Thrust and torque production of a squid-inspired swimmer with a bent nozzle for thrust vectoring

A three-dimensional pulsed-jet propulsion model consisting of a flexible body and a steerable bent nozzle in tethered mode is presented and studied numerically. By prescribing the body deformation and nozzle angle, we examine the flow evolution and propulsive/turning performance via thrust vectoring. Our results show that the vortex ring is no longer axis-symmetric when the jet is ejected at an angle with the incoming flow. A torque peak is observed during jetting, which is mainly sourced from the suction force (negative pressure) at the lower part of the internal nozzle surface when the flow is directed downward through an acute angle. After this crest, the torque is dominated by the positive pressure at the upper part of the internal nozzle surface, especially at a relatively low jet-based Reynolds number (O(10²)). The torque production increases with a larger nozzle bent angle as expected. Meanwhile, the thrust production remains almost unchanged, showing little trade-off between thrust and torque production which demonstrates the advantage of thrust vectoring via a bent nozzle. By decoupling the thrust at the internal and outer surfaces considering special characteristics of force generation by pulsed-jet propulsion, we find that variations in Reynolds number mostly affect the viscous friction at the outer surfaces. The influence of the maximum stroke ratio is also studied. Results show that both the time-averaged thrust and the torque decrease at a larger stroke ratio.