Pitch Amplitude Research Articles

Flapping-wing energy harvesting experiences with modified time variations at high re-number

AbstractWind-energy converters with rotating blades are most common for energy harvesting. In special cases a system of flapping wings may be of interest where the wings are oscillating in combined pitching and flapping (plunging) modes respectively. Then the ratio of pitching and plunging amplitudes is of main concern: If the amplitude of the pitching motion exceeds the amplitude of the induced angle of the plunging motion, energy transfer from the oncoming flow is present. To accomplish maximum energy transfers and maximum efficiencies a considerable number of parameters have to be varied. Most of the published investigations assume harmonic time variations of both pitching and plunging motion. In the present paper the time variation will be modified such that the stroke reversal times are favorably be influenced, i.e., the fraction of the period where the airfoil changes the angle of attack from its maximum to its minimum or vice versa. In the present paper this variation is represented by an analytical function. Further, the phase between pitch and plunge motion and the time dependent deformation of the airfoil-leading edge will be investigated. It will be shown that the different variations and modifications will lead to considerable increases of power transfer and efficiency.

Characteristics of gusts with different velocity profiles and control parameters

The characteristics of gust flow are essential for gust response and alleviation. To investigate the influence of control parameters on gusts with different velocity profiles, four vertical gust profiles were designed. Methods were proposed to generate them with two pitching airfoils in a low-speed water tunnel. The velocity field was measured via phase-locked particle image velocimetry. The coefficient of determination R2 was proposed to evaluate the generated gust profile quality, which referred to the quality of the vertical velocity profile. The influence of control parameters on different gust profiles was investigated, and the cause of the profile distortion was explored. For continuous sine gusts, the gust ratio GR increased approximately linearly with the pitching amplitude, while the gust ratio initially increased and then decreased with increasing frequency. As the two control parameters increased, the flow uniformity decreased because the airfoil wakes disturbed the measured flow field. In terms of continuous 1-cosine gusts, the gust ratio increased nonlinearly with pitching amplitude. Compared with those of the sine gusts, the GR values of the 1-cosine gusts were higher, whereas the R2 values were lower. In addition, the discrete and continuous gust profiles had similar distortion near the peaks. However, discrete gusts had lower R2 values than continuous gusts because the starting and stopping vortices of the pitching airfoils disturbed the gust flow. Based on these findings, a method to improve the profile quality and field uniformity by increasing the spacing of the pitching airfoils was proposed. This work can support further studies of gust response and alleviation during complex gust encounters.

Hydrodynamic Analysis of Different Formation Configurations of Catamaran in Regular Head Waves

When undertaking long-distance missions at sea, vessels aim to achieve an extended operational range through drag reduction and energy efficiency, while enhanced wave resilience also provides substantial benefits. In this work, the Delft-372 catamaran is utilized to investigate the feasibility of drag reduction and roll mitigation for catamaran formation sailing in waves, analyzing the effects of three different formation configurations and varying spacings. The overset grid method was employed to simulate vessel motions, while the Volume of Fluid (VOF) method captured the free surface. First, the numerical results of the catamaran’s resistance, pitch, and heave motion amplitudes under different wave conditions were compared with experimental data to verify the accuracy of the CFD numerical method, and a grid convergence analysis was performed. Next, numerical models of the Delft-372 catamaran were constructed in parallel, tandem, and lateral formations under wave conditions. The results of the single-ship simulation were employed as a benchmark to analyze the impact of different formation configurations and varying lateral and longitudinal spacings on the resistance, pitch, and heave motions of the catamarans. The study also examined the effects of wave interference between vessels and the combined influence of external waves on individual and overall hydrodynamic performance. Results indicated that the tandem formation outperformed the parallel and lateral formations, with optimal performance observed at the longitudinal distance of 1 LPP. Generally, during navigation, the follower catamaran should ideally be positioned in the trough of the stern wave of the leader catamaran.

