Pitch Amplitude Research Articles

Configuration optimization of two tandem airfoils at low Reynolds numbers

Optimization was used to find the best configuration of two airfoils in tandem placed into an incoming flow. Upstream airfoil (forefoil) was pitching at a fixed frequency, while the downstream airfoil (hindfoil) was kept at a fixed angle of attack. Study was performed at a low Reynolds number of 30,000 based on chord length. Selig-Donovan 7003 (SD7003) was used for both airfoils, which is a high-performance airfoil specially designed for low Reynolds number flows. The optimization studies were conducted using a genetic algorithm (GA) to maximize aerodynamic performance. The design variables in this study were: horizontal and vertical spacing between the airfoils and hindfoil's angle of attack. Since the optimization process is time-consuming, machine learning was used to train four artificial neural networks (ANNs) to be coupled with genetic algorithm to reduce the computational cost. Two separate optimization cases were considered at two different orders of magnitude in pitching amplitudes of the forefoil, while the pitching frequency was kept at constant value. We found that in both cases, optimum tandem configurations had a smaller combined drag coefficient in comparison with the addition of two separate airfoils. The case with high pitching amplitude produced higher magnitude of lift, while the low amplitude case resulted in a significant improvement in aerodynamic performance.

Numerical Study on the Tank Heel Determination Using Smoothed Particle Hydrodynamics

Tank heel minimization is a significant issue in the design of LNG fuel tanks because it is associated with stable suction pump operation and thermal shock requirements during LNG bunkering. This study examined how the LNG tank heel is minimized, maintaining a suction pump fully submerged in LNG during dynamic vessel motion. The study assumed two LNG fuel tanks mounted on the forward deck of a 50,000 deadweight class oil product carrier. Information on the dimensions and shape of the LNG fuel tank was determined from Wartsila’s brochure, and the specifications of Vanzetti’s suction pump were referred to. The LNG fuel tank and LNG heel were modeled as rigid elements and hydrodynamically smoothed-particles, respectively. The number of particles could be determined by performing even keel analyzes by adding or subtracting particles until the target head was satisfied under the gravity load. To simulate the motion of the LNG fuel tank, the pitch and roll periods and amplitudes of the ship were calculated using the DNV classification rules. Visual observations of the dynamic flow during the pitch and roll motions with respect to the ship’s center of mass showed that the roll motion was more critical from the viewpoint of the LNG heel than the pitch motion. After performing the simulations for three cycles of roll and pitch motions, the suction pump submergence was reviewed in the last cycle. Under the conditions assumed in this study, a filling ratio of 15% was determined as the minimum LNG tank heel. Although the LNG heel has customarily been determined, the LNG heel needs to be determined through hydrodynamic analyses of each vessel because it depends on the shape of the fuel tank and the vessel motion characteristics.

Numerical study of the propulsive performance of two-dimensional pitching foils at very high frequencies: scaling laws and turbulence effects

PurposeThis paper aims to analyze the propulsive performance of small-amplitude pitching foils at very high frequencies with double objectives: to find out scaling laws for the time-averaged thrust and propulsive efficiency at very high frequencies; and to characterize the Strouhal number above which the effect of turbulence on the mean values cannot be neglected.Design/methodology/approachThe thrust force and propulsive efficiency of a pitching NACA0012 foil at high reduced frequencies (k) and a Reynolds number Re = 16 000 are analyzed using accurate numerical simulations, both assuming laminar flow and using a transition turbulence model. The time-averaged results are validated with available experimental data for k up to about 12 (Strouhal number, St, up to 0.6). This study also compares the present numerical results with the predictions of theoretical models and existing numerical results. For a foil pitching about its quarter chord with amplitude α0 = 8o, the reduced frequency is varied here up to k = 30 (St up to 2), much higher than in any previous numerical or experimental work.FindingsFor this pitch amplitude, turbulence effects are found negligible for St ≲ 0.8, and affecting less than 10% to the time-averaged thrust coefficient for larger St Linear potential theory fails for very large k, even for the small pitch amplitude considered, particularly for the power coefficient, and therefore for the propulsive efficiency. It is found that St2 for large St, in agreement with recent models, and the propulsive efficiency decays as 1/k, in disagreement with the linear potential theory.Originality/valuePitching foils are increasingly studied as efficient propellers and energy harvesting devices. Their performance at very high reduced frequencies has not been sufficiently analyzed before. The authors provide accurate numerical simulations to discern when turbulence is relevant for the computation of the time-averaged thrust and efficiency and how their scaling with the reduced frequency is affected in relation to the laminar-flow predictions. This is relevant because some small-amplitude theoretical models predict high propulsive efficiency of pitching foils at very high frequencies over certain ranges of the structural parameters, and only very accurate numerical simulations may decide on these predictions.

