Flapping Foil Research Articles

Mechanism of wake-induced flow dynamics in tandem flapping foils: Effect of the chord and gap ratios on propulsion

The present study investigates the mechanisms of wake-induced flow dynamics in tandem National Advisory Committee for Aeronautics 0015 flapping foils at low Reynolds number of Re = 1100. A moving mesh arbitrary Lagrangian–Eulerian framework is utilized to realize the prescribed flapping motion of the foils while solving the flow via incompressible Navier–Stokes equations. The effect of the gap between the two foils on the thrust generation is studied for gaps of 1–10 times the chord of the downstream foil. The mean thrust as well as the propulsive efficiency vary periodically with the gap indicating alternate regions of higher and lower thrust generation, emphasizing the profound effect of upstream foil's wake interaction with the downstream foil. Five crucial wake–foil interactions leading to either favorable or unfavorable conditions for thrust generation are identified and different modes depending on the interactions are proposed for the tandem flapping foils. It is observed that the effect of the wake of the upstream foil on the downstream foil decreases with increasing gap. The study also focuses on the effect of the chord sizes of the upstream and the downstream foils on the propulsive forces, where the chord of the upstream foil is selected as 0.25–1 times the downstream foil's chord length. The effect of the chord size on the thrust is noticed to diminish as the chord size of the upstream foil decreases. Furthermore, the effect of the phase difference between the kinematics of the upstream and the downstream foils on flow dynamics is also explored along with its relationship with the chord sizes. For a fixed chord size, the effect of the phase difference on the propulsive performance is observed to be similar to that by varying the gap between the foils due to similar type of vortex interactions. The mechanisms of vortex interactions are linked to provide a comprehensive and generic understanding of the flow dynamics of tandem foils.

Parametric Analysis for Underwater Flapping Foil Propulsor

This paper researched into the harmonic and anharmonic underwater flapping foil propulsion systems to improve the efficiency of these bioinspired propulsors. The angle of attack, the pitching angle, the heaving amplitude, and the phase difference are parametrically investigated in this paper. A rigid two-dimensional NACA (National Advisory Committee for Aeronautics) 0012 airfoil is modeled with the aid of a commercial computational fluid dynamics software, FINE™/Marine. Unsteady Reynolds Average Navier-Stokes (URANS) equation is solved together with dynamic mesh to simulate the foil motion. The investigation first verifies the reliability of the developed modeling method against the benchmark data. Then, the systematic investigation is conducted and identifies that the heaving amplitude is most influential factor for the propulsion efficiency. Secondly, phase difference also has a significant influence on efficiency, but this effect is related to the reference working condition, which needs further study. Then, the pitching amplitude has little effect on the maximum efficiency value of flapping foil, while it will affect its optimal speed range. When the heaving amplitude ratio reaches 3 and the corresponding maximum angle of attack is about 9°, the maximum efficiency can reach 87%. The effect of anharmonic motion on the efficiency is very small and varies with the St number, but in summary, it can maintain the peak efficiency over a wider range of operations. In addition, the force and flow field characteristics of different efficiency points are compared and analyzed to distinguish their corresponding relationship with the propulsion efficiency.

Performance augmentation mechanism of tandem flapping foils with stroke time-asymmetry

The performance augmentation mechanism of a tandem-foil system undergoing time-asymmetric flapping with unequal up- and downstroke durations (velocities) is investigated at three different phase angles, 0°, 90°, and 180°. Specifically, an asymmetry ratio, ranging from 0 to 0.4, is introduced to quantify the degree of the stroke time-asymmetry and to serve as the primary kinematic parameter of interest that affects the foil performances. Numerical simulations are implemented to predict the force production and to investigate the associated mechanism at different asymmetry ratios and phase angles. Validations are performed using digital particle image velocimetry in water tunnel experiments with two identical 3D printed wings. The results suggest that the foil performances at proper phase angles can be enhanced by stroke time-asymmetry. The force production during in-phase flapping obtains 15% increment while that during counterstroke flapping achieves remarkable enhancements by 2.5 times, as the asymmetry ratio increases from 0 to 0.4. The study also demonstrates that such enhancements are achieved through the changes in foil flapping velocities and foil-vortex interactions between the unequal up- and downstrokes. These findings not only provide insights toward the characteristics of tandem foils which are operated in non-sinusoidal flapping strokes but also offer a reference to the design of efficient wing kinematics for high-performance biomimetic propulsors.

