Paul S. Krueger

The significance of vortex ring formation to the impulse and thrust of a starting jet

The recent work of Gharib, Rambod, and Shariff [J. Fluid Mech. 360, 121 (1998)] studied vortex rings formed by starting jets generated using a piston-cylinder mechanism. Their results showed that vortex rings generated from starting jets stop forming and pinch off from the generating jet for sufficiently large values of the piston stroke to diameter ratio (L/D), suggesting a maximization principle may exist for propulsion utilizing starting jets. The importance of vortex ring formation and pinch off to propulsion, however, rests on the relative contribution of the leading vortex ring and the trailing jet (which appears after pinch off) to the impulse supplied to the flow. To resolve the relative importance of the vortex ring and trailing jet for propulsion, a piston-cylinder mechanism attached to a force balance is used to investigate the impulse and thrust generated by starting jets for L/D ratios in the range 2–8. Two different velocity programs are used, providing two different L/D values beyond which pinch off is observed, in order to determine the effect of vortex ring pinch off. Measurements of the impulse associated with vortex ring formation show it to be much larger than that expected from the jet velocity alone and proportionally larger than that associated with a trailing jet for L/D large enough to observe pinch off. The latter result leads to a local maximum in the average thrust during a pulse near L/D values associated with vortex rings whose circulation has been maximized. These results are shown to be related to the nozzle exit over-pressure generated during vortex ring formation. The over-pressure is in turn shown to be associated with the acceleration of ambient fluid by vortex ring formation in the form of added and entrained mass.

Swimming dynamics and propulsive efficiency of squids throughout ontogeny

Squids encounter vastly different flow regimes throughout ontogeny as they undergo critical morphological changes to their two locomotive systems: the fins and jet. Squid hatchlings (paralarvae) operate at low and intermediate Reynolds numbers (Re) and typically have rounded bodies, small fins, and relatively large funnel apertures, whereas juveniles and adults operate at higher Re and generally have more streamlined bodies, larger fins, and relatively small funnel apertures. These morphological changes and varying flow conditions affect swimming performance in squids. To determine how swimming dynamics and propulsive efficiency change throughout ontogeny, digital particle image velocimetry (DPIV) and kinematic data were collected from an ontogenetic range of long-finned squid Doryteuthis pealeii and brief squid Lolliguncula brevis swimming in a holding chamber or water tunnel (Re = 20-20 000). Jet and fin wake bulk properties were quantified, and propulsive efficiency was computed based on measurements of impulse and excess kinetic energy in the wakes. Paralarvae relied predominantly on a vertically directed, high frequency, low velocity jet as they bobbed up and down in the water column. Although some spherical vortex rings were observed, most paralarval jets consisted of an elongated vortical region of variable length with no clear pinch-off of a vortex ring from the trailing tail component. Compared with paralarvae, juvenile and adult squid exhibited a more diverse range of swimming strategies, involving greater overall locomotive fin reliance and multiple fin and jet wake modes with better defined vortex rings. Despite greater locomotive flexibility, jet propulsive efficiency of juveniles/adults was significantly lower than that of paralarvae, even when juvenile/adults employed their highest efficiency jet mode involving the production of periodic isolated vortex rings with each jet pulse. When the fins were considered together with the jet for several juvenile/adult swimming sequences, overall propulsive efficiency increased, suggesting that fin contributions are important and should not be overlooked in analyses of the swimming performance of squids. The fins produced significant thrust and consistently had higher propulsive efficiency than did the jet. One particularly important area of future study is the determination of coordinated jet/fin wake modes that have the greatest impact on propulsive efficiency. Although such research would be technically challenging, requiring new, powerful, 3D approaches, it is necessary for a more comprehensive assessment of propulsive efficiency of the squid dual-mode locomotive system.

Thrust augmentation and vortex ring evolution in a fully pulsed jet

The time-averaged thrust of an incompressible fully pulsed jet containing a period of no flow between pulses is studied experimentally as a function of pulsing duty cycle Sr_L and the ratio of the ejected slug length (per pulse) to the jet diameter L/D. The parameter ranges investigated were 2≤L/D≤6 and 0.1≤Sr_L≤0.98. Significant thrust augmentation by pulsing was observed over the entire parameter range tested, both in terms of thrust compared to an equivalent steady jet with identical mass flux, denoted F_(SJ) >1, and in terms of thrust compared to an equivalent intermittent jet where vortex ring formation by pulsation was ignored, denoted F_(IJ) >1. F_(SJ) as high as 1.90 (90% thrust augmentation) was observed for the smaller L/D as Sr_L approached 1.0 (with larger F_(SJ) at lower Sr_L). The F_(IJ) results, which directly measured overpressure at the nozzle exit plane developed during vortex ring formation as the mechanism responsible for thrust augmentation, showed reduced augmentation at large L/D and Sr_L. The L/D dependence of F_(IJ) parallels single-pulse (Sr_L =0) results previously studied by the authors. The Sr_L dependence of F_(IJ) was linked to the interaction of forming vortex rings with vorticity from preceding pulses using digital particle image velocimetry (DPIV) measurements of the vorticity field. DPIV also revealed that the vortex rings tended to wander off axis and disintegrate as Sr_L became sufficiently large.

The formation number of vortex rings formed in uniform background co-flow

The formation of vortex rings generated by an impulsively started jet in the presence of uniform background co-flow is studied experimentally to extend previous results. A piston–cylinder mechanism is used to generate the vortex rings and the co-flow is supplied through a transparent shroud surrounding the cylinder. Digital particle image velocimetry (DPIV) is used to measure the development of the ring vorticity and its eventual pinch off from the generating jet for ratios of the co-flow to jet velocity (

Pulsed jet dynamics of squid hatchlings at intermediate Reynolds numbers

R_{v})

Propulsive efficiency of a biomorphic pulsed-jet underwater vehicle

in the range 0 – 0.85. The formation time scale for the ring to obtain maximal circulation and pinch off from the generating jet, called the formation number (

Vortex ring pinchoff in the presence of simultaneously initiated uniform background co-flow

F

Hydrodynamic fin function of brief squid, Lolliguncula brevis

), is determined as a function of

Vortex Rings in Bio-Inspired and Biological Jet Propulsion

R_{v}

The effect of Reynolds number on the propulsive efficiency of a biomorphic pulsed-jet underwater vehicle.

using DPIV measurements of circulation and a generalized definition of dimensionless discharge time or ‘formation time’. Both simultaneous initiation and delayed initiation of co-flow are considered. In all cases, a sharp drop in