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.
The aim of the present numerical study is to show that the recently developed Alternating Direction Reconstruction Immersed Boundary Method (ADR-IBM) (Giannenas and Laizet in Appl Math Model 99:606–627, 2021) can be used for Fluid–Structure Interaction (FSI) problems and can be combined with an Actuator Line Model (ALM) and a Computer-Aided Design (CAD) interface for high-fidelity simulations of fluid flow problems with rotors and geometrically complex immersed objects. The method relies on 1D cubic spline interpolations to reconstruct an artificial flow field inside the immersed object while imposing the appropriate boundary conditions on the boundaries of the object. The new capabilities of the method are demonstrated with the following flow configurations: a turbulent channel flow with the wall modelled as an immersed boundary, Vortex Induced Vibrations (VIVs) of one-degree-of-freedom (2D) and two-degree-of-freedom (3D) cylinders, a helicopter rotor and a multi-rotor unmanned aerial vehicle in hover and forward motion. These simulations are performed with the high-order fluid flow solver which is based on a 2D domain decomposition in order to exploit modern CPU-based supercomputers. It is shown that the ADR-IBM can be used for the study of FSI problems and for high-fidelity simulations of incompressible turbulent flows around moving complex objects with rotors.
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