Flexible Propulsors Research Articles

Underwater Propulsion Using Forced Excitation of a Flexible Beam

Abstract Aquatic animals commonly oscillate their fins, tails, or other structures to propel and control themselves in water. These elements are not perfectly rigid, so the interplay between their stiffness and the fluid loading dictates their dynamics. We examine the propulsive qualities of a tail-like flexible beam actuated by a dynamic moment over a range of frequencies and flow speeds. This is accomplished using the equations of fluid-immersed beams in combination with a set of tractable expressions for thrust and efficiency. We solve these expressions over the velocity–frequency plane and show that the flexible propulsor has regions of both positive and negative thrust. We also show the behavior of a sample underwater vehicle with fixed drag characteristics as an illustration of a realizable system.

A fundamental propulsive mechanism employed by swimmers and flyers throughout the animal kingdom.

Even casual observations of a crow in flight or a shark swimming demonstrate that animal propulsive structures bend in patterned sequences during movement. Detailed engineering studies using controlled models in combination with analysis of flows left in the wakes of moving animals or objects have largely confirmed that flexibility can confer speed and efficiency advantages. These studies have generally focused on the material properties of propulsive structures (propulsors). However, recent developments provide a different perspective on the operation of nature's flexible propulsors, which we consider in this Commentary. First, we discuss how comparative animal mechanics have demonstrated that natural propulsors constructed with very different material properties bend with remarkably similar kinematic patterns. This suggests that ordering principles beyond basic material properties govern natural propulsor bending. Second, we consider advances in hydrodynamic measurements demonstrating suction forces that dramatically enhance overall thrust produced by natural bending patterns. This is a previously unrecognized source of thrust production at bending surfaces that may dominate total thrust production. Together, these advances provide a new mechanistic perspective on bending by animal propulsors operating in fluids - either water or air. This shift in perspective offers new opportunities for understanding animal motion as well as new avenues for investigation into engineered designs of vehicles operating in fluids.

Development of a Stiffness‐Adjustable Articulated Paddle and its Application to a Swimming Robot

Stiffness of a swimming appendage is the key mediator between thrust generated and its beating frequency. Due to the advantageous role of flexible propulsors, they are widely adopted in previous swimming robots. As an optimal propulsor, stiffness is highly dependent on its beating frequency, and stiffness modulation is crucial when a robot is swimming with multiple beating frequencies. Herein, a novel swimming paddle that can switch two different stiffness states by sliding a laminate inside and its application to a swimming robot is studied. This paddle has 8 articulated joints and 20 passive flaps to achieve drag asymmetry with minimum control effort. A semiempirical model to estimate the stiffness change in good accuracy is also studied. The thrust modulation caused by stiffness change is comprehensively studied by varying frequency and range of motion. In addition, a nontethered swimming robot propelled by a bilateral pair of paddles is developed to investigate when and how the stiffness adjustment is useful. There is a threshold frequency dividing two regimes where one stiffness excels the other stiffness with respect to cost of transport. Finally, it is shown that the paddle thickness is closely related to the necessity of stiffness change mechanism.

Self-Propelled Swimming of a Flexible Propulsor Actuated by a Distributed Active Moment

The self-propelled swimming of a flexible propulsor is numerically investigated by using fluid-structure interaction simulations. A distributed active moment mimicking the muscle actuation in fish is used to drive the self-propulsion. The active moment imposed on the body of the swimmer takes the form of a traveling wave. The influences of some key parameters, such as the wavenumber, the amplitude of moment density and the Reynolds number, on the performance of straight-line swimming are explored. The influence of the ground effect on speed and efficiency is investigated through the simulation of near-wall swimming. The turning maneuver is also successfully performed by adopting a simple evolution law for the leading-edge deflection angle. The results of the present study are expected to be helpful to the design of bio-inspired autonomous underwater vehicles.

