On the transient dynamics of the wake and trajectory of free falling cones with various apex angles

Abstract

The early free fall stages of cones with a density ratio 1.18 and apex angles of $30^{\circ }$, $45^{\circ }$, $60^{\circ }$, and $90^{\circ }$ were studied using a wireless 3-axis gyroscope and accelerometer to describe the cone 3D motions, while particle image velocimetry was used to capture the induced flow in the near wake. The Reynolds number based on the cones diameter and the velocity at which the cone reaches the first local velocity maximum is found to consistently set the limit between two distinctive states. Relatively rapid growth in the cone nutation and departure from the vertical axis is observed after this Re is reached. Sequences of vertical velocity, swirling strength, LES-decomposed velocity, and pressure fields show the formation and growth of a large and initially symmetric recirculation bubble at the cone base. Those also highlight the presence of a symmetric 3D vortex rollup dominating the near wake in the early stages of the fall. A shear layer develops at the edge of the wake and manifests in the periodic shedding of Kelvin–Helmholtz vortices that, due to the nature of the recirculation bubble, reorganize to constitute a part of the rollup. Later in the fall, the wake loses symmetry and shows high population of vortical structures leading to turbulence. The asymmetric wake leads to strong interactions between the flow field and the cone evidenced by the shedding of a part of the 3D large-scale vortex rollup. This shedding process along with the cone rotation around its own axis provides a possible explanation of the helical wake structure observed in other studies.