Pulsed-jet Propulsion Research Articles

Impact of jet velocity profile on the propulsive performance and vortex ring formation of pulsed jet propulsion

A squid-inspired jet propulsion system that indudes a deformable body and a nozzle exit attached to it is numerically studied. By prescribing the body deformation during a single discharge, we examine the impact of jet speed profiles on the vortex ring formation and propulsion performance of the system. Our results show that a secondary vortex ring following the leading vortex ring can be produced by the reverse cosine jet speed pattern at a given maximum stroke ratio, and for the other profiles (i.e., constant, cosine, reverse cosine, half cosine and rever half cosine styles) only distributed vortices are seen behind the leading vortex ring. The constant jet speed produces the largest time-averaged thrust due to jet momentum flux related thrust associated with its large jet speed. Except for the constant speed style, the largest mean thrust production and propulsion factor are obtained by the reverse cosine profile among the other four styles attributed to the formation of the secondary vortex ring. Nevertheless, this secondary vortex ring would not be produced at a small maximum stroke ratio for the reverse cosine speed fashion. We also find that the mean thrust production can reach a maximum under a specific maximum stroke ratio (Γm = 7.60) when two vortex rings are produced. This work may provide insight into the mechanical and control design of jet-based biomimetic propellers and robots.

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.

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

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.

Pulsed-jet propulsion of a squid-inspired swimmer at high Reynolds number

An inflation–deflation propulsion system inspired by the jet propulsion mechanism of squids and other cephalopods is proposed. The two-dimensional squid-like swimmer has a flexible mantle body with a pressure chamber and a nozzle that serves as the inlet and outlet of water. The fluid–structure interaction simulation results indicate that larger mean thrust production and higher efficiency can be achieved in high Reynolds number scenarios compared with the cases in laminar flow. The improved performance at high Reynolds number is attributed to stronger jet-induced vortices and highly suppressed external body vortices, which are associated with drag force. Optimal efficiency is reached when the jet vortices start to dominate the surrounding flow. The mechanism of symmetry-breaking instability under the turbulent flow condition is found to be different from that previously reported in laminar flow. Specifically, this instability in turbulent flow stems from irregular internal body vortices, which cause symmetry breaking in the wake. A higher Reynolds number or smaller nozzle size would accelerate the formation of this symmetry-breaking instability.

Pulsed-jet propulsion via shape deformation of an axisymmetric swimmer

By using an axisymmetric immersed-boundary model, we numerically investigate the thrust generation of a deformable body via pulsed jetting. We focus on a single discharging process resulting from the deflation of the body as inspired by the jetting mechanism of cephalopods, such as squids. We examine three jet velocity profiles, namely, impulsive, half-cosine, and cosine, in the relatively low Reynolds number regime. For the impulsive profile, we demonstrate via wake visualization that the leading vortex ring does not pinch off from the trailing jet although its circulation stops growing after a critical formation number (hereby, the formation number is defined as the ratio between the length and diameter of the jet plug) of 6–7. The exact value of the critical formation number depends on the jet velocity profile, suggesting that jet acceleration and viscous dissipation play significant roles in vortex ring evolution. In terms of thrust generation, our results indicate that besides the jet momentum flux, an important source of thrust generation is jet acceleration. The implication is that the jet velocity profile is a key factor in determining the propulsive performance.

The genome of the giant Nomura\u2019s jellyfish sheds light on the early evolution of active predation

BackgroundUnique among cnidarians, jellyfish have remarkable morphological and biochemical innovations that allow them to actively hunt in the water column and were some of the first animals to become free-swimming. The class Scyphozoa, or true jellyfish, are characterized by a predominant medusa life-stage consisting of a bell and venomous tentacles used for hunting and defense, as well as using pulsed jet propulsion for mobility. Here, we present the genome of the giant Nomura’s jellyfish (Nemopilema nomurai) to understand the genetic basis of these key innovations.ResultsWe sequenced the genome and transcriptomes of the bell and tentacles of the giant Nomura’s jellyfish as well as transcriptomes across tissues and developmental stages of the Sanderia malayensis jellyfish. Analyses of the Nemopilema and other cnidarian genomes revealed adaptations associated with swimming, marked by codon bias in muscle contraction and expansion of neurotransmitter genes, along with expanded Myosin type II family and venom domains, possibly contributing to jellyfish mobility and active predation. We also identified gene family expansions of Wnt and posterior Hox genes and discovered the important role of retinoic acid signaling in this ancient lineage of metazoans, which together may be related to the unique jellyfish body plan (medusa formation).ConclusionsTaken together, the Nemopilema jellyfish genome and transcriptomes genetically confirm their unique morphological and physiological traits, which may have contributed to the success of jellyfish as early multi-cellular predators.

