Nonlinear characterization of concurrent energy harvesting from galloping and base excitations

An energy harvester is proposed to concurrently harness energy from base and galloping excitations. This harvester consists of a triangular cross-sectional tip mass attached to a multilayered piezoelectric cantilever beam and placed in an incompressible flow and subjected to a harmonic base excitation in the cross-flow direction. A coupled nonlinear-distributed-parameter model is developed representing the dynamics of the transverse degree of freedom and the generated voltage. The galloping force and moment are modeled by using a nonlinear quasi-steady approximation. Under combined loadings and when the excitation frequency is away from the global natural frequency of the harvester, the response of the harvester mainly contains these two harmonic frequencies. Thus, the harvester’s response is generally aperiodic and is either periodic with large period (i.e., period- \(n\) ), or quasi-periodic, or chaotic. To characterize the harvester’s response under a combination of vibratory base excitations and aerodynamic loading, we use modern methods of nonlinear dynamics, such as phase portraits, power spectra, and Poincaré sections. A further analysis is then performed to determine the effects of the wind speed, frequency excitation, base acceleration, and electrical load resistance on the performance of the harvester under separate loadings.     

结构振动对湍流近尾迹的影响

研究了圆柱绕流中流体与结构的相互作用,侧重结构振动对湍流尾迹的影响,用激光测振仪测量圆柱在升力方向的位移;用热线和LDA（二维）测量湍流的近尾迹,通过变化自由流的速度和圆柱体直径（特征尺寸）来变化雷诺数,用两个振动特性不同的（一个相对刚性,一个相对弹）圆柱来产生尾迹,研究固体结构振动对湍流近尾迹的平均速度场和湍流场的影响,结果表明,结构自由振动对湍流近尾迹场影响明显,该影响随雷诺数的变化不明显。     

Experimental investigation on the wake interference among wind turbines sited in atmospheric boundary layer winds

We examined experimentally the effects of incom-ing surface wind on the turbine wake and the wake interfer-ence among upstream and downstream wind turbines sited in atmospheric boundary layer (ABL) winds. The experi-ment was conducted in a large-scale ABL wind tunnel with scaled wind turbine models mounted in different incom-ing surface winds simulating the ABL winds over typical offshore/onshore wind farms. Power outputs and dynamic loadings acting on the turbine models and the wake flow char-acteristics behind the turbine models were quantified. The results revealed that the incoming surface winds significantly affect the turbine wake characteristics and wake interference between the upstream and downstream turbines. The velocity deficits in the turbine wakes recover faster in the incoming surface winds with relatively high turbulence levels. Varia-tions of the power outputs and dynamic wind loadings acting on the downstream turbines sited in the wakes of upstream turbines are correlated well with the turbine wakes charac-teristics. At the same downstream locations, the downstream turbines have higher power outputs and experience greater static and fatigue loadings in the inflow with relatively high turbulence level, suggesting a smaller effect of wake inter-ference for the turbines sited in onshore wind farms.     

DNS of heat transfer increase in a cylinder stagnation region due to wake-induced turbulence

Heat transfer in the stagnation point area of a heated cylinder is investigated using Direct Numerical Simulation (DNS). The heated cylinder is subjected to the turbulent wake of a smaller cylinder placed upstream. Two Reynolds numbers based on the diameter of the heated cylinder of 13,200 and 48,000 are chosen. In accordance with correlations in the literature, an increase in heat transfer compared to fully laminar flow is found for all angles along the front circumferential area of the heated cylinder. However, due to the presence of the wake, the maximum increase is shifted away from the centerline. The characteristic turbulence level and Nusselt number in the present study are an order of magnitude higher than those reported in previous simulations. The DNS results obtained, are in good agreement with an existing experimental correlation. Finally, relevant flow structures and instantaneous temperature fields are visualized.     