Cyclic pitch control for aerodynamic load reductions of floating offshore wind turbines under pitch motions

Floating offshore wind turbines suffer severe aerodynamics under platform motions. Novel control methods are urgently needed to improve power and load performances. A mechanical cyclic pitch control strategy is introduced in this paper, and the load reduction effect on the NREL 5-MW wind turbine is investigated under dominant pitch motions. The simulation is performed by the standalone Aerodyn_Driver code. Results show that the relative airflow under pitch motions can be equated to a linear sheared flow and is only related to wind velocity and pitch angular velocity. Cyclic pitch control hardly affects power and thrust but significantly changes aerodynamic moments. The resultant moment and moment axis azimuth are defined, and they are controlled respectively by pitch amplitude and phase. The optimal pitch parameter equations to minimize pitching and yawing moments are derived from fitting and derivation, and the standard deviations of aerodynamic moments are reduced by over 70 % under the sinusoidal pitch motion and steady inflow below rated operation. This paper provides a new idea for the individual pitch control structure, and the mechanism study for aerodynamic control is important and instructive to fill the technological gap in mature pitch control strategies for floating offshore wind turbines.

Hydrodynamic performance of pitching foils with two leading-edge protuberances

Inspired by the tubercles on humpback whales, the ‘tubercle-effect’ first identified by (Fish and Battle, 1995; Fish and Lauder, 2006) had been studied extensively to understand their influence on overall efficiency for airfoils and wings. Pitching and/or heaving motion of foils produces net thrust inspired from fin-based locomotion of aquatic animals, and is often being proposed as a greener means of propulsion having reduced acoustic signature. With this aim in mind, the present work investigates the effect of using tubercles on pitching motion of foils. The hydrodynamic characteristics of finite aspect ratio pitching foils having leading-edge modifications in the form of two protuberances are investigated using experiments. The thrust and efficiency with and without protuberances are investigated for pure pitching motions at reduced frequencies (1.8 – 3.2) and pitching amplitudes (7.5°- 20°) for Reynolds number 2 × 104. The experimental results are compared with inviscid linear theory calculations which over-predict the mean thrust, while the amplitude of the lift force and its variation with reduced frequency is similar. The performance improvements in terms of thrust and efficiency for the modified design are restricted to ≥15° pitching amplitudes at higher reduced frequencies. The wake vorticity patterns obtained using Computational Fluid Dynamics investigations show the influence of the leading-edge vortex, which gets modified when the protuberances are used. The transition from 2S wake to 2P wake with the increase in the amplitude of oscillation is captured. The reversal of von Kármán Vortex Street with the pitching frequency and thus the transition from drag to thrust generation is observed for both the baseline and modified foil designs. The results indicate that protuberances over the leading-edge of hydrofoils can influence the hydrodynamics during pitching motion and can be effectively employed for performance tailoring based on the geometry and motion characteristics. The simplified setup used here is also meant to serve as a basis towards future research including verification and validation work for numerical solvers.

On the Lock-In Phenomena near the Transonic Buffet Onset of a Prescribed Pitching Airfoil

The limit cycle oscillation (LCO) in the transonic buffet on the fixed supercritical airfoil OAT15A under Ma = 0.73, AoA = 3.5° and Re≈3×106, is successfully simulated by means of the Reynolds Stress Model. Further, the buffet lock-in phenomena under prescribed pitch conditions near the buffet onset are also studied by evaluating the modified energy exchange based on the pitching component of the moment coefficients as well as the normalized relative phase map between the pitching component of the moment coefficients and the airfoil’s angular velocity. The zero energy transfer branches in the modified energy map fail to indicate the lock-in boundaries, while the normalized phase map generally outlines the lock-in boundaries for small pitch amplitudes near the buffet onset, which suggests that the lock-in occurs where the moment is in phase with the angular velocity at small pitch amplitudes near the buffet onset. For pitch amplitudes larger than 0.4°, the lock-in onset deviates from the phase shift, possibly due to the fact the instantaneous angle of attack can be lower than the buffet onset where the buffet phenomena may vanish.