A Soft Aquatic Actuator for Unsteady Peak Power Amplification

A soft hydraulic actuator is presented which uses elastic energy storage for the purpose of pulsed-jet propulsion of soft unmanned underwater vehicles. The actuator consists of a flexible membrane that can be inflated using a micropump and whose elastic potential energy may be released on demand using a controllable valve, in a manner inspired by the swimming of squids and octopuses. It is shown that for equivalent initial elastic energy, the drop in peak thrust is linearly proportional to the decrease in nozzle cross section. Peak hydraulic power amplification of the soft actuator of approximately 75% is achieved with respect to that of the driving pump, confirming that passive elasticity can be exploited in aquatic propulsion to replicate the explosive motion skills of agile sea-dwelling creatures.

Patterns for efficient propulsion during the energy evolution of vortex rings

Compared with steady-jet propulsion, pulsed-jet propulsion can exhibit more efficient by manipulating the unsteady formation of vortex rings in the near wake. That is, energy is much better transferred and used in the form of vortices to generate propulsive force rather than a steady jet. This study is aimed at analyzing the energy evolution of vortex rings and revealing the patterns for efficient propulsion during the energy evolution. Of particular importance to the energy evolution of vortex rings is the pinch-off mechanism, which is owing to the limiting effects of energy and causes that vortex rings cannot grow indefinitely. Canonical vortex rings are generated by using a piston–cylinder apparatus and their time-dependent flow fields are measured using digital particle image velocimetry. During the energy evolution of vortex rings, overpressure and fluid flux at the exit plane are found to significantly contribute to their energy. Moreover, overpressure is the dominant pattern contributing to the energy of vortex rings and has a greater contribution than fluid flux at the early evolution stage, whereas the contribution of overpressure nearly disappears once vortex rings pinch off. By contrast, fluid flux continuously contributes to the energy of vortex rings until they physically separate from the trailing vortices. Based on the hyperbolic LCSs, distinguishable flow patterns are detected to correspond to the energy evolution of vortex ring. The appearance of a newly disconnected LCS in the trailing jet indicates the initial roll-up of a trailing vortex and the onset of pinch-off, which coincides with the end of overpressure contribution to the energy of vortex rings. A LCS barrier behind the vortex rings appears and prevents any fluid flux from entering the vortex rings, thereby indicating the end of pinch-off and corresponding to the end of fluid-flux contribution. Moreover, it is suggested that transferring or using energy by pressure is a more efficient pattern than fluid flux to generate hydrodynamic force, and enlarging the energy contribution to vortices can further enhance propulsive performance.

Hybrid parameter identification of a multi-modal underwater soft robot

We introduce an octopus-inspired, underwater, soft-bodied robot capable of performing waterborne pulsed-jet propulsion and benthic legged-locomotion. This vehicle consists for as much as 80% of its volume of rubber-like materials so that structural flexibility is exploited as a key element during both modes of locomotion. The high bodily softness, the unconventional morphology and the non-stationary nature of its propulsion mechanisms require dynamic characterization of this robot to be dealt with by ad hoc techniques. We perform parameter identification by resorting to a hybrid optimization approach where the characterization of the dual ambulatory strategies of the robot is performed in a segregated fashion. A least squares-based method coupled with a genetic algorithm-based method is employed for the swimming and the crawling phases, respectively. The outcomes bring evidence that compartmentalized parameter identification represents a viable protocol for multi-modal vehicles characterization. However, the use of static thrust recordings as the input signal in the dynamic determination of shape-changing self-propelled vehicles is responsible for the critical underestimation of the quadratic drag coefficient.

Underwater soft-bodied pulsed-jet thrusters: Actuator modeling and performance profiling

A new kind of underwater vehicle is developed by taking inspiration from cephalopods. Its actuation routine is scrutinized via a suitable model. Similar to octopuses and squids, these vehicles consist of an elastic, hollow shell capable of undergoing sequential stages of ingestion and ejection of ambient fluid, which is driven by the recursive inflation and deflation of the shell. The shell actively collapses, and in this way it expels water through a funnel; then it passively returns to the inflated shape, drawing ambient fluid into the cavity. By doing so, a pulsed-jet propulsion routine is performed that enables the vehicle to propel itself in water. Due to their soft nature, the actuation of these vehicles is largely dependent on the subtle management of the elastic response of the shell throughout the propulsion routine. A kinematic model of the actuation mechanism, thoroughly corroborated by experimental validation, is devised which elucidates the relationship between the active (collapse) and passive (refill) stages of the actuation. Upon association with the dynamics of the vehicle, this model permits the derivation of the generic performance profiles of this new kind of vehicle. It is acknowledged that, for given design specifications, an optimal swimming speed exists in coincidence with the coordinated operation between the crank mechanism driving the shell contraction and the onset of elastic energy, which determines the speed of inflation of the shell. These results are invaluable in the definition of rigorous design criteria and derivation of ad-hoc control laws for a new breed of optimized soft-bodied, pulsed-jet, unmanned underwater vehicles.

