Unsteady incompressible flows past two cylinders in tandem and staggered arrangements

A stabilized finite element formulation is employed to study incompressible flows past a pair of cylinders at Reynolds numbers 100 and 1000 in tandem and staggered arrangements. Computations are carried out for three sets of cylinder arrangements. In the first two cases the cylinders are arranged in tandem and the distance between their centres is 2·5 and 5·5 diameters. The third case involves the two cylinders in staggered arrangement. The distance between their centres along the flow direction is 5·5 diameters, while it is 0·7 diameter in the transverse direction. The results are compared with flows past a single cylinder at corresponding Reynolds numbers and with experimental observations by other researchers. It is observed that the qualitative nature of the flow depends strongly on the arrangement of cylinders and the Reynolds number. In all cases, when the flow becomes unsteady, the downstream cylinder, which lies in the wake of the upstream one, experiences very large unsteady forces that may lead to wake-induced flutter. The Strouhal number, based on the dominant frequency in the time history of the lift coefficient, for both cylinders attains the same value. In some cases, even though the near wake of the two cylinders shows temporal periodicity, the far wake does not. © 1997 John Wiley & Sons, Ltd.     

Passive control of a single flexible flag using two side-by-side flags

Numerical simulations using an improved version of the immersed boundary method are performed to explore a passive control concept for a single flexible flag in a viscous uniform flow. In order to control a single flag passively, we utilize the distinct dynamics of two side-by-side flags, characterized by in-phase and out-of-phase flapping modes depending on their spanwise gap distance. When the two side-by-side flags are in an in-phase flapping mode with a small spanwise gap distance, the flapping amplitude of a single downstream flag is highly enhanced due to synchronization between the vortices shed from the upstream and downstream flags. However, when the two upstream flags flap in an out-of-phase flapping mode with a large spanwise gap distance, the flapping of the single flag is significantly weakened with a reduction of the dominant flapping frequency. Because the upstream flags induce consecutive counter-rotating vortex pairs with a high frequency due to their flapping mode (out-of-phase state), relatively strong interaction with an upcoming vortex of the opposite rotational direction leads to flapping inhibition of the single flag. For an intermediate spanwise gap distance, the vortex-to-vortex interaction between the flags becomes more complicated, and a change of the flapping phases of the two side-by-side flags depending on streamwise gap distance between the upstream and downstream flags occurs. The interactions between coupled flags are documented through the root-mean-square cross-stream tail positions, frequency, drag coefficient, vorticity and pressure contours of the flags with varying non-dimensional parameters relevant to the problem. The proposed passive control concept of a single flag using two side-by-side flags is applicable to the development of energy harvesting systems to extract more energy and flapping control systems to suppress vibration.     

Vortex-induced vibrations of two mechanically coupled circular cylinders with asymmetrical stiffness in side-by-side arrangements

Vortex-induced vibrations of two mechanically coupled circular cylinders with asymmetrical stiffness in side-by-side arrangements are numerically investigated in a uniform flow at a low Reynolds number of 100. The oscillation system is restricted to the cross-flow direction, giving rise to a coupled two-degree-of-freedom response. Attention is placed on the two cylinders with a center-to-center gap ratio of 4 and a mass ratio of 10. The flow dynamics are described by the two-dimensional incompressible Navier–Stokes equations and resolved by the Characteristic-Based-Split finite element method. The stiffness of the first spring that connects the lower cylinder to the wall is chosen such that the vortex-induced vibration of the associated single cylinder with the same stiffness undergoes a pre-synchronization (state A), synchronization (state B) and post-synchronization (state C), respectively. In each state, the stiffness of the second spring connecting the lower and upper cylinders is varied to cover both synchronization and de-synchronization regimes. Numerical results show that the mechanically coupled system locks on the first-mode natural frequency in state A, while on the second-mode natural frequency in states B and C. In such a lock-in regime, the amplitude ratios of the two oscillating and coupled cylinders collapse well onto the corresponding first or second free-vibration mode. The overall coupling mechanism is further explained in terms of the hydrodynamic coefficients, frequency characteristics, wake patterns and effective added mass, quantifying the associated fluid-structure interactions against those governing a single-degree-of-freedom, single-cylinder system.     