Numerical analysis on the propulsive performance of oscillating wing in ground effect

The transient numerical simulation has been conducted by using of the Overlapping grid technique to investigate the ground wall effect on the propulsive performance of an oscillating wing. Both the two-dimensional and three-dimensional wing have been analyzed and the systematic analysis on the effect of the Reynolds number (Re), the average distance between the flapping foil and ground wall (h0) on the propulsive performance of oscillating wing are investigated with respect to the non-dimensional oscillating frequency (St). The simulation results demonstrate that the existence of the ground wall can produce significant influence on the fluid dynamics of oscillating wing and the ground wall effect has close connection to the magnitude of St number. In addition, the increase of Re number will facilitate the growth of both thrust force and propulsive efficiency of oscillating wing and that influence also has close connection with the St number. Finally, the existence of ground wall can also greatly improve the propulsive performance of three-dimensional oscillating wing, but the sensitivity of three-dimensional oscillating wing to the ground wall is lower than that of two-dimensional oscillating wing. The conclusions acquired here can be utilized to optimize the kinematics of the underwater vehicles swimming near ground wall.

A propulsion unit for ships based on water-treading of flapping foils

With the environmental deterioration and people's increasing attention to its protection, it is urgent to save energy and reduce emissions from ships. Reducing ships' drag and using a biomimetic propulsion device as the alternative power to drive them is an effective solution. In this paper, a ship propulsion unit composed of movable flapping foils is proposed. The flapping foils make a reciprocating treading motion in water to generate power to propel and heave ships. By heaving ships out of the water, the drag of the hull is eliminated, which considerably reduces energy consumption. By controlling the attack angle of flapping foils in groups, a good motion control performance can be obtained. Compared with hydrofoil ships, the propulsion unit can heave the ship out of the water at a low speed, and it utilizes both the lift and the drag from foils. It can actuate the ship with 6 degrees of freedom.

Investigation on Hydrodynamic Performance of Flapping Foil Interacting with Oncoming Von Kármán Wake of a D-Section Cylinder

Flapping foils are studied to achieve an efficient propeller. The performance of the flapping foil is influenced by many factors such as oncoming vortices, heaving amplitude, and geometrical parameters. In this paper, investigations are performed on flapping foils to assess its performance in the wake of a D-section cylinder located half a diameter in front of the foil. The effects of heaving amplitude and foil thickness are examined. The results indicate that oncoming vortices facilitate the flapping motion. Although the thrust increases with the increasing heaving amplitude, the propelling efficiency decreases with it. Moreover, increasing thickness results in higher efficiency. The highest propelling efficiency is achieved when the heaving amplitude equals ten percent of the chord length with a symmetric foil type of NACA0050 foil. When the heaving amplitude is small, the influence of the thickness tends to be more remarkable. The propelling efficiency exceeds 100% and the heaving amplitude is 10% of the chord length when the commonly used equation is adopted. This result demonstrates that the flapping motion extracts some energy from the oncoming vortices. Based on the numerical results, a new parameter, the energy transforming ratio (RET), is applied to explicate the energy transforming procedure. The RET represents that the flapping foil is driven by the engine or both the engines and the oncoming vortices with the range of RET being (0, Infini) and (−1, 0), respectively. With what has been discussed in this paper, the oncoming wake of the D-section cylinder benefits the flapping motion which indicates that the macro underwater vehicle performs better following a bluff body.

Optimal Efficiency and Heaving Velocity in Flapping Foil Propulsion

A novel model is proposed to estimate the optimal propulsive efficiency and the optimal dimensionless heaving velocity of a flapping foil based on a lift–drag ratio under the assumption of negligible pitching power. The optimal efficiency increases with the lift–drag ratio. The optimal Strouhal number of sinusoidal heaving motion approaches 0.318, within the range of 0.25–0.35 for optimal efficiency. In addition, the thrust generation of a foil requires that the product of the lift–drag ratio and the dimensionless heaving velocity must be greater than unity. To demonstrate how to use the new model to estimate the optimal propulsive efficiency and the optimal dimensionless heaving velocity, the lift–drag ratio is estimated using static tests of an impulsively started uniform flow over an infinitely thin flat plate for a range of angle of attack. To illustrate how to design kinematics to achieve the estimated optimal efficiency, two examples of flapping motions of a flat plate at a Reynolds number of 2000 are considered: sinusoidal and nonsinusoidal. Results show that the efficiency of nonsinusoidal flapping motion approaches the optimal efficiency using the lift–drag ratio estimated from static tests over the effective angle of attack of 6–30°.