Design and Control Strategy of Bio-inspired Underwater Vehicle with Flexible Propulsor

Biomimetics aims to take inspiration from nature and develop new models and efficient systems for a sustainable future. Bioinspired underwater robotics help develop future submarines that will navigate through the water using flexible propulsor. This research has focused on the Manta Ray species as batoid has a unique advantage over other species. This study also aims to improve AUV (Autonomous Underwater Vehicle) efficiency through biomimetic design, the purpose of which is to observe and study the marine environment, be it for sea exploration or navigation. The design and prototyping process of bioinspired AUVs have been mentioned in this study, along with testing a propulsive mechanism for efficient swimming and turning capabilities. The Robot was designed taking structural considerations from the actual Manta-Ray locomotion and body design. The propulsion mechanism and control circuit were then implemented on the developed systems. The prototype of the Manta Ray was able to generate a realistic swimming pattern and was tested in an acrylic tank. The experimental results obtained in the tank basin are very close to the results we observe in the real-world scenario in terms of the vehicle's forward and turning motion.

A Computational Model for Tail Undulation and Fluid Transport in the Giant Larvacean

Flexible propulsors are ubiquitous in aquatic and flying organisms and are of great interest for bioinspired engineering. However, many animal models, especially those found in the deep sea, remain inaccessible to direct observation in the laboratory. We address this challenge by conducting an integrative study of the giant larvacean, an invertebrate swimmer and “fluid pump” of the mesopelagic zone. We demonstrate a workflow involving deep sea robots, advanced imaging tools, and numerical modeling to assess the kinematics and resulting fluid transport of the larvacean’s beating tail. A computational model of the tail was developed to simulate the local fluid environment and the tail kinematics using embedded passive (elastic) and active (muscular) material properties. The model examines how varying the extent of muscular activation affects the resulting kinematics and fluid transport rates. We find that muscle activation in two-thirds of the tail’s length, which corresponds to the observed kinematics in giant larvaceans, generates a greater average downstream flow speed than other designs with the same power input. Our results suggest that the active and passive material properties of the larvacean tail are tuned to produce efficient fluid transport for swimming and feeding, as well as provide new insight into the role of flexibility in biological propulsors.

A novel cylindrical overlap-and-fling mechanism used by sea butterflies.

The clap-and-fling mechanism is a well-studied, unsteady lift generation mechanism widely used by flying insects and is considered obligatory for tiny insects flying at low to intermediate Reynolds numbers, Re However, some aquatic zooplankters including some pteropod (i.e. sea butterfly) and heteropod species swimming at low to intermediate Re also use the clap-and-fling mechanism. These marine snails have extremely flexible, actively deformed, muscular wings which they flap reciprocally to create propulsive force, and these wings may enable novel lift generation mechanisms not available to insects, which have less flexible, passively deformed wings. Using high-speed stereophotogrammetry and micro-particle image velocimetry, we describe a novel cylindrical overlap-and-fling mechanism used by the pteropod species Cuvierina atlantica In this maneuver, the pteropod's wingtips overlap at the end of each half-stroke to sequentially form a downward-opening cone, a cylinder and an upward-opening cone. The transition from downward-opening cone to cylinder produces a downward-directed jet at the trailing edges. Similarly, the transition from cylinder to upward-opening cone produces downward flow into the gap between the wings, a leading edge vortex ring and a corresponding sharp increase in swimming speed. The ability of this pteropod species to perform the cylindrical overlap-and-fling maneuver twice during each stroke is enabled by its slender body and highly flexible wings. The cylindrical overlap-and-fling mechanism observed here may inspire the design of new soft robotic aquatic vehicles incorporating highly flexible propulsors to take advantage of this novel lift generation technique.

Effects of Flexible Propulsors on Hydrodynamic Forces

We present experimental measurements of forward forces and external torques generated during forced oscillations of a tail on a fish-like body. The experiments were performed in a towing basin. Three panels having different flexural rigidity were tested over a range of oscillatory frequencies and leading edge amplitudes at 0 m/s and 0.35 m/s. The results show that tail panel flexibility enhances thrust production and thrust-to-input power ratios, with propulsive efficiencies reaching up to 45%.

