Flutter of an elastic plate in a channel flow: Confinement and finite-size effects

Passive elastic mechanism to mimic fish-muscle action in anguilliform swimming

“…The flag term is known to cause the beam to flutter above a critical flow velocity (this is called the flapping-flag instability, e.g. [29,[37][38][39]). In the range of parameters of the experiments (m % 0:96,Ũ [ ½0:2 À 4 and a [ ½50 À 150), the dissipative part has an order of magnitude 10-30 times greater than the other dimensionless fluid term, which makes it the main fluid contribution in the dynamical balance.…”

The origin of hysteresis in the flag instability

“…When the plate aspect ratio is asymptotically small however, the aerodynamic forces can be modelled using slender-body theory (Datta & Gottenberg 1975;Lemaitre et al 2005). The studies in these two asymptotic limits have been recently generalised by Eloy et al (2007) and Doaré et al (2011) who considered intermediate aspect ratios and confinement effects.…”

Effect of spanwise confinement on flag flutter: Experimental measurements

“…The experimental results show a good agreement with a model derived in a previous paper. 13 Velocity profiles and boundary layer thickness have been measured, showing that in the experiments, the gap sizes of interest, i.e., sizes small enough for the critical flow velocity to be significantly affected by the presence of the wall are of comparable magnitude as the boundary layer. It was shown that the dominant effect of the boundary layer should be stabilization so that the destabilization observed when c decreases can only be explained by a blockage effect in a purely potential flow model.…”

“…A reduction of the critical velocity was found but not important enough to reach the 2D limit, raising the question of the validity of the above mentioned assumption. This motivated the development of a 3D model taking into account the effect of spanwise boundaries, as proposed by Doaré et al 13 This model involves a matching between extended versions of the slender-body and 2D theories that take into account the spanwise confinement. The main result of the latter work is that the 2D limit is indeed reached when the gap tends to zero but with such a slow convergence that it should be almost impossible to attain this limit experimentally.…”

“…In the following, the 3D model of Eloy et al 10 will be referred to as the 3D 1 model, as it considers a 3D unbounded flow. The 3D model of Doaré et al 13 will be referred to as the 3D c model, as it considers a 3D flow with a clearance c between the plate and the wall.…”