The wake flow downstream of a propeller-rudder system

We report wall-resolved, large-eddy simulations for the case of a propeller operating upstream of a hydrofoil, mimicking a rudder. Our primary objective is the identification of wake features that are unique to this coupled system, when compared to open-water cases, which are usually the focus of experiments and computations in the literature. We were able to achieve unprecedented levels of numerical resolution, which capture the dynamics of all energetic eddies in the flow by using a scalable, conservative, structured solver in cylindrical coordinates. The boundary conditions on the rotating propeller and hydrofoil were enforced via an immersed boundary formulation. The largest values of turbulent stresses in the wake of the hydrofoil are achieved outwards from the radial coordinate of the tip of the propeller blades. This is due to spanwise gradients across the hydrofoil (in the direction parallel to the span of the hydrofoil), producing a displacement of the pressure side legs of the tip vortices towards outer coordinates, where they experience shear with the wake of the hydrofoil. The evolution of turbulence is non-monotonic across the streamwise direction. This is a consequence of the growing shear resulting from the complex interactions involving the shear layers from the trailing edge, the tip vortices and the two branches of the hub vortex coming from the two sides of the hydrofoil. Such a shear is reinforced by the spanwise velocities developed by the two branches of the propeller wake across the hydrofoil. Compared to an isolated propeller, these phenomena enhance turbulence production. The present results highlight that a downstream hydrofoil, typical of surface ships, is able to significantly intensify the wake signature of a propeller.     

Measurements of mean and turbulence quantities in the curved wake of an airfoil

Measurements of mean and turbulence quantities are presented for a curved wake of an airfoil. The wake is generated by placing a NACA 0012 airfoil of 0.150 m chord length at one chord length upstream of a 90° bend. The bend has a square cross-section of 0.457 m × 0.457 m, a mean radius-to-height ratio of R/H=1.17, and concave and convex radii of curvature 0.764 and 0.307 m, respectively. In addition to streamwise curvature, the wake is subjected to varying streamwise and radial pressure. The measurements were carried out at mainstream air velocities of 10, 15 and 20 m/s. The results are presented for the mean streamwise velocity, five components of turbulence stresses, the calculated wake half-width and the maximum velocity defect. The results showed the formation of an asymmetric wake about the wake centreline, with a larger wake half-width on the inner side. The wake half-width on both inner side and outer side of the wake decrease with mainstream velocity, whereas the maximum velocity defect, turbulence stresses increase with mainstream velocity. The turbulence stresses are enhanced on the inner side but suppressed on the outer side.     

Flow Field Around Single and Tandem Piers

The present study provides a comparison between the flow pattern around two circular piers in tandem and a single pier set up on a moderately rough flat bed in a laboratory flume. Velocities are measured by an Acoustic Doppler Velocimeter (ADV). The contours of the time-averaged velocity components, Reynolds shear stresses, turbulence intensities and turbulence kinetic energy at different planes are presented. Streamlines and vectors are used to study the flow features. The analysis of power spectra around the piers is also presented. The results show that the presence of downstream pier changes the flow structure to a great extent, particularly in the near-wake region. Within the gap between the two piers, a stronger and substantial upflow is shaped. However, a weaker transverse-deflection is formed in comparison with that in the single pier. Near the bed, the velocity of flow approaching the downstream pier decreases to 0.2–0.3 times of the approach mean velocity (U ₀) due to the sheltering effect of the upstream pier. In the wake of downstream pier, the flow structure is completely different from the one in the wake of single pier. In comparison with the single pier, the values of turbulence kinetic energy and turbulence intensities show a considerable decrease around the tandem piers. In tandem piers, the high values of turbulence characteristics are found near the downstream pier. There is a recirculation zones just upstream of the sheltered pier close to the bed and another behind that pier near the free surface. The results show a decrease in the strength of vortical structure in the wake of tandem piers in comparison with single pier. It is shown that the formation of flow with different Reynolds number along the flow depth due to the effect of bed roughness, as well as pier spacing, can influence the type of flow regime of tandem case. In addition to enhancing the flow structure indulgence, the present detailed measurements can also be used for verification of numerical models.     

Piezoelectric energy harvesting from concurrent vortex-induced vibrations and base excitations

We investigate the potential of using a piezoelectric energy harvester to concurrently harness energy from base excitations and vortex-induced vibrations. The harvester consists of a multilayered piezoelectric cantilever beam with a circular cylinder tip mass attached to its free end which is placed in a uniform air flow and subjected to direct harmonic excitations. We model the fluctuating lift coefficient by a van der Pol wake oscillator. The Euler–Lagrange principle and the Galerkin procedure are used to derive a nonlinear distributed-parameter model for a harvester under a combination of vibratory base excitations and vortex-induced vibrations. Linear and nonlinear analyses are performed to investigate the effects of the electrical load resistance, wind speed, and base acceleration on the coupled frequency, electromechanical damping, and performance of the harvester. It is demonstrated that, when the wind speed is in the pre- or post-synchronization regions, its associated electromechanical damping is increased and hence a reduction in the harvested power is obtained. When the wind speed is in the lock-in or synchronization region, the results show that there is a significant improvement in the level of the harvested power which can attain 150 % compared to using two separate harvesters. The results also show that an increase of the base acceleration results in a reduction in the vortex-induced vibrations effects, an increase of the difference between the resonant excitation frequency and the pull-out frequency, and a significant effects associated with the quenching phenomenon.     