Structural Dynamics of a Pulsed-Jet Propulsion System for Underwater Soft Robots

This paper entails the study of the pulsed-jet propulsion inspired by cephalopods in the frame of underwater bioinspired robotics. This propulsion routine involves a sequence of consecutive cycles of inflation and collapse of an elastic bladder, which, in the robotics artefact developed by the authors, is enabled by a cable-driven actuation of a deformable shell composed of rubber-like materials. In the present work an all-comprehensive formulation is derived by resorting to a coupled approach that comprises of a model of the structural dynamics of the cephalopod-like elastic bladder and a model of the pulsed-jet thrust production. The bladder, or mantle, is modelled by means of geometrically exact, axisymmetric, nonlinear shell theory, which yields an accurate estimation of the forces involved in driving the deformation of the structure in water. By coupling these results with those from a standard thrust model, the behaviour of the vehicle propelling itself in water is derived. The constitutive laws of the shell are also exploited as control laws with the scope of replicating the muscle activation routine observed in cephalopods. The model is employed to test various shapes, material properties and actuation routines of the mantle. The results are compared in terms of speed performance in order to identify suitable design guidelines. Altogether, the model is tested in more than 50 configurations, eventually providing useful insight for the development of more advanced vehicles and bringing evidence of its reliability in studying the dynamics of both man-made cephalopod-inspired robots and live specimens.

Biomimetic Vortex Propulsion: Toward the New Paradigm of Soft Unmanned Underwater Vehicles

A soft robot is presented which replicates the ability of cephalopods to travel in the aquatic environment by means of pulsed jet propulsion. In this mode of propulsion, a discontinuous stream of fluid is ejected through a nozzle and rolls into a vortex ring. The occurrence of the vortex ring at the nozzle-exit plane has been proven to provide an additional thrust to the one generated by a continuous jet. A number of authors have experimented with vortex thrusting devices in the form of piston-cylinder chambers and oscillating diaphragms. Here, the focus is placed on designing a faithful biomimesis of the structural and functional characteristics of the Octopus vulgaris. To do so, the overall shape of this swimming robot is achieved by moulding a silicone cast of an actual octopus, hence offering a credible replica of both the exterior and interior of an octopus mantle chamber. The activation cycle relies on the cable-driven contraction/release of the elastic chamber, which drives the fluid through a siphon-like nozzle and eventually provides the suitable thrust for propelling the robot. The prototype presented herein demonstrates the fitness of vortex enhanced propulsion in designing soft unmanned underwater vehicles.

Effect of vehicle configuration on the performance of a submersible pulsed-jet vehicle at intermediate Reynolds number

Recent results have demonstrated that pulsed-jet propulsion can achieve propulsive efficiency greater than that for steady jets when short, high frequency pulses are used, and the pulsed-jet advantage increases as Reynolds number decreases into the intermediate range (∼50). An important aspect of propulsive performance, however, is the vehicle configuration. The nozzle configuration influences the jet speed and, in the case of pulsed-jets, the formation of the vortex rings with each jet pulse, which have important effects on thrust. Likewise, the hull configuration influences the vehicle speed through its effect on drag. To investigate these effects, several flow inlet, nozzle, and hull tail configurations were tested on a submersible, self-propelled pulsed-jet vehicle (‘Robosquid’ for short) for jet pulse length-to-diameter ratios (L/D) in the range 0.5–6 and pulsing duty cycles (StL) of 0.2 and 0.5. For the configurations tested, the vehicle Reynolds number (Reυ) ranged from 25 to 110. In terms of propulsive efficiency, changing between forward and aft-facing inlets had little effect for the conditions considered, but changing from a smoothly tapered aft hull section to a blunt tail increased propulsive efficiency slightly due to reduced drag for the blunt tail at intermediate Reυ. Sharp edged orifices also showed increased vehicle velocity and propulsive efficiency in comparison to smooth nozzles, which was associated with stronger vortex rings being produced by the flow contraction through the orifice. Larger diameter orifices showed additional gains in propulsive efficiency over smaller orifices if the rate of mass flow was matched with the smaller diameter cases, but using the same maximum jet velocity with the larger diameter decreased the propulsive efficiency relative to the smaller diameter cases.

