The effect of the velocity program and duty cycle (St(L)) on the propulsive efficiency of pulsed-jet propulsion was studied experimentally on a self-propelled, pulsed-jet underwater vehicle, dubbed Robosquid due to the similarity of essential elements of its propulsion system with squid jet propulsion. Robosquid was tested for jet slug length-to-diameter ratios (L/D) in the range 2-6 and St(L) in the range 0.2-0.6 with jet velocity programs commanded to be triangular or trapezoidal. Digital particle image velocimetry was used for measuring the impulse and energy of jet pulses to calculate the pulsed-jet propulsive efficiency and compare it with an equivalent steady jet system. Robosquid's Reynolds number (Re) based on average vehicle velocity and vehicle diameter ranged between 1300 and 2700 for the conditions tested. The results indicated better propulsive efficiency of the trapezoidal velocity program (up to 20% higher) compared to the triangular velocity program. Also, an increase in the ratio of the pulsed-jet propulsive efficiency to the equivalent steady jet propulsive efficiency (eta(P)/eta(P, ss)) was observed as St(L) increased and L/D decreased. For cases of short L/D and high St(L), eta(P)/eta(P, ss) was found to be as high as 1.2, indicating better performance of pulsed jets. This result demonstrates a case where propulsion using essential elements of a biological locomotion system can outperform the traditional mechanical system equivalent in terms of efficiency. It was also found that changes in St(L) had a proportionately larger effect on propulsive efficiency compared to changes in L/D. A simple model is presented to explain the results in terms of the contribution of over-pressure at the nozzle exit plane associated with the formation of vortex rings with each jet pulse.
The effect of Reynolds number on the propulsive efficiency of pulsed-jet propulsion was studied experimentally on a self-propelled, pulsed-jet underwater vehicle, dubbed Robosquid due to the similarity of its propulsion system with squid. Robosquid was tested for jet slug length-to-diameter ratios (L/D) in the range 2-6 and dimensionless frequency (St(L)) in the range 0.2-0.6 in a glycerin-water mixture. Digital particle image velocimetry was used for measuring the impulse and energy of jet pulses from the velocity and vorticity fields of the jet flow to calculate the pulsed-jet propulsive efficiency, and compare it with an equivalent steady jet system. Robosquid's Reynolds number (Re) based on average vehicle velocity and vehicle diameter ranged between 37 and 60. The current results for propulsive efficiency were compared to the previously published results in water where Re ranged between 1300 and 2700. The results showed that the average propulsive efficiency decreased by 26% as the average Re decreased from 2000 to 50 while the ratio of pulsed-jet to steady jet efficiency (η(P)/η(P, ss)) increased up to 0.15 (26%) as the Re decreased over the same range and for similar pulsing conditions. The improved η(P)/η(P, ss) at lower Re suggests that pulsed-jet propulsion can be used as an efficient propulsion system for millimeter-scale propulsion applications. The Re = 37-60 conditions in the present investigation, showed a reduced dependence of η(P) and η(P)/η(P, ss)on L/D compared to higher Re results. This may be due to the lack of clearly observed vortex ring pinch-off as L/D increased for this Re regime.
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