Three-dimensional simulations of flow past two circular cylinders in side-by-side arrangements at right and oblique attacks

The flow past two identical circular cylinders in side-by-side arrangements at right and oblique attack angles is numerically investigated by solving the three-dimensional Navier–Stokes equations using the Petrov–Galerkin finite element method. The study is focused on the effect of flow attack angle and gap ratio between the two cylinders on the vortex shedding flow and the hydrodynamic forces of the cylinders. For an oblique flow attack angle, the Reynolds number based on the velocity component perpendicular to the cylinder span is defined as the normal Reynolds number Re_N and that based on the total velocity is defined as the total Reynolds number Re_T. Simulations are conducted for two Reynolds numbers of Re_N=500 and Re_T=500, two flow attack angles of α=0° and 45° and four gap ratios of G/D=0.5, 1, 3 and 5. The biased gap flow for G/D=0.5 and 1 and the flip-flopping bistable gap flow for G/D=1 are observed for both α=0° and 45°. For a constant normal Reynolds number of Re_N=500, the mean drag and lift coefficients at α=0° are very close to those at α=45°. The difference between the root mean square (RMS) lift coefficient at α=0° and that at α=45° is about 20% for large gap ratios of 3 and 5. From small gap ratios of 0.5 and 1, the RMS lift coefficients at α=0° and 45° are similar to each other. The present simulations show that the agreement in the force coefficients between the 0° and 45° flow attack angles for a constant normal Reynolds number is better than that for a constant total Reynolds number. This indicates that the normal Reynolds number should be used in the implementation of the independence principle (i.e., the independence of the force coefficients on the flow attack angle). The effect of Reynolds number on the bistable gap flow is investigated by simulating the flow for Re_N=100–600, α=0° and 45° and G/D=1. Flow for G/D=1 is found to be two-dimensional at Re_N=100 and weak three-dimensional at Re_N=200. While well defined biased flow can be identified for Re_N=300–600, the gap flow for Re_N=100 and 200 changes its biased direction too frequently to allow stable biased flow to develop.     

Flow-structure interactions of two parallel inverted flags with small separation distances in a water tunnel

In this study, the dynamics and flow fields of two parallel inverted flags are investigated using particle image velocimetry technology. The separation distance between two flags is less than two times the length of the flag, and the length ratio of these two flags is considered in the investigation. The results show that for the dynamic behaviours of two identical flags with a larger separation distance, the anti-phase and in-phase modes occur successively in the periodic oscillation as the flow velocity increases. The anti-phase and in-phase oscillations occur according to the formation position of the low-pressure and recirculation areas at different flow velocities. Moreover, a novel coupled flapping mode is observed at smaller separation distances: the contact anti-phase flapping mode, in which one flag oscillates with a large symmetric amplitude, and the other flag oscillates with a single-side large amplitude. As the separation distance further decreases, the in-phase mode appears for a larger range of flow velocity values, to avoid contact for the largest possible amplitude oscillation. Finally, as the length ratio decreases to 0.75, the oscillation frequency of the shorter flag becomes twice that of the longer flag, causing the in-phase and anti-phase oscillations to occur simultaneously in one cycle (i.e., the multi-phase flapping state). Interestingly, the two flags oscillate out of phase in the flapping apart process to avoid contact at a higher flow velocity. In general, the lower amplitude of the longer flag and two contact flags relative to that of an isolated flag clearly indicates the importance of two equal-length and non-contact flags for energy harvesting.     

Wake-induced vibration of tandem and staggered cylinders with two degrees of freedom

The wake-induced vibration (WIV) of two staggered cylinder with two degrees of freedom (2-dof) has been investigated by experiments in a water channel for Reynolds number between 2000 and 25 000. The streamwise separation was fixed to 4 diameters and the lateral separation varied between 0 and 3 diameters for tandem and staggered configurations. Results are presented in the form of trajectories of motion and dynamic response curves of displacements, frequencies and force coefficients. Excitation caused by the WIV mechanism is found to get weaker as the initial position of the downstream cylinder is increased from the centreline of the wake (tandem arrangement) towards the sides. For a lateral separation of 3 diameters wake interference was already found to be negligible. Evidence of a type of wake-stiffness concept is also observed to occur for 2-dof WIV in tandem arrangement, especially for higher reduced velocities. A similar mechanism may also be occurring for staggered arrangements around the centreline.     