Control of Reverse Flow over a Cantilevered Blade Using Passive Camber Morphing

In high-speed rotorcraft applications, large sections of a blade undergo reverse flow due to a high advance ratio. Flow separation at the sharp aerodynamic leading edge during reverse flow leads to negative lift, pitching moment, and drag penalties. The kinematics of a rotor blade leads to a dynamic stall in reverse flow, which further accentuates the problem by causing unsteady loading. The present experimental study shows that these problems can be mitigated by passively morphing the camber near the trailing edge of the blade. A finite-span cantilevered NACA 63-218 blade was examined at a chord-based Reynolds number of with and without trailing-edge morphing. The morphing was implemented by deflecting the last quarter-chord near the trailing edge by 5, 10, or 15 deg. Experiments included global measurements of the forces and moments using a load cell as well as detailed flow measurements using stereoscopic particle image velocimetry. A couple of scenarios were explored: static pitch and dynamic pitch at different pitch amplitudes and frequencies. Cambering of the blade near its trailing edge led to a significant reduction in the size of the separation region over the model, and of the wake. For the static pitch case, it led to a large reduction in drag and pitching moment and a minor reduction in negative lift. For the dynamic pitch cases, the hysteresis loop was significantly reduced, leading to a large reduction in unsteady loading.

Onset of dynamic stall of tubercled wings

In the present study, numerical simulation of the flow field of the tubercled NACA0021 (National Advisory Committee for Aeronautics) wing has been conducted with the large eddy simulation model. Then, proper orthogonal decomposition (POD) analysis has been carried out at trough and peak sections. According to the spatial distributions and temporal coefficients in the case of αA=5°, the physical backgrounds of corresponding POD modes could be identified, including flow attachment, separation, and the dynamic stall vortex (DSV). The onsets of local dynamic stall could be indicated with the extremum values of the DSV mode coefficients, which stay almost synchronized at trough and peak. Actually, the DSV is originally generated at trough and then moves to peak due to the spanwise convection induced by streamwise vorticity. The generation of the secondary vortex at trough is triggered with the streamwise pressure gradient, the development of which pinches off the feeding vorticity of the DSV and results in the detachment of the DSV. Eventually, the influence of pitching amplitude has also been discussed. The strength of the DSV at peak is increased with a larger pitching amplitude, which could be interpreted with the feeding sheet connected with the leading edge.

Seakeeping and resistance analysis of 1200 GT passenger ship fitted with NACA 4412 stern foil using CFD method

Seakeeping performance is one of the requirements to ensure the convenience and safety of life at sea, especially for passenger ships. In this paper, the result of computational fluid dynamics (CFD) analyses concerning the effect of NACA 4412 stern foil to the improvement of seakeeping quality and resistance of 1200 GT passenger ship are presented. The fitting of stern foil has become a popular method for the improvement of ship design. Stern foil is hydrofoil attached to the transom of the vessel located at the stern part below the waterline. The analysis was developed on the conditions of regular and irregular head waves. The CFD computation on 8 variations of the stern foil position and attack angle has been carried out by using Numeca Fine/Marine. The study confirms that the ship resistance decrease by 3.6 % at the service speed of the ship. The improvement of heaving and pitching amplitudes, as well as heaving acceleration, are significant for the hull vane located at 50% of displacement draft and 1% of displacement length with the attack angle of −4°.

Fluid structure interactions of a pitching wing at high angle of attack

This paper deals with the study of the flow around a pitching wing at high angle of attack. Different pitching amplitudes and frequencies are studied using DIC and LPT measurements. The Fluid Structure Interactions are shown and exhibit that the vortex shedding could be reduced by actuating the wing at specific frequencies.

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.

Wake-foil interactions and energy harvesting efficiency in tandem oscillating foils

Oscillating foils in synchronized pitch and heave motion can harvest hydrokinetic energy while leaving behind a distinct trail of alternating signed vortices. This work correlates the specific foil kinematics (frequency, pitch, and heave amplitude) with the resulting wake structure by defining three modes within the energy harvesting kinematic regime. Using an array of two tandem oscillating foils, the performance of the trailing foil is modeled by analyzing the wake between the two oscillating foils. The resulting efficiency of the trailing foil is redefined by accounting for the steady and unsteady components of the local flow, yielding a closer match to the single foil efficiency curve.