Power performance of a model floating wind turbine subjected to cyclic pitch motion: A wind tunnel study

Wind tunnel experiments were performed with a miniature floating wind turbine model to study the effects of cyclic pitch motion on its power performance. The cyclic pitch motion was prescribed by two key parameters: pitch frequency and amplitude. The power performance of the turbine model was investigated at a frequency range of 0.1 − 5.0Hz and an amplitude range of 0 − 30°. Both the mean and time variation of the power production were analyzed, and the effects of the pitch parameters, i.e., the pitch amplitude and frequency, were investigated and discussed. The results show a clear periodicity of power variation and its dependence on pitch frequency and amplitude. For relatively small pitch frequencies (0.5 − 3.0Hz), the mean power and periodic power variation can be predicted based on the uniform and steady flow assumption. Compared to the power output in the baseline case of no pitch dynamics, cyclic pitch motions were found to cause higher power fluctuations, which were contributed by both the pitch motion and flow turbulence. Finally, the temporal variation of the free-rotation speed, used as an indicator of available aerodynamic power, is found to be periodic when the turbine is under cyclic pitch motion. This suggests the possibility of applying dynamic rotor control strategies to maximize power production.

Impact of floating turbine motion on nacelle lidar turbulence measurements

We determine the impact of floating turbine motion on turbulence measurements from a four-beam lidar by emulating its scanning configuration and retrievals within atmospheric turbulence boxes. Since the elevation angle of the lidar beams is small and the two bottom lidar beams point closely to the horizontal plane, we also evaluate the turbulence estimation abilities of a two-beam lidar. For the two-beam nacelle lidar, the variance of the individual beams is close to the target u-variance and closer than that we compute by reconstructing the u-velocity component with the two lidar beams radial velocities. By using floating turbine motion measurements from Hywind, we show that the floating turbine motion impacts turbulence estimations of the nacelle lidar. Roll does not have a clear impact on nacelle-lidar turbulence, whereas both the beam and the u-reconstructed variances increase with pitch amplitude.

Visual scanning patterns of a talking face when evaluating phonetic information in a native and non-native language.

When comprehending speech, listeners can use information encoded in visual cues from a face to enhance auditory speech comprehension. For example, prior work has shown that the mouth movements reflect articulatory features of speech segments and durational information, while pitch and speech amplitude are primarily cued by eyebrow and head movements. Little is known about how the visual perception of segmental and prosodic speech information is influenced by linguistic experience. Using eye-tracking, we studied how perceivers' visual scanning of different regions on a talking face predicts accuracy in a task targeting both segmental versus prosodic information, and also asked how this was influenced by language familiarity. Twenty-four native English perceivers heard two audio sentences in either English or Mandarin (an unfamiliar, non-native language), which sometimes differed in segmental or prosodic information (or both). Perceivers then saw a silent video of a talking face, and judged whether that video matched either the first or second audio sentence (or whether both sentences were the same). First, increased looking to the mouth predicted correct responses only for non-native language trials. Second, the start of a successful search for speech information in the mouth area was significantly delayed in non-native versus native trials, but just when there were only prosodic differences in the auditory sentences, and not when there were segmental differences. Third, (in correct trials) the saccade amplitude in native language trials was significantly greater than in non-native trials, indicating more intensely focused fixations in the latter. Taken together, these results suggest that mouth-looking was generally more evident when processing a non-native versus native language in all analyses, but fascinatingly, when measuring perceivers' latency to fixate the mouth, this language effect was largest in trials where only prosodic information was useful for the task.

Experimental and numerical studies on a passively deformed coupled-pitching hydrofoil under the semi-activated mode

Flexibility is expected to positively affect the hydrodynamic and energy-harvesting performance of deformable hydrofoils, which have a simple structure and can be easily implemented in practical engineering applications. However, the characteristics of the fluid-structure interaction and power capturing are complicated. In this study, to reveal the fluid-structure interaction (FSI) mechanism and the effects of the passive deformation on the energy-harvesting performance, a flexible hydrofoil to conduct a coupled-pitching motion under the semi-activated mode was proposed and investigated experimentally and numerically. In the experimental study, a deformation-measuring technology based on a digital imaging algorithm was developed and employed for water channel tests. The effects of the hydrofoil profile and activated pitching amplitude on the deformation status, torque output, and energy-harvesting performance were studied experimentally. In the numerical study, a three-dimensional unsteady two-way FSI model was established and validated using experimental results. The influence mechanisms of the damping torque coefficient, activated pitching amplitude, and elasticity modulus on the passive deformation, its phase difference with the activated pitching angle, and the hydrodynamic and energy-harvesting performances were studied. Compared with the rigid hydrofoil, the energy-harvesting efficiency and power coefficient of the passively deformable hydrofoil could be increased by 4.8 % and 8.0 %, respectively, as the phase difference zone was close to 3π/4. In addition, positive and negative phase difference zones for performance enhancement were identified, which provides a future direction for optimizing flexible hydrofoils and control strategies.

