A free flexible flap in channel flow

Abstract

Fine fibre immersed in different flows is ubiquitous. For a fibre in shear flows, most motion modes appear in the flow-gradient plane. Here the two-dimensional behaviours of an individual flexible flap in channel flows are studied. The nonlinear coupling of the fluid inertia ( $\textit {Re}$ ), flexibility of the flap ( $K$ ) and channel width ( $W$ ) is discovered. Inside a wide channel (e.g. $W=4$ ), as $K$ decreases, the flap adopts rigid motion, springy motion, snake turn and complex mode in sequence. It is found that the fluid inertia tends to straighten the flap. Moreover, $\textit {Re}$ significantly affects the lateral equilibrium location $y_{eq}$ , therefore affecting the local shear rate and the tumbling period $T$ . For a rigid flap in a wide channel, when $\textit {Re}$ exceeds a threshold, the flap stays inclined instead of tumbling. As $\textit {Re}$ further increases, the flap adopts swinging mode. In addition, there is a scaling law between $T$ and $\textit {Re}$ . For the effect of $K$ , through the analysis of the torque generated by surrounding fluid, we found that a smaller $K$ slows down the tumbling of the flap even if $y_{eq}$ is comparable. As $W$ decreases, the wall confinement effect makes the flap easier to deform and closer to the centreline. The tumbling period would increase and the swinging mode would be more common. When $W$ further decreases, the flaps are constrained to stay inclined, parabolic-like or one-end bending configurations moving along with the flow. Our study may shed some light on the behaviours of a free fibre in flows.