Parametric automatic optimal design of USV hull form with respect to wave resistance and seakeeping

As the Unmanned Surface Vehicle (USV) plays an increasingly important role in ocean exploration, the performance requirements of the USV are becoming higher and higher. This paper presents a parametric automatic multi-objective optimization design of USV based on two-step optimization strategy. The focus of our work is on the parametric automatic optimization design of USV hull form with respect to resistance and seakeeping in waves. The wave resistance, the vertical acceleration of the center of gravity, and the pitch amplitude of the USV are selected as the optimization objectives. The parametric modeling and design variables are selected for the hull. Second order Response Surface Method (RSM) is used to build approximate model instead of numerical simulation in the optimization process to reduce the optimization time. The Particle Swarm Optimization (PSO) algorithm and Sequential Quadratic Programming (SQP) algorithm are used to solve the optimization model. Through the integration of NX, STAR-CCM+, and Excel in the intelligent platform, automatic optimization is realized. The effectiveness of the automatic optimization design method is verified by taking a 7 m USV as an example. This method provides a solution for the automatic optimization design of the USV hull form.

Research on hydrodynamic characteristics of horizontal axis tidal turbine with rotation and pitching motion under free surface condition

To obtain the hydrodynamic loads of a floating horizontal-axis tidal turbine with rotation and pitching motion under the free surface condition, a numerical simulation method based on CFD is established. The inflow direction load, power and pitching moment coefficients at different pitch periods, pitch amplitudes and blade tip-immersion depths were analyzed. The results show that the instantaneous values of the inflow direction load, power and pitching moment coefficients have obvious periodic fluctuations, and the fluctuation amplitude increases with the increase of the pitch frequency and amplitude. On this basis, the damping and additional mass coefficients are obtained based on the least square method. The damping coefficient of inflow direction load and power coefficients fluctuates periodically, and the fluctuation period is equal to the pitch period. The damping coefficient of pitching moment coefficient also fluctuates periodically, and the fluctuation period is not only related to pitch period, but also related to the rotation period of the turbine. The research findings can provide relevant data for studying the coupling motion of floating tidal current energy device and control design of the output electricity.

Vertical force generation of a vectorial thruster that employs a rigid flapping panel

The vertical force generation and flow features of a flapping panel that employs combined motion of horizontal oscillation, longitudinal rotation, and leading-edge-based pitching motion were investigated numerically. The sole vertical force generation is realized by combining the horizontal oscillation and longitudinal rotation, while the vertical force and forward thrust are obtained simultaneously by employing the combined motion of the horizontal oscillation, longitudinal rotation, and pitching motion about the leading edge of the panel. The effects of the phase shift (Ψ) of the longitudinal rotation and the amplitudes of the longitudinal rotation and pitching motion are investigated and discussed, respectively. Results show that the phase shift determines the instantaneous attitude of the panel and influences the directions of the instantaneous generated forces and thus plays an important role in the vertical force generation. The panel could generate stable forward thrust while maintaining the pitching motion constant and adjusting the longitudinal rotation amplitude, and in the meantime, the vertical force increases linearly with the rotation amplitude. On the other hand, the vertical force may change to the opposite direction when the longitudinal rotation is kept constant and the pitching amplitude is adjusted. The results of the current research show the potential of employing these kinds of combined motions to fish-tail-mimic propulsors of robotic fishes that pursue high maneuverability.

Opening the air‐chamber of an oscillating water column spar buoy wave energy converter to avoid parametric resonance

The oscillating-water-column (OWC) spar-buoy is a type of wave energy converter that may exhibit undesirable large roll and pitch amplitudes caused by a dynamic instability induced by parametric resonance. The occurrence of this phenomenon not only reduces the power extraction but significantly increases the structural loads on the buoy, the turbine rotor and on the mooring system. The paper compares the parametric resonance behaviour of two configurations of an OWC spar-buoy using experimental data obtained in a wave flume at a scale of 1:100. The configurations investigated were: (1) closed and (2) fully open-air chamber. The experimental tests covered a wide range of regular and irregular waves, as well as in free decay experiments. Results showed that opening the air chamber reduces the coupling between the buoy and the OWC within, thus shifting the damped natural heave frequency of the system in comparison with the closed chamber configuration. This effect changes parametric resonance characteristics of the two configurations due to the coupling between roll/pitch and heave modes. Moreover, for specific wave frequencies, the occurrence of parametric resonance observed when the chamber is closed do not occur while the air chamber is fully open. These results suggest the possibility of controlling a pressure relief valve installed on top of the device to reduce parametric resonance whenever this dynamic instability is detected.

