Impact of jet velocity profile on the propulsive performance and vortex ring formation of pulsed jet propulsion

A squid-inspired jet propulsion system that indudes a deformable body and a nozzle exit attached to it is numerically studied. By prescribing the body deformation during a single discharge, we examine the impact of jet speed profiles on the vortex ring formation and propulsion performance of the system. Our results show that a secondary vortex ring following the leading vortex ring can be produced by the reverse cosine jet speed pattern at a given maximum stroke ratio, and for the other profiles (i.e., constant, cosine, reverse cosine, half cosine and rever half cosine styles) only distributed vortices are seen behind the leading vortex ring. The constant jet speed produces the largest time-averaged thrust due to jet momentum flux related thrust associated with its large jet speed. Except for the constant speed style, the largest mean thrust production and propulsion factor are obtained by the reverse cosine profile among the other four styles attributed to the formation of the secondary vortex ring. Nevertheless, this secondary vortex ring would not be produced at a small maximum stroke ratio for the reverse cosine speed fashion. We also find that the mean thrust production can reach a maximum under a specific maximum stroke ratio (Γ_m = 7.60) when two vortex rings are produced. This work may provide insight into the mechanical and control design of jet-based biomimetic propellers and robots.