URANS vs. experiments of flow induced motions of multiple circular cylinders with passive turbulence control

Two-dimensional Unsteady Reynolds-Average Navier–Stokes equations with the Spalart–Allmaras turbulence model are used to simulate the flow induced motions of multiple circular cylinders with passive turbulence control (PTC) in steady uniform flow. Four configurations with 1, 2, 3, and 4 cylinders in tandem are simulated and studied at a series of Reynolds numbers in the range of 30 000<Re<120 000. Simulation results are verified by experimental data measured in the Marine Renewable Energy Laboratory. Good agreement was observed between the values of vorticity, amplitude ratio, and frequency ratio predicted by numerical simulations and experimental measurements. The amplitude and frequency response show the initial and upper branches in vortex induced vibration (VIV), transition from VIV to galloping, and galloping branch for all PTC-cylinders. The maximum amplitude of 2.9 diameters for the first cylinder is achieved at Re=104 356 in the numerical results. Compared with the first cylinder, the VIV initial branch starts at higher Re for the downstream cylinders due to the presence of the upstream cylinder(s). 2P and 2P+2S vortex patterns are observed at Re=62 049 and Re=90 254 for the single PTC-cylinder. Furthermore, the shed vortices of the downstream cylinders are strongly disrupted and modified by the vortices shed from the upstream one in the cases of multiple PTC-cylinders.     

Hopf bifurcation analysis of reaction–diffusion neural oscillator system with excitatory-to-inhibitory connection and time delay

The active control approach generally requires power input to suppress vibrations of structures, while the conventional passive manner often causes waste of energy after transferring vibrations of the primary structure to the auxiliary system. In this work, an innovative control strategy based on energy harvesting for efficiently suppressing the cross-flow-induced vibrations such as galloping is proposed. The novel design facilitates the harvester of not only alleviating the oscillation of the primary structure but also seizing the transferred vibrational energy. An analytical model for the coupled nonlinear dynamical system is established by utilizing the Euler–Lagrange principle and implementing the Galerkin discretization. The impacts of the electrical load resistance and tip mass of the energy harvester on the coupled frequency, damping, and the onset speed of instability of the coupled multi-mode system are investigated in details. The results show that there exists an optimal load resistance for each tip mass which maximizes the onset speed of galloping. For control purposes, it is found that there is a well-defined tip mass of the energy harvester at which the coupled system has the highest onset speed of instability, and hence, the bluff body has the lowest vibration amplitude for all considered load resistances. However, to efficiently harvest energy and control the bluff body, both the tip mass of the energy harvester and electrical load resistance can be accurately determined.     

On the effects of free-stream turbulence on axisymmetric disc wakes

Wind tunnel experiments have been used to study the effects of free-stream turbulence on the axisymmetric wake behind a disc. The disc and its wake were introduced to various turbulent streams having various levels of turbulence intensity and length scale. It was found that the presence of free-stream turbulence enhances the body??s drag and hence wake momentum deficit, if it is of sufficient strength, changes the far wake??s decay rate and prevents the appearance of self-similarity. The external turbulence causes a significant transformation in the wake??s turbulence structure. This gradually evolves towards the character of the free-stream turbulence itself and thus is characterised by much weaker turbulence (cross-stream) transport processes and a consequent dominance of shear stress production, which acts to maintain the shear stress and mean velocity profiles.     

Investigations on the presence of electrical frequency on the characteristics of energy harvesters under base and galloping excitations

