Stability of Kirigami parachutes in effectively infinite numerical domains

Abstract

Kirigami, the art of cutting flat sheets into deployable 3D structures, has recently inspired a new class of parachutes which can deploy into a naturally stable inverted canopy. However, the dynamic mechanism, fluid forces, and geometrical parameters that grant this stability have not yet been clearly identified. In this paper, we use a novel Biot-Savart far-field boundary condition to perform prescribed acceleration and free-falling simulations in effectively infinite domains, tracking the descent of a parameterized kirigami parachute. The far-field velocity is reconstructed from the interior vorticity, resulting in less than 0.1% variation in the predicted dynamics as the domain size is doubled. We first show the linear forces drop 2-5 times as the parachute is deployed due to increased permeability, whereas the moments increase due the counterbalancing effect of the increased lever-arm. Next, we find that the kirigami parachute achieves stable flight for deployment heights as small as half its radius, quickly damping out applied perturbations. For smaller deployments, the parachute tumbles due to side-slip and rotational coupling, as in falling disks. These effectively unbounded simulations identify that deployments approximately equal to the radius offer high drag forces with strong dynamic stability, providing a simple design rule for deployable parachutes.