Numerical study of a freely-falling maple seed

Abstract

Many winged seeds such as those of maples exploit autorotation to decrease the descending velocity and increase the dispersal distance for their conservation of species. They have a simple configuration without neuromuscular control for driving as in animal flight, and even those with damaged wing can still autorotate. It means that autorotating seeds have a mechanically robust design unlike the flapping or rotating-blade mechanism, and thus they fascinate many researchers to develop micro air vehicles (MAVs) equipped with sensors for the reconnaissance, munition, and atmospheric researches. In this study, high-fidelity numerical simulations are conducted for flow around a freely-falling maple seed using an immersed boundary method in a non-inertial reference frame. A three-dimensional seed model is obtained by scanning a maple seed (Acer palmatum). The seed reaches a steady autorotation after a transient period. This transient period depends on the initial position of a seed and is shorter when the wing leading edge or nut or trailing edge of the seed is initially positioned upward. During autorotation, a stable leading-edge vortex is attached on the surface of the rotating seed. Two different approaches are considered to obtain scaling laws describing the relation among the seed weight and geometry, and descending and rotating velocities. The first uses the conservation of mass, linear and angular momentum, and energy. In this approach, a model constant to be determined, called the axial induction factor, is obtained from the result of present simulation. The second approach employs a classical steady wing theory in which the vortical strength is scaled with the circulation around a wing and the lift force is modeled by the time derivative of vortical impulse. Available data from winged seeds are applied to the present scaling laws, showing excellent collapses onto the scaling laws. These theoretical analyses can provide a simple guideline for researchers who seek the evolutionary direction of the morphologies and kinematics on autorotating seeds or who design autorotation-based micro air vehicles.