The characteristics and performance of piezoelectric energy harvesters concurrently subjected to galloping and base excitations when using a complex electrical circuit are studied. The considered energy harvester is composed of a bilayered cantilever beam with a square cylindrical structure at its tip. Euler–Bernoulli beam theory, nonlinear quasi-steady hypothesis, and Galerkin method are used to develop a reduced order model of this system. The electrical circuitry of the harvester consists of a load resistance, a capacitance, and an inductance. The impacts of the electrical components of the harvester’s circuitry, the wind speed, and the base excitation frequency and acceleration on the broadband characteristics of the harvester, quenching phenomenon, and appearance of new nonlinear behaviors are deeply investigated and discussed. Different methods were used to characterize the new nonlinear phenomena that took place due to mechanical electrical interaction like the power spectrum and time history. When both coupled frequencies of electrical and mechanical types exist and are far from each other, it is shown that the quenching phenomenon is only related to the coupled frequency of mechanical type. It was also proven that this configuration results on high harvested power with low displacement near the electrical frequency. On the other hand, for a well-defined choice of the electrical components, the results show that a broadband configuration of the harvester can be designed. It is also indicated that the quenching phenomenon interacts with the appearance of hysteresis regions that depends on the value of the base acceleration and initial conditions. Moreover, it was shown that the presence of this inductance may result in broadband system harvesting more power from both galloping and base excitation.     

Large-scale structures visualization in a high Reynolds number,turbulent flat-plate wake at supersonic speed

A visual study is performed in a supersonic, two-dimensional wake; the high value of the Reynolds number ensures that the wake is turbulent from the trailing edge. The flow is seeded by fluid vaporization in one boundary layer upstream of the trailing edge; a light sheet is generated by a Q-switched, high energy ruby laser. The set of photographs taken from the trailing edge up to the far wake is then processed after digitization of the pictures. A progressive contamination of the lower part of the wake by the fluid initially present in the upper part can be observed. In the far wake region, well organized large scale structures can be visualized. Statistics are performed and the results are compared with previous hot-wire measurements and discussed in terms of downstream wake behaviour.This paper was presented at the 9th Symposium on turbulence, University of Missouri-Rolla, October 1–3, 1984     

Periodic and quasiperiodic galloping of a wind-excited tower under external excitation

The galloping of tall structures excited by steady and unsteady wind may be periodic or quasiperiodic (QP) with amplitudes having the same order of magnitude. While the onset of periodic and QP galloping was studied, their control on the other hand has received less attention. In this paper, we conduct analytical study on the effect of a fast harmonic excitation on the onset of periodic and QP galloping in the presence of steady and unsteady wind. We consider the cases where the unsteady wind activates either external excitation, parametric one or both. A perturbation analysis is performed to obtain close expressions of QP solution and the corresponding modulation envelopes. We show that at various loading situations, the periodic and QP galloping onset is significantly influenced by the amplitude of the fast external excitation. In the case where the unsteady wind activates parametric excitation, the QP galloping occurs with higher frequency modulation compared to the case where the unsteady wind activates external excitation. In the case where external and parametric excitations are activated simultaneously, fast harmonic excitation eliminates bistability in the amplitude response and gives rise to a new small QP modulation envelope.     

基于等效电路法的变三角截面驰振压电能量收集研究

随着能源危机的逐渐加剧，人们对压电俘能器研究的投入也与日俱增，目前常见的研究压电俘能器的模拟方法只能研究其接入简单的单一电阻负载电路时的性能，且不能解决压电俘能器的高强度直流电路耦合问题。因此，本文借助二阶范德波尔控制方程将压电俘能器的主要部件等效为电子元件，进而基于等效电路法建立了与变三角截面驰振压电振动俘能器相对应的等效电路模型。借助风洞实验验证了所建立的等效电路模型的准确性。采用该模型研究了外接电路，钝体顶角，外接电阻和来流速度对变三角截面驰振压电俘能器输出电压，输出功率和响应位移的影响，结果表明，随着电阻的增大，输出电压逐渐增大且增长率逐渐减小。交直流电路的最佳负载分别为1.05 MΩ和1.4 MΩ，当风速为7.03 m/s，钝体顶角为90°时，交直流电路输出电压和输出功率的峰值分别为41.34 V，0.974 mW和50.8 V，0.616 mW。随着钝体顶角的增大，输出电压，输出功率和响应位移均逐渐增大且增大的速度逐渐减小。等效电路模型可以高效，准确地对不同结构参数下和外界电路下的压电振动俘能器的输出功率，输出电压，响应位移及其影响因素进行研究，所提出的等效电路模型于加快对压电振动俘能器的研究与推广应用具有一定意义。     