Stability and coupled dynamics of three-dimensional dual inverted flags

Fluid–structure interaction of an inverted flag, which has a free leading edge and a clamped trailing edge, has drawn attention recently because of its novel properties such as divergence stability, a low stability threshold, and large-amplitude flapping motion. In this study, the stability and flapping behaviors of dual inverted flags with finite height are investigated for a side-by-side arrangement, and their noticeable characteristics are compared to those of dual conventional flags. The critical velocity at which the inverted flags break the equilibrium of a straight configuration reduces monotonically when a gap distance between the two flags becomes smaller and an aspect ratio becomes larger, which is also predicted by our linear stability analysis using simple theoretical models of two-dimensional flags and slender flags. After bifurcation, in addition to the synchronized in-phase and out-of-phase modes commonly observed in dual conventional flags, a novel attached mode appears which is mainly observed for small gap distance and small aspect ratio. In this non-linear mode, the leading edges of the two inverted flags touch each other on a midline, and the deformed inverted flags maintain static equilibrium. In a non-linear flapping regime, a new mechanism of a mode transition from an out-of-phase mode to an in-phase mode is identified, which is allowed by the collision of the two flags flapping with large amplitude.     

Energy harvesting from the secondary resonances of a nonlinear piezoelectric beam under hard harmonic excitation

Meccanica - This paper investigates the dynamical response of a nonlinear piezoelectric energy harvester under a hard harmonic excitation and assesses its output power. The system is composed of a...     

Flow-excited acoustic resonance of two side-by-side cylinders in cross-flow

The aeroacoustic response of two side-by-side circular cylinders in cross-flow is investigated experimentally. In order to investigate the effect of the gap between the cylinders on the acoustic resonance mechanism, six spacing ratios between the cylinders, in the range of T/D=1.25–3, have been investigated, where D is the diameter of the cylinders and T the centre-to-centre distance between them. Special attention is given to the intermediate spacing ratio range, which exhibits bistable flow regimes in the absence of resonance. During the tests, the acoustic cross-modes of the duct housing the cylinders are self-excited. For the intermediate spacing ratios, T/D=1.25, 1.35, 1.46 and 1.75, two distinct vortex-shedding frequencies at the off-resonance conditions are observed. These are associated with the wide and narrow wakes of the cylinders, as described in the literature. In this case, acoustic resonances occur at a Strouhal number, which is between those observed before the onset of resonance. The acoustic resonance synchronizes vortex shedding in the two wakes and thereby eliminates the bistable flow phenomenon. For large spacing ratios, T/D=2.5 and 3, vortex shedding occurs at a single Strouhal number at which the acoustic resonance is excited.     

Vortex-induced vibration of two elastically coupled cylinders in side-by-side arrangement

Vortex-induced vibration (VIV) of two elastically coupled circular cylinders in side-by-side arrangement is investigated numerically. The Reynolds-averaged Navier–Stokes equations are solved by the finite element method for simulating the flow and the equation of motion is solved for calculating the vibration. The mass ratio (the ratio of the mass of the cylinder to the displaced fluid mass) is 2 and the Reynolds number is 5000 in the simulations. Simulations are carried out for one symmetric configuration (referred to be Case A) and one asymmetric configuration (referred to be Case B). In both Case A and Case B, the primary response frequencies of the two cylinders are found to be the same both inside and outside the lock-in regimes. Five response regimes are found in both cases and they are the first-mode lock-in regime, the second-mode lock-in regime, the sum-frequency lock-in regime and two transition regimes. When the vibration is transiting from the first- to the second-mode lock-in regimes, the vibration of each cylinder contains both first- and the second-mode natural frequencies, and the vibrations are usually irregular. In the transition regime between the second-mode lock-in and the sum-frequency lock-in regimes, the response frequencies of both cylinders increases with an increase in the reduced velocity until they are close to the sum of the two natural frequencies. In both cases, the lower boundary reduced velocity of the total lock-in regime (the sum of the five lock-in regimes) is about 3 and the upper boundary reduced velocity is about 11 times the first-to-second-mode natural frequency ratio.     

并列仿生鱼自主游动的数值模拟研究

采用自适应浸没边界方法,数值模拟了两条并列仿生鱼在不同间距下的同相位和反相位自主游动。通过与相同游动参数下单条仿生鱼自主游动的比较,可以得到结论：（1）并列自主游动的速度小于单条鱼游动的速度,并且随着间距减小而减小。相同间距下,反相位并列游动时的速度大于同相位;（2）并列游动时的阻力均大于单条鱼,且随着间距减小而增大;（3）反相位游动时功率消耗随间距减小而增大,但同相位游动则相反;（4）当间距大于0.5个身长时,推进效率都略有增大。所以,在综合考虑了游动速度和推进效率两方面的因素后认为,鱼群中并列相邻的两条鱼应当以反相位摆动,且侧向间距保持在0.5个身长以上,这与自然界中观察的结果是一致的。     