Effect of blade pitch control on dynamic characteristics of a floating offshore wind turbine under platform pitching motion

Blade pitch control (BPC) is an indispensable part of a variable speed wind turbine, which maintains a stable power output by adjusting the blade pitch angle to adapt to the changing inflow speed introduced by the platform pitching motion (PPM). An integrated aeroelastic-servo transmission system of a floating offshore wind turbine (FOWT) is established and validated. Comparing with existing models, our model considers the effect of the BPC on the FOWT, apart from the dynamic characteristic of the drivetrain and the aeroelastic coupling of the blade. Firstly, dynamic behaviours of the FOWT under different tip speed ratios are compared. Then the performance of FOWT with and without the BPC influence is compared, followed by a dynamic analysis of the FOWT under a varying platform pitching amplitude. Results show that the tip speed ratio slightly alters the FOWT performance under the PPM. Considering the effect of the BPC, the fluctuation of the generator power reduce, but the aerodynamic thrust tends to enlarge the PPM. The non-torque loads induced by the PPM are insensitive to BPC. Fluctuation of the system response increases with increasing platform pitching amplitude.

Modeling and Test Results of an Innovative Gyroscope Wave Energy Converter

An improved Maximum Power Point Tracking (MPPT) method based on a purely mechanical wave energy converter (WEC) of gyroscope precession is proposed. The method adopts dynamic perturbation step adjustment, which improves the stability of power output and reduces steady-state oscillation. The paper introduces the principle of the device, establishes the mathematical model, and obtains the complete expression of power. The effect of wave frequency, pitch amplitude, power take-off (PTO) damping coefficient, and flywheel rotating speed on power output is analyzed. The output regression equation is established, and the extraction conditions of the maximum power are summarized and predicted. Aiming at the time-varying nature of actual ocean waves, a variable step size modified maximum power point (MPP) tracking control algorithm based on perturbation and observation (P&O) method is proposed. The algorithm has a unique technology to dynamically change the perturbation size, which not only improves the dynamic response but also reduces the oscillation. Besides, the boundary conditions ensure that the algorithm will not deviate from the motion trajectory, and the average filtering method and steady-state judgment can further reduce steady-state oscillation. In various ocean conditions, the proposed method has better output stability compared with other variable step size algorithms. Finally, different wave working conditions are given in the experiment, and the results verify the effectiveness of the proposed MPPT control strategy in experimental equipment. The device will be suitable for distributed power sources in small islands and ports.

Ultrasonic vibration–assisted incremental sheet metal forming

This paper presents a comprehensive investigation on the incremental sheet metal forming assisted by ultrasonic vibration (UV). With the aid of a new acoustoplasticity constitutive model which can accurately capture the deformation response to ultra-high strain rates, extensive numerical analyses on incremental sheet metal forming under UV were conducted by using the finite element method. Corresponding experimental investigations were also carried out to examine the capacity of the constitutive and numerical models. The effects of critical parameters, such as tool size, tool revolution speed, feed rate, pitch and tool vibration amplitude, on the forming force, maximum sheet thickness reduction and springback, were investigated in detail. It was found that the models can realistically predict the incremental sheet metal forming under UV. It is expected that this research can facilitate the development of ultrasonic vibration–assisted forming techniques.

Floating protective barriers: evaluation of seaworthiness through physical testing, numerical simulations and field deployment

Floating protective barriers provide essential protection to critical governmental, commercial, and private assets that are vulnerable to water-borne intrusion, such as liquefied natural gas terminals, tankers, etc. These barriers require additional evaluation in the case of their deployment at significant water depth in offshore environments. The seaworthiness of the Triton® barrier design developed by HALO Maritime Defense Systems (US) was investigated through a combination of field deployment, physical testing and numerical simulations. The full-scale Triton® barrier, deployed and inspected south-southwest of White Island, Isles of Shoals, New Hampshire, provided important information on its dynamic behavior and the overall structural integrity under monitored environmental conditions. Physical tests of a Froude-scaled barrier model were conducted in Chase Ocean Engineering Laboratory wave tank at the University of New Hampshire to properly measure response of the structure and its mooring to different single-frequency waves directed parallel and normal to the model. Both physical tests and field study load cases were numerically simulated in finite element Hydro-FE software. The comparisons indicated a good correspondence between physical tests and numerical models in terms of heave, pitch, roll and force response amplitude operators. Overall, the full-scale Triton® barrier has demonstrated robust performance during the offshore field deployment.