An autonomous flexible propulsor in a quiescent flow

Flapping motions of wings and fins are common in nature. Living organisms use such motions to float in a fluid or to propel themselves forward. Some entities, such as tadpoles, use distinct flexible components to generate propulsion. Here we introduce a propulsor consisting of a rigid circular head containing an energy source and a flexible fin for propulsion. The head imparts a sinusoidal torque to the leading edge of the fin and the flexible fin flaps along the leading edge. The flexible propulsor thus moves via an oscillating relative angle between the head and the leading edge of the fin. Unlike a self-propelled heaving and pitching fin, our ‘autonomous’ flexible propulsor has no prescribed motion or constraint referenced from outside coordinates. The immersed boundary method was used to model the interaction between the flexible propulsor and the surrounding fluid. A penalty method, in which the head and fin imparted a periodic torque to each other, was used to connect the head and the fin. The cruising speed and propulsive efficiency of the propulsor were explored as a function of the ratio of the head size to the fin length (D/L), the pitching amplitude (θp) and the pitching frequency (f). The cruising speed and the equilibrium position (geq) of the flexible propulsor near the ground were also examined. The optimal propulsive efficiency was achieved at the head ratio of D/L = 0.2 at θp = 30° and f = 0.2. The cruising speed of the flexible propulsor increased when operating near the ground. The gap distance between the propulsor and the ground was dynamically determined by the pitching motion.

Bioinspiration From Flexible Propulsors: Organismal Design, Mechanical Properties, Kinematics and Neurobiology of Pectoral Fins in Labrid Fishes

AbstractLabrid fishes use their pectoral fins for efficient high-speed cruising behavior, as well as for precision maneuvering in complex environments, making them good models for biomimicry applications in propulsor technology for aquatic vehicles. Lift-based labriform locomotion is a form of aquatic flight used by many species and is the sole mode of transport across most speeds by some of the largest wrasses and parrotfishes on coral reefs. Although basic and applied research has explored fin design in several species utilizing labriform propulsion, a detailed analysis of fin anatomy, fin mechanical properties, and well-resolved three-dimensional (3D) kinematics in high-performance aquatic flyers has not yet been attained. Here, we present recent research on fin structure, fin flexural stiffness, sensory abilities of fins, and a novel 3D approach to flexible fin kinematics. Our aims are to outline important future directions for this field and to assist engineers attempting biomimicry of maneuverable fin-based locomotion for applications in robotics. First, we illustrate the anatomical structure and branching patterns of the pectoral fin skeleton and the muscles that drive fin motion. Second, we present data on the flexural stiffness of pectoral fins in the parrotfish (Scarus quoyi), setting up a stiffness field that gives the fin propulsor its passive mechanical properties and enables hydrodynamically advantageous fin deformations during swimming. Third, we present 3D reconstructions of the kinematics of high-performanceScarusfins that greatly enhance our ability to reproduce fin motions for engineering applications and also yield insight into the functional role of the fin stiffness field. Lastly, recent work on mechanosensation is illustrated as key to understanding sensorimotor control of labriform locomotion. Research on pectoral fin structure, function, and neural control in large marine species with high-performance wing-like fins is important to the comparative biology of locomotion in fishes, and we suggest it is a productive area of research on fin function for applications in the design of quiet, efficient propulsors.

Experimental assessment of performance characteristics for pitching flexible propulsors

Using a flexible hydrodynamic foil that pitches to produce thrust, the most pertinent aspects of a fish-like propulsion system are replicated in a controlled environment. The pitching and flexing combination creates a hydroelastic coupling in which the fluid and flexible foil simultaneously affect each other's behavior. The project investigated relationships for the propulsors’ thrust and efficiency performance to gain a better understanding of the dynamic interaction with the surrounding fluid. The analysis was conducted through reduction of the measured force and torque data. The experiments took place in a large recirculating water channel, using full span flexible propulsor models and a higher Reynolds number than previous flexible propulsor experiments. The propulsor pitched about a fixed axis at its quarter chord, with a six-axis load cell measuring the forces and torques on the shaft. The efficiency of the propulsor and the Coefficients of Thrust and Lift are presented as functions of both Strouhal Number and Stiffness Coefficient. The ensemble data will facilitate the engineering of fish-like propulsion systems for future application of this technology.