Characteristics and suppression of flow-induced vibrations of two side-by-side circular cylinders

A free-vibration experiment was conducted to examine flow-induced vibration (FIV) characteristics of two identical circular cylinders in side-by-side arrangements at spacing ratio T^⁎ (=T/D)=0.1–3.2, covering all possible flow regimes, where T is the gap spacing between the cylinders and D is the cylinder diameter. Each of the cylinders was two-dimensional, spring mounted, and allowed to vibrate independently in the cross-flow direction. Furthermore, an attempt to suppress flow-induced vibrations was undertaken by attaching flexible sheets at the rear stagnation lines of the cylinders. Based on the vibration responses of the two cylinders, four vibration patterns I, II, III and IV are identified at 0.1≤T^⁎<0.2, 0.2≤T^⁎≤0.9, 0.9<T^⁎<2.1 and 2.1≤T^⁎≤3.2, respectively. Pattern I is characterized by the two cylinders vibrating inphase^, with the maximum amplitudes occurring at the same reduced velocity Ur=10.47 almost two times that (Ur=5.25) for an isolated cylinder. Pattern II features no vibration generated for either cylinder. Pattern III exemplifies the occurrence of the maximum vibration amplitude of a cylinder at a smaller Ur and that of the other cylinder at a higher Ur compared to its counterpart in an isolated cylinder. Pattern IV represents each cylinder response resembling an isolated cylinder response; the vibrations of the two cylinders are, however, coupled inphase or antiphase. Linking maximum vibration amplitudes to fluctuating lift forces acting on fixed cylinders reveals that fluid–structure interactions between two fixed cylinders and between two elastic cylinders are not the same, even though vibration is not significant. As such, while two fixed cylinders generate narrow and wide wakes at 0.2≤T^⁎<1.7, two elastic cylinders do the same for a longer range of T^⁎ (0.2≤T^⁎<2.1). The flexible sheets effectively suppress FIV of the two cylinders in patterns III and IV, and reduce the vibration amplitude in pattern I. For the effectively controlled cases (patterns III and IV), the flexible sheet of each cylinder folds into a semicircle at the base, forming two free edges.     

Phenomena and modeling of piezoelectric energy harvesting from freely oscillating cylinders

We investigate energy harvesting from vortex-induced vibrations of a freely moving rigid circular cylinder with a piezoelectric transducer attached to its transverse degree of freedom. The power levels that can be generated from these vibrations and variations of these levels with the freestream velocity are determined. A mathematical model that accounts for the coupled lift force, cylinder motion, and harvested voltage is presented. Linear analysis is performed to determine the effect of the electrical load resistance of the transducer on the natural frequency of the cylinder and the onset of synchronization (the shedding frequency is equal to the cylinder oscillating frequency) region. The impact of the nonlinearities on the cylinder response and harvested energy is investigated. The results show that the load resistance shifts the onset of synchronization to higher freestream velocities. For two different system parameters, the results show that the nonlinearities result in a hardening behavior for some values of the load resistance.     

面内压电振动能量采集动力学设计与性能研究

压电振动能量采集将环境中普遍存在的机械能转换为电能,可以实现自供能传感、控制与驱动,具备灵活、节能环保、可持续的优势,具有广阔的应用前景.为了促进压电振动能量采集器件的集成与融合,提出面内压电振动能量采集,将压电振动能量采集器进行扁平化设计,使其在二维平面内采集振动能量,在保证较大功率输出下能够显著减小器件所需三维空间.为了提高输出功率与工作频宽,设计了具有双稳态与力放大机制的面内压电振动能量采集器.考虑弯张小变形,通过能量法建立了面内压电振动能量采集器的机电耦合动力学模型.分析了关键设计参数对面内压电振动能量采集器性能的影响.数值仿真了面内压电振动能量采集器在简谐激励下的俘能性能,结果表明,通过合理的设计,面内压电振动能量采集器可以低频、宽频弱激励下有效俘获能量.面内压电振动能量采集设计方法有利于推动便携式、可穿戴式自供能等方面的应用和产业化.     

