Kinematics and dynamics of the auto-rotation of a model winged seed

Abstract

Numerical simulations of the auto-rotation of a model winged seed are presented. The calculations are performed by solving simultaneously the Navier-Stokes equations for the flow surrounding the seed and the rigid-body equations for the motion of the seed. The Reynolds number based on the descent speed and a characteristic chord length is varied in the range 80-240. Within this range, the seed attains an asymptotic state with finite amplitude auto-rotation, while for smaller values of the Reynolds number no auto-rotation is observed. The motion of the seed is characterized by the coning and pitch angles, the angular velocity and the horizontal translation of the seed. The values obtained for these quantities are qualitatively similar to those reported in the literature in experiments with real winged seeds. When increasing the Reynolds number, the seed tends to rotate at higher speeds, with less inclination with respect to the horizontal plane, and with a larger translation velocity. With respect to the aerodynamic forces, it is observed that, with increasing Reynolds number, the horizontal components decrease in magnitude while the vertical component increases. The force distribution along the wing span is characterized using both global and local characteristic speeds and chord lengths for the non-dimensionalisation of the force coefficients. It is found that the vertical component does not depend on the Reynolds number when using local scaling, while the chordwise component of the force does.

A Numerical Study of the Flow Around a Model Winged Seed in Auto-Rotation

“…Although the aim of this work is to characterize the flow, we start by summarizing the resulting motion of the seed and its variation with Re. More details can be found in Arranz et al [2].…”

“…The most important difference between the present code and the algorithm proposed by Uhlmann [33] is that the latter is designed to deal with spheres, where only their angular velocity and acceleration is needed (i.e., not their angular orientation). In the present simulations it is necessary to track the orientation of the seed, which is accomplished with the quaternion formulation described in Arranz et al [2]. The present algorithm has been validated by computing the motion of an oblate spheroid of aspect ratio 1.5 and density ratio ρ s /ρ f = 2.14 (where ρ s and ρ f are the spheroid and fluid density, respectively) settling under gravity in ambient fluid, a configuration for which high-fidelity data from a boundary-conforming spectral-element method is available [7].…”

“…where ρ s is the density of the seed. A more complete description of the geometric and inertial model of the seed can be found in Arranz et al [2].…”

“…The grid resolution consists of 512 3 grid points, which is equivalent to 48 points per chord length. The resolution was selected after performing a grid refinement study presented in Arranz et al [2]. In addition to the grid for the fluid domain, a Lagrangian grid for the seed needs to be defined.…”

“…The present paper focus on the analysis of the latter. Although we also briefly discuss the motion of the winged seed (since it affects the flow), the detailed analysis of the kinematics and dynamics of the seed is reported elsewhere [2].…”