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

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.This work was supported by grants TRA2013-41103-P (Mineco/Feder UE) and DPI2016-76151-C2-2-R (AEI/Feder UE). MGV was partially supported by a grant of the BBVA Foundation. The code was partially developed during a stay of MM (funded by BBVA) and MGV (funded by the Spanish Ministry of Education through the program José Castillejo) at the Karlsruhe Institute of Technology. The simulations were partially performed at the Steinbuch Centre for Computing (SCC), Karlsruhe. The computer resources, technical expertise and assistance provided by this center are thankfully acknowledged.Publicad