the Darcy number (<i>Da</i>) and the flow incidence ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> ). At <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi> <mml:mi>e</mml:mi> <mml:mo>=</mml:mo> <mml:mn>30</mml:mn></mml:mrow> </mml:math> , for a plate normal to the stream and vanishing <i>Da</i>, the wake shows a vortex dipole with a stagnation point on the plate surface. With increasing <i>Da</i>, the separation between the vortex dipole and the plate increases; the vortex dipole shortens and is eventually annihilated at a critical <i>Da</i>. For any value of <i>Da</i> below the critical one, the vortex dipole disappears with decreasing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> . However, at low <i>Da</i>, the two saddle-node pairs merge at the same <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> , annihilating the dipole; while at high <i>Da</i>, they merge at different <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> , resulting in a single recirculating region for intermediate incidences. The magnitudes of lift, drag, and torque decrease with <i>Da</i>. Nevertheless, there exists a range of <i>Da</i> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> , where the magnitude of the plate-wise force component increases with <i>Da</i>, 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 <i>Da</i> 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.