Study on Performance Enhancement of a Flapping Foil Energy Harvester Using Circulation Control

Abstract Oscillating motion, an effective way to harvest energy, has gradually become a hotspot in bionic motion research in recent years. Means of improving the energy-extraction efficiency of a flapping foil harvester have long been a focus of researchers. This paper proposes a new flapping foil harvester with circulation control and explores the effects of different parameters on its energy-extraction capacity to improve efficiency and achieve lowest cost. Setting the injection ports on the upper and lower surfaces near the trailing edge of the foil and implementing injection control during motion, the effects of the location of the injection port, pitching amplitude, momentum coefficient, reduced frequency, and jet mode on the circulation control flapping foil are systematically investigated under the condition of a Reynolds number of 13,800. The results show that circulation control can enhance the energy-extraction efficiency of a flapping foil across a wide range of parameters, in which the location of the injection port and momentum coefficient have the most obvious influence on efficiency, followed by pitching amplitude and reduced frequency. In addition, the jet mode is a crucial factor affecting net efficiency. Relative to the constant mode, the triangular mode of circulation control has the lowest energy consumption, and the net energy-extraction efficiency reaches up to 38.77% under a reduced frequency of 0.12, which is 22.24% higher than that of the plain flapping foil.

Implementation and validation of a strongly coupled numerical model of a fully passive flapping foil turbine

This paper presents the implementation and validation of a strongly coupled numerical model of a fully passive flapping foil turbine operating at a high Reynolds number. Thanks to a strong fluid–solid coupling strategy, the well known added-mass instability is mitigated while simulating a lightweight flapping foil. The numerical results are first validated in the case of a fixed foil undergoing static stall. The model is then validated with respect to numerical results available in the literature for a heavy flapping foil turbine. Finally, the numerical results of the strongly coupled model are compared to experimental data of a lightweight turbine prototype tested in a confined channel. The numerical results have shown to be in good agreement with the experimental measurements. Indeed, the kinematics and harvesting performances of the turbine prototype have been accurately reproduced by the numerical simulations. Besides, the leading edge vortex shedding observed in the experiments has also been precisely reproduced by the numerical results. The strongly coupled model implemented and validated in the present paper constitutes a useful tool for expanding the parameter space in the search for an optimised design of the fully passive flapping foil turbine.

Experimental optimisation of the pitching structural parameters of a fully passive flapping foil turbine

A reduced scale prototype of a fully passive flapping foil turbine has been designed and tested in a confined channel at a chord Reynolds number of 60 000. Thanks to an original dynamic tuning strategy of the mechanical properties, experiments have been conducted in a wide range of pitching structural parameters for three different pitching axis locations. The best performances have been achieved when the pitching axis is located at one third of the chord length, for which a hydraulic efficiency of 31.9% has been reached. Relatively good harvesting metrics have also been obtained while moving the pitching axis back to the trailing edge, as long as the pitching stiffness is increased accordingly. The experimental results showed as well that the energy harvested by the pitching motion is negligible compared with the heaving motion. However, a non-zero pitching viscous damping is required in order for the turbine to achieve its best performances.

Effects of Non-Sinusoidal Motion and Effective Angle of Attack on Energy Extraction Performance of a Fully-Activated Flapping Foil

Flapping foil energy harvesting systems are considered as highly competitive devices for conventional turbines. Several research projects have already been carried out to improve performances of such new devices. This paper is devoted to study effects of non-sinusoidal heaving trajectory, non-sinusoidal pitching trajectory, and the effective angle of attack on the energy extraction performances of a flapping foil operating at low Reynolds number (Re=1100). An elliptic function with an adjustable parameter S (flattening parameter) is used to simulate various sinusoidal and non-sinusoidal flapping trajectories. The flow around the flapping foil is simulated by solving Navier–Stokes equations using the commercial software Star CCM+ based on the finite-volume method. Overset mesh technique is used to model the flapping motion. The study is applied to the NACA0015 foil with the following kinetic parameters: a dimensionless heaving amplitude h0 = 1c, a shift angle between heaving and pitching motions = 90°, a reduced frequency f* = 0.14, and an effective angle of attack αmax varying between 15° and 50°, corresponding to a pitching amplitude in the range 0 = 55.51° to 99.51°. The results show that, the non-sinusoidal trajectory affects considerably the energy extraction performances. For the reference case (sinusoidal heaving and pitching motions, Sh = S =1), best performances are obtained for the effective angle of attack, αmax = 40°. At small effective angle of attack αmax 40°), non-sinusoidal pitching motion has a negative effect. Performances improvement is quite limited with the combined motions non-sinusoidal heaving/sinusoidal pitching.

