The Significance of Vortex Ring Formation and Nozzle Exit Over-Pressure to Pulsatile Jet Propulsion

Citation

Krueger, Paul Samuel (2001) The Significance of Vortex Ring Formation and Nozzle Exit Over-Pressure to Pulsatile Jet Propulsion. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3QWF-8G05. https://resolver.caltech.edu/CaltechETD:etd-09142005-111030

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Pulsatile jet propulsion can be accomplished using a fully-pulsed jet (i.e., a periodic series of starting jets or pulses), the unsteady nature of which engenders vortex ring formation. The significance of vortex ring formation for this type of propulsion is studied experimentally using a piston-cylinder mechanism to generate starting and fully-pulsed, round jets of water into water at a maximum jet Reynolds number of 13,000. Starting jets are considered separately since they are the limiting case of a fully-pulsed jet at zero pulsing frequency. Direct measurements of the total impulse per pulse (starting jets) and time-averaged thrust (fully-pulsed jets) are made using a force balance. Hotfilm anemometry is used to measure the jet velocity and Digital Particle Image Velocimetry (DPIV) is used to measure vortex ring position, vorticity, energy, circulation, and impulse. The pulses for both types of jets are generated using piston stroke to diameter ratios (L/D) in the range 2 to 8 for piston velocity programs in a generally positive-sloping (PS) or negative-sloping (NS) family. The range of L/D considered brackets the transition between the case where an individual vortex ring is produced with each pulse (small L/D) and the case where the vortex ring stops growing and pinches off from its generating jet, producing a trailing jet (large L/D). This transition occurs at a higher L/D for the PS ramps, allowing the effects of vortex ring formation and pinch off to be illuminated by comparison of the results for the NS and PS ramps. The significance of vortex ring formation is first analyzed for starting jets. Measurements of the total impulse per pulse as a function of L/D show that a leading vortex ring adds more impulse per unit L/D than a trailing jet. This leads to a maximum in the average thrust during a pulse at the L/Ds just before vortex ring pinch off is observed for both the PS and NS ramps. The propulsive benefit provided by a leading vortex ring over a trailing jet is connected to over-pressure at the nozzle exit plane during vortex ring formation. DPIV measurements demonstrate that nozzle exit over-pressure also makes an important contribution to energy and circulation. It is shown that this over-pressure can be related to the momentum that must be supplied by the forming vortex ring to ambient fluid in the form of added and entrained mass. A model is proposed for nozzle exit over-pressure near the initiation of an impulsive velocity program where entrainment can be ignored. The model readily accounts for the pressure contribution to circulation in the NS ramps, but modeling of entrainment is required to properly determine impulse and energy. For the fully-pulsed jet experiments, a normalized thrust, [...], is introduced to characterize the pressure effects associated with vortex ring formation. The pulsing frequency is expressed in dimensionless form as [...], which is between 0 and 1 for all fully-pulsed jets. A propulsive benefit from pressure ([...]) is observed for all L/D and [...] considered. At low [...], the results are similar to those for the starting jets. At higher [...], [...] decreases with L/D as with the starting jets, which is related to the existence of vortex ring pinch off for all observed [...]. At a fixed L/D, two dominant decreasing trends in [...] with [...] appear and seem to be related to the effects of previously ejected pulses on forming vortex rings. No dramatic increase in [...] with [...] (associated with the increased convective velocity of multiple coaxial vortex rings over that of individual vortex rings) is observed since (a) the ring separation is never reduced low enough to see an increase in the ring velocity (even for [...]), and (b) the vortex rings don't remain coaxial or coherent as [...].

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