Experimental study on the vortex structure and path instability of freely falling annular disks

Bodies freely falling in steady water or air are common scenes encountered in various scientific and engineering fields, including the flapping flight of birds and the reentry of a space shuttle. In this work, the freely falling annular thin disks with small dimensionless moments of inertia I* and Reynolds number Re are investigated experimentally in a water tank. We use stereoscopic vision to record the position and orientation of the disks. The flow structure behind the disks is studied by applying fluorescent dye visualization and PIV method. Varying the geometry dimensionless parameter (the inner to outer diameter ratio η and I*) of the disks reveals two new falling patterns. When η_crit1=0.6<η<η_crit2=0.8, the disks show a random lateral vibration while falling. For high η_crit2>0.8, the circular vortex loops shed frequently from the disk, which causes a lengthways vibration superimposed onto straight vertical motion. We also observe another two falling patterns reported previously: hula-hoop and helical motion. By comparing the wake structure of the two motions, we find that the vortex layer twists more violently in the hula-hoop motion, which is the reason for the different trajectory between them. Further research on flow field reveals that the torque on the disk that causes the vibration is due to the formation, elongation and shedding of the vortex.