Stabilizing effect of porosity on a flapping filament

• A new way of handling porosity in massive slender elastic structures is proposed.
• We investigate how porosity affects the stability of objects exposed to a fluid flow.
• Both lift and drag forces reduction by effect of pressure redistribution is observed.
• We derive and verify a relation between Darcy׳s porosity parameter and ours.
• We propose a simple resonance mechanism between characteristics time-scales.
• A possible experimental set-up to realize the same conditions is suggested.

A new way of handling, simultaneously, porosity and bending resistance of a massive filament is proposed. Our strategy extends the previous methods where porosity was taken into account in the absence of bending resistance of the structure and overcomes related numerical issues. The new strategy has been exploited to investigate how porosity affects the stability of slender elastic objects exposed to a uniform stream. To understand under which conditions porosity becomes important, we propose a simple resonance mechanism between a properly defined characteristic porous time-scale and the standard characteristic hydrodynamic time-scale. The resonance condition results in a critical value for the porosity above which porosity is important for the resulting filament flapping regime, otherwise its role can be considered of little importance. Our estimation for the critical value of the porosity is in fairly good agreement with our DNS results. The computations also allow us to quantitatively establish the stabilizing role of porosity in the flapping regimes.