Numerical study of propulsion performance in swimming fish using boundary element method

In this paper, hydrodynamic simulation of fish-like swimming for two types of aquatic animals including tuna fish and giant danio is presented. We employ an unsteady three-dimensional inviscid boundary element method including time stepping algorithm to capture the wake sheet and flow features around swimming fish in a straight course. At each time step, an unsteady Bernoulli equation was used to find the pressure distribution and thrust generated by the animal. To couple fluid solver with kinematic equations of flexible body, undulating motions of backbone were defined using a prescribed continuous function. Although the flexible motion mechanism controls the fish swimming but no structural model has been considered for the body, there is no fluid–solid interaction. To validate the model, we compare our results with the numerical work of Zhu et al. [1] and experimental results of Barrett et al. [2] and show that this methodology could be fast and reliable approach for the prediction of flexible propulsors.

Flapping dynamics of a flexible propulsor near ground

The flapping motion of a flexible propulsor near the ground was simulated using the immersed boundary method. The hydrodynamic benefits of the propulsor near the ground were explored by varying the heaving frequency (St) of the leading edge of the flexible propulsor. Propulsion near the ground had some advantages in generating thrust and propelling faster than propulsion away from the ground. The mode analysis and flapping amplitude along the Lagrangian coordinate were examined to analyze the kinematics as a function of the ground proximity (d) and St. The trailing edge amplitude ( $$a_\mathrm{tail}$$ ) and the net thrust ( $$\overline{{F}}_x$$ ) were influenced by St of the flexible propulsor. The vortical structures in the wake were analyzed for different flapping conditions.

Vortex interaction between two tandem flexible propulsors with a paddling-based locomotion

Schooling behaviours among self-propelled animals can benefit propulsion. Inspired by the schooling behaviours of swimming jellyfish, flexible bodies that self-propel through a paddling-based motion were modelled in a tandem configuration. This present study explored the hydrodynamic patterns generated by the interactions between two flexible bodies and the surrounding fluid in the framework of the penalty immersed boundary method. The hydrodynamic patterns produced in the wake revealed flow-mediated interactions between two tandem propulsors, including vortex–vortex and vortex–body interactions. Two tandem flexible propulsors paddling with identical amplitude and frequency produced stable configurations as a result of the flow-mediated interactions. Both the upstream and downstream propulsors benefited from the tandem configuration in terms of the locomotion velocity and the cost, compared with an isolated propulsion system. The interactions were examined as a function of the initial gap distance and the phase difference in the paddling frequency. The equilibrium gap distance between two propulsors remained constant, regardless of the initial gap distance, although it did depend on the phase difference in the paddling frequency.

Maximizing the efficiency of a flexible propulsor using experimental optimization

AbstractExperimental gradient-based optimization is used to maximize the propulsive efficiency of a heaving and pitching flexible panel. Optimum and near-optimum conditions are studied via direct force measurements and particle image velocimetry (PIV). The net thrust and power scale predictably with the frequency and amplitude of the leading edge, but the efficiency shows a complex multimodal response. Optimum pitch and heave motions are found to produce nearly twice the efficiencies of optimum heave-only motions. Efficiency is globally optimized when (i) the Strouhal number is within an optimal range that varies weakly with amplitude and boundary conditions; (ii) the panel is actuated at a resonant frequency of the fluid–panel system; (iii) heave amplitude is tuned such that trailing-edge amplitude is maximized while the flow along the body remains attached; and (iv) the maximum pitch angle and phase lag are chosen so that the effective angle of attack is minimized. The multi-dimensionality and multi-modality of the efficiency response demonstrate that experimental optimization is well-suited for the design of flexible underwater propulsors.

Effect of caudal fin flexibility on the propulsive efficiency of a fish-like swimmer

A computational model is used to examine the effect of caudal fin flexibility on the propulsive efficiency of a self-propelled swimmer. The computational model couples a penalization method based Navier–Stokes solver with a simple model of flow induced deformation and self-propelled motion at an intermediate Reynolds number of about 1000. The results indicate that a significant increase in efficiency is possible by careful choice of caudal fin rigidity. The flow-physics underlying this observation is explained through the use of a simple hydrodynamic force model and guidelines for bioinspired designs of flexible fin propulsors are proposed.