A multiparameter simulation-driven analysis of ship response when turning concerning a required number of irregular wave realizations

The growing implementation of Decision Support Systems on modern ships, digital-twin technology, and the introduction of autonomous vessels cause the marine industry to seek accurate modeling of vessel response. Despite the contemporary 6DOF models can be used to predict ship motions in irregular waves, the impact of their stochastic realization is usually neglected and remains under-investigated. Especially in the case of turning, differences arising from the stochastic representation of the waves may result in excessive ship motions or even stability failure during maneuver execution. Therefore, in this study, statistical distributions of maximum amplitudes of roll, pitch, and lateral acceleration calculated in two representative locations on board a passenger vessel were analyzed concerning stochastic wave realization and existing extremes. The research utilized 6DOF simulation data and numerous realizations of the irregular wave with random phases of its components. Furthermore, the required number of wave realizations allowing for capturing the actual ranges of ship response at an assumed confidence level has been determined and analyzed. Ultimately, the results were compared in the safety-critical cases concerning various wave and operational conditions. The outcome of this study may be found useful by all parties involved in developing maritime autonomous systems and modeling ship motions.

Study on the performance of a floating horizontal-axis tidal turbine with pitch motion under wave–current interaction

Waves can induce motion in the floating platforms that support tidal turbines, affecting their hydrodynamic loads. To study the non-constant hydrodynamic of floating tidal turbines in a wave condition, this paper investigates the effect of pitch motion on the power coefficient (CP), thrust coefficient (CT), and wake flow of a tidal turbine using computational fluid dynamics. A pitch motion experiment is designed to verify the validity of the numerical method. The results show that the CP and CT exhibit periodic fluctuations under pitch motion, with the fluctuation period being consistent with the pitch period. Waves do not change the overall fluctuation trend of the CP and CT, but they do complicate the fluctuations and increase the likelihood of blade fatigue damage. Pitch motion reduces the mean power, with large-amplitude pitch motions particularly likely to result in severe power loss. The low-velocity region of the wake under pitch motion exhibits significant periodic oscillations. The wake is more susceptible to the pitch period than the pitch amplitude, and small-period pitch motions force the wake to deform earlier, accelerating wake vortex dissipation and velocity recovery. Increasing the immersion depth reduces the effect of waves on tidal turbine performance, but is not conducive to wake recovery. In summary, the rational design of the immersion depth and limiting the movement amplitude of the floating platform have the potential to prolong the working life of tidal turbines and increase their power output.

Hydrodynamics and propulsion of a hydrofoil undergoing leading-edge pitching and traveling wave-based surface undulation

We numerically study the fluid–structure interaction of a free-stream flow across a hydrofoil pitching at its leading edge with superimposed traveling wave-based surface undulations. We utilize an in-house code that employs the sharp interface immersed boundary method and consider a constant pitching amplitude θ0 = 5°, a constant local amplitude-to-thickness ratio AL=0.15, and wave number K = 20 of surface undulation. We compare the effect of surface undulation on a pitching hydrofoil with that of a hydrofoil undergoing pure pitching or experiencing pure surface undulation. The findings reveal that surface undulation on the pitching hydrofoil increases thrust on the hydrofoil. The onset of asymmetry in the vortex street occurs at a lower pitching Strouhal number (St) due to the early formation of a vortex dipole. In addition to the presence of an asymmetric inverse von Kármán vortex street, higher pitching frequencies reveal re-deflection of the asymmetric inverse von Kármán vortices. We quantified dynamics of vortex dipole to explain the occurrence of asymmetric and re-deflected reverse von Kármán vortex street. Furthermore, the analysis reveals an optimum combination of St and phase speed that yields higher propulsive efficiency, as both motions compete in generating thrust. A linearly superimposed scaling analysis for the time-averaged thrust of the combined motion is also presented. The computations and scaling are found to be in good agreement.

