An Experimental Study Of Flag Flutter

International audienceThe study of flag flutter or the vibration of flexible plates is of critical importance in the understanding of many industrial problems, like paper printing (Watanabe et al. 2002a) and ae roelasticity of airplane wings, or biological subjects, for instance the dynamics of fish swimming or the human upper airway (Balint et al. 2005). We present an experimental study of the flutter instability of a flag. Our experiments are performed in a horizontal wind tunnel with a free stream velocity varying up to 20 m/s. One end of the flag is clamped to a pro¯led and vertical mast, the other end is left free. The flags tested are made of several materials (paper, plastic,...) of different flexural rigidity. At low velocities, the flag is parallel to the flow and motionless. Above a critical wind velo city, the flag exhibits periodic oscillations. The bifurcation is subcritical and the system shows a strong hysteresis cycle. We particulary focus on the variation of the instability threshold with respect to two non dimensional parameters : the mass ratio M (built upon the fluid density, the length L in the streamwise direction and the surface density of the flag) and the aspect ratio h/L where h is the flag span. When the mass ratio increases, different instability modes appear. We also find that the instability threshold decreases with increasing aspect ratio : for constant length, narrow flags are the most stable. This is in agreement with a recent theoretical study taking into account the finite aspect ratio of the flags (Eloy, Souilliez & Schouveiler 2005) Eventually, at highest h/L, a three dimensional mo- tion appears : the corners of the flag fold themselves up intermittently, the flutter instability is delayed and the threshold in no longer a decreasing function of h/L