Harmonic forcing of a laminar bluff body wake with rear pitching flaps

Abstract

A numerical study on the response of a two-dimensional bluff body wake subjected to harmonic forcing imposed by two rear pitching flaps is performed. The wake is generated by a rectangle at a height-based Reynolds number $Re=100$ , characterised by laminar vortex shedding. Two forcing strategies are examined corresponding to in-phase ‘snaking’ and out-of-phase ‘clapping.’ The effects of the bluff body aspect ratio ( $AR=1,2,4$ ), flapping frequency, flapping amplitude, flap length and Reynolds number are investigated. For the snaking motion, a strong fundamental resonance of the root mean square (r.m.s.) drag is observed when the wake is forced near the vortex shedding frequency. For the clapping motion, a weak subharmonic resonance is observed when the forcing is applied near twice the vortex shedding frequency resulting in an increase of the lift r.m.s. whereas the drag r.m.s. remains unaffected. Both resonances intensify the vortex shedding and a concomitant mean drag increase is observed for the snaking motion. Forcing away from the resonant regimes, both motions result in considerable drag reduction through wake symmetrisation and propulsion mechanisms. The formation of two vortex dipoles per oscillation period due to the flapping motion, which weaken the natural vortex shedding, has been identified as the main symmetrisation mechanism. A single scaling parameter is proposed to collapse the mean drag reduction of the forced flow for both motions over a wide range of flapping frequencies, amplitudes and flap lengths. Finally, the assessment of the performance of the forcing strategies has revealed that clapping is more effective than snaking.