Propulsion and energy harvesting performances of a flexible thin airfoil undergoing forced heaving motion with passive pitching and deformation of small amplitude

The fluid–structure interaction in a foil undergoing prescribed heave with passive pitching and flexibility about any pivot is formulated in the linear inviscid limit using a quartic approximation for the deflection. The resulting system of three algebraic equations is valid for arbitrary mass and stiffness distributions of the foil. The small pitching and deformation amplitudes result linearly from two of the equations, while the third equation provides the force at the pivot point that generates the heaving motion, and hence the power input. This general formulation allows to analyze jointly both the propulsion and the energy harvesting problems for this class of flapping foils. In the first case, the thrust force is readily obtained from the prescribed heave and the resulting pitching and deformation, and consequently the propulsive efficiency once the power input is computed. In the second problem, the energy may be harvested by linear and/or torsional dampers at the pivot point, so that the efficiency of the system is readily computed once the pitch motion and the power input are obtained. Thus, the present work allows for a depth parametric survey and analysis of these two physical problems. The best performance is usually obtained around the first natural frequency of the fluid–structure system, which is obtained here by minimizing an algebraic function. The formulation is validated by reproducing some previous results for both problems, most of them obtained numerically for rigid foils and without the simplicity nor the richness in the parameter space of the present formulation. The parametric range for which flexibility maximizes the propulsion and the energy harvesting efficiencies in relation to an otherwise identical rigid-foil system is analyzed.

Hydrodynamic and energy extraction properties of oscillating hydrofoils with a trailing edge flap

In order to improve the energy extraction efficiency of the oscillating hydrofoil, this research proposes a model of an oscillating hydrofoil with trailing edge flaps. In this study, firstly we established the equation of the flap swing motion equation and that of the effective angle of attack angle, then the model of simple oscillating hydrofoil structure was numerically simulated using the dynamic and moving grid technology of the CFD software. Secondly, the model of oscillating hydrofoil structure was modified with trailing edge flap and the model was numerically simulated with dynamic and mobile grid technology of CFD software with refined the equations of motion and the equation of effective attack angle of flap swinging. The simulation results show that the length, the pitching amplitude and the frequency of the trailing-edge flap significantly affect the efficiency of the energy extraction. There is an optimal range for each of the three main parameters to maximize the energy extraction efficiency and the time average efficiency for specific angle of attack compared to the primary hydrofoil. The use of the trailing-edge flap may increase the time averaged efficiency by 81%. The flap increases the camber angle of the hydrofoil, and improves the lift coefficient of the whole hydrofoil, which leads to the improvement of the energy extraction efficiency of the hydrofoil. With the increase of lift coefficient, the drag coefficient also increases. As for the reliability and stability of the oscillating hydrofoil device, the drag of the oscillating hydrofoil should be within the range that the oscillating hydrofoil device can bear while improving the time average efficiency.

Experimental study on unsteady aerodynamic characteristics of deformed blades for vertical axis wind turbine

Based on the self-deforming blade model and the related wind tunnel test platform, the experiments with synchronous deformation and pitch of the blade were carried out to simulate the operating condition of the blade on the vertical axis wind turbine (VAWT). Taking NACA0012 as the reference blade, the unsteady aerodynamic characteristics of the blade deformation at different deformation frequencies and amplitudes were investigated at low Reynolds number of 2.5 × 105. It is found that the maximum lift force of the blade with deformation amplitude of 0.06c is raised by nearly 60% compared with that of the rigid blade. Secondly, by applying the same deceleration frequency, same pitch amplitude and different initial angles of attack to the blade, it is observed that the flow hysteresis phenomena are obviously different from that of applying various synchronous pitch and deformation amplitudes, and the special aerodynamic characteristic curves are obtained. The lift force increases significantly with the rise of deformation amplitude and drag force, while the lift-drag ratio increases in one cycle. The study in this paper proves the applicability of the blade with this deformation law in the VAWT, and provides a reference for its application on the design of VAWT.