Flow-energy harvesting using a fully passive flapping foil: A guideline on design and operation

Following our previous work [Int. J. Mech. Sci. (2020), vol. 177, 105587], we searched the best power extraction performance of a novel flow-energy harvester, which utilizes a fully passive flapping foil to extract energy from air/water flows. A series of water-tunnel experiments were conducted on the same test model at the Reynolds number around 105. Through investigating the effects of two unexplored key parameters, a higher overall maximum power conversion efficiency of 42.7% was obtained at water speed 0.71 m/s and foil pitching amplitude 60∘, corresponding to a larger mean power output of about 1.51 W. A quasi-steady theoretical model was also developed to fast predict the system performance in a larger parameter space. It was found that, in addition to typical dynamics, i.e., a flapping cycle includes two pure-heaving phases and two stroke-reversal phases, the foil system can also continuously operate in a “no-pure-heaving” zone where a flapping cycle only includes two successive stroke-reversal phases. Through these experimental and theoretical studies, a useful guideline was proposed on the design and operation of the foil system.

Mapping and selection of profiles for morphing wing of a flapping foil

In the present article, a converter that uses the ocean currents as an electric power generation was presented. A flapping foil device whose movement is based on oscillation of a wing and is inspired by the fish fins was proposed. The purpose of the article was to implement a methodology to map and select wing profiles with greater capacity to generate torque capacity, and thus determine the profiles that would compose a morphing profile wing. Therefore, it is expected that as the foil oscillates, the wing modifies the thickness of the profile and obtains the optimal profile for certain operating situations. For this purpose, mathematical modeling was developed based on the kinematics, dynamics of the device and the hydrodynamic forces on the structure. Modeling is defined as quasi-steady and also consists of two algorithms, Alg-A and Alg-B, used to map the profiles with the highest torques. Alg-A has as search variable the lift coefficient and Alg-B the lift-to-drag ratio; in both cases, the aim was to find the profile that had the highest value of the search variable, and as a result, the largest torque among the eleven NACAs profiles stored in the database. After the simulation of all cases, it was concluded that Alg-A generates about 2% more torque than Alg-B. Finally, the morphing profile was compared with standard NACA profiles, and as a result, when evaluating the mean torque, it performed better in all cases. As for the maximum torque of the case, the morphing profile has a better performance in most cases. Thus, it is concluded that the theoretical model of morphing profile wing can be a more efficient solution than traditional profiles.

Propulsion performance of tandem flapping foils with chordwise prescribed deflection from linear potential theory

Analytical expressions are obtained for the propulsion and the wake structure of tandem flapping foils with chordwise deflection, explaining the propulsive performance improvement in relation to single foils or rigid-foil counterparts for certain combinations of frequency, spacing, and phase shift. The findings are of interest for the design of small aerial or aquatic vehicles using tandem propulsors.

Effects of aspect ratio on rolling and twisting foils

Flow features and forces of three-dimensional flapping foils are presented with aspect-ratio (AR) variations. The similitude of rolling and twisting kinematics is maintained across different ARs. An AR correction analogous to Prandtl finite-wing theory is developed, enabling future use of strip theory in the analysis and design of finite flapping foils.

Hydrodynamic stress maps on the surface of a flexible fin-like foil.