Numerical Study of an Innovative Concept for a Multibody Anti-Pitching Semi-Submersible Floating Wind Turbine

The floating offshore wind turbine provides a feasible solution for the development of renewable ocean energy. However, the sizeable rotor diameter of the wind turbine results in large wind heeling moments and pitch amplitude. It will increase the structural loads and cause safety problems. Additionally, the contradictory nature between the stability and the sea-keeping of the floating structure requires that the more flexible method should be adopted to reduce the motion response of the floating offshore wind turbine. Therefore, an innovative concept of a multibody anti-pitching semi-submersible floating offshore wind turbine, named the MBAPSF, is proposed in this paper. The MBAPSF consists of a 5 MW braceless semi-submersible wind turbine and three wave energy converters. The multibody coupled numerical model is established by using an F2A tool, and the dynamic performance of the MBAPSF is compared with that of the traditional semi-submersible wind turbine named the TSSF. The results show that the innovative concept proposed in this paper can reduce pitch motion up to approximately 27% under different load cases, and the maximum bending moment and shearing force at the tower base are also reduced by more than 10%. Meanwhile, WECs are beneficial for increases in the total power generation capacity.

Influence of vibration parameters and fin structure parameters on heat transfer performance under vibration conditions

The occurrence of vibration in engineering vehicles during operation is a common phenomenon, and the utilization of vibration-enhanced heat transfer serves as a viable approach to enhance the efficiency of heat transfer in radiators. This study designs a vibration test platform for heat exchangers to investigate the impact of different vibration parameters on heat transfer performance. Additionally, a fin vibration model is constructed using overlapping grid technology to simulate the behavior of flat fins under varying vibration conditions. Corrugated fins were chosen for investigation under vibration conditions, utilizing an orthogonal experimental approach to analyze the impact of fin structural parameters on heat exchanger performance. Findings indicate that vibration enhances the air side heat transfer coefficient of the heat exchanger, in experimental settings, the gas side heat transfer coefficient of the heat exchanger demonstrated a maximum increase of 12.28%. Simultaneously, vibration induces an escalation in pressure loss, with the maximum drop reaching 28.72%. The heat transfer factor j of the heat exchanger exhibits an augmentation in response to heightened vibration intensity, while they diminish with escalating speed. Furthermore, vibration alters the impact of structural factors of corrugated fins on heat transfer efficacy. During vibration, the sensitivity of fin height and wavelength intensifies, whereas the sensitivity of pitch and wave amplitude diminishes. The findings of this research offer valuable insights for further investigation into the heat transfer capabilities of fins under vibration.

Undulatory Propulsion at Milliscale on Water Surface.

The oscillatory pitch motion at the leading edge of a millimeter-scale flexible sheet on the water surface can generate undulatory locomotion for swimming, similar to a honeybee vibrating its wings for propulsion. The influence of various parameters on such swimming strategy remains unexplored. This study uses magnetic milliswimmers to probe the propulsion mechanics and impact of different parameters. It is found that this undulatory propulsion is driven by capillary forces and added mass effects related to undulatory waves of the milliswimmers, along with radiation stress stemming from capillary waves at the interface. Modifying the parameters such as actuation frequency, pitch amplitude, bending stiffness, and hydrofoil length alters the body waveform, thus, affecting the propulsion speed and energy efficiency. Although undulatory motion is not a prerequisite for water surface propulsion, optimizing body stiffness to achieve a proper undulatory waveform is crucial for efficient swimming, balancing energy consumption, and speed. The study also reveals that the induced water flow is confined near the water surface, and the flow structures evolve with varying factors. These discoveries advance the understanding of undulatory water surface propulsion and have implications for the optimal design of small-scale swimming soft robots in the future.

Effect of Strouhal number on propulsion of tandem flapping foils

Motivated by the energy efficient locomotion by flock of birds and school of fish to develop biomimetic systems, the current study studies the propulsive performance of the tandem configuration of two-foil system. The effects of the kinematic motion parameters such as heave and pitch amplitudes and flapping frequency on the propulsive performance of the tandem two-foil system is yet to be explored comprehensively due to the complex nature of the wake-foil interaction. Here, we numerically investigate these effects by utilizing a finite element based moving mesh framework to model the flapping foil motion subjected to fluid flow. The performance of the upstream foil is found to be similar to that of an isolated single foil. However, for the downstream foil, a beating phenomenon is observed in the thrust response when the flapping frequency is different for both the foils. This feature can help tune propulsive performance of the foil system. Furthermore, through a control volume analysis, we show that sole reliance on the time-averaged streamwise velocity may not yield correct trends for the mean thrust forces, which has been typically followed in the literature. Variation in the time-averaged pressure in the wake is significant in predicting correct thrust forces.