Linear instability mechanisms leading to optimally efficient locomotion with flexible propulsors

We present the linear stability analysis of experimental measurements obtained from unsteady flexible pitching panels. The analysis establishes the connections among the wake dynamics, propulsor dynamics, and Froude efficiency in flexible unsteady propulsion systems. Efficiency is calculated from direct thrust and power measurements and wake flowfields are obtained using particle image velocimetry. It is found that for flexible propulsors every peak in efficiency occurs when the driving frequency of motion is tuned to a wake resonant frequency, not a structural resonant frequency. Also, there exists an optimal flexibility that globally maximizes the efficiency. The optimal flexibility is the one where a structural resonant frequency is tuned to a wake resonant frequency. The optimally tuned flexible panels demonstrate an efficiency enhancement of 122%–133% as compared to an equivalent rigid panel and there is a broad spectrum of wake resonant frequencies allowing high efficiency swimming over a wide range of operating conditions. At a wake resonant frequency we find that the entrainment of momentum into the time-averaged velocity jet is maximized.

Flexible propulsors in ground effect

We present experimental evidence for the hydrodynamic benefits of swimming ‘in ground effect’, that is, near a solid boundary. This situation is common to fish that swim near the substrate, especially those that are dorsoventrally compressed, such as batoids and flatfishes. To investigate flexible propulsors in ground effect, we conduct force measurements and particle image velocimetry on flexible rectangular panels actuated at their leading edge near the wall of a water channel. For a given actuation mode, the panels swim faster near the channel wall while maintaining the same propulsive economy. In conditions producing net thrust, panels produce more thrust near the ground. When operating in resonance, swimming near the ground can also increase propulsive efficiency. Finally, the ground can act to suppress three-dimensional modes, thereby increasing thrust and propulsive efficiency. The planform considered here is non-biological, but the hydrodynamic benefits are likely to apply to more complex geometries, especially those where broad flexible propulsors are involved such as fish bodies and fins. Such fish could produce more thrust by swimming near the ground, and in some cases do so more efficiently.

Bending rules for animal propulsion

Animal propulsors such as wings and fins bend during motion and these bending patterns are believed to contribute to the high efficiency of animal movements compared with those of man-made designs. However, efforts to implement flexible designs have been met with contradictory performance results. Consequently, there is no clear understanding of the role played by propulsor flexibility or, more fundamentally, how flexible propulsors should be designed for optimal performance. Here we demonstrate that during steady-state motion by a wide range of animals, from fruit flies to humpback whales, operating in either air or water, natural propulsors bend in similar ways within a highly predictable range of characteristic motions. By providing empirical design criteria derived from natural propulsors that have convergently arrived at a limited design space, these results provide a new framework from which to understand and design flexible propulsors.

Biomimetic and Live Medusae Reveal the Mechanistic Advantages of a Flexible Bell Margin

Flexible bell margins are characteristic components of rowing medusan morphologies and are expected to contribute towards their high propulsive efficiency. However, the mechanistic basis of thrust augmentation by flexible propulsors remained unresolved, so the impact of bell margin flexibility on medusan swimming has also remained unresolved. We used biomimetic robotic jellyfish vehicles to elucidate that propulsive thrust enhancement by flexible medusan bell margins relies upon fluid dynamic interactions between entrained flows at the inflexion point of the exumbrella and flows expelled from under the bell. Coalescence of flows from these two regions resulted in enhanced fluid circulation and, therefore, thrust augmentation for flexible margins of both medusan vehicles and living medusae. Using particle image velocimetry (PIV) data we estimated pressure fields to demonstrate a mechanistic basis of enhanced flows associated with the flexible bell margin. Performance of vehicles with flexible margins was further enhanced by vortex interactions that occur during bell expansion. Hydrodynamic and performance similarities between robotic vehicles and live animals demonstrated that the propulsive advantages of flexible margins found in nature can be emulated by human-engineered propulsors. Although medusae are simple animal models for description of this process, these results may contribute towards understanding the performance of flexible margins among other animal lineages.