We determine the time dependence of pressure and shear stress distributions on the surface of a pitching and deforming hydrofoil from measurements of the three dimensional flow field. Period-averaged stress maps are obtained both in the presence and absence of steady flow around the foil. The velocity vector field is determined via volumetric three-component particle tracking velocimetry and subsequently inserted into the Navier-Stokes equation to calculate the total hydrodynamic stress tensor. In addition, we also present a careful error analysis of such measurements, showing that local evaluations of stress distributions are possible. The consistency of the force time-dependence is verified using a control volume analysis. The flapping foil used in the experiments is designed to allow comparison with a small trapezoidal fish fin, in terms of the scaling laws that govern the oscillatory flow regime. As a complementary approach, unsteady Euler-Bernoulli beam theory is employed to derive instantaneous transversal force distributions on the flexible hydrofoil from its deflection and the results are compared to the spatial distributions of hydrodynamic stresses obtained from the fluid velocity field.

Modified thrust empirical formula of a flapping foil by including the effects of azimuth angles

Wave energy is one of the most available sources of renewable energy in the world. It has been previously proven that the flapping foil can generate thrust forces using energy from the surface waves and an empirical formula was proposed to predict the thrust forces generated by a flapping foil consist of NACA0015 section (Kumar and Shin, 2019a). However, the proposed empirical formula was restricted to the head waves i.e. 0° azimuth angle which was not useful for the flapping foils encountering with oblique and following waves. Therefore, in this study, the thrust empirical formula was modified to include the effects of azimuth angles based on the experimentally obtained data. And the modified empirical equations were validated by the combination of foils experimentally.

Effects of Motion Parameters on the Propulsion and Energy Harvesting Performance of a Wave-Driven-Heaving Flapping Foil

The propulsion and energy harvesting performances of a flapping foil have been investigated base on immersed boundary method. The heaving and pitching motions are respectively driven by the wave and the external actuator. The effects of phase difference and frequency difference between the pitching and heaving motion as well as the nonharmonic pitching motions on the propulsion and energy harvesting performances were studied at the Re=1100. For the small pitching amplitude of 30°, the upstream propulsion is the highest when the phase difference is 270°, and the nonharmonic motion is ineffective for enhancing propulsion. For the large pitching amplitude of 76.3°, the downstream propulsion and energy harvesting efficiency are the highest when the phase difference is 247.5°. The optimum frequency difference is zero, i.e. the pitching frequency is equal to the wave frequency. Meanwhile, the nonharmonic motion is helpful for improving the propulsion and the energy harvesting efficiency. The downstream propulsion is increasing with the increase of nonharmonic parameter of β. The maximum time-averaged pure output power coefficient of 1.09 is obtained at β=1.85. But the highest energy harvesting efficiency of 45.58% is obtained at β=1.15.

Влияние отверстий в пористой поверхности земли на парящий полет насекомого

Aerodynamics of a flapping foil at low Reynolds number in close proximity to the ground in aperture effect are studied by numerical simulations based on the normal hovering motion mode. A vortex street is interestingly generated by both ground and aperture effects and the rotation of the foil. The study reveals that the aperture takes a force-reduction effect and a large enough aperture effectively can remove the ground force-enhancement effect produced when the foil is in close proximity to the ground. This paper provides an effective method of optimizing foil-flapping flight design of flying robotics over a porous plane.

A Model for Performance Estimation of Flapping Foil Operating as Biomimetic Stream Energy Device

During the recent period intensive research has focused on the advancement of engineering and technology aspects concerning the development and optimization of wave and current energy converters driven by the need to increase the percentage of marine renewable sources in the energy-production mix, particularly from offshore installations. Most stream energy-harvesting devices are based on hydro-turbines, and their performance is dependent on the ratio of the blade-tip speed to incident-flow speed. As the oncoming speed of natural-occurring currents varies randomly, there is a penalty for the latter device’s performance when operating at non-constant tip-speed ratio away from the design value. Unlike conventional turbines that are characterized by a single degree of freedom rotating around an axis, a novel concept is examined concerning hydrokinetic energy converters based on oscillating hydrofoils. The biomimetic device includes a rotating, vertically mounted, biomimetic wing, supported by an arm linked at a pivot point on the mid-chord. Activated by a controllable self-pitching motion the system performs angular oscillations around the vertical axis in incoming flow. In this work, the performance of the above flapping-foil, biomimetic flow energy harvester is investigated by application of a semi-3D model based on unsteady hydrofoil theory and the results are verified by comparison to experimental data and a 3D boundary element method based on vortex rings. By systematical application of the model the power extraction and efficiency of the system is presented for various cases including different geometric, mechanical, and kinematic parameters, and the optimal performance of the system is determined.