Numerical validation of the dynamic aerodynamic similarity criterion for floating offshore wind turbines under equivalent pitch motions

Floating offshore wind turbines, as large equipment for deep-sea wind energy utilization, must be carefully studied for their aerodynamic performances under platform motions. In experiments, the model wind turbine designed by the traditional thrust coefficient similarity is usually insufficient for unsteady aerodynamic reproductions of the prototype wind turbine. In this paper, a dynamic aerodynamic similarity criterion based on the mapping of the optimal tip speed ratio is introduced for wind tunnel model tests, and a model wind turbine is designed using the NREL 5-MW prototype wind turbine. In this case, to avoid the over-height model tower aroused in pitch motions, a method of equivalent surge motions instead of pitch motions is proposed and validated for feasibility. Then dynamic aerodynamic similarities under different pitch amplitudes and frequencies are validated by the Unsteady Blade Element Momentum theory. Results indicate that temporal and spatial characteristics and hysteresis effects of thrust and power coefficients all maintain better similarity with those of the prototype wind turbine than those of the model wind turbine designed by the traditional criterion. This paper provides a criterion with equivalent pitch motions for unsteady aerodynamic studies in wind tunnel model tests, especially the high-fidelity Hardware/Software-In-the-Loop test.

The power-extraction regime of a figure-eight trajectory flapping-foil turbine

At specified Reynolds numbers Re=ρvc/μ=5×105, this study investigates the power-extraction regime of a flapping-foil turbine executing a figure-eight trajectory. This study thoroughly explored the impacts of trajectory shape, heave and pitch amplitudes, phase difference, and pitch axis location on the power-extraction regime of a flapping turbine. A figure-eight trajectory substantially bolsters the energy harvesting capacity, achieving a peak efficiency of up to 50%. This trajectory capitalizes on the energy generated from the drag encountered by the flapping foil, thereby marking a significant efficiency breakthrough. This could denote a considerable progression for flapping foils tailored for heave and pitch motions since the free stream can be optimally harnessed by the trajectory we have established. In scenarios where the flapping foil undergoes the same maximum effective angle of attack, a wake diffusion spectrum aligns with the Betz limit threshold. Crucially, the closeness to this efficiency frontier suggests a universal maximum effective angle of attack—a consistent law that remains valid for the conventional flapping turbine design. It implies that selections for stroke and pitch amplitudes should be methodical rather than arbitrary. In addition, the positioning of the pitch axis ought to be modified in tandem with phase difference adjustments to bolster the synchronization between heaving motions and resultant lift. The ideal phase difference is variable, contingent on pitch amplitude and pitch axis position. Even with low pitch amplitudes, fine-tuning the phase difference guarantees that the energy harvesting efficiency does not fall below 30%. Such an enhancement would significantly broaden the operational envelope and the parameter space for flapping turbines.

Investigation on the performance of a torque-driven undulatory swimmer with distributed flexibility

The locomotion of fish provides insight for the design of efficient swimming robotic devices. The current study presents a systematic investigation of the locomotion performance of a fish-like swimmer with a wide range of parameter settings. Two-dimensional simulations with the immersed boundary method in the framework of Navier–Stokes equations are employed for the fluid–structure interaction analysis. Unlike most previous studies where the kinematics of the swimmer is predetermined, the locomotion of the current swimmer is the response of a single periodic torque applied to the anterior part. In addition, current simulations applied a direct correspondence between code units and real-world units, providing more engineering-related guidance for the future design of microrobotic swimmers. The effect of the distribution of body stiffness on swimming performance and propulsion generation is discussed with different pitch frequencies and amplitudes. It was shown that swimmers with a more flexible posterior part have an advantage in undulatory swimming performance when the pitch angle is low or moderate. However, such an advantage disappears when the pitch angle or actuating frequency exceed a certain level. An analysis of the phase-averaged vorticity field and thrust sequence is given to clarify the change in performance due to the variation of flexibility.