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

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 (StL) 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 (ηP/ηP, ss) increased up to 0.15 (26%) as the Re decreased over the same range and for similar pulsing conditions. The improved ηP/ηP, 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 ηP and ηP/ηP, sson 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.

The efficiency of pulsed-jet propulsion

Nature is often an inspiration for scientists and especially so in fluid dynamics. We observe and admire the beauty of birds and fish as they move through the air and water, and wonder how these forms of locomotion evolved and whether they are optimised for efficiency. A common feature of this locomotion is that the thrust is generated by the flapping of a wing or fin, creating an unsteady flow. Other less readily observed animals such as salps or squid eject a pulsed jet, raising the question of whether there is an advantage of this unsteady forcing over a steady jet. This is the question addressed by Ruiz, Whittlesey & Dabiri (J. Fluid Mech., this issue, vol. 668, 2011, pp. 5–32) who have carried out detailed flow and power-consumption measurements with a self-propelled vehicle in water. The vehicle has a novel propulsion mechanism that allows a comparison of the efficiency of a pulsed and steady jet to be compared. They show that significant increases in efficiency are possible with the pulsed jet, even allowing for the additional power needed to create the pulsed flow. They also show that vortex rings are produced by the unsteady jet and that the additional entrainment of ambient fluid into the ring and the higher pressure at the front of the ring are the cause of this increased efficiency.

Propulsive efficiency of a biomorphic pulsed-jet underwater vehicle

The effect of the velocity program and duty cycle (StL) 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 StL 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 (ηP/ηP, ss) was observed as StL increased and L/D decreased. For cases of short L/D and high StL, ηP/ηP, 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 StL 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.

Vortex ring velocity and minimum separation in an infinite train of vortex rings generated by a fully pulsed jet

A pulsed jet with a period of no flow between pulses (i.e., a fully pulsed jet) produces a multiplicity of vortex rings whose characteristics are determined by the jet pulsing parameters. The present study analyzes the case of impulsively initiated and terminated jet pulses in the limit of equal pulse duration and period to determine the minimum possible vortex ring separation obtainable from a fully pulsed jet. The downstream character of the flow is modeled as an infinite train of thin, coaxial vortex rings. Assuming inviscid flow and matching the circulation, impulse, kinetic energy, and frequency of the jet and vortex ring train allow the properties of the vortex ring train to be determined in terms of the ratio of jet slug length-to-diameter ratio (L/D) used for each pulse. The results show the minimum ring separation may be made arbitrarily small as L/D is decreased and the corresponding total ring velocity remains close to half the jet velocity for L/D 1.5. The results are discussed in the context of models of pulsed-jet propulsion.

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

Vortex rings were formed with a piston-cylinder mechanism in the presence of uniform background co-flow supplied through a shroud surrounding the cylinder. The jet and co-flow were started simultaneously. Ratios of the co-flow to jet velocity (Rv) in the range 0–1 were considered. The formation number (F) as a function of Rv was determined using the procedure of Gharib et al. [J. Fluid Mech. 360, 121 (1998)] and a generalized definition of formation time. The results show a sharp decrease in F as Rv increases from 0.5–0.75, suggesting possible performance limitations for pulsed-jet propulsion.

Jet-propelled swimming in scallops: swimming mechanics and ontogenic scaling

Scallop locomotion was investigated on the basis of an analysis of fluid forces acting on the body and the balance of the forces during swimming. A hydrodynamic model for unsteady jet propulsion was developed in which propulsion performance is characterized by three nondimensional parameters: the storage/discharge volume ratio, reduced clapping frequency, and reduced discharge frequency. Pulsed jet propulsion is designed to achieve high thrust, although not necessarily with low hydrodynamic propulsive efficiency, as was previously widely considered. Swimming in scallops is realized by orientating the body at a certain angle of attack and maintaining a minimum swimming speed to prevent sinking. The working frequency of the locomotor system is determined and adjusted by the swimming strategy (angle of attack, swimming speed, and trajectory angle). For Placopecten magellanicus, the optimum angle of attack is about 6° – 12°, at which swimming requires the lowest energy input (lowest frequency) and hydrodynamic behaviour is ideal (without severe separation and stall). To maintain level swimming, P. magellanicus, during almost all their life, must swim at 5 – 7 body lengths per second if postured at a 6° – 12° angle of attack. The estimated Froude efficiency decreases during growth from about 0.5 to 0.3 for level swimming and from about 0.4 to 0.2 for climbing at an angle of 25°. It is suggested that the heavy body and inferior hydrodynamic characteristics (low aspect ratio and imperfect planform shape) have prevented scallops from becoming good swimmers. These problems are enhanced as the animals grow.