Dynamics and energies of a wall-clamped flexible membrane in two different cross-flows

Abstract

In order to provide useful guidelines for optimizing piezoelectric energy harvesting designs under near-wall conditions, we experimentally investigate and compare the dynamics and energies of a wall-clamped flexible membrane (FM) in two different cross-flows, i.e., a separated flow induced by a forward-facing step (FFS) and a boundary layer (BL) flow, aiming at revealing the combined effects of the incoming flow and wall contact on flapping dynamics. Four dynamic modes were identified in both the FFS and BL cases by varying flow velocity and FM length: quasi-steady, regular-flapping, tip-contact, and body-contact modes. In the FFS cases, the recirculation zone induced by the step prevents the FM from lodging, whereas in the BL cases, the FM exhibits suppressed amplitudes and near-wall flapping behavior. The evolution of the two contact modes was examined in details, and the variations in contact time and contact distance during the transition between these two modes were quantitatively evaluated. Three-dimensional effects manifest differently in each case, with the FFS showing primarily spanwise bending and the BL case exhibiting pronounced twisting that impacts flapping stability. Energy analysis further reveals that, at high flow velocity, the FM's kinetic energy dominates over elastic strain energy, with significant energy dissipation occurring during wall contact.