Recent advancement of flow-induced piezoelectric vibration energy harvesting techniques: principles,structures, and nonlinear designs

Energy harvesting induced from flowing fluids (e.g., air and water flows) is a well-known process, which can be regarded as a sustainable and renewable energy source. In addition to traditional high-efficiency devices (e.g., turbines and watermills), the micro-power extracting technologies based on the flow-induced vibration (FIV) effect have sparked great concerns by virtue of their prospective applications as a self-power source for the microelectronic devices in recent years. This article aims to conduct a comprehensive review for the FIV working principle and their potential applications for energy harvesting. First, various classifications of the FIV effect for energy harvesting are briefly introduced, such as vortex-induced vibration (VIV), galloping, flutter, and wake-induced vibration (WIV). Next, the development of FIV energy harvesting techniques is reviewed to discuss the research works in the past three years. The application of hybrid FIV energy harvesting techniques that can enhance the harvesting performance is also presented. Furthermore, the nonlinear designs of FIV-based energy harvesters are reported in this study, e.g., multi-stability and limit-cycle oscillation (LCO) phenomena. Moreover, advanced FIV-based energy harvesting studies for fluid engineering applications are briefly mentioned. Finally, conclusions and future outlook are summarized.

     

A review of nonlinear piezoelectric energy harvesting interface circuits in discrete components

Piezoelectric energy harvesting is considered as an ideal power resource for low-power consumption gadgets in vibrational environments. The energy extraction efficiency depends highly on the interface circuit, and should be highly improved to meet the power requirements. The nonlinear interface circuits in discrete components have been extensively explored and developed with the advantages of easy implementation, stable operation, high efficiency, and low cost. This paper reviews the state-of-the-art progress of nonlinear piezoelectric energy harvesting interface circuits in discrete components. First, the working principles and the advantages/disadvantages of four classical interface circuits are described. Then, the improved circuits based on the four typical circuits and other types of circuits are introduced in detail, and the advantages/disadvantages, output power, efficiency, energy consumption, and practicability of these circuits are analyzed. Finally, the future development trends of nonlinear piezoelectric energy harvesting circuits, e.g., self-powered extraction, low-power consumption, and broadband characteristic, are predicted.

     

Flow induced oscillation of two rigid rectangular plates in a side-by-side configuration

The present work is an experimental study of two oscillating rigid plates placed in side-by-side configuration, hinged at their leading edges, subjected to low subsonic flow. This problem is investigated using smoke-wire flow visualization, hot-wire anemometry, and time resolved particle image velocimetry. It is found that beyond a critical Reynolds number, the plates set into oscillatory motion. This critical Reynolds number depends on the gap between the plates. It is also seen that this value of Reynolds number, at lower values of gap to thickness ratio (<7) is significantly higher than that of the single plate configuration value. The frequency and amplitude of the oscillating plates at various gaps and Reynolds numbers have been studied and compared with the characteristics of an oscillating single plate. It is also found that depending on the gap and acceleration of the free-stream, there exist two modes of oscillation - (i) in-phase and (ii) out-of-phase. For gap to thickness ratio less than 10, only in-phase oscillations take place for all values of free-stream velocity considered in the present work, whereas, when this ratio is greater than 10, the mode of oscillation depends on the initial conditions up to a certain free-stream velocity, beyond which the plates switch to in-phase mode. Smoke wire flow visualization technique along with time resolved particle image velocimetry reveal that the vorticity distributions around the plates are responsible for the initiation of the two modes of oscillations.     

Response and wake patterns of two side-by-side elastically supported circular cylinders in uniform laminar cross-flow

Vortex-induced vibrations (VIV) of two side-by-side elastically supported circular cylinders in a uniform flow with the Reynolds number of 100 are numerically investigated by using the immersed boundary method. The cylinders are constrained to oscillate in the cross-flow direction with a center-to-center spacing ratio $T/D$ ranging from 2 to 5. The structural damping is set to zero to enable large vibration amplitudes in the range of reduced velocity $U_r=3-10$. It is found that the proximity of the cylinders does not have a significant impact to the lock-in region and cylinder responses, except at a small spacing ratio of $T/D=2$. The critical spacing ratio is determined as $T/D=4$ and beyond that the interaction between the cylinders is negligible. The following six near-wake patterns are observed; the irregular pattern, in-phase flip-flopping pattern, out-of-phase flip-flopping pattern, in-phase-synchronized pattern, antiphase-synchronized pattern and the biased antiphase-synchronized pattern. These patterns are plotted in a plane of $U_r$ and $T/D$, together with approximate borderlines to distinguish one region from the others. The time histories, spectral features and wavelet transform contours of drag and lift forces are presented to elucidate the mechanisms of the in-phase and out-of-phase flip-flopping phenomena. It is established that the in-phase flip-flopping stems from the long-short near-wake pattern and its low-frequency flip-over, whereas the out-of-phase pattern originates from the large vortex shedding from the fictitious bluff-body with an augmented characteristic length.