Effect of nozzle geometry on the performance of pulsed-jet propulsion at low Reynolds number

Abstract

A pulsed-jet propulsive system which includes a deformable body and a nozzle affixed to it is proposed and numerically examined. The impact of nozzle geometry on the performance of the system during a single discharge at low Reynolds number is studied. A force decomposition algorithm is employed to decouple the thrust into three parts: normal stress at exit, jet flux, and time derivative of internal fluid momentum. This approach enables the investigation of underlying physics in thrust generation. Since its jet flow features negative radial velocity, the system with converging nozzles is found to produce over-pressure (dominant component of the exit normal stress) on the nozzle exit, making positive contributions to thrust. The diverging nozzles, with reversed radial velocity, tend to induce negative pressure on the exit, which diminishes the thrust generation. On the other hand, the contribution from exit pressure only accounts for a relatively small portion of the thrust, which is found to be dominated by the jet flux momentum. As a result, with fixed stroke ratio and time history of deformation the overall thrust generated by the system is determined mostly by the exit size of the nozzle D′. Specifically, the time-averaged thrust Ft¯ is found to be proportional to 1/D′4. The geometry of the nozzle also affects the efficiency. For example, the system without a nozzle turns out to be most efficient, followed by one with a short and divergent nozzle.