Experimental study of flow past a square cylinder at high Reynolds numbers

 Measurements of two-components of velocity in the wake of a square cylinder using a hot-wire anemometer are reported. Two Reynolds numbers, namely 8700 and 17,625, have been considered. The measurements were carried out in a low-speed, low-turbulence wind tunnel. Benchmark experiments at much lower Reynolds numbers show good agreement between the present experiments and published results. At higher Reynolds numbers, the experimental data reveal anticipated trends in terms of wake recovery and turbulence decay. Both velocity and velocity fluctuations show symmetry about the wake axis. The experimental data have been compared with the large eddy simulation (LES) calculation reported by Wang et al. [University of Illinois at Urbana – Champaign (1996) Report CFD 96-03] and LDV measurements of Lyn et al. [J Fluid Mech (1995) 304: 285–319]. The agreement among the three sets is generally acceptable in terms of the time-averaged velocity components, but not the velocity fluctuations. The turbulence fluctuations in the present experiments are seen to be lower than in the referred work. The differences have been traced to factors such as the aspect ratio, blockage ratio and upstream turbulence. Experiments with increased upstream turbulence did show a reduction in the discrepancy between the present experiments and the published data. An assessment of the experimental data in terms of physical mechanisms revealed that (a) streamwise normal stresses were correlated with the vortex centers, and (b) the turbulence kinetic energy profiles are similar to the turbulence shear stress. Spectral analysis of the velocity signals was carried out in the present work. Energy transfer from the mean flow to the streamwise velocity fluctuation was confirmed in the near wake. A redistribution of the kinetic energy between the streamwise and transverse components of velocity over a longer distance downstream was subsequently observed. Received: 17 May 1999/Accepted: 29 December 1999     

Characteristics of a trailing flap flow with small separation

Detailed measurements of pressure and velocity characteristics are reported for the flow on and downstream of a trailing flap, whose 16 degree angle of incidence resulted in boundary layer separation, a small region of recirculating flow, and a curved downstream wake. Emphasis is placed on the region of recirculating flow and on the downstream wake. The characteristics were quantified by the use of pressure, hot-wire, and flying hot-wire probes. The flow characteristics are compared to those of a similar flow but with a larger region of recirculation reported by Thompson and Whitelaw (1985). The relative importance of the terms in the transport equations for mean momentum and turbulence energy are quantified and the implications of the results for viscous-inviscid interaction methods and turbulence modelling are discussed.     

Three-dimensional wake dynamics of a blunt and divergent trailing edge airfoil

The wake dynamics of an airfoil with a blunt and divergent trailing edge is investigated experimentally at relatively high Reynolds. The near wake topology is examined versus different levels of free stream turbulence FST and angles of attack, while the downstream wake evolution is characterized at various levels of FST. The FST is found to have a significant effect on the shapes of turbulence profiles and on the downstream location where the flow reaches its quasi-asymptotic behavior. Streamwise vortices (ribs) corresponding to spanwise variations of turbulence quantities are identified in the near wake region. Simultaneous multi-point hot-wire measurements indicate that their spatial arrangement is similar to Williamson’s (Ann Rev Fluid Mech 29:477–539, 1996) mode B laminar wake flow topology. The results suggest that the statistical spanwise distribution of ribs is independent of FST effects and angle of attack as long as the vortex shedding Strouhal number remains approximately similar.     

固体颗粒对半球扰动尾迹影响的实验研究

采用粒子图像测速技术(particle image velocimetry, PIV)研究固体颗粒对放置在平板层流边界层中半球粗糙元尾迹的影响. 实验采集了清水和加入粒径为140 $\mu$m, 220 $\mu$m, 350$\mu$m聚苯乙烯固体颗粒4种工况下二维速度场信息, 基于半球半径的雷诺数为994 ($Re_R=RU/\upsilon$), 固体颗粒的体积浓度为$3.0\times10^{-5}$. 对比清水和两相工况下的平均速度剖面、湍流强度等宏观统计量, 分析固体颗粒对半球尾迹流动宏观特性的影响. 分别利用沿流向不同位置的流向脉动速度的二维空间相关系数和法向脉动速度的功率谱密度函数分析颗粒对尾迹结构演化过程及尾迹结构脱落频率的影响. 结果发现: 与清水相比, 回流区随颗粒粒径增大而逐渐增大; 颗粒使湍流强度增大, 回流区的存在导致在半球后流向位置$2R$前后区域湍流强度呈现不同变化趋势; 颗粒使尾迹结构的流向尺度减小并且随着颗粒粒径的增大先减小后增大; 在尾迹结构运动过程中颗粒的存在促进了尾迹结构的周期性加速和减速运动, 促进作用随着颗粒粒径的增大先增强后减弱; 颗粒的存在促进了尾迹结构的脱落, 脱落频率随颗粒粒径的增大先增大后减小.