A free flexible flap in channel flow

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 ( 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, Re significantly affects the lateral equilibrium location yeq , therefore affecting the local shear rate and the tumbling period T . For a rigid flap in a wide channel, when Re exceeds a threshold, the flap stays inclined instead of tumbling. As Re further increases, the flap adopts swinging mode. In addition, there is a scaling law between T and 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 yeq 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.